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THE 

ARCHITECTS'  AND  BUILDERS' 

HANDBOOK 


DATA  FOR 

ARCHITECTS,    STRUCTURAL    ENGINEERS, 

CONTRACTORS,  AND  DRAUGHTS-MEN 


BY 
The  Late  FRANK  E.  KIDDER,  C.  E.,  Ph.  D. 

AUTHOR  OF  "building  CONSTRUCTION  AND  SUPERINTENDENCE" 

COMPILED  BY  A  STAFF  OF  SPECIALISTS  AND 

THOMAS   NOLAN,   M.S.,  A.M.,  Editor-in-Chief 

FELLOW  OF  THE  AMERICAN  INSTITUTE  OF  ARCHITECTS;   PROFESSOR  OF 
ARCHITECTURAL  CONSTRUCriON,  UNIVERSITY  OF  PENNSYLVANIA 


SEVENTEENTH  EDITION,  ENLARGED 

TOTAL  ISSUE,    EIGHTY-FIVE   THOUSAND 


NEW  YORK 

JOHN  WILEY  &  SONS,  Inc. 

London:   CHAPMAN  &  HALL,  Limited 
1921 


The  Publishers  and  the  Editor-in-Ch'.ef  will  be  grateful  to  readers  of  this 
volume  who  will  call  attention  to  any  errors  of  omission  or  commission  therein. 
It  is  intended  to  make  our  publications  standard  works  of  study  and  reference, 
and,  to  that  end,  the  greatest  accuracy  is  sought.  It  rarely  happens  that  the 
early  editions  of  books  are  free  from  errors  ;  but  it  is  the  endeavor  of  the 
Publishers  to  have  them  removed,  and  it  is  therefore  desired  that  the  Editor- 
in-Chief  may  be  aided  in  his  task  of  revision,  from  time  to  time,  by  the  kindly 
criticism  of  readers. 

JOHN  WILEY  &  SONS,  Inc. 
432  Fourth  Avenue,  New  York 


Copyright.  1884,  1892.  1897.  1904, 

BY 

FRANK  E.   KIDDER 


Copyright,  1908, 

BY 

KATHERINE  E.   KIDDER 


Copyright,  1915,  1921, 

BY 

KATHERINE   E.   KIDDER 


COMPOSITION,  ELECrROrVPfNG,  PRINTING    AND    BINDINr, 
BRAUNWORTH    ft   CO.,  BROOKLYN,  N.  Y. 


XTbis  3Booft 


IS  RESPECTFULLY  DEDICATED  TO  THOSE  WHOSE  KINDNESS 
HAS  ENABLED  ME  TO  PRODUCE  IT 

TO  MY  PARENTS 
WHO  GAVE  ME  THE  EDUCATION  UPON  WHICH  IT  IS  BASED 

TO   MY  WIFE 

FOR  HER  LOVING  SYMPATHY,  ENCOURAGEMENT 
AND  ASSISTANCE 

TO  ORLANDO  W.  NORCROSS 

OF  WORCESTER,  MASS. 

WHOSE  SUPERIOR  PRACTICAL  KNOWLEDGE  OF  ALL  THAT 

PERTAINS   TO   BUILDING   HAS    GIVEN   ME    A   MORE 

INTELLIGENT  AND  PRACTICAL  VIEW  OF  THE 

SCIENCE  OF  CONSTRUCTION  THAN  I 

SHOULD  OTHERWISE  HAVE 

OBTAINED  * 


*  Dedication  to  First  Editicm, 


Ca^x'v  ^:Ci 


EDITORIAL  STAFF 

EDITOR-IN-CHIEF 

Thomas  Nolan,  Professor  of  Architectural  Construction,  University  of 
Pennsylvania. 

ASSOCIATE   EDITORS 

Herman  C.  Bp:rry,  Professor  of  Materials  of  Construction,  University 
of  Pennsylvania. 

J.  J.  CoSGROVE,  Consulting  Sanitary  Engineer. 

Robins  Fleming,  of  the  American  Bridge  Company,  New  York,  N.  Y. 

L.  A.  Harding,  formerly  Professor  of  Mechanical  Engineering,  Pennsyl- 
vania State  College. 

Malverd  a.  Howe,  Professor  Emeritus  of  Civil  Engineering,  Rose 
Polytechnic  Institute. 

F.  H.  KiNDL,  Late  Consulting  Engineer,  Pittsburgh,  Pa. 

Rudolph  P.  Miller,  Superintendent  of  Buildings,  Borough   of  Man- 
hattan, New  York,  N.  Y. 

Daniel  E.  Moran,  Consulting  Engineer,  New  York,  N.  Y. 

Emile  G.  Perrot,  Member  of  American  Society  of  Civil  Engineers. 

N.  A.  Richards,  of  Purdy  &  Henderson,  Inc.,  Civil  Engineers,  New 
York,  N.  Y. 

Edward  F.  Ries,  Consulting  Engineer,  San  Antonio,  Texas. 

Grenvill^  T.  Snelling,  Formerly  Instructor  in  Architectural  Engineer- 
ing, Columbia  University. 

A.    P.    Stradling,    Manager,    Philadelphia    Suburban    Underwriters' 
Association. 

W.  H.  TiMBiE,   Associate   Professor  of  Electrical  Engineering,  Mass- 
achusetts Institute  of  Technology. 

Charles  P.  Warren,  Late  Assistant  Professor  of  Architecture,  Columbia 
University. 

46944T 


NOTE  TO  SEVENTEENTH  EDITION 

With  this  edition  the  name  is  changed  from  Pocket-Book  to  Handbook. 
The  work  has  been  revised,  some  chapters  rewritten,  new  chapters  added, 
and  a  new  Index  made.     Many  cuts  have  been  reengraved. 

The  twenty-nine  chapters  of  Part  II  have  been  revised  where  necessary  to 
make  the  data  agree  with  the  latest  research  and  practice,  and  two  new  chapters 
have  been  added,  Chapter  XXX,  on  Specifications  for  the  Steelwork  of  Build- 
ings, by  Robins  Fleming,  and  Chapter  XXXI,  on  Domical  and  Vaulted  Struc- 
tures, by  Edward  F.  Ries.  Chapter  XXIII,  on  Fireproofing  of  Buildings,  and 
Chapter  XXIV,  on  Reinforced-Concrete  Construction,  have  been  rewritten  by 
Rudolph  P.  Miller.  In  Part  III,  the  sections  on  Heating  and  Ventilation,  and 
Chimney  Construction,  have  been  entirely  rewritten  by  Louis  A.  Harding. 
The  new  chapters  and  sections  'nclude  numerous  practical  exan  pies  of  every- 
day problems,  with  solutions  worked  out  in  complete  detail. 

In  addition  to  the  new  chapters  numerous  new  articles  have  been  added  to 
the  text  and  illustrations  of  Part  II,  on  the  fol'owing  subjects:  New  Data  on 
Building  Laws  Relating  to  Loads  on  Masonry;  Graphical  Method  of  Determin- 
ing the  Center  of  Gravity  of  Plane  Figures  or  Sections;  Graphical  Method  of 
Determining  Moments  of  Inertia  of  Plane  Figures;  Triangular  Loading;  End 
Connections  of  Tension-Members:  New  Wire-Data;  New  Matter  on  Gauges; 
New  Matter  on  Chains:  Graphical  Method  of  Determining  the  Deflection  of 
Beams;  Secondary  Stresses;  Angles  Used  as  Beams;  Data  on  Girderless 
Reinforced-Concrete  Floors;  Data  on  Tanks,  and  on  Stresses  in  Cylindrical 
Tanks,  etc.  Other  revisions  and  additions  have  been  made,  including  new 
sections  relating  to  the  Registration  of  Architects,  Standard  Documents  of  the 
American  Institute  of  Architects,  Architectural  Education,  etc. 

In  its  revised,  compact,  and  convenient  form,  the  Editor  believes  that  the 
work,  more  than  ever  before,  will  maintain  its  preeminence  as  the  authoritative 
Handbook  of  Building-Construction. 

Philadelphia,  July,  192 1. 

vi 


PREFACE  TO  SIXTEENTH  EDITION 

The  changes  In  the  fifteenth  edition,  published  in  1908,  consisted  principally 
of  the  rewriting  of  the  two  chapters  on  Fireproofing  of  Buildings  and  Reinforced 
Concrete. 

In  19 1 2  the  undersigned  was  asked  to  undertake  the  revision  of  the  entire  book 
with  the  cooperation  of  a  corps  of  Associate  Editors,  each  highly  qualified  to 
render  the  necessary  assistance  in  matters  pertaining  to  his  own  work.  On 
account  of  the  comprehensive  nature  of  the  contents  of  the  Pocket-Book,  the 
many  recent  changes  and  rapid  developments  in  different  fields  of  architectural 
construction,  and  the  consequent  effect  of  such  changes  on  the  interrelated 
subjects  treated,  the  Editor-in-Chief  decided  to  rewrite  and  reset  the  entire 
book.  After  more  than  three  years  of  arduous  labor,  in  which  the  Associate  Edi- 
tors and  many  other  contributors  have  most  ably  and  generously  assisted,  the 
New  Kidder  is  about  to  be  published. 

It  was  decided  to  retain  Mr.  Kidder's  original  arrangement  of  the  subject- 
matter  which  is  divided  into  three  Parts,  Part  I  dealing  with  practical  applica- 
tions of  Arithmetic,  Geometry  and  Trigonometry,  Part  II  with  the  Materials 
of  Construction  and  the  Strength  and  Stability  of  Structures,  and  Part  III  with 
miscellaneous  useful  information  for  architects  and  builders.  Each  of  the 
twenty-nine  chapters  of  Part  II,  however,  has  the  name  of  the  Associate  Editor 
who  revised  or  rewrote  it  printed  with  the  chapter-caption.  Part  I  has  been 
carefully  checked  and  much  of  the  matter  rearranged.  The  twenty-eight 
chapters  of  Part  II  have  been  rewritten  and  one  new  chapter  has  been  added  on 
Reinforced -Concrete  Mill  and  Factory- Construction.  Part  III  has  been  largely 
rewritten  and  all  subjects  retained  have  been  thoroughly  revised.  To  this  part, 
also,  much  new  matter  has  been  added,  such  as  extended  tables  of  Specific  Gravi- 
ties and  Weights  of  Substances,  Architectural  Acoustics,  Waterproofing  for 
Foundations,  the  Quantity  System  of  Estimating,  the  Standard  Documents  of 
the  American  Institute  of  Architects,  Educational  Societies  of  the  World  and 
extended  lists  of  Architectural  Schools,  Books  and  Periodicals. 

The  Editor-in-Chief  has,  with  very  few  exceptions,  personally  checked  on 
every  page  of  manuscript,  galley-proof  and  page-proof  the  equations,  formulas, 
computations  and  problems,  and  has  read  or  examined  carefully  every  word,  . 
figure  and  illustration,  every  detail  of  syntax,  paragraphing,  punctuation  and 
typography,  and  every  arrangement  of  tables,  captions,  classifications,  notation, 
Table  of  Contents  and  Index. 

He  is  responsible  for  many  changes  in  the  form  of  presentation  of  data  which 
it  is  hoped  will  add  to  the  Pocket-Book  still  more  of  that  efficiency  and  practical 
helpfulness  for  which  it  has  been  so  long  noted.  Some  of  these  changes  may  be 
briefly  mentioned.  The  text  has  been  e  tirely  reset;  the  type,  while  slightly 
smaller,  is  clearer  and  has  the  lines  and  paragraphs  separated  by  wide  leads; 
a  special  type  is  used  for  the  tables;  the  paragraphing  is  revised  throughout  and 
every  paragraph  has  a  black-face  type  caption  descriptive  of  the  subject-matter; 
words  in  italics  or  with  quotation-marks  are  seldom  used,  words  in  small  caps 
taking  their  place;  every  chapter  is  divided  into  numbered  chapter-subdivisions 
which  are  briefly  descriptive  of  the  classified  matter;    the  number  of  cross- 


/lii  rreface  to  Sixteenth  Edition 

references  is  largely  increased  and  the  page-numbers  of  such  references  are  almost 
always  added;  many  tables  and  diagrams  which  in  the  former  editions  read 
lengthwise  of  the  page  have  been  reset  or  reengraved  to  read  across  the  page  for 
greater  convenience;  the  number  of  illustrations  has  been  largely  increased,  many 
old  cuts  reused  have  been  reengraved,  and  some  diagrams  printed  with  lines  of 
different  colors  to  make  the  demonstrations  clearer;  a  descriptive  caption  has 
been  added  to  every  illustration;  the  abbreviations  Chap.  I,  Chap.  II,  etc.,  have 
been  printed  with  each  page-caption  of  the  left-hand  pages,  thus  avoiding  the 
necessity  of  referring  to  the  Table  of  Contents  to  locate  any  particular  chapter. 

The  Editor-in-Chief  decided  to  change  some  of  the  unit  stresses,  especially 
those  for  the  different  woods,  and  in  some  cases  to  recommend  more  conservative 
values,  and  he  believes  that  results  based  upon  such  stresses  conform  to  the  best 
engineering  practice.  This  change  necessitated  the  revision  of  many  tables  and 
problems  throughout  the  book  which  had  to  be  entirely  recalculated.  Numer- 
ous practical  problems  with  complete  solutions  have  been  added.  The  deriva- 
tion of  many  of  the  formulas  used  has  been  explained,  either  in  the  body  of  the 
text  or  in  extended  foot-notes,  for  those  who  wish  to  understand  as  well  as  to  use 
such  formulas,  and  numerous  cross-references  accompanying  them  enable  the 
reader  to  use  the  Pocket-Book  as  a  textbook  for  certain  parts  of  the  mechanics 
of  materials  as  well  as  a  handbook  for  office  work.  The  tables  of  the  properties 
of  structural  shapes,  of  safe  loads  for  columns,  beams  and  girders,  etc.,  have  been 
revised  and  numerous  new  tables  added.  The  Editor  has  found  that  it  is  the  con- 
sensus of  opinion  among  architects  that  the  insertion  of  these  tables  is  a  great 
convenience  and  for  their  ordinary  office  work  condenses  into  one  handy  vol- 
ume much  of  the  essential  data  of  several  manufacturers'  handl)ooks. 

The  difficulty  of  securing  a  unity  of  treatment  and  of  a-voiding  repetitions  and 
contradictions  in  a  book  of  reference  the  data  of  which  covers  so  many  subjects 
and  is  written  by  so  many  contributors  has  been  fully  realized;  but  it  is  believed 
that  in  these  respects  the  New  Kidder  is  reasonably  successful  and  will  meet 
with  the  approval  of  all  who  use  it. 

Acknowledgments  and  thanks  are  due  the  Associate  Editors  for  their  hearty 
cooperation  and  generous  contributions  of  the  time  and  labor  taken  from  their 
professional  work.  Acknowledgment  is  made,  also,  of  the  valuable  assistance 
of  all  others  who  have  furnished  new  or  revised  old  data,  and  of  many  helpful 
suggestions  from  Mrs.  F.  E.  Kidder  and  from  the  publishers. 

The  Editor-in-Chief  expresses  the  hope  that  for  the  architects  and  builders 
of  this  country  the  new  Pocket-Book  will  continue  to  be,  as  Mr.  Kidder  expressed 
it  in  his  preface  to  the  first  edition  in  1884,  "a  compendium  of  practical  facts, 
rules  and  tables  presented  in  a  form  as  convenient  for  application  as  possible, 
and  as  reliable  as  our  present  knowledge  will  permit;"  and  also,  in  its  present 
extension  and  fuller  development,  a  work  which  will  lead  to  a  still  clearer  under- 
standing of  the  essential  principles  of  sound  architectural*  construction. 

THOMAS  NOLAN. 
Philadelphia,  September,  1915. 


PREFACE  TO  FOURTEENTH   EDITION 

It  is  now  nearly  twenty  years  since  the  author,  then  quite  a  young  man, 
completed  the  first  edition  of  this  work,  which,  although  containing  but  586 
pages,  had  required  about  three  years  for  its  preparation.  At  that  time  the 
author  thought  he  had  covered  all  of  those  practical  details  relating  to  the 
planning  and  construction  of  buildings,  with  which  the  architect  was  concerned, 
tolerably  well,  and  it  would  appear  as  though  the  purchasers  of  the  book  thought 
so  too,  but  as  the  years  have  come  and  gone,  so  many  and  such  great  improve- 
ments have  taken  place  in  the  building  world,  so  many  articles  invented,  new 
methods  of  construction  developed,  higher  standards  established,  that  the  present 
edition,  although  containing  nearly  three  times  as  many  pages,  is  perhaps  not 
more  complete,  for  the  times,  than  was  the  first  edition. 

When  preparing  the  first  edition,  it  was  the  aim  of  the  author  to  give  to 
architects  and  builders  a  handbook  which  should  be,  in  its  field,  as  useful  ana 
reliable  as  Trautwine's  had  been  to  civil  engineers;  and  with  that  object  con- 
stantly in- view,  the  book  has  been  revised  from  time  to  time  to  meet  the  changed 
conditions  in  building  construction  and  equipment. 

About  three  years  ago  it  was  thought,  by  the  publishers  and  the  author,  that 
a  thorough  and  complete  revision  of  the  book  should  be  undertaken,  and  although 
the  re-writing  of  a  work  of  this  character,  even  with  the  thirteenth  edition  to 
work  from,  involved  many  months  of  close  and  constant  application,  the  utiliza- 
tion of  those  hours  which  one  ordinarily  takes  for  recreation,  and  at  the  best' 
more  or  less  interruption  to  his  regular  business,  and  consequent  reduction  in 
income,  the  writer  undertook  to  prepare  a  work  of  a  still  wider  scope,  and  which 
should  be  thoroughly  up-to-date  in  every  particular,  or  at  least  as  far  as  is 
practicable,  in  a  work  requiring  a  period  of  three  years  in  its  preparation,  and 
from  that  time  to  this  he  has  spared  no  labor  or  expense  to  make  the  book  as 
useful  and  complete  as  he  possibly  could,  without  making  it  too  bulky. 

In  this  revision  the  author  has  had  in  view: 

I  St.  A  reference-book  which  should  contain  some  information  on  every  subject 
(except  design)  likely  to  come  before  an  architect,  structural  engineer,  draughts- 
man, or  master-builder,  including  data  for  estimating  the  approximate  cost. 

2d.  To  as  thoroughly  cover  the  subject  of  architectural  engineering  as  is 
practicable  in  a  handbook. 

3d.  To  present  all  information  in  as  simple  and  convenient  a  form  for  immedi- 
ate appHcation  as  is  consistent  with  accuracy.  To  this  end  a  great  many  new 
tables,  arranged  and  computed  by  the  author,  have  been  inserted. 

At  the  time  the  first  edition  was  written,  the  term  "Architectural  Engineering" 
had  not  been  used  in  its  present  apphcation,  and  the  term  "Structural  Engineer- 
ing," when  used,  referred  almost  exclusively  to  bridge  work. 

To-day,  structural  and  architectural  engineers  are  concerned  almost  exclusively 
with  building  construction,  and  their  work  is  more  closely  allied  to  that  of  the 
architect  than  to  that  of  the  civil  engineer;  hence  the  author  has  had  in  mind 
the  needs  of  the  structural  engineer  and  draughtsman  as  well  as  those  of  the 
architect  and  builder,  and  the  book  should  be  of  nearly  equal  value  to  both. 


X  Preface  to  Fourteenth  Edition 

Where  it  was  impossible,  for  lack  of  space,  to  go  extensively  into  any  subject, 
references  to  other  books  or  sources  of  information  have  been  given,  so  that  in 
this  way  the  book  may  serve  as  a  general  index  to  the  many  hues  of  work, 
materials,  and  manufactured  products  entering  into  the  planning,  construction, 
and  equipment  of  buildings. 

To  attain  the  objects  in  view,  it  has  been  necessary  to  add  considerably  to  the 
number  of  pages,  but  as  experience  has  shown  that  the  book  is  used  principally 
at  the  desk  o?  draughting-table,  and  is  seldom  carried  in  the  r>ocket,  it  is  believed 
that  the  convenience  of  having  everything  in  one  book  will  more  than  offset  any 
disadvantage  resulting  from  increase  in  bulk. 

Nearly  the  entire  book  has  been  re-written,  and  great  pains  have  been  taken 
to  furnish  reliable  data.  A  large  number  of  experts  in  various  Hnes  have  assisted 
the  author,  as  is  manifest  by  the  foot-notes  and  references.  To  all  of  such,  and 
to  the  many  authors  of  technical  works,  and  to  the  publishers  of  technical 
journals,  who  have  kindly  consented  to  the  use  of  cuts  and  data,  the  author 
takes  pleasure  in  acknowledging  his  indebtedness,  x^lso  to  Mr.  E.  S.  Hand,  of 
New  York,  who,  for  many  years,  has  rendered  material  assistance  in  collecting 
data  along  the  line. of  manufactured  products. 

The  names  and  addresses  of  manufacturers  have  been  given  solely  for  the 
convenience  of  the  users  of  the  book,  and  not  for  any  pecuniary  considerations; 
in  fact,  if  money  considerations  had  solely  appealed  to  the  writer,  this  book  would 
never  have  been  re-written,  because  a  technical  work  of  this  character  can  never 
adequately  compensate,  in  money,  for  the  time,  labor,  and  thought  required  in 
its  preparation.  The  many  words  of  appreciation  which  have  come  to  the  author 
from  hundreds  of  those  who  have  found  the  book  useful  have  been  a  great 
stimulus  to  further  increase  its  usefulness. 

As  in  the  former  prefaces,  the  author  requests  that  any  one  discovering  errors 
in  the  work  or  who  may  have  any  suggestions  looking  to  the  further  improve- 
ment of  the  book,  will  communicate  the  same  to  him,  that  the  book  may  be  made 
as  complete  and  reliable  as  possible. 

Finally,  the  author  desires  to  acknowledge  his  indebtedness  to  the  publishers, 
who  have  heartily  seconded  his  efforts  in  every  particular,  and  who  have  spared 
no  pains  or  expense  to  make  a  jjerfect  handbook. 

F.  E.  KIDDER. 

Denver,  Colo.,  July  i8th,  1904. 


CONTENTS 

PART  I 

PRACTICAL   ARITHMETIC,   GEOMETRY,   AND 
TRIGONOMETRY 

PAGE 

Arithmetical  Signs  and  Characters 3 

Involution ; 3 

Evolution,  Square  Root,  Cu^e  Root,  Rules,  and  Tables 4 

Weights  and  Measures 25 

The  Metric  System 30 

Metric  Conversion  Tables 32 

Scripture  and  Ancient  Measures  and  Weights 34 

Geometry  and  Mensuration 36 

Geometrical  Problems 66 

Table  of  Chords 81 

Hip  and  Jack-Rai-ters 90 

Trigonometry  Formulas  and  Tables 90 

PART  II 

STRENGTH   OF  MATERIALS  AND   STABILITY    OF 
STRUCTURES 

Introduction 121 

Explanation  of  Notation  and  Symbols   . 122 

CHAPTER  I 

EXPLANATION   OF   TERMS    USED    IN   ARCHI- 
TECTURAL  ENGINEERING 


THOMAS  NOLAN 

professor   of   architectural   construction,    university   of   PENNSYLVANIA 

1.  Definitions  of  Some  of  the  Terms  Used  in  Mechanics  of  Materials  .      .       124 

2.  Classifications  of  the  Principal  Stresses  Caused  in  Bodies  by  External 

Forces 12" 

CHAPTER  II 
FOUNDATIONS 

by 
DANIEL  E.  MORAN 

member    of   AMERICAN    SOCIETY    OF    CIVIL   ENGINEERS 

1.  Definition  of  the  W^ord  and  Terms  Used 129 

2.  General  Requirements 129 

3.  Geological  Considerations 130 

xi 


xii  Contents 

PAGE 

4.  Composition  and  Classification  of  Rocks 130 

5.  Geology  of  Earthy  Material 132 

6.  Materials  Composing  Foundation-Beds 134 

7.  Characteristics  of  the  Materials  of  Foundation-Beds 135 

8.  Allowable  Loads  on  Materials  o^  Foundation-Beds 140 

9.  Unit  Loads  on  Foundation-Beds  Allowed  by  Building  Codes  ....  142 

10.  Investigation  of  th^  Site 142 

11.  Loading-Tests 145 

12.  Topographical  and  Specl\l  Conditions 146 

13.  Loads  Comng  on  the  Footings 148 

14.  Assumed  Loads  Specifled  by  Building  Codes 151 

15.  Proportioning  Supporting  Areas  for  Equal  Settlement 152 

16.  Determining  the  Supporting  Areas 160 

17.  Offset  Footings 163 

18.  The  Use  of  Cantilevers  in  Foundations 165 

19.  Stresses  in  Footing  Courses 169 

20.  Methods  of  Calculating  B ending-Stresses  in  Wall-Footings      ...  172 

21.  Bending  Moments  in  Footings  of  Columns  and  Piers 176 

22.  Design  of  the  Footings 178 

23.  Steel  Grillage  in  Foundations 181 

24.  Reinforced  Concrete  Footings 186 

25.  Timber  Footings  for  Temporary  Buildings      ...         186 

26.  GexNeral  Conditions  Affecting  Foundations  and  Footings      ....  188 

27.  Wooden-Pile  Foundations 188 

28.  Concrete-Pile  Foundations 196 

29.  Foundation  Piers  and  Foundation  Walls 200 

30.  Methods  of  Excavating  for  Foundations 200 

31.  Protection  of  Adjoining  Structures 214 


CHAFfER  III 

MASONRY  WALLS.     FOOTINGS   FOR  LIGHT 
BUILDINGS.      CEMENTS    AND    CONCRETES 

by 

THOMAS  NOLAN 

professor  of  architectural  construction,  university  of  pennsylv.^nia  ' 

1.  Footings  FOR  Light  Buildings 223 

2.  Cellar  Walls  and  Basement  Walls 228 

3.  Walls  of  the  Superstructure 229 

4.  Natural  Cements 235 

5.  Artificial  Cements 236 

6.  Concrete 240 

CHAPTER  IV 

RETAINING-WALLS,     BREAST-WALLS,     AND 
VAULT-WALLS 

BY 

GRENVILLE  TEMPLE  SNELLING 

late    member   of   AMERICAN  INSTITUTE   OF  ARCHITECTS 

1.  Mechanical  Principles  Involved 252 

2.  Retaining-Walls 255 

3.  Breast-Walls 262 

4.  Vault-Walls  . 263 


I 


Contents  xiii 

CHAPTER  V 


STRENGTH  OF   BRICK,  STONE,  MASS-CONCRETE, 
AND   MASONRY 

BY 

THOMAS  NOLAN 

PROFESSOR   OF   ARCHITECTURAL   CONSTRUCTION,    UNIVERSITY    OF   PENNSYLVANIA 

PAGE 

1.  Crushing  Strength  of  Stonework,  Brickwork,  Bricks,  Etc 265 

2.  Strength  of  Terra-Cotta  and  Terra-Cotta  Piers 276 

3.  Crushing  Strength  of  Building  Stones  .      .      .     ,. 279 

,4.  Compressive  Strength  of  Mortars  and  Concretes 282 

'  5.  Building  Laws  for  Working  Loads  on  Masonry 287 


CHAPTER  VI 
FORCES  AND   MOMENTS 

BY 

MALVERD   A.   HOWE 

emeritus  professor  of  civil  engineering,  rose  polytechnic  institute 

1.  Composition  and  Resolution  of  Forces 288 

2.  Moments  of  Forces 289 

3.  Center  of  Gravity 291 

CHAPTER  VII 
STABILITY  OF   PIERS  AND   BUTTRESSES 

BY 

GRENVILLE  TEMPLE  SNELLING 

late  member  of  american  institute  of  architects 

1.  Mechanical  Principles  Involved 297 

2.  Buttresses  with  Offsets 298 

3.  Line  of  Pressure  or  Line  of  Resistance 300 

4.  Method  of  Moments 301 

5.  Graphical  Method 303 

CHAPTER  VIII 
THE   STABILITY  OF   MASONRY  ARCHES 

BY 

GRENVILLE  TEMPLE  SNELLING 

late   MEMBER   OF   AMERICAN   INSTITUTE    OF    ARCHITECTS 

1.  Arches.     Definitions 305 

2.  Brick  Arches 306 

3.  Centers  for  Arches 308 

4.  Keystones 309 

5.  Graphical  Determination  of  the  Stability  of  Arches 311 


xiv  Contents 

CHAPTER  IX 

REACTIONS   AND    BENDING    MOMENTS    FOR 
BEAMS 

BY 

CHARLES   P.   WARREN 

LATE    ASSISTANT   PROFESSOR    OF   ARCHITECTURE,    COLUMBIA    UNIVERSITY 

PAGE 

1.  Reactions  for  Beams 322 

2.  Bending  Moments  in  Beams 324 

3.  Bending  Moments  in  Beams  for  Different  Kinds  of  Loading  ....  325 

4.  Graphic  Method  for  Determining  Bending  Moments  in  Beams  .      .  328 

5.  Reactions  and  Bending  Moments  for  Beams  with  Triangular  Loading 

AND  for  Beams  Fixed  at  Both  Ends 331 

CHAPTER  X 

PROPERTIES  OF  STRUCTURAL  SHAPES,  MOMENT 
OF  INERTIA,  MOMENT  OF  RESISTANCE,  SEC- 
TION-MODULUS, AND  RADIUS  OF  GYRATION 

BY 

CHARLES   P.  WARREN 

LATE    assistant   PROFESSOR    OF    ARCHITECTURE,    COLUMBIA    UNIVERSITY 

1.  The  Properties  of  Cross-Sections 332 

2.  Areas,  Moments  of  Inertia,  Section-Moduli,  and  Radii  of  Gyration  of 

Elementary  Sections ,  334 

3.  Transferring  Moments  of  Inertia  to  Other  Parallel  Axes       .     .      ,  338 

4.  Moments  of  Inertia  of  Compound  Sections 339 

5.  Radii  of  Gyration  of  Compound  Sections ...  344 

6.  Graphical  Method  of  Determining  the  Moment  of  Inertia  of  Plane 

Figures -"^^S 

7.  Dimensions^  Moments  of  Inertia,  Radii  of  Gyration,  and  Section-Moduli 

OF  Standard  Strucpural  Shapes 352 

CHAPTER  XI 

RESISTANCE   TO   TENSION,    PROPERTIES   OF 
IRON  AND   STEEL 

BY 

HERMAN  CLAUDE  BERRY 

professor   of   materials    of    construction,    university    of   PENNSYLVANIA 

1.  Definitions,  Working  Stresses,  and  Examples     .     .     -. 375 

2.  Wrought  Iron 377 

3.  Cast  Iron 379 

4.  Steel 380 

5.  Standard  Specifications  for  Structural  Steel  for  Buildings  .      .      .  383 

6.  Tension-Members 385 

7.  Wire f29 


Wire  Rope 


404 


9.  Cotton,  Hemp,  and  Manila  Rope 406 


10.  Ch.ains 


408 


Contents  xv 

CHAPTER  XII 

RESISTANCE    TO    SHEAR.     RIVETED    JOINTS. 
PINS  AND   BOLTS 

BY 

HERMAN  CLAUDE  BERRY 

PROFESSOR  OF  MATERIALS  OF  CONSTRUCTION,  UNIVERSITY  OF  PENNSYLVANIA 

PAGE 

1.  Shear 411 

2.  Riveted  Joints 413 

3.  Strength  of  Pins  in  Trusses 423 

4.  Strength  of  Bolts  in  Wooden  Trusses  and  Girders 429 

CHAPTER  XIII 

BEARING-PLATES  AND  BASES  FOR  COLUMNS, 

BEAMS,    AND    GIRDERS.     BRACKETS    ON 

CAST-IRON  COLUMNS 

BY 

HERMAN  CLAUDE  BERRY 

professor   of    materials   of   construction,    university   of   PENNSYLVANIA 

1.  Bearing-Plates  and  Bases 440 

2.  Bearing-brackets  on  Cast-iron  Columns 445 

CHAPTER  XIV 
STRENGTH  OF  COLUMNS,  POSTS,  AND   STRUTS 

BY 

CHARLES   P.  WARREN 

late    assistant   professor   of   architecture,    COLUMBIA    UNIVERSITY 

1.  General  Principles  and  Definitions 448 

2.  Strength  of  Short  Wooden  Columns 448 

3.  Strength  of  Wooden  Columns  or  Struts  Over  Ten  Diameters  in  Length. 

Formulas     .      .      .      . 449 

4.  Tables  of  Safe  Loads  for  Wooden  Columns 450 

5.  Eccentric  Loading  of  Wooden  Columns 453 

6.  Metal  Caps  and  Bolsters  for  Wooden  Columns 454 

7.  Crushing  of  Wood  Perpendicular  to  the  Grain 454 

8.  Cast-Iron  Columns 455 

9.  Design  of  Cast-Iron  Columns .  456 

10.  Strength  of  Cast-iron  Columns.     Formulas 459 

11.  Tables  of  Safe  Loads  for  Cast-Iron  Columns.     Examples  .....  461 

12.  Types,  Forms,  and  Connections  of  Steel  Columns 467 

13.  Strength  of  Steel  Columns.     Formulas 480 

14.  Design  of  Steel  Columns.     Examples. 482 

15.  Eccentric  Loading  of  Steel  Columns 485 

16.  Tables  of  Safe  Lo.ads  for  Steel  Columns 488 


xvi  Contents 

CHAPTER  XV 

STRENGTH    OF    BEAMS    AND    BEAM    GIRDERS. 
FRAMING  AND   CONNECTING  STEEL  BEAMS 

BY 

CHARLES   P.   WARREN 

LATE   ASSISTANT   PROFESSOR   OF   ARCHITECTURE,    COLUMBIA    UNIVERSITY 

PAGE 

1.  General  Principles  of  tue  Flexure  of  Beams 555 

2.  Formulas  for  Safe  Loads  for  Beams  for  Different  Conditions  of  Load- 

ing AND  Support 558 

3.  Steel  Beams  and  Girders 564 

4.  Tables  of  Safe  Loads  for  Steel  Beams  and  Girders.     Examples  .     .      570 

Oblique  Loading  of  I  Beams  and  Channels.     Tables 573 

Oblique  Loading  of  Angles  used  as  Beams 593 

5.  Framing  and  Connecting  Steel  Beams  and  Girders 612 


CHAPTER  XVI 

STRENGTH     OF     CAST-IRON     LINTELS     AND 
WOODEN  BEAMS 

BY 

F.  H.   KINDL 

late   corresponding    member   AMERICAN   INSTITUTE' OF   ARCHITECTS 

1.  Cast-Iron  Lintels 620 

2.  Sections,  Stresses,  Buckling,  AND  Deflection  of  Wooden  Beams  .     .     .  627 

3.  Constants  and  Coefficients  for  Beams 628 

4.  Flexural  Strength  of  Wooden  Beams 629 

5.  Application  OF  Formulas  FOR  Flexural.  Strengths  of  Wooden  Beams     .  631 

6.  Flexural  Strength  of  Beams 633 

7.  Tables  for  Strength  and  Stiffness  of  Wooden  Beams 635 

8.  Working  Unit  Stresses  for  Woods 647 

9.  Working  Unit  Stresses  FOR  Woods.    Taken  from  Building  Laws   .     .     .  647 


CHAPTER  XVII 

STRENGTH    OF    BUILT-UP,    FLITCHED,    AND 
TRUSSED   WOODEN  GIRDERS 

BY 

F.  H.  KINDL 

late   corresponding   member   AMERICAN   INSTITUTE   OF     ARCHITECTS 

1.  Built-Up  Wooden  Girders        652 

2.  Flitched  Beams  or  Flitch-Plate  Girders 655 

3.  Trussed  Beams  and  Girders 666 


Contents  xvii 

CHAPTER  XVIII 
STIFFNESS  AND   DEFLECTION  OF  BEAMS 

BY 

CHARLES  P.  WARREN 

LATE   ASSISTANT   PROFESSOR   OF    ARCHITECTURE,    COLUMBIA   UNIVERSITY 

PAGE 

1.  General  Principles  of  the  Deflection  of  Beams 663 

2.  Formulas  for  Loads,  Based  upon  the  Stiffness  of  Beams 665 

3.  Relative  Stiffness  of  Beams 666 

4.  Cylindrical  Beams 667 

5. 'Safe  Loads  for  Wooden  Beams  FOR  A  Given  Deflection 667 

6.  Nominal  and  Standard  Sizes  of  Wooden  Beams 667 

7.  Deflection  OF  Steel  Beams    . 668- 

8.  Graphical  Determination  of  Deflection  of  Beams 670 

I 

CHAl^ER  XIX 

STRENGTH  AND  STIFFNESS  OF  CONTINUOUS 
GIRDERS 

BY 

CHARLES   P.  WARREN 

LATE   assistant    PROFESSOR   OF   ARCHITECTURE,    COLUMBIA   UNIVERSITY 

1.  General  Considerations 671 

2.  Supporting  Forces  or  Reactions  of  Continuous  Girders 671 

3.  Bending  Moments  of  Continuous  Girders 673 

4.  Deflection  of  Continuous  Girders 674 

5.  Notes  on  Reactions,  Strength,  and  Stiffness  of  Continuous  Girders     .  675  ' 

6.  Formulas  for  the  Strength  and  Stiffness  of  Continuous  Girders     .      .  676 

7.  Continuous  Girders  in  Grillage  Foundations 678 

CHAPTER  XX 
RIVETED   STEEL  PLATE  AND   BOX   GIRDERS 

BY 

CHARLES  P.  WARREN 

late   assistant  professor   of  architecture,   COLUMBIA   UNIVERSITY 

1.  General  Notes  on  Plate  and  Box  Girders  .      .         681 

2.  Details  of  (Construction  of  Plate  and  Box  Girders 682 

3.  Design  of  Plate  and  Box  Girders 683 

4.  Explanation  of  Tables 688 

5.  Examples  of  Plate  and  Box  Girders 688 

6.  Tables  Used  in  the  Design  of  Plate  and  Box  Girders 702 

CHAPTER  XXI 

STRENGTH     AND     STIFFNESS     OF     WOODEN 
FLOORS 

BY 

THOMAS  NOLAN 

professor   of   architectural   construction,    university   of   PENNSYLVANIA 

1.  Loads  on  Floors  and  Weights  of  Floor-Construction 717 

2.  Tables  of  Weights  of  Merchandise 721 

3.  Determination  of  Sizes  of  Joists,  Beams,  or  Girders 724 


xviii  Contents. 

PAGE 

4.  Safe  Loads  for  Plank  Flooring 732 

5.  Tables  for  Maximum  Spans  for  Floor-Joists 737 

6.  Determination  of  Strength  of  an  Existing  Floor 746 

7.  Details  of  Floor-Framing 749 

8.  Stirrups  and  Joist-Hangers 750 

9.  Comparative  Strength  of  Different  Types  of  Joist-Hangers   ....  756 


CHAPTER  XXII 

WOODEN  MILL  AND   WAREHOUSE- 
CONSTRUCTION 

BY 

A.  P.  STRADLING 

manager,    PHILADELPHIA    SUBURBAN    UNDERWRITERS'    ASSOCIATION 

1.  Mill-Construction 758 

2.  What  Mill-Construction  Is 758 

3.  What  Mill-Construction  Is  Not 759 

4.  Standard  Mill-Construction 760 

5.  Belts,  Stairways  and  Elevator- Towers 764 

6.  Standard  Storehouse-Construction 765 

7.  Example  of  One-Story  Workshop 769 

8.  Saw-Tooth  Roof-Construction 772 

9.  Mill-Construction  as  Applied  to  Warehouses 777 

10.  Steel  and  Iron  Structural  Members  in  Warehouse-Construction   .      .  780 

11.  Structural  Details  of  Mill-Construction  as  Applied  to  Factories  and 

Warehouses 782 

12.  Connection  of  Floor-Beams  and  Girders 789 

13.  Wall  Supports  and  Anchors  for  Joists  and  Girders 792 

14.  Weakness  of  Wrought-Iron  Stirrups  when  Exposed  to  Fire  ....  794 

15.  Post  and  Girder-Connections 795 

16.  Form  and  Material  of  Post-Caps 795 

17.  Roofing-Materials        800 

18.  Partitions 801 

19.  Doors  and  Shutters 801 

20  Fire-Protection 801 

21  Cost  of  Mills  and  Factories  Built  on  the  Slow-Burning  Principle     .  802 
22.  Cost  of  Brick  Mill-Buildings  of  Slow-Burning  Construction  .     .  808 


CHAPTER  XXIII 
FIREPROOFING  OF  BUILDINGS 

by 

RUDOLPH  P.  MILLER 

superintendent   of   buildings,    borough   of   MANHATTAN,    NEW   YORK    CITY 

1.  Definitions,  Areas,  Heights,  AND  Costs 811 

2.  Fire-Resistance  of  Materials 814 

3.  Column-Protection 822 

4.  Fire-Proof  Floor-Construction 826 

5.  Fire-Proof  Roof-Construction 866 

6   Partitions  and  Wall-Coverings  ....  873 

7.  Fire-Proof  Flooring 892 

8.  Interior  Finish  and  Fittings 893 

9.  Protection  from  Outside  Hazard 001 

10.  Extinguishing  Devices  and  Precautionary  Measures 9(  :-, 


Contents 

CHAPTER  XXIV 

REINFORCED-CONCRETE   CONSTRUCTION 


RUDOLPH   P.  MILLER 

SUPERINV    NDENT  OF  BUILDINGS,  BOROUGH  OF  MANHATTAN,  NEW  YORK  CITY 

PAGE 

1.  Introductory  Notes 906 

2.  Materials  Used  in  Rfinforced-Concrfte  Construction 907 

3.  Design  of  R  fin  forced-Concrete  Construction 924* 

4.  Types  of  Reinforced-Concrete  Construction 948 

5.  Fire- Resistance  of  Reinforced-Concrete  Construction 955 

6.  Protection  Against  Corrosion  in  Reinforced-Concrete  Construction  960 

7.  Erection  of  Reinforced-Concrete  Constructtion 962 


CHAPTER   XXV 

REINFORCED-CONCRETE    FACTORY    AND    MILL- 
CONSTRUCTION 

BY 

EMILE  G.   PERROT 

MEMBER    of    AMERICAN    SOCIETY   OF   CIVIL   ENGINEERS 

1.  General  Principles  and  Details 968 

2.  Design  of  Floor  System 971 

3.  Design  of  Spandrel  Beams 975 

4.  Columns  and  Piers 976 

5.  Foundations  and  Footings 978 

6.  Stair-Design 983 

7.  Diagrams  and  Formulas  for  Beams  and  Slabs 984 

8.  Girderless  Floors 993 

CHAPTER  XXVI 
TYPES  OF   ROOF-TRUSSES 

BY 

MALVERD  A.  HOWE 

professor   emeritus  of  civil   engineering,    rose   POLYTECHNIC  INSTITUTE 

1.  Definitions 998 

2.  Types  of  Wooden  Trusses 998 

3.  Types  of  Steel  Trusses 1025 

4.  Arched  Trusses 1035 

5.  Cantilever  Trusses 1043 

CHAPTER  XXVII 
STRESSES   IN  ROOF-TRUSSES 

BY 

MALVERD  A.  HOWE 

professor  emeritus  of  civil  engineering,  rose  polytechnic  institute 

1.  Roof-Loads.     Data,  Weights    Materials,  Methods 1046 

2.  Examples  of  the  Computation  of  Roof-Loads 1054 

3.  Determination  of  Stresses  by  Computation 1058 


XX  Contents 

PAGE 

4.  Examples  Showing  Use  of  Tables  in  Stress-Computations       ....  1065 

5.  Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods  .     .  1065 

6.  Determination  of  Wind-Load  Stresses 1109 

7.  Trusses  with  Knee-Braces 1116 

8.  Arched  Trusses 1118 

9.  Trussed  Arches 1121 

10.  Arches  with  Solid  Ribs 1132 

11.  Influence-Lines  for  Simple  Be.ams  and  Trusses 1134 

12.  Secondary  Stresses  IN  Truss-Members 1137 

CHAKPER  XXVIII 

DESIGN     AND     CONSTRUCTION    OF     ROOF- 
TRUSSES 

BY 

MALVERD   A.  HOWE 

professor   emeritus    of    CIVIL    ENGINEERING,    ROSE    POLYTECHNIC   INSTITUTE 

1.  Design  of  Wooden  Trusses 1138 

2.  Design  of  Steel  Trusses 1144 

3.  Joints  of  W^ooden  Trusses 1149 

4.  Joints  of  Steel  Trusses 1160 

5.  Purlins  and  Purlin-Connections 1169 

CHAPTER  XXIX 
WIND-BRACING   FOR  TALL   BUILDINGS 

BY 

N.  A.  RICHARDS 

OF 
PURDY    &    HENDERSON,    INC.,    CIVIL   ENGINEERS 

1.  Data  for  Wind-Pressure.     Building  Laws 1171 

2.  Conditions  Determining  or  Affecting  Wind-Bracing 1172 

3.  General  Theory  of  Wind-Bracing 1173 

4.  Arrangement  of  Wind-Bracing 1174 

5.  Types  of  Wind-Bracing 1174 

6.  Computation  of  Wind-Stresses 1176 

7.  Illustration  of  Method  of  Coatputing  Wind-Stresses 1176 

8.  Analysis  of  Stresses  in  Different  Types  of  Wind-Bracing       .     .      .  1179 

9.  Combination  of  Dead  and  Live  Loads,  with  Wind-Load        .     .     ,      .  1183 

10.  Wind-Bracing  of  Water-Towers  and  Similar  Structures      ....    1184 

11.  Recent  Examples  of  Wind-Bracing  in  Tall  Buildings 1187 

CHAPTER  XXX 

SPECIFICATIONS    FOR    THE    STRUCTURAL 

STEELWORK  OF  BUILDINGS.     DATA  ON 

STRUCTURAL     STEEL 

by 
ROBINS  FLEMING 

OF   THE 

american  bridge  company,  new  york,  n.  y. 

1.  General 1194 

2.  M.\terial 1195 

3.  Loads 1196 


Contents  xxi 

PAGE 

4.  Stresses 1199 

5.  Design 1201 

6.  Details 1202 

7.  Workmanship 1202 

8.  Painting 1203 

9.  Inspection 1203 

10.  Erection 1203 

Data  on  Structural  Steel 1204 

CHAPTER  XXXI 
DOMICAL   AND    VAULTED    STRUCTURES 

BY 

EDWARD   F.  RIES 

consulting    engineer,    SAN    ANTONIO,    TEXAS 

1.  Domes •  .      .  1213 

(i)  Smooth-Shell  Domes 1213 

(2)  Ribbed  Domes      . 1222 

2.  Vaults 1231 

(1)  Barrel  Vaults 1231 

(2)  Groined  Vaults 1235 

(3)  Ribbed  Vaults 1240 


PART  III 

USEFUL  INFORMATION   FOR  ARCHITECTS,  BUILDERS, 
AND   SUPERINTENDENTS 

HEATING  AND  VENTILATION  OF  BUILDINGS 

BY 

LOUIS  A.  HARDING 

formerly  professor  of  mechanical  engineering,  PENNSYLVANIA  STATE  COLLEGE 

Physical  Units  and  the  Measurement  of  Heat 1247 

Heat 1249 

Steam ^_^  1.251 

Properties  of  Air 7     .  1254 

Estimating  Heating  Requirements  of  Buildings 1256 

Radiation 1264 

Fuels  and  Combustion 1271 

Steam-Heating  Boilers  and  Hot-Water  Boilers .•     .      .  1273 

Direct  Steam  Heating 1283 

Design  of  Low-Pressure  Steam-Heating  Systems 1291 

Gravity  Indirect  Heating 1298 

Direct  Hot-Water  Heating 1202 

Furnace  Heating 1310 

The  Design  of  a  Furnace-Heating  System 1312 

Hot-Blast  Heating " 1324 

Hot-Blast  Heaters 1329 

Design  of  Air-Ducts 1333 

Ventilating-Fans 1341 

Application  of  Hot-Blast  Heating  Data 1342 

Ventilation 1348 

State  Ventilation  Laws  and  Requirements 1364 

Specifications  for  Furnace-work 1357 

Specifications  for  Hot-Water  Heating-Apparatus  in  a  Residence     .      .      .  1359 
Specifications  for  a  Low-Pressure  Steam-Heating  Apparatus  for  Heating 

BY  Direct  Radiation 1361 


xxiv  Contents 

PAGE 

Vacuum-Cleaning 1708 

Waterproofing  for  Foundations 1709 

Force  of  the  Wind 1717 

Copies  of  Architects'  Tr^vcings     . 1718 

Horse-Power,  Pulleys,  Gears,  Belting,  .\nd  Shafting 1720 

Chain-Blocks,  Hoists,  and  Hooks 1723 

Bells 1725 

Symbols  for  the  Apostles  and  Saints 1727 

A  Circular  of  Advice  on  Professional  Practice  by  the  American  Institute 

of  Architects 1727 

Architectural  Competitions 1733 

Standard  Documents  of  the  American  Institute  of  Architects     ....  1748 

Registration  of  Architects 1768 

Educational  Institutions  Giving  Courses  in  Architecture 1779 

Architectural  Societies 1788 

Glossary 1 796 

Architectural  Terms  Used  in  Law 1851 


PART  I 

PRACTICAL 
ARITHMETIC,  GEOMETRY  AND  TRIGONOMETRY 

RULES,  TABLES  AND  PROBLEMS 


Involution  and  Evolutiou  3 

1.  PRACTICAL  ARITHMETIC 

Mathematical  Signs  and  Characters* 

The  following  signs  and  characters  are  generally  used  to  denote  and  abbrevi- 
ate the  several  mathematical  operations: 
The  sign  =  means  equal  to,  or  equality; 

—  means  minus  or  less,  or  subtraction; 
+  means  plus,  or  addition; 
X  means  multiphed  by,  or  multiplication; 
-7-  or/  means  divided  by,  or  division; 

are  indexes  or  powers,  meaning  that  the  number  to  which  they 
are  added  is  to  be  squared  (2)  or  cubed  {^) ; 
:  is  to  ) 
:  :  so  is  >  are  signs  of  proportion; 

:to       ) 
\/  is  the  RADICAL  SIGN  and  means  that  the  square  root  of  the  num- 
ber before  which  it  is  placed  is  to  be  extracted; 
\^  means  that  the  cube  root  of  the  number  before  which  it  is 
placed  is  to  be  extracted; 

the  BAR  indicates  that  all  the  numbers  under  it  are  to  be  taken 

together; 
( )  the  PARENTHESIS  means  that  all  the  numbers  between  are  to  be 
taken  as  one  quantity; 
.  means  decimal  parts;  thus,  2.5  means  2M0,  0.46  means  *Moo. 
°  means  degrees,  '  minutes  and  "  seconds; 
.*.  means  hence; 
'  means  feet; 
"  means  inches. 

Involution 

To  Square  a  Number,  multiply  the  number  by  itself,  and  the  product  will 
be  the  square;  thus,  the  square  of  18  =  18^  =  18  X  18  =  324. 

The  Cube  of  a  Number  is  the  product  obtained  by  multiplying  the  number 
by  itself,  and  that  product  by  the  number  again;  thus,  the  cube  of  14  =  14^  = 
14  X  14  X  14=  2  744. 

The  Fourth  Power  of  a  Number  is  the  product  obtained  by  multiplying 
the  number  by  itself  four  times;  thus,  the  fourth  power  of  10  =  10'*  =  10  X  10  X 
10  X  10=  10  000. 

Evolution 

Square  Root.     Rule  for  extracting  the  square  root  of  a  number: 

(i)  Divide  the  given  number  into  periods  of  two  figures  each,  commencing 

at  the  right  if  it  is  a  whole  number,  and  at  the  decimal  point  if  there  are  decimals; 

thus,  10236.81 26. 

(2)  Find  the  largest  square  in  the  left-hand  period,  and  place  its  root  in  the 
quotient;  subtract  the  said  square  from  the  left-hand  period,  and  to  the  re- 
mainder bring  down  the  next  period  for  a  new  dividend. 

(3)  Double  the  root  already  found,  and  annex  one  cipher  for  a  trial-divisor; 
see  how  many  times  it  will  go  in  the  dividend,  and  put  the  number  in  the  quotient 

*  See,  also,  pages  122  and  123,  Part  11. 


4  Practical  Arithmetic  Part  1 

and  also  in  place  of  the  cipher  in  the  divisor.     Multiply  this  final  divisor  by  the 

number  in  the  quotient  just  found,  subtract  the  product  from  the  dividend, 

and  to  the  rero-ainder  bring  down  the  next  period  for  a  new  dividend  and  proceed 

as  before.     If  it  should  be  found  that  the  trial  divisor  cannot  be  contained  in  the 

dividend,  bring  doM'n  the  next  period  for  a  new  dividend,  annex  another  cipher  j 

to  the  trial  divisor,  put  a  cipher  in  the  quotient  and  proceed  as  before. 

Example.  10236.81 26  (101.17,  the  square  root 

I 

201)0236 

201 

2021)3581 

2021 


20227)156026 

141589 

14437 

Cube  Root.  To  extract  the  cube  root  of  a  number,  point  off  the  numbel 
from  right  to  left  into  periods  of  three  figures  each,  and,  if  there  is  a  decimal, 
commence  at  the  decimal  point  and  point  off  into  periods,  going  both  ways. 

Ascertain  the  highest  root  of  the  first  period,  and  place  it  to  the  right  of  the 
number,  as  in  Long  division^  cube  the  root  thus  found  and  subtract  from  the 
first  period;  to  the  remainder  annex  the  next  period;  square  the  root  already 
found,  multiply  by  three  and  annex  two  ciphers  for  the  trial  divisor.  Find  how 
many  times  this  trial  divisor  is  contained  in  the  dividend  and  write  the  result 
in  the  root. 

Add  together  the  trial  divisor,  three  times  the  product  of  the  first  figure  of 
the  root  by  the  second  with  one  cipher  annexed,  and  the  square  of  the  second 
figure  in  the  root;  multiply  the  sum  by  the  last  figure  in  the  root,  and  subtract 
from  the  dividend;  to  the  remainder  annex  the  next  period  and  proceed  as  before. 
When  the  trial  divisor  is  greater  than  the  dividend,  write  a  cipher  in  the  root, 
annex  the  next  period  to  the  dividend  and  proceed  as  before. 
Example.     Required,  the  cube  root  of  493039  or  ■v^493039 

493039(79,  the  cube  root 
7  X  7  X  7  =  343 
7X7X3=  14700 


7X9X3=    1890 
9X9=        81 


1 667 1 


150039 


150039 


Example.    Required,  the  cube  root  of  403583.419  or  -v^403583.4ic 


403583-4 1 9  (73  •9»  the  cube  roo* 

7X7X7  =  343 

7X7X3=  14700 

7X3X3=      630 

3X3=         9 


15339 


73  X  73  X  3  =  1598700 
73 X  9X3=   19710 

9X9  = 81^ 

1618491 


60583 
46017 


14566419 
14566419 


"Evolution 


Example.     Required,  tlie  cube  r6dt  of  158252.632929  or  ^158252  632929 

158252.632929(54.09,  the  cube  root 
5X  5X5  =  125 
5X5X3= 


=  7500 
5X4X3=    600 

4X4  = 16^ 

8116 


540  X  540  X  3  =  87480000 

540  X   9X3=   145800 

9X9=      81 


87625881 


33252 


32464 


788632929 


788632929 


TABLES 

OF 

SQUARES,    CUBES,    SQUARE    ROOTS,   CUBE 
ROOTS   AND   RECIPROCALS 

From  I  to  1054 


The  following  table,  taken  from  Searle's  Field  Engineering,  will  be 
found  of  great  convenience  in  finding  the  square,  cube,  square  root,  cube 
root  and  reciprocal  of  any  number  from  i  to  1054.  The  reciprocal  of 
a  number  is  the  quotient  obtained  by  dividing  i  by  the  number.  Thus, 
the  reciprocal  of  8  is  i  -h  8  =  0.125. 


Practical  Arithmetic 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

1 

1 

1 

1.0000000 

1.0000000 

1.000000000 

2 

4 

'8 

1.4142136 

1.2599210 

.500000000 

3 

9 

27 

1 . 7320508 

1.4422496 

.333333333 

4 

16 

64 

2 . 0000000 

1.5874011 

.250000000 

5 

25 

125 

2.2360680 

1.7099759 

.200000000 

6 

36 

216 

2.4494897 

1.8171206 

. 166666667 

7 

49 

343 

2.6457513 

1.9129312 

.142857143 

8 

64 

512 

2.8284271 

2.0000000 

.125000000 

9 

81 

729 

3.0000000 

2.0800837 

.111111111 

10 

100 

1000 

3.1622VVV 

2.1544347 

. 100000000 

11 

121 

1331 

3.3166248 

2.2239801 

.090909091 

12 

144 

1728 

3.4641016 

2.2894286 

.083333333 

13 

169 

2197 

3.6055513 

2.3513347 

.076923077 

14 

196 

2744 

3.7416574 

2.4101422 

.071428571 

15 

225 

3375 

3.8729833 

2.4662121 

.066666667 

16 

256 

4096 

4.0000000 

2.5198421 

.062500000 

17 

289 

4913 

4.1231056 

2.5712816 

.058823529 

18 

324 

5832 

4.2426407 

2.6207414 

.055555556 

19 

361 

6859 

4.3588989 

2.6684016 

.052631579 

20 

400 

8000 

4.4721360 

2.7144177 

.050000000 

21 

441 

9261 

4.5825757 

2 . 7589243 

.047619048 

22 

484 

10648 

4.6904158 

2.8020393 

.045454545 

23 

529 

12167 

4.7958315 

2.8438670 

.043478261 

24 

676 

13824 

4.8989795 

2.8844991 

.041666667 

25 

625 

15625 

5.0000000 

2.9240177 

.040000000 

26 

676 

17576 

5.0990195 

2 . 9624960 

.038461538 

27 

729 

19683 

5.1961524 

3.0000000 

.037037037 

28 

784 

21952 

5.2915026 

3.0365889 

.035714286 

29 

841 

24389 

6.3851648 

3.0723168 

.034482759 

30 

900 

27000 

6.4772256 

3.1072325 

.033333333 

31 

961 

29791 

6.5677644 

3.1413806 

.032258065 

32 

1024 

32768 

5.6568542 

3.1748021 

.031250000 

33 

1089 

35937 

6.7445626 

3.2075343 

.030303030 

34 

1156 

39304 

5.8309519 

3.2396118 

.029411765 

35 

1225 

42875 

5.9160798 

3.2710663 

.028571429 

36 

1296 

46656 

6.0000000 

3.3019272 

.027777778 

37 

1369 

50653 

6.0827025 

3.3322218 

.027027027 

38 

1444 

54872 

6.1644140 

3.3619754 

.026315789 

39 

1521 

59319 

6.2449980 

3.3912114 

.025641026 

40 

1600 

64000 

6.3245553 

3.4199519 

.025000000 

41 

1681 

68921 

6.4031242 

3.4482172 

.024390244 

42 

1764 

74088 

6.4807407 

3.4760266 

.023809524 

43 

1849 

79507 

6.5574385 

3.5033981 

.023255814 

44 

1936 

85184 

6.6332496 

3.5303483 

.022727273 

45 

2025 

91125 

6.7082039 

3.5568933 

.022222222 

46 

2116 

97336 

6.7823300 

3.5830479 

.021739130 

47 

2209 

103823 

.6.8556546 

3.6088261 

.021276600 

48 

2304 

110592 

6.9282032 

3.6342411 

.020833333 

49 

2401 

117649 

7.0000000 

3.6593057 

.020408163 

50 

2500 

125000 

7.0710678 

3.6840314 

.020000000 

51 

2601 

132651 

7.1414284 

3.7084298 

.019607843 

52 

2704 

140608 

7.2111026 

3.7325111 

.019230769 

53 

2809 

148877 

7.2801099 

3 . 7562858 

.018867925 

54 

2916 

157464 

7.3484692 

3.7797631 

.018518519 

55 

3025 

166375 

7.4161985 

3.8029525 

.018181818 

56 

3136 

175616 

7.4833148 

3.8258624 

.017857143 

57 

3249 

185193 

7.5498344 

3.8485011 

.017543860 

58 

3364 

195112 

7.6157731 

3.8708766 

.017241379 

59 

3481 

205379 

7.6811457 

3.8929965 

.016949153 

60 

3600 

216000 

7.7459667 

3.9148676 

.016666667 

61 

3721 

226981 

7.8102497 

3.9364972 

.016393443 

62 

3844 

238328 

7.8740079 

3.9578915 

.016129032 

Squares,  Cubes,  Square  Roots,  Cube  Roots  and  Reciprocals        9 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

G3 

3969 

250047 

7.9372539 

3.9790571 

.015873016 

64 

4096 

262144 

8.0000000 

4.0000000 

.015625000 

65 

4225 

274625 

8.0622577 

4.0207256 

.015384615 

66 

4356 

287496 

8.1240384 

4.0412401 

.015151515 

67 

4489 

800763 

8.1853528 

4.0615480 

.014925373 

68 

4624 

314432 

8.24G2113 

4.0816551 

.014705882 

69 

4761 

328509 

8.3066239 

4.1015661 

.014492754 

70 

4900 

343000 

8.3666003 

4.1212853 

.014285714 

71 

5041 

357911 

8.4261498 

4.1408178 

.014084507 

72 

5184 

373248 

8.4852814 

4.1601676 

.013888889 

73 

5329 

389017 

8.5440037 

4.1793390 

.013698630 

74 

5476 

405224 

8.6023253 

4.1983364 

.013513514 

75 

5625 

421875 

8.6602540 

4.2171633 

.013333333 

76 

5776 

438976 

8.7177979 

4.2358236 

.013157895 

77 

5929 

456533 

8.7749644 

4.2543210 

.012987013 

78 

6084 

474552 

8.8317609 

4 . 2726586 

.012820513 

79 

6241  • 

493039 

8.8881944 

4.2908404 

.012658228 

80 

6400 

512000 

8.9442719 

4.3088695 

.012500000 

81 

6561 

531441 

9.0000000 

4.3267487 

.012345679 

82 

6724 

551368 

9.0553851 

4.3444815 

.012195122 

83 

6889 

571787 

9.1104336 

4.3620707 

.012048193 

84 

7056 

592704 

9.1651514 

4.3795191 

.011904762 

85 

7225 

614125 

9.2195445 

4.3968296 

.011764706 

86 

7396 

636056 

9.2736185 

4.4140049 

.011627907 

87 

75G9 

658503 

9.3273791 

4.4310476 

.011494253 

88 

7744 

681472 

9.3808315 

4.4479602 

.011363636 

89 

7921 

704969 

9.4339811 

4.4647451 

.011235955 

90 

8100 

729000 

9.4868330 

4.4814047 

.011111111 

91 

8281 

753571 

9.5393920 

4.4979414 

.010989011 

92 

8404 

778688 

9.5916630 

4.5143574 

.010869565 

93 

8649 

804357 

9.6436508 

4 . 5306549 

.010752688 

94 

8836 

830584 

9.6953597 

4.5468359 

.010638298 

95 

9025 

857375 

9.7467943 

4.5629026 

.010526316 

96 

9216 

884736 

9.7979590 

4.5788570 

.010416667 

97 

9409 

912673 

9.8488578 

4.5947009 

.010309278 

98 

9604 

941192 

9.8994949 

4.6104363 

.010204082 

99 

9801 

970299  ■ 

9.9498744 

4.6260650 

.010101010 

100 

10000 

1000000 

10.0000000 

4.6415888 

.010000000 

101 

10201 

1030301 

10.04987^6 

4.6570095 

.009900990 

102 

10404 

1061208 

10.0995049 

4.6723287 

.009803922 

103 

10609 

1092727 

10.1488916 

4.6875482 

.009708738 

104 

10816 

1124864 

10.1980390 

4.702GG94 

.009615385 

105 

11025 

1157625 

10.2469508 

4.7176940 

.009523810 

106 

11236 

1191016 

10.2956301 

4.7326235 

.009433962 

107 

11449 

1225043 

10.3440804 

4.7474594 

.009345794 

108 

11664 

1259712 

10.3923048 

4.7622032 

.009259259 

109 

11881 

1295029 

10.4403065 

4.7768562 

.009174312 

110 

12100 

1331000 

10.4880885 

4.7914199 

.009090909 

111 

12321 

1367631 

10.5356538 

4.8058955 

.009009009 

112. 

12544 

1404928 

10.5830052 

4.8202845 

.008928571 

113 

12769 

1442897 

10.6301458 

4.8345881 

.008849558 

114 

12996 

1481544 

10.6770783 

4.8488076 

.008771930 

115 

13225 

1520875 

10.7238053 

4 . 8629442 

.008695652 

116 

13456 

1560896 

10.7703296 

4.8769990 

.008620090 

117 

13689 

1601613 

10.8166538 

4.8909732 

.008547009 

118 

13924 

1643032 

10.8627805 

4.9048681 

.008474576 

119 

14161 

1685159 

10.9087121 

4.9186847 

.008403361 

120 

14400 

1728000 

10.9544512 

4.9324242 

.008333333 

121 

14641 

1771561 

11.0000000 

4.9460874 

.008264463 

122 

14884 

1815848 

11.0453610 

4.9596757 

.008196721 

123 

15129 

1860867 

11.0905365 

4.9731898 

.008130081 

124 

15376 

1906624 

11.1355287 

4.9866310 

.008064516 

10 


Practical  Arithmetic 


Part  1 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

125 

15625 

1953125 

11.1803399 

5.0000000 

.008000000 

126 

15876 

2000376 

11.2249722 

5.0132979 

.007936508 

127 

16129 

2048383 

11.2694277 

5.0265257 

.007874016 

128 

16384 

2097152 

11.3137085 

5.0390842 

.007812500 

129 

16641 

2146689 

11.3578167 

5.0527743 

.007751938 

130 

16900 

2197000 

11.4017543 

5.0657970 

.007692308 

131 

17161 

2248091 

11.4455231 

5.0787531 

.007633588 

132 

17424 

2299968 

11.4891253 

5.0910434 

.007575758 

133 

17689 

2352637 

11.5325626 

5.1044687 

.007518797 

134 

17956 

2406104 

11.5758369 

5.1172299 

.007462687 

135 

18225 

2460375 

11.6189500 

5.1299278 

.007407407 

136 

18496 

2515456 

11.6619038 

5.1425632 

.007352941 

137 

18769 

2571353 

11.7046999 

5.1551367 

.007299270 

138 

19044 

2028072 

11.7473401 

5.1676493 

.007246377 

139 

19321 

2085619 

11.7898261 

5.1801015 

.007194245 

140 

19600 

2744000 

11.8321596 

5.1924941 

.007142857 

141 

19881 

2803221 

11.8743421 

5.2048279- 

.007092199 

142 

20164 

28G3288 

11.9163753 

5.2171034 

.007042254 

143 

20449 

2924207 

11.9582607 

5.2293215 

.006993007 

144 

20736 

2985984 

12.0000000 

5.2414828 

.006944444 

145 

21025 

3048625 

12.0415946 

5.2535879 

.006896552 

146 

21316 

3112136 

12.0830460 

5.2656374 

.006849315 

147 

21609 

3176523 

12.1^43557 

5.2776321 

.006802721 

148 

21904 

3241792 

12.1655251 

5.2895725 

.006756757 

149 

22201 

3307949 

12.2065556 

5.3014592 

.006711409 

150 

22500 

3375000 

12.2474487 

5.3132928 

.006666667 

151 

22801 

3442951 

12.2882057 

5.3250740 

.006622517 

152 

23104 

3511808 

12.3288280 

5.3368033 

.006578947 

153 

23409 

3581577 

12.3693169 

5.3484812 

.006535948 

154 

23716 

3652264 

12.4096736 

5.3601084 

.006493506 

155 

24025 

3723875 

12.4498996 

5.3716854 

.006451613 

156 

24336 

3796410 

12.4899960 

5.3832126 

.006410256 

157 

24649 

3869893 

12.5299641 

5.3946907 

.006369427 

158 

24964 

3944312 

12.5698051 

5.4061202 

.006329114 

159 

25281 

4019679 

12.6095202 

5.4175015 

.006289308 

160 

25600 

4096000 

12. 649110a 

5.4288352 

.006250000 

161 

25921 

4173281 

12.6885775 

5.4401218 

.006211180 

162 

26244 

4251528 

12.7279221 

5.4513618 

.006172840 

163 

26509 

4330747 

12.7671453 

5.4625556 

.006134969 

164 

26896 

4410944 

12.8062485 

5.4737037 

.006097561 

165 

27225 

4492125 

12.8452326 

5.4848066 

.006060606 

166 

27556 

4574296 

12.8840987 

5.4958647 

.006024096 

167 

27889 

4657463 

12.9228480 

5.5068784 

.005988024 

168 

28224 

4741632 

12.9614814 

5.5178484 

.005952381 

169 

28561 

4826809 

13.0000000 

5.5287748 

.005917160 

170 

28900 

4913000 

13.0384048 

5 . 5396583 

.005882353 

171 

29241 

5000211 

13.0766968 

5.5504991 

.005847953 

172 

29584 

5088448 

13.1148770 

5.5612978 

.005813953 

173 

29929 

5177717 

13.1529464 

5.5720546 

.005780347 

174 

30276 

5208024 

13.1909060 

5.5827702 

.005747126 

175 

30625 

5359375 

13.2287566 

5.5934447 

.005714286 

176 

30976 

5451776 

13.2664992 

5.6040787 

.005681818 

177 

31329 

5545233 

13.3041347 

5.6146724 

.005649718 

178 

31684 

5639752 

13.3416641 

5.6252263 

.005617978 

179 

32041 

5735339 

13.3790882 

5.6357408 

.005586592 

180 

32400 

5832000 

13.4164079 

5.6462162 

.005555556 

181 

32761 

5929741 

13.4536240 

5.6566528 

.005524862 

182 

33124 

6028568 

13.4907376 

5.6670511 

.005494505 

183 

33489 

6128487 

13.5277493 

5.6774114 

.005464481 

184 

33856 

6229504 

13.5646600 

5.6877340 

.005434783 

185 

34225 

6331625 

13.6014705 

5.6980192 

.005405405 

186 

34596 

6434856 

13.6381817 

5.7082675 

.005376344 

Squares,  Cubes,  Square  Roots,  Cube  Roots  and  Reciprocals     11 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

187 

34969 

6539203 

13.6747943 

5.7184791 

.005347594 

188 

35344 

6644672 

13.7113092 

5.7286543 

.005319149 

189 

35721 

6751269 

13.7477271 

5.7387936 

.005291005. 

190 

36100 

6859000 

13.7840488 

5.7488971 

.005263158 

191 

36481 

6967871 

13.8202750 

5.7589652 

.005235602 

192 

36864 

7077888 

13.8564065 

5.7689982 

.005208333 

193 

37249 

7189057 

13.8924440 

5.7789966 

.005181347 

194 

37636 

7301384 

13.9283883 

5.7889604 

.005154639 

195 

38025 

7414875 

13.9642400 

5.7988900 

.005128205 

196 

38416 

7529536 

14.0000000 

5.8087857 

.005102041 

197 

38809 

7645373 

14.0356688 

5.8186479 

.005076142 

198 

39204 

7762392 

14.0712473 

5.8284767 

. 005050505 

199 

39601 

7880599 

14.1067360 

5.8382725 

.005025126 

200 

40000 

8000000 

14.1421356 

5.8480355 

.005000000 

201 

40401 

8120601 

14.1774469 

5.8577660 

.004975124 

202 

40804 

8242408 

14.2126704 

5.8674643 

.004950495 

203 

41209 

8365427 

14.2478068 

5.8771307 

.004926108 

204 

41616 

8489664 

14.2828569 

5.8867653 

.004901961 

205 

42025 

8615125 

14.3178211 

5.8963685 

.004878049 

20G 

42436 

8741816 

14.3527001 

5.9059406 

.004854369 

207 

42849 

8869743 

14.3874946 

5.9154817 

.004830918 

208 

43264 

8998912 

14.4222051 

5.9249921 

.004807692 

209 

43681 

9129329 

14.4568323 

5.9344721 

.004784689 

210 

44100 

9261000 

14.4913767 

5.9439220 

.004761905 

211 

44521 

9393931 

14.5258390 

5.9533418 

.004739336 

212 

44944 

9528128 

14.5602198 

5.9627320 

.004716981 

213 

45369 

9663597 

14.5945195 

5.9720926 

.004694836 

214 

45796 

9800344 

14.6287388 

5.9814240 

.004672897 

215 

46225 

9938375 

14.6628783 

5.9907264 

.004651163 

216 

46656 

10077696 

14.6969385 

6.0000000 

.004629630 

217 

47089 

10218313 

14.7309199 

6.0092450 

.004608295 

218 

47524 

10360232 

14.7648231 

6.0184617 

.004587156 

219 

47961 

^0503459 

14.7986486 

6.0276502 

.004566210 

220 

48400 

10648000 

14.8323970 

6.0368107 

.004545455 

221 

48841 

10793861 

14.8660687 

6.0459435 

.004524887 

222 

49284 

10941048 

14.8996644 

6.0550489 

.004504505 

223 

49729 

11089567 

14.9331845 

6.0641270 

.004484305 

224 

50176 

11239424 

14.9666295 

6.0731779 

.004464286 

225 

50625 

11390625 

15.0000000 

6.0822020 

.004444444 

226 

51076 

11543176 

15.0332964 

6.0911994 

.004424779 

227 

51529 

11697083 

15.0665192 

6.1001702 

.004405286 

228 

51984 

11852352 

15.0996689 

6.1091147 

.004385965 

229 

52441 

12008989 

15.1327460 

6.1180332 

.004366812 

230 

52900 

12167000 

15.1857509 

6.1269257 

.004347826 

231 

53361 

12326391 

15.1986842 

6.1357924 

.004329004 

232 

53824 

12487168 

15.2315462 

6.1446337 

.004310345 

233 

54289 

12649337 

15.2643375 

6.1534495 

.004291845 

234 

54756 

12812904 

15.2970585 

6.1622401 

.004273504 

235 

55225 

12977875 

15.3297097 

6.1710058 

.004255319 

236 

55696 

13144256 

15.3622915 

6.1797466 

.004237288 

237 

56169 

13312053 

15.3948043 

6 . 1884628 

.004219409 

238 

56644 

13481272 

.15.4272486 

6.1971544 

.004201681 

239 

57121 

13651919 

15.4596248 

6.2058218 

.004184100 

240 

57600 

13824000 

15.4919334 

6.2144650 

.004166667 

241 

58081 

13997521 

15.5241747 

6 . 2230843 

: 004149378 

242 

58564 

14172488 

15.5563492 

6.2316797 

.004132231 

243 

59049 

14348907 

15.5884573 

6.2402515 

.004115226 

244 

59536 

14526784 

15.6204994 

6.2487998 

.004098361 

245 

60025 

14706125 

15.6524758 

6.2573248 

.004081633 

246 

60516 

14886936 

15.6843871 

6.2658266 

.004065041 

247 

61009 

15069223 

15.7162336 

6.2743054 

.004048583 

248 

61504 

15252992 

15.7480157 

6.2827613 

.004032258 

12 


Practical  Arithmetic 


Part  1 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

249 

62001 

15438249 

15.7797338 

6.2911946 

.004016064 

250 

62500 

15625000 

15.8113883" 

6.2990053 

.004000000 

251 

63001 

15813251 

15.8429795 

6 . 3079935 

. 003984064 

252 

63504 

16003008 

15. -8745079 

6.3163596 

.003908254 

253 

64009 

16194277 

15.9059737 

6.3247035 

.003952569 

254 

64516 

16387064 

15.9373775 

6.3330256 

.003937008 

255 

65025 

16581375 

15.9687194 

6.3413257 

.003921569 

256 

65536 

16777216 

16.0000000 

6.3496042 

.003906250 

257 

6G049 

16974593 

16.0312195 

6.3578611 

.003891051 

258 

63531 

17173512 

16.0623784 

6 . 3600908 

.003875909 

259 

67081 

17373979 

16.0934769 

6.3743111 

.003861004 

260 

67600 

17576000 

16.1245155 

6.3825043 

.003846154 

20 1 

6S121 

17779581 

16.1554944 

6.3900705 

.003831418 

262 

68644 

17984728 

16.1864141 

6.3988279 

.003816794 

263 

69109 

18191447 

16.2172747 

6.4069585 

.003802281 

264 

69696 

18399744 

16.2480768 

6.4150687 

.003787879 

265 

70225 

18609625 

16.2788206 

6.4231583 

.003773585 

266 

70756 

18821096 

16.3095064 

6.4312276 

.003759398 

267 

71239 

19034103 

16.3401346 

6.4392767 

.003745318 

268 

71824 

19248832 

16.3707055 

6.4473057 

.003731343 

269 

72361 

19465109 

16.4012195 

6.4553148 

.003717472 

270 

72900 

19683000 

16.4316767 

6.4633041 

.003703704 

271 

73441 

19902511 

16.4620776 

6.4712736 

.003690037 

272 

73984 

20123648 

10.4924225 

6.4792236 

.003676471 

273 

74529 

20346417 

16.5227116 

6.4871541 

.003663004 

274 

75076 

20570824 

16.5529454 

6.4950653 

.003649635 

275 

75625 

20796875 

16.5831240 

6.5029572 

.003636364 

276 

76176 

21024576 

16.6132477 

6.5108300 

.003623188 

277 

76729 

21253933 

16.6433170 

6.5186839 

.003610108 

278 

77284 

21484952 

16.6733320 

6.5265189 

.003597122 

279 

77841 

21717639 

16.7032931 

6.5343351 

.003584229 

280 

78400 

21952000 

16.7332005 

6.5421326 

.003571429 

281 

78961 

22188041 

16.7630546 

6.5499116 

.003558719 

282 

79524 

22425768 

16 . 7928556 

6.5576722 

.003546099 

283 

80039 

22665187 

16.8220038 

6.5654144 

.003533569 

284 

80656 

22906304 

16.8522995 

6.5731385 

.003521127 

285 

81225 

23149125 

16.8819430 

6.5808443 

.003508772 

286 

81796 

23393056 

16.9115345 

6.5885323 

.003496503 

287 

82369 

23639903 

16.9410743 

6.5962023 

.003484321 

288 

82944 

23887872 

16.9705627 

6.6038545 

.003472222 

289 

83521 

24137569 

17.0000000 

6.6114890 

.003460208 

290 

84100 

24389000 

17.0293864 

6.6191060 

.003448276 

291 

84681 

24642171 

17.0587221 

6.6207054 

.003436426 

292 

85264 

24897088 

17.0880075 

6.6342874 

.003424658 

293 

85849 

25153757 

17.1172428 

6.6418522 

.003412909 

294 

86436 

25412184 

17.1464282 

6.6493998 

.003401301 

295 

87025 

25672375 

17.1755640 

6.6569302 

.003389831 

296 

87616 

25934336 

17.2046505 

6.0644437 

.003378378 

297 

88209 

26198073 

17.2336879 

6.6719403 

.003307003 

298 

88804 

26463592 

17.2626765 

6.6794200 

.003355705 

299 

89401 

26730899 

17.2916165 

6.6868831 

.003344482 

300 

90000 

27000000 

17.3205081 

6.6943295 

.003333333 

301 

90601 

27270901 

17.3493516 

6.7017593 

.003322259 

302 

91204 

27543608 

17.3781472 

6.7091729 

.003311258 

303 

91809 

27818127 

17.4068952 

6.7165700 

.003300330 

304 

92416 

28094464 

17.4355958 

6.7239508 

.003289474 

305 

93025 

28372625 

17.4642492 

6.7313155 

.003278089 

306 

93636 

28652016 

17.4928557 

6.7380041 

.003207974 

307 

94249 

28934443 

17.5214155 

6.7459967 

.003257329 

.'i08 

94864 

29218112 

17.5499288 

6.7533134 

.003246753 

309 

95481 

29503029 

17.5783958 

6.7606143 

. 003236246 

310 

96100 

29791000 

17.6068169 

6.7678995. 

.003225806 

Squares,  Cubes,  Square  Roots,  Cube  Roots  and  Reciprocals      13 


No. 

Squares 

Cubes 

Square 

roots 

Cube  roots 

Reciprocals 

311 

96721 

30080231 

17.6351921 

6.7751690 

.003215434 

312 

97344 

30371328 

17.6635217 

6.7824229 

.003205128 

313 

97969 

30064297 

17.6918060 

6.7896613 

.003194888 

314 

98596 

30959144 

17.7200451 

6.7908844 

.003184713 

315 

99225 

31255875 

17.7482393 

6.8040921 

.003174603 

316 

99856 

31554496 

17.7763888 

6.8112847 

.003164557 

317 

100489 

31855013 

17.8044938 

6.8184620 

.003154574 

318 

101124 

32157432 

17.8325545 

6.8256242 

.003144654 

319 

101761 

32461759 

17.8605711 

6.8327714 

.003134796 

320 

102400 

32768000 

17.8885438 

6.8399037 

.003125000 

321 

103041 

33076161 

17.9164729 

6.8470213 

.003115265 

322 

103684 

33386248 

17.9443584 

6.8541240 

.003105590 

323 

104329 

33698267 

17.9722008 

6.8612120 

.003095975 

324 

104976 

34012224 

18.0000000 

6.8682855 

.003086420 

325 

105625 

34328125 

18.0277564 

6.8753443 

.003076923 

320 

106276 

34645976 

18.0554701 

6.8823888 

.003067485 

327 

106929 

34965783 

18.0831413 

6.8894188 

.003058104 

328 

107584 

35287552 

18.1107703 

6.8964345 

.003048780 

329 

108241 

35611289 

18.1383571 

6.9034359 

.003039514 

330 

108900 

35937000 

18.1659021 

6.9104232 

.003030303 

331 

109561 

36264691 

18.1934054 

6.9173964 

.003021148 

332 

110224 

36594368 

18.2208672 

6.9243556 

.003012048 

333 

110889 

36926037 

18.2482876 

6.9313008 

.003003003 

334 

111556 

37259704 

18.2756669 

6.9382321 

.002994012 

335 

112225 

37595375 

18.3030052 

6.9451496 

.002985075 

336 

112896 

37933056 

18.3303028 

6.9520533 

.002976190 

337 

113569 

38272753 

18 . 3575598 

6.9589434 

. 002967359 

338 

114244 

38614472 

18.3847763 

6.9658198 

.002958580 

339 

114921 

38958219 

18.4119526 

6.9726826 

.002949853 

340 

115600 

39304000 

18.4390889 

6.9795321 

.002941176 

341 

116281 

39651821 

18.4661853 

6.9863681 

.002932551 

342 

116964 

40001688 

18.4932420 

6.9931906 

.002923977 

343 

117649 

40353607 

18.5202592 

7.0000000 

.002915452 

344 

118336 

40707584 

18.5472370 

7.0067962 

.002906977 

345 

119025 

41063625  . 

18.5741756 

7.0135791 

.002898551 

346 

119716 

41421736 

18.6010752 

7.0203490 

.002890173 

347 

120409 

41781923 

18.6279360 

7.0271058 

.002881844 

348 

121104 

42144192 

18.6547581 

7.0338497 

.002873563 

349 

121801 

42508549 

18.6815417 

7.0405806 

.002865330 

350 

122500 

42875000 

18.7083869 

7.0472987 

.002857143 

351 

123201 

43243551 

18.7349940 

7.0540041 

.002849003 

352 

123904 

43614208 

18.7616630 

7.0606967 

.002840909 

353 

124609 

43986977 

18.7882942 

7.0673767 

.002832801 

354 

125316 

44361864 

18.8148877 

7.0740440 

.002824859 

355 

126025 

44738875 

18.8414437 

7.0806988 

.002816901 

356 

126736 

45118016 

18.8679623 

7.0873411 

.002808989 

357 

127449 

45499293 

18.8944436 

7.0939709 

.002801120 

358 

128104 

45882712 

18.9208879 

7 . 1005885 

.002793216 

359 

128881 

46268279 

18.9472953 

7.1-071937 

.002785595 

360 

129600 

46656000 

18.9736660 

7.1137866 

.002777778 

361 

130321 

47045881 

19.0000000 

7.1203674 

.002770083 

632 

131044 

47437928 

19.0262976 

7.1269360 

.002762431 

363 

131769 

47832147 

19.0525589 

7.1334925 

.002754821 

364 

132496 

48228544 

19.0787840 

7.1400370 

.002747263 

365 

133225 

48627125 

19.1049732 

7.1465695 

.002739726 

366 

133956 

49027896 

19.1311265 

7.1530901 

.002732240 

367 

134689 

49430863 

19.1572441 

7.1595988 

.002724796 

368 

135424 

49836032 

19.1833261 

7.1660957 

.002717391 

369 

136161 

50243409 

19.2093727 

7.1725809 

.002710027 

370 

136900 

60653000 

19.2353841 

7.1790544 

.002702708 

371 

137641 

51064811 

19.2613603 

7.1855162 

.002695418 

372 

138384 

51478848 

19.2873015 

7.1919663 

.002688172 

14 


Practical  Arithmetic 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

373 

139129 

51895117 

19.3132079 

7.1984050 

.002680965 

374 

139876 

52313624 

19.3390796 

7.2048322 

.002673797 

375 

140625 

52734375 

19.3649167 

7.2112479 

.002666667 

376 

141376 

53157376 

19.3907194 

7.2176522 

.002659574 

377 

142129 

53582633 

19.4164878 

7.2240450 

002652520 

378 

142884 

54010152 

19.4422221 

7.2304268 

.002645503 

379 

143641 

54439939 

19.4679223 

7.2367972 

.002638522 

380 

144400 

54872000 

19.4935887 

7.2431565 

.002631579 

381 

145161 

55306341 

19.5192213 

7.2495045 

.002624672 

382 

145924  ' 

55742968 

19.5448203 

7.2558415 

.002617801 

383 

146689 

56181887 

19.5703858 

7.2621675 

.002610966 

384 

147456 

56623104 

19.5959179 

7.2684824 

.002604167 

385 

148225 

57066625 

19.6214169 

7.2747864 

.002597403 

386 

148996 

57512456 

19.6468827 

7.2810794 

.002590674 

387 

149769 

57960603 

19.6723156 

7.2873617 

.002583979 

388 

150544 

58411072 

19.6977156 

7.2936330 

.002577320 

389 

151321 

58863869 

19.7230829 

7.2998936 

.002570694 

390 

152100 

59319000 

19.7484177 

7.3061436 

.002564103 

391 

152881 

59776471 

19.7737199 

7.3123828 

.002557545 

392 

153664 

60236288 

19 . 7989899 

7.3186114 

.002551020 

393 

154449 

60698457 

19.8242276 

7.3248295 

.002544529 

394 

155236 

61162984 

19.8494332 

7.3310369 

.002538071 

395 

156025 

61629875 

19.8746069 

7.3372339 

.002531646 

396 

156816 

62099136 

19.8997487 

7.3434205 

.002525253 

397 

157609 

62570773 

19.9248588 

7.3495966 

.002518892 

398 

158404 

63044792 

19.9499373 

7.3557624 

.002512563 

399 

159201 

63521199 

19.9749844 

7.3619178 

.002506266 

400 

160000 

64000000 

20.0000000 

7.3680630 

.002500000 

401 

160801 

61481201 

20.0249844 

7.3741979 

.002493766 

402 

161604 

64964808 

20.0499377 

7.3803227 

.002487562 

403 

162409 

65450827 

20.0748599 

7.3864373 

.002481390 

404 

163216 

65939264 

20.0997512 

7.3925418 

.002475248 

405 

164025 

66430125 

20.1246118 

7.3986363 

.002469136 

406 

164836 

66923416 

20.1494417 

7.4047206 

.002463054 

407 

165649 

67419143 

20.1742410 

7.4107950 

.002457002 

408 

166464 

67917312 

20.1990099 

7.4168595 

.002450980 

409 

167281 

68417929 

20.2237484 

7.4229142 

.002444988 

410 

168100 

68921000 

20.2484567 

7.4289589 

.002439024 

411 

168921 

69426531 

20.2731349 

7.4349938 

.002433090 

412 

169744 

69934528 

20.2977831 

7.4410189 

.002427184 

413 

170569 

70444997 

20.3224014 

7.4470342 

.002421308 

414 

171396 

70957944 

20.3469899 

7.4530399 

.002415459 

415 

172225 

71473375 

20.3715488 

7.4590359 

.002409639 

416 

173056 

71991296 

20.3960781 

7.4650223 

.002403846 

417 

173889 

72511713 

20.4205779 

7.4709991 

.002398082 

418 

174724 

73034632 

20.4450483 

7.4769664 

.002392344 

419 

175561 

73560059 

20.4694895 

7.4829242 

.002386635 

420 

176400 

74088000 

20.4939015 

•7.4888724 

.002380952 

421 

177241 

74618461 

20.5182845 

7.4948113 

.002375297 

422 

178084 

75151448 

20.5426386 

7.5007406 

.002369668 

423 

178929 

75686967 

20 . 5669638 

7 . 5066607 

.002364066 

424 

179776 

76225024 

20.5912603 

7.5125715 

.002358491 

425 

180625 

76765625 

20.6155281 

7.5184730 

.002352941 

426 

181476 

77308776 

20.6397674 

7.5243652 

.002347418 

427 

182329 

77854483 

20.6639783 

7.5302482 

.002341920 

428 

183184 

78402752 

20.6881609 

7.5361221 

.002336449 

429 

184041 

78953589 

20.7123152 

7.5419867 

.002331002 

430 

184900 

79507000 

20.7364414 

7.5478423 

.002325581 

431 

185761 

80062991 

20.7605395 

7.5536888 

.002320186 

432 

186624 

80621568 

20.7846097 

7 . 5595263 

.002314815 

433 

187489 

81182737 

20.8086520 

7.5653548 

.002309469 

434 

188356 

81746504 

20.8326667 

7.5711743 

.002304147 

Squares,  Cubes,  Square  Roots,  Cube  Roots  and  Reciprocals      15 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

435 

189225 

82312875 

20.8566536 

7.5769849 

.002298851 

436 

190096 

82881856 

20.8806130 

7.5827865 

.002293578 

437 

190969 

83453453 

20.9045450 

7.6885793 

.002288330 

438 

191844 

84027672 

20.9284495 

7.5943633 

.002283105 

439 

192721 

84604519 

20.9523268 

7.6001385 

.002277904 

440 

193600 

85184000 

20.9761770 

7.6059049 

.002272727 

441 

194481 

85766121 

21.0000000 

7.6116626 

.002267674 

442 

195364 

86350888 

21.0237960 

7.6174116 

.002262443 

443 

196249 

86938307 

21.0475652 

7.6231519 

.002257336 

444 

197136 

87528384 

21.0713075 

7.6288837 

.002252252 

445 

198025 

88121125 

21.0950231 

7.6346067 

.002247191 

446 

198916 

88716536 

21.1187121 

7.6403213 

.002242152 

447 

199809 

89314623 

21.1423745 

7.6460272 

.002237136 

448 

200704 

89915392 

21.1660105 

7.6517247 

.002232143 

449 

201001 

90518849 

21 . 1896201 

7.6574138 

.002227171 

450 

202500 

91125000 

21.2132034 

7.6630943 

.002222222 

451 

203401 

91733851 

21.2367606 

7.6687665 

.002217295 

452 

204304 

92345408 

21.2602916 

7.6744303 

.002212389 

453 

205209 

92959677 

21 . 2837967 

7.6800857 

.002207506 

454 

206116 

93576664 

21.3072758 

7.6857328 

.002202643 

455 

207025 

94196375 

21.3307290 

7.6913717 

.002197802 

456 

207936 

94818816 

21.3541565 

7.6970023 

.002192982 

457 

208849 

95443993 

21.3775583 

7.7026246 

.002188184 

458 

209764 

96071912 

21.4009346 

7.7082388 

.002183406 

459 

210681 

96702579 

21.4242853 

7.7138448 

.002178649 

460 

211600 

97336000 

21.4476106 

7.7194426 

.002173913 

461 

212521 

97972181 

21.4709106 

7.7250325 

.002169197 

462 

213444 

98611128 

21.4941853 

7.7306141 

.002164502 

463 

214369 

99252847 

21.5174348 

7.7361877 

.002159827 

464 

215296 

99897344 

21.5406592 

7.7417532 

.002155172 

465 

216225 

100544625 

21.5638587 

7.7473109 

.002150538 

466 

217156 

101194696 

21.5870331 

7.7528606 

.002145923 

467 

218089 

101847563 

21.6101828 

7.7584023 

.002141328 

468 

219024 

102503232 

21.6333077 

7.7639.361 

.002136752 

469 

219961 

103161709 

21.6564078 

7.7694620 

.002132196 

470 

220900 

103823000 

21.6794834 

7.7749801 

.002127660 

471 

221841 

104487111 

21.7025344 

7.7804904 

.002123142 

472 

222784 

105154048 

21.7255610 

7.78.56928 

.002118644 

473 

223729 

105823817 

21.7485632 

7.7914875 

.002114165 

474 

224676 

106496424 

21.7715411 

7.7969745 

.002109705 

475 

225625 

107171875 

21.7944947 

7.8024538 

.002105263 

476 

226576 

107850176 

21.8174242 

7.8079254 

.002100840 

477 

227529 

108531333 

21.8403297 

7.8133892 

.002096436 

478 

228484 

109215352 

21.8632111 

7.8188456 

.002092050 

479 

229441 

109902239 

21.8860686 

7.8242942 

.002087683 

480 

230400 

110592000 

21.9089023 

7.8297353 

.002083333 

481 

231361 

111284641 

21.9317122 

7.8351688 

.002079002 

482 

232324 

111980168 

21.9544984 

7.8405949 

.002074689 

483 

233289 

112678587 

21.9772610 

7.8460134 

.002070393 

484 

234256 

113379904 

22.0000000 

5.8514244 

.002066116 

485 

235225 

114084125 

22.0227155 

7.8568281 

.002061856 

486 

236196 

114791256 

22.0454077 

7.8622242 

.002057613 

487 

237169 

115501303 

22.0680765 

7.8676130 

.002053388 

488 

238144 

116214272 

22.0907220 

7.8729944 

.002049180 

489 

239121 

116930169 

22.1133444 

7.8783684 

.002044990 

490 

240100 

117649000 

22.1359436 

7.8837352 

.002040816 

491 

241081 

118370771 

22.1585198 

7.8890946 

.002036660 

492 

242064 

119095488 

22.1810730 

7.8944468 

.002032520 

493 

243049 

119823157 

22 . 2036033 

7.8997917 

.002028398 

494 

244036 

120553784 
1^1287375 

22.2261108 

7.9051294 

.002024291 

495 

245025 

22 . 2485955 

7.9104599 

.002020202 

496 

246016 

122023936 

22.2710575 

7.9157832 

.002016129 

Practical  Arithmetic 


Part  1 


No. 

Squares  ' 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

497 

247009 

122763473 

22.2934968 

7.9210994 

.002012072 

498 

248004 

123505992 

22.3159136 

7.9264085 

.002008032 

499 

249001 

124251499 

22 . 3383079 

7.9317104 

.002004008 

500 

250000 

125000000 

22.3606798 

7.9370053 

.002000000 

501 

251001 

125751501 

22.3830293 

7.9422931 

.001996008 

502 

252004 

126506008 

22.4053565 

7.9475739 

.001992032 

503 

253009 

127263527 

22.4276615 

7.9528477 

.001988072 

504 

254016 

128024064 

22.4499443 

7.9581144 

.001984127 

505 

255025 

128787625 

22.4722051 

7.9633743 

.001980198 

506 

256036 

129554216 

22.4944438 

7.9686271 

.001976285 

507 

257049 

130323843 

22.5166605 

7.9738731 

.001972387 

508 

258064 

131096512 

22.5388553 

7.9791122 

.001968504 

509 

259081 

131872229 

22.5610283 

7.9843444 

.001964637 

510 

260100 

132651000 

22.5831796 

7.9895697 

.001960784 

511 

261121 

133432831 

22.6053091 

7.9947883 

.001956947 

512 

262144 

134217728 

22.6274170 

8.0000000 

.001953125 

513 

263109 

135005697 

22.6495033 

8.0052049 

.001949318 

514 

264196 

135796744 

22.6715681 

8.0104032 

.001945525 

515 

265225 

136590875 

22.6936114 

8.0155946 

.001941748 

516 

266256 

137388096 

22.7156334 

8.0207794 

.001937984 

517 

267289 

138188413 

22.7376340 

8.0259574 

.001934236 

518 

268324 

138991832 

22.7596134 

8.0311287 

.001930502 

519 

269361 

139798359 

22.7815715 

8.0362935 

.001926782 

520 

270400 

140608000 

22.8035085 

8.0414515 

.001923077 

521 

271441 

141420761 

22.8254244 

8.0466030 

.001919386 

522 

272484 

142236648 

22.8473193 

8.0517479 

.001915709 

523 

273529 

143055667 

22.8691933 

8.0568862 

.001912046 

524 

274576 

143877824 

22.8910463 

8.0620180 

.001908397 

525 

275625 

144703125 

22.9128785 

8.0671432 

.001904762 

526 

276676 

145531576 

22.9346899 

8.0722620 

.001901141 

527 

277729 

146363183 

22.9564806 

8.0773743 

.001897533 

528 

278784 

147197952 

22.9782506 

8.0824800 

.001893939 

529 

279841 

148035889 

23.0000000 

8.0875794 

.001890359 

530 

280900 

148877000 

23.0217289 

8.0926723 

.001886792 

531 

281961 

149721291 

23.0434372 

8.0977589 

.001883239 

532 

283024 

150568768 

23.0651252 

8 . 1028390 

.001879699 

533 

284089 

151419437 

23.0867928 

8.1079128 

.001876173 

534 

285156 

152273304 

23.1084400 

8.1129803 

.001872659 

535 

286225 

153130375 

23.1300670 

8.1180414 

.001869159 

536 

287296 

153990655 

23.1516738 

8.1230962 

.001865672 

537 

•288369 

154854153 

23.1732605 

8.1281447 

.001862197 

538 

289444 

155720872 

23 . 1948270 

8.1331870 

.001858736 

539 

290521 

156590819 

23.2163735 

8.1382230 

.001855288 

540 

291600 

157464000 

23.2379001 

8.1432529 

.001851852 

541 

292681 

158340421 

23 . 2594067 

8.1482765 

.001848429 

542 

293764 

1592200S8 

23 . 2808935 

8.1532939 

.001845018 

543 

294849 

160103007 

23 . 3023604 

8.1583051 

.001841621 

544 

295936 

160989184 

23 . 3238076 

8.1633102 

.001838235 

545 

297025 

161878625 

23.3452351 

8.1683092 

.001834862 

546 

298116 

162771333 

23.3666429 

8.1733020 

.001831502 

547 

299209 

163667323 

23.3880311 

8.1782888 

.001828154 

548 

300304 

164566592 

23.4093998 

8.1832695 

.001824818 

549 

301401 

165469149 

23.4307490 

8.1882441 

.001821494 

550 

302500 

166375000 

23.4520788 

8.1932127 

.001818182 

551 

303601 

167284151. 

23 . 4733892 

8.1981753 

.001814882 

552 

304704 

168196608 

23.4946802 

8.2031319 

.001811594 

553 

305809 

169112377 

23.5159520 

8.2080825 

.001808318 

554 

306916 

170031464 

23.53-72046 

8.2130271 

.001805054 

555 

308025 

170953875 

23.5584380 

8.2179657 

.001801802 

556 

309136 

171879616 

23.5796522 

8.2228985 

.001798561 

557 

310249 

172808693 

23 . 6008474 

8.2278254 

.001795332 

558 

311364 

173741112 

23.6220236 

8.2327463 

.001792115  * 

Squares,  Cubes,  Square  Roots,  Cube  Roots  and  Reciprocals      17 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

559 

312481 

174676879 

23.6431808 

8.2376614 

.001788909 

560 

313600 

175616000 

23.6643191 

8.2425706 

.001785714 

561 

314721 

176553481 

23 . 6854386 

8.2474740 

.001782531 

562 

315844 

177504328 

23.7065392 

8.252.3715 

.001779359 

563 

316969 

178453547 

23.7276210 

8.2572633 

.001776199 

564 

31S09G 

179406144 

23 . 7486S42 

8.2621492 

.001773050 

565 

319225 

180362125 

23.7697286 

8.2670294 

.001769912 

566 

320356 

181321496 

23.7907545 

8.2719039 

.001766784 

567 

321489 

182284263 

23.8117618 

8.2767726 

.001763668 

568 

322624 

183250432 

23 . 8327506 

8.2816355 

.001760563 

569 

323761 

184220000 

23.8537209 

8.2864928- 

.001757469 

570 

324900 

185193000 

23.8746728 

8.2913444 

.001754386 

571 

326041 

186169411 

23.8956063 

8.2961903 

.001751313 

572 

327184 

187149248 

23.9165215 

8.3010304 

.001748252  : 

673 

328329 

188132517 

23.9374184 

8.3058651 

.001745201 

574 

329476 

189119224 

23.9582971 

8.3106941 

.001742160 

575 

330625 

190109375 

23.9791576 

8.3155175 

.001739130 

576 

331776 

191102976 

24.0000000 

8.3203353 

.001736111 

577 

332929 

192100033 

24.0208243 

8.3251475 

.001733102 

578 

334084 

193100552 

24.0416306 

8 . 3299542 

.001730104 

579 

335241 

194104539 

24.0624188 

8.3347553 

.001727116 

580 

336400 

195112000 

24.0831891 

8.3395509 

.001724138 

581 

337561 

196122941 

24.1039416 

8.3443410 

.001721170 

582 

338724 

197137368 

24.1246702 

8.3491256 

.001718213 

583 

339889 

198155287 

24.1453929 

8.3539047 

.001715266 

584 

341056 

199176704 

24.1660919 

8.3-586784 

.001712329 

585 

342225 

200201625 

24.1867732 

8.3634466 

.001709402 

586 

343396 

201230053 

24.20743C9 

■  8.3682095 

.001706485  i 

587 

344569 

202262003 

24.2280829 

8.3729668 

.001703578 

588 

345744 

203297472 

24.2487113 

8.3777188 

.001700680 

589 

346921 

204336409 

24.2693222 

8.3824653 

.001697793  ■ 

590 

348100 

205379000 

24.2899156 

8.3872065 

.001694915  ! 

591 

349281 

206425071 

24.3104916 

8.3919423 

.001692047  ; 

592 

350464 

207474688 

24.3310501  . 

8 . 3966729 

.001689189  [ 

593 

351649 

208527857 

24.3515913 

8.4013981 

.001686341  < 

594 

352836 

209584584 

24.3721152 

8.4061180 

.001683502 

595 

354025 

210644875 

24.3926218 

8.4108326 

.001680672  , 

596 

355216 

211708736 

24.4131112 

8.4155419 

.001677852  : 

597 

356409 

212776173 

24.4335834 

8.4202460 

.001675042  : 

598 

357604 

213847192 

24.4540385 

8.4249448 

.001672241  i 

599 

358801 

214921799 

24.4744765 

8.4296383 

.001669449  . 

600 

360000 

216000000 

24.4948974 

8.4343267 

.001666667  : 

601 

361201 

217081801 

24.5153013 

8.4390098 

.001663894  ; 

602 

362404 

218167208 

24.5356883 

8.4436877 

.001661130  ' 

603 

363609 

219256227 

24.5560583 

8.4483605 

.-001658375 

604 

364816 

220348864 

24.5764115 

8.4530281 

.001655629 

605 

366025 

221445125 

24.5967478 

8.4576906 

.001652893 

606 

367236 

222545016 

24.6170673 

8.4623479 

.001650165 

607 

368449 

223648543 

24.6373700 

8.4670001 

.001647446 

608 

369664 

224755712 

24.6576560 

8.4716471 

.001644737 

609 

370881 

225866529 

24.6779254 

8.4762892 

.001642036 

610 

372100 

226981000 

24.6981781 

8.4809261 

.001639.344 

611 

373321 

228099131 

24.7184142 

8.4855579 

.001036661 

612 

374544 

229220928 

24.7386338 

8.4901818 

.001C33987 

613 

375769 

230346397 

24.7588368 

8.4948065 

.001631321 

614 

376996 

231475544 

24.7790234 

8.4994233 

.001628664 

615 

378225 

232608375 

24.7991935 

8.5040350 

.001626016 

616 

379456 

233744896 

24.8193473 

8.5086417 

.001623377  ! 

617 

380689 

234885113 

24.8394847 

8.5132435 

.001620746  ! 

618 

381924 

236029032 

24.8596058 

8.5178403 

.001618123  • 

619 

383161 

237176659 

24.8797106 

8.5224.321 

.001615509  ; 

620 

384400 

238328000 

24.8997992 

8.5270189 

.001612903  1 

Practical  Arithmetic 


Part  1 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

621 

385641 

239483061 

24.9198716 

8.5316009 

.001610306 

622 

386884 

240641848 

24.9399278 

8.5361780 

.001807717 

623 

388129 

241804367 

24.9599679 

8.5407501 

.001605136 

624 

389376 

242970624 

24.9799920 

8.5453173 

.001602564 

625 

390625 

244140625 

25 . 0000000 

8.5498797 

.001800000 

626 

391876 

245314376 

25.0199920 

8.5544372 

.001597444 

627 

393129 

246491883 

25.0399081 

8.5589899 

.001594898 

628 

394384 

247673152 

25.0599282 

8.5635.377 

.001592357 

629 

395641 

248858189 

25.0798724 

8.5680807 

.001589825 

630 

396900 

250047000 

25.0998008 

8.5726189 

.001587302 

631 

398161 

251239591 

25.1197134 

8.5771523 

.001584788 

632 

399424 

252435968 

25.1396102 

8.5816809 

.001582278 

633 

400689 

253636137 

25.1594913 

8.5862047 

.001579779 

634 

401958 

254840104 

25.1793566 

8.5907238 

.001577287 

635 

403225 

256047875 

25 . 1992063 

8.5952380 

.001574803 

636 

404495 

257259456 

25.2190404 

8.5997476 

.001572327 

637 

405769 

258474853 

25 . 2388589 

8.6042525 

.001589859 

638 

407044 

259394072 

25.2586619 

8 . 6087526 

.001567398 

639 

408321 

250917119 

25.2784493 

8.6132480 

.001564945 

640 

409600 

262144000 

25.2982213 

8.6177388 

.001562500 

641 

410881 

263374721 

25.3179778 

8.6222248 

.001580062 

642 

412164 

254609288 

25-.  3377189 

8.6267003 

.001557632 

643 

413449 

255847707 

25.3574447 

8.6311830 

.001555210 

644 

414736 

267089984 

25.3771551 

8.6356551 

.001552795 

645 

416025 

288336125 

25.3968502 

8.6401228 

.001550388 

646 

417316 

269586136 

25.4165301 

8.8445855 

.001547988 

647 

418609 

270840023 

25.4361947 

8.6490437 

.001545595 

648 

419904 

272097792 

25.4558441 

8.6534974 

.001543210 

649 

421201 

273359449 

25.4754784 

8.6579465 

.001540832 

650 

422500 

274625000 

25.4950976 

8.6823911 

.001538462 

651 

423801 

275894451 

25.5147016 

8.6668310 

.001536098 

652 

425104 

277187808 

25.5342907 

8.6712665 

.001533742 

653 

426409 

278445077 

25 . 5538647 

8.6756974 

.001531394 

654 

427716 

279723264 

25 . 5734237 

8.6801237 

.001529052 

655 

429025 

281011375 

25 . 5929678 

8.6845456 

.001526718 

656 

430336 

282300416 

25.6124969 

8.8889630 

.001524390 

657 

431649 

283593393 

25.6320112 

8.6933759 

.001522070 

658 

432964 

284890312 

25.6515107 

8.6977843 

.001519757 

659 

434281 

286191179 

25.6709953 

8.7021882 

.001517451 

660 

435600 

287496000 

25.6904652 

8.7065877 

.001515152 

661 

436921 

288804781 

25 . 7099203 

8.7109827 

.001512859 

662 

438244 

290117528 

25 . 7293807 

8.7153734 

.001510574 

663 

439569 

291434247 

25.7487864 

8.7197596 

.001508296 

664 

440896 

292754944 

25.7681975 

8.7241414 

.001506024 

665 

442225 

294079525 

25.7875939 

8.7285187 

.001503759 

666 

443556 

295408298 

25.8069758 

8.7328918 

.001501502 

667 

444889 

296740963 

25.8263431 

8.7372804 

.001499250 

668 

446224 

298077632 

25.8456960 

8.7416246 

.001497006 

669 

447561 

299418309 

25.8650343 

8.7459846 

.001494788 

670 

448900 

300763000 

25 . 8843582 

8.750.3401 

.001492537 

671 

450241 

302111711 

25.9036677 

8.7546913 

.001490313 

672 

451584 

303464448 

25 . 9229628 

8.7590383 

.001488095 

673 

452929 

304821217 

25.9422435 

8.7633809 

.001485884 

674 

454276 

306182024 

25.9615100 

8.7677192 

.001483680 

675 

455625 

307546875 

25.9807621 

8.7720.532 

.001481481 

676 

456976 

308915778 

26.0000000 

8.776.3830 

.001479290 

677 

458329 

310288733 

26.01922.37 

8.7807084 

.001477105 

678 

459684 

311685752 

26.0384331 

8.7850296' 

.001474926 

679 

461041 

313046839 

26.0576284 

8.7893468 

.004472754 

680 

462400 

314432000 

26.0768096 

8 . 7936593 

.001470588 

681 

463761 

315821241 

26.0959767 

8.7979679 

.001488429 

682 

465124 

317214568 

26.1151297 

8.8022721 

.001466276 

Squares,  Cubes,  Square  Roots,  Cube  Roots  and  Reciprocals     19 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

683 

466489 

318611987 

26.1342687 

8.8065722 

.001464129 

684 

467856 

320013504 

26.1533937 

8.8108681 

.001461988 

685 

469225 

321419125 

26.1725047 

8.8151598 

.001459854 

686 

470596 

322828856 

26.1916017 

8.8194474 

.001457726 

687 

471969 

324242703 

26.2106848 

8.8237307 

.001455604 

688 

473344 

325660672 

26.2297541 

8.8280099 

.001453488 

689 

474721 

327082709 

26.2488095 

8.8322S50 

.001451379 

690 

47#100 

328509000 

26.2078511 

8.8365559 

.001449275 

691 

477481 

329939371 

2G . 2868789 

8.8408227 

.001447178 

692 

478864 

331373888 

26 . 3058929 

8.8450854 

.001445087 

693 

480249 

332812557 

26.3248932 

8.8493440 

.001443001 

694 

481636 

334255384 

26.3438797 

8.8535985 

.001440922 

695 

483025 

335702375 

26.3628527 

8.8578489 

.001438849 

696 

484416 

337153536 

26.3818119 

8.8620952 

.001436782 

697 

485809 

338608873 

26.4007576 

8.8663375 

.001434720 

698 

487204 

340068392 

26. 41968^96 

8.8705757 

.001432665 

699 

488601 

341532099 

26.4386081 

8.8748099 

.001430615 

700 

490000 

343000000 

26.4575131 

8.8790400 

.001428571 

701 

491401 

344472101 

26.4764046 

8.88326G1 

.001426534 

702 

492804 

345948408 

26.4952826 

8.8874882 

.001424501 

703 

494209 

347428927 

26.5141472 

8.8917063 

.001422475 

704 

495616 

348913664 

26.5329983 

8.8959204 

.001420455 

705 

497025 

350402625 

26.5518361 

8.9001304 

.001418440 

706 

498436 

351895816 

26.5706605 

8.90433C6 

.001416431 

707 

499849 

353393243 

26.5894716 

8.9085387 

.001414427 

708 

501264 

354894912 

26.6082694 

8.9127369 

.001412429 

709 

502681 

356400829 

26.6270539 

8.9169311 

.001410437 

710 

504100 

357911000 

26.6458252 

8.9211214 

.001408451 

711 

505521 

359425431 

26.6645833 

8.9253078 

.001406470 

712 

506944 

360944128 

26.6833281 

8.9294902 

.001404494 

713 

508369 

362467097 

26.7020598 

8.9336687 

.001402525 

714 

509796 

363994344 

26.7207784 

8.9378433 

.001400560 

715 

511225 

365525875 

26.7394839 

8.9420140 

.001398601 

716 

512656 

367061696 

26.7581763 

8.9461809 

.001396648 

717 

514089 

368601813 

26.7768557 

8.9503438 

.001394700 

718 

515524 

370146232 

26.7955220 

8.9545029 

.001392758 

719 

516961 

371694959 

26.8141754 

8.9586581 

.001390821 

720 

518400 

373248000 

26.8328157 

8.9628095 

.001388889 

721 

519841 

374805301 

26.8514432 

8.9669570 

.001386963 

722 

521284 

376367048 

26.8700577 

8.9711007 

.001385042 

723 

522729 

377933067 

26 . 8886593 

8.9752406 

.001383126 

724 

524176 

379503424 

26.9072481 

8.9793766 

.001381215 

725 

525625 

381078125 

26.9258240 

8.9835089 

.001379810 

726 

527076 

382657176 

26.9443872 

8.9876373 

.001377410 

727 

528529 

384240583 

26.9629375 

8.9917620 

.001375516 

728 

529984 

385828352 

26.9814751. 

8.9958829 

.001373626 

729 

531441 

387420489 

27.0000000 

9.0000000 

.001371742 

730 

532900 

389017000 

27.0185122 

9.0041134 

.001369863 

731 

5343G1 

390617891 

27.0370117 

9.0082229 

.001367989 

732 

535824 

392223168 

27.0554985 

9.0123288 

.001366120 

733 

537289 

393832837 

27.0739727 

9.0164309 

.001364256 

734 

538756 

395446904 

27.0924344 

9.0205293 

.001362398 

735 

540225 

397065375 

27.1108834 

9.0246239 

.001360544 

736 

541696 

398688256 

27.1293199 

9.0287149 

.001358696 

737 

543169 

400315553 

27.1477439 

9.0328021 

.001356852 

738 

544644 

401947272 

27.1661554 

9.0368857 

.001355014 

739 

546121 

403583419 

27.1845544 

9.0409655 

.001353180 

740 

547600 

405224000 

27.2029410 

9.0450419 

.001351351 

741 

549081 

406869021 

27.2213152 

9.0491142 

.001349528 

742 

550564 

408518488 

27.2396769 

9.0531831 

001347709 

743 

552049 

410172407 

27.2580263 

9.0572482 

001345895 

744 

553536 

411830784 

27.2763634 

9.0613098 

001344086 

Practical  Arithmetic 


Part  1 


No. 

Squares 

Cubes 

Square 
'roots 

Cube  roots 

Reciprocals 

745 

555025 

413493625 

27.2946881 
27.3130006 

9.0653677 

.001342282 

746 

556516 

415160936 

9.0694220 

.001340483 

747 

558009 

416832723 

27.3313007 

9.0734726 

.001338688 

748 

559504 

418508992 

27 . 3495887 

9.0775197 

.001336898 

749 

561001 

420189749 

27 . 3678644 

9.0815631 

.001335113 

750 

562500 

421875000 

27.3861279 

9.0856030 

.001333333 

751 

564001 

423564751 

27.4043792 

9.0896392 

.001331558 

752 

565504 

425259008 

27.4226184 

9.0936719 

, .001329787 

753 

567009 

426957777 

27.4408455 

9.0977010 

.001328021 

754 

568516 

428661064 

27.4590604 

9.1017265 

.001326260 

755 

570025 

430368875 

27.4772633 

9.1057485 

.001324503 

756 

571536 

432081216 

27.4954542 

9.10976G9 

.001322751 

757 

573049 

433798093 

27.5136330 

9.1137818 

.001321004 

758 

574564 

435519512 

27.5317998 

9.1177931 

.001319201 

759 

576081 

437245479 

27.5499546 

9.1218010 

.001317523 

760 

577600 

438976000 

27.5680975 

9.1258053 

.001315789 

■  761 

579121 

440711081 

27.5862284 

9.1298061 

.001314060 

762 

580644 

442450728 

27.6043475 

9.1338034 

.001312336 

763 

582169 

444194947 

27.6224546 

9.1377971 

.001310616 

764 

583696 

445943744 

27.6405499 

.  9.1417874 

.001308901 

765 

585225 

447697125 

27.6586334 

9.1457742 

.001307190 

766 

586756 

449455096 

27.6767050 

9.1497576 

.001305483 

767 

588289 

451217663 

27.6947648 

9.1537375 

.001303781 

768 

589824 

452984832 

27.7128129 

9.1577139 

.001302083 

769 

591361 

454756609 

27.7308492 

9.1616869 

.001300390 

770 

592900 

456533000 

27.7488739 

9.1656565 

.001298701 

771 

594441 

458314011 

27.7668808 

9.1696225 

.001297017 

772 

595984 

460099648 

27.7848880 

9.1735852 

.001295337 

773 

597529 

461889917 

27.8028775 

9.1775445 

.001293661 

774 

599076 

463684824 

27.8208555 

9.1815003 

.001291990 

775 

600625 

465484375 

27.8388218 

9.1854527 

.001290323 

776 

602176 

467288576 

27.8567766 

9.1894018 

.001288060 

777 

603729 

469097433 

27.8747197 

9.1933474 

.001287001 

778 

605284 

470910952 

27.8926514 

9.1972897 

.001285347 

779 

60684a 

472729139 

27.9105715 

9.2012286 

.001283697 

780 

608400 

474552000 

27.9284801 

9.2051641 

.001282051 

781 

609961 

476379541 

27.9463772 

9.2090962 

.001280410 

782 

611524 

478211768 

27.9642629 

9.2130250 

.001278772 

783 

613089 

480048687 

27.9821372 

9.2169505 

.001277139 

784 

614656 

481890304 

28.0000000 

9.2208726 

.001275510 

785 

616225 

483736625 

28.0178515 

9.2247914 

.001273885 

786 

617796 

485587656 

28.0356915 

9.2287068 

.001272265 

787 

619369 

487443403 

28.0535203 

9.2320189 

.001270648 

788 

620944 

489303872 

28.0713377 

9.2365277 

.001269036 

789 

622521 

491169069 

28.0891438 

9.2404333 

.001267427 

790 

624100 

493039000 

28 . 1069386 

9.2443355 

.001265823 

791 

625681 

494913671 

28.1247222 

9 . 2482344 

.001264223 

792 

627264 

496793088 

28.1424946 

9.2521300 

.001262626 

793 

628849 

498677257 

28.1602557 

9 . 2560224 

.001261034 

794 

630436 

500566184 

28.1780056 

9.2599114 

.001259446 

795 

632025 

502459875 

28.1957444 

9.2637973 

.001257862 

796 

633616 

504358336 

28.2134720 

9 . 2676798 

.001256281 

797 

635209 

506261573 

28.2311884 

9.2715592 

.001254705 

798 

636804 

508169592 

28.2488938 

9.2754352 

.001253133 

799 

638401 

510082399 

28.2665881 

9.2793081 

.001251564 

800 

640000 

512000000 

28.2842712 

9.2831777 

.001250000 

801 

641601 

513922401 

28.3019434 

9.2870440 

.001248439 

802 

643204 

515849608 

28.3196045 

9.2909072 

.001246883 

803 

644809 

517781627 

28 . 3372546 

9.2947671 

.001245330 

804 

646416 

519718464 

28.3548938 

9.2986239 

.001243781 

805 

648025 

521660125 

28.3725219 

9.3024775 

.001242236 

806 

649636 

623606616 

28.3901391 

9.3063278 

.001240685 

Squares,  Cubes,  Square  Roots,  Cube  Roots  and  Reciprocals     21 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

807 

651249 

525557943 

28.4077454 

9.3101750 

.001239157 

808 

652864 

527514112. 

28.4253408 

9.3140190 

.001237624 

809 

654481 

529475129 

28.4429253 

9.3178599 

.001236094 

810 

656100 

531441000 

28.4604989 

9.3216975 

.001234568 

811 

657721 

533411731 

28.4780617 

9.3255320 

.001233046 

812 

659344 

535387328 

28.4956137 

9.3293634 

.001231527 

813 

660969 

537367797 

28.5131549 

9.3331916 

.001230012 

814 

662596 

539353144 

28.5306852 

9.3370167 

.001228501 

815 

664225 

541343375 

28 . 54820 18 

9 . 3408386 

.001226994 

81G 

665856 

543338496 

28.5657137 

9.3446575 

.001225490 

817 

667489 

545338513 

28.5832119 

9.3484731 

.001223990 

818 

669124 

547343432 

28.0006993 

9.3522857 

.001222494 

819 

670761 

549353259 

28.6181760 

9.3560952 

.001221001 

820 

672400 

551368000 

28.6356421 

9.3599016 

.001219512 

821 

674041 

553387661 

28 . 6530976 

9.3637049 

.001218027 

822 

675684 

555412248 

28.6705424 

9.3675051 

.001216545 

823 

677329 

557441767 

28.6879766 

9.3713022 

.001215067 

824 

678976 

559476224 

28.7054002 

9.3750963 

.001213592 

825 

680625 

561515625 

28.7228132 

9.3788873 

.001212121 

826 

682276 

563559976W. 

28.7402157 

9.3826752 

.001210654 

827 

683929 

565609283 

28.7576077 

9.3864600 

.001209190 

828 

685584 

567663552 

28.7749891 

9.3902419 

.001207729 

829 

687241 

569722789 

28.7923601 

9.3940206 

.001206273 

830 

688900 

571787000 

28.8097206 

9.3977964 

.001204819 

831 

690561 

573856191 

28.8270706 

9.4015691 

.001203369 

832 

692224 

575930368 

28.8444102 

9.4053387 

.001201923 

833 

693889 

578009537 

28.8617394 

9.4091054 

.001200480 

834 

695556 

580093704 

28.8790582 

9.4128690 

.001199041 

835 

697225 

582182875 

28.8963666 

9.4160297 

.001197605 

836 

698896 

584277056 

28.9136646 

9.4203873 

.001196172 

837 

700569 

586376263 

28.9309523 

9.4241420 

.001194743 

838 

702244 

588480472 

28.9482297 

9.4278936 

.001193317 

839 

703921 

590589719 

28.9654967 

9.4316423 

,001191895 

840 

705600 

592704000 

28.9827535 

9.4353880 

.001190476 

841 

707281 

594823321 

29.0000000 

9.4291307 

.001189001 

842 

708964 

596947688 

29.0172363 

9.4428704 

.001187648 

843 

710649 

599077107 

29.0344623 

9.4466072 

.001186240 

844 

712336 

601211584 

29.0516781 

9.4503410 

.001184834 

845 

714025 

603351125 

29.0688837 

9.4540719 

.001183432 

846 

715716 

605495736 

29.0860791 

9.4577999 

.001182033 

847 

717409 

607645423 

29 . 1032644 

9.4615249 

.001180638 

848 

719104 

609800192 

29.1204396 

9.4C52470 

.001179245 

849 

720801 

611960049 

29.1376046 

9.4689661 

.001177856 

850 

722500 

614125000 

29.1547595 

9.4726824 

.001176471 

851 

724201 

616295051 

29.1719043 

9.476G957 

.001175088 

852 

725904 

618470208 

29.1890390 

9.4S01061 

.001173709 

853 

727609 

620650477 

29.2061637 

9.4838136 

.001172333 

854 

729316 

622835864 

29.2232784 

9.4875182 

.001170960 

855 

731025 

625026375 

29.2403830 

9.4912200 

.001169591 

856 

732736 

627222016 

29.2574777 

9.4949188 

.001168224 

857 

734449 

629422793 

29.2745623 

9.498G147 

.001166861 

858 

736164 

631628712 

29.2916370 

9 . 5023078 

.001105501 

859 

737881 

633839779 

29.3087018 

9.5059980 

.001164144 

860 

. 739600 

636056000 

29.3257566 

9 . 5096854 

.001162791 

861 

741321 

638277381 

29.3428015 

9.5133699 

. .001161440 

862 

743044 

640503928 

29.3598365 

9.5170515 

.001160093 

863 

744769 

642735647 

29.3768616 

9.5207303 

.001158749 

864 

746496 

644972544 

29.3938769 

9.5244063 

.001157407 

865 

748225 

647214625 

29.4108823 

9 . 5280794 

.001156069 

866 

749956 

649461896 

29.4278779 

9.5317497 

.001154734 

867 

751689 

651714363 

29.4448637 

9.5354172 

.001153403 

868 

753424 

653972032 

29.4618397 

9.5390818 

.001152074 

22 


Practical  Arithmetic 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

869 

755161 

656234909 

29.4788059 

9.5427437 

.001150748 

870 

756900 

658503000 

29.4957624 

9.5464027 

.001149425 

871 

758641 

660776311 

29.5127091 

9.5500589 

.001148106 

872 

760384 

663054848 

29.5296461 

9.5537123 

.001146789 

873 

762129 

665338617 

29.5465734 

9 . 5573630 

.OG 1145475 

874 

763876 

667627624 

29.5634910 

9.5310108 

.001144165 

875 

765325 

669921875 

29 . 5803989 

9 . 5340559 

.001142857 

876 

707376 

672221376 

29.5972972 

9.5G829S2 

.001141553 

877 

769129 

674526133 

29.6141858 

9.5719377 

.001140251 

878 

770884 

676836152 

29.6310648 

9.57.55745 

.001138952 

879 

772641 

679151439 . 

29.6479342 

9.5792085 

.001137656 

880 

774400 

681472000 

29.6647939 

9..582S397 

.001136364 

881 

776161 

683797841 

29.6816442 

9.5864682 

.001135074 

882 

777924 

686128968 

29.6984848 

9.5900939 

.001133787 

883 

779689 

688465387 

29.7153159 

9.5937169 

.001132503 

884 

781456 

690807104 

29.7321375 

9.5973373 

.001131222 

885 

783225 

693154125 

29.7489496 

9.6009548 

.001129944 

886 

784996 

695506456 

29.7657521 

9.6045696 

.001128668 

887 

786769 

697864103 

29.7825452 

9.6081817 

.001127396 

888 

788544 

700227072 

29.7993289 

9.6117911 

.001126126 

889 

790321 

702595369 

29.8161030 

9.6153977 

.001124859 

890 

792100 

704939000 

29.8328678 

9.6190017 

.001123596 

891 

793SS1 

707347971 

29.8496231 

9.6226030 

.001122334 

892 

795664 

709732288 

29.8663690 

9.6262016 

.001121076 

893 

797449 

712121957 

29.8831056 

9.6297975 

.001119821 

894 

799236 

714516984 

29.8998328 

9.6333907 

.001118568 

895 

801025 

716917375 

29.9165506 

9.6369812 

.001117318 

896 

802816 

719323156 

29.9332591 

9.6405690 

.001116071 

897 

804609 

721734273 

29.9499583 

9.6441542 

.001114827 

898 

806404 

724150792 

29.9666481 

9.6477367 

.001113586 

899 

808201 

726572699 

29.9833287 

9.6513166 

.001112347 

900 

810000 

729000000 

30.0000000 

9.6548938 

.001111111 

901 

811801 

731432701 

30.0166620 

9 . 6584684 

.001109878 

902 

813604 

733870808 

30.0333148 

9.6620403 

.001108647 

903 

815409 

736314327 

30.0499584 

9.6656096 

.001107420 

904 

817213 

738763264 

30.0665928 

9.6691762 

.001106195 

905 

819025 

741217625 

30.0832179 

9 . 6727403 

.001104972 

906 

820836 

743677416 

30.0998339 

9.6763017 

.001103753 

907 

822649 

746142643 

30.1164407 

9.6798604 

.001102536 

908 

824464 

748613312 

30.1330383 

9.6834166 

.001101322 

909 

826281 

751089429 

30.1496269 

9.6869701 

.001100110 

910 

828100 

753571000 

30.1662063 

9.6905211 

.001098901 

911 

829921 

756058031 

30.1827765 

9.6940694 

.001097695 

912 

831744 

758550528 

30.1993377 

9.6976151 

.001096491 

913 

833569 

761048497 

30.2158899 

9.7011583 

.001095290 

914 

835396 

763551944 

30.2324329 

9.7046989 

.001094092 

915 

837225 

766060875 

30.2489669 

9.7082369 

.001092895 

916 

839056 

768575296 

30.2654919 

9.7117723 

.001091703 

917 

840889 

771095213 

30.2820079 

9.7153051 

.001090513 

918 

842724 

773620632 

30.2985148 

9.7188354 

.001089325 

919 

844561 

776151559 

30.3150128 

9.7223631 

.001088139 

92J 

846400 

778688000 

30.3315018 

9.7258883 

.001086957 

921 

848241 

781229961 

30.3479818 

9.7294109 

.001085776 

922 

850084 

783777448 

30.3644529 

9.7329309 

.001084599 

923 

851929 

786330467 

30.3809151 

9.7364484 

.001083423 

924 

853776 

788889024 

30.3973683 

9.7399634 

.001082251 

925 

855625 

791453125 

30.4138127 

9.7434758 

.001081081 

926 

857476 

794022776 

30.4302481 

9.7469857 

.001079914 

927 

859329 

796597983 

30.4466747 

9.75049.30 

.001078749 

928 

861184 

799178752 

30.4630924 

9.7539979 

.001077586 

929 

863041 

801765089 

30.4795013 

9.757.5002 

.001076426 

930 

864900 

804357000 

30.4959014 

9.7610001 

.001075269 

Squares,  Cubes,  Square  Roots,  Cube  Roots  and  Reciprocals     23 


No. 

Squares 

Cubes 

Square 

roots 

Cube  .roots 

Reciprocals 

931 

866761 

806954491 

30.5122926 

9.7644974 

.001074114 

932 

868624 

809557568 

30.5286750 

9.7679922 

.001072961 

933 

870489 

812166237 

30.5450487 

9.7714845 

.001071811 

934 

872356 

814780504 

30.5614136 

9.7749743 

.001070664 

935 

874225 

817400375 

30.5777697 

9.7784616 

.001069519 

936 

876096 

820025856 

30.5941171 

9.7819466 

.001068376 

937 

877969 

822656953 

30.6104557 

9.7854288 

.001067236 

938 

879844 

825293672 

30.6267857 

9.7889087 

.001066098 

939 

881721 

827936019 

30.6431069 

9.7923861 

.001064963 

940 

883600 

830584000 

30.6594194 

9.7958611 

.001063830 

941 

885481 

833237621 

30.6757233 

9.7993336 

.001062699 

942 

887364 

835896888 

30.6920185 

9.8028036 

.001061571 

943 

889249 

838561807 

30.7083051 

9.8062711 

.001060445 

944 

891136 

841232384 

30.7245830 

9.8097302 

.001059322 

915 

893025 

843908625 

30.7408523 

9.8131989 

.001058201 

946 

894916 

846590536 

30.7571130 

9.8166591 

.001057082 

947 

89G309 

849278123 

30.7733651 

9.8201169 

.001055966 

948 

898704 

851971392 

30.7896086 

9.8235723 

.001054852 

949 

900601 

854670349 

30.8058436 

9.8270252 

.001053741 

950 

902500 

857375000 

30.8220700 

9.8304757 

.001052632 

951 

904401 

860085351 

30.8382879 

9.83392S8 

.001051525 

952 

906304 

862801408 

30.8544972 

9.83736G5 

.001050420 

953 

908209 

865523177 

30.8706981 

9.8408127 

.001049318 

954 

910116 

868250064 

30.8868904 

9.8442536 

.001048218 

955 

912025 

870983875 

30.9030743 

9.8476920 

.001047120 

956 

913936 

873722816 

30.9192497 

9.8511280 

.001046025 

957 

915849 

876467493 

30.9354166 

9.8545617 

.001044932 

958 

917764 

879217912 

30.9515751 

9.8579929 

.001043841 

959 

919681 

881974079 

30.9677251 

9.8614218 

.001042753 

960 

921600 

884736000 

30.9838668 

9.8648483 

.001041667 

961 

923521 

887503681 

31.0CCCOOO 

9.8082724 

.001040583 

962 

925444 

890277128 

31.0161248 

9.8716941 

.001039501 

963 

927369 

893056347 

31.0322413 

9.8751135 

.001038422 

964 

929296 

895841344 

31.0483494 

9.8785305 

.001037344 

965 

931225 

898632125 

31.0644491 

9.8819451 

.001036269 

966 

933156 

901428696 

31.0805405 

9.8853574 

.001035197 

967 

935089 

904231063 

31.0960236 

9.8887673 

.001034126 

968 

937024 

907039232 

31.1126984 

9.8921749 

.001033058 

969 

938961 

909853209 

31.1287648 

9.8955801 

.001031992 

970 

940900 

912673000 

31 . 1448230 

9 . 8989830 

.001030928 

971 

942841 

915498611 

31 . 1608729 

9.9023835 

.001029866 

972 

944784 

918330048 

31.1769145 

9.9057817 

.001028807 

973 

946729 

921167317 

31.1929479 

9.9091776 

.001027749 

974 

948676 

924010424 

31.2089731 

9.9125712 

.001026694 

975 

950625 

926859375 

31.2249900 

9.9159624 

.001025641 

976 

952576 

929714176 

31.2409987 

9.9193513 

.001024590 

977 

954529 

932574833 

31.2569992 

9.9227379 

.001023541 

978 

956484 

935441352 

31.2729915 

9.9261222 

.001022495 

979 

958441 

938313739 

31.2889757 

9.9295042 

.001021450 

980 

960400 

941192000 

31.3049517 

9.9328839 

.001020408 

981 

962361 

944076141 

31.3209195 

9.9362013 

.001019368 

982 

964324 

940966168 

31 . 3368792 

9.9396363 

.001018330 

983 

966289 

949862087 

31.3528308 

9.9430092 

.001017294 

984 

968256 

952763904 

31.3687743 

9.9463797 

.001016260 

985 

970225. 

955671625 

31.3847097 

9.9497479 

.001015228 

986 

972196 

958585256 

31.4006369 

9.9531138 

.001014199 

987 

974169 

961 504803 

31.4165561 

9.9564775 

.001013171 

988 

976144 

964430272 

31.4324673 

9.9598389 

.001012146 

989 

978121 

967361669 

31.4483704 

9.9631981 

.001011122 

990 

980100 

970299000 

31.4642654 

9.9665549 

.001010101 

991 

982081 

973242271 

31.4801.525 

9.9699095 

.001009082 

992 

984064 

976191488 

31.4960315 

9.9732619 

.001008065 

24 


Practical  Arithmetic 


No. 

Squares 

Cubes 

Square 
roots 

Cube  roots 

Reciprocals 

DO.i 

98()049 

979146657 

31.5119025 

9.9766120 

.001007049 

9Ji 

9:^8036 

982107784 

31.5277655 

9.9799599 

.001006036 

995 

990025 

985074875 

31.5436206 

9.9833055 

.001005025 

993 

99::01G 

988047936 

31.5594677 

9.9866488 

.001004016 

997 

994009 

991026973 

31.5753068 

9.9899900 

.001003009 

90S 

99GC04 

994011992 

31.5911380 

9.9933289 

.001002004 

9dl 

93oo01 

997002999 

31.6069613 

9.9966656 

.001001001 

lOOU 

1000000 

1000000000 

31.6227766 

10.0000000 

.001000000 

1001 

1002001 

1003003001 

31.6385840 

10.0033322 

.0009990010 

1002 

1004004 

1006012008 

31.6543836 

10.0066622 

.0009980040 

1003 

100G009 

1009027027 

31.6701752 

10.0099899 

.0009970090 

1001 

10080 IS 

1012048064 

31.6859590 

10.0133155 

.0009960159 

lOOo 

1010025 

1015075125 

31.7017349 

10.0166389 

.0009950249 

1006 

1012036 

1018108216 

31.7175030 

10.0199601 

.0009940358 

1007 

1014049 

1021147343 

31.7332633 

10.0232791 

.0009930487 

1008 

1016064 

1024192512 

31.7490157 

10.0265958 

.0009920635 

1009 

1018081 

1027243729 

31.7647603 

10.0299104 

.0009910803 

1010 

1020100 

1030301000 

31.7804972 

10.0332228 

.0009900990 

1011 

1022121 

1033364331 

31.7962262 

10.0365330 

.0009891197 

1012 

1024144 

1036433728 

31.8119474 

10.0398410 

.0009881423 

1013 

1026169 

1039509197 

31.8276609 

10.0431469 

.0009871668 

1014 

1028196 

1042590744 

31.8433666 

10.0464506 

.0009861933 

1015 

1030225 

1045678375 

31.8590646 

10.0497521 

.0009852217 

1016 

1032256 

1048772096 

31.8747549 

10.0530514 

.0009842520 

1017 

1034289 

1051871913 

31.8904374 

10.0563485 

.0009832842 

1018 

1036324 

1054977832 

31.9061123 

10.0596435 

.0009823183 

1019 

1038361 

1058089859 

31.9217794 

10.0629364 

.0009813543 

1020 

1040400 

1061208000 

31.9374388 

10.0662271 

.0009803922 

1021 

1042441 

1064332261 

31.9530906 

10.0695156 

.0009794319 

1022 

1044484 

1067462648 

31.9687347 

10.0728020 

.0009784736 

1023 

1046529 

1070599167 

31.9843712 

10.0760863 

.0009775171 

1024 

1048576 

1073741824 

32.0000000 

10.0793684 

.0009765625 

1025 

1050625 

1076890625 

32.0156212 

10.0826484 

.0009756098 

1026 

1052676 

1080045576 

32.0312348 

10.0859262 

.0009746589 

1027 

1054729 

1083206683 

32.0468407 

10.0892019 

.0009737098 

1028 

1056784 

1086373952 

32.0624391 

10.0924755 

.0009727626 

1029 

1058841 

1089547389 

32.0780298 

10.0957469 

.0009718173 

1030 

1060900 

1092727000 

32.0936131 

10.0990163 

.0009708738 

1031 

1062961 

1095912791 

32.1091887 

10.1022835 

.0009699321 

1032 

1065024 

1099104768 

32.1247568 

10.1055487 

.0009689922 

1033 

1067089 

1102302937 

32.1403173 

10.1088117 

.0009680542 

1034 

1069156 

1105507304 

32.1558704 

10.1120726 

.0009671180 

1035 

1071225 

1108717875 

32.1714159 

10.1153314 

.0009661836 

1036 

1073296 

1111934656 

32.1869539 

10.1185882 

.0009652510 

1037 

1075369 

1115157653 

32.2024844 

10.1218428 

.0009643202 

1038 

1077444 

1118386872 

32.2180074 

10 . 1250953 

.0009633911 

1039 

1079521 

1121622319 

32.2335229 

10.1283457 

.0009624639 

1040 

1081600 

1124864000 

32.2490310 

10.1315941 

.0009615385 

1041 

1083681 

1128111921 

32.2645316 

10.1348403 

.0009606148 

1042 

1085764 

1131366088 

32 . 2800248 

10.1380845 

.0009596929 

1043 

1087849 

1134626507 

32.2955105 

10.1413266 

.0009587738 

1044 

1089936 

1137893184 

32.3109888 

10.1445667 

.0009578544 

1045 

1092025 

1141166125 

32 . 3264598 

10.1478047 

.0009569378 

1046 

1094116 

1144445336 

32.3419233 

10.1510406 

.0009560229 

1047 

1096209 

1147730823 

32 . 3573794 

10.1542744 

.0009551098 

1048 

1098304 

1151022592 

32.3728281 

10.15750G2 

.0009541985 

1049 

1100401 

1154320649 

32.3882695 

10.1507359 

.0009532888 

1050 

1102500 

1157625000 

32.4037035 

10.1639636 

.0009523810 

1051 

1104601 

1160935651 

32.4191301 

10.1671893 

.0009514748 

1052 

1106704 

1 164252608 

32.4345495 

10.1704129 

.0009505703 

1053 

1108809 

1167575877 

32.4499615 

10.1736344 

.0009496676 

1054 

1110916 

1170905464 

32.4653662 

10.1768539 

.0009487666 

Measures  of  Length 


2.  WEIGHTS    AND    MEASURES 

Measures  of  Length 

12  inches  =  i  foot 

3  feet  =  I  yard       =         36  inches 

5}-i  yards  =  i  rod         =      198  inches  =       i6J'^  feet 

40  rods  =  I  furlong  =    7  920  inches  =     660     feet  =220  yards 

8  furlongs  =  i  mile       =  63  360  inches  =  5  280     feet  =  i  760  yards  = 

I  yard  =  0.0005682  of  a  mile 

Gunter's  Chain 

7.92  inches  =  i  link 
100       links     =  I  chain  =  4  rods  =  66  feet 
80       chains  =  i  mile 


320  rods 


Ropes 

AND  Cables 

6  feet  =  I  fathom    1 20  fathoms  =  i  cat)le's  length 

Table  Showmg  Inches  Expressed  in  Decimals  of  a  Foot 

In 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

0 

Foot 

.0833 

.1667 

.2500 

.3333 

.4167 

.5000 

.5833 

.6667 

.7500 

.8333 

.9167 

1-32 

.0026 

.0859 

.1693 

.2526 

.3359 

.4193 

.5026 

.5859 

.6693 

.7526 

.8359 

.9193 

1-16  .0052 

.0885 

.1719 

.2552 

.3385 

.4219 

.5052 

.5885 

.6719 

.7552 

.8385 

.9219 

3-32 

.0078 

.0911 

.1745 

.2578 

.3411 

.4245 

.5078 

.5911 

.6745 

.7578 

.8411 

.9245 

1-8 

.0101 

.0938 

.1771 

.2604 

3438 

.4271 

.5104 

.5938 

.6771 

.7604 

.8438 

.9271 

5-32 

.0130 

.0964 

.1797 

.2630 

.3464 

.4297 

.5130 

.5964 

.6797 

.7630 

.8464 

.9207 

3-16 

.0156 

.0990 

.1823 

.2656 

.3490 

.4323 

.5156 

.5990 

.6823 

.7656 

.8490 

.9323 

7-32 

.0182 

.1016 

.1849 

.2682 

.3516 

.4349 

.5182 

.6016 

.6849 

.7682 

.8516 

.9349 

1-4 

.0208 

.1042 

.1875 

.2708 

.3542 

.4375 

.5208 

.6042 

.6875 

.7708 

.8542 

.9375 

9-32 

.0234 

.1068 

.1901 

.2734 

.3568 

.4401 

.5234 

.6068 

.6901 

.7734 

.8568 

.9401 

5-16 

.0260 

.1094 

.1927 

.2760 

.3594 

.4427 

.5260 

.6094 

.6927 

.7700 

.8594 

.9427 

11-32 

.0286 

.1120 

.1953 

.2786 

.3620 

.4453 

.5286 

.6120 

.0953 

.7786 

.8620 

.9453 

3-8 

.0313 

.1146  .1979 

.2813 

.3646 

.4479 

.5313 

.6146 

.6979 

.7813 

.8646 

.9479 

13-32 

.0339 

.1172 

.2005 

.2839 

.3672 

.4505 

.5339 

.6172 

.7005 

.7839 

.8672 

.9505 

7-16 

.0305 

.1198 

.2031 

.2865 

.3698 

.4531 

.5365 

.6198 

.7031 

.7865 

.8698 

.9531 

15-32 

.0391 

.1224 

.2057 

.2891 

.3724 

.4557 

.5391 

.6224 

.7057 

.7891 

.8724 

.9557 

1-2 

.0417 

.1250 

.2083 

.2917 

.3750 

.4583 

.5417 

.6250 

.7083 

.7917 

.8750 

.9583 

17-32 

.0443 

.1276 

.2109 

.2943 

.3776 

.4609 

.5443 

.6276 

.7109 

.7943 

.8776 

.9609 

9-16 

.0469 

.1302 

.2135 

.2969 

.3802 

.4635 

.5469 

.6302 

.7135 

.7969 

.8802 

.9635 

19-32 

.0495 

.1328 

.2161 

.2995 

.3828 

.4661 

.5495 

.6328 

.7161 

.7995 

.8828 

.9661 

5-8 

.0521 

.1354 

.2188 

.3021 

.3854 

.4688 

.5521 

.6354 

.7188 

.8021 

.8854 

.9688 

21-32 

.0547 

.1380 

.2214 

.3047 

.3880 

.4714 

.5547 

.6380 

.7214 

.8047 

.8880 

.9714 

11-16 

.0573 

.1406 

.2240 

.3073 

.3906 

.4740 

.5573 

.6406 

.7240 

.8073 

.8906 

.9740 

23-32 

.0599 

.1432 

.2266 

.3099 

.3932 

.4766 

.5599 

.6432 

.7266 

.8099 

.8932 

.9766 

3-4 

.0625 

.1458 

.2292 

.3125 

.3958 

.4792 

.5625 

„0458 

.7292 

.8125 

.8958 

.9792 

25-32 

.0651 

.1484 

.2318 

.3151 

.3984 

.4818 

.6651 

.6481 

.7318 

.8151 

.8984- 

.9818 

n-16 

.0677 

.1510 

.2344 

.3177 

.4010 

.4844 

.5677 

.6510 

.7344 

.8177 

.9010 

.9844 

27-32 

.0703 

.1536 

.2370 

.3203 

.4036 

.4870 

.5703 

.6536 

.7370 

.8203 

.9036 

.9870 

7-8 

.0729 

.1563 

.2396 

.3229 

.4063 

.4896 

.5729 

.6563 

.7396 

.8229 

.9063 

.9898 

29-32 

.0755 

.1589 

.2422 

.3255 

.-'<0S9 

.4922 

.5755 

.6589 

.7422 

.8255 

.9089 

.9922 

15-lP 

.0781 

.1615 

.2448 

.3281 

.4115 

.4948 

.5781 

.6615 

.74-48 

.8281 

.9115 

.9948 

31-32 

.0807 

.1641 

.2474 

.3307 

.4141 

.4974 

.5807 

.6641 

.7474 

.8307 

.9141 

.9974 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

26 


Weights  and  Measures 
Decimal  Equivalents  for  Fractions  of  an  Inch 


H2 

H4 

Decimals 

Frac- 
tions 

H2 

H4 

Decimals 

Frac- 
tions 

1 

0.015625 

33 

0.515625 

i 

2 

0.03125 

17 

34 

0.53125 

3 

0.046875 

35 

0.546875 

2 

4 

0.0625 

Me 

18 

36 

0.5625 

Me 

5 

0.078125 

37 

0.578125 

3 

6 

0.09375 

19 

38 

0.59375 

7 

0.109375 

39 

0.609375 

4 

8 

0.125 

H 

20 

40 

0.625 

H 

9 

0.140625 

41 

0.640625 

5 

10 

0.15625 

21 

42 

0.65625 

11 

0.171875 

43 

0.671875 

6 

12 

0.1875  . 

Me 

22 

44 

0.6875 

iMe 

13 

0.203125 

45 

0.703125 

7 

14 

0.21875 

23 

46 

0.71875 

15 

0.234375 

47 

0.734375 

8 

16 

0.25 

H 

24 

48 

0.75 

% 

17 

0.265625 

40 

0.765625 

9 

18 

0.28125 

.  .* 

25 

50 

0.78125 

19 

0.296875 

51 

0.796875 

io 

20 

0.3125 

Me 

26 

52 

0.8125 

iMe 

21 

0.328125 

53 

0.828125 

ii 

22 

0.34375 

27 

54 

0.84375 

23 

0.359375 

55 

0.859375 

12 

24 

0.375 

H 

28 

56 

0.875 

Ii 

25 

0.390625 

57 

0.890625 

13 

26 

0.40625 

29 

58 

0.90625 

27 

0.421875 

59 

0.921875 

14 

28 

0.4375 

Vie 

30 

60 

0.9375 

iMe 

29 

0.453125 

61 

0.953125 

ii 

30 

0.46875 

31 

62 

0.96875 

31 

0.484375 

63 

0.984375 

16 

32 

0.5 

H 

32 

64 

1. 

i 

Nautical  Measures 

A  nautical  or  sea-mile  is  the  length  of  a  minute  of  longitude  of  the  earth  at 
the  equator  at  the  level  of  the  sea.  It  is  assumed  that  6086.07  f t  =  1. 152664 
statute  or  land-miles  by  the  United  States  Coast  Survey. 

3  nautical  miles  =  i  league 


Miscellaneous  Measures 


I  palm  =  3  inches 
I  hai^d  =  4  inches 


I  span 
I  meter 


»  9  inches 
=  3.2809  feet 


Surface,  Volume  and  Cubic  Measures  2? 

Measures  of  Surface 

144  square  inches  =  i  square  foot 

9  square  feet       =  i  square  yard  =  i  296  square  inches 
100  square  feet       =  i  square  (architects'  measure) 

Land  MEASubE 

30H  square  yards  =  i  square  rod 

40  square  rods  =  i  square  rood  =  i  210  square  yards 

4  square  roods     |  =  i  acre  =  4  840  square  yards 

10  square  chains    \  =160  square  rods 

(640  acres  =  i  square  mile  =  3  097  600  square  yards  =  ) 

1 102  400  square  rods  =  2  560  square  roods  ) 

208.71  feet  square  =  i  acre  =  43S6o  square  feet 

A  SECTION  of  land  is  a  square  mile,  and  a  quarter-section  is  160  acres 

Measures  of  Volume 

1  gallon,  liquid  measure  =  231  cubic  inches,  and  contains  8.339  avoirdupois 
pounds  of  distilled  water  at  39.8°  F.,  or  58  333  grains 

I  cubic  foot  contains  7.48  liquid  gallons,  or  6.428  dry  gallons 

I  gallon,  dry  measure  =  268.8  cubic  inches 

I  bushel  (Winchester)  contains  2150.42  cubic  inches,  or  77.627  pounds  dis- 
tilled water  at  39.8°  F. 

A  heaped  bushel  contains  2747.715  cubic  inches 

Dry  Measure 

2  pints     =  I  quart    =  67.2  cubic  inches 

4  quarts  =  i  gallon  =    8  pints  =  268.8  cubic  inches 

2  gallons  =  I  peck     =16  pints  =    8  quarts  =  537.6  cubic  inches 
4  pecks    =  I  bushel  =  64  pints  =32  quarts  =  8  gallons 

=  2150.42  cubic  inches 
I  cord  of  wood  =128  cubic  feet 

Liquid  Measure 

4  gills       =  I  pint        =16  fluid  ounces 

2  pints     =  I  quart     -    8  gills  =32  fluid  ounces 

4  quarts  =  i  gallon     =32  gills  =  8  pints  =128  fluid  ounces 

In  the  United  States  and  Great  Britain  i  barrel  of  wine  or  brandy  =  311^^ 
gallons,  and  contains  4.21 1  cubic  feet. 

A  hogshead  is  63  gallons,  but  this  term  is  often  applied  to  casks  of  various 
capacities. 

Cubic  Measure 

1728  cubic  inches  =  i  cubic  foot 
27  cubic  feet      =  i  cubic  yard 

In  measuring  wood,  a  pile  of  wood  cut  4  feet  long,  piled  4  feet  high,  and  8  feet 
on  the  ground,  making  128  cubic  feet,  is  called  a  cord. 

16  cubic  feet  make  one  cord-foot. 

A  perch  of  stone  is  nominally  i6J'^  feet  long,  i  foot  high  and  iH  feet  thick, 
and  contains  24^  cubic  feet. 


2^  Weights  and  Measures  Part  1 

A  i:>erch  of  stone  is,  however,  often  computed  differently  in  different  localities; 
thus,  in  most  if  not  all  of  the  States  and  Territories  west  of  the  Mississippi, 
stone-masons  figure  rubble  by  the  perch  of  iQVz  cubic  feet.  In  Philadelphia, 
2  2  cubic  feet  are  called  a  perch.  In  Chicago,  stone  is  measured  by  the  cord  of 
lOo  cubic  feet. 

A  TON  of  shipping  is  42  cubic  feet  in  Great  Britain  and  40  cubic  feet  in  the 
United  States. 

Fluid  Measure 

60  minims  =  i  fluid  drachm 

8  fluid  drachms  =  i  ounce 
16  ounces  =  i  pint 

8  pints  =  I  gallon 

Miscellaneous  Measures 

Butt  of  Sherry    =  108  gallons  Puncheon  of  Brandy  =  no  to  120  gallons 

Pipe  of  Port        =115  gallons  Puncheon  of  Rum       =  100  to  no  gallons 

Butt  of  Malaga  =  105  gallons  Hogshead  of  Brandy  =    55  to    60  gallons 

Punckeon  of  Scotch  Whiskey,  Hogshead  of  Claret     =    46  gallons 
=  no  to  130  gallons 

Measures  of  Weight 

The  standard  avoirdupois  pound  is  the  weight  of  27.7015  cubic  inches  of 
distilled  water  weighed  in  air  at  39-^3°  F.,  with  the  barometer  at  30  inches. 
It  contains  7  000  grains.     One  pound  avoirdupois  =  1.2 153  pounds  troy. 

Avoirdupois,  or  Ordinary  Commercial  Weight 

I  drachm  =  27.343  grains 

16  drachms  =  i  ounce  (oz) 

16  ounces  =  i  pound  (lb) 

100  pounds  =  I  hundredweight    (cwt) 

20  hundredweight  =  i  ton 

In  collecting  duties  upon  foreign  goods  at  the  United  States  custom-houses, 
and  also  in  freighting  coal  and  selling  it  by  wholesale, 

28  pounds  =  I  quarter 

4  quarters,  or  112  pounds  =  i  hundredweight 
20  hundredweight  =  i  long  ton  =  2  240  pounds 

A  stone  =14  pounds 

A  quintal  =100  pounds 

The  following  measures  are  sanctioned  by  custom  or  law:  i  bushel  =  1.244 
cubic  feet  or  1J.4  cubic  feet,  nearly. 

32  pounds  of  oats  •    =  i  bushel 

45  pounds  of  Timothy-seed  =  i  bushel 
48  pounds  of  barley  =  i  bushel 

56  pounds  of  rye  =  i  bushel 

56  pounds  of  Indian  com  =  i  bushel 
50  pounds  of  Indian  meal  =  i  bushel 
60  pounds  of  wheat  =  i  bushel 

60  pounds  of  clover-seed  =  i  bushel 
60  pounds  of  potatoes  =  i  bushel 


Troy  Weight,  etc.     Weights  of  Coins  29 

56  pounds  of  butter  =  i  firkin 

100  pounds  of  meal  or  Hour  =  i  sack 

100  pounds  of  grain  or  flour  =  i  cental 

i(X)  pounds  of  dry  fish  =  i  quintal 

100  pounds  of  nails  =  i  cask 

196  pounds  of  flour  =  i  barrel 

200  pounds  of  beef  or  pork  =  i  barrel 

80  pounds  of  lime  =  i  bushel 

Troy  Weight 

Used  in  Weighing  Gold  or  Silver 

24  grains  =  i  pennyweight  (pwt) 

20  pennyweights  =  i  ounce  (oz) 

12  ounces  =  i  pound  (lb) 

A  CARAT  of  the  jewelers,  for  precious  stones,  is,  in  the  United  States,  3.2 
grains,  but  it  varies  according  to  different  authorities.  In  London,  3.17  grains, 
in  Paris,  3.18  grains  are  divided  into  4  jewelers'  grains.  Ihe  international 
carat  is  3.168  grains  or  200  milligrams.  In  troy,  apothecaries'  and  avoirdupois- 
weights,  the  grain  is  the  same,  i  pound  troy  being  equal  to  0.82286  pound 
avoirdupois. 

Apothecaries'  Weight 

Used  in  Compounding  Medicines  and  in  Putting  Up  Medical 
Prescriptions 

20  grains  (gr)  =  i  scruple    (Q)  8  drachms  =  i  ounce  (oz) 

3  scruples      =  i  drachm  (3)  12  ounces     =  i  pound  (lb) 

Measures  of  Value 

United  States  Standard 

10  mills  =  I  cent  10  dimes    =  i  dollar 

10  cents  =  I  dime  10  doUars  =  i  eagle 

The  standard  of  gold  and  silver  is  900  parts  of  pure  metal  and  100  of  alloy 
in  I  000  parts  of  coin. 

The  fineness  expresses  the  quantity  of  pure  metal  in  i  000  parts. 

The  REMEDY  of  THE  mint  is  the  allowance  for  deviation  from  the  exact  stand- 
ard fineness  and  weight  of  coins. 

Weights  of  Coins 


Double  eagle 

=  Si6 

troy  grains 

Eagle 

=  258 

troy  grains 

Dollar  (gold) 

=    25.8 

troy  grains 

Dollar  (silver) 

=  412.5 

troy  grains 

Half-dollar 

=  192 

troy  grains 

5-cent  piece  (nickel) 

=    77.K 

5  troy  grains 

3-cent  piece  (nickel) 

=    30 

troy  grains 

Cent  (bronze) 

=    48 

troy  grains 

30  Weights  and  Measures  ^art  1 

Measures  of  Time 

60  seconds  =  i  minute  365  days  =  1  common  year 

60  minutes  =  i  hour  366  days  =  i  leap-year 

24  hours      =  I  day 
A  SOLAR  DAY  IS  measured  by  the  rotation  of  the  earth  upon  its  axis,  with  respect 
to  the  sun. 

In  ASTRONOMICAL  COMPUTATIONS  and  in  NAUTICAL  TIME  the  day  commences  at 
noon,  and  in  the  former  it  is  counted  throughout  the  24  hours. 

In  CIVIL  COMPUTATIONS  the  day  commences  at  midnight,  and  is  divided  into 
two  parts,  of  12  hours  each. 

A  SOLAR  YEAR  is  the  time  in  which  the  earth  makes  one  revolution  around  the 
sun.  Its  average  time,  called  the  mean  solar  ye.\r,  is  365  days,  5  hours, 
48  minutes  and  49.7  seconds,  or  nearly  36534  days. 

A  mean  lunar  month,  or  lunation  of  the  moon,  is  29  days,  12  hours,  44  min- 
utes, 2  seconds  and  5.24  thirds.     It  is  equal,  on  the  average,  to  29.53  days. 

The  Calendar,  Old  and  New  Style 

The  Julian  Calendar  was  established  by  Julius  Csesar,  44  B.C.,  and  by  it  one 
day  was  inserted  in  every  fourth  year.  This  was  the  same  thing  as  assuming 
that  the  length  of  the  solar  year  was  365  days  and  6  hours,  instead  of  the  .value 
given  above,  thus  introducing  an  accumulative  error  of  11  minutes  and  12  sec- 
onds every  year.  This  calendar  was  adopted  by  the  church  in  325  a. d.,  at  the 
Council  of  Nice.  In  the  year  1582  the  annual  error  of  11  minutes  and  12  seconds 
had  amounted  to  10  daj^s,  which,  by  order  of  Pope  Gregory  XIII,  was  suppressed 
in  the  calendar,  and  the  5th  of  October  reckoned  as  the  15th.  To  prevent  the 
repetition  of  this  error,  it  was  decided  to  leave  out  three  of  the  inserted  days 
every  400  years,  and  to  make  this  omission  in  the  years  which  are  not  exactly 
divisible  by  400.  Thus,  of  the  years  1700,  1800,  1900  and  2000,  all  of  which 
are  leap-years  according  to  the  JuHan  Calendar,  only  the  last  is  a  leap-year 
according  to  the  Reformed  or  Gregorian  Calendar.  This  Reformed  Calendar 
was  not  adopted  by  England  until  1752,  when  11  days  were  omitted  from  the 
calendar.  The  two  calendars  are  now  often  called  the  Old  Style  and  the  New 
Style.  The  latter  style  is  now  adopted  in  every  Christian  country  except 
Russia. 

Circular  and  Angular  Measures 

Used  for  Measuring  Angles  and  Arcs,  and  for  Determining  Lati- 
tude AND  Longitude 
60  seconds  (")  =  i  minute  (') 

60  minutes        =  i  degree  (°) 

360  degrees         =  i  circumference  (C) 

The  second  is  usually  subdivided  into  tenths  and  hundredths. 
A  minute  of  the  circumference  of  the  earth  is  a  geographical  mile. 
The  DEGREES  of  the  earth's  circumference  on  a  meridian  average  69.16  com- 
mon miles. 

The  Metric  System 

The  metric  system  is  a  system  of  weights  and  measures  based  upon  a  unit 
called  a  meter. 

The  meter  was  intended  to  be  one  ten-millionth  part  of  the  distance  from  the 
equator  to  either  pole,  measured  on  the  earth's  surface  at  the  level  of  the  sea. 


The  Metric  System  31 

The  NAMES  of  derived  metric  denominations  are  'formed  by  prefixing  to  the 
name  of  the  primary  unit  of  measure: 

Milli,  a  thousandth  Hecto,  one  hundred 

Centi,  a  hundredth  Kilo,  a  thousand 

Deci,  a  tenth  Myria,  ten  thousand 

Deca,  ten 

This  system,  first  adopted  by  France,  has  been  extensively  adopted  by  other 
countries,  and  is  much  used  in  the  sciences  and  the  arts.  It  was  legalized  in 
1 866  by  Congress  to  be  used  in  the  United  States,  and  is  already  employed  by 
the  Coast  Survey,  and,  to  some  extent,  by  the  Mint  and  the  General  Post- 
Office. 

Linear  Measures 

The  METER  is  the  primary  unit  of  lengths. 

lo  millimeters  (mm)  =  i  centimeter  (cm)  =  0.3937  inch 

10  centimeters  =  i  decimeter  (dm)  ==  3.937  inches 

10  decimeters  =  i  meter  (m)  =  39.37  inches 

10  meters  =  i  decameter  =  393.37  inches 

10  decameters  =  i  hectometer  =328  feet  i  inch 

10  hectometers  =  i  kilometer  (km)  =  0.62137  mile 

10  kilometers  =  i  myriameter  =  6.2137  miles 

The  meter  is  used  in  ordinary  measurements;  the  centimeter,  or  milli- 
meter, in  reckoning  very  small  distances;  and  the  kilometer,  for  roads  of 
great  distances. 

A  CENTIMETER  is  about  %  of  an  inch;  a  meter  is  about  3  feet  3H  inches;  a 
kilometer  is  about  200  rods,  or  ^i  of  a  mile.     (See  page  $3.) 

Measures  of  Surface 

The  square  meter  is  the  primary  unit  of  ordinary  surfaces. 
The  are,  a  square,  each  of  whose  sides  is  ten  meters,  is  the  unit  of  landl 
measures. 

TOO  square  millimeters  (mm-)  =1  square  centimeter  (cm^)  =0.155  square  inch 

100  square  centimeters  =  i  square  decimeter  =  15.5  square  inches 

100  square  decimeters  =  i  square  meter  (m^)  =  i  550  square  inches,  or  1.196 

square  yards 
100  centiares,  or  square  meters  =  i  are  (a)  =  119.6  square  yards 

100  ares  =  i  hectare  (ha)         =  2.471  acres 

A  square  meter,  or  one  centiare,  is  about  10^  square  feet,  or  iH  square 
yards,  and  a  hectare  is  about  2}^^  acres. 

Cubic  Measure 

The  CUBIC  meter,  or  stere,  is  the  primary  unit  of  a  volume. 
I  000  cubic  millimeters  (mm^)  =  i  cubic  centimeter  (cm')  =  0.061  cubic  inch 
I  000  cubic  centimeters  =  i  cubic  decimeter  (dm')  =  61.022  cubic  inches 
I  000  cubic  decimeters  =  i  cubic  meter  (m')  =  35.314  cubic  feet 

The  stere  is  the  name  given  to  the  cubic  meter  in  measuring  wood  and  timber. 
A  tenth  of  a  stere  is  a  decistere,  and  ten  steres  are  a  decastere. 
A  CUBIC  METEi^,  or  STERE,  is  about  iH  cubic  yards,  or  about  2H  cord  feet, 


32  Weights  and  Measures  Part  1 

Liquid  and  Dry  Measures 
The  LITER  is  the  primary  unit  of  measures  of  capacity,  and  is  a  cube,  each  of 
whose  edges  is  a  tenth  of  a  meter  in  length. 

The  iiiccTOLiTKR  is  the  unit  in  measuring  large  quantities  of  grain,  fruits, 
roots  and  hquids. 

ID  milliliters  (ml)   =  i  centiliter  (cl)         =  0.338  fluid  ounce 

10  centiliters  =  i  deciliter  =  0.845  liquid  gill 

10  deciliters  =  i  liter  (1)  =  1.0567  liquid  quarts 

10  liters  =  I  decahter  =  2.6417  gallons 

10  decaliters  =  i  hectoliter  (hi)  =  2  bushels,  3.35  pecks 

10  hectoliters  =  i  kiloliter  =-  28  bushels,  i\i  pecks 

A  centiliter  is  about  H  of  a  fluid  ounce;  a  liter  is  about  iHs  liquid  quarts, 
or  9io  of  a  dry  quart;  a  hectoliter  is  about  2%  bushels;  and  a  kiloliter  is 
one  cubic  meter,  or  stere. 

Weights 

The  GRAM  is  the  primary  unit  of  weights,  and  is  the  weight  in  a  vacuum  of  a 
cubic  centimeter  of  distilled  water  at  the  temperature  of  39.2°  F. 
10  milligrams  (mg)  =  i  centigram  (eg)    =        0.1543  troy  grain 
10  centigrams  =  i  decigram  (dg)     =        1.543    troy  grains 

10  decigrams  =  i  gram  (g)  =      15.432    troy  grains 

10  grams  =  i  decagram  =        0.3527  avoirdupois  ounce 

10  decagrams  =  i  hectogram  =        3.5274  avoirdupois  ounces 

10  hectograms  =  i  kilogram  (kg)    =        2.2046  avoirdupois  pounds 

10  kilograms  =  i  myriagram  =      22.046    avoirdupois  pounds 

10  myriagrams         =  i  quintal  (q)  =    220.46      avoirdupois  pounds 

10  quintals  =  i  tonneau  (t)       =  2204.6        avoirdupois  pounds 

I  kilogram  per  kilometer     =  0.67195  pound  per  i  000  feet 
I  pound  per  thousand  feet  =  1.4882  kilograms  per  kilometer 
I  kilogram  per  square  milHmeter=  1  423  pounds  per  .square  inch 
I  pound  per  square  inch  =  0.000743  kilogram  per  square  millimeter 

The  gram  is  used  in  weighing  gold,  jewels,  letters  and  small  quantities  of 
things.  The  kilogram,  or,  for  brevity,  kilo,  is  used  by  grocers;  and  the 
tonneau,  or  metric  ton,  is  used  in  finding  the  weight  of  very  heavy  articles. 

A  GRAM  is  about  15'/^  grains  troy;  the  kilo  about  2H  pounds  avoirdupois; 
and  the  metric  ton,  about  2  205  pounds. 

A  KILO  is  the  weight  of  a  liter  of  water  at  its  greatest  density;  and  the  metric 
ton,  of  a  cubic  meter  of  water. 

Metric  numbers  are  written  with  the  decimal  point  (.)  at  the  right  of  the 
figures  denoting  the  unit;  thus  the  expression,  15  meters  3  centimeters,  is 
written,  15.03  m. 

When  metric  numbers  are  expressed  by  figures,  the  part  of  the  expression  at 
the  left  of  the  decimal  point  is  read  as  the  number  of  the  unit,  and  the  part  at 
the  right,  if  any,  as  a  number  of  the  lowest  denomination  indicated,  or  as  a 
decimal  part  of  the  unit;  thus,  46.525  m  is  read  46  meters  and  525  millimeters, 
or  46  and  525  thousandths  meters. 

In  writing  and  reading  metric  numbers,  according  as  the  scale  is  10,  100  or 
I  000,  each  denomination  should  be  allowed  one,  two  or  three  orders  of  figures. 

Metric  Conversion  Table 

The  following  metric  conversion  table  has  been  compiled  by  C.  W.  Hunt, 
and  is  most  convenient  in  dealing  with  metric  weights  and  measures: 


Metric  Conversion  Table 


Millimeters  X  0.03937 

Millimeters -^  25.4 

Centimeters  X  0.3937 

Centimeters  4-  2.54 

Meters  X  39-37 

Meters  X  3.281 

Meters  X  1.094 

Kilometers  X  0.621 

Kilometers -^  1.6093 

Kilometers  X  3280.7 

Square  millimeters  X  0.0155 

Square  millimeters -1-  645.1 

Square  centimeters  X  0.155 

Square  centimeters  4-  6.451 

Square  meters  X  10.764 

Square  kilometers  X  247.1 

Hectares  X  2.471 

Cubic  centimeters  4-  16.383 

Cubic  centimeters -^  3.69 

Cubic  centimeters  -f-  29.57 

Cubic  meters  X  35-315 

Cubic  meters  X  1.308 

Cubic  meters  X  264.2 

Liters  X  61.022 

Liters  X  33-84 

Liters  X  0.2642 

Liters -^  3.78 

Liters -4-  28.316 

Hectoliters  X  3-531 

Hectoliters  X  2.84 

Hectoliters  X  0.131 

Hectoliters  X  26.42       ^ 

Grams  X  15-432 

Grams  X  981 

Grams  (water)  -i-  29.57 

Grams -j-  28.35 

Grams  per  cubic  centimeter-?-  27.7 

Joule  X  0.7373 

Kilograms  X  2.2046 

Kilograms  X  35-3 

Kilograms^  1102.3 

Kilograms  per  sq  cm  X  14.223 

Kilogrammeters  X  7-233 

Kilograms  per  meter  X  0.672 

Kilograms  per  cubic  meter  X  0.062 

Kilograms  per  cheval-vapeur  X  2.235 

Kilowatts  X  1.34 

Watts  -^  746 

Watts  X  0.7373 

Calorie  X  3.968 

Cheval-vapeur  X  0.9863 

(Centigrade  X  1.8) +  32 

Francs  X  0.193 

Gravity,  Paris 


=  inches 

=  inches 

=  inches 

=  inches 

=  inches  (Act  of  Congres.s) 

=  feet 

=  yards 

=  miles 

=  miles 

=  feet 

=  square  inches 

=  square  inches 

=  square  inches 

=  square  inches 

=  square  feet 

=  acres 

=  acres 

=  cubic  inches 

=  fluid  drachms  (U.S.  Pharmacopoeia) 

=  fluid  ounce.     (U.S.  Pharmacopoeia) 

=  cubic  feet 

=  cubic  yards 

=  gallons  (231  cubic  inches) 

:  cubic  inches.     (Act  of  Congress) 

=  fluid  ounces.   (U.  S.  Pharmacopoeia) 

=  gallons  (231  cubic  inches) 

=  gallons  (231  cubic  inches) 

=  cubic  feet 

=  cubic  feet 

=  bushels  (2  150.42  cubic  inches) 

=  cubic  yards 

=  gallons  (231  cubic  inches) 

=  grains.     (Act  of  Congress) 

=  dynes 

:  fluid  ounces 

=  ounces  avoirdupois 

=  pounds  per  cubic  inch 

=  foot-pounds 

=  pounds 

=  ounces  avoirdupois 

:  tons  (2  000  pounds) 

:  pounds  per  square  inch 

=  foot-pounds 

:  pounds  per  square  foot 

=  pounds  per  cubic  foot 

=  pounds  per  horse-pow«r 

=  horse-power 

=  honse-power 

=  foot-pounds  per  second 

=  British  thermal  units  (B.T.U.) 

=  horse-power 

=  degrees  Fahrenheit 

=  dollars 

=  980.94  centimeter  per  second 


34 


Weights  and  Measures 


Part  1 


Metric  Conversion  Tables.  This  and  the  following  table  from  Moles- 
worth's  Metrical  Tables  will  be  found  of  great  convenience  in  figuring  plans 
to  be  executed  in  Mexico  and  other  countries  using  the  metric  system. 

Feet  Converted  into  Meters 


Feet 

0 

1 

2 

3 

4 

0 
10 
20 
30 
40 

50 
60 
70 
80 
90 

0.304794 
3.35274 
6.40068 
9.44863 
12.4966 

15.5445 
18.5925 
21.6404 
24.6884 
27.7363 

0.600589 
3.65753 
6.70548 
9.75342 
12.8014 

15.8493 
18.8973 
21.9452 
24.9931 
28.0411 

0.914383 
3.96233 
7.01027 
10.0582 
13.1062 

16.1541 
19.2020 
22  2500 
25.2979 
28.3459 

1.21918 
4.26712 
7.31507 
10.3630 
13.4110 

16.4589 
19.5068 
22.5548 
25.6027 
28.6507 

3.047945 
6.095890 
9.143835 
12.19178 

15.23972 
18.28767 
21.33561 
24.38356 
27.43150 

Scripture  and  Ancient  Measures  and 

Weights 

Scripture  Long  Measures 

Inches 

Feet        Inches 

Digit 

=    0.912                  Cubit 

=  I          9.888 

Palm 

=    3.648                 Fathom 

=  7         3-552 

Span 

=  10.944 

Egyptian  Long  Measures 

Nahud  cubit  = 

I  foot  5.71  inches          Royal  cubit  = 
Grecian  Long  Measures 

=  I  foot  8.66  inches 

Feet        Inches 

Feet        Inches 

Digit 

=            0.7554               Stadium 

=     604         4.5 

Pons  (foot) 

=  I    .     0.0875                Mile 

=  4835 

Cubit 

=  I         1.5984^^ 

Jewish  Long  Measures 

Cubit 

=  1.824  feet         Mile 

=  7  296  feet 

Sabbath-day's 

journey  =  3  648  feet         Day's  journey      =33.164  miles 

Roman  Long  Measures 

Inches 

Feet        Inches 

Digit 

=    0.72575            Cubit 

I         5-406 

Uncia  (inch) 

=    0.967               Passus 

=          4        10.02 

Pes  (foot) 

=  11.604               Mille  (millarium) 

=  4842 

Roman  Weight 
Ancient  Hbbra  =  0.7094  pound 


Arabian  foot 
Babylonian  foot 
Egyptian  finger 


Miscellaneous 


Feet 

=  I -095 
=  1. 140 
=  0.06145 


Hebrew  foot 
Hebrew  cubit 
Hebrew  sacred  cubit 


Feet 
=  1. 212 
=  1.817 
=  2.002 


Metric  Conversion  Tables 


35 


Feet  Converted  into  Meters  (Continued) 


Feet 

6 

6 

7 

8 

9 

0 

1.52397    • 

1.82877 

2.13356 

2.43836 

2.74315 

10 

4.57192 

4.87671 

5.18151 

5.48630 

5.79110 

20 

7:61986 

7.92466 

8.22945 

8.53425 

8.83904 

30 

10.6678 

10.9726 

11.2774 

11.5822 

11.8870 

40 

13.7158 

14.0205 

14.3253 

14.6301 

14.9349 

50 

16.7637 

17.0685 

17.3733 

17.6781 

17.9829 

60 

19.8116 

20.1164 

20.4212 

20.7260 

21.0308 

70 

22.8596 

23.1644 

23.4692 

23.7740 

24.0788 

80 

25.9075 

26.2123 

26.5171 

26.8219 

27.1267 

90 

28.9555 

29.2603 

29.5651 

29.8699 

30.1747 

Example.  44ft  =  13-411  meters  =  134-11  decimeters  =  i  341. i  centimeters=  13  411 
millimeters. 

The  above-mentioned  work  contains  eighty  pages  of  conversion  tables  similar  to  the 
above. 


Inches  and  Sixteenths  Converted  into  Millimeters 


Inches 

0 

1 

2 

3 

4 

5 

25.400 
26.987 

50.799 
52.387 

76.199 
77.786 

101.60 
103.19 

127.00 
128.59 

Me 

1.5875 

H 

3.1749 

28.574 

53.974 

79.374 

104.77 

130.17 

3/16 

.   4.7624 

30.162 

55.561 

80.961 

106.36 

131.76 

H 

6.3499 

31.749 

57.149 

82.549 

107.95 

133.35 

Vi6 

7.9374 

33.337 

58.736 

84 . 136 

109.54 

134.94 

H 

9.5248 

34.924 

60.324 

85.723 

111.12 

136.52 

7l6 

11.112 

36.512 

61.911 

87.311 

112.71 

138.11 

H 

12.700 

38.099 

63.499 

88.898 

114.30 

139.70 

Vxis 

14.287 

39.687 

65.086 

90.486 

115.89 

141.28 

H 

15.875 

41.274 

66.674 

92.073 

117.47 

142.87 

iMe 

17.462 

42.862 

68.261 

93.661 

119.06 

144.46 

■      % 

19.050 

44.449 

69.849 

95.248 

•     120.65 

146.05 

13/(6 

20.637 

46.037 

71.436 

96.836 

122.24 

147.63 

l^ 

22.225 

47.624 

73.024 

98.423 

123.82 

149.22 

1^6 

23.812 

49.212 

74.611 

100.01 

125.41 

150.81 

Inches 

6 

7 

8 

9 

10 

11 

152.40 
153.98 

177.80 
179.38 

203.20 
204.78 

228.60 
230.18 

254.00 
255.58 

279.39 
280.98 

Mfl 

H 

155.57 

180.97* 

206.37 

231.77 

257.17 

282.57 

3/16 

157.16 

182.56 

207.96 

233.36 

258.76 

284.16 

M 

158.75 

184.15 

209.55 

234.95 

260.35 

285.74 

M6 

160.33 

185.73 

211.13 

236.53 

261.93 

287.33 

% 

161.92 

187.32 

212.72 

238.12 

263.52 

288.92 

Me 

163.51 

188.91 

214.31 

239.71 

265.11 

290.51 

\i 

165.10 

190.50 

215.90 

241.30 

266.70 

292.09 

»/l6 

166.68 

192.08 

217.48 

242.88 

268.28 

293.68 

H 

168.27 

193.67 

219.07 

244.47 

269.87" 

295.27 

iHe 

169.86 

195.26 

220.66 

246.06 

271.46 

296.86 

% 

171.45 

196.85 

222.25 

247.65 

273.05 

298.44 

iMe 

173.03 

198.43 

223.83 

249.23 

274.63 

300.03 

74 

174.62 

200.02 

225.42 

250.82 

276.22 

301.62 

1^6 

176.21 

201.61 

227.01 

252.41 

277.81 

303.21 

For  meters,  move  the  decimal  point  three  figures  forward. 
Example.     SMe  inches  =  207.96   millimeters  =  20.796   centimeters 
meters  =  0.20796  meter. 


2.0796   deci- 


36  Geometry  and  Mensuration  Part  1 

3.  GEOMETRY  AND  MENSURATION 

Definitions 

A  POINT  is  that  which  has  only  position. 

A  PLANE  is  a  surface  in  which,  any  two  points  being  taken,  the  straight  line 
joining  them  will  be  wholly  in  the  surface. 

A  CURVED  LINE  is  a  line  of  which  no  part  is  straight  (Fig.  1). 


Fig.  1.    Curved  Line 


Fig.  2.    Parallel  Lines 


^ 

y^ 

K 

Oy^ 

R 

R 

y^o 

R 

R 

Fig.  3.    Angles 


Parallel  lines  are  such  as  are  wholly  in  the  same  plane,  and  have  the  same 
direction  (Fig.  2). 

A  broken  line  is  a  line  composed  of  a  series  of  dashes;  thus, . 

An  angle  is  the  opening  between  two  lines  meeting  at  a  point,  and  is  termed 
a  RIGHT  angle  when  the  two  lines  are  perpendicular  to  each  other,  an  acute 
ANGLE  when  it  is  less  or  sharper  than  a  right  angle,  and  an  obtuse  angle  when 
it  is  greater  than  a  right  angle.     Thus,  in  Fig.  3, 
A  A  A  A  SLTe  acute  angles, 
0  0  0  0  2iTC  obtuse  ANGLES  and  R  R  R  R  a,re  right  angles. 

Polygons 

A  polygon  is  a  portion  of  a  plane  bounded  by  straight  lines. 
A  TRIANGLE  is  a  polygon  of  three  sides. 

A  SCALENE  TRIANGLE  has  none  of  its  sides  equal;  an  isosceles  triangle  has 
two  of  its  sides  equal;  an  equilateral  triangle  has  all  three  of  its  sides  equal. 


Fig.  4.    Right-angled  Triangle 


Fig.  6.    Isosceles  Triangle 


Fig.  7.    Equilateral  Triangle 


A  right-angled  triangle  is  one  which  has  a  right  angle.  The  side  opposite 
the  right  angle  is  called  the  hypothenuse;  the  side  on  which  the  triangle  is 
supposed  to  stand  is  called  its  base  and  the  other  side,  its  altitude. 


Polygons 


37 


A  QUADRILATERAL  IS  a  polygon  of  four  sidec. 

Quadrilaterals  are  divided  into  classes,  as  follows:  the  trapezium  (Fig.  8). 
which  has  no  two  of  its  sides  parallel;  the  trapezoid  (Fig.  9),  which  has  two  of 
its  sides  parallel;  and  the  parallelogram  (Fig.  10),  which  is  bounded  by  two 
pairs  of  parallel  sides. 


Fig.  8.    Trapezium 


Fig.  9.    Trapezoid 


Fig.  10.    Parallelogram 


A' parallelogram  whose  sides  are  not  equal  and  whose  angles  are  not  right 
angles  is  called  a  rhomboid  (Fig.  11);  when  the  sides  are  all  equal,  but  the 
angles  are  not  right  angles,  it  is  called  a  rhombus  (Fig.  12),  and  when  the  angles 
are  right  angles,  it  is  called  a  rectangle  (Fig.  13).  A  rectangle,  all  of  whose 
sides  are  equal,  is  called  a  square  (Fig.  14).  Polygons,  all  of  whose  sides  are 
equal,  are  called  regular  polygons. 


Fig.  12. 
Rhombus 


Fig.  13 
Rectangle 


Fig.  14. 
Square 


Besides  the  square  and  equilateral  triangles,  there  are:  the  pentagon  (Fig.  15), 
which  has  five  sides;  the  hexagon  (Fig.  16),  which  has  six  sides;  the  heptagon 
(Fig.  17),  which  has  seven  sides;  and  the  octagon  (Fig.  18),  which  has  eight 
sides. 


Fig.  15. 
Pentagon 


Fig.  16. 
Hexagon 


Fig.  17. 
Heptagon 


Fig.  18. 
Octagon 


The  enneagon  or  nonagon  has  nine  sides;  the  decagon  has  ten  sides;  and 
the  dodecagon  has  twelve  sides. 

For  all  polygons,  the  side  upon  which  it  is  supposed  to  stand  is  called  its 
base;  the  perpendicular  distance  from  the  highest  side  or  angle  to  the  base 
(prolonged,  if  necessary)  is  called  the  altitude;  and  a  line  joining  any  two 
angles  not  adjacent  is  called  a  diagonal. 

A  perimeter  is  the  bounding  line  of  a  plane  figure. 

A  CIRCLE  is  a  portion  of  a  plane  bounded  by  a  curve,  all  the  points  of  which 
are  equidistant  from  a  point  within,  called  the  center  (Fig.  19). 

The  circumference  is  the  curve  which  bounds  the  circle. 

A  radius  is  any  straight  line  drawn  from  the  center  to  the  circumference. 

Any  straight  line  drawn  through  the  center  to  the  circumference  on  each  side 
is  called  a  diameter. 


38 


Geometry  and  Mensuration 


Parti 


An  ARC  of  a  circle  is  any  part  of  its  circumference. 

A  CHORD  is  any  straight  line  joining  two 
points  of  the  circumference,  as  bd,  Fig.  19. 

A  SEGMENT  is  a  portion  of  the  circle 
included  between  the  arc  and  its  chord,  as 
A,  Fig.  19. 

A  SECTOR  is  the  space  included  between 
an  arc  and  two  radii  drawn  to  its  ex- 
tremities, as  B,  Fig.  19.  In  the  figure,  ab 
is  a  radius,  cd  a  diameter  and  db  a  chord 
SUBTENDING  the  arc  bed.  A  tangent  is  a 
right  line  which  in  passing  a  curve  touches 
Fig.  19.    Circle  and  Parts  without  cutting  it,  as  fg,  Fig.  19. 

Volumes 

A  PRISM  is  a  volume  whose  ends  are  equal  and  parallel  polygons  and  whose 
sides  are  parallelograms. 

A  prism  is  triangular,  rectangular,  etc.,  according  as  its  ends  are  tri- 
angles, rectangles,  etc. 

A  cube  is  a  rectangular  prism  all  of  whose  sides  are  squares. 

A  cylinder  is  a  volume  of  uniform  diameter,  bounded  by  a  curved  surface 
and  two  equal  and  opposite  parallel  circles. 

A  PYRAMID  is  a  volume  whose  base  is  a  polygon  and  whose  sides  are  triangles 
meeting  in  a  point  called  the  vertex.  A  pyramid  is  triangular,  quadrangular, 
etc.,  according  as  its  base  is  a  triangle,  quadrilateral,  etc. 

A  CONE  is  a  volume  whose  base 
is  a  circle,  from  which  the  remain- 
ing surface  tapers  uniformly  to  a 
point  or  vertex  (Fig.  20) . 

A  CONIC  SECTION  is  the  plane 
figure  made  by  a  plane  cutting  a 
cone.    • 

An  ELLIPSE  is  the  section  of  a 
cone  cut  by  a  plane  passing 
obliquely  through  both  sides,  as  at 
ab,  Fig.  21. 

A  PARABOLA  is  a  section  of  a 
cone  cut  by  a  plane  parallel  to  its 
side,  as  at  cd.    > 

A  HYPERBOLA  is  a  section  of  a  cone  cut  by  a  plane  making  a  greater  angle 
with  the  base  than  that  made  by  the  side  of  the  cone,  as  at  eh. 

In  the  ellipse,  the  transverse  axis,  or  long  diameter,  is  the  longest  line 
that  can  be  drawn  in  it  The  conjugate  axis,  or  short  diameter,  is  a  line 
drawn  through  the  center  at  right-angles  to  the  long  diameter. 

A  frustum  of  a  pyramid  or  cone  is  that  which  remains  after  cutting  oflf  the 
upper  imrt  of  it  by  a  plane  parallel  to  the  base. 

A  sphere  is  a  volume  bounded  by  a  curved  surface,  all  points  of  which  are 
equidistant  from  a  point  within,  called  the  center. 

Mensuration  treats  of  the  measurement  of  lines,  surfaces  and  volumes. 

Rules 
To  compute  the  area  of  a  square,  a  rectangle,  a  rhombus  or  a  rhomboid. 
Rule.     Multiply  the  length  by  the  breadth  or  height.    Thus,  in  Figs.  22,  23 
or  24,  the  area  =  abX  be. 


Fig.  21. 
Cone  with  Section-lines 


Mensuration-Rules 


39 


Fig.  22.     Square 


Fig.  23.     Rectangle 


Fig.  24.     Parallelogram 


To  compute  the  area  of  a  triangle. 

Rule.     Multiply  the  base  by  the  altitude  and  divide  by  2. 

the  area  of  ahc  = 


abx  cd 


Thus,  in  Fig.  25. 


To  find  the  length  of  the  hypothenuse  of  a  right-angled  triangle  when  both 
sides  are  known. 

Rule.  Square  the  length  of  each  of  the  sides  making  the  right  angle,  add 
their  squares  together  and  take  the  square  root  of  their  sum.  Thus  (Fig.  26), 
the  length  oi  ac=  3,  and  oibc=  4;  then 

ab  =  V32  4-42  ^  V9  +16  =  V^ 

V25  =  5,     or    ab=  5 

To  find  the  length  of  the  base  or  altitude  of  a  right-angled  triangle  when 
the  length  of  the  hypothenuse  and  one  side  is  known. 

Rule.  From  the  square  of  the  length  of  the  hypothenuse  subtract  the  square 
of  the  length  of  the  other  side  and  take  the  square  root  of  the  remainder. 

To  find  the  area  of  a  trapezium  (Fig.  27). 

C 


Fig.  25. 
Scalene  Triangle 


Fig.  26. 
Right-angled  Triangle 


Rule.     Multiply  the  diagonal  by  the  sum  of  the  two  perpendiculars  falling 
upon  it  from  the  opposite  angles  and  divide  the  product  by  2.     Thus, 

ab  X  (ce  +  di) 


To  find  the  area  of  a  trapezoid  (Fig.  28). 

Rule.  Multiply  the  sum  of  the  two  parallel  sides  by  the  perpendicular  dis- 
tance between  them  and  divide  the  product  by  2. 

To  compute  the  area  of  an  irregular  polygon. 

Rule.  Divide  the  polygon  into  triangles  by  means  of  diagonal  lines  and  then 
add  together  the  areas  of  all  the  triangles,  as  4,  -5  and  C  (Fig.  29), 


40 


Geometry  and  Mensuration 


Part  1 


To  find  the  area  of  a  regular  polygon. 

Rule.  Multiply  the  length  of  a  side  by  the  perpendicular  distance  to  the 
center  (as  ao.  Fig.  30),  multiply  that  product  by  the  number  of  sides  and  divide 
the  result  by  2. 


Fig.  28.     Trapezoid        Fig.  29.     Irregular  Polygon     Fig.  30.     Regular  Polygon 

To  compute  the  area  of  a  regular  polygon  when  the  length,  only,  of  a  side 
is  given. 

Rule.  Multiply  the  square  of  the  side  b3^  the  multiplier  opposite  the  name  of 
the  polygon  in  column  A  of  the  following  table: 


Table  of  Factors  for 

Determining  the  Elements  of  Polygons 

Name  of  polygon 

Number 
of  sides 

A 

Factor  fo'r 
area 

B 

Factor  for 
radius  of 
circum- 
scribing 
circle 

C 

Factor  for 
length  of 
the  sides 

D 

Factor  for 

radius  of 

inscribed 

circle 

Triangle 

3 
4 
5 
6 
7 
8 
9 

10 
11 
12 

0.433013 
1 

1.720477 
2.598076 
3.633912 
4.828427 
6.181824 
7.694209 
9.36564 
11.196152 

0.5773 

0.7071 

0.8506 

1 

1.1524 

1.3066 

1.4619 

1.618 

1.7747 

1.9319 

1.732 

1.4142 

1.1756 

1 

0.8677 

0.7653 

0.684 

0.618 

0.5634 

0.5176 

0.2887 
0.5 
0.6882 
.    0.866 
1.0383 
a. 2071 
ji.3737 
i.5383 
1.7028 
1.866 

Tetragon 

Pentagon 

Hexagon 

Heptagon 

Nonagon . 

Decagon 

Undecagon 

Dodecagon  

To  compute  the  radius  of  a  circle  circumscribed  about  a  regular  polygon  when 
the  length,  only,  of  a  side  is  given. 

Rule.  Multiply  the  length  of  a  side  of  the  polygon  by  the  number  in  column 
B  of  table. 

Example.  What  is  the  radius  of  a  circle  that  will  contain  a  hexagon,  the 
length  of  one  side  being  5  in? 

Solution.     5  X  I  =  5  in. 

To  compute  the  length  of  a  side  of  a  regular  polygon  inscribed  in  a  given 
circle,  when  the  radius  of  the  circle  is  given. 

Rule.  Multiply  the  radius  of  the  circle  by  the  number  opposite  the  name  of 
the  polygon  in  column  C  of  table. 

Example.  What  is  the  length  of  the  side  of  a  pentagon  contained  in  a  circle 
8  ft  in  diameter? 

Solution.    8  ft  diameters-  2  =  4  ft  radius;  4  X  1.1756  =  4.7024  ft. 


Mensuration  of  Circles 


41 


To  compute  the  length  of  a  side  of  a  regular  polygon,  when  the  radius  of  the 
inscribed  circle  is  given. 

Rule.  Divide  the  radius  of  the  inscribed  circle  by  the  number  opposite  the 
name  of  the  polygon  in  column  D  of  table. 

To  compute  the  radius  of  a  circle  that  can  be  inscribed  in  a  given  regular 
polygon,  when  the  length  of  a  side  is  given. 

Rule.  IMultiply  the  Icn;^'th  of  a  side  of  the  polygon  by  the  number  opposite 
the  name  of  the  polygon  in  column  D. 

Example.  What  is  the  radius  of  the  circle  that  can  be  inscribed  in  an  octagon, 
the  length  of  one  side  being  6  in  ? 

Solution.     Gx  1.2071  =  7.2426  in. 

Circles 

To  compute  the  circumference  of  a  circle. 

Rule.  Multiply  the  diameter  by  3.1416.  For  many  purposes,  the  multiplier 
■i,\^  gives  suflficiently  accurate  results. 

Example.     What  is  the  circumference  of  a  circle  7  in  in  diameter? 

Solution.  7  X  3.1416  =  21.9912  in,  or  7  X  sVi  =  22  in,  the  error  in  this  last 
result  being  0.0088  in. 

To  find  the  diameter  of  a  circle  when  the  circumference  is  given. 

Rule.  Divide  the  circumference  by  3. 14 16,  or  for  a  very  close  approximate 
result,  multiply  by  7  and  divide  by  22. 

To  find  the  radius  of  an  arc  when  the  chord  and  rise  or  versed  sine  are  given. 

Rule.  Square  onk-half  the  chord  and  the  risk; 
divide  the  sum  of  these  squares  by  twice  the  rise;  the 
result  will  be  the  radius. 

Example.  The  length  of  the  chord  ac,  Fig.  31,  is  48 
in,  and  the  rise,  bo,  is  6  in.  What  is  the  radius  of  the 
arc? 


Solution.     Radius  = 


oc^  +  ho^       242  +  62 


=  Si  in 


Fig.    31.     Circular    Arc, 
Chord  and  Rise 


2  ho  12 

To  find  the  rise  or  versed  sine  of  a  circular  arc,  when  the  chord  and  radius 

are  given. 

Rule.  Square  the  radius;  also  square  one-half  the  chord;  subtract  the 
latter  from  the  former  and  take  the  square  root  of  the  remainder.  Subtract 
the  result  from  the  radius  and  the  remainder  will  be  the  rise. 

Example.  A  given  arc  has  a  radius  of  51  in  and  a  chord  of  48  in.  What  is 
the  rise? 

Solution.  Rise  =  radius  —  Vradius^  —  \^  chord^  =51—  V2  601  —  576  =  51  —  45 
=  6  in  =  rise 

To  compute  the  area  of  a  circle. 

Rule.  Multiply  the  square  of  the  diameter  by  0.7854,  or  multiply  the  square 
of  the  radius  of  3.1416. 

Example.     What  is  the  area  of  a  circle  10  in  in  diameter? 

Solution.     10  X  10  X  0.7854  =  78.54  sq  in,  or  5  X  5  X  3.1416  =  78.54  sq  in. 

Tables  of  Areas  and  Circumferences  of  Circles 

The  following  tables  will  be  found  very  convenient  for  finding  the  circum- 
ferences and  areas  of  circles. 


42 


Geometry  and  Mensuration 


Areas  and  Circumferences  of  Circles 

For  diameters  from  M  o  to  loo,  advancing  by  tenths 


Dia. 

Area 

Circum. 

Dia. 

Area 

Circum. 

Dia. 

Area 

Circum. 

0.0 
.1 
.2 
.3 
.4 

0.007854 
0.031416 
0.070GS6 
0.12560 

0.31416 

0.62832 
0.9424S 
1.2566 

5.0 
.1 
.2 
.3 
.4 

19.6350 
20.4282 
21.2372 
22.0018 
22.9022 

15.7080 
16.0221 
16.3363 
16.6504 
16.9640 

10.0 
.1 
.2 
.3 
.4 

78.5398 
80.1185 
81.7128 
83.3229 

84.9487 

31.4159 
31.7301 
32.0442 
32.3584 

32.6726 

.5 

.6 
.7 
.8 
.9 

0.19635 
0.28274 
0.3S4S5 
0.50266 
0.63617 

1.570S 
1.8850 
2.1991 
2.5133 
2.8274 

.5 

.6 
.7 
.8 
.9 

23.7583 
24.0301 
25.5176 
26.4208 
27.3397 

17.2788 
17.5929 
17.9071 
18.2212 
18.5354 

.5 

.6 

T 

'.8 
.9 

86.5901 
88.2473 
89.9202 
91.6088 
93.3132 

32.9867 
33.3009 
33.0150 
33.9292 
34.2434 

1.0 
.1 
.2 
.3 
.4 

0.7854 
0.9503 
1.1310 
1.3273 
1.5394 

3.1416 
3.4558 
3.7699 
4.0841 
4.3982 

6.0 
.1 
.2 
.3 
.4 

28.2743 
29.2247 
30.1907 
31.1725 
32.1699 

18.8496 
19.1037 
19.4779 
19.7920 
20.1002 

11.0 
.1 
.2 
.3 
.4 

95.0332 
90.7689 
98.5203 
100.2875 
102.0703 

34.5575 
34.8717 
35.1858 
35.5000 
35.8142 

.5 

;6 

i 

.9 

1.7671 
2.0106 
2.2698 
2.5447 
2.8353 

4.7124 
5.0265 
5.3407 
5.6549 
5.9690 

.5 

.6 
.7 

.8 
.9 

33.1831 
34.2119 
35.2565 
36.3168 
37.3928 

20.4204 
20.7345 
21.0487 
21.3028 
21.6770 

.5 

.6 
.7 
.8 
.9 

103.8689 
105.6832 
107.5132 
109.3588 
111.2202 

36.1283 
30.4425 
30.7566 
37.0708 
37.3850 

2.0 
.1 
.2 
.3 

.4 

3.1416 
3.4636 
3.8013 
4.1548 
4.5239 

6.2832 
6.5973 
6.9115 
7.2257 
7.5398 

7.0 

2 
.3 
.4 

38.4845 
39.5919 
40.7150 
41.8539 
43.0084 

21.9911 

22.3053 
22.0195 
22.9330 
23.2473 

12.0 
.1 
.2 
.3 
.4 

113.0973 
114.9901 
116.8987 
1 18.8229 
120.7628 

37.6991 
38.0133 
38.3274 
38.6416 
38.9557 

.5 

.6 
.7 
.8 
.9 

4.9087 
5.3093 
5.7256 
6.1575 
6.6052 

7.8540 
8.1681 
8.4823 
8.7965 
9.1106 

.5 

.6 
.7 
.8 
.9 

44.1786 
45.3646 
46.5663 
47.7836 
49.0167 

23.5619 
23.8701 
24.1903 
24.5044 
24.8180 

.5 

.6 
.7 
.8 
.9 

122.7185 
124.0898 
120.0709 
123.6790 
130.0981 

39.2699 
39.5841 
39.8982 
40.2124 
40.5265 

3.0 
.1 
.2 
.3 
.4 

7.0686 
7.5477 
8.0425 
8.5530 
9.0792 

9.4248 
9.7389 
10.0531 
10.3673 
10.6814 

8.0 
.1 
.2 
.3 

.4 

50.2655 
51.5300 
52.8102 
54.1061 
55.4177 

25.1327 

25.4 1G9 
25.7011 
20.0752 
26.3894 

13.0 
.1 

2 

!3 

.4 

132.7323 
134.7822 

136.8478 
138.9291 
141.0261 

40.8407 
41.1549 
41.4690 
41.7832 
42.0973 

.5 
.6 

.7 
.8 
.9 

9.6211 
10.1788 
10.7521 
11.3411 
11.9459 

10.9956 
11.3097 
11.6239 
11.9381 
12.2522 

.5 
.6 

.7 
.8 
.9 

56.7450 
58.0830 
59.4403 
60.8212 
62.2114 

26.703.'-^ 
27.0177 
27.3310 
27.6400 
27.9002 

.5 

.6 
.7 
.8 
.9 

143.1388 
145.2672 
147.4114 
149.5712 
151.7468 

42.4115 
42.7257 
43.0398 
43.3540 
43.6681 

4.0 
.1 
.2 
.3 

.4 

12.5664 
13.2025 
13.8544 
14.5220 
15,2053 

12.5664 
12.8805 
13.1947 
13.5088 
13.8230 

9.0 
.1 
.2 
.3 
.4 

63.6173 
65.0388 
60.4761 
67.9291 
69.3973 

28.2743 

28.5385 
28.9027 
29.2108 
29.5310 

14.0 
.1 

.2 
.3 
.4 

153.9380 
156.1450 

153.3677 
160.0001 
162.8602 

43.9823 
44.2965 
44.6106 
44.9248 
45.2389 

.5 
.6 
.7 
.8 
.9 

15.9043 
16.6190 
17.3494 
18.0956 
18.8574 

14.137? 
14.4513 
14.7655 
15.0796 
15.3938 

.5 

.6 
.7 
.8 
.9 

70.8822 
72.3823 
73.8981 
75.4296 
76.9769 

29.8451 
30.1593 
30.4734 
30.7876 
31.1018 

5 
.6 

.7 
.8 
.9 

105.1300 
167.4155 
169.7167 
172.0336 
174.3602 

45.5531 
45.8673 
46.1814 
46.4956 
46.8097  . 

Table  of  Areas  and  Circumferences  of  Circles 


43 


Areas  and  Circumferences  of  Circles  (Continued) 

Advancing  by  tenths 


Dia. 

15.0 
.1 
.2 
.3 
.4 

Area 

CircTim. 

Dia. 

Area 

Circum. 

Dia. 

Area 

Circum. 

176.7146 

179.0786 
181.4584 
183.8539 
180.2650 

47.1239 
47.4380 

47.7522 
48.0604 
48.3805 

20.0 
.1 
.2 
,3 
.4 

314.1593 
317.3087 
320.4739 
323.6547 
326.8513 

62.8319 
63.1460 
03.1002 
03.7743 
04.0885 

25.0 
.1 

.2 
.3 
!4 

490.8739 

494.8087 
498.7592 
502.7255 
506.7075 

78.5398 
78.8540 
79.1681 
79.4823 
79.7965 

.5 

.0 
.7 
8 
.9 

188.6919 
191.1345 
193.5928 
190.0668 
198.5565 

48.6947 
49.0088 
49.3230 
49.6372 
49.9513 

.5 

.6 
.7 
.8 
.9 

330.0636 
333.2916 
336.5353 
339.7947 
343.0698 

64.4026 
64.7108 
65.0310 
65.3451 
65.6593 

.5 

.0 
.7 
.8 
.9 

510.7052 
514.7185 
518.7476 
522.7924 
526.8529 

80.1106 
80.4248 
80.7389 
81.0531 
81.3672 

16.0 
.1 
.2 
.3 
.4 

201.0619 
203.5831 
206.1109 
208.6724 
211.2407 

50.2655 
50.5796 
50.8938 
51.2080 
51.5221 

21.0 
.1 
.2 
.3 

A 

346.3606 
349.6671 
352.9894 
356.3273 
359.6809 

65.9734 
66.2876 
66.6018 
66.9159 
67.2301 

26.0 
.1 
.2 
.3 
.4 

530.9292 
535.0211 
539.1287 
543.2521 
547.3911 

81.6814 
81.9956 
82.3097 
82.6239 
82.9380 

.5 

.6 
.7 
.8 
.9 

213.8246 
216.4243 
219.0397 
221.0708 
224.3176 

51.8303 
52.1504 
52.4040 
52.7788 
53.0929 

.5 

.6 
.7 
.8 
.9 

363.0503 
360.4354 
309.8361 
373.2526 
376.6848 

67.5442 

67.8584 
68.1720 
68.4867 
68.8009 

.5 
.6 

.7 
.8 
.9 

551.5459 
555.7163 
559.9025 
564.1044 
568.3220 

83.2522 
83.5664 
83.8805 
84.1947 
84.5088 

17.0 
.1 
.2 
.3 
.4 

220.9801 
220.6533 
232.3522 
235.0618 
237.7871 

53.4071 
53.7212 
54.0354 
54.3490 
54.6637 

22.0 
.1 
.2 
.3 
.4 

380.1327 
383.5963 
387.0750 
390.5707 
394.0814 

69.1150 
69.4292 
69.7434 
70.0575 
70.3717 

27.0 
.1 
.2 
.3 
.4 

572.5553 
576.8043 
581.0690 
585.3494 
589.6455 

84.8230 
85.1372 
85.4513 

85.7655 
86.0796 

.5 

.6 
.7 
.8 
.9 

240.5282 
243.2849 
246.0574 
248.8456 
251.6494 

54.9779 
55.2920 
55.6002 
55.9203 
50.2345 

.5 
.6 
.7 

.8 
.9 

397.6078 
401.1500 
404.7078 
408.2814 
411.8707 

70.6858 
71.0000 
71.3142 
71.6283 
71.9425 

.5 

.6 

.7 
.8 
.9 

593.9574 
598.2849 
602.6282 
606.9871 
611.3618 

86.3938 
86.7080 
87.0221 
87.3363 
87.6504 

18.0 
.1 
.2 
.3 
.4 

254.4690 
257.3043 
200.1553 
203.0220. 
265.9a44 

50.5480 
50.8028 
57.1770 
57.4911 
57.8053 

23.0 
.1 

.  .2 
.3 
A 

415.4756 
419.0963 
422.7327 
426.3848 
430.0526 

72.2566 
72.5708 
72.8849 
73.1991 
73.5133 

28.0 
.1 
.2 
.3 
.4 

615.7522 
620.1582 
624.5800 
629.0175 
633.4707 

87.9646 
88.2788 
88.5929 
88.9071 
89.2212 

.5 

.6 
.7 
.8 
.9 

268.8025 
271.7164 
274.6459 
277.5911 
280.5521 

58.1195 
58.4330 

58.7478 
59.0019 
59.3701 

.5 

.6 
.7 
.8 
.9 

433.7361 
437.4354 
441.1503 
444.8809 
448.6273 

73.8274 
74.1416 
74.4557 
74.7699 
75.0841 

.5 

.6 
.7 
.8 
.9 

637.9397 
642.4243 
646.9246 
651.4407 
655.9724 

89.5354 
89.8495 
90.1637 
90.4779 
90.7920 

19.0 
.1 
.2 
.3 
.4 

283,5287 
286.5211 
289.5292 
292.5530 
295.5925 

59.6903 
60.0044 
60.3180 
00.0327 
60.9409 

24.0 
.1 
.2 
.3 
.4 

452.3893 
456.1671 
459.9606 
463.7698 
467.5947 

75.3982 
75.7124 
76.0265 
76.3407 
76.6549 

29.0 
.1 

■  .2 
.3 
.4 

660.5199 
665.0830 
669.6019 
674.2505 
678.8668 

91.1062 
91.4203 
91.7345 
02.0487 
92.3628 

.5 

.6 
.7 
.8 
.9 

298.6477 
301.7186 
304.8052 
307.9075 
311.0255 

61.2611 
61.5752 
61.8894 
62.2035 
62.5177 

.5 
.6 
.7 

.8 
.9 

471.4352 
475.2916 
479.1636 
483.0513 
486.9547 

76.9690 
77.2832 
77.5973 
77.9115 

78.2257 

.5 

.6 
.7 
.8 
.9 

683.4928 
688.1345 
692.7919 
697.4050 
702.1538 

92.6770 
92.9911 
93.3053 
93.6195 
93.9336 

44 


Geometry  and  Mensuration 


Areas  and  Circumferences  of  Circles  (Continued) 
Advancing  by  tenths 


Dia. 


30.0 

'.2 
.3 
.4 


.0 

.7 
.8 
.9 

31.0 
.1 
.2 
.3 
.4 

.5 

.0 
.7 
.8 
.9 

32.0 
.1 
.2 
.3 
.4 

.5 

.6 

.7 
.8 
.9 

33.0 
.1 
.2 
.3 

.4 

.5 

.6 
.7 

.8 


34.0 
.1 
.2 
.3 
.4 

.5 

.6 
.7 

8 


Area       Circum.  Dia.       Area        Circum.  Dia.       Area       Circum 


706.8583 
711.5786 
710.3145 
721.0662 
725.S336 

730.0167 
735.4154 
710.2299 
7J5.0601 
749.9000 

754.7076 
759.6450 
704.5380 
769.4407 
774.3712 

779.3113 

784.2672 
789.23S8 
794.2260 
799.2290 

804.2477 
809.2821 
814.3322 
819.3980 
824.4796 

829.5768 
834.6898 
839.8185 
844.9628 
850.1229 

855.2986 
860.4902 
805.6973 
870.9202 

876.1588 

881.4131 
886.6831 
891.9688 
897.2703 
902.5874 

907.9203 
913.2688 
918.6331 
924.0131 
929.4088 

934.8202 
940.2473 
945.6901 
951.1486 
956.6228 


94.2478 
94.5619 
94.8761 
95.1903 
95.5044 

95.8186 
96.1327 
96.4469 
96.7611 
97.0752 

97.3894 
97.7035 
98.0177 
98.3319 
98.6460 

98.9602 
99.2743 
99.5885 
99.9026 
100.2108 

100.5310 
100.8^51 
101.159; 
101.4734 
101.7876 

102.1018 

102.1159 

102.7301 

103.044 

103.3584 

103.6726 
103.9807 
104.3009 
104.6150 
104.9292 

105.2434 
105.5575 
105.8717 
106.1858 
106.5000 

106.8142 
107.128; 
107.4425 
107.7566 
108.0708 

108.3849 
108.6991 
109.0133 
109.3274 
109.6416 


35.0 
.1 
.2 
.3 
.4 

.5 

.6 
.7 
.8 


36.0 


37.0 
.1 
.2 
.3 
.4 

.5 
.6 

.7 
.8 
.9 

38.0 
.1 

9 

!3 
.4 

.5 

.6 

.7 


39.0 
.1 
2 
!3 
.4 

.5 

.6 
.7 
.8 
.9 


962.1128 
967.6184 
973.1397 
978.6768 
984.2296 

989.7980 
995.3822 
1000.9821 
1006.5977 
1012.2290 

1017.8760 

1023.5387 

1029.2172 

1034.911 

1040.6212 

1046.3467 
1052.0'iSO 
1057.S449 
1063.6176 
1069.4060 

1075.2101 
1  OS  1.0299 
1086.P3654 
1092.7166 
1098.5835 

1104.4662 
1110.3645 
1110.2786 
1122.2083 
1128.1538 

1134.1149 
1140.0918 
1146.0844 
1152.0927 
1158.1167 

1104.1564 
1170.2118 
1176.2830 
1182.3698 
1 188.4724 

1194.5906 
1200.7246 
1200.8742 
1213.0396 
1219.2207 

1225.4175 
1231.6300 
1237.8582 
1244.1021 
1250.3617 


109.9557 
110.2699 
110.5841 
110.8982 
111.2124 

111.5265 
111.840: 
112.1549 
112.4690 
112.7832 

113.0973 
113.4115 
113.7257 
114.0398 
114.3510 

114.66']1 
114.9S2C 
115.290^ 
115.[J]0C 
115.9248 

116.23! 

110.5531 

116.8672 

117.1814 

117.495(1 

117.8097 
118.1239 
118.4380 
118.7522 
119.0604 

119.3805 
119.0947 
120.0088 
120.3230 
120.6372 

120.9513 
121.2655 
121.5700 
121.8938 
122.2080 

122.5221 
122.8303 
123.1504 
123.4640 

123.7788 

124.0929 
124.4071 
124  7212 
125.0351 
125.3495 


40.0 

'.2 
.3 
.4 

.5 

.6 

.7 
.8 
.9 

41.0 
.1 
.2 
.3 
.4 

.5 
.6 

7 
.8 
.9 

42.0 
.1 
.2 
.3 
.4 

.5 

.6 
,7 
.8 
.9 

43.0 
.1 
.2 
.3 
.4 


.6 

.7 
.8 
.9 

44.0 
-1 
.2 
.3 
.4 

.5 
.6 

.7 
.8 
.9 


1256.0371 

1262.9281 
1269.2348 
1275.5573  126.0002 
1281.8955  126.9203 

1288.2493 
1294.0189 
1301.0042 
1307  4052 
1313.8219 

1320.2543 
1326.7024 
1333.1003 
1339.0458 
1346.1110 

1352.0520 
1359.1780 
1305.7210 
1372.2791 
1378.8529 

1385.4424 
1392.0470 
1398  6685 
1405.3051 
1411.9574 

1418.0254 
1125.3092 
1432.0086 
1 438  7238 
1445.4546 

1452.2012 
1458.9635 
1405  74 
1472.5352 
1479.3446 

1480  1697 
1493.0105 
1499.8070 
1500.7393 
1513.0272 

1520.5308 
1527.4502 
1534.3853 
1541.3360 
1548.302i 

155  5.247 
1562.2826 
1569.2962 
1576.325' 
1583.3706 


Table  of  Areas  and  Circumferences  of  Circles 


45 


Areas  and  Circumferences  of  Circles  (Continued) 
Advancing  by  tenths 


Dia. 


45.0 
.1 
.2 
.3 
A 

.5 

.6 

.7 


.2 
.3 
.4 

.6 

.6 
.7 
.8 
.9 

47.0 
.1 
.2 
.3 
.4 

.5 

.6 

.7 
.8 


48.0 
.1 
.2 
.3 
.4 

.5 

.6 
.7 


49.0 
.1 
.2 
.3 


Area 


1590.4313 

1597.5077 
1G04.5999 
1G11.7077 
1G18.8313 

1625.9705 
1633.1255 
1640.2962 
1647.4826 
1654.6847 

1661.9025 
1669.1360 
1676.3853 
1683.6502 
1690.9308 

1698.2272 
1705.5392 
1712.8670 
1720.2105 
1727.5697 

1734.9445 
1742.3351 
1749.7414 
1757.1635 
1764.6012 

1772.0546 
1779.5237 
1787.0086 
1794.5091 
1802.0254 

1809.5574 
1817.1050 
1824.0684 
1832.2475 
1839.8423 

1847.4528 
1855.0790 
1862.7210 
1870.3786 
1878.0519 

1885.7409 
1893.4457 
1901.1662 
1908.9024 
1916.6543 

1924.4218 
1932.2051 
1940.0042 
1947.8180 
1955.0403 


Circum. 


141.3717 
141.6858 
142.0000 
142.3142 
142.6283 

142.9425 
143.2566 
143.5708 
143.8849 
144.1991 

144.5133 
144.8274 
145.1416 
145.4557 
145.7699 

146.0841 
146.3982 
146.7124 
147.0265 
147.3407 

147.6550 
147.9690 
148.2832 
148.5973 
148.9115 

149.2257 
149.5398 
149.8540 
150.1681 
150.4823 

150.7964 
151.1106 
151.4248 
151.7389 
152.0531 

152.3672 
152.6814 
152.9956 
153.3097 
153.6239 

153.9380 
154.2522 
154.5664 
154.8805 
155.1947 

155.5088 
155.8230 
156.1372 
156.4513 
156.7655 


Dia. 


50.0 
.1 
.2 
.3 
.4 

.5 

.6 

.7 


51.0 
.1 
.2 
.3 

.4 

.5 

.6 

.7 
.8 


52.0 

'.2 
.3 
.4 

.5 

.6 

.7 


53.0 
.1 
.2 
.3 
A 


54.0 
.1 
.2 
.3 
A 

.5 

.6 

.7 


Area 


1963.4954 
1971.3572 
1979.2348 
1987.1280 
1995.0370 

2002.9617 
2010.9020 
2018.8581 
2026.8299 
2034.8174 

2042.8206 
2050.8395 
2058.8742 
2066.9245 
2074.9905 

2083.0723 
2091.1697 
2099.2829 
2107.4118 
2115.5563 

2123.7166 
2131.8926 
2140.0843 
2148.2917 
2156.5149 

2164.7537 
2173.0082 

2181.2785 
2189.5644 
2197.8661 

2206.1834 
2214.5165 
2222.8653 
2231.2298 
2239.6100 

2248.0059 
2256.4175 

2264.8448 
2273.2879 
2281.7466 

2290.2210 
2298.7112 
2307.2171 
2315.7386 


Circum. 


2324.2759  170.9026 


2332.8289 
2341.3976 
2349.9820 
2358.5821 
2367.1979 


157.0796 
157.3938 
157.7080 
158.0221 
158.3363 

158.6504 
158.9646 
159.2787 
159.5929 
159.9071 

160.2212 
160.5354 
160.8495 
161.1637 
161.4779 

161.7920 
162.1062 
162.4203 
162.7345 
163.0487 

163.3628 
163.6770 
163.9911 
164.3053 
164.6195 

164.9336 
165.2479 
165.5619 
165.8761 
166.1903 

166.5044 
166.8186 
167.1327 
167.4469 
167.7610 

168.0752 
168.3894 
168.7035 
169.0177 
169.3318 

169.6460 
169.9602 
170.2743 
170.5885 


Diu. 


171.2168 
171.5310 
171.8451 
172.1593 
172.4735 


55.0 
.1 
.2 
.3 
A 

.5 

.6 

.7 
.8 
.9 

56.0 
.1 
.2 
.3 
A 

.5 

.6 
.7 
.8 
.9 

57.0 
.1 
.2 
.3 
.4 


.6 
.7 
.8 
.9 

58.0 
.1 
.2 
.3 
.4 

.5 

.6 
.7 
.8 
.9 

59.0 
.1 
.2 
.3 
.4 

.5 

.6 

.7 


Area 


2375.8294 
2384.4767 
2393.1396 
2401.8183 
2410.5126 

2419.2227 
2427.9485 
2436.6899 
2445.4471 
2454.2200 

2463.0086 
2471.8130 
2480.6330 

2489.4687 
2498.3201 

2507.1873 
2516.0701 
2524.9687 
2533.8830 
2542.8129 

2551.7586 
2560.7200 
2569.6971 
2578.6899 
2587.6985 

2596.7227 
2605.7626 
2614.8183 
2623.8890 
2632.9767 

2642.0794 
2651.1979 
2660.3321 
2669.4820 
2678.6476 

2687.8289 
2697.0259 
2706.2386 
2715.4670 
2724.7112 

2733.9710 
2743.2466 
2752.5378 
2761.8448 
2771.1675 

2780.5058 
2789.8599 
2799.2297 
2808.6152 
2818.0165 


46 


Geometry  and  Mensuration 


Part  1 


Areas  and  Circumferences  of  Circles  (Continued) 

Advancing  by  tenths 


Dia. 

Area 

Circum 

Dia. 

65.0 

'.2 
.3 
.4 

Area 

Circum 

Dia 

70.0 
.1 
.2 
.3 
.4 

Area 

Circum. 

60.0 
.1 
.2 
.3 
.4 

2827.433^ 
2836.866C 
2846.314^ 

2855.778"^ 
2865.2582 

188.495C 
188.8097 
189.1239 
189.438C 
189.7522 

3318-.3072 
3328.525b 
3338.759C 
3349.0085 
3359.273( 

204.2035 
204.5171 
204.831? 
205. 14U 

205.4602 

3848.451( 
3859.454-3 
3870.473( 

3881.5084 
3892.559C 

)  219.9115 
220.2256 
220.5398 
220.8540 
221.1681 

.5 

.6. 

.7 
.8 
.9 

2874.753C 
2884.264^ 
2893.7917 
2903.334S 

2912.8926 

190.066^ 
190.380£ 
190.6947 
191.008? 
191.323C 

.5 

.6 

.7 

.8 

)   .9 

3369.554S 
3379.S51C 
3390.163S 
3400.491S 
3410.S35C 

205.774S 
206.0885 
206.402C 
206.716? 
207.031C 

.5 
.6 
.7 

.8 
.9 

3903.6252 
3914.7072 
3925.8049 
3936.9182 
3948.0472 

221.4823 
221.7964 
222.1106 
222.4248 
222.7389 

61.0 
.1 

.2 
.3 
.4 

2922.466C 
2932.0565 
2941.6617 
2951.282S 
2960.9197 

191.637^ 
191.95K 
192.265^ 
192.579( 
192.893? 

66.0 
.1 
.2 
.3 
.4 

3421.1944 
3431.5695 
3441.9G0c 
3452.3669 
3462.7891 

207.3451 
207.6595 
207.9734 

208.2876 
208.6017 

71.0 
.1 
.2 
.3 
.4 

3959.1921 
3970.352f 
3981.5289 
3092.720? 
4003.9284 

223.0531 
223.3672 
223.6814 
223.9956 
224.3097 

.5 

.6 
.7 

.8 
.9 

2970.5722 
2980.2405 
2989.9244 
2999.6241 
3009.3395 

193.207S 
193.5221 
193.8362 
194.1504 
194.464C 

.5 

.6 

.7 
.8 
.9 

3473.2270 
3483.6807 
3494.1500 
3504.6351 
3515.1359 

208.9159 
209.2301 
209.5442 
209.8584 
210.1725 

.5 

.6 
.7 
.8 
.9 

4015.1518 
4026.3908 
4037.6456 
4048.9160 
4060.2022 

224.6239 
224.9380 
225.2522 
225.5664 
225.3805 

62.0 
.1 
2 

."3 
.4 

3019.0705 
3028.8173 
303S.5798 
3048.3580 
3058.1520 

194.7787 
195.0929 
195.-^071 
195.7212 
196.0354 

67.0 
.1 
.2 
.3 
.4 

3525.6524 
3536.1845 
3546.7324 
3557.2960 
3567.8754 

210.4867 
210.S009 
211.115C 
211.4292 
211.743c 

72.0 
.1 
2 

!3 

.4 

4071.5041 
4082.8217 
4094.1550 
4105.5040 
4110.8687 

226.1947 
226.5088 
226.8230 
227.1371 
227.4513 

.5 

.6 
.7 
.8 
.9 

3067.9616 
3077.7869 
3087.6279 
3097.4847 
3107.3571 

196.3495 
196.6637 
196.9779 
197.2920 
197.6062 

.5 

.6 
.7 
.8 
.9 

3578.4704 
3589.0811 
3599.7075 
3610.3497 
3621.0075 

212.0575 
212.3717 
212.6S5r 
213.000C 
213.3141 

.5 
.6 

.7 
.8 
.9 

4128.2491 
4139.6452 
4151.0571 
4102.4846 
4173.9279 

227.7655 
228.0796 
228.3938 
228.7079 
229.0221 

63.0 

'.2 
.3 
.4 

3117.2453 
3127.1492 
3137.0688 
3147.0040 
3156.9550 

197.9203 
198.2345 
198.548-7 
198.8628 
199.1770 

68.0 
.1 
.2 
.3 
.4 

3631.6811 
3642.3704 
3653.0754 
3663.79C0 
3674.5324 

213.628c 
213.9425 
214.2560 
214.5708 
214.8849 

73.0 
.1 
.2 
.3 

.4 

4185.3868 
4196.8615 
4208.3519 
4219.8579 
4231.3797 

229.3363 
229.6504 
229.9646 
230.2787 
230.5929 

.5 

.6 
.7 
.8 
.9 

3166.9217 
3176.9043 
3186.9023 
3196.9161 
3206.9456 

199.4911 
199.8053 
200.1195 
200.4336 
200.7478 

.5 

.6 
.7 
.8 
.9 

3685.2845 
3696.0523 
3706.8359 
3717.6351 
3728.4500 

215.1991 
215.5133 
215.8274 
216.1416 
216.4556 

.5 

.0 
.7 
.8 
.9 

4242.9172 
4254.4704 
4266.0394 
4277.6240 
4289.2243 

230.9071 
231.2212 
231.5354 
231.8495 
232.1637 

64.0 
.1 
.2 
.3 
.4 

3216.9909 
3227.0518 
3237.1285 
3247.2222 
3257.3289 

201.0620 
201.3761 
201.6902 
202.0044 
202.3186 

69.0 
.1 
.2 
.3 
.4 

3739.2807 
3750.1270 
3760.9891 
3771.8668 
3782.7603 

216.7699 
217.0841 
217.3982 
217.7124 
218.0265 

74.0 
.1 
.2 
.3 

.4 

4300.8403 
4312.4721 
4324.1195 
4335.7827 
4347.4616 

232.4779 
232.7920 
233.1062 
233.4203 
233.7345 

.5 

.6 
.7 
.8 
.9 

3267.4527 
3277.5922 
3287.7474 
3297.9183 
3308.1049 

202.6327 
202.9469 
203.2610 
203.5752 
203.8894 

.5 

.6 
.7 
.8 
.9 

3793.6695 
3804.5944 
3815.5350 
3826.4913 
3837.4633 

218.3407 
218.6548 
218.9690 
219.2832 
219.5973 

.5 

.6 
.7 
.8 
.9 

4359.1562 
4370.8664 
4382.5924 
4394.3341 
4406.0916 

234.0487 
234.3628 
234.6770 
234.9911 
235.3058 

Table  of  Areas  and  Circumferences  of  Circles 


47 


Areas  and  Circumferences  of  Circles  (Continued) 

Advancing  by  tenths 


Dia. 

Area 

Circum. 

Dia. 

Area 

Circum. 

Dia. 

Area 

Circum. 

75.0 
.1 
2 

!3 

.4 

4417.8G47 
4429.6535 
4441.4580 
4453.2783 
4465.1142 

2.35.6104 
235.9336 

2?.6.2478 
236.5019 
'236.8761 

80.0 
.1 
.2 
.3 
.4 

5026.5482 
5039.1225 
5051.7124 
5064.3180 
5076.0394 

251.3274 
251.6416 
251.9557 
252.2609 
252.5840 

85.0 
.1 
.2 
.3 
.4 

5674.5017 

5687.8614 
5701.2367 
5714.6277 
5728.0345 

207.0354 

207.3495 
207.0637 
267.9779 
268.2920 

.5 

.6 
.7 
.8 
.0 

4476.9650 
44SS.S332 
4500.7163 
4512.6151 
4524.5290 

237.1902 
237.50i4 

237.8186 
238.1327 
238.^469 

.5 

.6 
.7 
.8 
.9 

5089.5764 
5102.2292 
5114.8977 
5127.5810 
5140.2818 

252.8982 
253.2124 
253.5265 
253.8407 
254.1548 

.5 

.6 
.7 
.8 
.9 

5741.4569 
5754.8951 
5768.3490 
5781.8185 
5795.3038 

268.6062 
268.9203 
269.2345 
269.54S6 
260.8628 

76.0 

\2 
.3 
A 

4536.4598 
4548.4057 
4560.3673 
4572.3446 
4584.3377 

238.7610 
239.0752 
230.3894 
239.7035 
240.0177 

81.0 
.1 

;2 

.3 

.4 

5152.0973 
5165.7287 
5178.4757 
5101.2384 
5204.0168 

254.4600 
254.7832 
255.0973 
255.4115 
255.7256 

86.0 
.1 
.2 
.3 
.4 

5808.8048 
5822.3215 
5835.8539 
5849.4020 
5862.9659 

270 
270 
270 
271 
271 

1770 
4911 
8053 
1194 
4336 

.5 

.6 
.7 

.8 
.9 

4506.3464 
4608.3708 
4620.4110 

4632.4660 
4644.5:j84 

240.3318 
240.6460 
240.9602 
241.2743 
241.5885 

.5 
.6 
.7 
.8 
.9 

5216.8110 
5220.6208 
5242.4463 

5255.2876 
5268.1446 

256.0398 
256.3540 
256.6681 
256.9823 
257.2966 

.5 

.6 

.7 
.8 
.9 

5876.5454 
5890.1407 
5903.7516 
5917.3783 
5931.0206 

271 

272 
272 
272 
273 

7478 
0619 
3761 
6902 
0044 

77.0 

'.2 
,3 
.4 

4656.6257 
4668.72S7 
46S0.S474 
4602.9818 
4705.1310 

241.9026 
242.2168 
242.5310 
242.8451 
243.1592 

82.0 
.1 
.2 
.3 
.4 

5281.0173 
5203.0056 
5306.8097 
5310.7295 
5332.6650 

257.6106 
257.0247 
258.2389 
258.5531 
258.8672 

87.0 
.1 
.2 
.3 
.4 

5944.6787 
5958.3525 
5972.0420 
5985.7472 
5999.4081 

273.3186 
273.6327 
273.9469 
274.2610 
274.5752 

.5 
.6 
.7 

.8 
.0 

4717.2977 
4729.4792 
4741.6765 
4753.8894 
4766.1181 

243.4734 

243.7876 
244.1017 
244.4159 
244.7301 

.5 

.6 
.1 

.8 
.9 

5345.0162 
5358.5832 
5371.5658 
5384.5641 
5397.5782 

2:^9.1814 
250.4956 
250.8097 
260.1230 
200.4380 

.5 

.6 
.7 

.8 
.9 

0013.2047 
0020.9570 
0040.7250 
0054.5088 
0068.3082 

274.8894 
275.2035 
275.5177 
275.8318 
276.1460 

7S.0 
.1 
.2 
.3 
.4 

4778.3624 
4790.6225 
4802.8083 
4815.1897 
4827.4909 

245.0442 

245.3584 
245.6725 
245.9867 
246.3009 

83.0 
.1 
.2 
.3 
.4 

5410.6079 
5423.6534 
5436.7146 
5449.7915 
5462.8840 

260.752? 
261.0063 
261.3805 
261.6947 
202.0088 

88.0 
.1 
.2 
.3 
.4 

6082.1234 
0095.9542 
0109.8008 
0123.0031 
0137.5411 

276.4602 
276.7743 
277.0885 
277.4026 
277.7168 

.5 

.7 

.8 
.9 

4839.8198 
4852.1584 
4864.5128 
4876.8828 
4889.2685 

246.0150 
246.9292 
247.2433 
247.5575 
247.8717 

.5 

.6 
.7 
.8 
.9 

5475.9923 
5489.1168 
5502.2561 
5515.4115 

5528.5826 

262.3230 
202.0371 
202.9513 
263.2655 
263.5790 

.5 

.6 
.7 
.8 
.9 

0151.4348 
6165.3442 
6179.2693 
6193.2101 
6207.1606 

278.0309 
278.3451 
278.6593 
278.9740 
279.2870 

79.0 
.1 
2 

[3 
.4 

4901.0690 
4914.0871 
4026.5199 
4038.9685 
4951.4328 

248.1858 
248,5000 
2^8.8141 
249.1283 
249.4425 

84.0 
.1 
.2 
.3 
.4 

5541.7604 
5554.9720 
5568.1902 
5581.4242 
5594.6739 

203.8938 
204.2079 
204.5221 
264.8303 
205.1514 

89.0 
.1 
.2 
.3 
.4 

6221.1389 
6235.1268 
6249.1304 
6263.1498 
6277.1849 

279.6017 
279.9159 
280.2301 
280.5442 
280.8584 

.0 
.7 
.8 
.9 

4063.9127 
4976.4084 
4988.9108 
5001.4460 
5013.9897 

249.7566 
250.0708 
250.3850 
250.6991 
251.0133 

.5 

.0 
.7 
.8 
.9 

5607.9302 
5621.2203 
5634.5171 
5647.8206 
5661.1578 

265.4646 
265.7787 
266.0929 
266.4071 
266.7212 

.5 

.0 
.7 
.8 
.9 

6291.2350 
0305.3021 
6319.3843 
0333.4822 
0347.5958 

281.1725 
281.4867 
281.8009 
282.1150 
282.4292 

48 


Geometry  and  Mensuration 


Areas  and  Circumferences  of  Circles  (Continued) 

Advancing  by  tenths 


Dia. 

Area 

Circum. 

Dia. 

Area 

Circum. 

Dia. 

Area 

Circum. 

90.0 

63G1.7251 

282.7433 

293.7389 

97.0 

7389.8113 

304.7345 

93.5 

6866.1471 

.1 

6375.8701 

283.0575 

.0 

6880.8419 

294.0531 

.1 

7405.0559 

305.0486 

.2 

6390.0309 

283..7717 

.7 

6895.5524 

294.3072 

.2 

7420.3102 

305.3028 

.3 

6404.2073 

283.6858 

.8 

0910.2780 

294.6814 

.3 

7435.5922 

305.6770 

.4 

6418.3995 

284.0000 

.9 

6925.0205 

294.995^ 

.4 

7450.8839 

305.9911 

.5 

6432.6073 

284.3141 

94.0 

0939.7782 

295.3097 

.5 

7406.1913 

306.3053 

.6 

6446.8309 

284.6283 

.1 

6954.5515 

295.6239 

.0 

7481.5144 

306.6194 

.7 

6461.0701 

284.9425 

.2 

6909.3100 

295.9380 

.7 

7496.8532 

306.9336 

.8 

0475.3251 

285.2500 

.3 

0934.1453 

290.2522 

.8 

7512.2078 

307.2478 

.9 

6489.5958 

285.5708 

.4 

0998.9058 

296.5063 

.9 

7527.5780 

307.5619 

91.0 

6503.8822 

285.8849 

.5 

7013.8019 

296.8805 

98.0 

7542.9040 

307.8761 

.1 

6518.1843 

286.1991 

.6 

7028.0538 

297.1947 

.1 

7558.3050 

308.1902 

.2 

6532.5021 

286.5133 

.7 

7043.5214 

297.5088 

.2 

7573.7830 

308.5044 

.3 

r.546.835H 

286.8274 

.8 

7058.4047 

297.8230 

.3 

7589.2101 

308.8186 

A 

6561.1848 

287.1416 

.9 

7073.3033 

298.1371 

.4 

7604.0048 

309.1327 

.5 

0575.5498 

287.4557 

95.0 

7088.2184 

298.4513 

.5 

7020.1293 

309.4409 

.6 

6589.9304 

287.7099 

.1 

7103.1488 

298.7655 

.0 

7035.0095 

309.7010 

.7 

6604.3268 

288.0840 

.2 

7118.1950 

299.0790 

.7 

7651.1054 

310.0752 

.8 

6618.7388 

288.3982 

.3 

7133.0508 

299.3938 

.8 

7606.0170 

310.3894 

.9 

6633.1666 

288.7124 

.4 

7148.0343 

299.7079 

.9 

7682.1444 

310.7035 

92.0 

6647.6101 

289.0265 

.5 

7103.0276 

300.0221 

99.0 

7697.6893 

311.0177 

J 

6062.0692 

289.3407 

.6 

7178.0366 

300.3303 

.1 

7713.2461 

311.3318 

.2 

6676.5441 

289.0548 

.7 

7193.0012 

300.0504 

.2 

77^8.8200 

311.0400 

.3 

6691.0347 

289.9690 

.8 

7208.1016 

300.9040 

.3 

7744.4107 

311.9002 

.4 

6705.5410 

290.2832 

.9 

7223.1577 

301.2787 

.4 

7760.0166 

312.2743 

.5 

6720.0030 

200.5973 

90.0 

7238.2295 

301.5929 

.5 

7775.6382 

312.5885 

.6 

6734.6008 

299  9115 

.1 

7253.3170 

301.9071 

.0 

7791.2754 

312.9020 

•  .7 

6749.1542 

291.2256 

.2 

726S.4202 

302.2212 

.7 

7800.9284 

313.2108 

.8 

6763.7233 

291.5398 

.3 

7283  5391 

302.5354 

.8 

7822.5971 

313.5309 

.9 

6778.3082 

291.8540 

.4 

7298.6737 

302.8405 

.9 

7838.2815 

313.8451 

93.0 

6792.9087 

292.1681 

.5 

7313.8240 

303.1037 

100.0 

7853.9816 

314.1593 

.1 

6807.5250 

292.4823 

.6 

7328.9901 

303.4779 

.2 

6822.1569 

292.7904 

.7 

7344.1718 

303.7920 

.3 

68?6.8046 

293.1100 

.8 

7359.3093 

304.1002 

.4 

6851.4680 

293.4248 

.9 

7374.5824 

304.4203 

Table  of  Areas  and  Circumferences  of  Circles 


49 


Areas  of  Circles 

Advancing  by  eighths 
Areas 


Dia. 

0.0 

O.J 

o.i 

O.f 
0.1104 

O.J 

0.1903 

O.f 

o.i 

0, 

0 

0.0 

0.0122 

0.0490 

0.3068 

0.4417 

0.0013 

1 

0.7854 

0  9940 

1.227 

1.484 

1.707 

2.073 

2.405 

2.701 

2 

3.1416 

3  546 

3.976 

4.430 

4.908 

5.411 

5.939 

6.491 

3 

7.0GS 

7.669 

8.295 

8.946 

9.021 

10.32 

11.04 

11.79 

4 

12.50 

13.36 

14.18 

15.03 

15.90 

16.80 

17.72 

18.66 

5 

19.63 

20.02 

21.64 

22.69 

23.75 

24.85 

25.96 

27.10 

0 

28.27 

29.46 

30.07 

31.91 

S3.18 

34.47 

35.78 

37.12 

7 

38.48 

39.87 

41.28 

42.71 

44.17 

45.66 

47.17 

48.70 

8 

50.20 

5 1.84 

53.45 

55.08 

50.74 

58.42 

60.13 

61.86 

9 

03.61 

65.39 

67.20 

69.02 

70.88 

72.75 

74.66 

70.58 

10 

78.54 

80.51 

82.51 

84.54 

86.59 

88.60 

90.76 

92.88 

11 

95.03 

97.20 

99.40 

101.0 

103.8 

100.1 

108.4 

110.7 

12 

113.0 

115.4 

117.8 

120.2 

122.7 

125.1 

127.6 

130.1 

13 

132.7 

1S5.2 

137.8 

140.5 

148.1 

145.8 

148.4 

151.2 

11 

153.9 

150.6 

159.4 

1C2.2 

105.1 

167.9 

170.8 

173.7 

If) 

176.7 

179.6 

182.6 

185.6 

188.6 

191.7 

194.8 

197.9 

10 

201.0 

204.2 

207.3 

210.5 

213.8 

217.0 

220.3 

223.6 

17 

226.9 

230.3 

233.7 

2C7.1 

240.5 

248.9 

247.4 

250.9 

IS 

254.4 

258.0 

261.5 

265.1 

2G8.8 

272.4 

276.1 

279.8 

19 

283.5 

287.2 

291.0 

294.8 

298.0 

302.4 

306.3 

310.2       : 

20 

314.1 

318.1 

322.0 

326.0 

330.0 

334.1 

338.1 

342.2 

21 

316.3 

350.4 

354.6 

358.8 

203.0 

CG7.2 

371.5 

375.8 

22 

380.1 

384.4 

388.8 

393.2 

397.0 

402.0 

406.4 

410.9 

23 

415.4 

420.0 

424.5 

429.1 

433.7 

438.3 

443.0 

447.6 

24 

452.3 

457.1 

401.8 

46G.6 

471.4 

470.2 

481.1 

4S5.9 

2.^^ 

490.8 

405.7 

500.7 

505.7 

510.7 

515.7 

520.7 

525.8 

20 

530.9 

536.0 

541.1 

546.3 

551.5 

556.7 

502.0 

507.2 

27 

572.5 

577.8 

583.2 

5S8.5 

593.9 

5C9.3 

004.8 

610.2 

2R 

615.7 

621.2 

020.7 

632.3 

r37.9 

643.5 

649.1 

054.8 

29 

060.5 

660.2 

071.9 

677.7 

083.4 

689.2 

695.1 

700.9 

30 

706.3 

712.7 

7ia.(? 

724.6 

730.0 

736.6 

742.0 

748.0 

31 

754.8 

700.9 

767.0 

773.1 

779.3 

785.5 

791.7 

798.0 

32 

804.3 

810.6 

810.9 

823.2 

829.6 

836.0 

842.4 

848.8 

33 

855.3 

801.8 

808.3 

874.9 

881.4 

888.0 

894.6 

901.3 

34 

907.9 

914.7 

921.3 

928.1 

934.8 

941.6 

948.4 

95'^.3 

35 

962.1 

969.0 

975.9 

982.8 

989.8 

996.8 

1003.8 

1010.8 

36 

1017.9 

1025.0 

1032.1 

1039.2 

1046.3 

1053.5 

1060.7 

1008.0 

37 

1075.2 

1082.5 

1089.8 

1097.1 

1104.5 

1111.8 

1119.2 

U20.7 

38 

1134.1 

1141.6 

1149.1 

1156.6 

1164.2 

1171.7 

1179.3 

1180.9 

39 

1194.6 

1202.3 

1210.0 

1217.7 

1225.4 

1233.2 

1241.0 

1248.8 

40 

1256.6 

1264.5 

1272.4 

1280.3 

1288.2 

1296.2 

1304.2 

1312.2 

41 

1320.3 

1328.3 

1336.4 

1344.5 

1352.7 

1360.8 

1369.0 

1377.2 

42 

1385.4 

1393.7 

1402.0 

1410.3 

1418.6 

1427.0 

1435.4 

1443.8 

43 

1452.2 

1460.7 

1469.1 

1477.6 

1486.2 

1494.7 

1503.3 

1511.9 

44 

1520.5 

1529.2 

1537.9 

1546.6 

1555.3 

1564.0 

1572.8 

1581.6 

45 

1590.4 

1599.3 

1608.2 

1617.0 

1626.0 

1634.9 

1643.9 

1652.9 

50 


Geometry  and  Mensuration 


Circumferences  of  Circles 

Advancing  by  eighths 
Circumferences 


Dia. 

0.0 

O.i 

0.1 

o.f 

o.i 

O.f 

O.i 

O.J 

0 

0.0 

0.3927 

0.7854 

1.178 

1.570 

1.963 

2.356 

2.748 

3.141 

3.534 

3.927 

4.319 

4.712 

5.105 

5.497 

5.890 

2 

6.283 

6.675 

7.068 

7.461 

7.854 

8.246 

8.639 

9.032 

3 

9.424 

9.817 

10.21 

10.60 

10.99 

11.38 

11.78 

12.17 

4 

12.56 

12.95 

13.35 

13.74 

14.13 

14..52 

14.92 

15.31 

5 

15.70 

16.10 

16.49 

16.88 

17.27 

17.67 

18.06 

18.45 

(i 

18.84 

19.24 

19.03 

20.02 

20.42 

20.81 

21.20 

21.59 

7 

21.99 

22.38 

22.77 

23.10 

23.50 

23.95 

24.34 

24.74 

8 

25.13 

25.52 

25.91 

26.31 

26.70 

27.09 

27.48 

27.88 

9 

28.27 

28.66 

29.05 

29.45 

29.84 

30.23 

30.63 

31.02 

10 

31.41 

31.80 

32.20 

32.59 

32.98 

33.37 

33.77 

34.16 

11 

34.55 

3d  .95 

35.34 

35.73 

36.12 

36.52 

36.91 

37.30 

12 

37.69 

38.09 

38.48 

38.87 

39.27 

39.00 

40.05 

40.44 

13 

40.84 

41.23 

41.62 

42.01 

42.41 

42.S0 

43.19 

43.58 

14 

43.98 

44.37 

44.76 

45.16 

45.55 

45.94 

46.33 

46.73 

15 

47.12 

47.51 

47.90 

48.30 

48.69 

49.08 

49.48 

49.87 

16 

50.26 

50.65 

51.05 

51.44 

51.83 

52.22 

52.62 

53.01 

17 

53.40 

53.79 

51.19 

54.5S 

54.97 

55.37 

55.76 

5G.15 

18 

56.54 

56.94 

57.33 

57.72 

58.11 

58.51 

58.90 

59.29 

19 

59.69 

60.08 

00.47 

60.80 

61.26 

01.05 

02.04 

02.43 

20 

.62.83 

63.22 

63.61 

64.01 

64.40 

04.79 

05.18 

65.58 

21 

65.97 

66.30 

66.75 

67.15 

67.54 

07.93 

08.32 

68.72 

22 

69.11 

69.50 

69.90 

70.29 

70.08 

71.07 

71.47 

71 .86 

23 

72.25 

72.64 

73.04 

73.43 

73.82 

74.22 

74.61 

75.00 

24 

75.39 

75.79 

76.18 

76.57 

76.96 

77.36 

77.75 

78.14 

25 

78.54 

78.93 

79.32 

79.71 

80.10 

80.50 

80.89 

81.28 

26 

81.68 

82.07 

82.40 

82.85 

83.25 

83.04 

84.03 

84.43 

27 

84.82 

85.21 

85.60 

86.00 

86..39 

80.78 

87.17 

87.57 

28- 

87.96 

88.35 

88.75 

89.14 

89.53 

89.92 

90.32 

90.71 

29 

91.10 

91.49 

91.89 

92.28 

92.67 

93.00 

93.46 

93.85 

30 

94.24 

94.64 

95.03 

95.42 

95.&1 

96.21 

96.60 

96.99 

31 

97.39 

97.78 

c 

8.17 

98. .57 

93.96 

99.35 

99.75 

100.14 

32 

100.53 

100.92 

IC 

11.32 

101.71 

102.10 

102.49 

102.89 

103.29 

33 

103.67 

104.07 

1( 

)4.46 

104.85 

105.24 

105.64 

100.03 

106.42 

34 

106.81 

107.21 

1( 

)7.60 

107.99 

10S.39 

108.78 

109.17 

109..''>6 

35 

109.96 

110.35 

11 

0.74 

111.13 

111.53 

111.92 

112.31 

112.71 

36 

113.10 

113.49 

1 

3.88 

114.28 

114.67 

115.06 

115.45 

115.85 

37 

110.24 

110.63 

1 

17.02 

117.42 

117.81 

118.20 

118.00 

118.99 

38 

119.38 

119.77 

\i 

>0.17 

120.56 

120.95 

121.34 

121.74 

122.13 

39 

122.52 

122.92 

V. 

>3.31 

123.70 

124.09 

124.49 

124.88 

125.27 

40 

125.66 

126.06 

V. 

^6.45 

126.84 

127.24 

127.63 

128.02 

128.41 

41 

128.81 

129.20 

129.59 

129.98 

130.38 

130.77 

131.16 

131.55 

12 

131.95 

132.34 

132.73 

133.13 

133.52 

133.91 

134.30 

134.70 

43 

135.09 

135.48 

135.87 

136.27 

130.66 

137.05 

137.45 

137.84 

44 

"  138.23 

138.62 

139.02 

139.41 

139.80 

140.19 

140.59 

140.98 

45 

141.37 

141.70 

142.16 

142.55 

142  94 

143.34 

143.73 

144.12 

Table  of  Areas  and  Circumferences  of  Circles 


51 


Areas  and  Circumferences  of  Circles 

From  1  to  50  Feet 

Advancing  by  one  inch 


Diam., 

Area, 

Circum., 

Diam., 

Area, 

Circum., 

Diam., 

Area, 

Circum., 

ft  in 

sqft 

ft 

in 

ft  in 

sqft 

ft    in 

ft  in 

sqft 

ft    in 

1    0 

0.7854 

3 

m 

5    0 

1^.635 

15    8H 

9    0 

63.6174 

28    -^H 

1 

0.9217 

3 

m 

1 

20.2947 

15  IIH 

1 

64.8006 

28    63/ 

2 

1.069 

3 

8 

2 

20.9656 

16    234 

2 

65.9051 

28    9/2 

3 

1.2271 

3 

11 

3 

21.6475 

16    5H 

3 

67.2007 

29      /8 

4 

1.3962 

4 

21/8 

4 

22.34 

16    9 

4 

68.4166 

29    33/1 

0 

1.5761 

4 

5% 

5 

23.0437 

17      Vs 

5 

69.644 

29    7 

6 

1.7671 

4 

SV2 

6 

23.7583 

17    31/ 

6 

70.8823 

29  101/ 

7 

1.9689 

4  im 

7 

24.4835 

17    6/8 

7 

72.1309 

30    VA 

8 

2.1816 

5 

2% 

8 

25.2199 

17  m 

8 

73.391 

30    43/ 

9 

2.4052 

5 

5'A 

9- 

25.9672 

18      H 

9 

74.662 

30    7/. 

10 

2.6398 

5 

9 

10 

26.7251 

18    '6'A 

10 

75.9433 

30  11/A 

11 

2.8852 

6 

H 

11 

27.4943 

18    7A 

11 

77.2362 

31     iM 

2    0 

3.1416 

6 

3-% 

6    0 

28.2744 

18  lOH 

10    0 

78.54 

31    5 

1 

3.4087 

6 

m 

1 

29.0649 

19  m 

1 

79.854 

31    8H 

2 

3.6869 

6 

m 

2 

29.8668 

19    43/8 

2 

81.1795 

31  111/ 

3 

3.976 

7 

H 

3 

30.6796 

19  ly^ 

3 

82.516 

32    23/^ 

4 

4.276 

7 

VA 

4 

31.5029 

19  lOH 

4 

83.8627 

32    5I/2 

5 

4.5869 

7 

7 

5 

32.3376 

20    VA 

5 

85.2211 

32    8% 

6 

4.9087 

7  101/4  1 

6 

33.1831 

20    4% 

6 

86.5903 

32  ll/i 

7 

5.2413 

8 

13/8 

7 

34.0391 

20    81.^ 

7 

87.9697 

33    2/8 

8 

5.585 

8 

41/2 

8 

34.9065 

20  11/2 

8 

89.3638 

33    61/ 

9 

5.9335 

8 

7/8 

9 

35.7847 

21    2% 

9 

90.7627 

33    91/i 

10 

6.3349 

8 

103/4 

10 

36.6735 

21    5/2 

10 

92.1749 

34      34 

11 

6.6813 

9 

1/8 

11 

37.5736 

21    8% 

11 

93.5986 

34    3>12 

3    0 

7.0686 

9 

5 

7    0 

38.4846 

21  11^^ 

11    0 

95.0334 

34    65/ 

1 

7.4666 

9 

m 

1 

39.406 

22    3 

1 

96.4783 

34    93/ 

2 

7.8757 

9 

113/s 

2 

40.3388 

22    61/^ 

2 

97.9347 

35      % 

3 

8.2957 

10 

2/2 

3 

41.2825 

22    m 

3 

99.4021 

35    41/8 

4 

8.7265 

10 

5'H 

4 

42.2367 

23      Ys 

4 

100.8797 

35    71/4 

5 

9.1683 

10 

83/ 

5 

43.2022 

23    2H 

5 

102.3689 

35  105/8 

6 

9.6211 

10  im  1 

6 

44.1787 

23    634 

6 

103.8691 

36    1/2 

7 

10.0846 

11 

3 

7 

45.1656 

23    9U 

7 

105.3794 

36    4/2 

8 

10.5591 

11 

m 

,8 

46.1638 

24  m 

8 

106.9013 

36    734 

9 

11.0446 

11 

^% 

9 

47.173 

24  m 

9 

108.4342 

36  107/ 

10 

11.5409 

12 

/2 

10 

48.1962 

24    7/4 

10 

109.9772 

37    23/ 

11 

12.0481 

12 

Z^A 

11 

49.2236 

24  10->i 

11 

111.5319 

37    51/ 

4    0 

12.5664 

12 

63/ 

8    0 

50.2656 

25    VA 

12    0 

113.0976 

37    8% 

1 

13.0952 

12 

97^6 

1 

51.3178 

25  m 

1 

114.6732 

37  111/ 

2 

13.6353 

13 

1 

2 

52.3816 

25    7% 

2 

116.2607 

38    2Vs 

3 

14.1862 

13 

f/f 

3 

53.4562 

25  11 

3 

117.859 

38    53,4 

4 

14.7479 

13 

73'4 

4 

54.5412 

26    2M 

4 

119.4674 

38    8^i 

5 

15.3206 

13 

10/2 

5 

55.6377 

26    51/ 

5 

121.0876 

39    0 

6 

15.9043 

14 

\% 

6 

56.7451 

26    83^ 

6 

122.7187 

39    31^4 

7 

16.4986 

14 

m 

7 

57.8628 

26  11/2 

7 

124.3598 

39    63/^ 

8 

17.1041 

14 

■7% 

8 

58.992 

27    234 

8 

126.0127 

39    91/2 

9 

17.7205 

14 

11 

9 

60.1321 

27    53/ 

9 

127.6765 

40      % 

10 

18.3476 

15 

2H 

10 

61.2826 

27    9 

10 

129.3504 

40    33/ 

11 

18.9858 

15 

5H 

11 

62.4445 

28      H 

11 

131.036 

40  m 

62 


Geometry  and  Mensuration 
Areas  and  Circumferences  of  Circles  (Continued) 


Part 


Diam., 
ft  in 


Area, 
sq  ft 


Circum. 
ft    in 


13  0 
1 
2 
3 
4 
5 
6 
7 


9 
10 
11 

15  0 
1 
2 
3 
4 
5 


9 
10 
11 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 

J  0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

10 
11 


132.7326 

134.4391 

136.1574 

137.886; 

139.626 

141.3771 

143.1391 

144.9111 

146.6949 

148.4896 

150.2943 

152.1109 

153.9384 

155.7758 

157.625 

159.4852 

161.3553 

163.2373 

165.1303 

167.0331 

168.9479 

170.8735 

172.8091 

174.7565 

176.715 

178.6832 

180.6634 

1^2.6545 

184.6555 

186.6684 

188.6923 

190.726 

192.7716 

194.8282 

196.8946 

198.973 

201.0624 

203.1615 

205.2726 

207.3946 

209.5264 

211.6703 

213.8251 

215.9896 

218.1662 

220.3537 

222.551 

224.7608 

226.9806 

229.2105 

231.4525 

233.7055 

235.9682 

238.243 

240.5287 

242.8241 

245.1316 

247.45 

249.7781 

252.1184 


10 

IH 

m 

71/2 

lOH 
IH 

m 

8 

2H 

5^2 


Diam. 
ft   in 


43  113/4 

44  27/i 
44  6 

44  9H 

45  1/4 
45  3^2 

45  6H 

45  m 

46  '^A 
46    4 

46  7\i 

46  im 

47  11/2 

47  m 

47    7^4 

47  103^^ 

48  2^2 
48    51/8 

48  81/4 

48  im 

49  2H 
49    5-)4 

49  S% 

50  0 

50    'ZH 

50  61/4 

50  m 

51  1/2 
51  33/4 
51    61/2 

51  10 

52  IH 
52  41/4 
52    7% 

52  WA 

53  m 

53  47/i 

53  8 

53  im 

54  2H 
54  53/8 
54    81/2 

54  IIH 

55  2% 
55    6 

55  9H 

56  1/4 
56    3^2 


Area, 
sq  ft 


9 
10 
11 

20  0 
1 
2 
3 
4 
5 
6 
7 

•  8 
9 

10 
11 

21  0 
1 
2 
3 
4 
5 
6 
7 


Circum., 
ft    in 


254.4606 
256.8303 
259.2033 
261.5872 
263.9807 
266.3864 
268.8031 
271.2293 
273.6678 
276.1171 
278.5761 
281.0472 

283.5294 

286.021 

288.5249 

291.0397 

293.5641 

296.1107 

298.6483 

301.2054 

303.774: 

306.355 

308.9448 

311.5469 

314.16 

316.7824 

319.4173 

322.063 

324.7182 

327.3858 

330.0643 

332.7522 

335.4525 

338.1637 

340.8844 

343.6174 

346.3614 
349.1147 
351.8804 
354.6571 
357.4432 
360.2417 
363.0511 
365.8608 
368.7011 
371.5432 
374.3947 
377.2587 

380.1336 

383.0177 

385.9144 

388.822 

391.7389 

394.6683 

397.6087 

400.5583 

403.5204 

406.4935 

409.4759 

412.4707 


56  m 

56  9H 

57  li 
57    4 

57    71/^ 

57  101/4 

58  m 

58  41/^2 

58  75/8 

58  mi 

59  2 

59    5H 

59  81/4 

59  nvz 

6D    2H2 

60  5H 

60  83/4 

60  im 

31/8 


Diam. 
ft  in 


91/^2 


62  m 

63  m 

63  41/4 

63  7% 

63  IV/z 

64  m 

64  43/4 
64  71^ 

64  11 

65  21/4 
65  5-^8 
65  8M 

65  mi 


2% 


Z% 


7 
lOH 

1^8 
4^2 

7-^8 

1034 

m 
5 

81/4 

im 

2M2 

5-H 
8^4 


23 


Area, 
sq  ft 


9 
10 
11 

24  0 
1 
2 
3 
4 


6 

7 
8 
9 

10 
11 

I  0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 

0 
1 

2 
3 
4 
5 
6 
7 


26 


Circum., 
ft    in 


10 
11 

27  0 
'  1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 


415.4766 
418.4915 
421.5192 
424.5577 
427.6055 
430.6658 
433.7371 
436.8175 
439.9106 
443.0146 
446.1278 
449.2536 

452.3904 
455.5362 
458.6948 
461.8642 
465.0428 
468.2341 
471.4363 
474.6476 
477.8716 
481.1065 
484.3506 
487.6073 

490.875 

494.1516 

407.4411 

500.7415 

504.051 

507.3732 

510.7063 

514.0484 

517.4034 

520.7692 

524.1441 

527.5318 

530.9304 

534.3379 

537.7583 

541.1896 

.541.6299 

548.083 

551.5471 

555.0201 

558.5059 

562.0027 

565.5084 

569.027 

572.5566 

576.0949 

579.6463 

583.2085 

586.7796 

590.3637 

593.9587 

597.5625 

601.1793 

604.807 

608.4436 

612.0931 


72  3 

72  m 

72  m 

73  1/^ 
73  3H 
73  6^4 

73  97/i 

74  1 

74  m 

74  7!.4 


Table  of  Areas  and  Circumferences  of  Circles 


53 


W: 

Areas  and 

Circumferences  of  Circles 

(Continued) 

Diam., 

Area, 

Circum., 

Diam., 

Area, 

Circum., 

Diam., 

Area, 

Circum..  1 

ft  in 

sqft 

ft    in 

ft   in 

sqft 

ft 

in 

ft  in 

sqft 

ft 

in 

28    0 

615.7536 

87  111/2 

33    0 

855.301 

103 

8 

38    0 

1134.118 

119 

4/2 

619.4228 

88    2?/8 

1 

859.624 

103 

11/8 

1 

1139.095 

119 

7% 

2 

623.105 

88    5H 

2 

863.961 

104 

2/1 

2 

1144.087 

119 

10:>4 

3 

626.7982 

88    9 

3 

868.309 

104 

53/6 

3 

1149.089 

120 

2 

4 

630.5002 

89      Vs 

4 

872.665 

104 

8% 

4 

1154.110 

120 

5% 

5 

634.2152 

89    ZH 

5 

877.035 

104 

11>4 

5 

1159.124 

120 

8% 

6 

637.9411 

89  m 

6 

881.415 

105 

2% 

6 

1164.159 

120 

11% 

7 

641.6758 

89    dy> 

-7 

885.804 

105 

6 

7 

1169.202 

121 

21/2 

8 

645.4235 

90      Ys 

8 

890.206 

105 

9/8 

8 

1174.259 

121 

5% 

9 

649.1821 

90    Wi 

9 

894.619 

100 

H 

9 

1179.327 

121 

SH 

10 

652.9495 

90   m 

10 

899.041 

106 

3/8 

10 

1184.403 

121 

11/8 

11 

656.73 

90  11 H 

11. 

903.476 

106 

6% 

11 

1189.493 

122 

3/8 

29    0 

660.5214 

91  m 

34    0 

907.922 

106 

m 

39    0 

1194.593 

122 

61/4 

1 

604.3214 

91    m 

1 

912.377 

107 

% 

1 

1199.719 

122 

9/2 

2 

668.1346 

91    7^2 

2 

910.844 

107 

4 

2 

1204.824 

123 

/2 

3 

671.9587 

91  lOVs 

3 

921.323 

107 

71/i 

3 

1209.958 

123 

3% 

4 

675.7915 

92  vn 

4 

925.810 

107 

10/ 

4 

1215.099 

123 

644 

5 

679.6375 

92    4'/8 

5 

930. 3 n 

108 

1/8 

5 

1220.254 

123 

9% 

6 

683.4943 

92    S\i 

6 

934.822 

108 

4% 

6 

1225.420 

124 

1% 

7 

687.3598 

92  1114 

7 

939.342 

108 

7U 

7 

1230.594 

124 

4/ 

8 

691.2385 

93    2% 

8 

943.875 

108  lO/s 

8 

1235.782 

124 

7% 

9 

695.1028 

93    5/2 

9 

948.419 

109 

2 

9 

1240.981 

124  10/2 

10 

699.0263 

93    8>^ 

10 

952.972 

109 

oH 

10 

1246.188 

125 

1% 

11 

702.9377 

93  11^^ 

11 

957.538 

109 

834 

11 

1251.408 

125 

43/4 

30    0 

706.86 

94    2% 

35    0 

962.115 

109  11% 

40    0 

1256.64 

125 

7% 

1 

710.791 

94    6 

1 

966.770 

110 

2/8 

1 

12G1.879 

125 

11 

2 

714.735 

94  m 

2 

971.299 

110 

534 

2 

1267.133 

126 

2/ 

3 

718.69 

95      % 

3 

975.908 

110 

8% 

3 

1272. 39Z 

126 

53  6 

4 

722.654 

95    3/2 

4 

980.526 

111 

0 

4 

1277.669 

126 

8J-2 

5 

726.631 

95    (j-}i 

5 

985.158 

111 

3V8 

5 

1282.955 

126 

11% 

6 

730.618 

95  m 

6 

989.803 

111 

m 

6 

1288.252 

127 

2-)4 

7 

734.615 

96      % 

7 

994.451 

111 

9% 

7 

1293.557 

127 

5-^8 

8 

738.624 

96    4 

8 

999.115 

112 

1,.', 

8 

1298.876 

127 

9 

9 

742.645 

96    7/i 

9 

1003.79 

112 

SVi 

9 

1304.206 

128 

H 

10 

746.674 

96  10% 

10 

1008.473 

112 

6J/S 

10 

1309.543 

128 

3% 

11 

750.716 

97    V/2 

11 

1013.170 

112 

10 

11 

1314.895 

128 

6/2 

31    0 

754.769 

97  m 

36    0 

1017.878 

113 

1/s 

41    0 

1320.257 

128 

9% 

1 

758.831 

97    7H 

.     1 

1022.594 

113 

4/ 

1 

1325.628 

129 

H 

2 

762.906 

97  10/8 

2 

1027.324 

113 

7/8 

2 

1331.012 

129 

3% 

3 

766.992 

98    2 

3 

1032.004 

113  10/8 1 

3 

1336.407 

129 

7 

4 

771.086 

98    514 

4 

1036.813 

114 

m 

4 

1341.810 

129  10%  1 

5 

775.191 

98    8->8 

5 

1041.570 

114 

4/8 

5 

1347.227 

130 

m 

6 

779.313 

98  11/2 

6 

1040.349 

114 

8 

6 

1352.655 

130 

^Vi 

7 

783.440 

99    2H 

7 

1051.130 

114  ll/sl 

7 

1358.091 

130 

7% 

8 

787.581 

99    5% 

8 

1055.920 

115 

2H 

8 

1303.541 

130  10^4   I 

9 

791.732 

99    8/8 

9 

1060.731 

115 

5% 

9 

1369.031 

131 

1% 

10 

795.892 

100    0 

10 

1065.546 

115 

9/1 

10 

1374.47 

131 

5 

11 

800.065 

100    3H 

11 

1070.374 

115  11% 

11 

1379.952 

131 

8% 

32    0 

804.25 

100    6M 

37    0 

1075.2126 

116 

2% 

42    0 

1385.446 

131 

11% 

1 

808.442 

100  •  9/2 

1 

1080.059 

116 

6 

1 

1390.247 

132 

2/2 

2 

812.648 

101      H 

2 

1084.920 

116 

9/8 

2 

1336.462 

132 

6% 

3 

816.865 

101    3% 

3 

1089.791 

117 

M 

3 

1401.988 

132 

83/4 

4 

821.090 

101    6/8 

4 

1094.671 

117 

3/2 

4 

1407.522 

132 

11% 

5 

825.329 

101  10 

5 

1099.504 

117 

6/2 

5 

1413.07 

133 

3 

6 

829.579 

102    IH 

6 

1104.409 

117 

9/8 

6 

1418.629 

133 

6% 

7 

833.837 

102    4% 

7 

1109.381 

118 

% 

7 

1424.195 

133 

9H 

8 

838.108 

102    7/2 

8 

1114.307 

118 

4 

8 

1429.776 

134 

/2 

9 

842.391 

102  lOH 

9 

1119.244 

118 

7\i 

9 

1435.367 

134 

3% 

10 

846.681 

103  m 

10 

1124.189 

118  lOWl 

10 

i440.967 

134 

63/4 

11 

850.985 

103    4^^ 

11 

1129.148 

119 

1% 

11 

1446.580 

134 

9% 

54 


Geometry  and  Mensuration 
Areas  and  Circumferences  of  Circles  (Continued) 


Diam., 
ft  in 

Area, 
sqft 

Circum., 
ft    in 

Diam., 
ft  in 

.  Area, 
sq  ft 

Circum., 
ft    in 

Diam., 
ft  in 

Area, 
sqft 

Circum., 
ft    in 

43 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

10 
11 

1452.205 

1457.836 

1463.483 

1469.14 

1474.804 

1480.483 

1486.173 

1491.870 

1497.582 

1503.305 

1509.035 

1514.779 

135    1 

135    4H 
135    IM 

135  lOi--^ 

136  15/8 

136    4}4 
136    7% 

136  11 

137  2% 
137    5H 
137    8M 
137  11^ 

46    0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 

1661.906 

1667.931 

1673.97 

1680.02 

1686.077 

1692.148 

1698.231 

1704.321 

1710.425 

1716.541 

1722.663 

1728.801 

144  m 

144  9H 

145  % 
145    3 1/2 
145    65^ 

145  97.^ 

146  11/^ 
146    41/i 
146    71/ 

146  10)i 

147  ly-z 
147    4^i 

49    0 
1 
2 
3 
4 

7 
8 
9 
10 
11 

1885.745 
1892.172 
1898.504 
1905.037 
1911.497 
1917.961 
1924.426 
1930.919 
1937.316 
1943.914 
1950.439 
1956.969 

153  IIH 

154  2H 
154    51/2 
154    8H 

154  1174 

155  2^8 
155    6 

155  914 

156  i/i 
156    31/i 
156    6H 
156    9M 

44 
45 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 

1520.534 
1526.297 
1532.074 
1537.862 
1543.558 
1549.478 
1555.288 
1561.116 
1566.959 
1572.812 
1578.673 
1584.549 

1590.435 
1596  32j 
1602.237 
X608.155 
1614.082 
1020.023 
1625.974 
1G31.933 
1G37.907 
1G43.801 
1649.883 
1655.889 

138    2-K 
138    5^ 

138  9 

139  \i 
139    314 
139    6H 

139  9^ 

140  % 
140    VA 
140   iy2 

140  10 ^ 

141  IH 

141  m 

141    IM 

141  1024 

142  VA 
142    5 

142  •  m 

142  n\i 

143  2'>i 
143    51/2 
143    8% 

143  11^^ 

144  3 

47  0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

10 
11 

48  0 
1 
2 
3 
4 
5 
6 
7 
8 
9 

10 
11 

1734.947 
1741.104 
1747.274 
1753.455 
1759.643 
1785.845 
1772.059 
1778.28 
1784.515 
1700.761 
1797.015 
1803.283 

1809.562 
1815.848 
1822.149 
1828.460 
1834.779 
1841.173 
1847.457 
1853.809 
1860.175 
1866.552 
1872.937 
1879.335 

147 
147 

148 
148 
148 
148 
149 
149 
149 
loOfe 
150 
150 

150 
151 
151 
151 
151 
152 
152 
152 
152 
153 
153 
153 

m 
11 

21/^ 
5H 
83^ 

111/2 

2% 

m 
31/1 

% 

lOi/i 

m 
m 

IVi 
lOH 

p/ 

81/i 

50    0 

1963.5 

157 

''A 

Circular  Arcs 

To  find,  by  the  following  table,  the  length  of  a  circular  arc  when  its  chord  and 
height,  or  versed  sine  is  given. 

Rule.  Divide  the  height  by  the  chord;  find  in  the  column  of  heights  the 
number  equal  to  this  quotient;  take  out  the  corresponding  number  from  the 
cokimn  of  lengths;   and  multiply  this  number  by  the  given  chord. 

Example.  The  chord  of  an  arc  is  80  and  its  versed  sine  is  30.  What  is  the 
length  of  the  arc? 

Solution.  30H-  80=  0.375.  The  length  of  an  arc  for  a  height  of  0.375  i^i 
from  table,  1.34063.    80  X  1.34063  =  107.2504=  length  o'f  arc. 


Table  of  Circular  Arcs 


Table  of  Circular  Arcs 


Hts 


.001 

.00? 

.003 

.004 

.005 

.000 

.007 

.008 

.009 

.010 

.011 

.012 

.013 

.014 

.015 

.016 

.017 

.018 

.019 

.020 

.021 

.022 

.023 

.024 

.025 

.026 

.027 

.028 

.029 

.030 

.031 

.032 

.033 

.034 

.035 

.036 

.037 

.038 

.039 

.040 

.041 

.042 

.043 

.044 

.045 

.046 

.047 

.048 

.049 

.050 

.051 

.052 

.053 

.054 

.055 

.056 

.057 

.058 

.059 

.060 

.061 


Lengths 


1.00001 

1.00001 

1.00002 

1.00004 

1.00007 

1.00010 

1.00013 

1.00017 

1.00022 

1.00027 

1.00032 

1.00038 

1.00015 

1.00053 

1.00061 

1.00069 

1.00078 

1.000S7 

1.00097 

1.00107 

1.00117 

1.00128 

1.00140 

1.00153 

1.00167 

1.001S2 

1.00196 

1.00210 

]  .00225 

1.00240 

1.00256 

1.00272 

1.00289 

1.00307 

1.00327 

1.00345 

1.00304 

1.00384 

1.00405 

1.00426 

1.00447 

1.00469 

1.00492 

1.00515 

1.00539 

1.00563 

1.00587 

1.00612 

1.00638 

1.00665 

1.00692 

1/  3720 

1.00748 

1.00776 

1.00805 

1.00834 

1.00864 

1.00S95 

1.00026 

1.00957 

1.00989 


Hts  I-engths  Hts  Length,' 


.002 

.063 

.064 

.065 

.066 

.067 

.068 

.009 

.070 

.071 

.072 

.073 

.074 

.075 

.076 

.077 

.078 

.079 

.080 

.081 

.082 

.083 

.084 

.085 

.086 

.087 

.088 

.089 

.000 

.091 

.092 

.093 

.09^ 

.095 

.096 

.097 

.098 

.099 

.100 

.101 

.102 

.103 

.104 

.105 

.106 

.107 

.108 

.109 

.110 

.111 

.112 

.113 

.114 

.115 

.116 

.117 

.118 

.119 

.120 

.121 

.122 


1.01021 

1.01054 

1.01088 

1.01123 

1.01158 

1.01193 

1.01228 

1.01264 

1.01.301 

1.01338 

1.01376 

1.01414 

1.01453 

1.01493 

1.01533 

1.01573 

1.01614 

1.01656 

1.0169S 

1.01741 

1.01784 

1.01828 

1.01872 

1.01916 

1.01961 

1.02006 

1.02052 

1.02098 

1.02145 

1.02192 

1.02240 

1.02289 

1.02339 

1.02389 

1.02440 

1.02491 

1.02542 

1.02593 

1.02645 

1.02698 

1.02752 

1.02806 

1.02860 

1.02914 

1.02970 

1.03026 

1.03082 

1.03139 

1.03196 

1.03254 

1.03312 

1.03371 

1.03430 

1.03490 

1.03551 

1.03611 

1.03672 

1.03734 

1.03797 

1.03860 

1.03923 


.123 

.124 

.125 

.126 

.127 

.128 

.129 

.130 

.131 

.132 

.133 

.134 

.135 

.136 

.137 

.138 

.139 

.140 

.141 

.142 

.143 

.144 

.145 

.146 

.147 

.148 

.149 

.150 

.151 

.152 

.153 

./54 

.155 

.156 

.157 

.158 

.159 

.160 

.161 

.162 

.163 

.164 

.165 

.166 

.167 

.168 

.169 

.170 

.171 

.172 

.173 

.174 

.175 

.176 

.177 

.178 

.179 

.180 

.181 

.182 

.183 


1.039S7 

1.04051 

l.Ollir 

1.041S1 

1.04247 

1.04313 

1.04.380 

1.04447 

1.04515 

1.04584 

1.04652 

1.04722 

1.04792 

1.04802 

1.04932 

1.05003 

1.05075 

1.05147 

1.05220 

1.05293 

1.05367 

1.05441 

1.05516 

1.05591 

1.05667 

1.05743 

1.05819 

1.05896 

1.05073 

1.00051 

1.06 ISO 

1.00200 

1 .06288 

1.06368 

1.06449 

1.06530 

1.06611 

1.06693 

1.06775 

1.068-58 

1.06941 

1.07025 

1.07109 

1.07194 

1.07279 

1.07365 

1.07451 

1.07537 

1.07624 

1.07711 

1.07799 

1.07888 

1.07977 

1.08066 

1.08156 

1.08246 

1.08337 

1.08428 

1.08519 

1.08611 

1.08704 


Hts  Lengths  Hts  Lengths 


.184 

.185 

.186 

.187 

.188 

.189 

.100 

.191 

.192 

!i93 

.194 

.195 

.196 

.197 

.198 

.199 

.200 

.201 

.202 

.203 

.204 

.205 

.206 

.207 

.208 

.209 

.210 

.211 

.212 

.213 

.214 

.215 

.216 

.217 

.218 

.219 

.220 

.221 

.222 

.223 

.224 

.225 

.226 

.227 

.228 

.229 

.230 

.231 

.232 

.233 

.234 

.235 

.236 

.237 

.238 

.239 

.240 

.241 

.242 

.243 

.244 


1.08797 

1.08890 

1.08984 

1 .09079 

1.09174 

1 .09269 

1.09365 

1.09461 

1.09557 

1.09654 

1.09752 

1.098.50 

1.09949 

1.10048 

1.10147 

1.10247 

1.10347 

1.10447 

1.10548 

1.10650 

1.10752 

1.10S55 

1.10958 

1.11062 

1.11165 

1.11269 

1.11374 

1.11479 

1.11584 

1.11690 

1.11796 

1.11904 

1.12011 

1.12118 

1.12225 

1.12334 

1.12444 

1.12554 

1.12664 

1.12774 

1.12885 

1.12997 

1.13108 

1.13219 

1.133S1 

1.13444 

1.13557 

1.13671 

1.13785 

1.13900 

1.14015 

1.14131 

1.14247 

1.14363 

1.14480 

1.14.597 

1.14714 

1.14832 

1.14951 

1.15070 

1.15189 


.245 

.246 

.247 

.248 

.249 

.250 

.251 

.252 

.253 

.254 

.255 

.256 

.257 

.258 

.259 

.260 

.261 

.262 

.263 

.204 

.265 

.266 

.267 

.268 

.269 

.270 

.271 

.272 

.273 

.274 

.275 

.'>76 

.277 

.278 

.279 

.280 

.281 

.282 

.283 

.284 

.285 

.286 

.287 

.288 

.289 

.290 

.291 

.292 

.293 

.291 

.295 

.296 

.297 

.298 

.299 

.200 

.301 

.302 

.303 

.304 

.305 


1.15308 
1.15428 
1.15549 
1.15670 
1.15791 
1.15912 
1.16034 
1.16156 
1.16279 
1.16402 
1.16526 
1.16650 
1.16774 
1.16899 
1.17024 
1.17150 
1.17276 
1.17403 
,  1.17530 
I  1.17657 
1.17784 
1.17912 
1.18040 
1.18169 
1.18299 
1.18429 
1.18559 
1.18689 
1.18820 
1.18951 
1.19082 
1.19214 
1.19346 
1.19479 
1.19612 
1.19746 
1.19880 
1.20014 
1.20149 
1.20284 
1.20419 
1.205.55 
1.20691 
1.20827 
1.20964 
1.21102 
1.21239 
1.21377 
1.2;515 
1.2/654 
1.21794 
1.21933 
1.22073 
1.22213 
1.22354 
1.22495 
1.22636 
1.22778 
1.22920 
1.23063 
1.23206 


56 


Geometry  and  Mensuration 


Part  1 


Table  of  Circular  Arcs  (Continued) 


His 

Lengths 

[its 

Lengths 

1.29209 
1.29366 

Hts 

[(Cngths 

Hts 

Lengi-hs 

Hts 

[icngths 

.30fi 
.307 

1.23349 
1  23492 

.345 
.346 

384 

1.35575 

.423 
.424 

1.42402 

1.425S3 

.462 
.463 

1.49051 
1.49842 

.385 

1.35744 

!308 

1.23036 

.347 

1.29523 

.386 

1.35914 

.425 

1.42704 

.464 

1.50033 

!309 

1.23781 

.348 

1.29681 

.387 

1.36084 

.426 

1.42945 

.465 

1.50224 

.310 

1.23926 

.349 

1 .29839 

.388 

1.36254 

.427 

1.43127 

.460 

1.50416 

!311 

1.24070 

.350 

1.29997 

.389 

1.36425 

.428 

1.43309 

.4()7 

1.501)08 

.312 

1.24216 

.351 

1.30156 

.390 

1.36596 

.429 

1.43491 

.468 

1.50,i00 

!313 

1.24301 

.35-^ 

1.30315 

.391 

1.36767 

.430 

1.43673 

.409 

1.50992 

!314 

1 .24507 

.353 

1.30474 

.392 

1.36939 

.431 

1.43850 

.470 

1.51185 

!315 

1.24654 

.354 

1.30634 

.393 

1.37111 

.432 

1 .44039 

.471 

1.51378 

.316 

1.24801 

.355 

1.30794 

.394 

1.37283 

.433 

1.44222 

.472 

1.51571 

!317 

1.2494S 

.356 

1.30954 

.395 

1.37455 

.434 

1.44405 

.473 

1.51764 

318 

1.25095 

.357 

1.31115 

.396 

1.37628 

.435 

1.44589 

.474 

1.51958 

.319 

1.25243 

.358 

1.31276 

.397 

1.87801 

.436 

1.44773 

.475 

1.52152 

320 

1.25391 

.359 

1.31437 

.398 

1.37974 

.437 

1.44957 

.476 

1.52340 

.321 

1  25540 

.360 

1.31599 

.399 

1.38148 

.438 

1.45142 

.477 

1.52541 

322 

1.25689 

.301 

1.31701 

.400 

1.38322 

.439 

1.45327 

.478 

1.52736 

.323 

1  '->5838 

.362 

1.31923 

.401 

1.38496 

.440 

1.15512 

.479 

1.52931 

!324 

1.25988 

.363 

l.?2086 

.402 

1.38671 

.441 

1.45697 

.480 

1.53126 

325 

1.26138 

.364 

1.32249 

.403 

1.38846 

.442 

1.45883 

.481 

1.53322 

.320 

1 .26288 

.365 

1.32413 

.404 

1.39021 

.443 

1.46069 

.482 

1.53518 

327 

1 .26437 

.366 

1.32577 

.405 

1.39196 

.444 

1 . t6255 

.483 

1.53714 

.328 

1.26588 

.307 

1.32741 

.406 

1.39372 

.445 

1.46441 

.484 

1.53010 

329 

1.26740 

.368 

1.32905 

.407 

1.39548 

.446 

1.46621 

.485 

1.54106 

.330 

1.26892 

.369 

1.33069 

.408 

1.30724 

.447 

1.46815 

.486 

1.54302 

.331 

1 .27044 

.370 

1.33234 

.409 

1.39900 

.448 

1.47002 

.487 

1.54499 

332 

1.27196 

.371 

1.33309 

.410 

1.40077 

.449 

1.471S9 

.488 

1 .54696 

.333 

1.27349 

.372 

1.33564 

.411 

1.40254 

.450 

1.4737V 

.489 

1.54893 

.334 

1.27502 

.373 

1.33730 

.412 

1.40432 

.451 

1.47565 

.490 

1.55091 

.335 

1.27656 

.374 

1.33S96 

.413 

1.40G10 

.452 

1.47753 

.491 

1.55289 

.336 

1.2:^810 

.375 

1.34063 

.414 

1.40788 

.453 

1.47942 

.492 

1.554S7 

.337 

1.27964 

.376 

1.34229 

.415 

1.40900 

.454 

1.48131 

.493 

1.55685 

.338 

1.2811S 

.377 

1.34396 

.416 

1.41145 

.455 

1.48320 

.491 

1.55884 

.339 

1.28273 

.378 

1.34563 

.417 

1.41324 

.456 

1.48509 

.495 

1.56083 

.340 

1.28428 

.379 

1.34731 

.418 

1.41503 

.457 

1.48699 

.490 

1 .56282 

341 

1.28583 

.380 

1 .34899 

.419 

1.41682 

.458 

1.48880 

.407 

1.56481 

.342 

1.28739 

.381 

1.35068 

.420 

1.41861 

.459 

1 .4.9070 

.498 

1.56681 

343 

1 .28895 

.382 

1.35237 

.421 

1.42041 

.460 

1 .49269 

.409 

1 .56881 

.344 

1.29052 

.383 

1.35400 

.422 

1.42221 

.461 

1.49460 

.500 

1 .57080 

Table  of  Lengths  of  Circular  Arcs  whose  Radius  is  i 

Rule.  Knowing  the  measure  of  the  circle  and  the  measure  of  the  arc  in  degrees 
minutes  and  seconds;  take  from  the  table  the  lengths  opposite  the  number  o 
degrees,. minutes  and  seconds  in  the  arc,  and  muUiply  their  sum  by  the  radius  o 
the  circle. 

Example.    AVhat  is  the  length  of  an  arc  subtending  an  angle  of  13°  27'  8> 

with  a  radius  of  8  ft. 

Solution.     Length  for  13°  =  0.2268928 

27'  =  0.0078540 

8"  =  0.0000388 

13°  27'  8"=  0.2347856 


Length  of  arc    =  i  .8782848  ft 


Table  of  Circular  Arcs 


57 


Lengths 

of  Circular  Arcs. 

Radius  = 

E 

Sec 
1 

Length 
n. 0000048 

Min 

Length, 

Deg 

Length 

Deg 

Length 

1 

0.0002909 

1 

0.0174533 

61 

1.0646508 

2 

0.0000097 

2 

0.0005818 

2 

0.0349066 

62 

1.0821011 

3 

0.0000145 

3 

0.0008727 

3 

0.0523599 

63 

1.0095574 

4 

0.0000194 

4 

0.0011636 

4 

0.069S132 

64 

1.1170107 

5 

0.0000242 

5 

0.0014544 

5 

0.0872665 

65 

1.1314640 

6 

0.0000291 

6 

0.0017453 

6 

0.1047198 

66 

1.1519173 

7 

0.0000339 

7 

0.0020362 

7 

0.1221730 

67 

1.1693706 

8 

0.0000388 

8 

0.0023271 

8 

0.1396263 

68 

1.1868239 

9 

0.0000436 

9 

0.0026180 

9 

0.1570796 

69 

1.2042772 

10 

0.0000485 

10 

0.0029089 

10 

0.1745329 

70 

1.2217305 

11 

0 . 0000533 

11 

0.0031998 

11 

0.1919862 

71 

1.2391838 

12 

0.0000582 

12 

0.0034907 

12 

0.2094395 

72 

1.2566371 

13 

0 . 0000030 

13 

0.0037815 

13 

0.2268928 

73 

1.2740904 

14 

0.0000G79 

14 

0.0040724 

14 

0.2443461 

74 

1.2915436 

15 

0.0000727 

15 

0.0043633 

15 

0.2617994 

75 

1 . 3089969 

IG 

0.0000776 

16 

0.0046542 

16 

0.2792527 

76- 

1 . 3264502 

17 

0.0000^24 

17 

0.0049451 

17 

0.2967060 

77 

1 . 3439035 

18 

0.0000873 

IS 

0.0052360 

18 

0.3141503 

78 

1.3613568 

19 

0.0000921 

19 

0.0055269 

19 

0.3310126 

79 

1.3788101 

20 

0.0000970 

20 

0.0058178 

20 

0.3490659 

80 

1.3962634 

21 

O.OOOIOIS 

21 

0.0061087 

21 

0.3665191 

81 

1.4137167 

22 

0.0001067 

22 

0.0063995 

22 

0.3839724 

82 

1.4311700 

23 

0.0001115 

23 

0.0006904 

23 

0.4014257 

83 

1.4486233 

24 

0.0001164 

24 

0.00G0813 

24 

0.4188790 

84 

1 . 4660766 

25 

0.0001212 

25 

0.0072722 

25 

0.4303323 

85 

1.4835299 

20 

0.0001261 

26 

0.0075631 

26 

0.4537856 

86 

•1.5009S32 

27 

0.0001300 

27 

0.0078540 

27 

0.4712389 

87 

1.5184364 

28 

0.0001357 

28 

0.0081449 

28 

0.4886922 

88 

1.5358897 

29 

0.0001406 

29 

0.00S4358 

29 

0.50614 '5 

89 

1.5533430 

30 

0.0001454 

30 

0.0087266 

30 

0.5235988 

90 

1.5707963 

31 

0.0001503 

31 

0.0090175 

31 

0  5410521 

91 

1.5882496 

32 

0.0001551 

32 

0 . 00930S4 

32 

0.5585054 

92 

1 . 6057029 

33 

0.0001600 

33 

0.0095993 

33 

0.5750587 

93 

1.6231562 

31 

0.0001648 

34 

0.0098902 

34 

0.5934119 

94 

1 . 6406095 

35 

0.0001097 

35 

0.0101811 

35 

0.6108652 

95 

1.6580628 

36 

0.0001745 

36 

0.0101720 

36 

0.6283185 

96 

1.6755161 

37 

0.0001794 

37 

0.0107629 

37 

0.6457718 

97 

1.6929094 

S8 

0.0001842 

38 

0.0110538 

38 

0.6632251 

98 

1.7104227 

39 

0.0001891 

39 

0.0113446 

39 

0.0806784 

99 

1.7278760 

40 

0.0001939 

40 

0.0116355 

40 

0.0981317 

100 

1.7453293 

41 

0.0001988 

41 

0.0119264 

41 

0.7155850 

101 

1.7627825 

42 

0 . 0002036 

42 

0.0122173 

42 

0.7330383 

102 

1.7802358 

43 

0.0002085 

43 

0.0125082 

43 

0.7504916 

103 

1 . 7976891 

44 

0.0002133 

44 

0.0127991 

44 

0.7679449 

104 

1.8151424 

45 

0.0002182 

45 

0.0130900 

45 

0.7853982 

105 

1  8325957 

46 

0.0002230 

46 

0.0133809 

40 

0.8028515 

106 

1.8500490 

47 

0.0002279 

47 

0.0136717 

47 

0.8203047 

107 

1.8675023 

48 

0.0002827 

48 

0.0139626 

48 

0.83775f:0 

108 

1 . 8849556 

49 

0.0002376 

49 

0.0142535 

49 

0.8552113 

109 

1.9024089 

50 

0.0002124 

50 

0.0145444 

50 

0.8726646 

110 

1.9198622 

51 

0.0002473 

51 

0.0148353 

51 

0.8901179 

111 

1.9373155 

52 

0.0002521 

52 

0.0151262 

52 

0.9075712 

112 

1.9547688 

53 

0.0002570 

53 

0.0154171 

53 

0.9250245 

113 

1.9722221 

54 

0.0002618 

54 

0.0157080 

54 

0.9424778 

114 

1.9896753 

55 

0.0002666 

55 

0.0159989 

55 

0.9599311 

115 

2.0071286 

56 

0.0002715 

56 

0.0162897 

56 

0.9773844 

116 

2.0245819 

57 

0.0002763 

57 

0.0165806 

57 

0.9948377 

117 

2.0420352 

58 

0.0002812 

58 

0.0168715 

58 

1.0122910 

118 

2. 0.^^91885 

59 

0.0002860 

59 

0.0171624 

59 

1  0297443 

119 

2.0769418 

60 

0.0002909 

60 

0.0174533 

60 

:'  .0471976 

120 

2.0943951 

Fig.    32.      Circular   Arc, 


58  Geometry  and  Mensuration  Part  1 

To  compute  the  chord  of  an  arc  when  the  chord  of  half  the  arc  and  the  versed 
sine  are  given. 

(The  versed  sine  is  the  perpendicular  ho,  Fig.  32.) 
Rule.     From  the  square  of  the  chord  of  half  the  arc 
subtract  the  square  of  the  versed  sine,  and  take  twice 
the  square  root  of  the  remainder. 

Example.     The  chord  of  half  the  arc  is  6o,  and  the 
Chord  and  Rise  ^^^'    versed  sine  36.     What  is  the  length  of  the  chord  of  the 
arc? 

Solution.     6o2  —  36-  =  2  304;     V  2  304  =  48;  and  48  X  2  =  96,  the  chord. 

To  compute  the  chord  of  an  arc  when  the  diameter  and  versed  sine  are  given. 

Multiply  the  versed  sine  by  2  and  subtract  the  product  from  the  diameter; 
then  subtract  the  square  of  the  remainder  from  the  square  of  the  diameter  and 
take  the  square  root  of  that  remainder. 

Example.  The  diameter  of  a  circle  is  100  and  the  versed  sine  of  an  arc  36. 
What  is  the  chord  of  the  arc? 

Solution.  36X2=72;  100—72=28;  1002—282=9216;  ^9216=96, 
the  chord  of  the  arc. 

To  compute  the  chord  of  half  an  aic  when  the  chord  of  the  arc  and  the  versed 
sine  are  given. 

Rule.  Take  the  square  root  of  the  sum  of  the  squares  of  the  versed  sine  and 
of  half  the  chord  of  the  arc. 

Example.  The  chord  of  an  arc  is  96  and  the  versed  sine  36.  What  is  the  chord 
of  half  the  arc? 

Solution.     V362  4-  482  =  60. 

To  compute  the  chord  of  half  an  arc  when  the  diameter  and  versed  sine  are 
given. 

Rule.  Multiply  the  diameter  by  the  versed  sine  and  take  the  square  root 
of  their  product. 

To  compute  a  diameter. 

Rule  I.     Divide  the  square  of  the  chord  of  half  the  arc  by  the  versed  sine. 

Rule  2.  Add  the  square  of  half  the  chord  of  the  arc  to  the  square  of  the 
versed  sine  and  divide  this  sum  by  the  versed  sine. 

Example.  What  is  the  radius  of  an  arc  whose  chord  is  96  and  whose  versed 
sine  is  36? 

Solution.  48^+  362  =  3  600;  3  600  ^  36  =  100,  the  diameter;  and  the  radius 
=  50. 

To  compute  the  versed  sine. 

Rule.     Divide  the  square  of  the  chord  of  half  the  arc  by  the  diameter. 

To^  compute  the  versed  sine  when  the  chord  of  the  arc  and  the  diameter  are 
given. 

Rule.  From  the  square  of  the  diameter  subtract  the  square  of  the  chord  j 
and  extract  the  square  root  of  the  remainder;  subtract  this  root  from  the  diam- 
eter and  halve  the  remainder. 

To  compute  the  length  of  an  arc  of  a  circle  when  the  number  of  degrees  and  ! 
the  radius  are  given. 

Rule  I.  Multiply  the  number  of  degrees  in  the  arc  by  3.1416  multiplied  by  ■ 
the  radius  and  divide  by  180.  The  result  will  be  the  length  of  the  arc  in  the) 
same  unit  as  the  radius. 


Circles  and  Spheres  6^ 

Rule  2.  Multiply  the  radius  of  the  circle  by  0.01745  and  the  product  by  the 
degrees  in  the  arc. 

Example.  The  number  of  degrees  in  an  arc  is  60  and  the  radius  is  10  in. 
What  is  the  length  of  the  arc  in  inches? 

Solution.  10X3-1416x60=1884.96;  and  1884.96-7-180=10.47  in.  Or, 
10  X  0.01745  X  60  =  10.47  in. 

To  compute  the  length  of  the  arc  of  a  circle  when  the  length  is  given  in  de- 
grees, minutes  and  seconds. 

Rule,  (i)  Multiply  the  number  of  degrees  by  0.01745329  and  the  product 
by  the  radius.  (2)  Multiply  the  number  of  minutes  by  0.00029  and  that  prod- 
uct by. the  radius.  (3)  Multiply  the  number  of  seconds  by  0.0000048  times 
the  radius.  (4)  Add  together  these  three  results  for  the  length  of  the  arc. 
(See  also,  table,  page  57.) 

Example.     What  is  the  length  of  an  arc  of  60°  10'  5",  the  radius  being  4  ft? 

Solution,     (i)  60°  X  0.01745329  X  4  =  4.188789  ft 

(2)  10' X  0.00029        X  4=0.0116      ft 

(3)  s"  X  0.0000048    X  4  =  0.000096  ft 

(4)  The  length  of  the  arc  =  4.200485  ft 

To  compute  the  area  of  a  sector  of  a  circle  when  the  degrees  of  the  arc  and 
the  radius  are  given  (Fig.  33). 

(The  degrees  of  the  arc  are  the  same  as  the  angle  aob.) 

Rule.     Multiply  the  number  of  degrees  in  the  arc  by 
the  area  of  the  whole  circle  and  divide  by  360. 

Example.     What  is  the  area  of  a  sector  of  a  circle  whose 
radius  is  5  and  length  of  arc  60°? 

Solution.     Area    of    circle  =  10  X  10  X  0.7854  =  78.54 

Hence,  area  of  sector  =  — '■ =  13.09 

360 

Note.     If  the  length  of  the  arc  is  given  in  degrees  and 
minutes,  reduce  it  to  minutes,  multiply  by  the  area  of  the  whole  circle  and  divide 
by  21  600. 

To  compute  the  area  of  a  sector  of  a  circle  when  the  length  of  the  arc  and 
radius  are  given. 

Rule.  Multiply  the  length  of  the  arc  by  half  the  length  of  the  radius.  The 
product  is  the  area. 

To  compute  the  area  of  a  segment  of  a  circle  when  the  chord  and  versed  sine 
of  the  arc  and  the  radius  or  diameter  of  the  circle  are  given. 

(The  versed  sine  is  the  distance  cd,  Fig.  33.) 

Rule  I.  When  the  segment  is  less  than  a  semicircle,  (i)  Find  the  area  of 
the  sector  having  the  same  arc  as  the  segment.  (2)  Find  the  area  of  a  triangle 
formed  by  the  chord  of  the  segment  and  the  radii  of  the  sector.  (3)  Take  the 
difference  of  these  areas. 

Rule  2.  When  the  segment  is  greater  than  a  semicircle.  Find,  by  the  pre- 
ceding rule,  the  area  of  the  lesser  portion  of  the  circle  and  subtract  it  from  the 
area  of  the  whole  circle.     The  remainder  will  be  the  area. 

To  compute  the  area  of  the  surface  of  a  sphere. 

Rule.  Multiply  the  diameter  by  the  circumference.  The  product  will  be 
the  area  of  the  surface. 


60 


Geometry  and  Mensuration 


Part  1 


^m 


Example.     What  is  the  area  of  the  surface  of  a  sphere  lo  in  in  diameter? 
Solution.     Circumference  of   sphere  =  ic  X  3.1416  =  31.416  in;    10X31.416 
=  314.16  sq  in,  the  area  of  surface  of  sphere. 
To  compute  the  total  area  of  the  surface  of  a  segment  of  a  sphere. 
Rule.     Multiply  the  height  {be,  Fig.  34)  by  the  circumference  of  the  sphere 
and  add  the  product  to  the 
area  of  the  base.  ^^^         """^s^ 

To  find  the  area  of  the  /^  ^\ 

base,  having  the  diameter 
of  the  sphere  and  the 
length  of  the  versed  sine 
of  the  arc  abd,  find  the 
length  of  the  chord  ad  by 
the  rule  on  page  58.  Hav- 
ing, then,  the  length  of  the 
chord  ad  for  the  diameter 
of  the  base,  find  the  area 
of  the  base. 

Example.  The  height,  be,  of  a  segment  abd,  is  36  in,  and  the  diameter  of  the 
sphere  is  100  in  (Fig.  34).  What  is  the  area  of  the  convex  surface  and  the  area 
of  the  whole  surface?  • 

Solution.     100X3.1416  =  314. 16  in,  the  circumference  of  sphere 

36  X  314-16  =  11309.76  sq  in,  the  area  of  the  convex  surface 

100-  (36  X  2)  =  28 

Vioo^  —  282  =  96,  the  chord  ad 

962  X  0.7854  =  7238.2464  sq  in,  the  area  of  the  base 

11309.76  +  7238.2464=  18548.0064  sq  in,  the  total  area 

To  compute  the  total  area  of  the  surface  of  a  spherical  zone. 
Rule.     Multiply  the  height,  cd  (Fig.  35),  by  the  circumference  of  the  sphere 
(or  the  convex  surface  and  add  to  it  the  area  of  the  two  ends  for  the  total  area. 


Fig.  34. 
Segment  of  Sphere 


d 


Fig.  35. 
Zone  of  Sphere 


Spheroids,  or  Ellipsoids  of  Revolution 

Definition.  Spheroids,  or  ellipsoids,  are  figures  generated  by  the  revolution 
of  a  semiellipse  about  one  of  its  diameters. 

When  the  revolution  is  about  the  long  diameter,  they  are  prolate;  and 
when  it  is  about  the  short  diameter,  they  are  oblate. 

A  PROLATE  SPHEROID  is  approximately  cigar-shaped  and  an  oblate  spheroid 
is,  in  form,  somewhat  like  a  watch. 

To  compute  the  area  of  the  surface  of  a  spheroid. 

Let  a  =  H  the  long  axis;   let  6  =  H  the  short  axis; 

let 


v^ 


2-62 


a2  t       a' 

Then,  the  area  of  the  surface  of  the  oblate  spheroid 


:  2  7ra2  + 


'-f'»=(:-^) 


and  the  area  of  the  surface  of  the  prolate  spheroid 
=  2  7ro2  -f  2  irao • 


Surfaces  and  Solids 


61 


in  the  first  formula,  natural  logarithms  must  be  used.  The  natural  loga- 
rithm may  be  obtained  by  multiplying  the  common  logarithm  by  2.302.  The 
value  of  the  expression  sin~^  e  may  be  determined  by  finding  the  angle  whose 
natural  sine  is  equal  to  e  and  dividing  this  angle  by 
57.3. 

Note.  Although  the  above  formulas  are  compli- 
cated, no  simpler  rules  that  give  correct  results  can  be 
given. 

To  compute  the  area  of  the  surface  of  a  cylinder. 

Rule.  Multiply  the  length  of  the  cylinder  by  the 
circumference  of  one  of  the  ends  and  add  to  the 
product  the  areas  of  the  two  ends. 

To  compute  the  area  of  a  circular  ring  (Fig.  36).  ^'^^'  ^^'    Circular  Ring 

Rule.  Find  the  area  of  both  circles  and  subtract  the  area  of  the  smaller  from 
the  area  of  the  larger;  the  remainder  will  be  the  area  of  the  ring. 

To  compute  the  area  of  the  surface  of  a  cone. 

Rule.  Multiply  the  circumference  of  the  base  by  one-half  the  slant-height 
or  side  of  the  cone,  for  the  convex  area.  Add  to  this  the  area  of  the  base,  for 
the  whole  area. 

Example.  The  diameter  of  the  base  of  a  cone  is  3  in  and  the  slant-height  15  in. 
What  is  the  area  of  the  surface  of  the  cone? 

Solution.     3X3. 1416  =    9.4248  =  circumference  of  base 

9.4248  X  7}'4  =  70.686  sq  in  =  area  of  convex  surface 

2>y^2>y\  07854  =    7.068  sq  in  =  area  of  base 

Area  of  entire  surface  of  cone  =  77.754  sq  in 

To  compute  the  area  of  the  surface  of  the  frustum  of  a  cone  (Fig.  37). 

Rule.  Multiply  the  sum  of  the  circumferences  of 
the  two  ends  by  the  slant-height  of  the  frustum  and 
divide  by  2,  for  the  area  of  the  convex  surface.  Add 
the  areas  of  the  two  ends. 

To  compute  the  area  of  the  surface  of  a  pyramid. 

Rule.  Multiply  the  perimeter  of  the  base  by  one- 
half  the  slant-height  and  add  to  the  product  the  area 
of  the  base. 

To  compute  the  area  of  the  surface  of  the  frustum  of  a 
pyramid. 

Rule.  Multiply  the  sum  of  the  perimeters  of  the 
two  ends  by  the  slant-height  of  the  frustum,  halve  the 
product,  and  add  to  the  result  the  areas  of  the  two 
ends. 


Fig.  37.  Frustum  of  Cone 


Mensuration  of  Solids 

To  compute  the  volume  of  a  prism.     (See  page  38  for  definition  of  a  prism.) 
Rule.     Multiply  the  area  of  the  base  or  end  by  the  altitude  or  perpendicular 

height. 
This  rule  applies  to  prisms  with  bases  or  ends  of  any  shape,  as  long  as  these 

bases  or  ends  are  parallel. 


62 


Geometry  and  Mensuration 


Part  1 


To  compute  the  volume  of  a  prismoid. 

Definition.  A  prismoid  is  a  soUd  with  parallel  but  unequal  ends  or  bases 
and  with  quadrilateral  sides. 

Rule  To  the  sum  of  the  areas  of  the  two  ends  or  bases  add  four  times  the 
area  of  the  middle  section  parallel  to  them,  and  multiply  this  sum  by  one-sixth 
of  the  altitude  or  perpendicular  height. 


Fig.  38.     Quadrangular  Prismoid 


Fig.  39.     Prism  Truncated  Obliquely 


Example.     What  is  the  volume  of  a  quadrangular  prismoid,  as  Fig.  38,  in 
which  ab=6  in,  cd=4  in,  ac  =  he  =  lo  in,  ce  =  8  in,  e/  =  8  in  and  ih  =  6  in? 


Solution.     Area  of  top 

Area  of  bottom 


6  +  4 


8  +  6 


X  lo  =  50  sq  in 


X  10  =  70  sq  in 


6  +  6 

Area  of  middle  section      =  X  10  =  60  sq  in 

2 

[50  +  70  +  (4  X  60)]  X%  =  480  cu  in 

Note.     The  length   of    the    end    of    the 
middle   section   (as  at   inn,  in  Fig.   38)  = 
cd-\-ef 
2 

To  find  the  volume  of  a  prism  truncated 
obliquely. 
(I        Rule.     Multiply  the  area  of  the  base  by 
the  average  height  of  the  edges. 

Example.  What  is  the  volume  of  a 
truncated  prism  (Fig.  39)  in  which  ef  =  6 
mjh  =  10  in,  ea  =  10  in,  ci=  12  in,  dh  =  10 
in  and/&  =  8  in? 

Fig.  40.    Wedge  or  Right  Triangular        Solution.      Area    of    base  =  6  X  10  =60 
Prism 


sq  in 


Average  height  of  edges 


10+12  +  8+10 


60  X  10  =  6cx5  cu  in 


Regular  Polyhedrons 


63 


To  compute  the  volume  of  a  wedge  or  right  triangular  prism  when  the  ends  are 
parallel  and  equal. 

Rule.     Multiply  the  area  of  one  end  by  the  length  of  the  wedge. 

To  compute  the  volume  of  a  wedge  when  the  ends  are  not  parallel. 

Rule.  Add  together  the  lengths  of  the  three  edges,  ab,  cd  and  ef  (Fig.  40); 
multiply  their  sum  by  the  altitude  or  perpendicular  height  of  the  wedge,  and 
then  by  the  breadth  of  the  back,  and  divide  the  product  by  6. 

Regular  Polyhedrons 

Definition.  A  regular  polyhedron  is  a  soHd  contained  within  a  certain  num- 
ber of  similar  and  equal  plane  faces,  all  of  which  are  equal  regular  polygons. 
The  following  is  a  list  of  all  the  regular  polyhedrons: 

(i)  The  TETRAHEDRON,  or  pyramid. 

(2)  The  HEXAHEDRON,  or  cube,  which  has  six  square  faces. 

(3)  The  OCTAHEDRON,  which  has  eight  triangular  faces. 

(4)  The  DODECAHEDRON,  which  has  twelve  pentagonal  faces. 

(5)  The  ICOSAHEDRON,  which  has  twenty  triangular  faces. 
To  compute  the  volume  of  a  regular  polyhedron. 

Rule  I.  When  the  radius  of  the  circumscribing  sphere  is  given.  Multiply 
the  cube  of  the  radius  of  the  sphere  by  the  multiplier  opposite  to  the  polyhedron 
in  column  2  of  the  following  table. 

Rule  2.  When  the  radius  of  the  inscribed  sphere  is  given.  Multiply  the  cube 
of  the  radius  of  the  inscribed  sphere  by  the  multiplier  opposite  to  the  polyhedron 
in  column  3  of  the  table. 

Rule  3.  When  the  area  of  the  surface  of  the  polyhedron  is  given.  Cube  the 
surface  given,  extract  the  square  root,  and  multiply  the  root  by  the  multipliel 
opposite  to  the  polyhedron  in  column  4  of  the  table. 

Table  of  Factors  for  Determining  the  Volumes  of  Regular  Polyhedrons 


Figure 

1 

Number 
of  sides 

2 

Factor  for 

volume  by 

radius  of 

circumscribing 

sphere 

3 

Factor  for 

volume  by 

radius  of 

inscribed 

circle 

4 

Factor  for 

volume  by 

surface 

Tetrahedron 

Hexahedron 

4 
6 

8 
12 
20 

0.5132 

1.5396 

1.33333 

2.78517 

2.53615 

13.85641 
8.0000 
6.9282 
5.55029 
5.05406 

0.0517 
0.06804 
0.07311 
0.08169 
0.0856 

Octahedron 

Dodecahedron 

Icosahedron 

To  compute  the  volume  of  a  cylinder. 

Rule.     Multiply  the  area  of  the  base  by  the  altitude  or  length. 

To  compute  the  volume  of  a  cone. 

Rule.     Multiply  the  area  of  the  base  by  one-third  the  altitude. 

To  compute  the  volume  of  the  frustum  of  a  cone  (Fig.  41) . 

Rule.  Add  together  the  squares  of  the  diameters  of  the  two  ends  or  bases 
and  the  product  of  the  two  diameters;  multiply  this  sum  by  0.7854,  and  this 
product  by  the  altitude,  and  then  divide  this  last  product  by  3. 


64 


Geometry  and  Mensuration 


Part  1 


Example.     What  is  the  volume  of  a  frustum  of  a  cone  9  in  in  height,  5  in  in 
diameter  at  the  base  and  3  in  in  diameter  at  the  top? 

Solution.  5'  +  32  =  34.  3x5=15.  15  -It  34  =  49, 
the  sum  of  the  squares  of  the  two  diameters  added  to 
the  product  of  tlie  diameters  of  the  ends.  49  X  0.7854 
=  38.4846. 

38.4846  X  9  ^       . 

=  115.4538  cu  m 

3 

To  compute  the  volume  of  a  pyramid. 
Rule.     Multiply  the  area  of  the  base  by  the  altitude 
or  perpendicular   height,   and   take  one-third   of   the 
product. 

To  compute  the  volume  of  the  frustum  of  a  pyramid. 

Rule.     Find  the  height  that  the  pyramid  would  be  if 

Fig.  41.   Frustum  of  Cone    the  top  were  put  on,  and  then  compute  the  volume  of 

the  completed  pyramid  and  the  volume  of  the  part 

added;  subtract  the  latter  from  the  former,  and  the  remainder  will  be  the  volume 

of  the  frustum. 

To  compute  the  volume  of  a  sphere. 
Rule.     Multiply  the  cube  of  the  diameter  by  0.5236. 
To  compute  the  volume  of  a  segment  of  a  sphere. 

Rule  I.     To  three  times  the  square  of  the  radius  of  its  base  add  the  square  ot 
its  height;  multiply  this  sum  by  the  height  and  the 
product  by  0.5236. 

Rule  2.  From  three  times  the  diameter  of  the 
sphere  subtract  twice  the  height  of  the  segment; 
multiply  this  remainder  by  the  square  of  the  height 
and  the  product  by  0.5236. 

Example.  The  segment  of  a  sphere  has  a  radius, 
ac  (Fig.  42),  of  7  in  for  its  base,  and  a  height,  ch,  of 
4  in:  what  is  its  volume? 

Solution.     (By  Rule  i .)     3X7'=  i47,  and  147  +  42 
=  163,  or  three  times  the  square  of  the  radius  of  the 
base    plus    the    square    of    the    height.     163  X  4  X 
0.5236=341.3872    cu 
segment. 

Second  Solution.  By  the  rule  for  finding  the 
diameter  of  a  circle  when  a  chord  and  its  versed 
sine  are  given,  we  find  that  the  diameter  of  the 
sphere  in  this  case  is  16.25  in;  then,  by  Rule  2, 
(3  X  16.25)- (2X4)  =  40-75;  and  40.75  X  4^  X 
05236=341.3872  cu  in,  the  volume  of  the 
segment. 

To  compute  the  volume  of  a  spherical  zone 
Definition.     The  part  of  a  sphere  included  be- 
tween two  parallel  planes  (Fig.  43). 
Rule.     To  the  sum  of  the  squares  of  the  radii  of  the  two  ends  add  one-third 
of  the  square  of  the  height  of  the  zone;  multiply  this  sum  by  the  height  and  that 
product  by  1.5708. 


Fig.  42. 
in  =  the 


Segment  of  Sphere 
volume    of    the 


Fig.  43.     Zone  of  Sphere 


Figures  of  Revolution  and  Irregular  Figures 


65 


To  compute  the  volume  of  a  prolate  spheroid.     (See  page  60.) 

Rule.  Multiply  the  square  of  the  short  axis  by  the  long  axis  and  this  product 
by  0.5236. 

To  compute  the  volume  of  an  oblate  spheroid. 

Rule.  Multiply  the  square  of  the  long  axis  by  the  short  axis  and  this  product 
by  0.5236. 

To  compute  the  volume  of  a  paraboloid  of  revolution  (Fig.  44). 

Rule.  Multiply  the  area  of  the  base 
by  half  the  altitude. 

To  compute  the  volume  of  a  hyperbo- 
loid  of  revolution  (Fig.  45). 

Rule.  To  the  square  of  the  radius 
of  the  base  add  the  square  of  the 
middle  diameter;  multiply  this  sum 
by  the  height  and  the  product  by 
0.5236. 

To  compute  the  volume  of  any  figure 
of  revolution. 

Rule.  Multiply  the  area  of  the  generating  surface  by  the  circumference 
described  by  us  center  of  gravity. 

To  compute  the  volume  of  an  excavation,  where  the  ground  is  irregular  and 
the  bottom  of  the  excavation  is  level  (Fig.  46). 

Rule.  Divide  the  surface  of  the  ground  to  be  excavated  unto  equal  squares 
of  about  10  ft  on  a  side,  and  ascertain  by  means  of  a  level  the  height  of  each 
corner,  a,  a,  a,  b,  h,  h,  etc.,  above  the  level  to  which  the  ground  is  to  be  excavated. 
Then  add  together  the  heights  of  all  the  corners  that  come  in  one  square  only. 

Next  take  twice  the  sum  of  the 


Fig.    44.      Parabo- 
loid of  Revolution 


45.     Hyperboloid 
of  Revolution 


a 


a 


heights  of  all  the  corners  that 
come  in  two  squares,  as  b,  b,  b; 
next  three  times  the  sum  of  the 
heights  of  all  the  corners  that 
come  in  three  squares,  as  c,  c,  c; 
and  then  four  times  the  sum  of 
the  heights  of  all  the  corners 
that  belong  to  four  squares,  as 
d,  d,  d,  etc.  Add  together  all 
these  quantities,  and  multiply 
their  sum  by  one-fourth  the  area 
of  one  of  the  squares.  The 
result  will  be  the  volume  of  the 
excavation. 
Example.  Let  the  plan  of  an  excavation  for  a  cellar  be  as  shown  in  Fig.  46, 
and  the  heights  of  each  corner  above  the  proposed  bottom  of  the  cellar  be  as 
given  by  the  numbers  in  the  figure.     Then  the  volume  of  the  cellar  will  b^tf^ 

.02 

Tiatdoi^i 


6 

3           4 

C 

d 

e          h 

3 

4 

'Z 

3 

U 

4' 

d 

d 

d 

1 

- 

1 

3 

a 

2 

c 

2 

3 

i 

1         1 

b 

'J           b 

a 

r 

ig.  46. 

Plan  of  I 

ixcavatio 

n 

follows,  the  area  of  each  square  being  10  X  10  =  100  sq  ft: 
Volume  =  H  of  100  (a 's  +  2  6  '5  +  3  c  's  +  4  ^  's) 

The  a's  in  this  case  =4  +  6  +  3  +  2  +  1  +  7  +  4 

2  X  the  sum  of  the  6's  =  2  X  (3  +  6  +  i  +  4  +  3  +  4) 

3  X  the  sum  of  the  c's  =  3  X  (i  +  3  +  4) 

4  X  the  sum  of  the  J's  =  4  X  (2  +  3  +  6  +  2) 


=  27 

=  42 
=  24 
=  52 

145 


Volume  =  25  X  145  =  3  625  cu  ft,  the  quantity  of  earth  to  be  excavated* 


66 


Geometrical  Problems 


Part  1 


4.   GEOMETRICAL  PROBLEMS 

Problem  i.     To  bisect,  or  divide  into  equal  parts,  a  given  line,  ab  (Fig.  47). 

From  a  and  h,  with  any  radius  greater  than  half  of  ah,  describe  arcs  inter- 
secting in  c  and  d.  The  line  cd,  connecting  these  intersections,  will  bisect  ah 
and  be  perpendicular  to  it. 


r 


'^■ 


(d 


Fig.  47.    Line  Bisected 


Fig.  48.    Perpendicular  from 
Point  to  Given  Line 


Fig.    49.       Perpendicular 
from  Point  to  Given  Line 


Problem  2.  To  draw  a  perpendicular  to  a  giv«n  straight  line  from  a  point  with- 
out it. 

First  Method  (Fig.  48).  From  the  point  a  describe  an  arc  cutting  the  line 
be  in  two  places,  as  e  and  /.  From  e  and  /  describe  two  arcs,  with  the  same 
radius,  intersecting  in  g\  then  a  line  drawn  from  a  to  g  is  perpendicular  to  the 
line  he. 

Second  Method  (Fig.  49).  From  any  two  points,  d  and  c,  at  some  distance 
apart  in  the  given  line,  and  with  radii  da  and  ea  respectively,  describe  arc 


d 


-¥. 


b 

Fig.  50. 


\^ 


/d 


Perpendicular  from  Point 
in  Given  Line 


Fig.  51.  Perpendicular 
from  Extremity  of 
Given  Line 


cutting  at  a  and  e.  Draw  ae,  which  is  the  perpendicular  reequired.  This 
method  is  useful  where  the  given  point  is  opposite  the  end  of  the  line,  or  nearly 
so. 

Problem  3.  To  draw  a  perpendicular  to  a  straight  line  from  a  given  point,  a, 
in  that  line. 

First  Method  (Fig.  50).  With  any  radius,  from  the  given  point  a  in  the  line, 
describe  arcs  cutting  the  line  in  the  points  b  and  c.  Then  with  h  and  c  as  centers, 
and  with  any  radius  greater  than  ab  or  ac,  describe  arcs  cutting  each  other  at 
d.    The  line  da  is  the  perpendicular  required. 


Geometrical  Problems 


67 


Second  Method  (Fig.  51),  when  the  given  point  is  at  the  end  of  the  line. 

From  any  point,  b,  outside  of  the  line,  and  with  a  radius  ba,  describe  a  semi- 
circle passing  through  a  and  cutting  the  given  Hne 
at  d.     Through  b  and  d  draw  a  straight  line  inter- 
secting the  semicircle  at  e.     The  line  ea  will  then  be 
perpendicular  to  the  Hne  ac  at  the  point  a. 

Third  Method  (Fig.  52),  or  the  3,  4  and  5  Method. 
From  the  point  a  on  the  given  line  measure  off  4  in, 
or  4  ft,  or  4  of  any  other  unit  and  with  the  same  unit 
of  measure  describe  an  arc,  with  a  as  a  center  and 
3  units  as  a  radius.  Then  from  b  describe  an  arc 
with  a  radius  of  5  units,  cutting  the  first  arc  in  c. 
Then  ca  is  the  perpendicular  required.  This  method 
is  particularly  useful  in  laying  out  a  right  angle  on 

the  ground,  or  framing  a  house  where  the  foot  is  used  as  the  unit  and  the  lines 
are  laid  off  by  the  straight-edge. 

In  laying  out  a  right  angle  on  the  ground,  the  proportions  of  the  triangle  may 
be  30,  40  and  50,  or  any  other  multiple  of  3,  4  and  5;  and  it  can  best  be  laid 
out  with  the  tape.  Thus,  first  measure  off,  say  40  feet  from  a  (Fig.  52)  on  the 
given  Hne;   then  let  one  person  hold  the  end  of  the  tape  at  b,  another  hold  the 


Fig.  52.  Perpendicular 
from  Extremity  of  Given 
Line 


d 


Fig.  53.     Straight  Line  Parallel  to  Given  Line 


tape  at  the  80-ft  mark  at  a,  and 
a  third  person  take  hold  of  the 
tape  at  the  50-ft  mark,  with  his 
thumb  and  finger,  and  pull  the 
tape  taut.  The  50-ft  mark  will 
then  be  at  the  point  c  in  the  line 
of  the  perpendicular. 

Problem  4.    To  draw  a  straight 
line  parallel  to  a  given  line  at  a 
given  distance  away  (Fig.  53). 
From  any  two  points  near  the  ends  of  the  given  line  describe  two  arcs  about 
opposite  the  given  line.     Draw  the  line  cd  tangent  to  these  arcs  and  it  will  be 
parallel  to  ab. 
Problem  5.     To  construct  an  angle  equal  to  a  given  angle  (Fig.  54). 
With  the  point  A ,  at  the  apex  of  the  given  angle,  as  a  center,  and  any  radius, 
describe  the  arc  BC.     With  the  point  a,  at  the  vertex  of  the  new  angle,  as  a 

J5/. 


\ 


A  B        a 

Fig.  54.     Angle  Equal  to  Given  Angle  Fig.  55.     Angle  of  60** 

center,  and  with  the  same  radius  as  before,  describe  an  arc,  as  BC.  With  BC 
as  a  radius  and  6  as  a  center,  describe  an  arc  cutting  the  other  arc  at  c.  Then 
will  cab  be  equal  to  the  given  angle  CAB. 

Problem  6.  From  a  point  on  a  given  line  to  draw  a  line  making  an  angle  of 
60°  with  the  given  line  (Fig.  55). 

Take  any  distance,  as  ab,  as  a  radius,  and  with  a  as  a  center,  describe  the  arc 
be.    With  6  as  a  center  and  with  the  same  radius,  describe  an  arc  cutting  the 


68 


Geometrical  Problems 


Part  1 


Fig.  56.     Angle  of  45° 


first  one  at  c.    Draw  from  a  a  line  through  c,  and  it  will  make  with  ab  an  angle 

of  60". 

'    Problem  7.    From  a  given  point,  A,  on  a  given  line,  AE,  to  draw  a  line  making 

an  angle  45°  with  the  given  line  (Fig.  56). 

Measure  off  from  Ay  on  AE,  any  distance,  Ab,  and 
at  b  draw  a  line  perpendicular  to  AE.  Measure  off 
on  this  perpendicular  be  equal  to  Ab  and  draw  a  Une 
from  A  through  c.  This  line  Ac  will  make  an.  angle  of 
45°  with  AE. 

Problem  8.  From  any  point.  A,  on  a  given  line,  to 
draw  a  line  which  will  make  any  desired  angle  with  the 
given  line  (Fig.  57). 

To  solve  this  problem  the  tables  of  chords  on  pages  81 
to  89  are  used.  Find  in  the  table  the  length  of  chord 
to  a  radius   i,  for  the  given  angle.     Then  take  any 

radius,  as  large  as  convenient  and  describe  an  arc  of  a  circle  be,  with  ^  as  a 

center.     Multiply  the  chord  of  the  angle,  found  in  the  table,  by  the  length  of 

the  radius  Ab,  and  with  the  product  as  a  new  radius  and  with  6  as  a  center, 

describe  a  short  arc  cutting  be  in  d.     Draw  a  hne 

from  A  through  d  and  it  will  make  the  required 

angle  with  DE. 
Example.     Draw  a  line  from  A  on  DE,  making 

an  angle  of  44°  40'  with  DE  (Fig.  57). 

Solution.     The  largest  convenient  radius  for  the 

arc  is  8  in.     With  ^   as  a  center  and  8  in  as  a 

radius,  describe  the  arc  be.     In  the  table  of  chords, 

the  chord  for   an   angle  or  arc   of  44°  40'   to   a 

radius   i    is  0.76.     Multiplying  this  by  8  in,   the 

length  of  the  new  radius  is  6.08  in;  and  with  this  as  radius  and  with  6  as  a 

center,  describe  an  arc  cutting  be  in  d.    Ad  will  be  the  line  required. 
Problem  8a. 

two-foot  rule. 


A  5      ' 

Fig.   57.     Line  Making  Any 
Angle  with  Given  Line 


To  lay  off  a  given  angle  approximately,  by  means  of  an  ordinary 


Tables  of 

Angles  Corresponding 

to  openings  of 

a  Two-Foot  Rule* 

In. 

Deg.  Min. 

In. 

Deg.  Min. 

In. 

Deg.  Min. 

In. 

Deg.  Min. 

In. 

Deg.  Min. 

M 

1  12 

11  22 

m 

21  37 

32   3 

8')4 

42  46 

1  48 

2H 

11  58 

22  13 

63/4 

32  40 

43  24 

\^ 

2  24 

12  34 

"h 

22  50 

33  17 

9 

44   3 

3  00 

'h 

13  10 

23  27 

7' 

33  54 

44  42 

H 

3  36 

13  46 

5 

24   3 

34  33 

"\i 

45  21 

4  11 

3 

14  22 

24  39 

"h 

35  10 

45  59 

1 

4  47 

5  23 

H 

14  58 

"h 

25  16 

35  47 

"h 

46  38 

15  34 

25  53 

Vi 

36  25 

47  17 

H 

5  58 

16  10 

"Vi 

26  30 

37   3 

H 

47  56 

6  34 

"h 

16  46 

27   7 

"% 

37  41 

48  35 

H 

7  10 

17  22 

^i 

27  44 

38  19 

16 

49  15 

7  46 

"h 

17  59 

28  21 

'%" 

38  57 

49  54 

% 

8  22 

18  35 

6 

28  58 

39  35 

"h 

50  34 

8  58 

4" 

19  12 

29  35 

H 

40  13 

51  13 

2 

9  34 

19  48 

H 

30  11 

40  51 

H 

51  53 

10  10 

H 

20  24 

30  49 

'ii 

41  29 

52  33 

H 

10  46 

21  OG 

"h 

31  26 

42   7 

*  Trau twine. 


Fig.  58.     Angle  Bisected 


Geometrical  Problems  69 

Lay  one  leg  of  the  rule  on  the  paper  or  board  with  its  inner  edge  coinciding 
with  the  given  line.  Open  the  rule  until  the  distance  between  the  inner  edges  at 
the  ends  correspond  with  that  given  for  the  angle  in  the  following  table;  then 
draw  a  line  by  marking  along  the  inner  edge  of  the  other  leg,  and  it  will  give  the 
desired  angle  within  a  very  close  approxi- 
mation. 

Problem  9.  To  bisect  a  given  angle,  as 
BAG  (Fig.  68). 

With  ^  as  a  center  and  any  radius, 
describe  an  arc,  as  cb.  With  c  and  b  as 
centers,  and  any  radius  greater  than  one- 
half  of  cb,  describe  two  arcs,  intersecting 
in  d.  Draw  from  A  a  line  through  d  and 
it  will  bisect  the  angle  BAC. 

Problem  10.     To  bisect  the  angle  included  between  two  lines,  as  AB  and  CD, 
when  the  vertex  of  the  angle  is  not  on  the  drawing  (Fig.  69). 

Draw/e  parallel  to  AB  and 
cd  parallel  to  CD,  so  that  the 
two  hues  intersect,  as  at  i. 
Bisect  the  angle  eid,  as  in  the 
preceding  problem,  and  draw 
a  line  through  i  and  0  which 
will  bisect  the  angle  between 
the  two  given  lines. 

Problem  11.  Through  two 
given  points,  B  and  C,  to 
describe  an  arc  of  a  circle  with 
a  given  radius  (Fig.  60). 

With  B  and  C  as  centers 

and  with  a  radius  equal  to  the 

given  radius,  describe  two  arcs  intersecting  at  A .     With  ^  as  a  center  and  the 

same  radius,  describe  the  arc  be,  which  will  pass  through  the  given  points,  B  and  C. 

Problem   12.     To    find 

the    center    of    a    given 

circle  (Fig.  61). 

Draw  any  chord  in  the 

circle,  as  ab,  and  bisect 

this  chord  by  the  per- 
pendicular cd.    This  Hne 

will    pass    through    the 

center  of  the  circle  and 

ef  will  be  a  diameter  of 
the  circle.  Bisect  ef,  and  the  center  0  will  be  the 
center  of  the  circle. 


Fig.  59.     Angle  Bisected.     Angle  not  on  Drawing 


Fig.  60.  Circular  Arc  Through 
Two  Given  Points 


Fig.  61. 


Center  of  Given 
Circle 


Problem  13.     To  draw  a  circular  arc  through  three 
given  points,  as  A,  B  and  C  (Fig.  62). 

Draw  lines  from  yl  to  ^  and  from  B  to  C.     Bisect 
AB  and  BC  by  the  lines  aa  and  ec  and  prolong  these  lines  until  they  intersect 
at  0,  which  will  be  the  center  for  the  arc  sought.     With  <?  as  a  renter  and  Ao 
as  a  radius,  describe  the  arc  ABC. 


70 


Geometrical  Problems 


Part  1 


Fig.  62.     Circular  Arc  Through 
Three  Given  Points 


Fig.  63.     Frame  for  Drawing  Circular  Arc 


Problem  14.  To  describe  a  circular  arc  passing  through  three  given  points 
when  the  center  is  not  available,  by  means  of  a  triangle  (Fig.  63). 

Let  A,  B  and  C  be  the  given  points.  Insert  two  stiff  pins  or  nails  at  A  and  C. 
Place  two  strips  of  wood,  SS,  as  shown  in  the  figure,  one  against  A ,  the  other 
against  C,  and  inclined  so  that  their  intersection  shall  come  at  the  third  point, 
B.  Fasten  the  strips  together  at  their  intersection  and  nail  a  third  strip,  T, 
to  their  other  ends,  so  as  to  make  a  firm  triangle.  Place  the  pencil-point  at  B, 
and,  keeping  the  edges  of  the  triangle  against  A  and  C,  move  the  triangle  to  the 
left  and  right.     The  pencil-point  will  describe  the  required  arc. 

When  the  points  A  and  C  are  at  the  same  distance  from  B,  if  a  strip  of  wood 
is  nailed  to  the  triangle,  so  that  its  edge  de  is  at  right-angles  to  a  line  joining 
A  and  C,  as  the  triangle  is  moved  one  way  or  the  other,  the  edge  de  will  always 
point  to  the  center  of  the  circle.     This  principle  is  used  in  linear  perspective. 

Problem  15.  To  describe  a  circular  arc  which  will  be  tangent  at  a  given  point, 
A,  to  a  straight  line,  and  pass  through  a  given  point,  C,  outside  the  line  (Fig.  64). 

Draw  from  A  a  line  perpendicular  to  the  given  line.  Connect  A  and  C  by  a 
straight  line  and  bisect  this  line  by  the  perpendicular  ac.  The  point  where  these 
two  perpendiculars  intersect  is  the  center  of  the  circle. 

A 


Fig.  64.     Circular  Arc  Tangent 
to  Line  at  Given  Point 


Reversed  Curve   Between   Parallel   Lines 


Problem  16.  To  connect  two  parallel  lines  by  a  reversed  curve  composed  of 
two  circular  arcs  of  equal  radius,  and  tangent  to  the  lines  at  given  points,  as  A 
and  B  (Fig.  65). 

Join  A  and  B  and  divide  the  line  into  two  equal  parts  at  C.  Bisect  CA  and 
CB  by  perpendiculars.  At  A  and  B  erect  perpendiculars  to  the  given  lines,  and 
the  intersections  a  and  b  will  be  the  centers  of  the  arcs  composing  the  required 
curve. 


Geometrical  Problems 


71 


Fig.  66.     Curve  of  Three  Circular  Arcs 


Problem  17.  On  a  given  line,  as  AB  (Fig.  66),  to  construct  a  compound  curve 
of  three  arcs  of  circles,  the  radii  of  the  two  side  arcs  being  equal  and  of  a  given 
length,     and     their     centers  P 

being  in  the  given  line.  The 
central  arc  is  to  pass  through 
a  given  point,  C,  on  the  per- 
pendicular bisecting  the  given 
line,  and  is  to  be  tangent  to 
the  other  two  arcs. 

Draw  the  perpendicular 
CD.  Lay  off  Aa,  Bh  and  Cc, 
each  equal  to  the  given  radius 
of  the  side  arcs;  draw  ac\ 
bisect  ac  by  a  perpendicular. 
The  intersection  of  this  line 
with  the  perpendicular  CD 
is  the  required  center  of  the 
central  arc.  Through  a  and  h  draw  the  lines  Dc  and  De'\  from  a  and  h,  with 
the  given  radius,  equal  to  A  a,  Bb,  describe  the  arcs  Ae'  and  Be;  from  Z)  as  a 
center,  and  with  CD  as  a  radius,  describe  the  arc  eCe' 
which  completes  the  curve  required. 

Problem  18.  To  con- 
struct a  triangle  upon  a 
given  straight  line  or  base, 
the  length  of  the  two  sides 
being  given  (Figs.  67  and 
63). 

First.     An  equilateral  tri- 
angle (Fig.  67).     With  the 
extremities  A    and  B  of  the  given  line  as  centers  and  with  AB  as  a  radius, 
describe  arcs  cutting  each  other  at  C.     Join  ylC  and  2^C  ►». 

Second.  A  scalene  triangle  (Fig.  68).  Let  AD  he  the  given  base  and  the  othe/ 
two  sides  be  equal  to  C  and  B.  With  Z>  as  a  center,  and  with  a  radius  equal  to 
C,  describe  at  E  an  arc  of  indefinite  length.  With 
^  as  a  center  and  with  J5  as  a  radius,  describe  an  arc 
cutting  the  first  at  E.  Join  E  with  A  and  D. 
ADE  is  the  required 
triangle. 

Problem  19.  To 
describe  a  circle  about 
a  triangle  (Fig  69). 

Bisect  two  of  the 
sides,  as  ^  C  and  CB, 
of  the  triangle,  and 
at  their  centers,  erect 
perpendicular     lines, 
as  ae  and  he,  intersecting  at  c.    With  c  as  a  center,  and  eC  as  a  radius,  describe 
a  drcle.     It  will  pass  through  A  and  B. 
Problem  20.     To  inscribe  a  circle  in  a  triangle  (Fig.  70). 

Bisect  two  of  the  angles,  A  and  B,  of  the  triangle  by  lines  cutting  each  other 
at  0.  With  o  as  a  center,  and  with  oe  as  a  radius,  describe  a  circle.  It  will  be 
tangent  to  the  other  two  sides. 


Fig.  67.    Equilateral  Tri- 
;ingle  on  Given  Base 


Fig.  68.     Scalene  Triangle  on 
Given  Base 


]  ig.  69.    Triangle  and  Cir- 
cumscribed Circle 


Triangle  and  Inscribed 
Circle 


72 


Geometrical  Problems 


Part  1 


Problem  21.  To  inscribe  a  square  in  a  circle  and  to  describe  a  circle  about  a 
square  (Fig.  71). 

To  inscribe  the  square.  Draw  two  diameters,  AB  and  CD,  at  right-angles 
to  each  other.     Join  the  points  A,  D,  B  and  C.    ADBC  is  the  inscribed  square. 

To  describe  the  ckcle.  Draw  the  diagonals  as  before,  intersecting  at  E,  and 
with  E  as  a  center  and  ^£  as  a  radius,  describe  the  circle. 


Fig.  71.     Inscribed  Square  and 
Circumscribed  Circle 


Fig.  72.     Inscribed  Circle  and 
Circumscribed  Square 


Problem  22.  To  inscribe  a  circle  in  a  square  and  to  describe  a  square  about  a 
circle  (Fig.  72). 

To  inscribe  the  circle.  Draw  the  diagonals  AB  and  CD,  intersecting  at  E. 
Draw  the  perpendicular  EG  to  one  of  the  sides.  Then  with  £  as  a  center,  and 
EG  as  a  radius,  describe  a  circle.  It  will  be  tangent  to  all  four  sides  of  the 
square. 

To  describe  the  square.  Draw  two  diameters,  AB  and  CD,  at  right-angles 
to  each  other,  and  prolonged  beyond  the  circumference.  Draw  the  diameter 
OF,  bisecting  the  angle  CEA  or  BED.  Draw  lines  through  G  and  F  perpen- 
dicular to  GF,  and  terminating  in  the  diagonals.  Draw  AD  and  CB  to  com- 
plete the  square. 

Problem  23.     To  inscribe  a  pentagon  in  a  circle  (Fig.  73). 


Fig.  73.     Circle  and  Inscribed 
*     Pentagon 


Circle    and    Inscribed 
Hexagon 


Draw  two  diameters,  AB  and  CD,  at  right-angles  to  each  other.  Bisect  AO 
at  E.  With  jE  as  a  center  and  EC  as  a  radius,  cut  OB  at  F.  With  C  as  a  center 
and  CF  as  a  radius,  cut  the  circle  at  G  and  H.  With  these  points  as  centers  and 
the  same  radius,  cut  the  circle  at  /  and  /.  Join  /,  J,  G,  C  and  H.  IJGCIII  is 
the  inscribed  regular  pentagon. 


i 


J  I!, 


Geometrical  Problems 


73 


Problem  24.     To  inscribe  a  regular  hexagon  in  a  circle  (Fig.  74). 
Lay  off  on  the  circumference  the  radius  of  the  circle  six  times,  and  connect 
the  points. 

Problem  25.  To  construct  a  regular  hexagon  upon  a  given  straight  line,  AB 
(Fig.  75). 

From  A  and  B,  with  a  radius  equal  to  AB,  describe  arcs  intersecting  at  0. 
With  O  as  a  center  and  a  radius  equal  to  AB,  describe  a  circle,  and  from  A  or 
B  lay  off  the  lengths  BC,  CD,  DE,  EF  and  FA  on  the  circumference  of  the  circle. 
ABCDEFA  is  the  required  regular  hexagon. 


Fig.  75.    Regular  Hexagon  on  Given 
Line 


Fig.  76. 


Regular  Octagon  on  Given 
Line 


Problem  26.  To  construct  a  regular  octagon  upon  a  given  straight  line,  AB 
(Fig.  76). 

Produce  the  line  AB  both  ways  and  draw  the  perpendiculars  A  a  and  Bb,  of 
indefinite  length.  Bisect  the  external  angles  at  A  and  B  and  make  the  length 
of  the  bisecting  lines  equal  to  AB.  From  //  and  C  draw  lines  parallel  to  ^ a  or 
Bb  and  equal  in  length  to  AB.  From  G  and  D  as  centers  describe  arcs,  with 
a  radius  AB,  cutting  the  perpendiculars  A  a  and  Bb  in  F  and  E.  Draw  GF, 
FE  and  ED.    ABCDEFGIIA  is  the  required  octagon. 


Fig.  77.     Square  and  Inscribed 
Regular  Octagon 


Fig.  78.     Circle  and  Inscribed 
Regular  Octagon 


Problem  27.     To  construct  a  regular  octagon  in  a  square  (Fig.  77). 

Draw  the  diagonals  AD  and  BC  and  from  yl,  B,  C  and  D,  with  a  radius  equa^ 
to  AO,  describe  arcs  cutting  the  sides  of  the  square  in  a,  b,  c,  d^>»j  /pA  and  i 
Draw  at,  hf.  ed  and  cb»    aihfedcba  is  the  required  octagon.        <\  ^n.-^l'  <.  . 


74 


Geometrical  Problems 


Part  1 


Problem  28.    To  inscribe  a  regular  octagon  in  a  circle  (Fig.  78). 

Draw  two  diameters,  AB  and  CD,  at  right-angles  to  each  other.  Bisect  the 
angles  AOD  and  AOC  by  the  diameters  EF  and  GIL  A~EDHBFCGA  is  the 
required  octagon. 

Problem  29. ,  To  inscribe  a  circle  within  a  regular  polygon. 

First.  When  the  polygon  has  an  even  number  of  sides,  as  in  Fig.  79.  Bisect 
two  opposite  sides  at  A  and  B,  draw  AB  and  bisect  it  at  C  by  a  diagonal,  DEy 
connecting  two  opposite  angles,  as  D  and  E.  The  circle  drawn  with  a  radius 
CA  and  with  C  as  a  center  is  the  inscribed  circle  required. 


Fig.  79.  Regular  Polygon,  Even 
Number  of  Sides,  with  Inscribed 
and  Circumscribed  Circles 


Fig.  80.  Regular  Polygon,  Odd 
Number  of  Sides,  with  In- 
scribed and  Circumscribed 
Circles 


Second.  When  the  number  of  sides  is  odd,  as  in  Fig.  80.  Bisect  two  of  the 
adjacent  sides  as  at  A  and  B,  and  draw  lines,  AE  and  BD,  to  the  opposite  angles, 
and  intersecting  at  C.  The  circle  drawn  with  C  as  a  center  and  CA  as  a  radius 
is  the  inscribed  circle  required. 

Problem  30.     To  draw  a  circumscribing  circle  around  a  regular  polygon. 

First.  When  the  number  of  sides  is  even,  as  in  Fig.  79.  Draw  two  diagonals 
from  opposite  angles,  as  E.D  and  Gil,  intersecting  at  C.  The  circle  drawn  with 
C  as  a  center  and  with  CD  as  a  radius  is  the  circumscribing  circle  required. 

Second.  When  the  number  of  sides  is  odd,  as  in  Fig.  80.  Determine  the 
center,  C,  as  in  the  last  problem.  The  circle  drawn  with  C  as  a  center  and  CD 
as  a  radius,  is  the  circumscribing  circle  required. 


Problems  on  the  Ellipse,  the  Parabola,  the  Hyperbola  and  the 
Cycloid 

The  Ellipse 

Problem  31.  To  describe  an  ellipse,  the  length  and  breadth,  or  the  two  axes, 
being  given. 

First  Method  (Fig.  81),  the  two  axes,  AB  and  CD,  being  given.  On  AB  and 
CD  as  diameters  and  from  the  same  center,  O,  describe  the  circles  AGBII  and 
CLDK.  Take  any  convenient  number  of  points  on  the  circumference  of  the 
outer  circle,  as  h,  b',  h",  etc.,  and  from  them  draw  lines  to  the  center,  O,  cutting 
the  inner  circle  at  the  points  a,  a',  a",  etc.,  respectively.  From  the  points 
ht  b',  etc.,  draw  lines  parallel  to  the  shorter  axis  CD]   and  from  the  points  a, 


The  Ellipse 


75 


a',  etc.,  draw  lines  parallel  to  the  longer  axis  AB,  and  intersecting  the  first  set 
of  lines  at  c,  c' ,  c",  etc.  These  last  points  will  be  points  in  the  ellipse,  and  by 
determining  a  sufficient  number  of  them,  the  ellipse  can  be  drawn. 


Fig.  81.     Ellipse  Described  on  Given  Axes. 


Second  Method  (Fig.  82) .  Take  the  straight-edge,  made  of  a  stiff  piece  of  paper, 
cardboard  or  wood,  and  from  some  point  as  a,  mark  off  ah  equal  to  half  the 
shorter  diameter  CD,  and  *ac  equal  to  half  the  longer  diameter  AB.  Place 
the  straight-edge  so  that  the 
point  h  is  on  the  longer  and 
the  point  c  on  the  shorter 
diameter.  Then  will  the  point 
a  be  over  a  point  in  the  ellipse. 
Make  on  the  paper  a  dot  at  a 
and  move  the  straight-edge 
around,  always  keeping  the 
points  h  and  c  over  the  major 
and  minor  axes  respectively. 
In  this  way  any  number  of 
points  in  the  ellipse  may  be 
determined  and  the  ellipse 
drawn. 

Third     Method     (Fig.     83). 
Given,  the  two  axes,  AB  and 
CD.    From  the  point  Z>  as  a 
center,  and  a  radius  AO,  equal  to  one-half  of  AB,  describe  an  arc  cutting  AB 
at  F  and  F' .    These  two  points  are  called  the  foci  of  the  ellipse. 

Note.  One  property  of  the  ellipse  is,  that  the  sums  of  the  distances  of  any 
two  points  on  the  circumference  from  the  foci  are  the  same.  Tl^us  F'D  -V  DF  «• 
F'E^EPoiF'G-^GF, 


Fig.  82.    Ellipse  Described  with  Straight-Edge 


76 


Geometrical  Problems 


Part  1 


Fix  two  pins  in  the  axis  AB  set  F  and  F'  and  loop  upon  them  a  thread,  of 
cord  equal  in  length,  when  fastened  to  the  pins,  to  AB,  so  as,  when  stretched 

as  per  dotted  Hne  FDF\  it 
will  just  reach  to  the  extremity 
D  of  the  short  axis.  Place  a 
pencil-point  inside  the  chord, 
as  at  E,  and  move  the 
pencil  along,  keeping  the  cord 
stretched  tight.  The  pencil- 
point  will  trace  the  ellipse 
required. 

Problem  32.  To  draw  a  tan- 
gent to  an  ellipse  at  a  given 
point  on  the  curve  (Fig.  84). 

Let  it  be  required  to  draw 
a  tangent  at  the  point  E  on 
the  ellipse  shown.  First  de- 
termine the  foci  F  and  F'  as  in 
the  third  method  for  describing 
an  ellipse,  and  from  E  draw 
Hues  EF  and  EF'.  Prolong  EF'  to  a,  so  that  Ea  equals  EF.  Bisect  the  angle 
aEF  by  describing  arcs  from  a  and  F  as  centers,  as  shown  at  b,  and  through  b 
draw  a  line  through  E.  This  line  is  the  tangent  required.  If  it  is  required  to 
draw  a  line  normal  to  the  curve  at  E,  as,  for  instance,  the  joint  of  an  elliptical 


Fig.  83.     Ellipse  Described  with  String  and  Pencil 


Fig.  84.     Tangent  Drawn  to  Point  on  Ellipse 


arch,  bisect  the  angle  FEE',  and  draw  the  bisecting  line  through  E,  and  it  will 
be  the  normal  to  the  curve  and  the  proper  Hne  at  that  point  for  the  joint  of  an 
elliptical  arch. 

Problem  33.  To  draw  a  tangent  to  an  ellipse  from  a  given  point  outside  of  the 
curve  (Fig.  86). 

From  the  given  point  T  as  a  center,  and  with  a  radius  equal  to  the  distance 
to  the  nearer  focus  F,  describe  an  arc  of  a  circle.  From  F'  as  a  center,  and 
with  a  radius  equal  to  the  length  of  the  longer  axis  of  the  ellipse,  describe  arcs 
cutting  the  circle  just  described  at  a  and  b.  Draw  lines  from  F'  to  a  and  b, 
cutting  the  ellipse  at  E  and  G.  Draw  lines  from  T  through  E  and  G  and  they 
will  be  the  tangents  required. 


The  Ellipse 


77 


Fig.  85.    Tangent  Drawn  to  Ellipse  from  Point  Outside 


Problem  34.     To  describe  an  ellipse  approximately,  by  means  of  circular  arcs. 

First.  With  arcs  of  two  radii  (Fig.  86).  Take  half  the  difference  of  the  two 
axes  AB  and  CD,  and  set  it  off  from  the  center  O  to  a  and  c  on  OA  and  OC; 
draw ac and  onAB  set  off  half  ac  from  a  tod;  draw di  parallel  to  ac;  set  off  Oe  equal 
to  Od;   join  ei  and  draw  em  and  dm  parallel  respectively  to  id  and  ie.    With 


c 

/ 

\.4' 

i 
\ 
\ 

\2 

y\     ^ 

0               / 

'^<^ 

\ 

/ 
m 

X 

Fig.  { 


Ellipse  Described  with  Circular  Arcs  of  Two  Radii 


m  as  a  center  and  with  a  radius  mC,  describe  an  arc  through  C,  terminating  in 
the  points  1  and  2  on  tnd  and  me  produced.  With  »  as  a  center^  and  with  iD 
as  a  radius,  describe  an  arc  through  D,  terminating  in  points  3  and  4  on  ie  and 
id  produced.  With  d  and  e  as  centers,  describe  arcs  through  A  and  B,  connecting 
the  points  i  and  4  and  2  and  3.  The  four  arcs  thus  described  form  approximately 
an  ellipse.  This  method  is  not  satisfactory  when  the  conjugate  or  minor  axis 
is  less  than  two-thirds  the  transverse  or  major  axis. 


78 


Geometrical  Problems 


Part  1  i 


^  Another  method  of  approximating  an  ellipse  by  means  of  arcs  of  two  radii,  i 
is  shown  in  Fig.  87,  the  axis  major  AB  and  the  semiminor  axis  OC  being 

given.  Draw  the  rec-  j 
tangle  AabBA,  and  the 
diagonal  CB.  Lay  off 
Cc  equal  to  the  differ- 
ence between  OB  and 
OC.  Bisect  cB  at  M  and 
erect  the  perpendicular 
YD,  intersecting  CO  pro- 
duced at  Y  and  05, 
at  X.  Make  Qx'  =  Ox. 
Then  will  x,  x',  and  Y 
be  the  three  centers  re- 
quired, the  curves  be- 
coming tangent  at  D 
and  at  the  corresponding 
point  on  the  left-hand 
side  of  the  ellipse.  This 
method  results  in  a 
curve  which  is  slightly 
fuller  at  the  haunches  than  the  curve  drawn  by  the  preceding  method. 
Second.     With  arcs  of  three  radii  (Fig.  88).     On  the  transverse  or  major  axis 


Fig.  87.    Ellipse  Described  with  Circular  Arcs  of  Two  Radii 


'^\ 


/ 
/ 
/ 
/ 
/       . 


//-- 
i"> 


¥ 


Fig.  88.     Ellipse  Described  with  Circular  Arcs  of  Three  Radii 


ABl  draw  the  ;ectang]e  AGEBA,  equal  in   height  to  OC,  half  the  conjugate  or 
minor  axis.   Draw  AC  and  draw  GD  perpendiculai-  to  AC.   Set  off  OK  equal  to 


The  Parabola  and  Hyperbola 


i79 


JC,  and  on  AK  as  a  diameter  describe  the  semicircle  ANK.  Extend  OC  to 
L  and  to  D.  Set  off  OM  equal  to  CL,  and  with  Z)  as  a  center  and  with  a  radius 
DM,  describe  an  arc.  With  A  and  B  as  centers  and  with  a  radius  OL,  cut  AB 
It  P  and  P.  From  //  as  a  center,  and  with  a  radius  HF,  cut  the  arc  ah  at  a. 
W  and  6  are  determined  in  like  manner.  The  points  //,  a,  D,  b  and  W,  are 
the  centers  of  the  arcs  required. 

Produce  the  lines  all,  Da,  Dh,  and  hlV,  and  thus  determine  the  lengths  of 
the  arcs.  This  method  is  practicable  for  all  ellipses.  It  is  often  employed 
[or  vaults,  stone  arches  and  bridges. 

The  Parabola 

Problem  35.  To  describe  a  parabola  when  the  vertex  A,  the  axis  AB  and  a 
point,  M,  of  the  curve  are  given  (Fig.  89). 

Construct  the  rectangle  ABMCA.  Divide  MC  into  any  number  of  equal 
parts,  four  for  instance.  Divide  AC  in  like  manner.  Connect  Ai,  A2  and  As. 
Through  i',  2',  3',  draw  parallels  to  the  axis  AB.  The  intersections  I,  II  and 
III,  of  these  lines,  are  points  in  the  required  curve. 


Fig.  89.     Parabola  and  Tangent  to  Point  on  Parabola 

Problem  36.     To  draw  a  tangent  to  a  given  point,  II,  of  the  parabola  (Fig.  89). 

From  the  given  point  II  let  fall  a  perpendicular  on  the  axis  ^iJ  at  b.  Produce 
the  axis  to  the  left  of  ^1.  Make  yl  a  equal  to  ^&.  A  line  drawn  through  a  and 
II  is  the  tangent  required.     The  lines  perpendicular  to  the  tangent  are  called 

NORMALS. 

To  draw  a  normal  to  any  point,  as  I,  the  tangent  to  any  other  point,  11  being 
given. 

Draw  the  normal  He.  From  I,  let  fall  a  perpendicular  Id,  on  the  axis  AB. 
Lay  off  de  equal  to  be.  The  line  le  is  the  normal  required.  The  tangent  may  be 
drawn  at  I  by  laying  off  a  perpendicular  to  the  normal  le  at  I. 


The  Hyperbola 

If  from  any  point,  P,  of  an  hyperbola,  two  straight  lines  are  drawn  to  two 
fixed  points,  as  F  and  F',  the  foci  of  the  hyperbola,  their  difference  is  alwayS 
the  same.  ,:, 

Problem  37.  To  describe  an  hyperbola  when  a  vertex,  a,  the  given  diflferenc© 
ab  and  one  of  the  foci,  F  are  given  (Fig.  90).  ;        ' 

Draw  the  axis  AB  oi  the  hyperbola,  with  the  given  distance  ab  and  the  focua 


80 

F  marked  on  it. 


Geometrical  Problems 


Part  1 


From  b  lay  off  bFx  equal  to  aF  to  determine  the  other  focus  Fu 
Take  any  point,  as  i  on.  AB, 
and  with  ai  as  a  radius  and  F 
as  a  center,  describe  two  short 
arcs  above  and  below  the  axis. 
With  6 1  as  a  radius,  and  F'  as 
a  center,  describe  arcs  cutting 
those  just  described,  at  P  and 
P'.  Take  several  points,  as  2, 
3  and  4,  and  determine  the  cor- 
responding points  Pi,  Pi  and 
P4  in  the  same  way.  The 
curve  passing  through  these 
points  is  an  hyperbola. 

To  draw  a  tangent  to  any 
point  of  an  hyperbola,  draw 
lines  from  the  given  point  to 
each  of  the  foci  and  bisect 
the  angle  thus  formed.  The 
bisecting  hne  is  the  tangent 
required. 


Fig.  90.     Hyperbola  Described 


The  Cycloid 

The  CYCLOtD  is  the  curve  described  by  a  point  on  the  circumference  of  a  circle 
rolling  in  a  straight  line. 

Problem  38.     To  describe  a  cycloid  (Fig.  91). 

Draw  the  straight  hne  AB.     Describe  the  generating  circle  tangent  to  this 
Ime  at  its  middle  point  D,  and  through  the  center  C,  of  the  circle,  draw  the  line 


Fig.  91.     Cycloid  Described 

EE  parallel  to  A  B.  Let  fall  a  perpendicular  from  C  upon  A  B.  Divide  the  semi- 
circumference  into  any  number  of  equal  parts,  for  example,  six.  Lay  oH  on  AB 
and  CE  distances  Ci',  i'2',  etc.,  equal  to  the  divisions  of  the  circumference. 
Draw  the  chords  Di,  D2,  etc.  From  the  points  i',  2',  3',  etc.,  on  the  Hne  CE, 
with  radii  equal  to  the  generating  circle,  describe  arcs  as  shown.  From  the 
points  i',  2',  3',  4',  5',  etc.,  on  the  line  BA,  and  with  radii  equal  respectively  to 
the  chords  2)r,  2>2,  Dz,  D4,  D5,  describe  arcs  cutting  the  preceding  arcs. 
Tlie  intersections  are  points  of  the  required  cyt:loid. 

tSfJo)  t)ii' 


Table  of  Chords 


SI 


Table  of  Chords.     Radius  =  i.oooo 


0" 


0.0000 
0.0003 
0.0006 
0.0009 
0.0012 
0.0015 
0.0017 
0.0020 
0.0023 
0.0026 
0.0029 

0.0032 
0.0035 
0.0038 
O.OOil 
0.0044 
0.0017 
0.0049 
0.0052 
0.0055 
0.0058 

0.0061 
0.0084 
0.0067 
0.0070 
0.0073 
0.0076 
0.0079 
0.0081 
0.0084 
0.0087 

0.0090 
0.00:)3 
0.0096 
0.0099 
0.0102 
0.0105 
0.0108 
0.0111 
0.0113 
0.0116 

0.0119 
0.0122 
0.0125 
0.0128 
0.0131 
0.0134 
0.0137 
0.0140 
0.0143 
0.0145 

0.0148 
0.0151 
0.0154 
0.0157 
0.0160 
0.0163 
0.0166 
0.0169 
0.0172 
0.0175 


0175 
0177 
0180 

.0183 
0186 

.0189 
0192 

.0195 
0198 
0201 
0204 

0207 
0209 
0212 
0215 
0218 
0221 
0224 
0227 
0230 
0233 

0236 
0239 
0241 
0244 
0247 
0250 
0253 
.0256 
0259 
0262 

0265 
0268 
0271 
0273 
0276 
0279 
0282 
0285 
0288 
,0291 

,0294 
0297 

,0300 
0303 
0305 
0308 
0311 
0314 
0317 

.0320 

0323 
0326 
0329 
0332 
0335 
0337 
0340 
0343 
0346 


0349 
0352 
0355 
0358 
0361 
0364 
0368 
0369 
0372 
0375 
0378 

0381 
.0384 
0387 
.0390 
0393 
03^6 
0398 
0401 
0404 
0407 

0410 
0413 
0416 
0419 
0422 
0425 
0428 
0430 
0433 
0436 

0439 
0442 
0445 
0448 
0451 
0454 
0457 
0460 
,0462 
,0465 

,0468 
,0471 
,0474 
0477 
0489 
.0483 
0486 
.0489 
0492 
0494 


0497 

0500 

0503 

0506 

0509 

0512 

0515 

0518  0 

0521  !0 

0524  0 


0524 
0526 
0529 
0532 
0535 
0538 
0541 
0544 
0547 
0550 
0553 

0556 
0558 
0561 
0564 
0567 
0570 
0573 
0576 
0579 
0582 

0585 
0588 
0590 
0593 
0596 
0599 
0602 
0605 
0608 
0611 

0614 
0617 
0619 
0622 
0625 
0628 
0631 
0634 
0637 
0640 

0643 
0646 
0649 
0651 
0654 
0657 
0669 
0663 
0666 
,0669 

0672 
0675 
0678 

.0681 
0683 
0686 

.0689 
0692 
0695 


0698 
0701 
0704 
0707 
0710 
0713 
0715 
0718 
0721 
0724 
0727 

0730 
0733 
0736 
0739 
0742 
0745 
0747 
0750 
0753 
0756 

0759 
0762 
0765 
0768 
0771 
0774 
0776 
0779 
0782 
0785 

0788 
0791 
0794 
0797 
0800 
0803 
0806 
,0808 
,0811 
.0814 

,0817 
.0820 
.0823 
.0826 
.0829 
.0832 
.0835 
.0838 
.0840 
.0843 


0, 
0. 
0, 
0. 
0. 
0, 
0. 
0. 
0. 
0. 

0. 
0. 
0, 
0. 
0. 
0. 
0. 
0 
0 
0 

0 
0. 
0 
0. 
0 
0. 
0 
0 
0 
0 

0 
0 
0 
0 
0 
0 
0 
0 
0 
0 

0. 
0. 
0. 
0. 
0. 
0, 
0. 
0. 
0, 
0.0872 


0849 
0852 
0855 
0858 
0861 
0864 
0867 


0872 
0875 


0881 
0884 
0887,0 
0890  0 


0893 
0896 
0899 
0901 

0904 
0907 
0910 
0913 

.0916 
0919 

.0922 
0925 
0928 

.0931 


0933  0. 
0936  0. 
0939  0. 
0942  0. 
0945,0. 
0948  0. 
0951  0, 
.095410. 
0957J0. 
0960  0. 


1047 
1050 
1053 
1055 
1058 
1061 
1064 
1067 
1070 
1073 
1076 

1079 
1082 
1084 
108' 
1090 
1093 
1006 
1099 
1102 
1105 

1108 
1111 
1114 


V 


1221 
1224 
1227 
1230 
1233 
1235 
1238 
1241 
1244 
1247 
1250 

1253 
1256 
1259 
1262 
126; 
1267 
1270 
1273 
1276 
1279 


0962  0 

0965  0 

0968  0 

0971 

0974 

0977 

0980 

0983 

0986 

0989 


0992 
0994 
0997 

.  1000 
1003 

.1006 
1009 
1012 
1015 
1018 

1021 
1023 
1026 
1029 
1032 
1035 
1038 
1041 
1044 
1047 


11160, 
11190 
11220. 
11250. 
11280. 
11310. 
11340. 

11370. 
1140  0. 
1143|0. 
1145J0. 
1480. 


H" 


1282 
1285 
1288 
1291 
1294 
12960 
1299  0 
1302  0 
1305  0 
1308  0 


1151 
1154 
1157 
1160 
1163 

1166 
1169 
1172 
1175 
1177 
1180 
1183 
1186 
1189 
1192 


1195 
1198 
1201 
1204 
1206 
.1209 
12120. 
12150. 
12180. 
1221  0. 


1311 
1314 
1317 
1320 
1323 
1325 
1328 
1331 
1334 
1337 

1340 
1343 
1346 
1349 
1352 
1355 
1357 
1360 
1363 
1366 


1369 

1372 

1375 

1378 

1381 

1384 

1386  0. 

1389  0 

13920 

13950 


1395 

1398 
1401 
1404 
1407 
1410 
1413 
1415 
1418 
1421 
1424 

1427 
1430 
1433 
1436 
1439 
1442 
1444 
1447 
1450 
1453 

1456 
1459 
1462 
1465 
1468 
1471 
1473 
.1476 
1479 
1482 

1485 
1488 
1491 
1494 
1497 
1500 
1502 
150i 
1508 
1511 

1514 
1517 
1520 
1523 
1526 
1529 
1531 
.1534 
1537 
1540 


1543 
1546 
1549 
1552 
1555 
1558 
1560 
1563 
1566 
1569 


1569 
1572 
1575 
1578 
1581 
1584 
1587 
1589 
1592 
1595 
1598 

1601 
.1604 
1607 
1610 
1613 
.1616 
1618 
1621 
1624 
.1627 

1630 
1633 
1636 
1639 
1642 
1645 
1647 
1650 
1653 
1656 

1659 
1662 
1665 
1668 
1671 
1674 
1676 
1679 
1682 
1685 

1688 
1691 
1694 
1697 
1700 
1703 
1705 
1708 
1711 
1714 

1717 
1720 
1723 
1726 
1729 
1732 
1734 
1737 
1740 
1743 


10° 


1743 
1746 
1749 
1752 
1755 
1758 
1761 
1763 
1766 
.1769 
1772 

1775 

1778 
1781 
1784 
1787 
1789 
1792 
1795 
1798 
1801 

1804 
1807 
1810 
1813 
1816 
1818 
1821 
1824 
1827 
1830 

1833 
1836 
1839 
1842 

.1845 
1847 

.1850 
1853 

.1856 
1859 


1862 
1865 
1868 
1871 
1873 
1876 
1879 
1882 
1885 
1888 

1891 
1894 
1897 
1900 
1902 
1905 
1908 
1911 
1914 
1917 


82 


Geometrical  Problems 


Part  1 


Table  of  Chords  (Continued).     Radius  =  i.oooo 


M.      U° 


12° 


13° 


14° 


15° 


16° 


17° 


18° 


19° 


30° 


31° 


0.1917  0 
0.1920  0. 
0.1923  0. 
0.1926  0. 
0. 1928)0. 
0.1931iO. 
0.1934|0. 
0. 193710. 
0.19400. 
0.1943iO. 
0.1946jO. 

0.19190. 
0.1952,0. 
0.1955  0. 
0.19570. 
0.19600. 
0.1963  0. 
0.1966  0. 
0.1969'0. 
0.1972  0. 
0.1975  0. 


0  1978 
0.1981 
0.1983 
0.1986 
0.1989 
0.1992 
0.1995 
0.1998 
0.2001 
0.2004 

0.2007 

0.2010 

0.2012 

0.201 

0.2018 

0.2021 

0.2024 

0.2027 

0.2030 

0.2033 

0.2036 
0.2038 
0.2041 
0.2044 
0.2047 
0.2050 
0.2053 
0.2056 
0.2059 
0.2062 

0.2065 
0.2067 
0.2070 
0.2073 
0.2076 
0.2079 
0.2082 
0.2085 
0.2088 
0.2091 


2091 
2093 
2096 
2099 
2102 
2105 
2108 
2111 
2114 
2117 
2119 

2122 
2125 
2128 
2131 
2134 
2137 
2140 
2143 
2146 
2148 

2151 
2154 
2157 
2160 
2163 
2166 
2169 
2172 
2174 
2177 


2264 
2267 
2270 
2273 
2276 
2279 
2281 
2284 
2287 
2290 
2293 


2296 

2299 

2302 

2305 

2307 

2310 

2313 

2316 

2319lO 

2322  0 


2325'0 

2328  0 

2331 

2333 

2336 

2339 

2342 

2345 

2348 

2351 


2180 

2183 

2186 

2189 

2192 

2195 

2198 

2200  0 

2203  0 

2206  0 


2209 
2212 
2215 
2218 
2221 
2224 
2226 
2229 
2232 
2235 

2238 
2241 
2244 
2247 
.2250 
2253 
2255 
2258 
2261 
.2264 


2354 
2357 
2359 
2362 
2365 
2368 
2371 
2374 
2377 
2380 

2383 
2385 
2388 
2391 
2394 
2397 
2400 
2403 
2406 
2409 

2411 
2414 
2417 
2420 
2423 
2426 
2429 
2432 
2434 
2437 


2437 
2440 
2443 
2446 
2449 
2452 
2455 
2458 
2460 
2463 
2466 

2469 
2472 
2475 

2478 
2481 
2484 
2486 
2489 
2492 
2495 

2498 
2501 
2504 
2507 
2510 
2512 
2515 
2518 
2521 
2524 

2527 
2530 
2533 
2536 
2538 
2541 
2544 
2547 
2550 
2553 

2556 
2559 
2561 
2564 
2567 
2570 
2573 
2576 
2579 
2582 

2585 
2587 
2590 
2593 
2596 
2599 
2602 
2605 
2608 
2611 


2611 
2613 
2616 
2619 
2622 
2625 
2628 
2631 
2634 
2636 
2639 

2642 
2645 
2648 
2651 
2654 
2657 
2660 
2662 
2665 
2668 

2671 
2674 
2677 
2680 
2683 
2685 
2688 
2691 
2694 
2697 

2700 
2703 
2706 
2709 
2711 
2714 
2717 
2720 
2723 
2726 

2729 
2732 
2734 
2737 
2740 
2743 
2746 
2749 
2752 
2755 

2758 
2760 
2763 
2766 
2769 
2772 
2775 
2778 
2781 
2783 


2783 
2786 
2789 
2792 
2795 
2798 
2801 
2804 
2807 
2809 
2812 

2815 
2818 
2821 
2824 
2827 
2830 
2832 
2835 
2838 
2841 

2844 
2847 
2850 
2853 
2855 
2858 
2861 
2864 
2867 
2870 

2873 
2876 
2878 
2881 
2884 
2887 
2890 
2893 
2896 
2899 

2902 
2904 
2907 
2910 
2913 
2916 
2919 
2922 
2925 
2927 

2930 
2933 
2936 
2939 
2942 
2945 
2948 
2950 
2953 
2956 


2956 
2959 
2962 
2965 
2968 
2971 
2973 
2976 
2979 
2982 
2985 


2988  0 
2991  0 
2994  0 
0 
0 
0 
0 
0 
0 
0 

0. 
0. 
0. 
0. 
0, 
0. 
0. 
0 
0. 
0, 


2996 
2999 
3002 
3005 
3008 
3011 
3014 

3017 
3019 
3022 
3025 
3028 
3031 
3034 
3037 
3040 
3042 

3045  0 
0 
3051 
3054 
3057 
3060 
3063 
3065 
3068 
3071 


3074 
3077 
3080 
3083 
3086 
3088 
3091 
3094 
3097 
3100 

3103 
3106 
3109 
3111 
3114 
3117 
3120 
3123 
3126 
3129 


.3129 
3132 
3134 
3137 
3140 

.3143 
3146 
3149 
3152 

.3155 
3157 

3160 
3163 
3166 
3169 
3172 
.3175 
.3178 
.3180 
.3183 
3186 

3189 
3192 
3195 
3198 
3200 
3203 
3206 
3209 
3212 
3215 

3218 
3221 
3223 
3226 
3229 
3232 
3235 
3238 
3241 
3244 

3246 
3249 
3252 
3255 
3258 
3261 
3264 
3267 
3269 
3272 

3275 

3278 
3281 
3284 
3287 
3289 
3292 
3295 
3298 
3301 


3301 
3304 
3307 
3310 
3312 
3315 
3318 
3321 
3324 
,3327 
.3330 

3333 
3335 
3338 
3341 
3344 
3347 
3350 
3353 
3355 
3358 

3361 
3364 
3367 
3370 
3373 
3376 
3378 
3381 
3384 
3387 

3390 
3393 
3396 
3398 
3401 
3404 
3407 
3410 
3413 
3416 

3419 
3421 
3424 
3427 
3430 
3433 
3436 
3439 
3441 
3444 

3447 
3450 
3453 
3456 
3459 
3462 
3464 
3467 
3470 
3473 


3473 
3476 
3479 
3482 
3484 
3487 
3490 
3493 
3496 
3499 
3502 

3504 
3507 
3510 
3513 
3516 
3519 
3522 
3525 
3527 
3530 

3533 
3536 
3539 
3542 
3545 
3547 
3550 
3553 
3556 
3559 

3562 
.3565 
3567 
3570 
3573 
3576 
3579 
3582 
3585 
3587 

3590 
.3593 
3596 
3599 
3602 
3605 
3608 
3610 
3613 
3616 

3619 
.3522 
3625 
3628 
3630 
3633 
3636 
3639 
.3642 
3645 


3645 
3648 
.3650 
3653 
3656 
3659 
3662 
3665 
3668 
3670 
3673 

3676 
3679 
3682 
3685 

.3688 
3690 
3693 
3696 

.3699 
3702 

3705 
3708 
3710 
3713 
3716 
3719 
3722 
3725 
3728 
3730 


0.3733 

0.3736 

0.3739 

0.3742 

0.3745 

0.3 

0.3750 

0.3753 

0.3756 

0.3759 

0.3762 
0.3765 
0.3768 
0.3770 
0.3773 
0.3776 
0.3779 
0.3782 
0.3785 
0.3788 

0.3790 
0.3793 
0.3796 
0.3799 
0.3802 
0.3805 
0.3808 
0.3810 
0.3813 
0.3816 


Table  of  Chords 


m 


Table  of  Chords  (Continued).     Radius  =  i.oooo 


M.      22° 


33° 


24° 


35° 


36° 


37° 


38° 


39° 


30° 


31°       33° 


9 
10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

41 

42 
43 
44 
45 
46 
47 
48 
49 
50 

51 

52 
53 
54 
55 
56 
57 
58 
59 


0.3816 
0.3819 
0.3822 
0.3825 
0.3828 
0.3830 
0.3833 
0.3836 
0.3839 
0.3842 
0.3845 

0.3848 
0.3850 
0.3853 
0.3856 
0.3859 
0.3862 
0.3865 
0.3868 
0.3870 
0.3873 

0.3876 
0.3879 
0.3882 
0.3885 
0.3888 
0.3890 
0.3893 
0.3896 
0.3899 
0.3902 

0.3905 
0.3908 
0.3910 
0.3913 
0.3916 
0.3919 
0.3922 
0.3925 
0.3927 
0.3930 

0.3933 
0.3936 
0.3939 
0.3942 
0.3945 
0.3947 
0.3950 
0.3953 
0.3956 
0.3959 

0.3962 
0.3965 
0.3967 
0.3970 
0.3973 
0.3976 
0.3979 
0.3982 
0.3985 
0.3987 


3987 
3990 
3993 
3996 
3999 
4002 
4004 
4007 
4010 
4013 
4016 

4019 
4022 
4024 
4027 
4030 
4033 
4036 
4039 
4042 
4044 

4047 
4050 
4053 
4056 
4059 
4061 
4064 
4067 
4070 
4073 

4076 
4079 
4081 
4084 
4087 
4090 
4093 
4096 
4098 
4101 

4104 
4107 
4110 
4113 
4116 
4118 
4121 
4124 
4127 
,4130 

,4133 
,4135 
,4138 
.4141 
.4144 
.4147 
.4150 
.4153 
.4155 
,4158 


4158 
4161 
4164 
4167 
4170 
4172 
4175 
,4178 
,4181 
,4184 
,4187 

4190 
4192 
4195 
4198 
4201 
4204 
4207 
4209 
4212 
4215 

4218 
4221 
4224 
4226 
4229 
4232 
4235 
4238 
4241 
4244 

4246 
4249 
4252 
4255 

4258 
4261 
4263 
4266 
4269 
.4272 

4275 

4278 
.4280 
4283 
4286 
4289 
.4292 
4295 
.4298 
4300 

4303 
4306 
4309 
4312 
4315 
4317 
4320 
4323 
4326 
4329 


.4329 
.4332 
.4334 
.4337 
.4340 
.4343 
.4346 
.4349 
.4352 
.4354 
:4357 


4360 
4363 
4366 
4369 
4371 
4374 
4377 
4380 
4383 
4386 


4388  0. 
4391  0. 
4394  0. 


4397 
4400 
4403 
4405 
4408 
4411 
4414 

4417 
4420 
4422 
4425 
4428 
4431 
,4434 
,4437 
.4439 
.4442 

444, 
4448 
4451 
4454 
4456 
4459 
4462 
4465 
4468 
4471 

4474 
4476 
4479 

4482 
4485 
,4488 
4491 
4493 
4496 
4499 


4499 
4502 
4505 
4508 
4510 
4513 
4516 
4519 
4522 
4525 
4527 

4530 
4533 
4536 
4539 
4542 
4544 
4547 
4550 
4553 
4556 

4559 
4561 
4564 
4567 
4570 
4573 
4570 
4578 
4581 
4584 

4587 
4590 
4593 
4595 
4598 
4601 
4604 
4607 
4609 
4612 

4615 
4618 
4621 
4624 
4626 
4629 
4632 
4635 
4638 
4641 

4643 
4646 
4649 
4652 
4655 
4658 
4660 
4663 
4666 
4669 


4669 
4672 
4675 
,4677 
,4680 
,4083 
,4686 
.4689 
.4692 
.4694 
4697 

4700 
4703 
4706 
4708 
4711 
4714 
4717 
4720 
4723 
4725 

4728 
4731 
4734 
4737 
4740 
4742 
474, 
4748 
4751 
4754 

.4757 
4759 
4762 
4765 
4768 

.4771 
4773 
4776 
4779 

.4782 

4785 
4788 
4790 
4793 
4796 
4799 
4802 
4805 
,4807 
,4810 

,4813 
,4816 
,4819 
.4822 
.4824 
.4827 
.4830 
.4833 
.4836 
.4838 


4838 
4841 
4844 
4847 
4850 
4853 
4855 
4858 
.4861 
4864 
4867 

4869 

4872 
4875 
4878 
4881 
4884 
4886 
4889 
4892 
4895 


4901 
4903 
4906 
4909 
4912 
4915 
4917 
4920 
4923 

4926 
4929 
4932 
4934 
4937 
4940 
4943 
4946 
4948 
4951 

4954 
4957 
4960 
4963 
4965 
,4968 
.4971 
4974 
4977 
.4979 


4982 
4985 
4988 
4991 
4994 
4996 
4999 
.5002 
5005 
.5008 


-U 


5008 
5010 
5013 
5016 
5019 
5022 
5024 
5027 
5030 
5033 
5036 

5039 
5041 
5044 
5047 
5050 
5053 
5055 
5058 
5001 
5064 

5067 
5070 
5072 
5075 
5078 
5081 
5084 
5086 
5089 
5092 

5095 
5098 
5100 
5103 
5106 
5109 
5112 
5115 
5117 
5120 

5123 
5126 
,5129 
5131 
5134 
,5137 
.5140 
.5143 
5145 
.5148 

5151 
5154 
5157 
5160 
5162 
5165 
5168 
5171 
5174 
5176 


5176 
5179 
5182 
5185 
5188 
5190 
5193 
5196 
5199 
5202 
5204 

5207 
5210 
5213 
5216 
5219 
5221 
5224 
5227 
5230 
5233 

5235 
5238 
5241 
5244 
5247 
5249 
5252 
5255 
5258 
5261 

5263 
,5266 
5269 
5272 
5275 
5277 
,5280 
,5283 
5286 
.5289 

5291 
5294 
5297 
5300 
5303 
5306 
5308 
5311 
5314 
5317 

5320 
5322 
5325 
5328 
5331 
5334 
5336 
5339 
5342 
5345 


5345 
5348 
5350 
5353 
5356 
5359 
5362 
5364 
5367 
5370 
5373 

5376 

5378 
5381 
5384 
5387 
5390 
5392 
5395 
5398 
5401 

5404 
5406 
5409 
5412 
5415 
5418 
5420 
5423 
5426 
5429 

5432 
5434 
5437 
5440 
5443 
5446 
5448 
5451 
5454 
5457 

5460 
5462 
5465 
5468 
5471 
5474 
4576 
5479 
5482 
,5485 

,5488 
,5490 
.5493 
.5496 
.5499 
.5502 
.5504 
.5507 
.5510 
.6513 


5513 
5516 
5518 
5521 
5524 
5527 
5530 
5532 
5535 
5538 
5541 

5543 
5546 
5549 
5552 
5555 
5557 
5560 
5563 
5566 
5569 

5571 
5574 
5577 

5580 
5583 
5585 
5588 
5591 
5594 
5597 

5599 
.5602 
5605 
5608 
5611 
5613 
5616 
5619 
5622 
5625 

5627 
5630 
5633 
5636 
5638 
5641 
5644 
5647 
5650 
5652 

5655 
5658 
5661 
5664 
5666 
5669 
5672 
5675 
.5678 
.5680 


84 


Geometrical  Problems 


Part  1 


[Table  of  Chords  (Continued).     Radius  =  i.oooo 


M. 


0.5680 
0.5683 
0.5686 
0.5689 
0.5691 
0.5694 
0.5697 
0.5700 
0.5703 
0.5705 
0.5708 

0.571 

0.5714 

0.5717 

0.5719 

0.5722 

0.5725 

0.5728 

0.5730 

0.5733 

0.5736 

0.5739 
0.5742 
0.5744 
0.5747 
0.5750 
0.5753 
0.5756 
0.5758 
0.5761 
0.5764 

0.5767 
0.5769 
0.5772 
0.5775 
0.5778 
0.5781 
0.5783 
0.5786 
0.5789 
0.5792 

0.5795 
0.5797 
0.5800 
0.5803 
0.5806 
0.5808 
0.5811 
0.5814 
0.5817 
0.5820 

0.5822 
0.5825 
0.5828 
0.5831 
0.5834 
0.5836 
0.5839 
0.5842 
0.5845 
0.5847 


W 


5847 
5850 
5853 
5856 
5859 
5861 
5864 
5867 
5870 
5872 
5875 

5878 
5881 
5884 
5886 
5889 
5892 
5895 
5897 
5900 
5903 

5906 
5909 
5911 
5914 
5917 
5920 
5922 
5925 
5928 
5931 

5934 
5936 
5939 
5942 
5945 
5947 
5950 
5953 
5956 
5959 

5961 
5964 
5967 
5970 
5972 
5975 
5978 
5981 
5984 


5989 
5992 
5995 
5997 
6000 
6003 
6006 
6009 
6011 
6014 


35° 


6014 
6017 
.6020 
6022 
6025 
6028 
6031 
6034 
6036 
6039 
6042 

6045 
6047 
6050 
6053 
6056 
6058 
6061 
6064 
6067 
6070 

.6072 
6075 
6078 
6081 
,6083 
6086 
6089 
6092 
6095 
,6097 

6100 
6103 
6106 
6108 
6111 
6114 
6117 
6119 
6122 
6125 

6128 
6130 
6133 
6136 
6139 
6142 
6144 
6147 
6150 
6153 

6155 
6158 
6161 
6164 
6166 
6169 
6172 
6175 
6178 
6180 


36° 


6180 
6183 
6186 
6189 
6191 
6194 
6197 
6200 
6201 
6205 


6211 
6214 
6216 
6219 
6222 
6225 
6227 
,6230 
6233 
6236 

6238 
6241 
6244 
6247 
6249 
6252 
6255 
6258 
6260 
6263 

6266 

6269 

6272 

6274 

62 

6280 

6283 

6285 

6288 

6291 

6294 
6296 
6299 
6302 
6305 
6307 
6310 
6313 
6316 
6318 

6321 
6324 
6327 
6330 
6332 
6335 
6338 
6341 
6343 


37° 


6346 
6349 
6352 
6354 
6357 
6360 
6363 
6365 
6368 
6371 
6374 


6376 
.6379 
6382 
6385 
6387 
6390 
6393 
6396 
6398 
6401 

.6404 
6407 
6410 
6412 
6415 
6418 
6421 
6423 
6426 
6429 

.6432 
6434 
643' 
6440 
6443 
6445 
6448 
6451 
6454 
6456 

6459 
6462 
6465 
6467 
6470 
6473 
6476 
6478 
6481 
6484 

6487 
6489 
6492 
6495 
6498 
6500 
6503 
6506 
6509 
6511 


6511 
6514 
6517 
6520 
6522 
6525 
6528 
6531 
6533 
6536 
6539 

6542 
6544 
6547 
6550 
6553 
6555 
6558 
6561 
6564 
6566 

6569 
6572 
6575 
6577 
6580 
6583 
6586 
6588 
6591 
6594 

6597 
6599 
6602 
6605 
6608 
6610 
6613 
6616 
6619 
6621 

6624 
662' 
6630 
6632 
6635 
6638 
6640 
6643 
6646 
6649 

6651 
6654 
6657 
6660 
6662 
6665 
6668 
6671 
6673 
6676 


39° 


6676 
6679 
6682 
6684 
6687 
6690 
6693 
6695 
6698 
6701 
6704 

6706 
6709 
6712 
0fl5 
6717 
6720 
6723 
6725 
6728 
6731 

6734 
6736 
39 
6742 
6745 
747 
6750 
6753 
6756 
6758 

6761 
6764 
676' 
6769 
6772 
6775 
6777 
6780 
6783 
6786 


6791 
6794 
6797 
6799 
6802 
6805 
6808 
6810 
6813 

6816 
6819 
6821 
6824 
6827 
6829 
6832 
6835 
6838 
6840 


40° 


6840 
6843 
6846 
6849 
6851 
6854 
6857 
6860 
6862 
6865 


41° 


6870  0, 
6873  0, 
6876  0, 
0 
0 
0 
0 
0 


6887 
6890 
6892 
6895 


6901 
6903 
6906 
6909 
6911 
6914 
6917 
6920 
6922 

6925 
6928 
6931 
6933 
6936 
6939 
6941 
6944 
6947 
6950 

6952 
6955 
6958 
6961 
6963 
6966 
6969 
6971 
6974 
6977 


6982 
6985 
6988 
6991 
6993 
6996 
6999 
7001 
7004 


7004 
7007 
7010 
7012 
7015 
7018 
7020 
7023 
7026 
7029 
7031 

7034 
7037 
7040 
7042 
7045 
7048 
7050 
7053 
7056 
7059 

7061 
7064 
7067 
7069 
'072 
7075 
7078 
7080 
7083 
7086 

7089 
7091 
7094 
7097 
7099 
7102 
7105 
7108 
7110 
7113 

7116 
7118 
7121 
7124 
7127 
7129 
7132 
7135 
7137 
7140 


43° 


7143  0. 
7146  0. 


7148 
7151 
7154 
7156 
7159 
7162 
7165 
167 


7167 
7170 
7173 
7176 
7178 
7181 
7184 
7186 
7189 
7192 
7195 

7197 
7200 
7203 
7205 
7208 
7211 
7214 
7216 
7219 
7222 

7224 
7227 
7230 
7232 
7235 
7238 
7241 
7243 
7246 
7249 

7251 
7254 
7257 
7260 
7262 
7265 
7268 
7270 
7273 
7276 

7279 
7281 
7284 
7287 
7289 
7292 
7295 
7298 
7300 
7303 

7306 
7308 
7311 
7314 
7316 
7319 
7322 
7325 
7327 
7330 


43° 


7330 
7333 
7335 
7338 
7341 
7344 
7346 
7349 
7352 
7354 
7357 

7360 
7362 
7365 
7368 
7371 
7373 
7376 
7379 
7381 
7384 

7387 
.7390 
7392 
.7395 
7398 
7400 
7403 
7406 
7408 
741 


7414 
7417 
7419 
7422 

.7425 
7427 

.7430 
7433 
7435 
7438 

7441 
7443 
7446 
7449 
7452 
7454 
7457 
7460 
7462 
7465 

7468 
'471 
7473 
7476 
7479 
7481 
7484 
7487 
7489 
7492 


Table  of  Chords 


M 


Table  of  Chords  (Continued).  Radius  =  i.oooo 


44° 


45° 


46° 


47° 


48° 


49° 


60° 


51° 


53°   63 


64° 


0.7492  0. 
0.7495  0. 
0.7498'0. 


0.7500 
0.7503 
0.7506 
0.7508 
0.7511 
0.7514 
0.7516 
0.7519 

0.7522 
0.7524 
0.7527 
0.7530 
0.7533 
0.7535 
0.7538 
0.7541 
0.7543 
0.7546 


7549 
7551 
7554 
7557 
7569 
7562 
7565 
7568 
7570 
7o73 


0.7576 
0.7578 
0.7581 
0.7581 
0.7586 
0.7589 
0.7592 
0.7595 
0.7597 
0.7600 

0.7603 
0.7605 
0.7608 
0.7611 
0.7613 
0.7616 
0.7619 
0.7621 
0.7624 
0.7627 

0.7629 
0.7632 
0.7635 
0.7638 
0.7640 
0.7643 
0.7646 
0.7648 
0.7651 
0.7654 


7654  0 
7656  0 
7659  0 


7662 
7664 
7667 
7670 
7672 
7675 
7678 
7681 


,7815  0 
,7817  0 
,7820  0 
78230 
78250 
7828,0 
7831  0 
7833  0 
7836,0 
7839  0 
7841  0 


7683  0 
76S6  0 
0 
7691 
7694 
7697 
7699 
7702 
7705 
7707 


7710 
7713 
7715 
7718 
7721 
7723 
7726 
7729 
7731 
7734 


7737 
7740 
7742 
7745  0 
7748  0 
7750  0 


7975  0. 
7978,0. 
7980  lo, 
7983'0. 
7986  0. 
.7988,0. 
7991  0. 
79941 0. 
7996,0. 
7999  0. 
8002  0. 


7844  0. 
7847  0. 
7849  0, 
7852,0. 

785510. 
785710. 
7863  0. 


7863 
7865 
7868 


78710 
7873  0. 
7876  0 
7879  0 
7882  0. 
78810 
7887  0. 
7890  0 
7892  0 
7895  0 


7753 
7756 

7758 
7761 


7764  0. 
766  0 


7769 

7772 
7774 
7777 
7780 
7782 
7785 
7788 

7791 
7793 
7796 
7799 
7801 
7804 
7807 
7809 
7812 
7815 


7898 
7900 
7903 
7906 
7908 
7911 
7914 
7916 
7919 
7922 

7924 
7927 
7930 
7932 
7935 
7938 
7940 
7943 
7946 
7948 

7951 
7954 
7956 
7959 
7962 
7964 
7967 
7970 
7972 
7975 


8004 
8007 
8010 
8012 
8015 
8018 
8020 
8023 
8026 
8028 

8031 
8034 
8036 
8039 
8042 
8044 
8047 
8050 
8052 
8055 

8058 
8060 
8063 
8066 
8068 
8071 
8074 
8076 
8079 
8082 

8084 
808: 
8090 
8092 
8095 
8098 
8100 
8103 
8105 
8108 

8111 
8113 
8116 
8119 
8121 
8124 
8127 
8129 
8132 
8135 


8135 
8137 
8140 
8143 
8145 
8148 
8151 
8153 
8156 
8159 
8161 

.8164 
8167 
8169 
8172 
8175 
8177 
8180 
8183 
8185 
8188 


.8294  0. 
8297  !o, 
8299  jo, 
8302  0. 


8304 
8307 
.8310 
.8312 
8315 
8318 
8320 

8323 
8326 
8328 
8331 
8334 
8336 
8339 
8341 
8344 
8347 


8190  0 

8193  0 

8196  0 

8198 

8201 

8204 

8206 

8209 

8212 

8214 


8452  0 
8455  0. 
8458  0 
8460  jo 
846310 
8466  0 
8468,0 
8471'0 


8349  0. 
8352  0. 


8217 
8220 
8222 
8225 
8228 
8230 
8233 
8236 
8238 
8241 

8244 
8246 
8249 
8251 
8254 
8257 
8259 
8262 
8265 
8267 

8270 
8273 
8275 
8278 
8281 
8283 
8286 
8289 
8291 
8294 


0.8376  0 

0 

0 

0 

0 


8355 
8357 
8360 
8363 
8365 
8368 
8371 
8373 


.8378 
.8381 
.8384 


8389 
8392 
8394 
8397 
8400 

8402 
8405 
8408 
8410 
8413 
8415 
8418 
8421 
8423 
8426 

8429 
8431 
8434 
8437 
8439 
8442 
8444 
8447 
8450 
8452 


8473 
8476 
8479 

8481 
8484 
8487 
8489 
8492 
8495 
8497 
8500 
8502 
8505 

8508 
8510 
8513 
8516 
8518 
8521 
8523 
8526 
8529 
8531 

8534 
8537 
8539 
8542 
8545 
8547- 
8550 
8552 
8555 
8558 

8560 
8563 
8566 

8568 
8571 
8573 
8576 
8579 
8581 
8584 

8587 
8589 
8592 
8594 
8597 
8600 
8602 
8605 
8608 
8610 


8610  0 
8613,0 
86150 
8618'0 
86210 
8623,0 
8626  0 
8629:0 
8631  0 
8634 lO 
0. 


8767  0. 
8770  0. 


8639 
8642 
8644 
8647 
8650 
8652 
8655 
8657 
8660 


0.8665  0. 

0 

0, 

0. 

0, 

0. 

0. 

0. 

0. 

0. 


.8668 
.86/1 
.8673 
.8676 
.8678 
.8681 
.8684 
.8686 


8692 
8694 
8697 
8699 
8702 
8705 
8707 
8710 
8712 
8715 

8718 
8720 
8723 
8726 
8728 
8731 
8734 
8736 
8739 
8741 

8744 
8747 
8749 
8752 
8754 
8757 
8760 
8762 
8765 
8767 


8773 
8775 
8778 
8780 
8783 
8786 
8788 
8791 
8794 

8796 
8799 
8801 
8804 
8807 
8809 
8812 
8814 
8817 
8820 

8822 
8825 
8828 
8830 
8833 
8835 
8838 
8841 
8843 
8846 


8851 
8854 
8856 
8859 
8861 
8864 
8867 
8869 
8872 

8874 
8877 
8880 
8882 
8885 
8887 
8890 
8893 
8895 


0.8898 


8900 
8903 
8906 


8924 
8927 
8929 
8932 
8934 
8937 
8940 
8942 
8945 
8947 
8950 

8953 
8955 

8958 
8960 
8963 


8971 
8973 
8976 

8979 
8981 
8984 


8911 

8914 

89160 

89190 

8921,0 

8924  0 


8992 
8994 
8997 
8999 
9002 

9005 
9007 
9010 
9012 
9015 
9018 
9020 

.9023 
9025 

.9028 

9031 
9033 
9036 
9038 
9041 
9044 
9046 
9049 
9051 
9054 

9056 
9059 
9062 
9064 
9067 
9069 
9072 
9075 
9077 
9080 


9082 
9085 
9088 
.9090 
9093 
.9095 
9098 
9101 
9103 
9106 

9108 
9111 
9113 
9116 
9119 
9121 

.9124 
9126 

.9129 
9132 

9134 
9137 
9139 
9142 
9145 
9147 
9150 
9152 
9155 
9157 

9160 
9163 
9165 
.9168 
9170 
9173 
9176 
9178 
9181 
9183 

9186 
9188 
9191 
9194 
9196 
9199 

.9201 
9204 
9207 

.9209 

9212 
9214 
9217 
9219 
9222 
9225 
9227 
9230 
9232 
9235 


86 


Geometrical  Problems 


Table  of  Chords 

(Continued). 

Radius 

=  i.oooo 

M. 

66° 

66° 

67° 

68° 

59° 

60° 

61° 

62° 

63° 

64° 

M. 

0' 

0' 

0.9235 

0.9389 

0.9543 

0.9696 

0.9848 

1.0000 

1.0151 

1.0301 

1.0450 

1.0598 

1 

0.9238 

0.9392 

0.9546 

0.9699 

0.9851 

1.0003 

1.0153 

1.0303 

1.0452 

1.0601 

1 

2 

0.9240 

0.9395 

0.9548 

0.9701 

0.9854 

1.0005 

1.0156 

1.0306 

1.0455 

1.0603 

2 

3 

0.9243 

0.9397 

0.9551 

0.9704 

0.9S56 

1.0008 

1.0158 

1.0308 

1.0457 

1.0606 

3 

4 

0.9245 

0.9400 

0.9553 

0.9706 

0.9859 

1.0010 

1.0161 

1.0311 

1.0460 

1.0608 

4 

5 

0.9248 

0.9402 

0.9556 

0.9709 

0.9861 

1.0013 

1.0163 

1.0313 

1.0462 

1.0611 

5 

6 

0.9250 

0.9405 

0.9559 

0.9711 

0.9864 

1.0015 

1.0106 

1.0316 

1.0465 

1.0613 

6 

7 

0.9253 

0.9407 

0.9561 

0.9714 

0.9866 

1.0018 

1.0168 

1.0318 

1.0467 

1.0616 

7 

8 

0.9256 

0.9410 

0.9564 

0.9717 

0.9869 

1.0020 

1.0171 

1.0321 

1.0470 

1.0618 

8 

9 

0.9258 

0.9413 

0.9566 

0.9719 

0.9871 

1.0023 

1.0173 

1.0323 

1.0472 

1.0621 

9 

10 

0.9261 

0.9415 

0.9569 

0.9722 

0.9874 

1.0025 

1.0176 

1.0326 

1.0475 

1.0623 

10 

11 

0.9263 

0.9418 

0.9571 

0.9724 

0.9876 

1.0028 

1.0178 

1.0328 

1 .0477 

1.0626 

11 

12 

0.9266 

0.9420 

0.9574 

0.9727 

0.9879 

1.0030 

1.0181 

1.0331 

1.0480 

1.0628 

12 

13 

0.9268 

0.9423 

0.9576 

0.9729 

0.9881 

1.0033 

1.0183 

1.0333 

1.0482 

1.0630 

13 

14 

0.9271 

0.9425 

0.9579 

0.9732 

0.9884 

1.0035 

1.0186 

1.0336 

1.0485 

1.0633 

14 

15 

0.9274 

0.9428 

0.9581 

0.9734 

0.9886 

1.0038 

1.0188 

1.0338 

1.0487 

1.0635 

15 

16 

0.9276 

0.9430 

0.9584 

0.9737 

0.9889 

1.0040 

1.0191 

1.0341 

1.0490 

1.0638 

16 

17 

0.9279 

0.9433 

0.9587 

0.9739 

0.9891 

1.0043 

1.0193 

1.0343 

1.0492 

1.0640 

17 

18 

0.9281 

0.9436 

0.9589 

0.9742 

0.9894 

1.0045 

1.0196 

1.0346 

1.0495 

1.0643 

18 

19 

0.9284 

0.9438 

0.9592 

0.9744 

0.9897 

1.0048 

1.0198 

1.0348 

1.0497 

1.0645 

19 

20 

0.9287 

0.9441 

0.9594 

0.9747 

0.9899 

1.0050 

1.0201 

1.0351 

1.0500 

1.0648 

20 

21 

0.9289 

0.9443 

0.9597 

0.9750 

0.9902 

1.0053 

1.0203 

1.0353 

1.0502 

1.0650 

21 

22 

0.9292 

0.9446 

0.9599 

0.9752 

0.9904 

1.0055 

1.0206 

1.0356 

1.0504 

1.0653 

22 

23 

0.9294 

0.9448 

0.9602 

0.9755 

0.9907 

1.0058 

1.0208 

1.0358 

1.0507 

1.0655 

23 

24 

0.9297 

0.9451 

0.9604 

0.9757 

0.9909 

1.0060 

1.0211 

1.0361 

1.0509 

1.0658 

24 

25 

0.9299 

0.9454 

0.9607 

0.9760 

0.9912 

1.0063 

1.0213 

1.0363 

1.0512 

1.0660 

25 

26 

0.9302 

0.9456 

0.9610 

0.9762 

0.9914 

1.0065 

1.0216 

1.0366 

1.0514 

1.0662 

26 

27 

0.9305 

0.9459 

0.9612 

0.9765 

0.9917 

1.0068 

1.0218 

1.0368 

1.0517 

1.0665 

27 

28 

0.9307 

0.9461 

0.9615 

0.9767 

0.9919 

1.0070 

1.0221 

1.0370 

1.0519 

1.0667 

28 

29 

0.9310 

0.9464 

0.9617 

0.9770 

0.9922 

1.0073 

1.0223 

1.0373 

1.0522 

1.0670 

29 

30 

0.9312 

0.9466 

0.9620 

0.9772 

0.9924 

1.0075 

1.0226 

1.0375 

1.0524 

1.0672 

30 

31 

0.9315 

0.9469 

0.9622 

0.9775 

0.9927 

1.0078 

1.0228 

1.0378 

1.0527 

1.0675 

31 

32 

0.9317 

0.9472 

0.9625 

0.9778 

0.9929 

1.0080 

1.0231 

1.0380 

1.0529 

1.0677 

32 

33 

0.9320 

0.9474 

0.9627 

0.9780 

0.9932 

1.0083 

1.0233 

1.0383 

1.0532 

1.0680 

33 

34 

0.9323 

0.9477 

0.9630 

9.9783 

0.9934 

1.0086 

1.0236 

1.0385 

1.0534 

1.0682 

34 

35 

0.9325 

0.9479 

0.9633 

0.9785 

0.9937 

1.0088 

1.0238 

1.0388 

1.0537 

1.0685 

35 

36 

0.9328 

0.9482 

0.9635 

0.9788 

0.9939 

1.0091 

1.0241 

1.0390 

1.0539 

1.0687 

36 

37 

0.9330 

0.9484 

0.9638 

0.9790 

0.9942 

1.0093 

1.0243 

1.0393 

1.0542 

1.0690 

37 

38 

0.9333 

0.9487 

0.9640 

0.9793 

0.9945 

1.0096 

1.0246 

1.0395 

1.0544 

1.0692 

38 

39 

0.9335 

0.9489 

0.9643 

0.9795 

0.9947 

1.0098 

1.0248 

1.0398 

1.0547 

1.0694 

39 

40 

0.9338 

0.9492 

0.9645 

0.9798 

0.9950 

1.0101 

1.0251 

1.0400 

1.0549 

1.0697 

40 

41 

0.9341 

0.9495 

0.9648 

0.9800 

0.9952 

1.0103 

1.0253 

1.0403 

1.0551 

1.0699 

41 

42 

0.9343 

0.9497 

0.9650 

0.9803 

0.9955 

1.0106 

1.0256 

1.0405 

1.0554 

1.0702 

42 

43 

0.9346 

0.9500 

0.9653 

0.9805 

0.9957 

1.0108 

1.0258 

1.0408 

1.0556 

1.0704 

43 

44 

0.9348 

0.9502 

0.9655 

0.9808 

0.9960 

1.0111 

1.0261 

1.0410 

1.0559 

1.070V 

44 

45 

0.9351 

0.9505 

0.9658 

0.9810 

0.9962 

1.0113 

1.0263 

1.0413 

1.0.^,61 

1.0709 

45 

46 

0.9353 

0.9507 

0.9661 

0.9813 

0.9965 

1.0116 

1.0266 

1.0415 

1 .0564 

1.0712 

46 

47 

0.9356 

0.9510 

0.9663 

0.9816 

0.9967 

1.0118 

1.0268 

1.0418 

1.0566 

1.0714 

47 

48 

0.9359 

0.9512 

0.9666 

0.9818 

0.9970 

1.0121 

1.0271 

1.0420 

1.0.569 

1.0717 

48 

49 

0.9361 

0.9515 

0.9668 

0.9821 

0.9972 

1.0123 

1.0273 

1.0423 

1.0571 

1.0719 

49 

50 

0.9364 

0.9518 

0.9671 

0.9823 

0.9975 

1.0126 

1.0276 

1.0425 

1.0574 

1.0721 

50 

51 

0.9366 

0.9520 

0.9673 

0.9826 

0.9977 

1.0128 

1.0278 

1.0428 

1.0576 

1.0724 

51 

52 

0.9369 

0.9523 

0.9676 

0.9828 

0.9980 

1.0131 

1.0281 

1.0430 

1.0579 

1.0726 

52 

53 

0.9371 

0.9525 

0.9678 

0.9831 

0.9982 

1.0133 

1.0283 

1.0433 

1.0581 

1.0729 

53 

54 

0.9374 

0.9528 

0.9681 

0.9833 

0.9985 

1.0136 

1.0286 

1.0435 

1.0584 

1.0731 

54 

55 

0.9377 

0.9530 

0.9683 

0.9836 

0.9987 

1.0138 

1.0288 

1.0438 

1.0586 

1.0734 

55 

56 

0.9379 

0.9533 

0.9686 

0.9838 

0.9990 

1.0141 

1.0291 

1.0440 

1.0589 

1.0736 

56 

57 

0.9382 

0.9536 

0.9689 

0.9841 

0.9992 

1.0143 

1.0293 

1.0443 

1.0591 

1.0739 

57 

58 

0.9384 

0.9538 

0.9691 

0.9843 

0.9995 

1.0146 

1.0296 

1.0445 

1.0593 

1.0741 

58 

59 

0.9387 

0.9541 

0.9694 

0.9846 

0.9998 

1.0148 

1.0298 

1.0447 

1.0596 

1.0744 

59 

60 

0.9389 

0.9543 

0.9696 

0.9848 

1.0000 

1.0151 

1.0301 

1.0460 

1.0598 

1.0746 

60 

Table  of  Chords 

87 

Table  of  Chords  (Continued). 

Radius  =  i.oooo 

/  M. 

65° 

66° 

67° 

68° 

69° 

70° 

71° 

73° 

78° 

M. 

0' 

1.0746 

1.0893 

1 . 1039 

1.1184 

1 . 1328 

1 . 1472 

1.1614 

1.1756 

1.1896 

0' 

1 

1.0748 

1.0895 

1.1041 

1.1186 

1.1331 

1 . 1474 

1.1616 

1.1758 

1 . 1899 

1 

■  2 

1.0751 

1.0898 

1.1044 

1.1189 

1 . 1333 

1.1476 

1.1619 

1.1760 

1.1901 

2 

3 

1.0753 

1.0900 

1 . 1046 

1.1191 

1.1335 

1.1479 

1.1621 

1.1763 

1 . 1903 

3 

4 

1.0756 

1.0903 

1.1048 

1.1194 

1.1338 

1.1481 

1.1624 

1.1765 

1.1906 

4 

5 

1.0758 

1.0005 

1.1051 

1.11% 

1.1340 

1 . 1483 

1.1626 

1.1707 

1.1908 

5 

6 

1.0761 

1.0907 

1.1053 

1.1198 

1.1342 

1 . 1486 

1.1628 

1.1770 

1.1910 

6 

7 

1.0763 

1.0910 

1 .  1056 

1.1201 

1 . 1345 

1 . 1488 

1.1631 

1.1772 

1.1913 

7 

8 

1.0766 

1.0912 

1.1058 

1 . 1203 

1.1347 

1.1491 

1.1633 

1.1775 

1.1915 

8 

:         9 

1.0768 

1.0915 

1.1016 

1.1206 

1.1350 

1.1493 

1.1635 

1.1777 

1.1917 

9 

1  10 

1.0771 

1.0917 

1.1063 

1.1208 

1 . 1352 

1.1495 

1.1638 

1.1779 

1.1920 

10 

11 

1.0773 

1.0920 

1.1065 

1.1210 

1 . 1354 

1 . 1498 

1.1640 

1.1782 

1.1922 

11 

12 

1.0775 

1.0922 

1.1068 

1.1213 

1.1357 

1.1500 

1.1 042 

1.1784 

1.1924 

12 

13 

1.0778 

1.0924 

1.1070 

1.1215 

1 . 1359 

1 . 1502 

1.1015 

1.1780 

1.1927 

13 

14 

1.0780 

1.0927 

1.1073 

1.1218 

1.1362 

1.1505 

1.1047 

1.1789 

1.1929 

14 

15 

1.0783 

1.0929 

1 . 1075 

1.1220 

1 . 1364 

1 . 1507 

1.1050 

1.1791 

1.1931 

15 

16 

1.0785 

1.0932 

1.1078 

1.1222 

1 . 1366 

1.1510 

1.1052 

1.1793 

1.1934 

16 

17 

1.0788 

1.0934 

1.1080 

1.1225 

1 . 1369 

1.1512 

1.1654 

1.1790 

1 . 1936 

17 

18 

1.0790 

1.0937 

1 . 1082 

1.1227 

1.1371 

1.1514 

1.1657 

1.1798 

1.1938 

18  : 

;  19 

1.0793 

1.0939 

1 . 1085 

1 . 1230 

1 . 1374 

1.1517 

1.1650 

1.1800 

1.1941 

19 

20 

1.0795 

1.0942 

1.1087 

1 . 1232 

1.1376 

1.1519 

1.1661 

1.1803 

1.1943 

20 

21 

1.0797 

1.0944 

1.1090 

1.1234 

1 . 1378 

1.1522 

1.1664 

1.1805 

1 . 1946 

21 

22 

1.0800 

1.0946 

1.1092 

1.1237 

1.1381 

1.1524 

1.1606 

1 . 1807 

1.1948 

22 

23 

1.0802 

1.0949 

1 . 1094 

1.1239 

1 . 13S3 

1.1526 

1.1068 

1.1810 

1 . 1950 

23 

24 

1.0805 

1.0951 

1 . 1097 

1.1242 

1.1386 

1.1529 

1.1071 

1.1812 

1 . 1952 

24 

25 

1.0807 

1.0954 

1.1099 

1.1244 

1 . 1388 

1.1531 

1.1073 

1.1814 

1 . 1955 

25 

26 

1.0810 

1.0956 

1.1102 

1.1246 

1.1390 

1.1533 

1.1076 

1.1817 

1.1957 

20 

27 

1.0812 

1.0959 

1.1104 

1.1249 

1 . 1393 

1.1536 

1.1078 

1 . 1819 

1 . 1959 

27 

■  28 

1.0815 

1.0961 

1.1107 

1.1251 

1.1395 

1.1538 

1.1080 

1.1S21 

1.1962 

28 

29 

1.0817 

1.0903 

1.1109 

1 . 1254 

1 . 1398 

1.1541 

1.1083 

1.1824 

1 . 1964 

29 

30 

1.0820 

1.0966 

1.1111 

1.1256 

1.1400 

1.1543 

1.1685 

1.1826 

1.1966 

30 

31 

1.0822 

1.0968 

1.1114 

1.1258 

1.1402 

1,1545 

1.1687 

1.1829 

1.1969 

31 

32 

1.0824 

1.0971 

1.1116 

1.1261 

1 . 1405 

1.1548 

1.1690 

1.1831 

1.1971 

32 

33 

1.0827 

1.0973 

1.1119 

1.1263 

1.1407 

1 . 1550 

1.1692 

1.1833 

1.1973 

33 

34 

1.0829 

1.0976 

1.1121 

1.1266 

1 . 1409 

1.1552 

1.1094 

1 . 1836 

1.1976 

34 

35 

1.0832 

1.0978 

1.1123 

1.1268 

1.1412 

1.1555 

1.1697 

1 . 1838 

1.1978 

35 

36 

1.0834 

1.0980 

1.1126 

1.1271 

1.1414 

1.1557 

1.1099 

1.1840 

1.1980 

36 

37 

1.0837 

1.0983 

1.1128 

1.1273 

1.1417 

1.1560 

1.1702 

1.1843 

1.1983 

37 

38 

1.0839 

1.0985 

1.1131 

1 . 1275 

1.1419 

1.1562 

1.1704 

1 . 1845 

1 . 1985 

38 

39 

1.0841 

1.0988 

1.1133 

1.1278 

1.1421 

1.1564 

1.1706 

1.1847 

1.1987 

39 

40 

1.0844 

1.0990 

1.1136 

1.1280 

1.1424 

1.1567 

1.1709 

1.1850 

1.1990 

40 

41 

1.0846 

1.0993 

1.1138 

1.1283 

1.1426 

1.1569 

1.1711 

1.1852 

1.1992 

41 

42 

1.0849 

1.0995 

1.1140 

1.1285 

1.1429 

1.1571 

1.1713 

1.1854 

1.1994 

42 

43 

1.0851 

1.0997 

1.1143 

1.1287 

1.1431 

1.1574 

1.1716 

1.1857 

1.1997 

43 

44 

1.0854 

1 .  1000 

1.1145 

1.1290 

1 . 1433 

1.1576 

1.1718 

1.1859 

1 . 1999 

44 

45 

1.0856 

1 . 1002 

1.1148 

1.1292 

1.1436 

1.1579 

1.1720 

1.1861 

1.2001 

45 

46 

1.0859 

1 . 1005 

1.1150 

1.1295 

1.1438 

1.15S1 

1.1723 

1.1864 

1.2004 

46 

47 

1.0861 

1 . 1007 

1.1152 

1.1297 

1.1441 

1.15S3 

1.1725 

1.1806 

1.2000 

47 

48 

1.0863 

1.1010 

1.1155 

1.1299 

1.1443 

1.1586 

1.1727 

1.1868 

1.2008 

48 

49 

1.0866 

1.1012 

1.1157 

1.1302 

1.1445 

1.1588 

1.1730 

1.1871 

1.2011 

49 

50 

1.0868 

1.1014 

1.1160 

1.1304 

1.1448 

1.1590 

1.1732 

1.1873 

1.2013 

50 

51 

1.0871 

1.1017 

1.1162 

1.1307 

1.1450 

1.1593 

1.1735 

1.1875 

1.2015 

51 

52 

1.0873 

1.1019 

1.1165 

1.1309 

1.1452 

1 . 1595 

1.1737 

1.1878 

1.2018 

52 

53 

1.0876 

1.1022 

1.1167. 

1.1311 

1.1455 

1 . 1598 

1.1739 

1 . 1880 

1.2020 

53 

54 

1.0878 

1 .  1024 

1.1169 

1.1314 

1.1457 

1.1600 

1 . 1742 

1 . 1882 

1.2022 

54 

55 

1.0881 

1.1027 

1.1172 

1.1316 

1.1460 

1.1602 

1.1744 

1 . 1885 

1.2025 

55 

56 

1.0883 

1 .  1029 

1.1174 

1.1319 

1.1462 

1.1605 

1 . 1746 

1.1887 

1.2027 

56 

57 

1.0885 

1.1031 

1.1177 

1.1321 

1 . 1464 

1.1607 

1.1749 

1.1889 

1.2029 

57 

58 

1.0888 

1 . 1034 

1.1179 

1.1323 

1.1467 

1.1609 

1 . 1751 

1 . 1892 

1.2032 

58 

59 

1.0890 

1.1036 

1.1181 

1.1326 

1.1469 

1.1612 

1.1753 

1.1894 

1.2034 

59 

60 

1.0893 

1 . 1039 

1.1184 

1.1328 

1.1472 

1.1614 

1.1756 

1 . 1896 

1.2036 

60 

88 


Geometrical  Problems 


Table  of  Chords  (Continued).     Radius  =  i.oooo 


M. 

74° 

75° 

76° 

77° 

78° 

79° 

80° 

81° 

858° 

M. 

0' 

1.2036 

1.2175 

1.2313 

1.2450 

1.2586 

1.2722 

1.2856 

1.2989 

1.3121 

0' 

1 

1.2039 

1.2178 

1.2316 

1.2453 

1.2589 

1.2724 

1.2858 

1.2991 

1.3123 

1 

2 

1.2041 

1.2180 

1.2318 

1.2455 

1.2591 

1.2726 

1.2860 

1.2993 

1.3126 

2' 

3 

1.2043 

1.2182 

1.2320 

1.2457 

1.2593 

1.2728 

1.2862 

1.2996 

1.3128 

3 

4 

1.2046 

1.2184 

1.2322 

1.2459 

1.2595 

1.2731 

1.2865 

1.2998 

1.3130 

4 

5 

1.2048 

1.2187 

1.2325 

1.2462 

1.2598 

1.2733 

1.2867 

1.3000 

1.3132 

5 

,   6 

1.2050 

1.2189 

1.2327 

1.2464 

1.2G00 

1.2735 

1.2869 

1.3002 

1.3134 

6 

!   7 

1.2053 

1.2191 

1.2329 

1.2466 

1.2602 

1.2737 

1.2871 

1.3004 

1.3137 

7 

\      8 

1.2055 

1.2194 

1.2332 

1.2468 

1.2604 

1.2740 

1.2874 

1.3007 

1.3139 

8 

9 

1.2057 

1.2196 

1.2334 

1.2471 

1.2607 

1.2742 

1.2876 

1.3009 

1.3141 

9 

10 

1.2060 

1.2198 

1.2336 

1.2473 

1.2609 

1.2744 

1.2878 

1.3011 

1.3143 

10 

11 

1.2063 

1.2201 

1.2338 

1.2475 

1.2611 

1.2746 

1.2880 

1.3013 

1.3145 

11 

12 

1.2064 

1.2203 

1.2341 

1.2478 

1.2614 

1.2748 

1.2882 

1.3015 

1.3147 

12 

13 

1.2066 

1.2205 

1.2343 

1.2480 

1.2616 

1.2751 

1.2885 

1.3018 

1.3150 

13 

,  14 

1.2069 

1.2208 

1.2345 

1.2482 

1.2618 

1.2753 

1.2887 

1.3020 

1.3152 

14 

15 

1.2071 

1.2210 

1.2348 

1.2484 

1.2620 

1.2755 

1.2889 

1.3022 

1.3154 

15 

'  16 

1.2073 

1.2212 

1.2350 

1.2487 

1.2623 

1.2757 

1.2891 

1.3024 

1.315G 

16 

17 

1.2076 

1.2214 

1.2352 

1.2489 

1.2625 

1.2760 

1.2894 

1.3027 

1.3158 

17 

18 

1.2078 

1.2217 

1.2354 

1.2491 

1.2627 

1.2762 

1.2896 

1.3029 

1.3161 

18 

19 

1.2080 

1.2219 

1.2357 

1.2493 

1.2629 

1.2764 

1.2898 

1.3031 

1.3163 

19 

20 

1.2083 

1.2221 

1.2359 

1.2496 

1.2632 

1.2766 

1.2900 

1.3033 

1.3165 

20 

21 

1.2085 

1.2224 

1.2361 

1.2498 

'1.2634 

1.2769 

1.2903 

1.3035 

1.3167 

21 

22 

1.2087 

1.2226 

1.2364 

1.2500 

1.2636 

1.2771 

1.2905 

1.3038 

1.3160 

22 

23 

1.2090 

1.2228 

1.2366 

1.2503 

1.2638 

1.2773 

1.2907 

1.3040 

1.3172 

23 

24 

1.2092 

1.2231 

1.2368 

1.2505 

1.2641 

1.2775 

1.2909 

1.3042 

1.3174 

24 

25 

1.2094 

1.2233 

1.2370 

1.2507 

1.2643 

1.2778 

1.2911 

1.3044 

1.3170 

25 

26 

1.2097 

1.2235 

1.2373 

1.2509 

1.2645 

1.2780 

1.2914 

1.3046 

1.3178 

26 

27 

1.2099 

1.2237 

1.2375 

1.2512 

1.2648 

1.2782 

1.2916 

1.3049 

1.3180 

27 

28 

1.2101 

1.2240 

1.2377 

1.2514 

1.2650 

1.2784 

1.2918 

1.3051 

1.3183 

28 

29 

1.2104 

1.2242 

1.2380 

1.2516 

1.2652 

1.2787 

1.2920 

1.3053 

1.3185 

29 

30 

1.2106 

1.2244 

1.2382 

1.2518 

1.2654 

1.2789 

1.2922 

1.3055 

1.3187 

30 

31 

1.2108 

1.2247 

1.2384 

1.2521 

1.2656 

1.2791 

1.2925 

1.3057 

1.3189 

31 

32 

1.2111 

1.2249 

1.2386 

1.2523 

1.2659 

1.2793 

1.2927 

1.3060 

1.3191 

32 

33 

1.2113 

1.2251 

1.2389 

1.2525 

1.2661 

1.2795 

1.2929 

1.3062 

1.3193 

33 

34 

1.2115 

1.2254 

1.2391 

1.2528 

1.2663 

1.2798 

1.2931 

1.3064 

1.3196 

34 

35 

1.2117 

1.2256 

1.2393 

1.2530 

1.2665 

1.2800 

1.2934 

1.3066 

1.3198 

35 

36 

1.2120 

1.2258 

1.2396 

1.2532 

1.2668 

1.2802 

1.2936 

1.3068 

1.3200 

36 

37 

1.2122 

1.2260 

1.2398 

1.2534 

1.2670 

1.2804 

1.2938 

1.3071 

1.3202 

37 

38 

1.2124 

1.2263 

1.2400 

1.2537 

1.2672 

1.2807 

1.2940 

1.3073 

1.3204 

38 

39 

1.2127 

1.2265 

1.2402 

1.2539 

1.2674 

1.2809 

1.2942 

1.3075 

1.3207 

39 

40 

1.2129 

1.2267 

1.2405 

1.2541 

1.2677 

1.2811 

1.2945 

1.3077 

1.3209 

40 

41 

1.2131 

1.2270 

1.2407 

1.2543 

1.2679 

1.2813 

1.2947 

1.3079 

1.3211 

41 

42 

1.2134 

1.2272 

1.2409 

1.2546 

1.2681 

1.2816 

1.2949 

1.3082 

1.3213 

42 

43 

1.2136 

1.2274 

1.2412 

1.2548 

1.2683 

1.2818 

1.2951 

1.3084 

1.3215 

43 

44 

1.2138 

1.2277 

1.2414 

1.2550 

1.2686 

1.2820 

1.2954 

1.3086 

1.3218 

44 

45 

1.2141 

1.2279 

1.2416 

1.2552 

1.2688 

1.2822 

1.2956 

1.3088 

1.3220 

45 

46 

1.2143 

1.2281 

1.2418 

1.2555 

1.2690 

1.2825 

1.2958 

1.3090 

1.3222 

46 

47 

1.2145 

1.2283 

1.2421 

1.2557 

1.2692 

1.2827 

1.2960 

1.3093 

1.3224 

47 

48 

1.2148 

1.2286 

1.2123 

1.2559 

1.2695 

1.2829 

1.2962 

1.3095 

1.3220 

48 

49 

1.2150 

1.2288 

1.2425 

1.2562 

1.2697 

1.2831 

1.2965 

1.3097 

1.322S 

49 

50 

1.2152 

1.2290 

1.2428 

1.2564 

1.2699 

1.2833 

1.2967 

I.Z09Q 

1.3231 

50 

51 

1.2154 

1.2293 

1.2430 

1.2566 

1.2701 

1.2836 

1.2969 

1.3101 

1.3233 

51 

52 

1.2157 

1.2295 

1.2432 

1.2568 

1.2704 

1.2838 

1.2971 

1.3104 

1.3235 

52 

53 

1.2159 

1.2297 

1.2134 

1.2571 

1.2706 

1.2840 

1.2973 

1.3106 

1.3237 

53 

54 

1.2161 

1.2299 

1.2437 

1.2573 

1.2708 

1.2842 

1.2976 

1.3108 

1.3239 

54 

55 

1.2164 

1.2302 

1.2439 

1.2575 

1.2710 

1.2845 

1.2978 

1.3110 

1.3242 

55 

56 

1.2166 

1.2304 

1.2441 

1.2577 

1.2713 

1.2847 

1.2980 

1.3112 

1.3244 

56 

57 

1.2168 

1.2306 

1.2443 

1.2580 

1.2715 

1.2849 

1.2982 

1.3115 

1.3246 

57 

58 

1.2171 

1.2309 

1.2446 

1.2582 

1.2717 

1.2851 

1.2985 

1.3117 

1.3248 

58 

59 

1.2173 

1.2311 

1.2448 

1.2584 

1.2719 

1.2854 

1.2987 

1.3119 

1.3250 

59 

60 

1.2175 

1.2313 

1.2450 

1.2586 

1.2722 

1.2856 

1.2989 

1.3121 

1.3252 

60 

Table  of  Chords 

$» 

Table  of  Chords  (Concluded) 

.  Radius 

=  1. 0000 

M. 

83° 

84° 

85" 

86° 

87° 

88° 

89° 

M. 

1  0' 

1.3252 

1.3383, 

1.3512 

1.3640 

1.3767 

1.3893 

1.4018 

0' 

1 

1.3255 

1.3385 

1.3514 

1.3642 

1.3769 

1.3895 

1.4020 

1 

2 

1.3257 

1.3387 

1.3516 

1.3644 

1.3771 

1.3897 

1.4022 

2 

3 

1.3259 

1.3389 

1.3518 

1.3616 

1.3773 

1.3899 

1.4024 

3 

4 

l.a261 

1.3391 

1.3520 

1.3618 

1.3776 

1.3902 

1.4026 

4 

5 

1.3263 

1.3393 

1.3523 

1.3651 

1.3778 

1.3904 

1.4029 

5 

6 

1.3265 

1.3396 

1.3525 

1.3653 

1.3780 

1.3906 

1.4031 

6 

7 

1.3268 

1.3398 

1.3527 

1.3655 

1.3782 

1.3008 

1.4033 

7 

8 

1.3270 

1.3400 

1.3529 

1.3657 

1.3784 

1.3910 

1.4035 

8 

9 

1.3272 

1.3402 

1.3531 

1.3659 

1.3786 

1.3912 

1.4037 

9 

10 

1.3274 

1.3404 

1.3533 

1.3661 

1.3788 

1.3914 

1.4039 

10 

11 

1.3276 

1.3406 

1.3535 

1.3663 

1.3790 

T.3916 

1.4041 

11 

12 

1.3279 

1.3409 

1.3538 

1.3665 

1.3792 

1.3918 

1.4043 

12 

13 

1.3281 

1.3111 

1.3540 

1.3668 

1.3794 

1.39.20 

1.4045 

13 

14 

1.3283 

1.3413 

1.3542 

1.3670 

1.3797 

1.3922 

1.4047 

14 

15 

1.3285 

1.3415 

1  3544 

1.3672 

1.3799 

1.3925 

1.4049 

15 

16 

1.3287 

1.3417 

1.3546 

1.3674 

1.3801 

1.3927 

1.4051 

16 

17 

1.3289 

1.3119 

1.3548 

1.3676 

1.3S03 

1.8929' 

1.4053 

17 

18 

1.3292 

1  3421 

1.3550 

1.3678 

1.3805 

1.3931 

1.4055 

18 

19 

1.3294 

1.3424 

1.3552 

1.3680 

1.3807 

1.3033 

1.4058 

19 

20 

1.3296 

1.3426 

1.3555 

1.3682 

1.8809 

1.3935 

1.4060 

20 

21 

22 

1.3298 
1.3300 

1.3428 

1.3557 

1  3685 

1.3811 
1.3813 

1.3937 
1.3939 

1.4062 
1.4064 

21 

22 

1.3430 

1.3559 

1.3687 

23 

1.3302 

1.3432 

1.3561 

1.3680 

1.3816 

1.3941 

1.4066 

23 

24 

1.3305 

1.3434 

1.3563 

1.3091 

1.3818 

1.3043 

1.4068 

24 

25 

1.3307 

1.3437 

1.3565 

1.3693 

1.3820 

1.3945 

1.4070 

25 

26 

1.3309 

1.3439 

1.3567 

1.3695 

1.3822 

1.3947 

1.4072 

26 

27 

1.3311 

1.3441 

1.3570 

1.3697 

1.3824 

1.3950 

1.4074 

27 

28 

1.3313 

1.3443 

I  3572 

1.3639 

1.3826 

1.3952 

1.4076 

28 

29 

1.3315 

1.3445 

1.3574 

1.3702 

1.3828 

1.3954 

1.4078 

29 

30 

1.3318 

1.3447 

1.3576 

1.3704 

1.3830 

1.3956 

1.4080 

30 

31 

1.3320 

1.3449 

1.3578 

1.3706 

1.3832 

1.3958 

1.4082 

31 

32 
33 

1.3322 
1.3324 

1.3452 

1.3580 

1.3708 
1.3710 

1.3834 
1.3837 

1.3960 
1.3962 

1.4084 
1.4086 

32 
33 

1.3454 

1.3582 

34 

1.3326 

1.3456 

1.3585 

1.3712 

1.3839 

1.3964 

1.4089 

34 

35 

1.3328 

1.3458 

1.3587 

1.3714 

1.3841 

1.3966 

1.4091 

35 

36 

1.3331 

1.3460 

1.3589 

1.3716 

1.3843 

1.3968 

1.4093 

36 

37 

1.3333 

1.3462 

1.3591 

1.3718 

1.3845 

1.3970 

1.4095 

37 

38 

1.3335 

1.3465 

1.3503 

1.3721 

1.3847 

1.3972 

1.4097 

38 

3!) 

1.3337 

1.3467 

1.3595 

1.3723 

1.3849 

1.3975 

1.4099 

39 

40 

1.3339 

1.3469 

1.3597 

1.3725 

1.3851 

1.3977 

1.4101 

40 

41 

1.3341 

1.3471 

1.3599 

1.3727 

1.3853 

1.3979 

1.4103 

41 

42 

1.3344 

1.3473 

1.3602 

1.3729 

1.3855 

1.3981 

1.4105 

42 

43 

1.3346 

1.3475 

1.3604 

1.3731 

1.3858 

1.3983 

1.4107 

43 

44 

1.3348 

1.3477 

1.3606 

1.3733 

1.3860 

1.3985 

1.4109 

44 

45 

1.3350 

1.3480 

1 . 3008 

1.3735 

1.3862 

1.3987 

1.4111 

45 

46 

1.3352 

1.3482 

1.3610 

1.3738 

1.3864 

1.3989 

1.4113 

46 

47 

1.3354 

1.3484 

1.3612 

1.3740 

1.3866 

1.3991 

1.4115 

47 

48 

1.3357 

1.3486 

1.3614 

1.3742 

1.3868 

1.3993 

1.4117 

48 

49 

1.3359 

1.3488 

1.3617 

1.3744 

1.3870 

1.3995 

1.4119 

49 

50 

1.3361 

1.3490 

1.3619 

1.3746 

1.3872 

1.3997 

1.4122 

50 

51 

1.3363 

1.3492 

1.3621 

1.3748 

1.3874 

1.3999 

1.4124 

51 

52 

1.3365 

1.3495 

1.3623 

1.3750 

1.3876 

1.4002 

1.4126 

52 

53 

1.3367 

1.3497 

1.3625 

1.3752 

1.3879 

1.4004 

1..4128 

63 

54 

1.3370 

1.3499 

1.3627 

1.3754 

1.3881 

1.4006 

1.4130 

54 

55 

1.3372 

1.3501 

1.3629 

1.3757 

1.3883 

1.4008 

1.4132 

55 

56 

1.3374 

1.3503 

1  3631 

1.3759 

1,3885 

1.4010 

1.4134 

56 

57 

1  3376 

1.3505 

1.3634 

1.3761 

1.3887 

1.4012 

1.4136 

67 

58 

1.3378 

1.3508 

1.3636 

1.3763 

1.3889 

1.4014 

1.4138 

58 

59 

1.3380 

1.3510 

1.3638 

1.3765 

1.3891 

1.4016 

1.4140 

59 

60 

1.3383 

1.3512 

1.3640 

1.3767 

1.3893 

1.4018 

1.4142 

60 

90 


Trigonometry 


Part  1 


Lengths  and  Bevels  of  Hip-Rafters  and  Jack-Rafters 
Method  of  Determining  the  Lengths  and  Bevels.  The  lines  ab  and  be 
(Fig.  92)  represent  the  outside  of  the  walls  at  the  angle  of  a  building;  be  is  the 
seat  of  the  hip-rafter  and  gf  of  a  jack-rafter.  Draw  eh  at  right-angles  to  be 
and  make  it  equal  to  the  rise  of  the  roof';  join  b  and  //  and  hb  will  be  the  length 
of  the  hip-rafter.    Through  e  draw  di  at  right-angles  to  be.    With  t  as  a  center 

h 
a 


h 

Fig.  92. 


m    g  d  c 

Lengths  and  Bevels  of  Hip-rafters  and  Jack-rafters 


and  with  the  radius  bh,  describe  the  arc  hi,  cutting  di  in  i.  Join  b  and  i  and 
extend  gf  to  meet  bi  in  j;  then  gj  is  the  length  of  the  jack-rafter.  The  length  of 
each  jack-rafter  is  found  in  the  same  manner,  by  extending  its  seat  to  cut  the 
line  6/.  From /  draw /y^  at  right-angles  to /g;  also// at  right-angles  to  ie.  Make 
fk  equal  to//  by  the  arc  Ik,  or  make  gk  equal  to  gj  by  the  arci^;  then  the  angle 
at  J  is  the  top  bevel  of  the  jack-rafters,  and  the  angle  at  k  the  down  bevel. 

Backing  of  the  Hip-Rafter.  At  any  convenient  point  in  be  (Fig.  92),  as  o, 
draw  mn  at  right-angles  to  be.  From  o  describe  a  circle,  tangent  to  bh,  cutting 
be  in  s.  Join  m  and  s  and  n  and  s.  The  lines  jns  and  ns  form  at  s  the  proper 
angle  for  beveling  the  top  of  the  hip-rafter. 

5.  TRIGONOMETRY 

It  is  not.  the  purpose  of  the  author  to  teach  the  principles  or  uses  of  trigonom- 
etry; but  for  the  benefit  of  those  readers  who  have  already  acquired  a  knowledge 
of  this  science,  the  following  convenient  formulas  and  tables  of  natural  sines, 
cosines,  tangents  and  cotangents  have  been  inserted.  To  those  who  know  how 
to  apply  these  trigonometric  functions,  they  will  often  be  found  of  great  con- 
venience and  utility.  These  tables  are  taken,  by  permission,  from  Searle's  Field 
Engineering,  John  Wiley  &  Sons,  Inc.,  publishers. 


Trigonometrical  Functions 
Trigonometric  Functions 


91 


Let  A  (Fig.  93)  =  angle  BAC  =  arc  BF  and  let  the  radius  AF  =  AB  =  AH  =  i 
Then 

sin  A  =  BC 

cos  A  =  AC 

tan  A  =  DF 

cot  A=  HG 

sec  A  =  AD 

cosec  A  =  AG 

versin  A  =  CF  =- BE 

covers  A  =  BK  =  HL 

exsec  A  =  BD 
coexsec  A  =  BG 
chord  A  =  BF 
chord  2  A=  BI  =  2BC 


Fig.  93.     Functions  of  Right-angled 
Triangle 


In  the  right-angled  triangle  ABC  (Fig.  93)  let  AB  -=  c,  AC  =  b  and  BC  =  a 
Then 


(I) 

(2) 

(3) 
(4) 
(5) 


sin  A  ■■ 


=  cosB 


cos  A  =  -  =  sin  B 


tan  A  =  -r  =  cot  J5 


cot  A  =  -  =  tan  J5 


sec  A  =  r  =  cosec  B 


(6)  cosec  A  =  -  —  sec  B 

(7)  vers  A  =  =  covers  B 

(8)  exsec  A  =  — ^ —  =  coexsec  B 

(9)  covers  A  =  =  versin  B 


(11)  a  =  csin A  =  6tan A 

(12)  b  =  c  cos  A  =  a  cot  A 

,    .  c  b 

(13)  c  =  -^ — -  =  — -j- 

sin  A       cos  A 

(14)  a  =  c  cos  B  =  b  cot  B 

(15)  6  =  csin J5  =  ctanS 


(17)  fl  =  V(c  +  fe)(c-6) 


(21)   area  = 


(18)  6  =  V  (c  +  o)  (c  -  a) 

(19)  c  =  Va2  +  62 

(20)  C  =  90°  =  A  +  5 


0^ 


Trigonometry 

Solution  of  Oblique  Triangles 


Part  1 


■A 

V 

/ 

\a 

/ 

\             1 

h 

o                          1 

Fig.  94.     Oblique-angled  .Triangle 

Given 

Required 

Formulas 

(22) 

A.B,a 

C,b,c 

C  =  i8o°  -  (A  4- 5)               ^"^i^*^^^^ 

c  =  -A-^  sin  (A  -f  B) 
sin  A 

(23) 

A.a,b 

B,C,c 

sin  B  =  ^^^  'b                  C  ==  i8o°  -  (A  +  J3) 
a 

c  =  -^ — -  •  sin  C 

sin  A 

(24) 

C,a,b 

\^{A-^B) 

Vz  (A  +  B)  =  90°  -  H  C 

(25) 

mA-B) 

tan  '/^  (A  -  J5)  =  ^  tan  3^^  (A  +  B) 
a  +  b 

(26) 

A,B 

A=WiA+B)  +  H{A-B) 
B  =  V2U+B)-H(A-B) 

(27) 

c 

,     ,  ^,  cos  1/^  (A  +  B)      .        , ,  sin  H  (A  -f  B) 
^~  ^"  +  ^^  cos^i(A  -^B)  "^'^      ^^  sin^HA  -5) 

(28) 
(29) 

(30) 

a,  b,  c 

Area 
A 

Let 
cos 

Yz  ab  siA  C 

s-Hia  +  b+c);      smHA-\/^'-^l^'-'^ 

/,,1=.iA(^-«>.tnnU.i-V/^^-?^(^-^> 

cos,.-         ^           ^^         ,    -    -_-         ^          ^(5-0) 

(31) 
(32) 

-in  "     .2^5(5-0)  (5-6)  (5-c) 

Area 

K  = 

6c 

6c 

=  V5  (5  -  C)  (5  -  b)  {S  -  C) 

(33) 

A.B,C,a 

Area 

„       a2  sin  B  sin  C 
K  —             .      . 
2  Sin  A 

Trigonometrical  Functions 
Oblique  Triangles.     General  Formulas 


(34)  sin  A  = r  =  Vi  —  cos'^  A  =  tan  A  cos  A 

cosec  A 

(35)  sin  A  =  2  sin  J/i  A  cos  \i  A  ==  vers  A  cot  }'i  A 

(36)  sin  A  =  Vi7^  vers  2  A  =  Vi,^  (i  —  cos  2  A) 


(37)  cos  A  =  7  =  v^i  —  sin2  A  =  cot  A  sin  A 

sec  A 

(38)  cos  A  =  I  —  vers  A  =  2  cos^  >ia  A  —  i  =  i  —  2  sin^  \^  A 


(39) 

cos  A 

=  cos2  \iA—  sin2  Yi  A  =  ^Yi  +  Yi  cos  2  A 

(40) 

tan  A 
tan  A 

=       '      -  "'''  1  -  ^sec^  A      I 
cot  A       cos  A 

,  /      I                    v^i  —  cos'-^  A           sin  2  A 

(41; 

▼   cos'-^  A                      cos  A              I  +  cos  2  A 

(42) 

tan  A 
cot  A 

I  —  cos  2  A       vers  2  A                  ,      ^  , ,   . 

=  — : —  =  —. 7-  =  exsec  A  cot  Y2  A 

^^  sin  2  A            sin  2  A 

(43) 

-       \  -^°'^,^  --  Vcosec^A-i 
tan  A       sin  A 

(44) 

cot  A 

sin  2  A            sin  2  A        i  +  cos  2  A 
~  I  —  cos  2  A  ^  rers  2  A           sin  2  A 

(45) 

cot  A 

tan  1/2  A 

(46)  vers  A  =  I  —  cos  A  =  sin  A  tan  Yz  A  =  2  sin2  J.^  A 

(47)  vers  A  =  exsec  A  cos  A 

(48)  exsec  A  =  sec  A  —  I  =  tan  A  tan  J^^  A  = -r- 


—   4/ 1  ~  cos  A  _  w  vers  A 


(49)  sin3'iA 

(50)  sin  2  A  =  2  sin  A  cos  A 


^    X         1/  ^        4/1  + cos  A 
(si)  cos  YA=y 


(52)     cos  2  A  =  2  cos2  A  —  I  =  cos2  A  —  sin2  A  =  i  —  2  sin^  A 

[  —  cos  A 
-cos  A 


,    .  ^      ,,    .  tan  A  .  ,    .       I -cos  A        4/f  -c 

(53)  tani/^A  =  ^-^^^^  =  cosec  A  -  cot  A  =  -^^^^^  ==  V  fT^ 


.    .    ^  .  2  tan  A 

(54)    tan  2  A  == 


(55)  cot3'iA  = 

(56)  cot  2  A  = 


I  -  tan2  A 

sin  A    _  ij4-  cos  A  _  i 

vers  A  sin  A  cosec  A  —  cot  A 

cot2  A  —  I 
2  cot  A 


94  Trigonometry  Part  1 

Oblique  Triangles.     General  Formulas  (Continued) 


j 

(57) 

H  vers  A                       i  —  cos  A 

versAA      ^^Vi-y^versA       2+^2(1  +  003^) 

(58) 

vers  2  A  =  2  sin^  A 

(59) 

I  —  cos  A  ' 

exsec^^A  =  ,    ,          ...    ^/—, — ; 7-- 

(i  +  cos  A)  +  V2  (I  +  cos  A) 

(6o) 

.         2tan2A 

exsec  2  A  =  :^ — — -r 

I  —  tan2  A 

(6i) 

sin  (A  ±  B)  =  sin  A  cos  B  zksinB  cos  A 

(62) 

cos  (A  dz  B)  —  cos  A  cos  B  =F  sin  A  sin  B 

(63) 

sin  A  +  sin  5  =  2  sin  H  (A  +  B)  cos  H  (A  -  B) 

(64) 

sin  A  -  sin  B  =  2  cos  H  (A  +  B)  sin  H  (A  -  i3) 

(65) 

cos  A  +  cos  ij  =  2  cos  I/-2  (A  +  B)  cos  i/l2  (A  -  B) 

(66) 

cosB-cosA  =  2smy2U+B)smy2{A-B) 

(67) 

sin2  A  -  sin2  B  =  cos2  B-  cos2  A  =  sin  (A  +  jB)  sin  (A  -  B) 

(68) 

cos2  A  -  sin2  B  =  cos  (A  +  B)  cos  (A  -  B) 

(69) 

tanl    I  tan^-^^^^^^+^^ 

xan  j-i  -\-  lan  i?  —          .          „ 
cos  A  cos  5 

(70) 

.       ^       „      sin  (A  -  B) 

tan  A  —  tan  B  =  ^^; rr 

cos  A  cos  B 

Tabic  of  Natural  Sines  and  Cosines 


95 


0 

0° 

1° 

■    2^^ 

3^^    1 

4° 

' 

Sine 
.00000 

Cosin 
One. 

Sine 
.01745 

Cosin 
.99985 

Sine 

Cobin 

Sine 

Cosin 

Sine 

Cosin 

.03490 

.99939 

.05234 

.99803 

.06976 

.99756 

60 

1 

.00029 

One. 

.01774 

.99984 

.03519 

.99938 

.05263 

.99861 

.07005 

.99754 

59 

2 

.00058 

One. 

.01803 

.99984 

.03548 

.99937 

.05292 

.99860 

.07034 

.99752 

58 

3 

.00087 

One. 

.01832 

.99983 

.03577 

.99936 

.05321 

.9985S 

.07063 

.99750 

57 

4 

.00116 

One. 

.01862 

.99983 

.03606 

.99935 

.05350 

.99857 

.07092 

.99748 

56 

5 

.00145 

One. 

.01891 

.99982 

.03635 

.99934 

.05379 

.99855 

.07121 

.99746 

55 

6 

.00175 

One. 

.01920 

.99982 

.03664 

.99933 

.05408 

.99854 

.07150 

.99744 

54 

7 

.00204 

One. 

.01949 

.99981 

.0369? 

.99932 

.05437 

.99852 

.07179 

.99742 

53 

8 

.00233 

One. 

.01978 

.99980 

.03723 

.99931 

.05466 

.99851 

.07208 

.99740 

52 

9 

.00262 

One. 

.02007 

.99989 

.03752 

.99930 

.05495 

.99849 

.07237 

.99738 

51 

10 

.00291 

One. 

.02030 

.99979 

.03781 

.99929 

.05524 

.99847 

.07266 

.99736 

50 

11 

.00320 

.99909 

.02065 

.99979 

.0381C 

.99927 

.05553 

.99846 

.07295 

.99734 

49 

12 

.00349 

.99999 

.02094 

.99978 

.02839 

.99926 

.05582 

.99844 

.07324 

.99731 

48 

13 

.00378 

.99999 

.02123 

.99977 

.03808 

.99925 

.05611 

.99842 

.07353 

.99729 

47 

14 

.00407 

.99999 

.02152 

.99977 

.03897 

.99924 

.05640 

.99841 

.07382 

.99727 

40 

15 

.00436 

.99999 

.02181 

.99976 

.0392C 

.99923 

.05669 

.99839 

.07411 

.99725 

45 

16 

.00465 

09990 

.02211 

.99976 

.03955 

.99922 

.05698 

.99838 

.07440 

.99723 

44 

17 

.00495 

!99999 

.02240 

.99975 

.03984 

.99921 

.05727 

.99836 

.07469 

.99721 

43 

18 

.00524 

.99999 

.02269 

.99974 

.04013 

.99919 

.05756 

.99834 

.07498 

.99719 

42 

19 

.00553 

.99998 

.02298 

.99974 

.04042 

.99918 

.05785 

.99833 

.07527 

.99716 

41 

20 

.00582 

.99998 

.02327 

.99973 

.04071 

.99917 

.05814 

.99831 

.07556 

.99714 

40 

21 

.00611 

.99998 

.02356 

.99972 

.04100 

.99916 

.05844 

.99829 

.07585 

.99712 

39 

22 

.00640 

.99998 

.02385 

.99972 

.04129 

.99915 

.05873 

.99827 

.07614 

.99710 

38 

23 

.00669 

.99998 

.02414 

.99971 

.04159 

.99913 

.05902 

.99826 

.07643 

.99708 

37 

24 

.00698 

.99998 

.02443 

.99970 

.04188 

.99912 

.05931 

.99824 

.07672 

.99705 

36 

25 

.00727 

.99997 

.02472 

.99969 

.04217 

.99911 

.05960 

.99822 

.07701 

.99703 

35 

26 

.00756 

.90997 

.02501 

.99960 

.04246 

.99910 

.05989 

.99821 

.07730 

.99701 

34 

27 

.00785 

.99997 

.02530 

.99968 

.04275 

.09909 

.06018 

.99819 

.07759 

.99699 

33 

28 

.00814 

.99997 

.02560 

.99967 

.04304 

.99907 

.06047 

.99817 

.07788 

.99696 

32 

29 

.00844 

.99996 

.02589 

.99966 

.04333 

.99900 

.00076 

.99815 

.07817 

.99694 

31 

30 

.00873 

.99996 

.02618 

.99966 

.04362 

.99905 

.06105 

.99813 

.07846 

.99692 

30 

31 

.00902 

.99996 

.02647 

.99905 

.04391 

.99004 

.06134 

.99812 

.07875 

.99689 

29 

32 

.00931 

.99996 

.02676 

.99964 

.04420 

.99902 

.06163 

.99810 

.07904 

.99687 

28 

33 

.00960 

.99995 

.02705 

.99963 

.04449 

.99901 

.06192 

.99808 

.07933 

.99685 

27 

34 

.00989 

.99995 

.02734 

.99963 

.04478 

.99900 

.06221 

.99806 

.07962 

.99683 

26 

35 

.01018 

.99995 

.02703 

.99962 

.04507 

.99898 

.062.50 

.99804 

.07991 

.99680 

25 

36 

.01047 

.99995 

.02792 

.99961 

.04536 

.99897 

.06279 

.99803 

.08020 

.99678 

24 

37 

.01076 

.99994 

.02821 

.99960 

.04565 

.99896 

.06308 

.99801 

,08049 

.99676 

23 

38 

.01105 

.99994 

.02850 

.99959 

.04594 

.99894 

.06337 

.99799 

.08078 

.99673 

22 

39 

.01134 

.99994 

.02879 

.99959 

.04623 

.99893 

.06366 

.99797 

.08107 

.99671 

21 

40 

.01164 

.99993 

.02908 

.99958 

.04653 

.99892 

.06395 

.99795 

.08136 

.99668 

20 

41 

.01193 

.99993 

.02938 

.99957 

.04682 

.99890 

.06424 

.99793 

.08165 

.99666 

19 

42 

.01222 

.09993 

.02907 

.99956 

.04711 

.99889 

.06453 

.99792 

.08194 

.99664 

18 

43 

.01251 

.99992 

.02996 

.99955 

.04740 

.99888 

.06482 

.99790 

.08223 

.99661 

17 

44 

.01280 

.99992 

.03025 

.99954 

.04769 

.99886 

.06511 

.99788 

.08252 

.99659 

16 

45 

.01309 

.99991 

.03054 

.99953 

.04798 

.99885 

.06540 

.99786 

.08281 

.99657 

15 

46 

.01338 

.99991 

.03083 

.90952 

.04827 

.99883 

.06569 

.99784 

.08310 

.99654 

14 

47 

.01367 

.99991 

.03112 

.99952 

.04856 

.99882 

.06598 

.99782 

.08339 

.99652 

13 

48 

.01396 

.99900 

.03141 

.99951 

.04885 

.99881 

.06627 

.99780 

.08368 

.99649 

12 

49 

.01425 

.99990 

.03170 

.99950 

.04914 

.99879 

.06656 

.99778 

.08397 

.99647 

11 

50 

.01454 

.99989 

.03199 

.99949 

.04943 

.99878 

.06685 

.99776 

.0M26 

.99644 

10 

51 

.01483 

.99989 

.03228 

.99948 

.04972 

.99876 

.06714 

.99774 

.08455 

.99642 

9 

52 

.01513 

.99989 

.03257 

.09947 

.05001 

.99875 

.06743 

.99772 

.08484 

.99639 

8 

53 

.01542 

.99988 

.03286 

.99946 

.05030 

.99873 

.06773 

.99770 

.08513 

.99637 

7 

54 

.01571 

.99988 

.03316 

.99945 

.05059 

.99872 

.06802 

.99768 

.08542 

.99635 

6 

55 

.01600 

.99987 

.03345 

.99944 

.05088 

.99870 

.06831 

.99766 

.08571 

.99632 

5 

56 

.01629 

.99987 

.03374 

.99943 

.05117 

.99869 

.06860 

.99764 

.08600 

.99630 

4 

57 

.01658 

.99986 

.03403 

.99942 

.05146 

.99867 

.06889 

.99762 

.08629 

.99627 

3 

58 

.01687 

.99986 

.03432 

.99941 

.05175 

.99866 

.06918 

.99760 

.08658 

.99625 

2 

59 

.01716 

.99985 

.03461 

.99940 

.05205 

.99864 

.06947 

.99758 

.08687 

.99622 

1 

60 

.01745 

.99985 

.03490  .99939 

.05234 

.99863 

.06976 

.99756 

.08716 

.99619 

0 

' 

Oosin 

Sine 

Cosin  Sine 

Cosin  Sine  | 

Cosin  Sine 

Cosin 

Sine 

' 

8< 

)° 

88°    1 

8' 

7^        1 

86°        85° 

96 


Trigonometry 


Part  1 


' 

5° 

G*" 

r  • 

8° 

9° 

/ 

Sine 

(/osin 

Sine 

Cosin 

Sine 

Coyiu 

Sine 

Cosin 
.99027 

Sine 

Cosin 

0 

.08716 

.99619 

.10453 

.99452 

.12187 

.99255 

.13917 

.15643 

.98769 

~m 

1 

.08745 

.99617 

.10482 

.99449 

.12216 

.99251 

.13946 

.99023 

.15672 

.98764 

59 

2 

.08774 

.99614 

.10511 

.99440 

.12245 

.99248 

.13975 

.99019 

.15701 

.98700 

58 

3 

.08803 

.99612 

.10510 

.99443 

.12274 

.99244 

.14004 

.99015 

.15730 

.98755 

57 

4 

.08831 

.99600 

.10509 

.99440 

.1230i 

.99240 

.14033 

.99011 

.15758 

.98751 

56 

5 

.08860 

.99607 

.10597 

.99437 

.12331 

.99237 

.14001 

.99000 

.15787 

.98746 

55 

6 

.08889 

.99604 

.10620 

.99434 

.12300 

.99233 

.14090 

.99002 

.15816 

.98741 

54 

7 

.08918 

.99002 

.10655 

.99431 

.12389 

.99230 

.14119 

.98998 

.15845 

.98737 

53 

8 

.08947 

.99599 

.10684 

.9942S 

.12418 

.99220 

.1414S 

.98994 

.15873 

.98732 

52 

9 

.08976 

.99596 

.10713 

.99424 

.12447 

.99222 

.14177 

.98990 

.15902 

.98728 

51 

10 

.09005 

.99594 

.10742 

.99421 

.12476 

.99219 

.14205 

.98986 

.15931 

.98723 

50 

11 

.09034 

.99591 

.10771 

.99418 

.12504 

.99215 

.14234 

.98982 

.15959 

.98718 

49 

12 

.09063 

.99588 

.10800 

.99415 

.12533 

.99211 

.14263 

.98978 

.15988 

.98714 

48 

13 

.09092 

.99586 

.10S29 

.99412 

.12502 

.99208 

.14292 

.98973 

.16017 

.98709 

47 

14 

.09121 

.99583 

.10858 

.99409 

.12591 

.99204 

.14320 

.98909 

.16046 

.98704 

46 

15 

.09150 

.99580 

.10887 

.99400 

.12020 

.99200 

.14349 

.98905 

.16074 

.98700 

45 

16 

.09179 

.99578 

.10916 

.99402 

.12049 

.99197 

.14378 

.98961 

.16103 

.98695 

44 

17 

.09208 

.99575 

.10945 

.99399 

.12078 

.99193 

.14407 

.98957 

.10132 

.98690 

43 

18 

.09237 

.99572 

.10973 

.99306 

.12700 

.99189 

.14436 

.98953 

.16160 

.98686 

42 

19 

.09266 

.99570 

.11002 

.09393 

.12735 

.99180 

.14464 

.98948 

.16189 

.98681 

41 

20 

.09295 

.99567 

.11031 

.99390 

.12704 

.99182 

.14493 

.98944 

.16218 

.98676 

40 

21 

.09324 

.99564 

.11060 

.99386 

.12793 

.99178 

.14522 

.98940 

.16246 

.98671 

39 

22 

.09353 

.99582 

.11039 

.99383 

.12822 

.99175 

.14551 

.98930 

.16275 

.98667 

38 

23 

.09382 

.99559 

.11118 

.99380 

.12851 

.99171 

.14580 

.98931 

.16304 

.98662 

37 

24 

.09411 

.99556 

.11147 

.99377 

.12880 

.99107 

.14608 

.98927 

.16333 

.98057 

36 

25 

.09440 

.99553 

.11176 

.99374 

.12908 

.99103 

.14637 

.98923 

.16361 

.98652 

35 

26 

.09469 

.99551 

.11205 

.99370 

.12937 

.99100 

.14660 

.98919 

.16390 

.98648 

34 

27 

.09498 

.99548 

.11234 

.99307 

.12960 

.99156 

.14095 

.98914 

.16419 

.98643 

33 

28 

.09527 

.99545 

.11203 

.99304 

.12995 

.99152 

.14723 

.98910 

.16447 

.98638 

32 

29 

.09556 

.99542 

.11291 

.99300 

.13024 

.99148 

.14752 

.98900 

.16476 

.98633 

31 

30 

.09585 

.99549 

.11320 

.99357 

.13053 

.99144 

.14781 

.98902 

.16505 

.98629 

30 

31 

.09614 

.99537 

.11349 

.99351 

.13081 

.99141 

.14810 

.98897 

.16533 

.98624 

29 

32 

.09642 

.99534 

.11378 

.99351 

.13110 

.99137 

.14838 

.98893 

.16562 

.98619 

28 

33 

.09671 

.99531 

.11407 

.99347 

.13139 

.09133 

.14807 

.98889 

.16591 

.98614 

27 

34 

.09700 

.99528 

.11431 

.99344 

.13108 

.99129 

.14890 

.98884 

.16620 

.98609 

26 

35 

.09729 

.99526 

.11405 

.99341 

.13197 

.99125 

.14925 

.98880 

.16648 

.98604 

25 

36 

.09758 

.99523 

.11494 

.99337 

.13220 

.99122 

.14954 

,98876 

.16677 

.9S600 

24 

37 

.09787 

.99520 

.11523 

.99334 

.13254 

.99118 

.14982 

.98871 

.10700 

.98595 

23 

38 

.09816 

.99517 

.11552 

.99331 

.13233 

.99114 

.15011 

.98867 

.10734 

.98590 

22 

39 

.09845 

.99514 

.11530 

.99327 

.13312 

.99110 

.15040 

.98863 

.16763 

.98585 

21 

40 

.09874 

.99511 

.11609 

.99324 

.13341 

.99106 

.15009 

.98858 

.16792 

.98580 

20 

41 

.09903 

.99508 

.11638 

.99320 

.13370 

.99102 

.15097 

.98854 

.16820 

.98575 

19 

42 

.09932 

.9950e 

.11667 

.99317 

.13399 

.99098 

.15126 

.98849 

.10849 

.98570 

18 

43 

.09961 

.99503 

.11696 

.99314 

.13427 

.99094 

.15155 

.98845 

.10878 

.98565 

17 

44 

.09990 

.99500 

.11725 

.99310 

.13450 

.99091 

.15184 

.98841 

.10906 

.98561 

16 

45 

.10019 

.99497 

.11754 

.99307 

.13485 

.99087 

.15212 

.98836 

.16935 

.98556 

15 

46 

.10018 

.99494 

.11783 

.99303 

.13514 

.99083 

.15241 

.98832 

.16964 

.98551 

14 

47 

.10077 

.99491 

.11812 

.99300 

.13543 

.99079 

.15270 

.98827 

.16992 

.98546 

13 

48 

.10106 

.99488 

.11840 

.99297 

.13572 

.99075 

.15290 

.98823 

.17021 

.98541 

12 

49 

.10135 

.99485 

.11869 

.99293 

.13600 

.99071 

.15327 

.98818 

.17050 

.98536 

11 

50 

.10164 

.99482 

.11898 

.99290 

.13629 

.99067 

.15350 

.98814 

.17078 

.98531 

10 

51 

.10192 

.99479 

.11927 

.99286 

.13658 

.99063 

.15385 

.98809 

.17107 

.98526 

9 

52 

.10221 

.99476 

.11956 

.99283 

.13687 

.99059 

.15414 

.98805 

.17136 

.98521 

8 

53 

.10250 

.99473 

.11985 

.99279 

.13716 

.99055 

.15442 

.98800 

.17164 

.98516 

7 

54 

.10279 

.99470 

.12014 

.99276 

.13744 

.99051 

.15471 

.98796 

.17193 

.98511 

6 

55 

.10308 

.99467 

.12043 

.99272 

.13773 

.99047 

.15500 

.98791 

.17222 

.98506 

5 

56 

.10337 

.99464 

.12071 

.99269 

.13802 

.99043 

.15529 

.98787 

.17250 

.98501 

4 

57 

.10366 

.99401 

.12100 

.99265 

.13831 

.99039 

.15557 

.98782 

.17279 

.98496 

3 

58 

.10395 

.99458 

.12129 

.99262 

.13860 

.99035 

.15586 

.98778 

.17308 

.98491 

2 

59 

.10424 

.99455 

.12158 

.99258 

.13889 

.99031 

.15615 

.98773 

.17336 

.98486 

1 

60 

.10453 

.99452 

.12187 

.99255 

.13917 

.99027 

.15643 

.98769 

.17365 

.98481 

0 

t 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

/ 

84°   1 

83°   1 

82°   1 

81»   1 

80°   1 

Table  of  Natural  Sines  and  Cosines 


9r 


.' 

10^ 

_   11°  ___J 

lti°   1 

13°    1 

14°    1 

/ 

Sine* 

('osin 

Sine 

Cosin 

Sine 
.20791 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

0 

.17305 

.98481 

.19081 

.98103 

.97815 

.22495 

.97437 

.24192 

.97030 

60 

1 

.17393 

.98470 

.19109 

.98157 

.20820 

.97809 

.22523 

.97430 

.24220 

.97023 

59 

2 

.17422 

.98471 

.19138 

.98152 

.20848 

.97803 

.22552 

.97424 

.24249 

.97015 

58 

3 

.17451 

.98406 

.19107 

.98140 

.20877 

.97797 

.22580 

.97417 

.24277 

.97008 

67 

4 

.17479 

.98401 

.19195 

.98140 

.20905 

.97791 

.22008 

.97411 

.24305 

.97001 

50 

5 

.17508 

.98455 

.19224 

.98135 

.20933 

.97784 

.22037 

.97404 

.24333 

.90994 

55 

6 

.17537 

.98450 

.19252 

.98129 

.20902 

.97778 

.22005 

.97398 

.24302 

.90987 

64 

7 

.17505 

.98445 

.19281 

.98124 

.20990 

.97772 

.22093 

.97391 

.24390 

.90980 

53 

8 

.17594 

.98440 

.10309 

.98118 

.21019 

.97700 

.22722 

.97384 

.24418 

.96973 

52 

9 

.17023 

.98435 

.19338 

.98112 

.21047 

.97700 

.22750 

.97378 

.24440 

.90900 

51 

10 

.17051 

.98430 

.19300 

.98107 

.21070 

.97754 

.22778 

.97371 

.24474 

.96959 

50 

11 

.17080 

.98425 

.19395 

.98101 

.21104 

.97748 

.22807 

.97305 

.24503 

.90952 

49 

12 

.17708 

.98420 

.19423 

.98090 

.21132 

.97742 

.22835 

.97358 

.24531 

.90945 

48 

13 

.17737 

.98414 

.19452 

.98090 

.21101 

.97735 

.22803 

.97351 

.24559 

.90937 

47 

14 

,17700 

.98409 

.19481 

.98084 

.21189 

.97729 

.22892 

.97345 

.24587 

.90930 

40 

15 

.17794 

.98404 

.19509 

.98079 

.21218 

.97723 

.22920 

.97338 

.24015 

.90923 

45 

IG 

.17823 

.98399 

.19538 

.98073 

.21240 

.97717 

.22948 

.97331 

.24044 

.90910 

44 

17 

.17852 

.98394 

.19500 

.98007 

.21275 

.97711 

.22977 

.97325 

.24072 

.90909 

43 

18 

.17880 

.98389 

.19595 

.98001 

.21303 

.97705 

.23005 

.97318 

.24700 

.90902 

42 

10 

.17909 

.98383 

.19C23 

.98050 

.21331 

.97098 

.23033 

.97311 

.24728 

.90894 

41 

20 

.17937 

.98378 

.19652 

.98050 

.21300 

.97092 

.23002 

.97304 

.24750 

.90887 

40 

21 

.17900 

.98373 

.19080 

.98044 

.21388 

.97080 

.23090 

.97298 

.24784 

.96880 

39 

22 

.17995 

.98308 

.19709 

.98039 

.21417 

.97080 

.23118 

.97291 

.24813 

.96873 

38 

23 

.18023 

.98302 

.19737 

.98033 

.21445 

.97073 

.23140 

.97284 

.24841 

.90860 

37 

24 

.18052 

.98357 

.19700 

.98027 

.21474 

.97007 

.23175 

.97278 

.24809 

.96858 

36' 

25 

.18081 

.98352 

.19794 

.98021 

.21502 

.97001 

.23203 

.97271 

.24897 

.96851 

35 

20 

.18109 

.98347 

.19823 

.98010 

,21530 

.97055 

.23231 

.97204 

.24925 

.96844 

34 

27 

.18138 

.98341 

.19851 

.98010 

.21559 

.97048 

.23200 

.97257 

.24954 

.96837 

33 

28 

.18100 

.98330 

.19880 

.98004 

.21587 

.97042 

.23288 

.97251 

.24982 

.96829 

32 

29 

.18195 

.98331 

.1990S 

.97998 

.21010 

.97030 

.23310 

.97244 

.25010 

.96822 

31 

30 

.18224 

.98325 

.19937 

.97992 

.21044 

.07030 

.23345 

.97237 

.25038 

.90815 

30 

31 

.18252 

.18281 

.98320 

.19905 

.97987 

.21072 

.97023 

.23373 

.97-230 

.25000 

.90807 

29 

32 

.98315 

.19994 

.97981 

.21701 

.97017 

.23401 

.97223 

.25094 

.90800 

28 

33 

.18309 

.98310 

.20022 

.97975 

.21729 

.97011 

.23429 

.97217 

.25122 

.96793 

27 

34 

.18338 

.98304 

.20051 

.97909 

.21758 

.97004 

.23458 

.97210 

.25151 

.96786 

26 

35 

.18307 

.98299 

.20079 

.97903 

.21780 

.97598 

.23480 

.97203 

.25179 

.96778 

25 

36 

.18395 

.98294 

.20108 

.97958 

.21814 

.97592 

.23514 

.97190 

.25207 

.96771 

24 

37 

.18424 

.98288 

.20130 

.97952 

.21843 

.97585 

.23542 

.97189 

.25235 

.96704 

23 

38 

.18452 

.98283 

.20105 

.97940 

.21871 

.97579 

.23571 

.97182 

.25203 

.90750 

22 

39 

.18481 

.98277 

.20193 

.97940 

.21899 

.97573 

.23599 

.97170 

.25291 

.96749 

21 

40 

.18509 

.98272 

.20222 

.97934 

.21928 

.97500 

.23027 

.97109 

.25320 

.96742 

20 

41 

.18538 

.98207 

.20250 

.97928 

.21950 

.97500 

.22050 

.97102 

.25348 

.96734 

19 

42 

.18507 

.98201 

.20279 

.97922 

.21985 

.97553 

.23084 

.97155 

.25370 

.96727 

18 

43 

.18595 

.98250 

.20307 

.97910 

.22013 

.975!7 

.23712 

.97148 

.25404 

.96719 

17 

44 

.18024 

.98250 

.20330 

.97910 

.22041 

.97541 

.23740 

.97141 

.25432 

.96712 

16 

45 

.18052 

.98245 

.20304 

.97905 

.22070 

.97534 

.23709 

.97134 

.25400 

.90705 

15 

40 

.18081 

.98240 

.20393 

.97899 

.22098 

.97528 

.23797 

.97127 

.25488 

.90097 

14 

47 

.18710 

.98234 

.20421 

.97893 

.22120 

.97521 

.23825 

.97120 

.25516 

.96690 

13 

48 

.18738 

.98229 

.20450 

.97887 

.22155 

.97515 

.23853 

.97113 

.25545 

.96682 

12 

49 

.18707 

.98223 

.20478 

.97881 

.22183 

.97508 

.23882 

.97100 

.25573 

.96675 

11 

50 

.18795 

.98218 

.20507 

.97875 

.22212 

.97502 

.23910 

.97100 

.25001 

.96667 

10 

51 

.18824 

.98212 

.20535 

.97809 

.22240 

.97490 

.23938 

.97093 

.25629 

.90060 

9 

52 

.18852 

.98207 

.20503 

.97803 

.22208 

.97489 

.23900 

.97080 

.25057 

.96653 

8 

53 

.18881 

.98201 

.20592 

.97857 

.22297 

.97483 

.23995 

.97079 

.25085 

.96645 

7 

54 

.18910 

.98190 

.20020 

.97851 

.22325 

.97470 

.24023 

.97072 

.25713 

.90038 

6 

55 

.18938 

.98190 

.20049 

.97845 

.22353 

.97470 

.24051 

.97005 

.25741 

.90030 

5 

50 

.18907 

.98185 

.20077 

.97839 

.22382 

.97403 

.24079 

.97058 

.25709 

.90023 

4 

57 

.18995 

.98179 

.20700 

.97833 

.22410 

.97457 

.24108 

.97051 

.25798 

.90015 

3 

58 

.19024 

.98174 

.20734 

.97827 

.22438 

.97450 

.24130 

.97044 

.25820 

.96608 

2 

59 

.19052 

.98108 

.20703 

.97821 

.22407 

.97444 

.24104 

.97037 

.25854 

.96600 

1 

00 

.19081 

.98103 

.20791 

.97815 

.22495 

.97437 

.24192 

.97030 

.25882 
Cosin 

.96593 

0 

T 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Sine 

■ 

79° 

78° 

77° 

7r.'>   1 

75° 

Trigonometry  ' 


Part 


' 

15°    1 

1«°   1 

17°    1 

18°   1 

19°   1 

t 
60 

Sine 

Cosin 

Sine 

Cosin 

Sine 

</osin 

Sine 

Cosin 

Sine 

Cusin 

0 

.25S82 

.96593 

.27564 

.96126 

.29237 

.95630 

.30902 

.95106 

.32557 

.94.552 

1 

.25910 

.96585 

.27592 

.96118 

.29265 

.05622 

.30920 

.9.3097 

.32584 

.94542 

50 

2 

.25938 

.96578 

.27620 

.96110 

.29293 

.95613 

.30957 

.95088 

.32612 

.94533 

5,j 

3 

.25966 

.91)570 

.27648 

.96102 

.29321 

.95605 

.30985 

.95079 

.•32639 

.94.323 

57 

4 

.25994 

.96562 

.27676 

.96004 

.29348 

.95596 

.31012 

.95070 

.32667 

.94514 

5i) 

5 

.26022 

.96555 

.27704 

.96036 

.2<t37<; 

.95588 

.31040 

.95061 

.32694 

.94504 

55 

6 

.26050 

.96547 

.27731 

.96078 

.29404 

.95579 

.3106S 

.95052 

.32722 

.94495 

54 

7 

.26079 

.96510 

.27759 

.96070 

.29432 

.9.'3571 

.31095 

.9.5043 

.32740 

.94485 

53 

8 

.26107 

.9(i532 

.27787 

.96062 

.20460 

.95562 

.31123 

.9,3033 

.32777 

.94476 

52 

9 

.26135 

.96524 

.27815 

.96054 

.29487 

.955.''>4 

.31151 

.95024 

.32804 

.94466 

51 

10 

.26163 

.96517 

.27843 

.90046 

.29515 

.95545 

.31178 

.95015 

.32832 

.94457 

50 

11 

.26191 

.96500 

.27871 

.96037 

.20543 

.95536 

.31206 

.95006 

.32850 

.94447 

40 

12 

.26219 

.96502 

.27890 

.96029 

.20571 

.95528 

.31233 

.94097 

.32SS7 

.94438 

4.N 

13 

.26247 

.03494 

.27927 

.96021 

.20599 

.9.5519 

.31261 

.94088 

.32914 

.94428 

47 

14 

.2627a 

.96486 

.27955 

.96013 

.29626 

.9.3511 

.31289 

.94079 

.32942 

.94418 

4". 

15 

.26303 

.96479 

.27983 

.96005 

.20654 

.95502 

.31316 

.94970 

.32900 

.94409 

45 

16 

.26331 

.96471 

.28011 

.95097 

.20632 

.95493 

.31344 

.94961 

.32007 

.94399 

44 

17 

.26359 

.96163 

.28030 

.95959 

.20710 

.95485 

.31372 

.94952 

.33024 

.94390 

43 

18 

.26387 

.96456 

.2:3067 

.95981 

.20737 

.95476 

.31399 

.94043 

.33051 

.94380 

42 

19 

.26415 

.96448 

.23095 

.95972 

.20765 

.9.3467 

.31427 

.94933 

.33070 

.94370 

41 

20 

.26443 

.96440 

.28123 

.95904 

.29703 

.95459 

.31454 

.94924 

.33106 

.94361 

40 

21 

.26471 

.96433 

.28150 

.95956 

.20821 

.95450 

.31482 

.94915 

.33134 

.94351 

30 

22 

.26500 

.96125 

.28178 

.95948 

.20349 

.95441 

.31510 

.94906 

.33161 

.94342 

38 

23 

.26528 

.96417 

.2S206 

.95940 

.20370 

.95433 

.31537 

.94397 

.33180 

.94332 

37 

24 

.26556 

.96410 

.28234 

.95031 

.20001 

.95424 

.31.305 

.94888 

.33216 

.94322 

Oii 

25 

.26584 

.96402 

.28262 

.95923 

.20032 

.95115 

.31503 

.94878 

.33244 

.94313 

35 

26 

.26612 

.96394 

.28200 

.95915 

.20960 

.95107 

.31620 

.94869 

.33271 

.94303 

3t 

27 

.26640 

.96386 

.2S318 

.95907 

.20037 

.95398 

.31648 

.94860 

.33298 

.94293 

33 

28 

.26668 

.96379 

.28346 

.95898 

.30015 

.95389 

.31675 

.94851 

..3332(5 

.94284 

32 

29 

.26696 

.96371 

.23374 

.95890 

.30043 

.95380 

.31703 

.94842 

.33353 

.94274 

3i 

30 

.26724 

.96363 

.28402 

.9.5882 

.30071 

.95372 

.31730 

.94832 

.3.3381 

.94264 

30 

31 

.26752 

.96355 

.28-^29 

.95874 

.30008 

.95363 

.31758 

.94823 

.33408 

.94254 
.94245 

20 

32 

.26780 

.96347 

.28457 

.95865 

.30126 

.95354 

.31786 

.94814 

.3.34u(i 

28 

33 

.26808 

.96310 

.28485 

.05857 

.30154 

.95345 

.31813 

.94805 

.33463 

.94235 

27 

34 

.26836 

.96332 

.28513 

.95840 

.30182 

.95337 

.31841 

.94795 

.33400 

.94225 

26 

35 

.26864 

.96324 

.28541 

.9.5841 

.30200 

.95328 

.31868 

.94786 

.33518 

.94215 

25 

36 

.26892 

.963 IC 

.28560 

.95832 

.30237 

.95319 

.31896 

.94777 

.33545 

.94206 

24 

37 

.26920 

.96308 

.28597 

.95824 

.30205 

.95310 

.31923 

.94768 

.33573 

.94196 

23 

38 

.269tS 

.06301 

.28n_5 

.95816 

.30292 

.95301 

.31051 

.047.58 

.33600 

.94186 

22 

39 

.26071) 

.96293 

.28652 

.95807 

.30320 

.95293 

.31979 

.94749 

.33627 

.94176 

21 

40 

.2700J 

.96285 

.28680 

.95799 

.30348 

.95284 

.32006 

.94740 

.33655 

.94167 

20 

41 

.27032 

.96277 

.2870^ 

.95791 

.30376 

.95275 

.32034 

.94730 

.33682 

.94157 

19 

42 

.27060 

.96269 

.28736 

.95782 

.30103 

.95266 

.32061 

.94721 

.33710 

.94147 

18 

43 

.27088 

.96261 

.28764 

.95774 

.30431 

.95257 

.32080 

.94712 

.23737 

.94137 

17 

44 

.27116 

.96253 

.28792 

.95766 

.30450 

.95248 

.32116 

.94702 

.33764 

.94127 

16 

15 

.27144 

.96246 

.28820 

.95757 

.30436 

.95240 

..32144 

.94693 

.33792 

.94118 

15 

46 

.27172 

.96238 

.28847 

.05710 

.30514 

.9.3231 

.32171 

.94684 

.33819 

.94108 

14 

47 

.27200 

.96230 

.28875 

.95740 

.30542 

.95222' 

.32190 

.94674 

.33846 

.94098 

13 

48 

.27228 

.96222 

.28903 

.95732 

.30570 

.95213 

..32227 

.94665 

.33874 

.94088 

12 

49 

.27256 

.96214 

.28931 

.95724 

.30597 

.95204 

.32254 

.946.56 

.33901 

.94078 

11 

50 

.27284 

.96206 

.28959 

.95715 

.30625 

.95195 

.32282 

.94646 

.33929 

.94068 

10 

51 

.27312 

.96198 

.28987 

.95707 

.30653 

.95186 

.32309 

.94637 

.33956 

.94058 

9 

52 

.27340 

.96190 

.29015 

.95698 

.30680 

.95177 

.32337 

.94627 

.33983 

.94049 

8 

53 

.27368 

.961S2 

.29042 

.95690 

.3070S 

.95168 

.32364 

.94618 

.34011 

.94039 

7 

54 

.27396 

.96171 

.29070 

.95681 

.30736 

.05150 

.32392 

.94609 

.34038 

.94029 

6 

55 

.27424 

.96166 

!  .29098 

.05673 

.30763 

.95150 

.32419 

.94509 

.34065 

.94019 

5 

56 

.27452 

.96158 

1.29126 

.95664 

..30791 

.95142 

.32447 

.94590 

.34093 

.94009 

4 

57 

.27480 

.96150 

.29154 

.95656 

.30810 

.95133 

.32474 

.93580 

.34120 

.93999 

3 

58 

.27508 

.96142 

•;. 29182 

.95647 

.30846 

.95124 

.32502 

.94571 

.34147 

.93989 

2 

59 

.27536 

.96134 

1 .29209 

.95630 

.30874 

.95115 

.32529 

.94561 

.34175 

.93979 

1 

GO 

.27564 

.96126 

1.29237  .95630 

j 

.30902 

.95106 

.32557 

.94552 

.34202 

.93969 

0 

' 

Cosin 

Sine 

Cosin  Sine 

ICosin 

Sine 

Cosin  1  Sine 

Cosin 

Sine 

f 

74° 

1    73° 

1    72° 

71° 

70° 

Table  of  Natural  Sines  and  Cosines 


99 


0 

1 

2 
3 

4 
5 
6 
7 
8 
9 
10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

31 

32 
33 
34 
35 
36 
37 
38 
39 
40 

41 

42 
43 
44 
45 
46 
47 
48 
49 
50 

51 
52 
53 
54 
55 
56- 
57 
68 
59 
60 


20^ 


Sine  Cosin 


.34202 
.34229 
,34257 
,34284 
,34311 
.34339 
3436G 
.34393 
,31421 
.34448 
.34475 

34503 
34530 
.34557 
.34584 
.34012 
.34639 
,3400(j 
,3409-i 
,34721 
,34748 

,34775 
,34803 
,34830 
.34857 
.31884 
.34912 
.34939 
.3496() 
.34993 
.35021 

.35048 
3507i 
.3510; 
.35130 
.35157 
.35184 
.35211 
.35239 
.35266 
.35293 

35320 
35347 
35375 
35402 
,35429 
.35456 
.35484 
.35511 
35538 
,35565 

,35592 
.35619 
.35647 
.35674 
.35701 
.35728 
.35755 
.35782 
..35810 
.35837 


,93969 
.93959 
.93949 
.93939 
.93929 
.93919 
,93909 
.93899 
,93889 
.93879 
.93869 

.93859 
.9334! 
.93839 
.93829 
.93819 
.93809 
.93799 
.93789 
93779 
.93769 


,93759 
,9374', 
,9373,': 
,93728 
.93718 
,93708 
,93698 
.93688 
.93677 
.93667 

.93657 
.93647 
.93637 
.93626 
.93016 
.9360G 
.93596 
.93585 
.93575 
.93565 

.93555 
.93544 
.93534 
.93524 
.93514 
93503 
,93493 
,93483 
,93472 
.93462 

.93452 
.03441 
.93431 
.93420 
.93410 
.93400 
.93389 
.93379 
.93368 
.93358 


2\° 


Sine  Cosin 


Cosin  Sine 
69°  ~~ 


,35837 
,35864 
35891 
35918 
35945 
35973 
,36000 
,36027 
,36054 
,36081 
,36108 

,36135 
,36162 
,30190 
.36217 
.36244 
.30271 
.30298 
.36325 
.36352 
.36379 

.36406 
.36434 
.36401 
.304SJ: 
.365  U 
.3654:; 
.30509 
.36596 
.36623 
.36650 

.36677 
.3670' 
.36731 
.3675,'^ 
.3678.^ 
.3681:; 
.36839 
.30867 
.3689- 
.36921 

.36948 

.36975 

.37002 

.37029 

.37056 

.370: 

.37110 

.37137 

.37104 

.37191 

.37218 
.3724, 
.37272 
.37299 
.37326 
.37353 
.37380 
.37407 
.37434 
37401 


93358 
.93348 
.93337 
.93327 
.93316 
,93306 
.93295 
.9328.': 
,93274 
,93264 
,9325: 

.93243 
.93232 
.93222 
.93211 
.93201 
.93190 
.93180 
.93169 
.93159 
.93148 

,93137 
.93127 
,93110 
.93100 
.9309i 
.93084 
.93074 
.93063 
.93052 
.93042 

.93031 
.93020 
.93010 
.92999 
.9298. 
.92978 
.92967 
.92956 
.92945 
.92935 

.92924 
.92913 
.92902 
92892 
.92831 
,92870 
,92859 
,92849 
,92838 
.92827 

928 10 
,92805 
.92794 
.92784 
.92773 
.92762 
.92751 
.92740 
.92729 
.92718 


33" 


Sine  Cosin 


,37461 
,37488 
,37515 
,37542 
,37569 
,37595 
,37622 
,37649 
,37676 
,37703 
.37730 

.37757 
.37784 
.37811 
.37838 
.37865 
.3789: 
.37919 
.37946 
.37973 
.37999 

.38026 
.38053 
.38080 
.38107 
.38134 
.38161 
.38188 
.38215 
.38241 
.38268 

.38295 
.38322 
.38349 
.38376 
.38403 
.38430 
.38456 
.38483 
.3851C 
.3853' 

.38564 
.38591 
.38617 
.38644 
.38671 
.3869S 
.38725 
38752 
38778 
38805 

38832 

,38859 

.38886 

.3891 

.38939 

.38966 

.38993 

.39020 

.39046 

.3907; 


Cosin  I  Sine  Cosin 


92718 
.92707 
.92()97 
.92686 
.92675 
92664 
.92653 
.92642 
.92031 
.92620 
.92609 

.92598 
.92587 
.92570 
.92505 
,92554 
.92543 
.92532 
.92521 
.92510 
.92499 

.92488 
.92477 
.92400 
.92455 
.92444 
.92432 
.92421 
.92410 
.92399 
.92388 

.92377 
.92300 
.92355 
.92343 
9''332 
.92321 
.92310 
.92299 
.9228' 
.92276 

.92205 
.92254 
.92243 
.92231 
.92220 
.92209 
.92198 
.92180 
.92175 
.92164 

.92152 
.92141 
,92130 
,92119 
.9210' 
.92096 
.92085 
.92073 
,92062 
.92050 


23° 


Sine  Cosin 


.Sin 


fi8° 


67° 


,39073 
,39100 
,39127 
.39153 
.39180 
.39207 
.39234 
.39260 
.39287 
.39314 
.39341 

.39367 
.39394 
.39421 
,39448 
,39474 
.39501 
.39528 
.39555 
.395S1 
.39608 

.39635 
.39661 
.39688 
.39715 
.39741 
.39768 
.39795 
.39822 
.39848 
.39875 

.39902 
.39928 
.39955 
.39982 
.40008 
.40035 
.40062 
.40088 
.40115 
.40141 

.40168 
.40195 
.40221 
.40248 
.40275 
.40301 
.40328 
.40355 
.40381 
.40408 

.404; 

.40461 

.40488 

.40514 

.40541 

.40567 

.40594 

.40621 

.40047 

.40674 


.92050 
.92039 
,92028 
.92016 
.92005 
.91994 
,91982 
.91971 
,91959 
.91948 
.91930 

,91925 
,91914 
.91902 
.91891 
.91879 
.91808 
.91850 
.91845 
.91833 
.91822 

.91810 
.91799 
.91787 
.91775 
.91764 
.91752 
.91741 
.91729 
.91718 
.91706 

.91694 
.91683 
.91671 
.91660 
.91648 
.91636 
.91625 
.91613 
.91601 
.91590 

.91578 
.9150b 
.91555 
.91543 
.91531 
.91519 
.01508 
.91496 
.91484 
.91472 

.91461 
.91449 
.91437 
.91425 
.91414 
.91402 
.91390 
.91378 
.91366 
.91355 


Sine  Cosin 


Cosin 


Sine 


40674 
40700 
,40727 
,40753 
,40780 
,40806 
,40833 
.40860 
.40886 
.40913 
.40939 

.40966 

.40992 

.41019 

.410-15 

.41072 

.41098 

.41125 

.41 

.41178 

.41204 

.41231 
.4125" 
.41284 
.41310 
.41337 
.41363 
.41390 
.41416 
.41443 
.41409 

41496 
,41522 
.41549 
.41575 
.41602 
.41628 
.41655 
.41681 
.41707 
.41734 

41760 
,41787 
,41813 
,41«40 
,41866 
.41892 
.41919 
.41945 
.41972 
.41998 

.42024 
.42051 
.42077 
.42104 
.42130 
.42156 
.42183 
.42209 
.42235 
.42262 


91355 
.91343 
,91331 
,91319 
,91307 
.91295 
.91283 
.91272 
.91200 
.91248 
.91236 

.91224 

.9121 

.91200 

.91188 

.91176 

.91164 

.91152 

.91140 

.91128 

.91116 


Cosin 


.91104 
.91092 
.91080 
.91068 
.91056 
.91044 
.91032 
.91020 
.91008 
.90996 

.90984 
.90972 
90960 
,90948 
.90936 
.90924 
.90911 
.90899 
.9088" 
.90875 

.90863 
.90851 
.90839 
,90820 
,90814 
.90802 
.90790 
.9077^ 
.9070(; 
.9C753 

.90741 
.90729 
.90717 
.90704 
.90692 
.90680 
.90668 
.90055 
.90643 
.90631 


Sine 


00 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

49 
48 
47 
40 
45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

29 
28 
27 
2G 
25 
24 
23 
22 
21 
20 

19 
18 
17 
16 
15 
14 
13 
12 
11 
10 


100 


Trigonometry 


Part  1 


/ 
0 

25° 

'^6° 

27° 

.   28° 

29° 

f 

Sine 
.42262 

C'osin 
.90631 

Sine 
.43837 

Cosin 

.89879 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

.45399 

.89101 

.46947 

.88295 

.48481 

.87462 

60 

1 

.42288 

.90618 

.43863 

.89867 

.45425 

.89087 

.40973 

.88281 

.48506 

.87448 

59 

2 

.42315 

.90606 

.43889 

.89854 

.45451 

.89074 

.46999 

.88267 

.48532 

.87434 

58 

3 

.42341 

.90594 

.43916 

.89841 

.45477 

.89001 

.47024 

.88254 

.48557 

.87420 

57 

4 

.42367 

.90582 

.43942 

.89828 

.45503 

.89048 

.47050 

.88240 

.48583 

.87400 

56 

5 

.42394 

.90569 

.43968 

.89816 

.45529 

.89035 

.47076 

.88226 

.48608 

.87391 

55 

6 

.42420 

.90557 

.43994 

.89803 

.45554 

.89021 

.47101 

.88213 

.48634 

.87377 

54 

7 

.42416 

.90545 

.44020 

.89790 

.45580 

.89008 

.47127 

.88199 

.48659 

.87363 

53 

8 

.42473 

.90532 

.41046 

.89777 

.45000 

.88995 

.47153 

.88185 

.48684 

.87349 

52 

9 

.42499 

.90520 

.44072 

.89764 

.45632 

.88981 

.47178 

.88172 

.48710 

.87335 

51 

10 

.42525 

.90507 

.44098 

.89752 

.45658 

.88968 

.47204 

.88158 

.48735 

.87321 

50 

11 

.42552 

.90495 

.44124 

.39739 

.45684 

.88955 

.47229 

.88144 

.48761 

.87306 

49 

12 

.42578 

.90483 

.44151 

.89720 

.45710 

.88942 

.47255 

.88130 

.48786 

.87292 

48 

13 

.42604 

.90470 

.44177 

.89713 

.45736 

.88928 

.47281 

.88117 

.48811 

.87278 

47 

U 

.42631 

.90458 

.44203 

.89700 

.45762 

.88915 

.47306 

.88103 

.48837 

.87264 

40 

15 

.42657 

.90446 

.44229 

.89087 

.45787 

.88902 

.47332 

.88089 

.48862 

.87250 

45 

16 

.42683 

.90133 

.44255 

.89674 

.45813 

.88888 

.47358 

.88075 

.48888 

.87235 

44 

17 

.42709 

.90421 

.44281 

.89662 

.45839 

.88875 

.47383 

.88062 

.48913 

.87221 

43 

18 

.42736 

.90408 

.44307 

.89649 

.45865 

.88862 

.47409 

.88048 

.48938 

.87207 

42 

19 

.42762 

.90396 

.44333 

.89636 

.45891 

.88848 

.47434 

.88034 

.48964 

.87193 

41 

20 

.42788 

.90383 

.44359 

.89623 

.45917 

.88835 

.47460 

.88020 

.48989 

.87178 

40 

21 

.42815 

.90371 

.44385 

.89610 

.45942 

.88822 

.47486 

.88006 

.49014 

.87164 

39 

22 

.42841 

.90358 

.44411 

.89597 

.45908 

.88808 

.47511 

.87993 

.49040 

.87150 

38 

23 

.42867 

.90340 

.44437 

.89584 

.45994 

.88795 

.47537 

.87979 

.49065 

.87136 

37 

24 

.42S94 

.90334 

.44464 

.89571 

.40020 

.88782 

.47562 

.87965 

.49090 

.87121 

30 

25 

.42920 

.90321 

.44490 

.89558 

.46046 

.88768 

.47588 

.87951 

.49116 

.87107 

35 

26 

.42946 

.90309 

.44516 

.89545 

:46072 

.88755 

747614 

.87937 

.49141 

.87093 

34 

27 

.42972 

.90296 

.44542 

.89532 

.46097 

,88741 

.47039 

.87923 

.49166 

.87079 

33 

28 

.42999 

.90284 

.44508 

.89519 

.46123 

.88728 

.47605 

.87909 

.49192 

.87064 

32 

29 

.43025 

.90271 

.44594 

.89506 

.46149 

.88715 

.47090 

.87896 

.49217 

.87050 

31 

30 

43051 

.90259 

.44620 

.89493 

.46175 

88701 

.47710 

.87882 

.4924? 

87036 

30 

31 

.43077 

.90246 

.44646 

.89480 

.46201 

.88688 

.47741 

.87868 

.49268 

.87021 

29 

32 

.43104 

.90233 

.44672 

.89467 

.46220 

.88674 

.47707 

.87854 

.49293 

.87007 

28 

33 

.43130 

.90221 

.44698 

.89454 

.46252 

.88661 

.47793 

.87840 

.49318 

.86993 

27 

34 

.43156 

.90208 

.44724 

.89441 

.46278 

.88647 

.47818 

.87826 

.49344 

.86978 

20 

35 

.13182 

.90196 

.44750 

.89428 

.46304 

.88634 

.47844 

.87812 

.49369 

.86964 

25 

36 

.43209 

.90183 

.44776 

.89415 

.46330 

.88620 

.47869 

.87798 

.49394 

.86949 

24 

37 

.43235 

.90171 

.44802 

.89402 

.46355 

.88607 

.47895 

.87784 

.49419 

.86935 

23 

38 

.43261 

.90158 

.44828 

.89389 

.46381 

.88593 

.47920 

.87770 

.49445 

.86921 

22 

39 

.43287 

.90146 

.44854 

.89376 

.46407 

.88580 

.47946 

.87756 

.40470 

.86906 

21 

40 

.43313 

.90133 

.44880 

.89363 

.46433 

.88566 

.47971 

.87743 

.49495 

.86S92 

20 

41 

.43310 

.90120 

.44906 

.89350 

.46458 

.88553 

.47997 

.87729 

.49521 

.80878 

19 

42 

.43366 

.9010S 

.44932 

.89337 

.46484 

.88539 

.48022 

.87715 

.49546 

.86863 

18 

43 

.43392 

.90095 

.44958 

.89324 

.46510 

.88526 

.48048 

.87701 

.49571 

.86849 

17 

44 

.43418 

.90082 

.44984 

.89311 

.16536 

.88512 

.48073 

.87687 

.49596 

.86834 

16 

45 

.43445 

.90070 

.45010 

.89298 

.46561 

.88499 

.48099 

.87673 

.49622 

.86820 

15 

46 

.43471 

.90057 

.45036 

.89285 

.46587 

.88485 

.48124 

.87659 

.49647 

.86805 

14 

47 

.43497 

.90045 

.45062 

.89272 

.46613 

.88472 

.48150 

.87645 

.49672 

.86791 

13 

48 

.43523 

.90032 

.45088 

.89259 

.46639 

.88458 

.48175 

.87631 

.49697 

.86777 

12 

49 

.43549 

.90019 

.45114 

.89245 

.46664 

.88445 

.48201 

.87617 

.49723 

.86762 

11 

50 

.43575 

.90007 

.45140 

.89232 

.46690 

.88431 

.48226 

.87603 

.49748 

.86748 

10 

61 

.43602 

.89994 

.45166 

.89219 

.46716 

.88417 

.48252 

.87589 

.49773 

.86733 

9 

52 

.43628 

.89981 

.45192 

.89206 

.46742 

.88404 

.48277 

.87575 

.49798 

.86719 

8 

53 

.43654 

.89968 

.45218 

.89193 

.46767 

.88390 

.48303 

.87561 

.49824 

.86704 

7 

54 

.43680 

.89956 

.45243 

.89180 

.46793 

.88377 

.48328 

.87546 

.49849 

.86690 

6 

55 

.43706 

.89943 

.45269 

.89167 

.46819 

.88363 

.48354 

.87532 

.49874 

.86675 

5 

56 

.43733 

.89930 

.45295 

.89153 

.46844 

.88349 

.48379 

.87518 

.49899 

.86601 

•4 

57 

.43759 

.89918 

.45321 

.89140 

.46870 

.88336 

.48405 

.87504 

.49924 

.86646 

3 

58 

.43785 

.89905 

.45347 

.89127 

.46896 

.88322 

.48430 

.87490 

.49950 

.86632 

2 

59 

.43811 

.89892 

.45373 

.89114 

.46921 

.88308 

.48456 

.87476 

.49975 

.86617 

1 

60 

.43837 

.89879 

.45399 
Cosin 

.89101 
Sine 

.46947 

.88295 

.48481 

.87462 

.50000 

.80603 

0 

' 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

/ 

64°   1 

63°   1 

62°    1 

61°   1 

60°   1 

Table  of  Natural  Sines  and  Co'shies 


101 


' 

30° 

31" 

1    33° 

33° 

34° 

60 

Sine 

Cosin 

Sine 

Cosin 

.85717 

Sine 

Cosin 

Sine 
.54404 

Cosin 

.83867 

Sine 
.55919 

Cosin 
.82904 

0 

.50000 

.86603 

.51504 

.52902 

.84805 

1 

.50025 

.80588 

.51529 

.85702 

.53017 

.84789 

.54488 

.83851 

.55943 

.82S87 

59 

2 

.50050 

.86573 

.51554 

.85087 

.53041 

.84774 

.54513 

.83835 

.55968 

.82871 

68 

3 

.50076 

.86559 

.51579 

.85672 

.53006 

.84759 

.54537 

.83819 

.55992 

.82855 

57 

4 

.50101 

.86544 

.51604 

.85657 

.53091 

.84743 

.54561 

.83804 

.56010 

.82839 

56 

5 

.50126 

.86530 

.51628 

.85642 

.53115 

.84728 

.54586 

.83788 

.50040 

.82822 

56 

6 

.50151 

.86515 

.51653 

.85027 

.53140 

.84712 

.54610 

.83772 

.56004 

.82800) 

54 

7 

.50176 

.86501 

.51678 

,85612 

.53164 

.84697 

.54035 

.83750 

.56088 

.82790 

63 

8 

.50201 

.86486 

.51703 

.85597 

.53189 

.84681 

.54659 

.83740 

.50112 

.82773 

52 

9 

.50227 

.86471 

.51728 

.85582 

.53214 

.84606 

.54083 

.83724 

.50136 

.82757 

51 

10 

.50252 

.86457 

.51753 

.85567 

.53238 

.84650 

.54708 

.83708 

.56100 

.82741 

50 

11 

.50277 

.86442 

.51778 

.85551 

.53263 

.84035 

.54732 

.83092 

.56184 

.82724 

49 

12 

.50302 

.86427 

.51803 

.85536 

.53288 

.84619 

.54756 

.83076 

.56208 

.82708 

48 

13 

.50327 

.86413 

.51828 

.85521 

.53312 

.84604 

.54781 

.83660 

.56232 

.82692 

47 

14 

.50352 

.86398 

.51852 

.85506 

.53337 

.84588 

.54805 

.83645 

.56256 

.82675 

46 

15 

.50377 

.86384 

.51877 

.85491 

.53361 

.84573 

.54829 

.83029 

.56280 

.82669 

45 

16 

.50403 

.86369 

.51902 

.85476 

.53386 

.84557 

.54854 

.83013 

.56305 

.82643 

44 

17 

.5042^? 

.86354 

.51927 

.85401 

.53411 

.84542 

.54878 

.83597 

.50329 

.82626 

43 

18 

.50453 

.86340 

.51952 

.85446 

.53435 

.84520 

.54902 

.83581 

.50353 

.82610 

42 

19 

.50478 

.86325 

.51977 

.85431 

.53400 

.84511 

.54927 

.83505 

.50377 

.82593 

41 

20 

.50503 

.86310 

.52002 

.85416 

.53484 

.84495 

.54951 

.83549 

.56401 

.82577 

40 

21 

.50528 

.86295 

.52020 

.85401 

.53509 

.84480 

.54975 

.83533 

.50425 

.82501 

39 

22 

.50553 

.86281 

.52051 

.85385 

.53534 

.84404 

.51999 

.83517 

.50449 

.82544 

38 

23 

.50578 

.86266 

.52076 

.85370 

.53558 

.84448 

.55024 

.83501 

.56473 

.82528 

37 

24 

.50603 

.86251 

.52101 

.85355 

.53583 

.84433 

.55048 

.83485 

.56497 

.82511 

36 

25 

.50628 

.86237 

.52126 

.85340 

.53607 

.84417 

.55072 

.83409 

.56521 

.82496 

35 

26 

.5065} 

.86222 

.52151 

.85325 

.53032 

.84402 

.55097 

.83453 

.56545 

.82478 

34 

27 

.50079 

.86207 

.52175 

.85310 

.53056 

.84380 

.55121 

.83437 

.56569 

.82462 

33 

28 

.50704 

.86192 

.52200 

.85294 

.53081 

.84370 

.55145 

.83421 

.56593 

.82446 

32 

29 

.50729 

.86178 

.62225 

.85279 

.53705 

.84355 

.55109 

.83405 

.56617 

.82429 

31 

30 

.50751 

.80103 

.52250 

.85264 

.53730 

.84339 

.55194 

.83389 

.56641 

.82413 

30 

31 

.50770 

.80148 

.52275 

.85249 

.53754 

.84324 

.55218 

.83373 

.56005 

.82390 

29 

32 

.50804 

.86133 

.52299 

.85234- 

.53779 

.84308 

.55242 

.83350 

.56689 

.82380 

28 

33 

.50829 

.86119 

.52324 

.85218 

.53804 

.84292 

.55206 

.83340 

.56713 

.82303 

27 

34 

.50854 

.86104 

.52349 

.85203 

.53828 

.84277 

.55291 

.83324 

.56730 

.82347 

26 

35 

.50.^79 

.86089 

.52874 

.85188 

.53853 

.84201 

.55315 

.83308 

.50700 

.82330 

25 

36 

.50904 

.86074 

.52399 

.85173 

.53877 

.84245 

.55339 

.83292 

.56784 

.82314 

24 

37 

.50929 

.86059 

.52423 

.85157 

.53902 

.84230 

.55363 

.83270 

.56808 

.82297 

23 

38 

.50954 

.86045 

.52448 

.85142 

.53920 

.84214 

.55388 

.83200 

.66832 

.82281 

22 

39 

.50979 

.80030 

.52473 

.85127 

.53951 

.84198 

.55412 

.83244 

.56850 

.82264 

21 

40 

.51004 

.86015 

.52498 

.85112 

.53975 

.84182 

.55430 

.83228 

.56880 

.82248 

20 

41 

.51029 

.8G000 

.52522 

.85090 

.54000 

.84107 

.55400 

.83212 

.56904 

.82231 

19 

42 

.51054 

.85985 

.52547 

.85081 

.54024 

.84151 

.55484 

.83195 

.56928 

.82214 

18 

43 

.51079 

.85970 

.52572 

.85066 

.54049 

.84135 

.55509 

.83179 

.60952 

.82198 

17 

44 

.51104 

.85956 

.52597 

.85051 

.54073 

.84120 

.55533 

.83103 

.56976 

.82181 

16 

45 

.51129 

.85941 

.52021 

.85035 

.54097 

.84104 

.55557 

.83147 

.57000 

.82165 

15 

46 

.51154 

.85926 

.52646 

.85020 

.54122 

.840SS 

.55581 

.83131 

.57024 

.82148 

14 

47 

.51179 

.85911 

.52671 

.85005 

.54146 

.84072 

.55005 

.83115 

.57047 

.82132 

13 

48 

.51204 

.85896 

.52096 

.84989 

.54171 

.84057 

.55630 

.83098 

.57071 

.82116 

12 

49 

.51229 

.85881 

.52720 

.84974 

.54195 

.84041 

.55654 

.83082 

.67095 

.82098 

11 

50 

.51254 

.85866 

.52745 

.84959 

.54220 

.84025 

.55078 

.83000 

.57119 

.82082 

10 

51 

.51279 

.85851 

.52770 

.84943 

.54244 

.84009 

.55702 

.83050 

.57143 

.82005 

9 

52 

.51304 

.85836 

.52794 

.84928 

.54209 

.83994 

.55726 

.83034 

.67167 

.82048 

8 

53 

.51329 

.85821 

.52819 

.84913 

.54293 

.83978 

.55750 

.83017 

.57191 

.82032 

7 

54 

.51354 

.85806 

.52844 

.84897 

.54317 

.83962 

.55775 

.83001 

.57215 

.82016 

fi 

55 

.51379 

.85792 

.52800 

.84882 

.54342 

.83940 

.55799 

.82985 

.67238 

.81999 

5 

56 

.51404 

.85777 

.52893 

.84866 

.54306 

.83930 

.55823 

.82969 

.57202 

.81982 

4 

57 

.51429 

.85762 

.52918 

.84851 

.54391 

.83915 

.55847 

.82953 

.57286 

.81965 

3 

58 

.51454 

.85747 

.52943 

.84836 

.54415 

.83899 

.55871 

.82930 

.57310 

.81949 

2 

59 

.51479 

.85732 

.52967 

.84«20 

.54440 

.83883 

.55895 

.82920 

.57334 

.81932 

1 

00 

.51504 

.85717 

.52992 

.84805 

.54404 

.83807 

.55919 
Cosin 

.82904 

.67358 

.81915 

0 

' 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Sine 

Cosin 

Sine 

/ 

59°    1 

58"    1 

57°    1 

56°    1 

55° 

2 

Trigonometry 

Part 

/ 

35° 

30° 

37° 

Sine  jCosin 

•  38° 

39° 

' 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

C'Osin 

~o 

.57358 

.81915 

:58779 

.80902 

.00182 

.79304 

.01500 

.78801 

.02932 

.77715 

00 

1 

.57381 

.81899 

.58802 

.80885 

.00205 

.79840 

.01589 

.78783 

.02955 

.77090 

59 

0 

.57405 

.81882 

.58820 

.80807 

.00228 

.79829 

.01012 

.78705 

.02977 

.77078 

58 

3 

.57429 

.81805 

.58849 

.80850 

^10251 

.79811 

.01035 

.78747 

.03000 

.77000 

57 

4 

.57453 

.81848 

.58873 

.80833 

.00274 

.79703 

.^51058 

.78729 

.03022 

.77041 

50 

5 

.57477 

.81832 

.58800 

.80810 

.00298 

.79770 

.01081 

.78711 

.03045 

.77023 

55 

0 

.57501 

.81815 

.58920 

.80799 

.00321 

.70758 

.01704 

.78094 

.030(58 

.77005 

54 

7 

.57324 

.81798 

.58943 

.80782 

.00344 

.79741 

.0172{; 

.78(i7t) 

.t)30*)0 

.77580 

53 

8 

.57548 

.81782 

.58907 

.80705 

.00307 

.79723 

.01749 

.78058 

.03113 

.77508 

52 

9 

.57572 

.81705 

.58990 

.80748 

.00390 

.79700 

.01772 

.78040 

.03135 

.77550 

51 

10 

.57590 

.81748 

.59014 

.80730 

.00414 

.79088 

.01795 

.78022 

.03158 

.77531 

50 

11 

.57019 

.81731 

.59037 

.80713 

.00437 

.79071 

.01818 

.78004 

.03180 

.77513 

40 

12 

.57043 

.81714 

.5901)1 

.8000i; 

.00400 

.79()53 

.01841 

.785S0 

.03203 

.77404 

48 

13 

.57007 

.81098 

.59084 

.80079 

.()0J83 

.79035 

.01804 

.78508 

.03225 

.77470 

47 

14 

.57091 

.81081 

.59108 

.^00^)2 

.00500 

.79018 

.01887 

.78550 

.03248 

.77458 

40 

15 

.57715 

.81004 

.59131 

.80044 

.00529 

.79000 

.01909 

.785.32 

.03271 

.77439 

45 

10 

.57738 

.81047 

.59154 

.80027 

.00553 

.79583 

.01932 

.78514 

.03293 

.77421 

44 

17 

.57702 

.81031 

.59178 

.80')10 

.00570 

.79505 

.01955 

.78490 

.03310 

.77402 

43 

IS 

.57780 

.81014 

.59201 

.80503 

.00599 

.79547 

.01978 

.78478 

.03338 

.77384 

42 

19 

.57810 

.81597 

.59225 

.8057() 

.00''22 

.79530 

.02001 

.78400 

.03301 

.77300 

41 

20 

.57833 

.81580 

.592  48 

.805.58 

.00015 

.79512 

.02024 

.784  42 

.03383 

.77347 

40 

21 

.57857 

.81503 

.59272 

.80541 

.00008 

.79494 

.02040 

.78424 

.03400 

.77329 

39 

22 

.57881 

.81540 

.50295 

.80524 

.00091 

.79477 

.02009 

.78  405 

.03428 

.77310 

38 

23 

.57901 

.81530 

.59318 

.80507 

.00714 

.79  459 

.02092 

.783S7 

.03451 

.77202 

37 

24 

.57928 

.81513 

.59342 

.80480 

.00738 

.79441 

.02115 

.78309 

.03473 

.77273 

36 

25 

.57952 

.81490 

.59305 

.80472 

.00701 

.79424 

.0213S 

.78351 

.03490 

.77255 

35 

20 

.57970 

.81479 

.59389 

.80455 

.00784 

.79400 

.02100 

.78333 

.0.3518 

.77230 

34 

27 

.57999 

.81402 

.59412 

.80438 

.00807 

.70388 

.02183 

.78315 

.03540 

.77218 

•33 

28 

.58023 

.81445 

.59431) 

.80420 

.00330 

.70371 

.02200 

.78297 

.03503 

.77199 

32 

29 

.rt^'Oil 

.8142S 

.59459 

.80403 

.00853 

.70353 

.02220 

.78270 

.03585 

.77181 

31 

30 

.58070 

.81412 

.59482 

.80380 

.00870 

.79335 

.02251 

.78201 

.03008 

.77102 

30 

31 

.58094 

.81395 

.59500 

.80308 

.00899 

.79318 

.02274 

.78243 

.G3030 

.77144 

29 

32 

.58118 

.81378 

.59529 

.80351 

.()0922 

.79300 

•.02297 

.78225 

.03053 

.77125 

28 

33 

.58141 

.81301 

.59552 

.80334 

.00945 

.79282 

.02320 

.78200 

.03075 

.77107 

27 

34 

.58105 

.81344 

.59570 

.80310 

.<)0908 

.79204 

.02342 

.78188 

.03098 

.77088 

26 

35 

.58189 

.81327 

.59599 

.80290 

.00001 

.79247 

.02305 

.78170 

.03720 

.77070 

25 

6Cy 

.58212 

.81310 

.59022 

.80282 

.01015 

.79220 

.02388 

.78152 

.03742 

.77051 

24 

37 

.58230 

.81293 

.59040 

.80204 

.01038 

.79211 

.02411 

.78134 

.03705 

.77033 

23 

38 

.58200 

.81270 

.59009 

.80247 

.01001 

.79193 

.02433 

.78110 

.03787 

.77014 

22 

39 

.58283 

.81259 

.59093 

.80230 

.01084 

.70170 

.02450 

.78098 

.03810 

.70996 

21 

to 

.58307 

.81242 

.59710 

-.80212 

.01107 

.79158 

.02479 

.78079 

.03832 

.70977 

20 

41 

.58330 

.81225 

.59739 

.80195 

.01130 

.79140 

.02502 

.78001 

.03854 

.70959 

19 

42 

.58354 

.81208 

.59703 

.80178 

.01153 

.79122 

.02524 

.78043 

.03877 

.70940 

18 

43 

.58378 

.81191 

.59780 

.801  (K) 

.01170 

.79105 

.02547 

.78025 

.03899 

.70921 

17 

44 

.58401 

.81174 

.59809 

.80143 

.01199 

.79087 

.02570 

.78007 

.()3922 

.70903 

16 

45 

.58425 

.81157 

.59832 

.80125 

.01222 

.79009 

.02592 

.77988 

.03944 

.70884 

15 

40 

.58449 

.81140 

.59850 

.80108 

.01245 

.79051 

.02015 

.77970 

.03900 

.70800 

14  ; 

47 

.58472 

.81123 

.59879 

.80091 

.01208 

.79033 

.02038 

.77952 

.03989 

.70847 

13  i 

48 

.58490 

.8110<) 

.59902 

.80073 

.01291 

.79010 

.02000 

.77934 

.04011 

.76828 

12 

49 

.58519 

.81089 

.59920 

.8005() 

.01314 

.78998 

.02083 

.77910 

.64033 

.70810 

11 

50 

.58543 

.81072 

.59949 

.80038 

.01337 

.78980 

.02700 

.77897 

.64050 

.70791 

10 

51 

.58507 

.81055 

.59972 

.80021 

.01300 

.78902 

.02728 

.77879 

.64078 

.70772 

9 

52 

.5S590 

.81038 

.59995 

.80003 

.01383 

.78944 

.02751 

.77801 

.64100 

.7'>754 

8 

53 

.58014 

.81021 

.00019 

.7998() 

.01400 

.78920 

.0':>774 

.77843 

.64123 

.70735 

7 

54 

.58037 

.81004 

.00042 

.79908 

.01429 

.78908 

.02790 

.77824 

.61145 

.70717 

6 

55 

.58001 

.80987 

.00005 

.79951 

.01451 

.78S()1 

.02819 

.77800 

.64107 

.7t>098 

5 

50 

.5S0S4 

.80070 

.00089 

.79934 

.01474 

.78-^^73 

.02842 

.77788 

.04190 

.70079 

4 

57 

.5^708 

.80953 

.00112 

.79910 

.01497 

.788.55 

.02804 

.77709 

.64212 

.70001 

3 

58 

.5^731 

.80930 

.00135 

.79899 

.01520 

.78837 

.02887 

.v;/5i 

.64234 

.7604? 

2 

59 

.58755 

.80019 

.00158 

.79881 

.01543 

.78819 

.02909 

.77733 

.04250 

.76623 

1 

60 

.58779 

.80902 

.00182 

.79804 

.01500 

.78801 

.02932 

.77715 

.64279 

.76604 

0 

r 

Cosin 

Sine 

Cosin  Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

f 

54°   1 

53° 

52° 

51°   1 

50° 

Table  of  Natural  Sines  and  Cosines 


103 


/ 
0 

40°    1 

_   41"   1 

42°    1 

43°    1 

44° 

' 

Sine 

.04279 

Cosin 
.7()004 

Sine 

Cosin 

Sine 
.00913 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

.05(500 

.75471 

.74314 

.68200 

.73135 

.(5940(5 

.71934 

60 

1 

.04301 

.7058(> 

.(55028 

.75452 

.00935 

.74295 

.08221 

.73110 

.09487 

.71914 

59 

2 

.04323 

.70507 

.(55(550 

.75433 

.()()950 

.74270 

.68242 

.73090 

.(59508 

.71894 

68 

3 

.04340 

.7()548 

.(55(572 

.75414 

.(5(5978 

.7425(5 

.08204 

.7307(5 

.09529 

.71873 

57 

4 

.043(;8 

.70530 

.(55(594 

.75395 

.0(5999 

.74237 

.08285 

.73050 

.(59549 

.71853 

50 

5 

.04390 

.70511 

.(55710 

.75375 

.(57021 

.74217 

.08300 

.73030 

.09570 

.71833 

55 

0 

.04412 

.70492 

.(55738 

.75350 

.07043 

.74198 

.08327 

.73010 

.(59591 

.71813 

54 

7 

.04435 

.70473 

.(55759 

.75337 

.070(54 

.74178 

.08349 

.72990 

.09012 

.71792 

53 

8 

.()4457 

.70455 

.(55781 

.75318 

.0708(5 

.74159 

.08370 

.72970 

.09033 

.71772 

52 

9 

.04479 

.7()  13(1 

.(55803 

.75299 

.07107 

.74139 

.08391 

.72957 

.09054 

.71752 

61 

10 

.04501 

.70417 

.(55825 

.752S0 

.07129 

.74120 

.08412 

.72937 

.09075 

.71732 

50 

11 

.04521 

.70398 

.05847 

.75201 

.07151 

.74100 

.68434 

.72917 

.09090 

.71711 

49 

12 

.04540 

.70380 

.(558(59 

.75241 

.07172 

.74080 

.08455 

.72897 

.09717 

.71091 

48 

13 

.04508 

.70301 

.(55891 

.75222 

.07194 

.74001 

.08476 

.72877 

.09737 

.71(571 

47 

14 

.64590 

.7()342 

.(55913 

.75203 

.07215 

.74041 

.68497 

.72857 

.09758 

.71(>50 

40 

1.5 

.04012 

.70323 

.(55935 

.75184 

.67237 

.74022 

.68518 

.72837 

.(59779 

.71630 

45 

10 

.04635 

.70304 

.05950 

.75105 

.07258 

.74002 

.68539 

.72817 

.09800 

.71610 

44 

17 

.64057 

.7028(-: 

.(55978 

.75140 

.67280 

.73983 

.08501 

.72797 

.09821 

.71590 

43 

18 

.04079 

.70207 

.(50000 

.75120 

.07301 

.73903 

.08582 

.72777 

.(59842 

.71569 

42 

19 

.04701 

.70248 

.00022 

.75107 

.07323 

.73044 

.0800? 

.72757 

.(59802 

.71549 

41 

20 

.04723 

.70229 

.0(5044 

.75088 

.07344 

.73924 

.08024 

.72737 

.09883 

,71529 

40 

21 

.04740 

.70210 

.00000 

.75009 

.07300 

.73004 

.08045 

.72717 

.09904 

.71508 

39 

22 

.04708 

.70192 

.(50088 

.75050 

.07387 

.73885 

.08000 

.72097 

.(59925 

.71488 

38 

23 

.04790 

.70173 

.0(5109 

.75030 

.07409 

.73805 

.08088 

.72077 

.(5994(5 

.71408 

37 

24 

.04812 

.70154 

.0(5131 

.75011 

.07430 

.73840 

.08709 

.72657 

.(599(50 

.71447 

30 

25 

.(i48.i4 

.70135 

.0(5153 

.74992 

.07452 

.73820 

.08730 

.72037 

.09J)87 

.71427 

35 

20 

.6485() 

.70110 

.00175 

.74973 

.07473 

.73800 

.(58751 

.72017 

.70008 

.71407 

34 

27 

.64878 

.70097 

.'1(5197 

.74953 

.07495 

.73787 

.08772 

.72597 

.70029 

.7138(5 

33 

28 

.04901 

.7()078 

.00218 

.74934 

.07510 

.73707 

.08793 

.72577 

.7(M)49 

.713(5(5 

32 

29 

.04923 

.70059 

.0(5240 

.74915 

.(57538 

.73747 

.(58814 

.72557 

.70070 

.71345 

31 

30 

.()4945 

.70041 

.(5(5202 

.74890 

.07559 

.73728 

.08835 

.72537 

.70091 

.71325 

30 

31 

.04907 

.700*22 

.00284 

.74870 

.07580 

.73708 

.08857 

.72517 

.70112 

.71305 

29 

32 

.()4989 

.70003 

.6030(5 

.74857 

.(•  7(502 

.73(588 

.08878 

.72497 

.70132 

.71284 

28 

33 

.05011 

.75984 

.00327 

.74838 

.07(523 

.73009 

.(58899 

.72477 

.70153 

.71264 

27 

34 

.05033 

.75905 

.0(5349 

.74818 

.07(545 

.73049 

.08920 

.72457 

.70174 

.71243 

20 

35 

.05055 

.7594(5 

.00371 

.74799 

.07(50(5 

.73029 

.(58941 

.72437 

.70195 

.71223 

25 

30 

.(>5077 

.75927 

.0(5393 

.74780 

.(5708S 

.73010 

.0S902 

.72417 

.70215 

.71203 

24 

37 

.05100 

.75908 

.«)()414 

.747(50 

.07709 

.73590 

.08983 

.72397 

.7023(5 

.71182 

23 

3S 

.05122 

.75889 

.0(543(5 

.74741 

.07730 

.73570 

.(50004 

.72377 

.70257 

.711(52 

22 

39 

.05144 

.75870 

.0(5458 

.74722 

.07752 

.73551 

.(59025 

.72357 

.70277 

.71141 

21 

40 

.0510() 

.7585 1 

.0(5480 

.74703 

.07773 

.73531 

.(5904(5 

.72337 

.70298 

.71121 

20 

41 

.05188 

.75832 

.00501 

.74083 

.07705 

.73511 

.69007 

.72317 

.70319 

.71100 

19 

42 

.05210 

.75813 

.0(5523 

.74001 

.(;7810 

.73491 

.09088 

.72297 

.70339 

.71080 

18 

43 

.05232 

.75794 

.00545 

.74044 

.07837 

.73472 

.(59109 

.72277 

.703(50 

.71059 

17 

44 

.05254 

.75775 

.005(50 

.74025 

.07859 

.73452 

.09130 

.72257 

.70381 

.71039 

10 

45 

.05270 

.75750 

.0(5588 

.74000 

.(57880 

.73132 

.(59151 

.7223(5 

.70401 

.71019 

15 

40 

.()5298 

.75738 

.(5(5010 

.7458(5 

.07901 

.73413 

.(59172 

.72210 

.70422 

.70998 

14 

47 

.05320 

.75719 

.0(5032 

.745(57 

.(57923 

.73393 

.(59193 

.72190 

.70443 

.70978 

13 

4S 

.05342 

.75700 

.0(5(553 

.74548 

.07941 

.73373 

.t  592 14 

.72170 

.70403 

.70957 

12 

,49 

.05304 

.75080 

,(50075 

.74528 

.079(55 

.73353 

.09235 

.72150 

.70484 

.70937 

11 

50 

.05380 

.75()01 

.(5(5(597 

.74509 

.07987 

.73333 

.0025(5 

.72130 

.70505 

.70916 

10 

51 

.05408 

.7504^2 

.0()718 

.74489 

.08008 

.73314 

.09277 

.72110 

.70525 

.7089(5 

9 

52 

.05430 

.75023 

.0(5740 

.74470 

.08029 

.73294 

.(59298 

.72095 

.70540 

.70875 

8 

53 

.05452 

.75004 

.00702 

.74451 

.(58051 

.73274 

.09319 

.72075 

.70507 

.70855 

7 

54 

.05474 

.75585 

.00783 

.74431 

.08072 

.73254 

.(59340 

.72055 

.70587 

.70834 

6 

55 

.05490 

.75501) 

.00805 

.74412 

.68093 

.73234 

.()9301 

.72035 

.70008 

.70813 

5 

50 

.05518 

.75547 

.0(5827 

.7't392 

.08115 

.73215 

.09382 

.72015 

.70028 

.70793 

4 

57 

.05540 

.75528 

.00848 

.74373 

.08130 

.73195 

.09403 

.71995 

.70049 

.70772 

3 

5S 

.05502 

.75509 

.00)870 

.74353 

.08157 

.73175 

.(59424 

.71974 

.70070 

.70752 

2 

59 

.05584 

.75490 

.0(5891 

.74334 

.68179 

.73155 

.69445 

.71954 

.70090 

.70731 

1 

60 

.05000 

.75471 

.0(5913 

74314 

.08200 
Cosin 

.73135 

.69466 

.71934 

.70711 

.70711 

0 

/ 

Cosin 

Sine 

Cosin 

Sine 

Sine 

Cosin 

Sine 

Cosin 

Sine 

' 

_ 

4?)° 

48° 

47° 

46° 

45° 

104 


Trigonometry 


' 

0^ 

1°      1 

2°     1 

3° 

1 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.00000 

Infinite. 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

60 

1 

.00029 

3437.75 

.01775 

56.3506 

.03521 

28.3994 

.05270 

18.9755 

59 

2 

.00058 

1718.87 

.01804 

55.4415 

.03550 

28.1664 

.05299 

18.8711 

58 

3 

.00087 

1145.92 

.01833 

54.5613 

.03579 

27.0372 

.05328 

18.7678 

57 

4 

.00116 

859.436 

.01862 

53.7086 

.03600 

27.7117 

.05357 

18.6656 

56 

5 

.00M5 

687.549 

.01801 

52.8S21 

.03638 

27.4899 

.05387 

18.5615 

55 

0 

.00175 

572.957 

.01920 

52.0807 

.03667 

27.2715 

.05416 

18.4645 

54 

7 

.00204 

401.106 

.01940 

51.3032 

.03096 

27.0566 

.05145 

18.3655 

53 

8 

.00233 

429.718 

.01978 

50.5485 

.03725 

26.8450 

.05474 

18.2677 

52 

9 

.00262 

381.971 

.02007 

49.8157 

.03754 

26.6367 

.05503 

18.1708 

51 

10 

.00291 

343.774 

.02036 

40.1039 

.03783 

26.4316 

.05533 

18.0750 

50 

11 

.00320 

312.521 

.02066 

48.4121 

.03812 

26.2296 

.05502 

17.9802 

49 

12 

.00349 

286.478 

.02005 

47.7305 

.03842 

26.0307 

.05591 

17.8863 

48 

13 

.00378 

264.441 

.02124 

47.0853 

.03871 

25.8348 

.05620 

17.7934 

47 

14 

.00407 

245.552 

.02153 

46.4489 

.03900 

25.6418 

.05649 

17.7015 

46 

15 

.00436 

229.182 

.02182 

45.8294 

.03929 

25.4517 

.05678 

17.6100 

45 

13 

.00465 

214.858 

.02211 

45.2261 

.03958 

25.2644 

.05708 

17.5205 

44 

17 

.00495 

202.219 

.02240 

44.6386 

.03987 

25.0798 

.05737 

17.4314 

43 

18 

.00524 

190.984 

.022C9 

44.0661 

.04016 

24.8078 

.05766 

17.3182 

42 

19 

.00553 

180.932 

.02298 

43.5081 

.04046 

24.7185 

.05795 

17.2558 

41 

20 

.00582 

171.885 

.02328 

42.9641 

.04075 

24.5418 

.05824 

17.1603 

40 

21 

.00611 

163.700 

.02357 

42.4335 

.04104 

24.367^ 

.05854 

17.0837 

39 

22 

.oor>io 

156.259 

.02386 

41.9158 

.04183 

24.1957 

.05883 

16.9990 

38 

23 

.00669 

149.465 

.02415 

41.4106 

.04162 

24.0263 

.05912 

16.9150 

37 

24 

.00698 

143.237 

.02444 

40.9174 

.04191 

23.8593 

.05041 

16.8319 

36 

25 

.00727 

137.507 

.02473 

40.4358 

.04220 

23.6945 

.05970 

16.7496 

35 

26 

.00756 

132.219 

.02502 

39.9055 

.04250 

23.5321 

.05999 

16.6681 

84 

27 

.00785 

127.321 

.02531 

39.5059 

.04270 

23.3718 

.06029 

16.5874 

33 

28 

.00815 

122.774 

.02560 

39.0568 

.01308 

23.2137 

.06058 

16.5075 

32 

29 

.00844 

118.540 

.02589 

38.6177 

.04837 

23.0577 

.06037 

16.4283 

31 

30 

.00873 

114.589 

.02619 

38.1885 

.04366 

22.0038 

.06116 

16.3499 

30 

31 

.00902 

110.892 

.02648 

37.7686 

.04305 

22.7519 

.06145 

16.2722' 

29 

32 

.00031 

107.426 

.02677 

37.3579 

.04424 

22.6020 

.06175 

16.1952 

28 

33 

.00060 

104.171 

.02706 

36.9560 

.04454 

22.4541 

.00204 

16.1190 

27 

34 

.00989 

101.107 

.02735 

36.5627 

.04483 

22.3081 

.06233 

16.0435 

26 

35 

.01018 

98.2179 

.02764 

36.1776 

.04512 

22.1640 

.06262 

15.9687 

25 

36 

.01047 

95.4895 

.02703 

35.8006 

.04541 

22.0217 

.06291 

15.8945 

24 

37 

.01076 

92.9085 

.02822 

35.4313 

.04570 

21.8813 

.06321 

15.8211 

23 

38 

.01105 

90.4633 

.02851 

35.0695 

.04599 

21.7426 

.06850 

15.7483 

22 

39 

.01135 

88.1436 

.02881 

34.7151 

.04628 

21.6056 

.06379 

15.6762 

21 

40 

.01164 

85.9398 

.02010 

34.3678 

.04658 

21.4704 

.06408 

15.6048 

20 

41 

.01193 

83.8435 

.02939 

34.0273 

.04687 

21.3369 

.06437 

15.5340 

19 

42 

.01222 

81.8470 

.02968 

33.6935 

.04710 

21.2049 

.06467 

15.4638 

18 

43 

.01251 

79.9434 

.02997 

33.3662 

.04745 

21.0747 

.06496 

15.3943 

17 

44 

.01280 

78.1263 

.03026 

33.0452 

.04774 

20.9460 

.06525 

15.3254 

16 

45 

.01309 

76.3900 

.03055 

32,7303 

.01803 

20.8188 

.06554 

15.2571 

15 

46 

.01333 

74.7292 

.03084 

82.4213 

.04833 

20.6932 

.06584 

15.1893 

14 

47 

.01367 

73.1300 

.03114 

32.1181 

.04862 

20.5691 

.06613 

15.1222 

13 

48 

.01396 

71.6151 

.03143 

31.8205 

.04891 

20.4465 

.06612 

15.0557 

12 

49 

.01425 

70.1533 

.03172 

31.5284 

.04920 

20.3253 

.06671 

14.9898 

11 

50 

.01455 

68.7501 

.03201 

31.2410 

.04949 

20.2056 

.06700 

14.9244 

10 

51 

.01484 

67.4019 

.03230 

30.9599 

.04978 

20.0872 

.06730 

14.8596 

9 

52 

.01513 

06.1055 

.03259 

30.6833 

.05007 

19.9702 

.06759 

14.7954 

8 

53 

.01542 

64.8580 

.03288 

30.4116 

.05037 

19.8546 

.06788 

14.7317 

7 

54 

.01571 

63.6567 

.03317 

30.1446 

.05066 

19.7403 

.06817 

14.6685 

6 

55 

.01600 

62.4992 

.03346 

29.8823 

.05005 

19.6273 

.06847 
.06876 

14.6059 

5 

56 

.01629 

61.3829 

.03376 

29.6245 

.05124 

19.5156 

14.5438 

4 

57 

.01658 

60.3058 

.03405 

29.3711 

.05153 

19.4051 

.06905 

14.4823 

3 

58 

.01687 

59.2659 

.03434 

29.1220 

.05182 

19.2959 

.06934 

14.4212 

2 

59 

.01716 

58.2612 

.03463 

28.8771 

.05212 

19.1879 

.06963 

14.3607 

1 

GO 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

.06993 

14.3007 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

' 

89°     1 

88°     1 

87°     1 

86° 

Table  of  Natural  Tangents  and  Cotangents 


105 


' 

4° 

5' 

n»    1 

T 

/ 

Tang 

CJotang 

Tang 
.08749 

CV>tang 

Tang 

Cotang 

Tang 

Cotang 

0 

.06993 

14.3007 

11.4301 

.10510 

9.51436 

.12278 

8.14435 

60 

1 

.07022 

14.2411 

.08778 

11.3919 

.10540 

9.48781 

.12308 

8.12481 

59 

2 

.07051 

14.1821 

.08807 

11.3540 

.10509 

9.46141 

.12338 

8.10536 

58 

3 

.07080 

14.1235 

.08837 

11.3163 

.10599 

9.43515 

.12367 

8.08600 

57 

4 

.07110 

14.0655 

.08866 

11.2789 

.10628 

9.40904 

.12397 

8.06674 

56 

5 

.07139 

14.0079 

.08895 

11.2417 

.10657 

9.38307 

.12426 

8.04756 

55 

6 

.07168 

13.9507 

.08925 

11.2048 

.10087 

9.35724 

.12456 

8.02848 

54 

7 

.07197 

13.8940 

.08954 

11.1681 

.10710 

9.33155 

.12485 

8.00948 

53 

8 

.07227 

13.8378 

.08983 

11.1316 

.10740 

9.30599 

.12515 

7.99058 

52 

9 

.0725G 

13.7821 

.09013 

11.0954 

.10775 

9.28058 

.12544 

7.97176 

51 

10 

.07285 

13.7267 

.09042 

11.0594 

.10805 

9.25530 

.12574 

7.95302 

50 

11 

.07314 

13.6719 

.09071 

11.0237 

.10834 

9.23016 

.12603 

7.93438 

49 

12 

.07344 

13.6174 

.09101 

10.9832 

.10803 

9.20518 

.12633 

7.91582 

48 

13 

.07373 

13.5634 

.09130 

10.9529 

.10893 

9.18028 

.12662 

7.89734 

47 

14 

.07402 

13.5008 

.aU59 

10.9178 

.10922 

9.15554 

.12692 

7.87895 

46 

15 

.07431 

13.4566 

.09189 

10.8829 

.10952 

9.13093 

.12722 

7.86064 

45 

10 

.07461 

13.4039 

.09218 

10.8483 

.10981 

9.10646 

.12751 

7.84242 

44 

17 

.07490 

13.3515 

.09247 

10.8139 

.11011 

9.08211 

.12781 

7.82428 

43 

18 

.07519 

13.2996 

.09277 

10.7797 

.11040 

9.05789 

.12810 

7.80622 

42 

19 

.07548 

13.2480 

.09306 

10.7457 

.11070 

9.03379 

.12840 

7.78825 

41 

20 

.07578 

13.1969 

.09335 

10.7119 

.11099 

9.00983 

.12869 

7.77035 

40 

21 

.07607 

13.1461 

.09365 

10.6783 

.11128 

8.98598 

.12899 

7.75254 

39 

22 

.07036 

13.0958 

.09394 

10.6450 

.11158 

8.96227 

.12929 

7.73480 

38 

23 

.07665 

13.0458 

.09423 

10.6118 

.11187 

8.93867 

.12958 

7.71715 

37 

24 

.07695 

12.9962 

.09453 

10.5789 

.11217 

8.91520 

.12988 

7.69957 

36 

25 

.07724 

12.9469 

.09482 

10.5462 

.11240 

8.89185 

.13017 

7.68208 

35 

2G 

.07753 

12.8981 

.09511 

10.5136 

.11270 

8.86862 

.13047 

7.66466 

34 

27 

.07782 

12.8496 

.09541 

10.4813 

.11305 

8.84551 

.13076 

7.64732 

33 

28 

.07812 

12.8014 

.09570 

10.4491 

.11335 

8.82252 

.13106 

7.63005 

32 

29 

.07841 

12.7536 

.09600 

10.4172 

.11304 

8.79964 

.13136 

7.61287 

31 

30 

.07870 

12.7002 

.09629 

10.3854 

.11394 

8.77689 

.13165 

7.59575 

30 

31 

.07899 

12.6591 

.09658 

10.3538 

.11423 

8.75425 

.13195 

7.57872 

29 

32 

.07929 

12.6124 

.09688 

10.3224 

.11452 

8.73172 

.13224 

7.56176 

23 

33 

.07958 

12.5660 

.09717 

10.2913 

.11482 

8.70931 

.13254 

7.54487 

27 

34 

.07087 

12.5199 

.09746 

10.2602 

.11511 

8.08701 

.13284 

7.52806 

26 

35 

.08017 

12.4742 

.09776 

10.2294 

.11541 

8.06482 

.13313 

7.51132 

25 

3G 

.08046 

12.4288 

.09805 

10.1988 

.11570 

8.04275 

.13343 

7.49465 

24 

37 

.08075 

12.3838 

.09834 

10.1083 

.11000 

8.02078 

.13372 

7.47806 

23 

38 

.08104 

12.3390 

.09864 

10.1381 

.11029 

8.59893 

.13402 

7.46154 

22 

39 

.08134 

12.2946 

.09893 

10.1080 

.11659 

8.57718 

.13432 

7.44509 

21 

40 

.08163 

12.2505 

.09923 

10.0780 

.11688 

8.55555 

.13461 

7.42871 

20 

41 

.08192 

12.2067 

.09952 

10.0483 

.11718 

8.53402 

.13491 

7.41240 

19 

42 

.08221 

12.1632 

.09981 

10.0187 

.11747 

8.51259 

.13521 

7.39616 

18 

43 

.08251 

12.1201 

.10011 

9.98931 

.11777 

8.49128 

.13550 

7.37999 

17 

44 

.08280 

12.0772 

.10040 

9.96007 

.11806 

8.47007 

.13580 

7.36389 

16 

45 

.08309 

12.0346 

.10069 

9.93101 

.11836 

8.44890 

.13609 

7.34786 

15 

40 

.08339 

11.9923 

.10099 

9.90211 

.11865 

8.42795 

.13639 

7.33190 

14 

47 

.08368 

11.9504 

.10128 

9.87338 

.11895 

8.40705 

.13669 

7.31600 

13 

48 

.08397 

11.9087 

.10158 

9.84482 

.11924 

8.38025 

.13698 

7.30018 

12 

49 

.08427 

11.8673 

.10187 

9.81641 

.11954 

8.36555 

.13728 

7.28442 

11 

60 

.08456 

11.8262 

.10216 

9.78817 

.11983 

8.34496 

.13758 

7.26873 

10 

51 

.08485 

11.7853 

.10246 

9.76009 

.12013 

8.32446 

.13787 

7.25310 

9 

52 

.08514 

11.7448 

.10275 

9.73217 

.12042 

8.30406 

.13817 

7.23754 

8 

53 

.08544 

11.7045 

.10305 

9.70441 

.12072 

8.28376 

.13846 

7.22204 

7 

54 

.08573 

11.6645 

.10334 

9.67680 

.12101 

8.26355 

.13876 

7.20561 

6 

55 

.08602 

11.6248 

.10363 

9.64935 

.12131 

8.24345 

.13906 

7.19125 

5 

56 

.08632 

11.5853 

.10393 

9.62205 

.12160 

8.22344 

.13935 

7.17594 

4 

57 

.08661 

11.5461 

.10422 

9.59490 

.12190 

8.20352 

.13965 

7.16071 

3 

58 

.08690 

11.5072 

.10452 

9.56791 

.12219 

8.18370 

.13995 

7.14553 

2 

59 

.08720 

11.4685 

.10481 

9.54106 

.12249 

8:i6308 

.14024 

7.13042 

1 

60 

.08749 

11.4301 

.10510 

9.51436 

.12278 

"8.14435 

.14054 

7.11537 

0 

1 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

t 

85° 

84°     1 

83*^     1 

82° 

106 


Trigonometry 


t 

8°     i 

9»     1 

lO'^     1 

11° 

t 

Tang 

Cotaiig 

Tang 

(Jotang 

Tang 

Cotang 

Tang 
.19438 

Cotang 

0 

.14054 

7.11537 

.15838 

6.31375 

.17033 

5.07128 

5.14455 

60 

1 

.14084 

7.10038 

.15808 

6.30189 

.17003 

5.00105 

.19408 

5.13058 

69 

2 

.14113 

7.0S546 

.15898 

0.29007 

.17093 

5.05205 

.19498 

5.12802 

5S 

3 

.14143 

7.07059 

.15928 

6.27829 

.17723 

5.04248 

.19529 

5.12009 

57 

4 

.14173 

7.05579 

.15958 

6.26055 

.17753 

5.03295 

.19559 

5.11279 

50 

5 

.14202 

7.04105 

.15988 

6.254S0 

.17783 

5.02344 

.19589 

5.10490 

55 

6 

.14232 

7.02637 

.10017 

0.24321 

.17813 

5.01397 

.19019 

5.09704 

54 

7 

.14202 

6.91174 

.10047 

6.23100 

.17843 

5.0U52 

.19049 

5.08921 

53 

8 

.14291 

6.99718 

.10077 

0.22003 

.17873 

5.50511 

.19080 

5.08139 

52 

9 

.14321 

6.9S268 

.16107 

0.20851 

.17903 

5.58573 

.19710 

5.07300 

51 

10 

.14351 

6.96823 

.16137 

0.19703 

.17933 

5.57038 

.19740 

5.00584 

50 

11 

.14381 

6.95385 

.16167 

6.18559 

.17903 

5.50706 

.19770 

5.05809 

49 

12 

.14110 

6.93952 

.16190 

0.17419 

.17903 

5.55777 

.19801 

5.05037 

48 

13 

.14440 

6.92525 

.16220 

6.10283 

.18023 

5.54851 

.19831 

5.04207 

47 

14 

.14170 

6.91104 

.10250 

G.15151 

.18053 

5.53927 

.19801 

5.03499 

4(j 

15 

.14499 

6.89688 

.10280 

0.14023 

.18083 

5.53007 

.19891 

5.02731 

16 

.14529 

6.88278 

.10310 

6.12899 

.18113 

5.52090 

.19921 

5.01971 

4-! 

17 

.14559 

6.86874 

.10340 

0.11779 

.18143 

5.51176 

.19952 

5.01210 

43 

18 

.14588 

6.85475 

.10370 

6.10004 

.18173 

5.50204 

.19982 

5.00451 

42 

19 

.14618 

6.84082 

.10405 

6.09552 

.18203 

5.49356 

.20012 

4.99095 

41 

20 

.14648 

6.82694 

.10435 

6.0^444 

.18233 

5.48451 

.20042 

4.98940 

40 

21 

.14678 

6.S1312 

.16465 

6.07340 

.18203 

5.47548 

.20073 

4.98188 

30 

22 

.14707 

0.79936 

.16405 

6.00240 

.18293 

5.40048 

.20103 

4.97433 

3 

23 

.14737 

6.78564 

.10525 

0.05143 

.18323 

5.45751 

.20133 

4.90090 

37 

24 

.14707 

6.77199 

.10555 

6.04051 

.18353 

5.44857 

.20104 

4.95945 

30 

25 

.14790 

6.75838 

.10585 

0.02902 

.18384 

5.43006 

.20194 

4.95201 

35 

20 

.14826 

0.74483 

.10015 

0.01878 

.18414 

5.43077 

.20224 

4.94400 

34 

27 

.14856 

0.73133 

.10045 

0.00707 

.18444 

5.42192 

.20254 

4.93721 

33 

28 

.14886 

6.71789 

.10074 

5.99720 

.18474 

5.41309 

.20285 

4.92984 

32 

29 

.14915 

6.70450 

.10701 

5.98040 

.18504 

5.40429 

.20315 

4.92249 

31 

30 

.14945 

C.69116 

.10734 

5.97570 

.18534 

5.39552 

.20345 

4.91510 

SO 

31 

.14975 

6.67787 

.10704 

5.90510 

.18504 

5.38077 

.20376 

4.907S5 

20 

32 

.15005 

6.06403 

.10794 

5.95448 

.18594 

5.37805 

.20406 

4.90050 

2'; 

33 

.15034 

6.65144 

.10824 

5.94390 

.18024 

5.30930 

.20430 

4.89330 

27 

3i 

.15004 

6.63S31 

.10854 

5.93335 

.18054 

5.30070 

.20406 

4.88005 

2(1 

35 

.15094 

6.02523 

.10884 

5.922Sa 

.18034 

5.35200 

.20497 

4.87882 

'^5 

8() 

.15124 

6.61219 

.10914 

5.91230 

.18714 

5.34345 

.20527 

4.87162 

21 

37 

,15153 

6.59921 

.10944 

5.90191 

.18745 

5.33437 

.20557 

4.80444 

23 

38 

.15183 

6.58027 

.16974 

5.S9151 

.18775 

5.32031 

.20588 

4.85727 

22 

39 

.15213 

0.57339 

.17004 

5.88114 

.18805 

5.31778 

.20018 

4.85013 

21 

40 

.15243 

0.50055 

.17033 

5.87080 

.18835 

5.30928 

.20048 

4.84300 

20 

41 

.15272 

G.54777 

.17003 

5.80051 

.18865 

5.30080 

.20079 

4.83590 

19 

42 

.15302 

0.53503 

.17033 

5.85024 

.18895 

5.29235 

.20709 

4.82882 

18 

43 

.15332 

6.52234 

.17123 

5.84001 

.18925 

5.2S393 

.20739 

4.82175 

17 

44 

.15362 

6.50970 

.17153 

5.829C2 

.18955 

5.27553 

.20770 

4.81471 

10 

45 

.15391 

6.49710 

.17183 

5.81900 

.18980 

5.20715 

.20800 

4.80769 

15 

46 

.15421 

6.48456 

.17213 

5.80953 

.19010 

5.25880 

.20830 

4.S0O0S 

14 

47 

.15451 

6.47200 

.17243 

5.79944 

.19046 

5.25048 

.20801 

4.79370 

13 

48 

.15481 

6.45901 

.17273 

5.78938 

.19076 

5.24218 

.20891 

4.78073 

12 

49 

.15511 

6.44720 

.17303 

5.77930 

.19106 

5.23391 

.20921 

4.77978 

11 

50 

.15540 

6.43484 

.17333 

5.70937 

.19136 

5.22539 

.20952 

4.77280 

10 

51 

.15570 

6.42253 

.17303 

5.75941 

.19106 

5.21744 

.20982 

4.70595 

9 

52 

.15600 

6.41020 

.17393 

5.74949 

.19197 

5.20925 

.21013 

4.75900 

Q 

53 

.15030 

0.39804 

.17423 

5.73900 

.19227 

5.20107 

.21043 

4.75219 

7 

54 

.15060 

0.3S587 

.17453 

5.72974 

.19257 

5.19293 

.21073 

4.74534 

0 

55 

.15689 

0.37374 

.17483 

5.71992 

.19287 

5.18480 

.21104 

4.73851 

5 

56 

.15719 

6.36165 

.17513 

5.71013 

.19317 

5.17071 

.21134 

4.73170 

4 

57 

.15749 

6.34901 

.17543 

5.70037 

.19347 

5.10803 

.21104 

4.72490 

3 

5S 

.15779 

6.33701 

.17573 

5.09004 

.19378 

5.10058 

.21195 

4.71813 

2 

59 

.15809 

6.32506 

.17003 

5.08094 

.19408 

5.15250 

.21225 

4.71137 

1 

60 

.15838 

0.31375 

.17033 

5.07128 

.19438 

5.14455 

.21250 

4.70463 

0 

■* 

Cotan? 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

» 

81°     i 

80°     1 

79°     1 

78° 

Table  of  Natural  Tangents  and  Cotangents 


107 


/ 

1."      1 

13°  _   11 

T4°     II 

15°     1 

/ 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Jot.ang 

0 

.21256 

4.70463 

.23087 

4.33148 

.24933 

4.01078 

.20795 

3.73205 

60 

1 

.21286 

4.69791 

.23117 

4.32573 

.24904 

4.00582 

.26826 

3.72771 

59 

2 

.21316 

4.69121 

.23148 

4.32001 

.24995 

4.000S0 

.26857 

3.72338 

58 

3 

.21347 

4.68452 

.23179 

4.31430 

.25026 

3.99592 

.26888 

3.71907 

57 

4 

.21377 

4.67786 

.23209 

4.30800 

.25050 

3.99099 

.26920 

3.71476 

56 

5 

.21408 

4.67121 

.23240 

4.30291 

.25087 

3.98007 

.26951 

3.71046 

55 

G 

.21438 

4.66458 

.23271 

4.29724 

.25118 

3.98117 

.20982 

3.70616 

54 

7 

.214G9 

4.65797 

.23301 

4.29159 

.25149 

3.97627 

.27013 

3.70188 

53 

8 

.21490 

4.65138 

.23332 

4.28595 

.25180 

3.97139 

.27044 

3.69761 

52 

9 

.21520 

4.64480 

.23303 

4.28032 

.25211 

3.90051 

.2707G 

3.69335 

51 

10 

.215G0 

4.63825 

.23393 

4.27471 

.25242 

3.96165 

.27107 

3.88909 

50 

11 

.21590 

4.63171 

.23424 

4.20911 

.25273 

3.95080 

.27138 

3.08485 

49 

12 

.21021 

4.02518 

.23455 

4.20352 

.25304 

3.95190 

.27169 

3.08001 

48 

13 

.21051 

4.61808 

.23485 

4.25795 

.25335 

3.94713 

.27201 

3.07038 

47 

11 

.210^>2 

4.01219 

.23510 

4.25239 

.25300 

3.94232 

.27232 

3.07217 

46 

15 

.21712 

4.60572 

.23547 

4.24085 

.25397 

3.93751 

.27263 

3.0()79G 

45 

IG 

.21743 

4.59927 

.23578 

4.24132 

.25428 

3.93271 

.27294 

3.06376 

44 

17 

.21773 

4.59283 

.23608 

4.235S0 

.25459 

3.92793 

.27326 

3.65957 

43 

IS 

.21804 

4.58041 

.23639 

4.23030 

.25400 

3.92310 

.27357 

3.65538 

42 

19 

.21834 

4.58001 

.23070 

4.22481 

.25521 

3.91839 

.27388 

3.65121 

41 

20 

.21864 

4.57363 

.23700 

4.21933 

.25552 

3.91304 

.27419 

3.64705 

40 

21 

.21895 

4.56720 

.23731 

4.213S7 

.25583 

3.90890 

.27451 

3.64289 

39 

22 

.21925 

4.50091 

.23702 

4.20842 

.25014 

3.90417 

.27482 

3.63874 

38 

23 

.21956 

4.55458 

.23703 

4.20208 

.25045 

3.89945 

.27513 

3.63461 

37 

24 

.21986 

4.54826 

.23823 

4.19750 

.2507G 

3.89474 

.27545 

3.63048 

36 

25 

.22017 

4.54106 

.23854 

4.19215 

.25707 

3.89004 

.27576 

3.62636 

35 

20 

.22047 

4.53508 

.23885 

4.18075 

.25738 

3.88530 

.27007 

3.62224 

34 

27 

.22078 

4.52941 

.23910 

4.18137 

.25709 

3.88008 

.27638 

3.61814 

33 

28 

.22108 

4.52310 

.23046 

4.17000 

.25800 

3.87001 

.27070 

3.61405 

32 

29 

.22139 

4.51093 

.23977 

4.17004 

.25831 

3.87130 

.27701 

3.60996 

31 

30 

.22109 

4.51071 

.24008 

4.1G530 

.25862 

3.86671 

.27732 

3.60588 

30 

31 

.22200 

4.50451 

.24039 

4.15997 

.25893 

3.80208 

.27704 

3.60181 

29 

32 

.22231 

4.49S32 

.24009 

4.15405 

.25924 

3.85745 

.27795 

3.59775 

28 

33 

.22201 

4.49215 

.24100 

4.14934 

.25955 

3.85284 

.27826 

3.59370 

27 

34 

.22292 

4.48000 

.24131 

4.14405 

.25986 

3.84824 

.27858 

3.58966 

26 

35 

.22322 

4.47986 

.24162 

4.13877 

.20017 

3.84304 

.278S9 

3.58562 

25 

3G 

.22353 

4.47374 

.24193 

4.13350 

.20048 

3.83906 

.27921 

3.58160 

24 

37 

.22383 

4.40704 

.24223 

4.12825 

.20079 

3.83449 

.27952 

3.57758 

23 

38 

.22414 

4.46155 

.24254 

4.12301 

.20110 

3.82992 

.27983 

3.57357 

22 

39 

.22444 

4.45548 

.24285 

4.11778 

.20141 

3.82537 

.28015 

3.56957 

21 

40 

.22475 

4.44942 

.24310 

4.1125G 

.26172 

3.82083 

.28040 

3.56557 

20 

41 

.22505 

4,44338 

.24347 

4.10730 

.26203 

3.81630 

.28077 

3.56159 

19 

42 

.22536 

4.43735 

.24377 

4.10216 

.26235 

3.81177 

.28109 

3.55761 

18 

43 

.22567 

4.43134 

.24408 

4.09699 

.20206 

3.80720 

.28140 

3.55364 

17 

44 

.22597 

4.42534 

.24439 

4.09182 

.20297 

3.80276 

.28172 

3.54968 

16 

45 

.22628 

4.41936 

.24470 

4.08666 

.20328 

3.79827 

.28203 

3.54573 

15 

40 

.22658 

4.41340 

.24501 

4.08152 

.26359 

3.79378 

.28234 

3.54179 

14 

47 

.22689 

4.40745 

.24532 

4.07039 

.20390 

3.78931 

.28266 

3.53785 

13 

48 

.22719 

4.40152 

.24562 

4.07127 

.20421 

3.78485 

.28297 

3.53393 

12 

49 

.22750 

4.39500 

.24503 

4.00016 

.26452 

3.78040 

.28329 

3.53001 

11 

50 

.22781 

4.38909 

.24024 

4.06107 

.26483 

3.77595 

.28360 

3.52609 

10 

51 

.22811 

4.38381 

.24055 

4.05599 

.26515 

3.77152 

.28391 

3.52219 

9 

52 

.22842 

4.37793 

.24686 

4.05092 

.20546 

3.76709 

.28423 

3.51829 

8 

53 

.22872 

4.37207 

.24717 

4.045S6 

.26577 

3.70268 

.28454 

3.51441 

7 

54 

.22903 

4.36023 

.24747 

4.04081 

.26008 

3.75828 

.28486 

3.51053 

f) 

55 

.22934 

4.36040 

.24778 

4.03578 

.20039 

3.75388 

.28517 

3.50666 

5 

50 

.22964 

4.35459 

.24809 

4.03076 

.20070 

3.74950 

.28549 

3.50279 

4 

57 

.22995 

4.34879 

.24840 

4.02574 

.20701 

3.74512 

.28580 

3.49894 

3 

58 

.23026 

4.34300 

.24871 

4.02074 

.20733 

3.74075 

.28612 

3.49509 

2 

59 

.23056 

4.33723 

.24902 

4.01576 

.20704 

3.73640 

.28643 

3.49125 

1 

60 

.23087 

4.33148 

.24933 

4.01078 

.20795 

3.73205 

.28675 

3.48741 

0 

Cotanp 

Tang 

Cotang 

Tang 

Cot  an  p 

r  Tang 

' 

» 

Cotang 

d  Tang 

77° 

76° 

75° 

1     74° 

108 


Trigonometry 


Part 


/ 

10"     1 

17»__    1 

18°     II 

19°     1 

60 

Tang 

Uotang 

Tang 

Uotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.28675 

3.48741 

.30573 

3.27085 

.32492 

3.07768 

.34433 

2.90421 

1 

.28706 

3.48359 

.30005 

3.26745 

.32524 

3.07464 

.34465 

2.90147 

59 

2 

.28738 

3.47977 

.30037 

3.26406 

.32556 

3.07160 

.34498 

2.89873 

58 

3 

.28709 

3.47596 

.30009 

3.26067 

.32588 

3.06857 

.34530 

2.89600 

57 

4 

.28800 

3.47210 

.30700 

3.25729 

.32021 

3.06554 

.34563 

2.89327 

56 

5 

.28832 

3.4f^837 

.30732 

3.25392 

.32653 

3.06252 

.34596 

2.89055 

55 

6 

.288C4 

3.40458 

.30704 

3.25055 

.32685 

3.05950 

.34628 

2.88783 

54 

7 

.288P5 

3.46080 

.30796 

3.24719 

.32717 

3.05649 

.34661 

2.88511 

53 

8 

.28927 

3.45703 

.30828 

3.24383 

.32749 

3.05349 

.34693 

2.8S240 

52 

9 

.28958 

3.45327 

.30800 

3.24049 

.32782 

3.05049 

.34720 

2.87970 

51 

10 

.28990 

3.44951 

.30891 

3.23714 

.32814 

3.04749 

.34758 

2.87700 

50 

11 

.29021 

3.44576 

.30923 

3.23381 

.32846 

3.04450 

.34791 

2.87430 

49 

12 

.29053 

3.44202 

.30955 

3.23048 

.32878 

3.04152 

.34824 

2.87161 

48 

13 

.29084 

3.43829 

.30987 

3.22715 

.32911 

3.03854 

.34850 

2.86892 

47 

14 

.29110 

3.43450 

.31019 

3.22384 

.32943 

3.03556 

.34889 

2.86624 

46 

15 

.29147 

3.43084 

.31051 

3.22053 

.32975 

3.03260 

.34922 

2.86356 

45 

16 

.29179 

3.42713 

.31083 

3.21722 

.33007 

3.02963 

.34954 

2.86089 

44 

17 

.29210 

3.42343 

.31115 

3.21392 

.33040 

3.02667 

.34987 

2.85822 

43 

18 

.29242 

3.41973 

.31117 

3.21003 

.33072 

3.02372 

.35020 

2.85555 

42 

19 

.29274 

3.41004 

.31178 

3.20734 

.33104 

3.02077 

.35052 

2.85289 

41 

20 

.29305 

3.41230 

.31210 

3.20406 

.33136 

3.01783 

.35085 

2.85023 

40 

21 

.29337 

3.40869 

.31242 

3.20079 

.33109 

3.01489 

.35118 

2.84758 

39 

22 

.29368 

3.40502 

.31274 

3.19752 

.33201 

3.01196 

.35150 

2.84494 

38 

23 

.29409 

3.40136 

.31300 

3.19426 

.33233 

3.00903 

.35183 

2.84229 

37 

24 

.29432 

3.39771 

.31338 

3.19100 

.33200 

3.00611 

.35216 

2.83965 

36 

25 

.29403 

3.39406 

.31370 

3.18775 

.33298 

3.00319 

.35248 

2.83702 

35 

26 

.29495 

3.39042 

.31402 

3.18451 

.33330 

3.00028 

.35281 

2.83439 

34 

27 

.29520 

3.38679 

.31434 

3.18127 

.33303 

2.99738 

.35314 

2.83176 

33 

28 

.29558 

3.38317 

.31406 

•3.17804 

.33395 

2.99447 

.35340 

2.82914 

32 

29 

.29590 

3.37955 

.31498 

3.17481 

.33427 

2.99158 

.35379 

2.82653 

31 

30 

.29021 

3.37594 

.31530 

3.17159 

.33400 

2.98868 

.35412 

2.82391 

30 

31 

.29053 

3.37234 

.31562 

3.1683S 

.33492 

2.98580 

.35445 

2.82130 

29 

32 

.29085 

3.30875 

.31594 

3.10517 

.33524 

2.98292 

.35477 

2.81870 

28 

33 

.29716 

3.36510 

.31626 

3.16197 

.33557 

2.98004 

.35510 

2.81010 

27 

34 

.29748 

3.3615S 

.31058 

3.15877 

.33589 

2.97717 

.355!  3 

2.81350 

20 

35 

.29780 

3.35800 

.31690 

3.15558 

.33021 

2.97430 

.35570 

2.81091 

25 

36 

.29811 

3.35443 

.31722 

3.15240 

.38054 

2.97144 

.35608 

2.80833 

24 

37 

.29St3 

3.35087 

.31754 

3.14922 

.33086 

2.96858 

.3.5641 

2.80574 

23 

38 

.29875 

3.34732 

.31780 

3.14G05 

.33718 

2.90573 

.35674 

2.80310 

22 

39 

.29900 

3.34377 

.31818 

3.14288 

.33751 

2.96288 

.35707 

2.80059 

21 

40 

.29938 

3.34023 

.31850 

3.13972 

.33783 

2.96004 

.35740 

2.79802 

20 

41 

.29970 

3.33670 

.31882 

3.13656 

.33816 

2.95721 

.35772 

2.79545 

19 

42 

.30001 

3.33317 

.31914 

3.13341 

.33848 

2.05437 

.35805 

2.79289 

18 

43 

.30033 

3.32965 

.31940 

3.13027 

.33881 

2.95155 

.35838 

2.79033 

17 

44 

.30005 

3.32614 

.31978 

3.12713 

.33913 

2.94872 

.35871 

2.78778 

10 

45 

.30097 

3.32264 

.32010 

3.12400 

.33945 

2.94591 

.35904 

2.78523 

15 

46 

.30128 

3.31914 

.32042 

3.12087 

.33978 

2.94309 

.35937 

2.78209 

14 

47 

.30100 

3.31565 

.32074 

3.11775 

.34010 

2.94028 

.35009 

2.78014 

13 

48 

.30192 

3.31216 

.32106 

3.11464 

.34043 

2.93748 

.30002 

2.77701 

12 

49 

.30224 

3.30868 

.32139 

3.11153 

.34075 

2.934G8 

.30035 

2.77507 

11 

50 

.30255 

3.30521 

.32171 

3.10842 

.34108 

2.93189 

.30068 

2.77254 

10 

51 

.30287 

3.30174 

.32203 

3.10532 

.34140 

2.92010 

.36101 

2.77002 

9 

52 

.30319 

3.29829 

.32235 

3.10223 

.34173 

2.92032 

.36134 

2.70750 

8 

53 

.30351 

3.29483 

.32207 

3.09914 

.34205 

2.92354 

.36167 

2.70498 

7 

54 

.30382 

3.29139 

.32299 

3.09600 

.34238 

2.92070 

.36199 

2.70247 

6 

55 

.30414 

3.28795 

.32331 

3.09298 

.34270 

2.91799 

.30232 

2.75996 

5 

56 

.30140 

3.28452 

.32303 

3.0899] 

.34303 

2.91523 

^6265 

2.75746 

4 

57 

.30478 

3.28109 

.32390 

3.08685 

.34335 

2.91240 

.36298 

2.75496 

3 

58 

.30509 

3.27767 

.32428 

3.08379 

.34368 

2.90971 

.30331 

2.75246 

1 

59 

.30541 

3.27426 

.32400 

3.08073 

.34400 

2.90696 

.30364 

2.74997 

0 

60 

.30573 

3.27085 

.32492 

3.07768 

.34433 

2.90421 

.36397 

2.74748 

2 

t 

Cotang 

Tang 

Cotang 

Tang 

C-otang 

Tang 

Cotang 

Tang 

0 

73° 

72° 

71° 

70° 

Table  of  Natural  Tangents  and  Cotangents 


109 


r 
0 

20°    1 

21°           1 

22°     1 

23° 

/ 

Tang 
.36397 

Cotang 
2.74748 

Tang 

.38386 

(Jotang 
2.00509 

Tang 

Cotang 

Tang 

Cotang 

.40403 

2.47509 

.42447 

2.35585 

60 

1 

.36430 

2.74499 

.38420 

2.00283 

.40436 

2.47302 

.42482 

2.35395 

69 

2 

.36463 

2.74251 

.38453 

2.60057 

.40470 

2.47095 

.42516 

2.35205 

58 

3 

.36496 

2.74004 

.38487 

2.59831 

.40504 

2.46888 

.42551 

2.35015 

57 

4 

.36529 

2.73756 

.38520 

2.59606 

.40538 

2.46682 

.42585 

2.34825 

56 

5 

,36562 

2.73509 

.38553 

2.59381 

.40572 

2.46476 

.42619 

2.34636 

55 

6 

.36595 

2.73263 

.38587 

2.59156 

.40606 

2.46270 

.42654 

2.34447 

64 

7 

.36628 

2.73017 

.38620 

2.58932 

.40640 

2.46065 

.42688 

2.34258 

53 

8 

.36661 

2.72771 

.38654 

2.58708 

.40674 

2.45860 

.42722 

2.34069 

52 

9 

.36694 

2.72526 

.38687 

2.58484 

.40707 

2.45055 

.42757 

2.33881 

51 

10 

.36727 

2.72281 

.38721 

2.58261 

.40741 

2.45451 

.42791 

2.33693 

60 

11 

.36760 

2.72036 

.38754 

2.58038 

.40775 

2.45246 

.42826 

2.33505 

49 

12 

.36793 

2.71792 

.38787 

2.57815 

.40809 

2.45043 

.42860 

2.33317 

48 

13 

.36826 

2.71548 

.38821 

2.57593 

.40843 

2.44839 

.42894 

2.33130 

47 

14 

.36859 

2.71305 

.38854 

2.57371 

.40877 

2.44636 

.42929 

2.32943 

46 

15 

.36892 

2.71062 

.388S8 

2.57150 

.40911 

2.44433 

.42963 

2.32756 

45 

16 

.36925 

2.70819 

.38921 

2.56928 

.40945 

2.44230 

.42998 

2.32570 

44 

17 

.36958 

2.70577 

.38955 

2.56707 

.40979 

2.44027 

.43032 

2.32383 

43 

IS 

.36991 

2.70335 

.38988 

2.66487 

.41013 

2.43825 

.43067 

2.32197 

42 

19 

.37024 

2.70094 

.39022 

2.56266 

.41047 

2.43623 

.43101 

2.32012 

41 

20 

.37057 

2.69853 

.39055 

2.56046 

.41081 

2.43422 

.43136 

2.31826 

40 

21 

.37090 

2.69612 

.39089 

2.55827 

.41115 

2.43220 

.43170 

2.31641 

39 

22 

.37123 

2.69371 

.39122 

2.55608 

.41149 

2.43019 

.43205 

2.31456 

38 

23 

.37157 

2.69131 

.39156 

2.55389 

.41183 

2.42819 

.43239 

2.31271 

37 

24 

.37190 

2.68892 

.39190 

2.55170 

.41217 

2.42618 

.43274 

2.31086 

36 

25 

.37223 

2.68653 

.39223 

2.54952 

.41251 

2.42418 

.43308 

2.30902 

35 

26 

.37256 

2.68414 

.39257 

2.54734 

.41285 

2.42218 

.43343 

2.30718 

34 

27 

.37289 

2.68175 

.39290 

2.54516 

.41319 

2.42019 

.4.3378 

2.30534 

33 

28 

.37322 

2.67987 

.39324 

2.54299 

.41353 

2.41819 

.43412 

2.30351 

32 

29 

.37355 

2.67700 

.39357 

2.54082 

.41387 

2.41620 

.43447 

2.30167 

31 

30 

.37388 

2.67462 

.39391 

2.53865 

.41421 

2.41421 

.43481 

2.29984 

30 

31 

.37422 

2.67225 

.39425 

2.53648 

.41455 

2.41223 

.43516 

2.29801 

29 

32 

.37455 

2.66989 

.39458 

2.53432 

.41490 

2.41025 

.43550 

2.29619 

28 

33 

.37188 

2.66752 • 

.39492 

2.53217 

.41524 

2.40827 

.43585 

2.29437 

27 

34 

.37521 

2.66516 

.39526 

2.53001 

.41558 

2.40629 

.43620 

2.29254 

26 

35 

.37554 

2.66281 

.39559 

2.52786 

.41592 

2.40432 

.43654 

2.29073 

25 

36 

.37588 

2.66046 

.39593 

2.52571 

.41626 

2.40235 

.43689 

2.28891 

24 

37 

.37621 

2.65811 

.39626 

2.52357 

.41660 

2.40038 

.43724 

2.28710 

23 

38 

.37654 

2.65576 

.39660 

2.52142 

.41094 

2.39841 

.43758 

2.28528 

22 

39 

.37687 

2.65342 

.39694 

2.51929 

.41728 

2.39645 

.43793 

2.28348 

21 

40 

.37720 

2.65109 

.39727 

2.51715 

.41763 

2.39449 

.43828 

2.28167 

20 

41 

.37754 

2.64875 

.39761 

2.51502 

.41797 

2.39253 

.43862 

2.27987 

19 

42 

.37787 

2.64642 

.39795 

2.51289 

.41831 

2.39058 

.43897 

2.27806 

18 

43 

.37820 

2.64410 

.39829 

2.51076 

.41865 

2.38863 

.43932 

2.27626 

17 

44 

.37853 

2.64177 

.39862 

2.50864 

.41899 

2.38668 

.43966 

2.27447 

16 

45 

.37887 

2.63945 

.39896 

2.50652 

.41933 

2.38473 

.44001 

2.27267 

15 

40 

.37920 

2.63714 

.39930 

2.50440 

.41968 

2.38279 

.44036 

2.27088 

14 

47 

.37953 

2.634S3 

.39963 

2.50229 

.42002 

2.38084 

.44071 

2.26909 

13 

43 

.37986 

2.63252 

.39997 

2.50018 

.42030 

2.37891 

.44105 

2.26730 

12 

49 

.38020 

2.63021 

.40031 

2.49S07 

.42070 

2.37697 

.44140 

2.26552 

11 

50 

.38053 

2.62791 

.40065 

2.49597 

.42105 

2.37504 

.44175 

2.26374 

10 

51 

.38086 

2.62561 

.40098 

2.49386 

.42139 

2.37311 

.44210 

2.26196 

9 

52 

.38120 

2.62332 

.40132 

2.49177 

.42173 

2.37118 

.44244 

2.26018 

8 

53 

.38153 

2.62103 

.40166 

2.48967 

.42207 

2.36925 

.44279 

2.25840 

7 

54 

.38186 

2.61874- 

.40200 

2.48758 

.42242 

2.36733 

.44314 

2.25663 

6 

55 

.38220 

2.01646 

.40234 

2.48549 

.42276 

2.36541 

.44349 

2.25486 

5 

56 

.38253 

2.61418 

.40267 

2.48340 

.42310 

2.36349 

.44384 

2.25309 

4 

57 

.38286 

2.61190 

.40301 

2.48132 

.42345 

2.36158 

.44418 

2.25132 

3 

58 

.38320 

2.60963 

.40335 

2.47924 

.42379 

2.35967 

.44453 

2,24956 

2 

59 

.38353 

2.60736 

.40369 

2.47716 

.42413 

2.35776 

.44488 

2.24780 

1 

60 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.355S5 
Tang 

.44523 

2.24604 

0 

' 

Cotarig 

Tang 

Cotang 

Tang 

Cotang 

Cotang 

Tang 

> 

60° 

68°     1 

67°     1 

66°    1 

110 


Trigonometry 


' 

24** 

25° 

26°     1 

27° 

/ 

Tang 

Cotang 

Tang 

Cotang 

Tang 

.48773 

Cotang 

Tang 

Cotang 

0 

.44523 

2.24604 

.46631 

2.14451 

2.05030 

.50053 

1.96261 

60 

1 

.44558 

2.24428 

.46666 

2.14288 

.48809 

2.04S79 

.50089 

1.96120 

59 

2 

.44593 

2.24252 

.46702 

2.14125 

.48845 

2.04728 

.51026 

1.95979 

58 

3 

.44627 

2.24077 

.46737 

2.13903 

.48881 

2.04577 

.51063 

1.95838 

57 

4 

.44662 

2.23902 

.46772 

2.13801 

.48917 

2.04420 

.51009 

1.9569S 

50 

5 

.44697 

2.23727 

.46S08 

2.13639 

.48953 

2.04270 

.51136 

1.95557 

55 

6 

.44732 

2.23553 

.46843 

2.13177 

.48989 

2.04125 

.51173 

1.95417 

54 

7 

.44767 

2.23378 

.40879 

2.13316 

.49020 

2.03975 

.51209 

1.95277 

53 

8 

.44802 

2.23204 

.46914 

2.13154 

.49062 

2.03825 

.51246 

1.95137 

52 

9 

.44837 

2.23030 

.46950 

2.12993 

.49098 

2.03075 

.51283 

1.94997 

51 

10 

.44872 

2.22857 

.46985 

2.12832 

.49134 

2.03520 

.51319 

1.94858 

50 

11 

.44907 

2.22683 

.47021 

2.12671 

.49170 

2.03370 

.51356 

1.94718 

49 

12 

.44942 

2.22510 

.47056 

2.12511 

.49200 

2.03227 

.51393 

1.94579 

48 

13 

.44977 

2.22337 

.47092 

2.12350 

.49242 

2.03078 

.51430 

1.94440 

47 

14 

.45012 

2.22164 

.47128 

2.12190 

.49278 

2.02929 

.51407 

1.94301 

46 

15 

.45047 

2.21992 

.47163 

2.12030 

.49315 

2.02780 

.51503 

1.94162 

45 

16 

.45082 

2.21819 

.47109 

2.11871 

.49351 

2.02031 

.51540 

1.94023 

44 

17 

.45117 

2.21647 

.47234 

2.11711 

.49387 

2.02483 

.51577 

1.93885 

43 

18 

.45152 

2.21475 

.47270 

2.11552 

.49423 

2.02335 

.51014 

1.93746 

42 

19 

.45187 

2.21304 

.47305 

2.11392 

.49459 

2.02187 

.51051 

1.9360S 

41 

20 

.45222 

2.21132 

.47341 

2.11233 

.49495 

2.02039 

51088 

1.93470 

40 

21 

.45257 

2.20961 

.47377 

2.11075 

.49532 

2.01891 

.51724 

1.93332 

39 

22 

.45292 

2.20790 

.47412 

2.10916 

.49508 

2.01743 

.51701 

1.93195 

38 

23 

.45327 

2.20619 

.47448 

2.10758 

.40004 

2.01590 

.51798 

1.93057 

37 

24 

.45362 

2.20149 

.47483 

2.10000 

.49040 

2.01449 

.51835 

1.92920 

36 

25 

.45397 

2.20278 

.47519 

2.10442 

.49077 

2.01302 

.51872 

1.92782 

35 

20 

.45432 

2.20108 

.47555 

2.10284 

.49713 

2.01155 

.51909 

1.92645 

34 

27 

.45467 

2.19938 

.47590 

2.10126 

.49749 

2.01008 

.51946 

1.92508 

33 

28 

.45502 

2.10769 

.47626 

2.09909 

.49780 

2.00802 

.51983 

1.92371 

32 

29 

.45538 

2.19599 

.47662 

2.09811 

.49822 

2.00715 

.52020 

1.92235 

31 

30 

.45573 

2.19430 

.47698 

2.09654 

.49858 

2.00509 

.52057 

1.92098 

30 

31 

.45608 

2.19261 

.47733 

2.09498 

.49894 

2.00423 

.52094 

1.91962 

29 

32 

.45643 

2.19092 

.47769 

2.09341 

.40031 

2.00277 

.52131 

1.91826 

28 

33 

.45678 

2.18923 

.47805 

2,09184 

.40007 

2.00131 

•  .52108 

1.91690 

27 

34 

.45713 

2.18755 

.47840 

2.09028 

.50004 

1.99980 

.52205 

1.91552 

26 

35 

.45748 

2.18587 

.47876 

2.08872 

.50040 

1.99841 

.52242 

1.91414 

25 

36 

.45784 

2.18419 

.47912 

2.08716 

.50076 

1.99095 

.52279 

1.91288 

24 

37 

.45819 

2.18251 

.47948 

2.08500 

.50113 

1.99550 

.52316 

1.91142 

23 

38 

.45854 

2.18084 

.47984 

2.08405 

.50149 

1.99400 

.52353 

1.91017 

22 

39 

.45889 

2.17916 

.48019 

2.08250 

.50185 

1.09201 

.52390 

1.90870 

21 

40 

.45924 

2.17749 

.48055 

2.08094 

.50222 

1.99110 

.52427 

1.90741 

20 

41 

.45960 

2.17582 

.48091 

2^07939 

.50258 

1.98972 

.52464 

1.90607 

19 

42 

.45995 

2.17416 

.48127 

2.07785 

.50395 

1.98828 

.52501 

1.90472 

18 

43 

.46030 

2.17249 

.48163 

2.07630 

.50331 

1.98084 

.52538 

1.90337 

17 

44 

.46065 

2.17083 

.48198 

2.07476 

.50368 

1.98540 

.52575 

1.90203 

16 

45 

.46101 

2.16917 

.48234 

2.07321 

.50404 

1.98390 

.52613 

1.90069 

15 

46 

.46136 

2.16751 

.48270 

2.07167 

.50441 

1.98253 

.52650 

1.89935 

14 

47 

.46171 

2.165S5 

.48306 

2.07014 

.50477 

1.98110 

.52687 

1.89801 

13 

48 

.46206 

2.16420 

.48342 

2.06860 

.50514 

1.97060 

.52724 

1.89667 

12 

49 

.46242 

2.16255 

.48378 

2.06700 

.50550 

1.97823 

.52701 

1.80533 

11 

50 

.46277 

2.16090 

.48414 

2.00553 

.50587 

1.97681 

.52798 

1.89400 

10 

51 

.46312 

2.15925 

.48450 

2.06-100 

.50623 

1.97538 

.52836 

1.89266 

9 

52 

.46348 

2.15760 

.48486 

2.06247 

.50060 

1.97395 

.52873 

1.89133 

8 

53 

.46383 

2.15596 

.48521 

2.06094 

.50696 

1.97253 

.52910 

1.89000 

7 

54 

.46418 

2.15432 

.48557 

2.05942 

.50733 

1.97111 

.52947 

1.88867 

6 

55 

.46454 

2.15268 

.48593 

2.05790 

.50769 

1.90909 

.52985 

1.S8734 

5 

56 

.46489 

2.1510i 

.48620 

2.05637 

.50806 

1.96827 

.53022 

1.88602 

4 

57 

.46525 

2.14940 

.48665 

2.05485 

.50843 

1.96085 

.53059 

1.88469 

3 

58 

.46560 

2.14777 

.48701 

2.05333 

.50879 

1.96544 

.53090 

1.88337 

2 

59 

.46595 

2.14614 

.48/37 

2.05182 

.50916 

1 .96402 

.53134 

1.88205 

1 

60 

.46631 

2.14451 

.48773 

2.05030 

.50953 

1.96261 

.53171 

1.88073 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tarig 

# 

65°     1 

64°     1 

63°     1 

62°     1 

Table  of  Natural  Tangents  and  Cotangents 


111 


' 

28°     1 

29°     1 

30°     1 

31° 

1 
60 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.53171 

1.88073 

.55431 

1.80405 

.57735 

1.73205 

.60086 

1.66428 

1 

.53208 

1.87941 

.55469 

1.80281 

.57774 

1.72089 

,60126 

1.66318 

59 

2 

.53246 

1.87809 

.55507 

1.80158 

.57813 

1.72973 

.60165 

1.66209 

58 

3 

.53283 

1.87677 

.55545 

1.80034 

.57851 

1 .72857 

.60205 

1.66099 

57 

4 

.53320 

1.87546 

.55583 

1.79911 

.57890 

1.72741 

.60245 

1.65990 

56 

5 

.5335S 

1.87415 

.55621 

1.79788 

.57929 

1.72625 

.60284 

1.65881 

55 

0 

.53395 

1.87283 

.55659 

]  .79605 

.57968 

1.72509 

.60324 

1.65772 

54 

7 

.53132 

1.87152 

.55697 

1.79542 

■  .58007 

1.72393 

.60364 

1.65663 

53 

8 

.53470 

1.87021 

.55736 

1.79419 

.58046 

1.72278 

.60403 

1.65554 

52 

9 

.53507 

1.86891 

.55774 

1.79296 

.58085 

1.72163 

.60443 

1.65445 

51 

10 

.53545 

1.86760 

.55812 

1.79174 

.58124 

1.72047 

.60483 

1.65337 

50 

11 

.53582 

1.86630 

.55850 

1.79051 

.58162 

1.71932 

.60522 

1.65228 

49 

12 

.53620 

1.86499 

.55888 

1.78929 

.58201 

1.71817 

.60562 

1.65120 

48 

13 

.53657 

1.86369 

.55926 

1.78807 

.58240 

1.71702 

.60602 

1.65011 

47 

14 

.53694 

1.86239 

.55964 

1.78685 

.58279 

1.71588 

.60042 

1.64903 

46 

15 

.53732 

1.S6109 

.56003 

1.78563 

.58318 

1.71473 

.60681 

1.64795 

45 

16 

.53769 

1.S5979 

.56041 

1.78441 

.58357 

1.71358 

.60721 

1.64687 

44 

17 

.53807 

1.85850 

.56079 

1.78319 

.58396 

1.71244 

.60761 

1.64579 

43 

18 

.53844 

1.S5720 

.56117 

1.78198 

.58435 

1.71129 

.60801 

1.64471 

42 

19 

.53882 

1.85591 

.56156 

1.78077 

.58474 

1.71015 

.60841 

1.64363 

41 

20 

.53920 

1.85462 

.56194 

1.77955 

.58513 

1.70901 

.60881 

1.64256 

40 

21 

.53957 

1.85333 

.56232 

1.77834 

.58552 

1.70787 

.00921 

1.64148 

39 

22 

.53995 

1.85204 

.56270 

1.77713 

.58591 

1.70673 

.60960 

1.04041 

38 

23 

.54032 

1.85075 

.56309 

1.77592 

.58631 

1.70560 

.61000 

1.63934 

37 

24 

.54070 

1.84946 

.56347 

1.77471 

.58670 

1.70446 

.61040 

1.63826 

36 

25 

.54107 

1.84818 

.56385 

1.77351 

.58709 

1.70332 

.01080 

1.63719 

35 

20 

.54145 

1 .84689 

.56424 

1.77230 

.58748 

1.70219 

.61120 

1.63612 

34 

27 

.54183 

1.84561 

.56462 

1.77110 

.58787 

1.70106 

.61160 

1.63505 

33 

28 

.54220 

1.84433 

.56501 

1.76990 

.58826 

1.69992 

.61200 

1.63398 

32 

29 

.54258 

1.84305 

.56539 

1.76869 

.58865 

1.69879 

.61240 

1.63292 

31 

30 

.54296 

1.84177 

.56577 

1.76749 

.58905 

1.69766 

.61280 

1.63185 

30 

31 

.54333 

1.84049 

.56616 

1.76629 

.58944 

1.69653 

.61320 

1.63079 

29 

32 

.54371 

1.83922 

.56654 

1.76510 

.58983 

1.69541 

.61300 

1.62972 

28 

33 

.54409 

1.83794 

.56693 

1.76390 

.59022 

1.69428 

.61400 

1.62866 

27 

34 

.54446 

1.83667 

.56731 

1.7C271 

.59061 

1.69316 

.61440 

1.62760 

26 

35i 

.54484 

1.83540 

.56769 

1.76151 

.59101 

1.69203 

.61480 

1.62654 

25 

36 

.54522 

1.83413 

.56808 

1.76032 

.59140 

1.69091 

.61520 

1.62548 

24 

37 

.54560 

1.83286 

.56846 

1.75913 

.59179 

1.68979 

.61561 

1.62442 

23 

38 

.54597 

1.83159 

.56885 

1.75794. 

.59218 

1.68866 

.61601 

1.62336 

22 

39 

.54635 

1.83033 

.56923 

1.75675 

.59258 

1.68754 

.61641 

1.62230 

21 

40 

.54673 

1.82906 

.56962 

1.75556 

.59297 

1.68643 

.61681 

1.62125 

20 

41 

.54711 

1.82780 

.57000 

1.75437 

.59336 

1.08531 

.61721 

1.62019 

19 

42 

.54748 

1.82654 

.57039 

1.75319 

.59376 

1.68419 

.61761 

1.61914 

18 

43 

.54786 

1.82528 

.57078 

1.75200 

.59415 

1.68308 

.61801 

1.61808 

17 

44 

.54824 

1.82402 

.57116 

1.75082 

.59454 

1.68196 

.61842 

1.61703 

16 

45 

.54862 

1.8227C 

.57155 

1.74964 

.59494 

1.68085 

.61882 

1.61598 

15 

46 

.54900 

1.82150 

.57193 

1.74846 

.59533 

1.67974 

.61922 

1.61493 

14 

47 

.54938 

1.82025 

.57232 

1.74728 

.50573 

1.67863 

.61962 

1.61388 

13 

48 

.54975 

1.81899 

.57271 

1.74610 

.59612 

1.67752 

.62003 

1.612«^3 

12 

49 

.55013 

1.81774 

.57309 

1.74492 

.59651 

1.67641 

.62043 

1.61179 

11 

50 

.55051 

1.81649 

.57348 

1.74375 

.59691 

1.07530 

.62083 

1.61074 

10 

51 

.55089 

1.81524 

.57386 

1.74257 

.59730 

1.67419 

.62124 

1.60970 

9 

52 

.55127 

1.81399 

.57425 

1.71140 

.59770 

1 .67309 

.62164 

1.60865 

8 

53 

55165 

1.81274 

.57464 

1.74022 

.59809 

1.67198 

.62204 

1.60761 

7 

54 

.55203 

1.81150 

.57503 

1.73905 

.59849 

1.67088 

.62245 

1.60657 

6 

55 

.55241 

1.81025 

.57541 

1.73788 

.59888 

1.66978 

.62285 

1.60553 

5 

56 

.55279 

1.80901 

.57580 

1.73671 

.59928 

1.66867 

.62325 

1.60449 

4 

57 

.55317 

1.80777 

.57619 

1.73555 

.59967 

1.66757 

.62366 

1.60345 

3 

58 

.55355 

1.80653 

.57657 

1.73438 

.60007 

1.66647 

.62406 

1.60241 

2 

59 

55393 

1.80529 

.57696 

1.73321 

.60046 

1.66538 

.62446 

1.60137 

1 

()0 

.55431 

1.80405 

.57735 

1.73205 

.60086 

1.66428 

.62187 

1.60033 

0 

~ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tanff 

/ 

61° 

60° 

59°     1 

58° 

112 


Trigonometry 


0 

fjgo 

33° 

34°     1 

35° 

/ 

Tung 
.62487 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Colang 

1.00033 

.64941 

1.53986 

.07451 

1.48256 

.70021 

1.42815 

60 

1 

.62527 

1.59930 

.64982 

1.53888 

.07493 

1.48163 

.70001 

1.42726 

59 

2 

.62568 

1.59820 

.65024 

1.53791 

.67536 

1.48070 

.70170 

1.42038 

58 

3 

.62008 

1.59723 

.65005 

1.53093 

.07578 

1.47977 

.70151 

1.42550 

57 

4 

.62649 

1.59620 

.65106 

1.53505 

.67620 

1.47885 

.70194 

1.42402 

50 

5 

.626S9 

1.59517 

.05148 

1.53497 

.67663 

1.47792 

.70238 

1.42374 

55 

6 

.62730 

1.59414 

.65189 

1.53400 

.07705 

1.47699 

.70281 

1.42280 

54 

7 

.62770 

1.59311 

.65231 

1.53302 

.07748 

1.47607 

.70325 

1.42198 

53 

8 

.62811 

1.59208 

.05272 

1.53205 

.07790 

1.47514 

.70308 

1.42110 

52 

9 

.02852 

1.59105 

.05314 

1.53107 

.67832 

1.47422 

.70412 

1.42022 

51 

10 

.62892 

1.59002 

.65355 

1.53010 

.67875 

1.47330 

.70455 

1.41934 

50 

It 

.62933 

1.58900 

.65397 

1.52913 

.67917 

1.47238 

.70499 

1.41847 

49 

12 

.62973 

1.58797 

.C543S 

1.52810 

.67900 

1.47140 

.70542 

1.41759 

48 

13 

.63014 

1.5S695 

.65480 

1.52719 

.68002 

1.47053 

.70580 

1.41072 

47 

14 

.63055 

1.58593 

.65521 

1.52022 

.68045 

1.4690? 

.70029 

1.41584 

40 

15 

.63095 

1.58490 

.65503 

1.52525 

.68088 

1.40870 

.70073 

1.41497 

45 

10 

.63136 

1.58388 

.65004 

1.52429 

.08130 

1.40778 

.70717 

1.41409 

44 

17 

.03177 

1.58286 

.05040 

1.52332 

.08173 

1.40080 

.70700 

1.41322 

43 

18 

.63217 

1.58184 

.05088 

1.52235 

.08215 

1.40595 

.70804 

1.41235 

42 

10 

.63258 

1.58083 

.65729 

1.52139 

.08258 

1.40503 

.70848 

1.41148 

41 

20 

.63299 

1.57981 

.65771 

1.52043 

.08301 

1.40411 

.70891 

1.41061 

40 

21 

.03340 

1.57879 

.65813 

1.51940 

.68343 

1.40320 

.70935 

1.40974 

39 

22 

.63380 

1.57778 

.65.^54 

1.51850. 

.68386 

1.40220 

.70979 

1.40887 

38 

23 

.63421 

1.57070 

.65390 

1.51751 

.68429 

1.40137 

.71023 

1.40800 

37 

24 

.03462 

1.57575 

.65938 

1.51053 

.68471 

1.40040 

.71000 

1.40714 

36 

25 

.03503 

1.57474 

.65980 

1.51502 

.68514 

1.45955 

.71110 

1.40027 

35 

20 

.63544 

1.57372 

.66021 

1.51400 

.68557 

1.4  5804 

.71154 

1.40540 

34 

27 

.03584 

1.57271 

.66003 

1.51370 

.68000 

1.45773 

.71198 

1.40454 

33 

28 

.63625 

1.57170 

.60105 

1.51275 

.68642 

1.45682 

.71242 

1.40307 

32 

29 

.63000 

1.57009 

.60147 

1.51179 

.68685 

1.45592 

.71285 

1.40281 

31 

30 

.63707 

1.50909 

.00189 

1.51084 

.68728 

1.45501 

.71329 

1.40105 

30 

31 

.63748 

1.50808 

.00230 

1.50988 

.08771 

1.45410 

.71373 

1.40109 

29 

32 

.03789 

1.56707 

.00272 

1.5C893 

.68814 

1.45320 

.71417 

1.40022 

28 

33 

.63830 

1.56007 

.03314 

1.50797 

.68357 

1.45229 

.71401 

1.39930 

27 

31 

.03871 

1 .505^0 

.00350 

1.50703 

.08900 

1.45139 

.71505 

1.39850 

26 

35 

.63912 

1.50406 

.00398 

1.50007 

.08942 

1.45049 

.71549 

1 .39704 

25 

30 

.63953 

1. 503^^0 

.00440 

1.50512 

.08985 

1.44958 

.71593 

1 .39679 

24 

37 

.63994 

1.50205 

.00482 

1.50417 

.09023 

1.44808 

.71037 

1.39593 

23 

3S 

.04035 

1.561C5 

.00524 

1.50322 

.09071 

1.44778 

.71081 

1.39507 

22 

39 

.04070 

1.5G0G5 

.60500 

1.50228 

.09114 

1.44688 

.71725 

1.39421 

21 

40 

.04117 

1.55966 

.00608 

1.50133 

.09157 

1.44598 

.71709 

1.39330 

20 

41 

.04158 

1.55866 

.00050 

1.50038 

.09200 

1.44508 

.71813 

1.39250 

19 

42 

.04199 

1.55700 

.66692 

1.49944 

.09243 

1.44418 

.71857 

1.39105 

18 

43 

.04240 

1.55000 

.60734 

1.49849 

.09280 

1.44329 

.71901 

1.39079 

17 

44 

.64231 

1.55507 

.60770 

1.49755 

.69:^29 

1.44239 

.71940 

1.38994 

16 

45 

.04322 

1.55407 

.00818 

1.49001 

.09372 

1.44149 

.71990 

1.3S909 

15 

46 

.64303 

1.55308 

.00800 

1.49506 

.69416 

1.44000 

.72034 

1.38824 

14 

47 

.64404 

1.55209 

.66902 

1.49472 

.69459 

1.43970 

.72078 

1 .38738 

13 

48 

.64446 

1.55170 

.66944 

1.49378 

.69502 

1.43881 

.72122 

1.38053 

12 

49 

.64487 

1.55071 

.06986 

1.49284 

.69545 

1 .43792 

.72107 

1.38508 

11 

50 

.64528 

1.54972 

.67028 

1.49190 

.69588 

1.43703 

.72211 

1.38484 

10 

51 

.64569 

1.54873 

.67071 

1.49097 

.69631 

1.43614 

.72255 

1.38399 

9 

"12 

.64610 

1.54774 

.67113 

1.49003 

.69675 

1.43525 

.72299 

1.38314 

8 

53 

.64652 

1.54075 

.67155 

1.48909 

.69718 

1.43436 

.72344 

1.38229 

7 

54 

.64693 

1.54576 

.67197 

1.48810 

.69761 

1.43347 

.72388 

1.38145 

6 

55 

.64734 

1.54478 

.67239 

1.48722 

.69804 

1 .43258 

.72432 

1.38000 

5 

56 

.64775 

1.54379 

.67282 

1.48029 

.69847 

1.43109 

.72477 

1.37976 

4 

57 

.64817 

1.542S1 

.67324 

1.48536 

.69301 

1 .43080 

.72521 

1.37891 

3 

58 

.64858 

1.54183 

.67300 

1.48442 

.69934 

1.42992 

.72505 

1 .37807 

2 

59 

.64899 

1.54085 

.67409 

1.48349 

.69977 

1.42903 

.72010 

1.37722 

1 

GO 

.64941 

1.53986 

.67451 

1.48256 
Tang 

.70021 

1.42815 

.72054 
Cotang 

1 .37038 

0 

Cotang 

Tang 

Cotang 

Cotang 

Tang 

Tang 

' 

rr-'yo      1 

cco      1 

KK^              1 

C^o 

•  1 

i 

•T 

\3 

»>o      ' 

a 

>*     1 

Table  of  Natural  Tangents  and  Cotangents 


113 


' 

36°     1 

37°     1 

38°     1 

31>°     1 

' 

Tang 

Cotang 

Tang 

Cotnng 

Tang 

Cotang 

Tang 

Cotang 

0 

.72654 

1.37638 

.75355 

1.32704 

.78120 

1.27994 

.80978 

1.23490 

60 

1 

.72699 

1.37554 

.75401 

1.32624 

.78175 

1.27917 

.81027 

1.23410 

59 

2 

.72743 

1.37470 

.75447 

1.32544 

.78222 

1.27841 

.81075 

1.23343 

58 

3 

.72788 

1.37386 

.75492 

1.32464 

.78269 

1.27764 

.81123 

1.23270 

57 

4 

.72832 

1.37302 

.75538 

1.32384 

.78316 

1.27688 

.81171 

1.2319G 

50 

5 

.72877 

1.37218 

.75584 

1.32304 

.78363 

1.27611 

.81220 

1.23123 

65 

r> 

.72921 

1.37134 

.75029 

1.32224 

.78410 

1.27535 

.81208 

1 .23050 

54 

7 

.72966 

1.37050 

.75675 

1.32144 

.78457 

1.27458 

.81310 

1.22977 

53 

8 

.73010 

1.36967 

.75721 

1.32064 

.78504 

1.27382 

.81364 

1.22904 

52 

9 

.73055 

1.36883 

.75767 

1.31984 

.78551 

1.27306 

.81413 

1.22831 

51 

10 

.73100 

1.36800 

.75812 

1.31904 

.78598 

1.27230 

.81461 

1.22758 

50 

11 

.73144 

1.36716 

.75858 

1.31825 

.78645 

1.27153 

.81510 

1.22685 

49 

12 

.73189 

1.36633 

.75904 

1.31745 

.78692 

1.27077 

.81558 

1.22012 

48 

13 

.73234 

1.36549 

.75950 

1.31606 

.78739 

1.27001 

.81006 

1.22539 

47 

14 

.73278 

1.36466 

.75996 

1.31586 

.78786 

1.20925 

.81655 

1.22107 

46 

15 

.73323 

1.36383 

.76042 

1.31507 

.78834 

1.26849 

.81703 

1.22394 

45 

11] 

.73368 

1.36300 

.76088 

1.31427 

.78881 

1.26774 

.81752 

1.22321 

44 

17 

.73413 

1.36217 

.76134 

1.31348 

.78928 

1.26698 

.81800 

1.22249 

43 

18 

.73457 

1.36134 

.76180 

1.31209 

.78975 

1.20622 

.81849 

1.22176 

42 

19 

.73502 

1.36051 

.76226 

1.31190 

.79022 

1.26546 

.81898 

1.22104 

41 

20 

.73547 

1.35968 

.76272 

1.31110 

.79070 

1.26471 

.81946 

1.22031 

40 

21 

.73592 

1.35885 

.76318 

1.31031 

.79117 

1.26395 

.81995 

1.21959 

39 

22 

.73637 

1.35802 

.76304 

1.30952 

.79164 

1.26319 

.82044 

1.21886 

38 

23 

.73681 

1.35719 

.70410 

1.30873 

.79212 

1.26244 

.82092 

1.21814 

37 

24 

.73726 

1.35637 

.70450 

1.30795 

.79259 

1.26169 

.82141 

1.21742 

30 

25 

.73771 

1.35554 

.76502 

1.30710 

.79306 

1.26093 

.82190 

1.21670 

35 

26 

.73816 

1.35472 

.76548 

1.30637 

.79354 

1.26018 

.82238 

1.21598 

34 

27 

.73861 

1.35389 

.76594 

1.30558 

.79401 

1.25943 

.82287 

1.21526 

33 

28 

.73906 

1.35307 

.76640 

1.30480 

.79449 

1.25867 

.82336 

1.21454 

32 

29 

.73951 

1.35224 

.76680 

1.30401 

.79496 

1.25792 

.82385 

1.21382 

31 

30 

.73996 

1.35142 

.76733 

1.30323 

.79544 

1.25717 

.82434 

1.21310 

30 

31 

.74041 

1.35060 

.76779 

1.30244 

.79591 

1.25642 

.82483 

1.21238 

29 

32 

.74086 

1.34978 

.76825 

1.30106 

.79639 

1.25567 

.82531 

1.21166 

28 

33 

.74131 

1.34890 

.76871 

1.30087 

.79686 

1.25492 

.82580 

1.21094 

27 

34 

.74176 

1.34814 

.76918 

1.30009 

.79734 

1.25417 

.82629 

1.21023 

26 

35 

.74221 

1.34732 

.76964 

1.29931 

.79781 

1.25343 

.82678 

1.20951 

25 

30 

.74267 

1.34G50 

.77010 

1.29853 

.79829 

1.25268 

.82727 

1.20879 

24 

37 

.74312 

1 .34508 

.77057 

1.29775 

.79877 

1.25193 

.82776 

1.20808 

23 

38 

.74357 

1.34487 

.77103 

1.29606 

.79924 

1.25118 

.82825 

1.20736 

22 

39 

.74402 

1.34^05 

.77149 

1.29618 

.79972 

1.25044 

.82874 

1.20665 

21 

40 

.74447 

1.34323 

.77196 

1.29541 

.80020 

1.24969 

.82923 

1.20503 

20 

41 

.74492 

1.34242 

.77242 

1.29403 

.80067 

1.24895 

.82972 

1.20522 

19 

42 

.74538 

1.34100 

.77289 

1.29385 

.80115 

1.24820 

.83022 

1.20451 

18 

43 

.74583 

1.34079 

.77335 

1.29307 

.80163 

1.24740 

.83071 

1.20379 

17 

44 

.74628 

1.33908 

.77382 

1.29229 

.80211 

1.24672 

.83120 

1.20308 

16 

45 

.74674 

1.33010 

.77428 

1.29152 

.80258 

1.24597 

.83169 

1.20237 

15 

40 

.74719 

1.33825 

.77475 

1.29074 

.80300 

1.24523 

.83218 

1.20166 

14 

47 

.7470^ 

1.33754 

.77521 

1.28997 

.80354 

1.24449 

.83268 

1.20095 

13 

48 

.74810 

1.33073 

.77568 

1.28910 

.80402 

1.24375 

.83317 

1.20024 

12 

49 

.74855 

1 .33592 

.77615 

1.28842 

.80450 

1.24301 

.83366 

1.19953 

11 

50 

.74900 

1.33511 

.77661 

1.28764 

.80498 

1.24227 

.83415 

1.19882 

10 

51 

.74946 

1.33430 

.77708 

1 .28687 

.80546 

1.2415?. 

.83405 

1.19811 

9 

52 

.74991 

1.33349 

.77754 

1.2S610 

.80594 

1.24079 

.83514 

1.19740 

8 

53 

.75037 

1.33208 

.77801 

1.28533 

.80642 

1.24005 

.83564 

1.10669 

7 

54 

.75082 

1.33187 

.77848 

1.28456 

.80090 

1.23931 

.83613 

1.19599 

0 

55 

.75128 

1.33107 

.77895 

1.28379 

.80738 

1.23858 

.83062 

1.19528 

5 

5G 

.75173 

1 .33026 

.77941 

1.28302 

.80786 

1.23784 

^.83712 

1.19457 

4 

57 

.75219 

1.32946 

.77988 

1.28225 

.80834 

1.23710 

.83761 

1.19387 

3 

58 

.75264 

1.32865 

.78035 

1.28148 

.80882 

1.23037 

.83811 

1.19316 

2 

59 

.75310 

1.32785 

.78082 

1.28071 

.80930 

1.23503 

.83860 

1.19246 

1 

60 

.75355 

1.32704 

.78129 

1.27994 

.80978 

1.23490 

.83910 

1.19175 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

' 

-^o        1 

~"  ^";;o  "  1 

--0          1 

5 

»j     ' 

52     1 

5 

1     1 

5'^" 

U' 

114 


Trigonometry 


/ 

40° 

41° 

42°     1 

43° 

' 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.83910 

1.19175 

.86929 

1.15037 

.90040 

1.11061 

.93252 

1.07237 

60 

1 

.83960 

1.19105 

.86980 

1.14969 

.90093 

1.10996 

.93306 

1.07174 

59 

2 

.84009 

1.19035 

.87031 

1.14902 

.90146 

1.10931 

.93360 

1.07112 

58 

3 

.84059 

1.18964 

.87082 

1.14S34 

.90199 

1.10867 

.93415 

1.07049 

57 

4 

.84108 

1.18894 

.87133 

1.14767 

.90251 

1.10802 

.93409 

1.00987 

56 

5 

.84158 

1.18824 

.87184 

1.14699 

.90304 

1.10737 

.93524 

1.06925 

55 

G 

.84208 

1.18754 

.87236 

1.14632 

.90357 

1.10672 

.93578 

1 .00802 

54 

7 

.84258 

1.18684 

.87287 

1.14565 

.90410 

1.10607 

.93633 

1.00800 

53 

8 

.84307 

1.18614 

.87338 

1.14498 

.90463 

1.10543 

.93688 

1.06738 

52 

9 

.84357 

1.18544 

.87389 

1.14430 

.90516 

1.10478 

.93742 

1.06076 

51 

10 

.84407 

1.18474 

.87441 

1.14363 

.90569 

1.10414 

.93797 

1.06613 

50 

11 

.84457 

1.18404 

.87492 

1.14296 

.90621 

1.10349 

.93852 

1.06551 

49 

12 

.84507 

1.18334 

.87543 

1.14229 

.90074 

1.10285 

.93906 

1.06489 

48 

13 

.84556 

1.18264 

.87595 

1.14162 

.90727 

1.10220 

.93961 

1.06427 

47 

14 

.84606 

1.18194 

.87646 

1.14095 

.90781 

1.10156 

.94016 

]  .06365 

46 

15 

.84656 

1.18125 

.87698 

1.14028 

.90834 

1.10091 

.94071 

1 .06303 

45 

16 

.84706 

1.18055 

.87749 

1.13961 

.90887 

1.10027 

.94125 

1.06241 

44 

17 

.84756 

1.17986 

.87801 

1.13894 

.90940 

1.09963 

.94180 

1.06179 

43 

18 

.84806 

1.17916 

.87852 

1.13828 

.90993 

1.09899 

.94235 

1.06117 

42 

19 

.84856 

1.17846 

.87904 

1.13761 

.91046 

1.09834 

.94290 

1.00056 

41 

20 

.84906 

1.17777 

.87955 

1.13694 

.91099 

1.09770 

.94345 

1.05994 

40 

21 

.84956 

1.17708 

.88007 

1.13627 

.91153 

1.09706 

.94400 

1 .05932 

39 

22 

.85006 

1.17638 

.88059 

1.13561 

.91206 

1.09642 

.94455 

1.05870 

38 

23 

.85057 

1.1 7509 

.88110 

1.13494 

.91259 

1.09578 

.94510 

1.05809 

37 

24 

.85107 

1.17500 

.88162 

1.13428 

.91313 

1.09514 

.94565 

1.05747 

36 

25 

.85157 

1.17430 

.88214 

1.13361 

.91366 

1.09450 

.94620 

1.05685 

35 

20 

.85207 

1.17361 

.88265 

1.13295 

.91419 

1.09386 

.94676 

1.05624 

34 

27 

.85257 

1.17292 

.88317 

1.13228 

.91473 

1.09322 

.94731 

1.05562 

33 

28 

.85308 

1.17223 

.88369 

1.13162 

.91526 

1.09258 

.94786 

1.05501 

32 

29 

.85358 

1.17154 

.88421 

1.13096 

.91580 

1.09195 

.94841 

1.05439 

31 

30 

.85408 

1.17085 

.88473 

1.13029 

.91633 

1.09131 

.94896 

1.05378 

30 

31 

.85458 

1.17016 

.88524 

1.12963 

.91687 

1.09067 

.94952 

1.05317 

29 

32 

.85509 

1.16947 

.88576 

1.12897 

.91740 

1.09003 

.95007 

1.05255 

28 

33 

.85559 

1.16878 

.88628 

1.12S31 

.91794 

1.08940 

.95062 

1.05104 

27 

34 

.85609 

1.16309 

.886S0 

1.12765 

.91847 

1.08876 

.95118 

1.05133 

26 

35 

.85660 

1.16741 

.88732 

1.12699 

.01901 

1.08813 

.95173 

1.05072 

25 

36 

.85710 

1.16672 

.88784 

1.12633 

.91955 

1.08749 

.95229 

1.05010 

24 

37 

.85761 

1.16603 

.88836 

1.12657 

.92008 

1.08086 

.95284 

1.04949 

23 

38 

.85811 

1.16535 

.88888 

1.12501 

.92002 

1.08622 

.95340 

1.04888 

22 

39 

.85862 

1.10466 

.88940 

1.12435 

.92116 

1.03559 

.95395 

1.04827 

21 

40 

.85912 

1.16398 

.88992 

1.12369 

.92170 

1.08490 

.95451 

1.04766 

20 

41 

.85963 

1.16329 

.89045 

1.12303 

.92224 

1.08432 

.95506 

1.04705 

10 

42 

.86014 

1.16261 

.89097 

1.12238 

.92277 

1 .0S309 

.95502 

1.04644 

18 

43 

.86064 

1.16192 

.89140 

1.12172 

.92331 

1.08300 

.95618 

1.01583 

17 

44 

.86115 

1.16124 

.89201 

1.12106 

.92385 

1.08243 

.95673 

1.04522 

16 

45 

.86166 

1.10056 

.89253 

1.12041 

.92439 

1.08170 

.95729 

1.04461 

15 

46 

.86216 

1.15987 

.89306 

1.11975 

.92493 

1.0811« 

.95785 

1.04401 

14 

47 

.86267 

1.15919 

.89358 

1.11909 

.92547 

1.08053 

.95841 

1.04340 

13 

48 

.86318 

1.15851 

.89410 

1.11844 

.92601 

1.07990 

.95897 

1.04279 

12 

49 

.86368 

1.15783 

.89463 

1.11778 

.92655 

1.07927 

.95952 

1.04218 

11 

50 

.86419 

1.15715 

.89515 

1.11713 

.92709 

1.07864 

.96008 

1.04158 

10 

51 

.86470 

1.15047 

.89567 

1.11G48 

.92763 

1.07801 

.96004 

1.04097 

9 

52 

.86521 

1.15579 

.89620 

1.11582 

.02817 

1.07738 

.96120 

1.04036 

8 

53 

.86572 

1.15511 

.89672 

1.11517 

.92872 

1.07676 

.00170 

1.03976 

7 

54 

.86623 

1.15443 

.89725 

1.11452 

.92926 

1.07613 

.96232 

1.03915 

6 

55 

.80674 

1.15375 

.89777 

1.11387 

.92980 

1.07550 

.96288 

1.03855 

5 

56 

.86725 

1.1530^ 

.89830 

1.11321 

.93034 

1.07487 

.96344 

1.03794 

4 

57 

.86770 

1.15240 

.89883 

1.11256 

.93088 

1.07425 

.96400 

1.03734 

3 

58 

.80827 

1.15172 

.89935 

1.11191 

.93143 

1.07362 

.90457 

1.03674 

2 

59 

.86878 

1.15104 

.89988 

1.11126 

.93197 

1.07299 

.96513 

1.03613 

1 

60 

.86929 

1.15037 

.90040 
Cotang 

1.11061 
Tang 

.93252 

1.07237 

.90509 
Cotang 

1.03553 
Tang 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

4»» 

48°     ' 

47°     1 

46° 

Table  of  Natural  Tangents  and  Cotangents 


115 


^ 

A 

' 

14° 

, 

, 

44° 

44° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

1 

2 
3 

4 
5 
6 
7 
8 
9 
10 

11 
12 
13 
14 

15 
16 
17 

18 
19 
20 

.96509 
.96625 
.96681 
.96738 
.96791 
.968.50 
.96907 
.96963 
.97020 
.97076 
.97133 

.97189 
.97246 
.97302 
.97359 
.97416 
.97472 
.97529 
.97586 
.97643 
.97700 

1.03553 
1.03493 
1.03433 
1.03372 
1.03312 
1.03252 
1.03192 
1.03132 
1.03072 
1.03012 
1.02952 

1.02892 
1.02832 
1.02772 
1.02713 
1.02653 
1.02593 
1.02533 
1.02474 
1.02414 
1.02355 

60 
59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

.97700 
.97756 
.97813 
.97870 
.97927 
.97984 
.98041 
.98098 
.98155 
.98213 
.98270 

.98327 
.98384 
.98441 
.98499 
.98556 
.98613 
.98671 
.98728 
.98786 
.98843 

1.02355 
1.02295 
1.02236 
1.02176 
1.02117 
1.02057 
1.01998 
1.01939 
1.01879 
1.01820 
1.01761 

1.01702 
1.01642 
1.01583 
1.01524 
1.01465 
1.01406 
1.01347 
1.01288 
1.01229 
1.01170 

40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

29 
28 
27 
26 
25 
24 
23 

92 

21 
20 

40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

.98843 
.98901 
.98958 
.99016 
.99073 
.99131 
.99189 
.99247 
.99304 
.99362 
.99420 

.99478 
.99536 
.99594 
.99652 
.99710 
.99768 
.99826 
.99884 
.99942 
1.00000 

1.01170 
1.01112 
1.01053 
1.00994 
1.00935 
1.00876 
1.00818 
1.00759 
1.00701 
1.00642 
1.00583 

1.00525 
1.00467 
1.00408 
1.00350 
1.00291 
1.00233 
1.00175 
1.00116 
1 .00058 
1.00000 

20 
19 
18 
17 
16 
15 
14 
13 
12 
11 
10 

9 
8 
7 
6 
5 
4 
3 
2 

0 

' 

Cotang 

Tang 

t 

' 

Cotang 

Tang 

' 

/ 

Cotang 

Tang 

/ 

45° 

45^ 

45° 

_ 

il« 


Trigonometry 


N. 

itural 

Se 

:ants  and 

Cosecan 

ts 

De 

gre< 

j_                        Secants 

*   ,0' 

10' 

20' 

30' 

40' 

50' 

60' 

( 

)   1.00000 

1.00001 

1.00002 

1.00004 

1.00007 

1.00011 

1.00015 

89 

I   1.00015 

1.00021 

1.00027 

1.00034 

1.00042 

1.00051 

1.00061 

88 

2   1.00061 

1.00072 

1.00083 

1.00095 

1.00108 

1.00122 

1.00137 

87 

J   1.00137 

1.00153 

1.00169 

1.00187 

1.00205 

1.00224 

1.00244 

86 

I   1.00244 

1.00265 

1.00287 

1.00309 

1.00333 

1.00357 

1.00382 

85 

5   1.00382 

1.00408 

1.00435 

1.00463 

1.00491 

1.00521 

1.00551 

84 

5   1.00551 

1.00582 

1.00614 

1.00647 

1.00681 

1.00715 

1.00751 

83 

r   1.00751 

1.00787 

1.00825 

1.00863 

1.00902 

1.00942 

1.00983 

82 

S   1.00983 

1.01024 

1.01067 

1.01111 

1.01155 

1.01200 

1.01247 

81 

1 

J   1.01247 

1.01294 

1.01342 

1.01391 

1.01440 

1.01491 

1.01543 

80 

li 

3   1.01543 

1.01595 

1.01 

649 

1.01703 

1.01758 

1.01815 

1.01872 

79 

1 

I   1.01872 

1.01930 

1.01 

989 

1.02049 

1.02110 

1.02171 

1.02234 

78 

IJ 

I        1.02234 

1.02298 

1.02 

362 

1.02428 

1.02494 

1.02562 

1.02630 

77 

i: 

J   1.02630 

1.02700 

1.02 

770 

1.02842 

1.02914 

1.02987 

1.03061 

76 

1' 

I   1.03061 

1.03137 

1.03 

213 

1.03290 

1.03368 

1.03447 

1.03528 

75 

1 

)   1.03528 

1.03609 

1.03 

691 

1.03774 

1.03858 

1.03944 

1.04030 

74 

1 

3   1,04030  , 

.1.04117 

1.04 

206 

1.04295 

1.04385 

1.04477 

1.04569 

73 

1 

J        1.04569 

1.04663 

1.04 

757 

1.04853 

1.04950 

1.05047 

1.05146 

72 

1 

I        1.05146 

1.05246 

1.05 

347 

1.05449 

1.05552 

1.05657 

1.05762 

71 

i< 

)   1.05762 

1.05869 

1.05 

976 

1.06085 

1.06195 

1.06306 

1.06418 

70 

2( 

3   1.06418 

1.06531 

1.06645 

1.06761 
1.07479 

1.06878 
1.07602 

1.06995 
1.07727 

1.07115 
1.07853 

69 

2 

I   1.07115 

1.07235 

1.07356 

68 

2. 

I        1.07853 

1.07981 

1.08109 

1.08239 

1.08370 

1.08503 

1.08636 

67 

2 

J   1.08636 

1.08771 

1.08907 

1.09044 

1.09183 

1.09323 

1.09464 

66 

2^ 

1   1.09464 

1.09606 

1.09750 

1.09895 

1.10041 

1.10189 

1 . 1033S 

65 

2. 

>   1.10338 

1.10488 

1.10640 

1.10793 

1.10947 

1.11103 

1.11260 

64 

2 

3   1  11260 

1.11419 

1.11579 

1.11740 

1.11903 

1.12067 

1 . 12233 

63 

2 

7        1.12233 

1 . 12400 

1.12568 

1.12738 

1.12910 

1 . 13083 

1 . 13257 

62 

2 

?   1.13257 

1 . 13433 

1.13610 

1.13789 

1.13970 

1.14152 

1 . 14335 

61 

2 

3   1.14335 

1.14521 

1.14707 

1.14896 

1.15085 

1.15277 

1.15470 

60 

3 

3   1.15470 

1.15665 

1.15861 

1.16059 

1.16259 

1 . 16460 

1.16663 

59 

3 

I   1.16663 

1.16868 

1.17075 

1.17283 

1.17493 

1.17704 

1.17918 

58 

3 

2   1.17918 

1.18133 

1.18350 

1 . 18569 

1.18790 

1.19012 

1.19236 

57 

3. 

J   1.19236 

1 . 19463 

1.19691 

1 . 19920 

1.20152 

1.20386 

1.20622 

56 

3^ 

I   1.20622 

1.20859 

1.21099 

1.21341 

1.21584 

1.21830 

1.22077 

55 

3. 

5   1.22077 

1.22327 

1.22579 

1.22833 

1.23089 

1.23347 

1.23607 

54 

3 

3   1.23607 

1.23869 

1.24134 

1.24400 

1.24669 

1.24940 

1.25214 

53 

3 

J        1.25214 

1.25489 

1.25767 

1.26047 

1.26330 

1.26615 

1.26902 

52 

3^ 

?   1.26902 

1.27191 

1.27483 

1.27778 

1.28075 

1.28374 

1.28676 

51 

3< 

3   1.28676 

1.28980 

1.29287 

1.29597 

1.29909 

1.30223 

1.30541 

30 

4( 

3   1.30541 

1.30861 

1.31183 

1.31509 

1.31837 

1.32168 

1.32501 

49 

4 

I   1.32501 

1.32838 

1.33177 

1.33519 

1.33864 

1.34212 

1.34563 

48 

4 

I        1.34563 

1.34917 

1.35274 

1.35634 

1.35997 

1.36363 

1.36733 

47 

4. 

J   1.36733 

1.37105 

1.37481 

1.37860 

1.38242 

1.38628 

1.39016 

46 

4^ 

1   1.39016 

1.39409 

1.39804 

1.40203 

1.40606 

1.41012 

1.41421 

45 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

De- 

Cosecants 

grees 

Table  of  Natural  Secants  and  Cosecants 


117 


Natural  Secants  and  Cosecants  (Continued) 

De- 

Cosecants 

grees 

C 

10' 

20' 

30' 

40' 

50' 

60' 

0 

oo 

343.77516 

171.88831 

114.59301 

85.94561 

68.75736 

57.29869 

89 

1 

57.29869 

49.11406 

42.97571 

38.20155 

34.38232 

31.25758 

28.65371 

88 

2. 

28.65371 

26.45051 

24.56212 

22.92559 

21.49368 

20.23028 

19.10732 

87 

3 

19.10732 

18.10262 

17.19843 

16.38041 

15.63679 

14.95788 

14.33559 

86 

4 

14.33559 

13.76312 

13.23472 

12.74550 

12.29125 

11.86837 

11.47371 

85 

5 

11.47371 

11.10455 

10.75849 

10.43343 

10.12752 

9.83912 

9.56677 

84 

6 

9.56677 

9.30917 

9.06515 

8.83367 

8.61379 

8.40466 

8.20551 

83 

7 

8.20551 

8.01565 

7.83443 

7.66130 

7.49571 

7.33719 

7.18530 

82 

8 

7.18530 

7.03962 

6.89979 

[6.76547 

6.63633 

6.51208 

6.39245 

81 

9 

6.39245 

6.27719 

6.16607 

6.05886 

5.95536 

5.85539 

5.75877 

80 

10 

5.75877 

5.66533 

5.57493 

5.48740 

5.40263 

5.32049 

5.24084 

79 

11 

5.24084 

5.16359 

5.08863 

5.01585 

4.94517 

4.87649 

4.80973 

78 

12 

4.80973 

4.74482 

4.68167 

4.62023 

4.56041 

4.50216 

4.44541 

77 

13 

4.44541 

4.39012 

4.33622 

4.28366 

4.23239 

4.18238 

4.13357 

76 

14 

4.13357 

4.08591 

4.03938 

3.99393 

3.94952 

3.90613 

3.86370 

75 

15 

3.86370 

3.82223 

3.78166 

3.74198 

3.70315 

3.66515 

3.62796 

74 

16 

3.62796 

3.59154 

3.55587 

3.52094 

3.48671 

3.45317 

3.42030 

73 

17 

3.42030 

3.38808 

3.35649 

3.32551 

3.29512 

3.26531 

3.23607 

72 

18 

3.23607 

3.20737 

3.17920 

3.15155 

3.12440 

3.09774 

3.07155 

71 

.  19 

3.07155 

3.04584 

3.02057 

2.99574 

2^7135 

2.94737 

2.92380 

70 

20  ' 

2.92380 

2.90063 

2.87785 

2.85545 

2.83342 

2.81175 

2.79043 

69 

21 

2.79043 

2.76945 

2.74881 

2.72850 

2.70851 

2.68884 

2.66947 

68 

22 

2.66947 

2.65040 

2.63162 

2.61313 

2.59491 

2.57698 

2.55930 

67 

23 

2.55930 

2.54190 

2.52474 

2.50784 

2.49119 

2.47477 

2.45859 

66 

24 

2.45859 

2.44264 

2.42692 

2.41142 

2.39614 

2.38107 

2.36620 

65 

25 

2.36620 

2.35154 

2.33708 

2.32282 

2.30875 

2.29487 

2.28117 

64 

'  26 

2.28117 

2.26766 

2.25432 

2.24116 

2.22817 

2.21535 

2.20269 

63 

27 

2.20269 

2.19019 

2.17786 

2.16568 

2.15366 

2.14178 

2.13005 

62 

28 

2.13005 

2.11847 

•2.10704 

2.09574 

2.08458 

2.07356 

2.06267 

61 

29 

2.06267 

2.05191 

2.04128 

2.03077 

2.02039 

2.01014 

2.00000 

60 

30 

2.00000 

1.98998 

1.98008 

1.97029 

1.96062 

1.95106 

1.94160 

59 

31 

1.94160 

1.93226 

1.92302 

1.91388 

1.90485 

1.89591 

1.88708 

58 

32 

1.88708 

1.87834 

1.86990 

1.86116 

1.85271 

1.84435 

1.83608 

57 

33 

1.83608 

1.82790 

1.81981 

1.81180 

1.80388 

1.79604 

1.78829 

56 

34 

1.78829 

1.78062 

1.77303 

1.76552 

1.75808 

1.75073 

1.74345 

55 

35 

1.74345 

1.73624 

1.72911 

1.72205 

1.71506 

1.70815 

1.70130 

54 

36 

1.70130 

1.69452 

1.68782 

1.68117 

1.67460 

1.66809 

1.66164 

53 

37 

1.66164 

1 . 65526 

1.64894 

1.64268 

1.63648 

1.63035 

1.62427 

52 

38 

1.62427 

1.61825 

1.61229 

1.60639 

1.60054 

1.59475 

1.58902 

51 

39 

1.58902 

1.58333 

1.57771 

1.57213 

1.56661 

1.56114 

1.55572 

50 

40 

1.55572 

1.55036 

1.54504 

1.53977 

1.53455 

1.52938 

1.52425 

49 

41 

1.52425 

1.51918 

1.51415 

1.50916 

1.50422 

1.49933 

1.49448 

48 

42 

1.49448 

1.48967 

1.48491 

1.48019 

1.47551 

1.47087 

1.46628 

47 

43 

1.46628 

1.46173 

1.45721 

1.45274 

1.44831 

1.44391 

1.43956 

46 

44 

1.43956 

1.43524 

1.43096 

1.42672 

1  42251 

1.41835 

1.41421 

45 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

De- 

grees 

Secants 

«f  t^'- 


liA^biJuA 


:3;;>p-"i    r 


PART  II 

STRENGTH    OF    MATERIALS    AND    STABILITY 
OF   STRUCTURES 


JI  THAS 


Introduction  121 

INTRODUCTION 
EXPLANATION  OF    SUBJECT-MATTER  AND  NOTATION 

1.   Introduction  to  Part  II 

Subject-Matter  of  Part  II.  In  the  twenty-nine  chapters  of  Part  II  are 
given  the  necessary  rules,  formulas  and  data  for  computing  the  strength  and 
stability  of  all  ordinary  forms  of  building-construction,  whether  of  wood,  steel, 
concrete  or  masonry,  and  in  fact  of  all  but  the  more  intricate  problems  of  steel 
construction,  with  which  few  architects  care  to  cope,  and  which,  indeed,  are 
more  especially  within  the  province  of  the  engineer. 

The  Rules  and  Formulas  have  been  reduced  to  their  simplest  forms,  and, 
in  general,  require  only  an  elementary  knowledge  of  mathematics  to  understand 
them.  The  appUcation  of  the  formulas  is  explained  and  in  most  cases  their 
derivation,  and  it  is  believed  that  the  formulas,  constants  and  working  stresses 
are  representative  of  conservative  and  approved  contemporary  practice. 

Constants  and  "Working  Stresses.  In  the  use  of  constants  for  the  strength 
of  materials,  the  authors  and  editors  have  been  guided  by  tlie  practice  of  leading 
structural  engineers,  by  the  available  records  of  tests  and  by  their  own  expe- 
rience of  many  years  as  practicing  and  consulting  architects  and  engineers. 
The  varying  conditions  of  building-construction  have  been  taken  into  account 
and  an  attempt  made  to  adapt  the  values  to  the  practical  conditions  usually 
governing  such  construction.  Every  possible  precaution  has  been  taken  to 
prevent  the  misapplication  of  rules  and  formulas  and  to  insure  absolute  safety 
without  undue  waste  of  materials. 

Tables.  Much  thought  and  labor  have  been  expended  on  the  preparation 
of  the  numerous  tables,  to  insure  their  accuracy  and  to  arrange  them  in  the 
most  convenient  form  for  use  by  architects  and  builders.  Many  of  these  tables 
were  computed  by  the  authors  and  editors,  all  have  been  carefully  verified,  and 
it  is  believed  that  they  may  be  used  with  perfect  confidence.  In  all  cases,  un- 
less otherwise  noted,  they  give  the  same  values  that  would  be  obtained  by 
using  the  formulas  specially  referred  to,  while  they  afford  a  great  saving  of 
time  and  labor  and  reduce  to  a  minimum  the  danger  of  errors  in  making  the 
necessary  computations. 

Treatment  of  the  Subject.  Owing  to  the  nature  of  the  subjects  treated 
and  the  large  number  of  pages  required  to  include  them  all  in  one  book  of  refer- 
ence, some  forms  of  construction,  such  as  foundations,  masonry  and  fire-proof 
construction,  roof-trusses,  etc.,  are  treated  rather  briefly.  The  intention  is  to 
give  the  data  needed  for  immediate  use  rather  than  a  complete  discussion  of 
all  the  principles  involved.  Those  who  wish  a  more  complete  treatise  on  masons* 
work  in  general  are  referred  to  the  ninth  edition  of  Kidder's  Building-Con- 
struction and  Superintendence,  Part  I,  Masons'  Work.*  References  are  made 
in  the  different  chapters  to  various  other  books  and  periodicals  containing  more 
complete  information  on  some  of  the  subjects. 

*  This  has  been  recently  completely  rewritten,  by  Professor  Thomfts  Nolan,  and  the 
data  in  it  supplements  the  matter  of  Kidder's  Pocket-Book.       .ri«»}imi  It.' 


122  Explanation  of  Subject-Matter  and  Notation  Part  2 

2.   Explanation  of  the  Notation  or  Symbols  used  in  Part  II  * 

Besides  the  usual  mathematical  signs  and  characters  in  general  use,  the  fol- 
lowing abbreviations  and  symbols  are  frequently  used: 

A  area  of  cross-section;  also,  a  constant  used  in  Chapter  XVI  and  equal 
to  Ms  the  safe  unit  fiber-stress; 

a,  b,  c,  .  .  .  m,  etc.,  known  or  given  distances; 

b      breadth,  as  of  beams; 

C      coefficient  of  strength; 

c  normal  distance  from  neutral  axis  of  cross-section  of  beam  to  most 
distant  fiber  in  same; 

d      diameter,  as  of  rivets;  exterior  diameter;  depth,  as  of  beams; 

di     interior  diameter; 

E     modulus  of  elasticity; 

Ea,  Ec  modulus  of  elasticity  for  steel  and  concrete  respectively  (as  in  re- 
inforced concrete); 

e       total  deformation  or  change  in  length,  as  in  a  bar; 

F      shearing-modulus  of  elasticity; 

f       maximum  deflection  for  a  beam; 

h      distance  between  parallel  axes  for  moments  of  inertia; 

/       moment  of  inertia  about  a  line; 

I/c  section-modulus  or  section-factor; 

/      polar  moment  of  inertia; 

J'     polar  moment  of  inertia  of  bolts  about  shaft-axis; 

K  total  elastic  resistance  of  a  bar;  resilience,  work;  also,  a  factor  or  con- 
stant used  in  formulas  for  reinforced  concrete; 

/       length;  span  of  a  beam; 

M     bending  moment; 

Afmax     maximum  bending  moment; 

Ml,  Mi,  etc.,  bending  moments  at  supports  of  beams; 

Mr  or  SI /c    moment  of  resistance; 

n      number  of  loads,  spans,  etc.; 

P      external  force;  concentrated  load; 

Pi,  Pi,  Pi,  etc.,  concentrated  loads  on  beams; 

P  pitch  of  rivets;  eccentricity  of  load  on  .column;  ratio  of  cross-section 
of  .steel  to  cross-section  of  beam  (reinforced  concrete); 

r  radius  of  curvature;  radius;  radius  of  gyration;  ratio  of  Ea  for  steel 
to  Ec  for  concrete  (reinforced  concrete); 

R\,  Rf,  Rz,  etc.,  reactions  at  the  supports  of  a  beam; 

S  unit  stress,  with  subscripts  /,  c  and  s  for  unit  stress  in  tension,  com- 
pression and  .shear,  respectively; 

Sh     buckling  resistance  in  webs  of  steel  beams; 

Sh    horizontal  unit  shearing-stress  in  beams; 

Se     elastic  limit; 

Sf    modulus  of  rupture,  or  computed  flexural  strength; 

/i,  h,  etc.,  thicknesses; 

V     vertical  shear; 

W  weight  of  a  bar  or  beam;  total  uniform  load  on  beam  (may  include 
weight  of  beam) ; 

wl     total  uniform  load  on  a  beam  (may  include  weight  of  beam); 

w  weight  of  a  cubic  unit  of  material;  uniform  load  on  beam,  per  lineal 
unit  of  length; 

*  See,  also,  page  3  of  Part  I. 


Explanation  of  the  Notation  or  Symbols  128 

X,  y,  2,  variable  distances; 

a,  /3,  etc.,  material  constants; 

<f>     constant  depending  upon  material; 

6      an  angle. 
Greek  letters  are  used  generally  for  signs  of  operation,  for  abstract  numbers 
and  for  angles.     2  is  employed  as  a  symbol  of  summation. 
The  following  are  the  Greek  letters  most  in  use: 

a  Alpha,  /S  Beta,  e  Epsilon,  rj  Eta, 

0  Theta,  k   Kappa,  X  Lambda,  jj,  Mu, 

V  Nu,  IT  Pi,  p  Rho,  cr  Sigma, 

T  Tau,  <f>  Phi,  xj/  Psi,  w  Omega. 

Note.  In  a  few  places  in  the  book  it  has  been  considered  necessary  or  advis- 
able by  some  of  the  associate  editors  to  give  a  different  meaning  to  one  or 
more  of  the  above  symbols  or  to  introduce  different  symbols  for  the  meanings 
given  in  the  list,  but  in  all  such  cases  the  new  symbols  or  meanings  have  been 
very  clearly  indicated. 

The  term  breadth  is  used  to  denote  the  horizontal  thickness  of  a  beam  or 
the  smaller  dimension  of  the  cross-section  of  a  rectangular  column,  post  or 
strut,  and  is  always  measured  in  inches  unless  expressly  stated  otherwise. 

The  term  depth  denotes  the  vertical  height  of  a  beam  or  girder,  and  is  always 
measured  in  inches  unless  expressly  stated  otherwise. 

The  term  length  denotes  the  distance  between  supports  and  is  always  meas- 
ured in  feet  unless  expressly  stated  otherwise. 

Abbreviations.  In  order  to  shorten  the  formulas,  the  tabulations  of  computa- 
tions, etc.,  and  throughout  the  text  generally,  to  economize  space,  the  units  of 
measurement  are  generally  abbreviated.  For  example,  foot  and  feet  are  abbre- 
viated, ft;  inch  and  inches,  in;  pound  and  pounds,  lb;  square,  sq;  cubic,  cu; 
linear,  lin;  inch-pound  or  inch-pounds,  in-lb;  foot-pound  or  foot-pounds,  ft-lb; 
ounces,  oz;  horse-power,  h.p.;  gallons,  gal;  etc.;  and  no  periods  are  placed  after 
these  abbreviations,  except  at  the  ends  of  sentences.  Where  the  word  ton  is 
used  in  this  volume,  it  always  means  the  net  ton  of  2  ooo  lb. 


124  Terms  Used  in  Arcbitectural  Engineering  Chap.  1 


CHAPTER  I 

EXPLANATION    OF    TERMS  USED  IN  AECHITECTURAL 
ENGINEERING 

By 
THOMAS   NOLAN 

PROFESSOR   OF  ARCHITECTURAL   CONSTRUCTION,    UNIVERSITY   OF   PENNSYLVANIA 

1.   De^nitions  of  Some  of  the  Terms  Used  in  the  Mechanics  of 
Materials  * 

Terms  Used  in  Architectural  Engineering.  The  following  terms  fre- 
quently occur  in  discussions  of  the  principles  of  architectural  engineering  and 
an  understanding  of  their  meaning  is  essential. 

Mechanics  is  the  branch  of  physics  that  treats  of  the  phenomena  caused  by 
the  action  of  forces  on  material  bodies. 

Applied  Mechanics  treats  of  thp  law3  of  mechanics  as  applied  to  construc- 
tion in  the  useful  arts,  as  in  beams,  trusses,  arches,  etc. 

Mechanics  of  Materials  treats  of,  the  jefTects  of  forces  in  causing  changes 
in  the  size  and  shape  of  bodies.        ,  . 

Rest  is  the  relation  that  exists  between  two  points  when  the  straight  line 
joining  them  does  not  change  in  length  or  direction.  A  body  is  at  rest  relatively 
to  a  point  when  any  point  in  the  body  is  at  rest  relatively  to  the  first-mentioned 
point. 

Motion  is  the  relation  that  exists  between  two  points  when  the  straight  line 
joining  them  changes  in  length  or  direction,  or  in  both.  A  body  moves  rela- 
tively to  a  point  when  any  point  in  the  body  moves  relatively  to  the  first-men- 
tioned point. 

Force  is  that  which  changes,  or  tends  to  change,  the  state  of  rest  or  motion 
of  the  body  acted  upon.     It  is  a  cause  regarding  the  essential  nature  of  which  • 
we  are  ignorant.     In  the  mechanics  of  materials  we  do  not  deal  with  the  nature 
of  forces,  but  only  with  the  laws  of  their  action. 

Equilibrium  is  that  condition  of  a  body  in  which  the  forces  acting  upon  it 
balance  or  neutralize  each  other;  or,  it  is  that  condition  of  a  force-system  in 
which  the  resultant  of  the  force-system  is  zero. 

Statics  is  the  branch  of  Mechanics  that  treats  of  the  conditions  of  equilibrium. 
It  is  divided  into:  • 

(i)  Statics  of  rigid  bodies. 

(2)  Statics  of  practically  incompressible  fluids. 

In  building-construction  we  have  to  deal  only  with  the  former. 

Structures  are  artificial  constructions  In  which  all  the  parts  are  intended  to 
be  in  equilibrium  and  at  rest  relatively  to  each  other,  as  in  the  case  of  a  bridge- 
truss  or  roof-truss.  They  consist  of  two  or  more  solid  bodies,  generally  called 
PIECES  or  MEMBERS,  which  are  connected  at  different  parts  of  their  surfaces 
called  JOINTS. 

*  In  addition  to  the  terms  defined  here,  many  others  are  defined  in  the  chapters  of 
OJart  II,  and  especially  in  Chapters  VI,  IX,  X,  XIV,  XV,  XVI,  XX  and  XXIV. 


Definitions  of  Terms  125 

In  general  there  are  three  conditions  of  equilibrium  in  a  structure. 
(i)  The  external  forces  acting  upon  the  whole  structure  must  balance  each 
other.     These  forces  are: 

(a)  The  weight  of  the  structure; 
{b)  The  loads  it  carries; 

(c)  The  upward  supporting  forces,  reactions  or  resistances  under  or  around 
the  foundations. 

(2)  The  forces  acting  upon  each  piece  of  the  structure  must  balance  each 
other.     These  forces  are,  for  each  piece: 

(a)  The  weight  of  the  piece; 

(b)  The  loads  it  carries; 

(c)  The  resistances  or  reactions  at  its  joints. 

(3)  The  forces  acting  upon  each  of  the  parts  into  which  any  piece  may  be 
supposed  to  be  divided  must  balance  each  other. 

The  Stability  of  a  Structure  requires  the  fulfilment  of  conditions  (i)  and 
(2),  that  is,  the  abihty  of  the  structure  to  resist  the  displacement  of  any  of  its 
parts. 

The  Strength  of  a  Piece  or  Member  consists  in  the  fulfilment  of  condi- 
tion (3),  that  is,  the  ability  of  a  piece  to  resist  breaking. 

The  Stiffness  of  a  Piece  or  Member  consists  in  the  ability  of  a  piece  to 
resist  bending. 

The  Theory  of  Structures  is  divided  into  two  parts:  /  , 

(i)  That  which  treats  of  strength  and  stiffness,  dealing  only  with  single 

pieces  and  generally  known  as  the  strength  of  materials  or  the  mechanics 

OF  materials,  before  defined. 

(2)  That  which  treats  of  stability,  dealing  with  the  structures  themselves. 

Stress  is  an  internal  force  that  resists  a  change  in  shape  or  size  caused  by 
external  forces.  When  the  applied  external  forces  reach  certain  intensities 
the  internal  stresses  hold  them  in  equilibrium. 

The  Intensity  of  a  Stress  is  measured  by  the  unit  stress,  (See  Unit 
Stress.)  The  intensity  of  the  stress  per  square  inch  on  any  normal  surface 
of  a  solid  is  the  total  stress  divided  by  the  area  of  the  section  in  square  inches. 
Thus,  if  a  bar  10  ft  long  and  2  in  square  has  a  load  of  8  000  lb  pulling  in  the 
direction  of  its  length,  the  stress  on  any  normal  section  of  the  bar  is  8  000  lb; 
and  the  intensity  of  the  stress  per  square  inch  is  8  000  lb/4  sq  in  =  2  000  lb  per 
sq  in. 

Deformation.*  When  a  solid  body  is  acted  upon  by  an  external  force  an 
alteration  takes  place  in  the  volume  and  shape  of  the  body,  and  this  alteration 
is  called  the  deformation.  In  the  case  of  the  bar  given  above,  the  deformation 
is  the  amount  that  the  bar  stretches  under  its  load. 

The  Ultimate  Strength  is  the  highest  unit  stress  a  piece  of  material  can 
sustain  and  it  is  the  unit  stress  at  or  just  before  rupture. 

The  Working  Unit  Stress  is  the  ultimate  stress  divided  by  the  factor  of 
safety . 

The  Safe  Load  is  the  load  that  a  piece  can  support  without  exceeding  the 
working  unit  stresses. 

*  In  mechanics  the  term  strain  is  now  synonymous  with  the  term  deformation.  On 
account  of  the  tendency  to  confuse  the  terms  strain  and  stress  the  term  deformation, 
is  used  to  denote  change  in  shape  and  the  term  strain  is  omitted  in  all  discussions  in  the 
Pocket-Book. 


126  Terms  used  in  Architectural  Engineering  Chap.  1 

The  Factor  of  Safety  *  of  a  piece  of  material  under  stress  is  the  ratio  of 
the  ultimate  strength  of  the  material  to  the  actual  unit  stress  on  the  section- 
area;  or  it  is  the  number  by  which  the  ultimate  unit  stress  must  be  divided  to 
give  the  working  unit  stress.  In  designing  a  piece  of  material  to  sustain  a  cer- 
tain load,  it  is  required  that  it  shall  be  perfectly  safe  under  all  circumstances; 
and  hence  it  is  necessaj*y  to  make  an  allowance  for  any  defects  in  the  material, 
workmanship,  etc.  It  is  obvious,  that,  for  materials  of  different  composition, 
different  factors  of  safety  are  required.  Thus,  steel  being  more  homogeneous 
than  wood  and  less  Hable  to  defects,  does  not  require  as  high  a  factor  of  safety. 
Again,  different  kinds  of  stresses  require  different  factors  of  safety.  Thus,  a 
long  wooden  column  or  strut  requires  a  higher  factor  of  safety  than  a  wooden 
beam.  As  the  factors  of  safety  thus  vary  for  different  kinds  of  stresses  and 
materials,  the  proper  factors  for  the  different  kinds  of  stresses  and  conditions  are 
given  in  considering  the  resistance  of  the  various  materials  to  those  stresses 
under  varying  conditions. 

The  Unit  Stress  is  the  stress  on  a  unit  of  section-area,  and  is  usually  expressed 
in  pounds  per  square  inch.     (See  Intensity  of  Stress.) 

Dead  Loads  and  Live  Loads.  The  term  dead  load  means  a  load  that  is 
applied  and  increased  gradually  and  that  finally  remains  constant,  such  as  the 
weight  of  a  structure  itself. 

The  term  live  load  means  a  load  that  is  applied  suddenly  and  causes  vibra- 
tions, such  as  a  train  traveling  over  a  railway  bridge.  It  has  been  found  by 
experience  that  the  effect  of  a  live  load  on  a  beam  or  other  piece  of  material 
has  twice  the  destructive  tendency  of  a  dead  load  of  the  same  magnitude  or 
intensity.  Hence  a  piece  of  material  designed  to  carry  a  live  load  should  have 
a  factor  of  safety  twice  as  large  as  one  designed  to  carry  a  dead  load.  The 
load  due  to  a  crowd  of  people  walking  on  a  floor  is  usually  considered  to  produce 
an  effect  which  is  a  mean  between  that  of  a  dead  load  and  a  live  load,  and  a 
suitable  factor  of  safety  is  adopted  accordingly.  In  municipal -ordinances  and 
laws  relating  to  the  allowable  loads  for  floors,  the  loads  to  be  supported  by  the 
floors,  exclusive  of  their  inherent  construction  and  stationary  fixtures,  are  gen- 
erally referred  to  as  the  live  loads  no  matter  of  what  they  may  consist;  but 
the  term  does  not  have  the  exact  significance  given  to  it  by  many  engineers 
and  as  explained  in  the  paragraph  above. 

The  Modulus  of  Rupture  or  Computed  Flexural  Strength  is  the  value 
of  the  UNIT  fiber-stress  S,  computed  from  the  flexure-formula  M  =  Sl/c, 
when  a  beam  is  ruptured  under  a  transverse  load.  Its  value  is  intermediate 
between  the  ultimate  tensile  and  compressive  strengths  of  a  material. 

The  Elastic  Limit  is  that  unit  stress  at  which  the  deformation  of  a  piece  of 
material  begins  to  increase  in  a  faster  ratio  than  the  applied  loads.  It  is 
sometimes  called  the  elastic  strength. 

The  Modulus  of  Elasticity  or  Coefficient  of  Elasticity.  In  treatises 
on  physics  this  is  often  called  Young's  modulus.  It  we  take  a  bar  of  any  elastic, 
material,  say  one  inch  square,  of  any  length,  and  secured  at  one  end,  and  to  the 
other  apply  a  force,  say  a  certain  number  of  pounds  P,  pulling  in  the  direction 

*  The  ELASTIC  LIMITS  of  materials  must  be  considered  in  deciding  upon  working  unit 
stresses  and  in  forming  a  judgment  of  the  security  of  materials  under  stress.  When  the 
elastic  limit  is  considered  the  actual  allowable  unit  stress  is  made  a  certain  percentage  of 
'it,  as  35  or  50%,  according  to  varying  conditions.  Both  ultimate  strengths  and  elas- 
tic limits  must  be  taken  into  account  in  practice.  But  the  use  of  the  factor  of  safkty, 
as  determined  by  the  old  method,  is  still  a  great  help  in  the  study  and  application  of 
the  principles  of  the  mechanics  of  materials,  and  is  used  frequently  in  the  Pocket-Book. 


Classification  of  the  Principal  Stresses  127 

)l"  ii  s  length,  we  shall  find  by  careful  measurement  that  the  bar  has  been  stretched 
1  elongated  by  the  action  of  the  force.  If  we  divide  the  total  elongation  e, 
1  inches,  by  the  original  length  /  of  the  bar,  in  inches,  we  shall  have  cjl,  the 
;  .n  ELONGATION  €,  or  the  elongation  of  the  bar  per  unit  of  length;  and  if  ,we 
J i vide  the  unit  stress  S,  developed  (that  is,  in  this  case,  the  external  force  P, 
divided  by  the  area  of  the  cross-section  A,  or  P I  A)  by  this  ratio  we  shall  have 
what  is  known  as  the  modulus  of  elasticity,  E.      Expressed  in  symbols  and 

rj  A 

by  equations,  E  =  Sle  =  — r—.     Hence,  we  may  define  the  modulus  of  elas- 

ejl 

ticity  as  the  ratio  of  the  unit  stress  to  the  unit  deformation.  Another  definition 
is,  the  force  which  would  elongate  a  bar  of  i  sq  in  in  cross-section  to  double  its 
original  length,  if  that  could  be  done  without  exceeding  the  elastic  limit 
of  the  material.  This  is  evident  from  the  above  equation;  for  if  ^  =  i  and 
e=  I,  E  will  equal  P.  These  formulas  apply  only  when  the  unit  stress  S  or  P/A 
is  less  than  the  elastic  limit  of  the  material,  e  is  an  abstract  number, 
because  e  and  /  are  both  linear  quantities,  and  hence  E  is  expressed  in  the  same 
unit  as  S,  that  is,  in  pounds  per  square  inch. 

As  an  example  of  one  method  of  determining  the  modulus  of  elasticity  of  any 
material  the  following  illustration  is  given:  ^ 

Suppose  we  have  a  bar  of  wrought  iron,  2  in  square  and  lo  ft  long,  securely 
fastened  at  one  end,  and  to  the  other  end  we  apply  a  tensile  force  of  40  000  lb. 
This  force  causes  the  bar  to  stretch,  and  by  careful  measurement  we  find  the 
elongation  to  be  0.0414  in.  As  the  bar  is  10  ft,  or  120  in  long,  if  we  divide 
0.0414  by  120,  we  shall  have  the  elongation  of  the  bar  per  unit  of  length.  Per- 
forming this  operation,  we  have  as  the  result,  0.00034  in.  As  the  bar  is  2  in 
square,  the  area  of  cross-section  is  4  sq  in,  and  hence  the  stress  per  square  inch 
is  TO  000  lb.  Dividing  10  000  by  0.00034,  we  have,  as  the  modulus  of  elas- 
ticity of  the  bar,  29  400  000  lb  per  sq  in.  This  is  the  method  generally  employed 
to  determine  the  modulus  of  elasticity  of  iron  ties;  but  E  can  also  be  deter- 
mined from  the  deflection  of  beams,  and  it  is  in  that  way  that  its  values  for 
most  woods  have  been  found.  The  modulus  of  elasticity  is  used  in  the  deter- 
mination of  the  stiffness  of  beams. 

The  Moment  of  a  Force  with  respect  to  an  axis  is  the  product  obtained 
by  multiplying  the  magnitude  of  the  force  by  the  shortest  distance  from  the 
axis  to  its  line  of  action.  The  shortest  distance  is  called  the  lever-arm  of 
the  force.  The  moment  of  the  force  is  the  measure  of  the  tendency  of  the  force 
to  cause  rotation  about  the  axis.     (See  Chapter  VI  and  IX.) 

The  Center  of  Gravity  of  a  body  is  the  point  in  the  body  through  which 
the  resultant  of  the  forces  exerted  by  gravity  upon  all  the  particles  of  the 
body  passes.  A  body  may  be  balanced  upon  a  point  placed  above  or  below 
the  center  of  gravity,  because  the  resultant  of  any  number  of  forces  may  be 
held  in  equilibrium  by  an  equal  and  opposite  force.  Another  definition  of  the 
center  of  gravity  of  a  body  or  bodies  is:  a  point  such  that  there  is  no  tend- 
ency TO  rotation  about  any  axis  drawn  through  it.  (For  center  of  gravity 
of  surfaces,  lines  and  solids,  see  Chapter  VI.) 

2.    Classification  of  the  Principal  Stresses  Caused  in  Bodies  by 
External  Forces 

Tension  is  the  stress  that  resists  the  tendencj^of  two  forces  acting  away  from 
each  other  to  pull  apart  two  adjoining  planes  of  a  body. 

Compression  is  the  stress  that  resists  the  tendency  of  two  forces  acting  toward 
each  other  to  push  together  two  adjoining  planes  of  a  body. 


128  Terms  Used  in  Architectural  Engineering  Chap.  1 

Shear  is  the  stress  that  resists  the  tendency  of  two  equal  parallel  forces  act- 
ing in  opposite  directions  to  cause  two  adjoining  planes  of  a  body  to  slide  one 
on  the  other. 

Torsion  is  the  stress  that  resists  the  tendency  of  forces  to  twist  a  body. 

Combined  Stresses.  Parts  of  structures  are  often  acted  upon  by  several 
external  forces  which  develop  stresses  of  different  character,  such  as  combined 
flexure  and  compression,  flexure  and  tension,  flexure  and  torsion,  shear  and  axial 
compression  or  tension,  torsion  and  compression,  etc. 


General  Requirements  129 


CHAPTER    II 

FOUNDATIONS 

By 
DANIEL  E.  MORAN 

MEMBER  0F_  AMERICAN   SOCIETY  OF    CIVIL  ENGINEERS 

1.   Definition  of  the  Word  and  Terms  Used 

Definitions.  The  word  Foundation  is  derived  from  the  Latin  verb  fundare 
meaning  to  establish  or  lay  the  base,  bottom,  keel  or  foundation  of  anything. 
The  English  word  is  used  in  the  broadest  possible  way  to  describe  the  base, 
physical  or  otherwise,  on  which  anything  is  supported,  and  in  technical  language 
it  may  be  used  to  describe  any  part  of  a  structure  on  which  a  subsequent  oper- 
ation or  construction  is  superimposed.  Thus  a  plaster  wall  may  be  called  the 
foundation  for  a  fabric  to  be  stretched  thereon  and  the  fabric  in  turn  becomes 
the  foundation  for  various  coats  of  paint  or  other  decorations.  More  specifi- 
cally and  in  relation  to  a  building  or  other  complete  structure  the  word  founda- 
tion is  unfortunately  applied  indiscriminately  (i)  to  construction  below  grade, 
such  as  footing  courses,  cellar  walls,  etc.,  forming  the  lower  section  of  the  struc- 
ture; (2)  to  the  natural  material,  the  particular  part  of  the  earth's  surface  on 
which  the  construction  rests;  and  (3)  to  special  construction  such  as  piling  or 
piers  used  to  transmit  the  loads  of  the  building  to  firm  substrata.  In  view  of 
the  indefinite  meaning  of  the  word  it  is  advisable  to  use  it  either  to  distinguish 
work  below  grade,  or  below  the  tier  of  beams  nearest  to  grade,  from  work  above 
grade.  In  even  a  still  more  restricted  sense,  it  might  include  only  the  work 
below  the  cellar  or  basement-floor  to  rock  or  other  solid  foundation-bed. 
(See  Chapter  II,  Subdivision  29,  Chapter  III,  Subdivision  2,  and  Water- 
proofing for  Foundations,  Part  III.) 

The  Foundation-Bed.  The  natural  material  on  which  the  construction 
rests  is  called  the  foundation-bed.  Walls,  piers  and  columns  below  grade 
are  called,  in  general,  foundation  walls,  piers  and  columns  to  distinguish 
them  from  similar  construction  above  grade  and  occasionally  those  only 
below  the  basement-floor  are  so  called;  the  lower  portions  of  walls,  piers  or 
columns  which  are  spread  to  provide  a  safe  base  will  be  called  footing  courses. 

2.   General  Requirements 

The  Object  of  Foundations.    The  object  to  be  borne  in  mind  in  designing 

any  foundation  is  to  provide  a  safe  and  permanent  base  for  the  superstructure 
such  that  the  movement  of  the  base  and  of  the  superimposed  structure  shall  be 
the  least  possible  and  shall  result  in  the  least  possible  damage  to  the  structure. 
To  fully  meet  the  above  requireiAents  the  design  and  construction  should  ful- 
fill the  following  conditions: 

(i)  The  Materials  of  Construction  should  be  proof  against  all  deteriorating 
influences,  or,  if  any  of  the  materials  arc  liable  to  deterioration  they  should  be 
permanently  protected. 

(2)  Stresses  and  Future  Changes.  No  part  of  the  foundation-structure 
should,  under  any  combination  of  loadings,  be  stressed  beyond  safe  limit*,  and 
the  possibility  of  future  additions  or  changes  in  the  superstructure,  or  of  a  change 
in  the  use  of  the  building,  should  be  kept  in  mind. 


130  Foundations  Chap.  2 

(3)  The  Load  on  the  Natural  Bed  should  be  kept  within  the  safe  limit  for  such 
*naterial,  under  the  worst  conditions  to  which  it  may  be  exposed.  In  fixing 
this  limit  the  amount  of  settlement  allowable  will  in  many  cases  determine  the 
limit  rather  than  the  safe  ultimate  bearing  capacity. 

(4)  Adjoining  Excavations.  The  possible  danger  to  the  structure  or  to  the 
stability  of  the  foundation-bed  from  adjoining  excavations  or  other  disturbing 
causes  should  be  guarded  against  as  far  as  possible. 

Physical  Conditions  of  the  Site.  In  order  to  meet  the  above  requirements, 
the  design  should  be  suited  to  the  physical  conditions  existing  at  the  location. 
The  architect  or  engineer  should  personally  examine  the  site.  He  should  secure 
all  available  information  relative  thereto  and,  if  necessary,  should  make  borings 
and  tests  so  as  to  secure  reliable  information  on  which  to  base  his  design  for  the 
foundation.  The  first  step  is,  therefore,  a  detailed  and  exhaustive  study  of  the 
«ite  to  determine  the  characteristics  of  the  foundation-bed  on  which  the  struc- 
ture is  to  rest. 

3.    Geological  Considerations 

Character  of  the  Foundation-Bed.  A  knowledge  of  geology  is  of  material 
assistance  in  many  cases  in  making  a  proper  estimate  of  the  character  of  the 
foundation-bed.  While  it  is  not  proposed  in  the  hmits  of  this  chapter  to  go  into 
any  general  geological  discussion  the  following  notes  may  be  of  value  in  assisting 
the  architect  to  determine  whether  any  given  deposits  can  be  rehed  upon  as 
affording  a  stable  foundation-bed.  Broadly  speaking,  as  the  location  of  the 
building  may  be  in  any  part  of  the  world,  so  the  materials  encountered  may 
belong  to  any  one  of  the  many  geological  formations  forming  the  surface  of  the 
earth.  For  practical  purposes,  however,  the  materials  met  with  are  roughly 
divided  into  rock,  or  materials  other  than  rock,  roughly  defined  as  earth. 

4.   Composition  and  Classification  of  Rocks 

Composition  of  Rocks.  Rocks,  and  the  earthy  deposits  derived  from  rocks, 
>ire  composed  of  various  minerals  of  which  many  hundred  kinds  are  known, 
each  varying  from  the  others  in  some  particular  of  chemical  composition,  form 
of  crystallization  or  other  characteristic.  A  rock  or  an  earthy  deposit  may  con- 
sist almost  entirely  of  a  single  mineral,  but  it  is  usually  composed  of  several 
distinct  minerals  or  of  mixtures  of  minerals.  The  principal  classes  of  rock- 
forming  minerals  are: 

(i)  The  Silica  Minerals,  composed  of  silica  (Si02)  in  different  forms; 

(2)  Silicates  or  combinations  of  silica,  with  various  metallic  bases;   • 

(3).  Calcareous  Minerals  composed  of  calcite  or  carbonate  of  lime  (CaCOs) 
and  its  combinations. 

(i)  Silica  Minerals  are  different  forms  of  the  oxide  of  silicon,  Igiown  as 
Silica.    In  the  crystalline  state  silica  is  known  as 

Quartz.  This  is  the  most  abundant  of  all  Vninerals.  Owing  to  its  hardness 
and  insolubihty  it  resists  decomposition  and  abrasion  better  than  the  minerals 
with  which  it  is  associated  and  grains  of  it  form  the  principal  constituent  of 
sandy  deposits.  In  finely  comminuted  particles  it  forms  a  part  of  most  of  the 
clays. 

Flint,  Chert,  Agate,  etc.,  are  non-crystalline  varieties  of  silica.  Silica  also 
forms  the  cementing  material  in  many  sandstones  and  other  rocks. 

(2)  Silicates  or  combinations  of  silica  with  various  bases  are  second  in  im- 
portance only  to  quartz. 


Composition  and  Classification  of  Rocks  131 

Feldspar,  an  important  constituent  of  granite  and  other  igneous  rocks,  is  a 
silicate  of  alumina  with  potash,  soda  or  lime.  When  exposed  to  the  action  of 
water  it  slowly  decomposes,  forming  silicate  of  alumina,  the  base  of  clay.  The 
decomposition  of  granite  results  in  the  formation  of  clay  and  crystals  of  quartz 
and  mica.  The  mica  is  very  slowly  affected  and  the  quartz  is  practically  un- 
changed. 

Mica.  The  various  mica  minerals  are  silicates  of  alumina,  with  potash  and 
other  constituents.  All  varieties  are  soft  and  spUt  into  thin  elastic  plates. 
Small  particles  of  mica  are  frequently  found  in  sand. 

Hornblende  and  Augite  are  sihcates  of  lime,  magnesia,  iron  and  alumina  and 
are  of  frequent  occurrence. 

Chlorite,  Talc  and  Soapstone  Travertine  are  hydrated  silicates  formed  from 
other  silicates  by  a  chemical  change  in  which  a  certain  amount  of  water  is 
absorbed.  These  minerals  are  soft  and  have  a  soapy  feel.  Special  care  should 
be  taken  in  building  foundations  on  rock  of  this  character  to  guard  against  any 
sliding  on  the  foundation-bed  or  between  parts  of  the  foundation-bed. 

(3)  Calcareous  Minerals.  The  following  are  the  principal  calcareous  miner- 
als: 

Calcite  (CaCOs),  carbonate  of  lime,  when  pure  and  crystallized,  is  known  as 
Iceland  Spar.  It  is  soluble  in  water  containing  CO2.  Calcite  in  varying  de- 
grees of  purity  forms  limestone  and  marbles.  As  a  result  of  its  solubihty 
caverns  and  voids  are  frequently  found  in  limestone. 

Dolomite  is  a  carbonate  of  lime  and  magnesia.  It  forms  the  so-called  Dolo- 
MiTic  Limestones,  which  are  less  soluble  than  the  calcite  hmestone. 

Selenite,  Gypsum,  Alabaster,  Anhydrite,  Aragonite  and  Apatite  are  other  and 
less  important  lime-minerals. 

Classification  of  Rocks.  Rocks  are  classified  not  only  according  to  the 
minerals  of  which  they  are  composed,  but  also  according  to  the  way  in  which 
they  have  been  formed,  as: 

(i)  Igneous  Rocks,  which  have  soHdified  from  a  molten  condition; 

(2)  Sedimentary  Rocks,  which  have  been  formed  under  water  by  mechani- 
cal pressure  or  by  cementation  due  to  chemical  or  organic  proceesses; 

(3)  Metamorphic  or  Plutonic  Rocks,  which  have  changed  from  their  original 
character  as  igneous  or  sedimentary  rocks. 

(i)  Igneous  or  Plutonic  Rocks  are  not  truly  stratified.  They  may  be 
granular,  crystalline  or  glassy  in  texture.  Granite,  syenite,  basalt,  trap,  etc., 
are  examples.  Lava,  pumice  and  obsidian  are  volcanic  products,  as  are  also 
certain  deposits  of  mud  and  ash.  With  the  exception  of  volcanic  ash  and  mud, 
the  igneous  rocks  are  enduring  and  are  not  liable  to  present  any  unforeseen  weak- 
ness as  foundation-beds. 

(2)  Sedimentary  Rocks  are  composed  of  sand,  clay  and  other  materials 
resulting  from  the  breaking  down  of  the  original  igneous  rocks.  These  materials 
were  deposited  in  horizontal  beds  generally  by  settling  from  water,  and  the  con- 
solidation into  rock  was  generally  affected  under  water  by  chemical,  mechanical 
or  organic  action.  The  resultant  rock-masses  are  stratified  as  a  result  of  their 
constituent  materials  having  been  deposited  in  layers.  As  sand  and  clay  are 
the  most  abundant  products  of  rock-decomposition,  so  the  sedimentary  rocks 
are  most  frequently  siliceous  (sandy)  or  argillaceous  (clayey). 

Sandstone  is  composed  of  grains  of  sand  cemented  together  by  silica,  oxides 
of  iron,  or  carbonate  of  lime.    The  durability  of  sandstone  depends  on  the  solu!» 


132  Foundations  Chap.  2 

bility  of  the  cementing  material.  Carbonate  of  lime  being  soluble,  sandstones 
containing  it  as  cementing  material  yield  to  the  weather  and  are  not  as  reliable 
as  sandstones  having  silica  or  iron  oxide  as  cementing  material. 

Argillaceous  Rocks  contain  clay  with  fine  sand,  mud,  etc.,  and  while  shale  and 
some  other  varieties  are  compact  and  hard  when  first  uncovered,  they  are  liable 
to  deterioration  when  exposed  to  frost,  water  and  other  disintegrating  agencies. 

Limestone  is  composed  more  or  less  of  carbonate  of  lime  derived  from  the 
calcareous  skeletons  of  marine  animal  and  vegetable  organisms.  The  char- 
acter of  limestone  varies  greatly.  In  so-called  fossiliferous  limestones, 
fossils  of  shells  or  corals  indicate  clearly  its  origin,  but  in  other  Hmestones  there 
are  no  fossils  or  other  indications  of  the  organic  origin  of  the  calcareous  material. 
Admixtures  of  sand,  clay,  or  other  impurities  may  make  it  difficult  to  distinguish 
certain  limestones  from  sandstones  or  shales. 

Dolomite  is  a  limestone  containing  a  high  percentage  of  magnesia. 

Hydraulic  Limestone  is  a  limestone  containing  clay. 

Chalk  is  a  soft  limestone  composed  of  the  fine  shells  of  minute  marine  organ- 
isms. In  general,  the  purer  the  limestone  the  more  soluble  it  is  and  the  greater 
the  danger  from  fissures  or  caverns  due  to  the  action  of  water. 

(3)  Metamorphic  or  Plutonic  Rocks  are  rocks  which  have  been  formed 
from  sedimentary  or  igneous  rocks  by  heat,  compression,  or  moisture,  acting 
alone  or  in  combination.  Thus  by  heat  from  a  nearby  intrusion  of  molten  rock, 
limestone  is  changed  into  a  crystalline  marble.  The  general  effect  of  meta- 
MORPHISM  is  to  produce  a  hard  or  durable  rock. 

Quartzite,  a  metamorphosed  sandstone,  is  a  crystalline  rock  of  great  hardness 
and  durability. 

Slate  is  a  hard  dense  rock,  sometimes  with  a  well-defined  tendency  to  split  into 
thin  plates.  It  has  been  formed  by  metamorphic  action  from  clayey  shales  and 
is  generally  durable,  but  liable  to  slide  along  planes  which  are  sometimes  par- 
allel to  the  cleavage,  or  along  seams  which  are  not  parallel  to  the  cleavage. 

Gneiss  is  a  "laminated  metamorphic  rock  that  usually  corresponds  mlner- 
alogically  to  some  one  of  the  plutonic  types."  *  There  are  many  varieties,  best 
classified  in  accordance  with  the  igneous  rocks  to  which  they  most  nearly  corre- 
spond in  composition.  Some  varieties  resemble  granite,  but  the  laminated  or 
striped  aspect  is  generally  characteristic.  They  are  generally  compact  and 
durable. 

Schists  are  similar  to  gneiss  but  are  more  finely  foliated  or  striped.  In  mica- 
schist  there  are  layers  or  foliations  composed  of  fine  grains  or  plates  of  mica. 
Mica-schists  are  liable  to  decomposition  and  it  frequently  happens  that  excava- 
tions have  to  be  carried  to  great  depths  through  decomposed  rock  of  this  char- 
acter before  solid  rock  is  encountered.  The  material  resulting  from  the  decom- 
position of  this  rock  contains  fine  grains  of  mica  and  other  fine  material  and, 
when  wet,  acts  as  quicksand. 

Rock  as  a  Foundation.  All  rock,  if  sound  and  not  liable  to  slippage,  is 
proverbially  a  solid  foundation  and  capable  of  supporting  any  weight  which  a 
building  is  likely  to  impose  on  it.  Care  should  be  taken  that  rock  liable  to 
disintegration  is  protected  from  the  weather,  water-action,  or  other  disintegrat- 
ing influences. 

5.    Geology  of  Earthy  Material 

Earth  and  Soil.  Materials  other  than  rock,  resulting  from  the  disintegra- 
tion of  rock-masses,  are  broadly    classed  as  earth.    The  word  soil,  when  used 

*  Kemp. 


Geology  of  Earthy  Matenal  133 

to  designate  any  earthy  material  not  rock,  is  a  misnomer,  in  that  the  idea  oi 
FERTILITY,  or  the  lack  of  it,  is  conveyed  when  the  word  soil  is  used. 

The  agencies  producing  the  disintegration  of  the  rock  masses  which  form  or 
underlie  the  entire  surface  of  the  earth,  are  various,  but  for  the  purpose  of  this 
chapter  they  may  be  defmed  as  (i)  chemical  and  (2)  mechanical. 

(i)  Chemical  Agencies.  By  chemical  action  or  decomposition,  a  rock- 
mass  of  great  strength  and  hardness  and  of  complicated  mineralogical  structure 
may  disintegrate  into  a  noncoherent  mass  of  elementary  minerals.  Thus  a 
f  eldspathic  granite  under  the  combined  action  of  water  and  varying  temperature 
disintegrates,  the  crystals  of  feldspar  changing  chemically  and  forming  the 
hydrated  silicate  of  aluminum  known  as  clay,  while  the  crystals  of  quartz, 
mica  or  hornblende,  being  more  resistant  to  chemical  action,  retain  their  chem- 
ipal  identity  but  become  detached  particles  of  sand. 

(2)  Mechanical  Agencies.  By  the  mechanical  agencies,  such  as  the  action 
of  frost,  moving  water  or  ice,  fragments  of  rock  are  detached  from  the  ledge  of 
which  they  originally  formed  part  and  are  subsequently  transported,  by  the 
action  of  glaciers  or  streams,  or  by  the  wave-action  in  bodies  of  water.  The 
attrition  between  the  materials  thus  roughly  thrown  about  breaks  up  the  rock- 
masses  into  smaller  and  smaller  pieces  without  altering  the  composition  of  the 
rock-material. 

Flowing  Water,  As  flowing  water  more  readily  transports  small  particles 
than  large  ones,  the  larger  pieces  of  rock  move  intermittently  during  periods  of 
storm  or  flood  and  are  deposited  as  soon  as  the  velocity  of  the  water  falls;  while 
the  smaller  particles  are  held  in  suspension  longer  and,  as  the  velocity  of  the 
stream  falls,  are  deposited  in  the  order  of  their  size,  the  largest  first.  The 
rapid  upper  courses  of  streams  and  rivers  in  mountainous  regions  constantly  roll 
and  grind  together  the  materials  in  their  rocky  beds,  the  heavy  masses  being 
moved  slowly.  The  attrition  between  the  fragments  forms  gravel  and  sand 
which  are  washed  down  stream  to  be  deposited,  as  the  current  slackens,  first  as 
BEDS  of  gravel,  then  as  sand-bars,  and  finally,  in  the  slow-moving  lower 
levels,  as  beds  of  silt  and  alluvium. 

Glaciers  and  Glacial  Deposits.  The  action  of  glaciers  is  similar  to  the  ac- 
tion of  streams.  Glacial  deposits,  the  so-called  glacial  drifts,  are  composed 
of  sand,  clay,  gravel  and  boulders  but,  in  general,  there  is  a  noticeable  differ- 
ence between  glacial  deposits  and  deposits  made  by  rivers  or  streams.  In  glacial 
deposits  the  boulders  frequently  exhibit  groovings  or  scratches  on  their  faces 
and  the  edges  and  surfaces  of  the  boulders  are  generally  sharp,  so  that  a 
boulder  may  appear  as  if  it  had  been  recently  fractured.  They  rarely  exhibit 
the  smooth,  water-worn  and  rounded  surfaces  found  on  boulders  formed  by 
water-action.  Moreover,  the  glacial  boulders  may  be  found  singly,  or  unas- 
sociated  with  other  boulders  in  a  deposit  of  sand  or  gravel.  The  deposit  differs 
from  a  river-deposit  in  that  there  is  no  classification  as  to  size;  the  boulders  may 
occur  on  the  surface  or  may  be  disseminated  as  if  by  accident  through  the  sand 
and  gravel  forming  the  body  of  the  deposit.  Such  glacial  deposits  partake  of 
the  character  of  a  rough  artificial  fill  without  the  stratification  or  classification 
as  to  size  which  is  characteristic  of  river-deposits.  In  glacial  moraines  or  dump- 
ing grounds  it  not  infrequently  happens  that  the  surface-water  finds  underground 
passages  forming  so-called  sink-holes.  A  line  of  glacial  deposits  extends  across 
the  continent  of  North  America  from  Long  Island  westward.  The  southern 
limits  can  be  determined  by  reference  to  geological  maps. 

Glacial  and  River-Deposits  Distinguished.  It  is  important  to  distinguish 
between  glacial  and  river-deposits,  because,  while  the  occurrence  of  glacial 
boulders  gives,  in  general,  little  or  no  information  as  to  the  character  and  value 


134  Foundations  Chap.  2 

of  the  surrounding  deposits,  the  occurrence  of  boulders,  on  the  other  hand,  in 
river-deposits  is  generally  an  indication  that  the  bed  of  which  they  form  a  part 
has  been  thoroughly  consohdated  as  a  result  of  the  river-action  which  formed  it; 
and,  also,  because  such  deposits  generally  extend  down  to  rock  or  to  some  com- 
pact material  which  at  the  time  the  deposit  was  made  was  capable  of  resisting 
the  action  of  rapidly  flowing  water. 

Wave-Action  on  Lakes  and  Along  Coast-Lines  is  constantly  working  on 
the  materials  composing  the  beach.  Rock-masses  are  broken  away  from  cliffs 
and  ground  together,  producing  boulders,  gravel  and  sand.  The  sand,  being 
carried  more  readily  by  the  tidal  currents,  is  deposited  in  the  more  sheltered  loca- 
tions and  forms  beaches,  while  the  larger  rock-masses  remain  near  the  point 
of  origin  in  bars  and  reefs. 

Beds  of  Sand,  Gravel  and  Boulders  deposited  by  the  action  of  waves  oh 
the  shores  of  seas  or  lakes  are  not  necessarily  constant  in  character  and  tests 
should  be  made  to  determine  the  character  of  the  material  underlying  such 
BEACH-FORM^VTiONS.  In  large  river-valleys  where  the  general  formation  is 
composed  of  silt  or  other  fine  material  little  reliance  should  be  placed  on  the 
occurrence  of  beds  of  gravel,  even  if  such  beds  extend  over  large  areas.  Tests 
should  be  made  to  determine  that  such  beds  are  not  underlain  by  less  trust- 
worthy materials.  Where  tributary  streams  discharge  into  large  valleys  they 
may  deposit  bars  of  sand,  gravel  and  boulders  on  top  of  the  silt,  peat,  or 
other  materials  formerly  deposited  by  the  main  river.  (See  page  136.)  The 
general  topographical  conditions  should  serve  as  an  indication  of  danger  in  such 
cases. 

Results  of  Chemical  and  Mechanical  Action.  As  a  result  of  the  fore- 
going brief  description  of  the  agencies  at  work  it  may  be  seen  that  ice,  wave 
and  stream-action  ahke  tend  to  disrupt  rock-masses  and  to  produce  boulders, 
gravel,  sand  and  finer  materials.  The  ultimate  result  of  the  combination  of 
chemical  action  and  mechanical  action  is  to  reduce  the  hardest  rocks  to  the 
finest  sand,  the  most  impalpable  clays,  silts  and  muds;  and  the  action  of  wind, 
wave  and  moving  water  is  to  classify  such  materials  in  deposits  of  grains  of 
uniform  size. 

6,    Materials  Composing  Foundation-Beds 

Classification  and  Definitions.  The  following  list  includes  the  materials 
which  are  most  frequently  encountered,  with  their  definitions. 

Rock  (solid  rock,  bed-rock,  or  ledge).  Undisturbed  rock-masses  forming  an 
undisturbed  part  of  the  original  rock-formation. 

Decayed  Rock  (rotten  rock).  Sand,  clays  and  other  materials  resulting 
from  the  disintegration  of  rock-masses,  lacking  the  coherent  qualities  but 
occupying  the  space  formerly  occupied  by  the  original  rock. 

Loose  Rock.  Rock-masses  detached  from  the  ledge  of  which  they  originally 
formed  a  part. 

Boulders.  Detached  rock-masses  larger  than  gravel,  generally  rounded  and 
worn  as  a  result  of  having  been  transported  by  water  or  ice  a  considerable  dis- 
tance from  the  ledges  of  which  they  originally  formed  a  part. 

Gravel.  Detached  rock-particles,  generally  water-worn,  romided  and  inter- 
mediate in  size  between  sand-particles  and  boulders. 

Sand.  Non-coherent  rock-particles  smaller  than  H  in  in  maximum  dimen- 
sion. 


Characteristics  of  the  Materials  of  Foundation-Beds  135 

Clay.     The  material  resulting  from  the  decomposition  and  hydration  of  feld- 

spathic  rocks,  being  hydrated  silicate  of  alumina,  generally  mixed  with  powdered 

feldspar,  quartz  and  other  materals. 

Hard-Pan,     Any   strongly  coherent  mixture   of   clay  or  other   cementing 

material  with  sand,  gravel,  or  boulders. 

Silt.     A  finely  divided  earthy  material  deposited  from  running  water. 
Mud.     Finely  divided  earthy  material  generally  containing  vegetable  matter 

and  deposited  from  still  or  slowly  moving  water. 

Dirt.     Loosely  used  to  describe  any  earthy  material. 

Soil.     Earthy  material  capable  of  supporting  vegetable  life  and  generally 

limited  to  material  containing  decayed  vegetable  or  animal  matter. 
Mould.     Earthy  material  containing  a  large  proportion  of  humus  or  vegetable 

matter. 

Loam.     Earthy  material  containing  a  proportion  of  vegetable  matter- 
Peat.     Compressed  and  partially  carbonized  vegetable  matter. 

7.    Characteristics  of  the  Materials  of  Foundation-Beds 

Solid  Rock,  or,  as  it  is  locally  known,  bed-rock,  or  ledge,  is  proverbially 
a  solid  foundation.  The  harder  rocks,  such  as  granite,  trap,  slate,  sandstone, 
limestone,  etc.,  are  all  capable  of  carrying  the  load  of  any  ordinary  structure. 
The  softer  rocks,  among  which  may  be  classed  the  shales,  shaley  slates  and 
certain  marley  Hmestones  and  clay  stones,  should  not  be  loaded  with  more  than 
IS  tons  per  sq  ft  unless  they  are  tested  for  greater  loads.  In  all  cases  where 
foundations  are  to  be  placed  on  what  is  supposed  to  be  solid  rock,  care  should  be 
taken  to  determine  whether  or  not  the  supposed  solid  consists  of  a  detached 
portion  and,  also,  in  case  the  bedding-planes  of  the  rock  are  inclined,  if  there  is 
danger  from  a  slip  of  the  layer  forming  the  foundation-bed.  (See  pages  139  and 
146  as  to  side-slope  locations.) 

Decayed  Rock.  Certain  igneous  or  metamorphic  rocks  such  as  granites, 
gneisses,  etc.,  frequently  disintegrate,  forming  so-called  rotten  rock  or  decayed 
ROCK.  The  decayed  rock  is  generally  found  in  conformity  with  the  ledge  of 
which  it  originally  formed  a  part.  It  may  retain  the  stratification,  color  and 
markings  of  the  solid  rock,  but  as  a  result  of  the  disintegrating  effect  of  water 
or  other  agents,  it  has  lost  the  solid  character  of  the  original  rock.  When 
struck  with  a  hammer  it  does  not  give  the  characteristic  ringing  sound  of  sohd 
rock.  It  may  be  fairly  compact  and  hard,  or  so^soft  as  to  be  readily  excavated 
with  pick  and  shovel.  The  amount  of  such  disintegrated  rock  overlying  the 
solid  rock  varies  greatly;  in  some  cases  the  removal  of  a  few  inches  will  disclose 
the  solid  rock,  in  other  cases  the  layer  of  decayed  rock  may  be  many  feet  in  thick- 
ness. Test-borings  in  rotten  rock  give  samples  similar  to  the  samples  from  solid 
rock;  so  that  it  frequently  happens  that  while  the  foundations  are  planned  for 
solid  rock  the  excavations  disclose  a  thick  layer  of  rotten  rock.  In  such  cases, 
if  it  is  impracticable  to  carry  the  footings  down  to  solid  rock,  it  may  be  necessary 
to  increase  the  size  of  the  footings  or  to  adopt  some  other  expedient. 

Loose  Rock.  Where  a  rock-mass  detached  from  the  ledge  of  which  it  orig- 
inally formed  a  part  is  encountered  it  must  not  be  loaded  in  excess  of  the  safe 
capacity  of  the  material  by  which  it  is  surrounded.  If  the  voids  between  ad- 
joining pieces  of  loose  rock  are  completely  filled  in  with  hard-pan,  compact 
gravel,  sand,  or  clay,  the  loading  may  be  the  same  as  for  the  filling-in  material 
but  care  should  be  taken  to  determine  that  no  voids  exist.    In  natural  rock* 


136  Foundations  Chap.  2 

fills,  as  in  artificial  rock-fills,  it  may  happen  that  large  voids  exist  between  the 
rock-masses,  forming  passageways  for  streams  of  water,  in  which  case  there  is 
extreme  danger  of  settlements. 

Boulders,  Gravel  and  Sand.  Boulders  are  rock-masses  which  have  been 
transported  by  water  or  ice-action.  Boulders  are  sometimes  found  dissemin- 
ated through  sand  and  clay  and  in  such  cases  the  load  should  be  limited  by  the 
safe  load  of  the  material  in  which  they  are  found.  At  other  times  boulders  are 
found  in  beds,  packed  closely  together,  with  the  interstices  filled  in  with  gravel, 
sand,  or  clay.  In  such  cases  it  is  usually  safe  to  assume  that  no  further  con- 
solidation of  the  mass  is  likely  to  take  place.  If  the  bed  of  boulders  extends  to 
rock,  they  will  safely  sustain  any  load  wliich  will  not  crush  them. 

Gravel.  The  name  gravel  is  given  to  rock-particles  larger  than  sand  and 
smaller  than  the  rock-masses  known  as  boulders.  If  compact,  and  if  no 
underlying  bed  of  poorer  material  exists,  gravel  forms  a  most  desirable  founda- 
tion-bed, equal  to  sand  or  boulders  in  supporting  power  and  not  as  Hable  to 
be  disturbed  by  adjoining  excavations  or  pumping  operations.  If  cemented 
it  may  partake  of  the  quality  of  hard-pan  or  rock.  Care,  however,  should  be 
taken  to  determine  whether  or  not  the  bed  of  gravel  has  been  deposited  over  a 
layer  of  silt  or  ciuicksand.  It  is  possible  for  this  dangerous  condition  to  exist. 
(See  page  134.) 

Sand.  Sand  is  composed  of  comminuted  rock-material.  As  quartz  is  the 
most  abundant  rock-mineral  and  as  its  hardness  and  insolubility  make  it  highly 
resistant  to  disintegrating  action,  it  will  be  found  to  be  the  principal  constituent 
of  most  deposits  of  sand  or  sandy  material.  Grains  of  mica,  feldspar,  garnet 
and  other  minerals  are  frequently  found.  Sand  is  described  as  being  fine, 
MEDIUM,  or  coarse,  according  to  the  size  of  the  grains  of  which  it  is  composed. 

Coarse  Sand  may  contain  particles  of  gravel,  but  after  eliminating  all 
particles  which  will  not  pass  a  screen  with  4  meshes  to  the  inch  it  will  be  found 
that  a  large  proportion  of  the  remaining  material  is  too  coarse  to  pass  a  40-mesh 
sieve. 

Fine  Sand,  on  the  other  hand,  may  contain  no  particles  which  will  not  pass 
A  20-mesh  sieve,  and  a  considerable  proportion  which  will  pass  a  loo-mesh  sieve. 

Very  Fine  Sand  is  frequently  mistaken  for  clay  and,  indeed,  generally  does 
contain  some  clay,  as  clay  generally  contains  fine  sand. 

Uniform  Sand  is  sand  in  which  there  is  relatively  a  small  variation  in  the 
size  of  the  particles. 

Balanced  Sand  is  sand  in  which  the  size  of  the  particles  varies  from  large  to 
small  and  in  which  there  is  no  great  difference  in  the  numbers  of  particles  of 
each  size. 

Clean  Sand  contains  no  clay  or  loam,  but  a  pure  sand  containing  a  large  per- 
centage of  fine  particles  is  often  considered  to  be  not  clean. 

Sharp  Sand  is  clean  sand  containing  coarse,  angular  grains.  When  firmly 
grasped  in  the  hand  it  gives  a  note,  due  to  the  particles  slipping  over  each  other. 
Sharp  sand  is  generally  esteemed  for  use  in  mortar,  although  it  requires  more 
cement  to  fill  the  voids  and,  in  the  writer's  opinion,  is  not  as  desirable  as  a  clean, 
rounded  sand. 

Rounded  or  Buckshot  Sand  is  composed  of  rounded  grains  not  cemented 
together. 

Quicksand.  This  term  is  popularly  used  to  describe  any  fine  sand,  or  mix- 
ture of  fine  sand  and  clay,  which,  when  wet,  forms  a  soft,  unstable  material. 


Characteristics  of  the  Materials  of  Foundation-Beds  13^ 

In  the  popular  mind  quicksand  is  supposed  to  have  some  mysterious  and  peculiar 
qualities  which  result  in  a  tendency  to  flow  like  water  and  to  suck  in  animate 
and  inanimate  objects.  These  manifestations  are  connected  with  various 
theories  as  to  the  composition  of  quicksand,  some  persons  insisting  that  quick- 
sand must  contain  Hakes  of  mica  or  some  slippery  mineral,  others  that  the 
particles  must  be  extremely  fine  or  spherical  in  shape,  while  others  contend 
that  there  must  be  a  certain  proportion  of  fine  clay  with  the  sand.  The  fact 
is  that  any  uncemented  sand,  when  subjected  to  the  action  of  moving  water, 
will  move  and  that  any  sand  moving  as  the  result  of  the  action  of  water  becomes 
a  quicksand.  The  finer  the  sand  the  more  readily  it  is  affected  by  a  current  of 
water,  so  that  fine  sands  are  more  trouljlcsome  than  coarse  sands.  A  coarse 
sand,  having  large  voids,  permits  the  flow  of  a  certain  amount  of  water  through 
them;  if  this  flow  has  not  sufficient  velocity  to  disturb  the  particles  of  the  sand, 
the  sand  can  be  drained  without  moving  it.  In  a  fine  sand,  having  very  small 
voids,  a  similar  flow  of  water  will  cause  the  whole  mass  to  move  and  there  is 
great  difficulty  in  draining  it  without  producing  a  current  sufficient  to  cause  it 
to  move  or  flow. 

Excavations  in  Quicksand  are  made  difficult  by  the  tendency  of  the  sand 
forming  the  sides  of  the  excavation  to  flow  into  the  excavation;  and  even  if  the 
sides  of  the  excavation  are  protected,  it  not  infrequently  happens  that  the 
bottom  of  the  excavation  will  lift,  that  is,  there  will  be  a  movement  of  material 
from  points  outside  of  the  line  into  the  excavation,  the  movement  in  general 
following  a  curved  line,  and  carrying  the  sand,  under  the  protected  side  walls 
of  the  excavation.  In  such  cases  some  advantage  may  be  gained  by  surround- 
ing the  excavation  with  driven  wells  and  draining  the  soil  by  continued  pumping 
through  sand;  in  other  cases,  wooden  or  steel  sheeting  may  be  driven  to  a  point 
below  the  depth  to  which  the  excavation  is  to  be  carried,  or  to  some  underlying 
layer  of  impervious  material,  in  which  case  the  sheeting  will  act  as  a  coffer-dam 
to  cut  off  the  flow  of  material.  Such  sheeting,  however,  must  be  practically 
watertight,  as  extremely  fine  sand,  when  in  the  condition  of  quicksand,  will 
flow  through  very  small  apertures. 

Quicksand  as  a  Foundation-Bed  is  objectionable  on  account  of  the  danger 
of  its  moving  or  flowing,  in  case  it  finds  any  outlet  such  as  would  be  afforded  by 
an  adjoining  excavation.  Cases  are  known  where  excavations  have  permitted 
the  escape  of  quicksand  and  resulted  in  the  settlement  of  buildings  at  a  very 
considerable  distance.  Such  settlements  have  occurred  not  only  when  the 
footings  themselves  rested  on  quicksand,  but  also  when  they  were  on  a  stratum 
of  coarse  sand,  gravel  or  clay  of  good  quality  which  rested  on  an  underlying 
stratum  of  quicksand. 

Pockets  of  Quicksand.  It  frequently  happens  that  pockets  of  fine  sand  are 
found  in  deposits  of  mixed  character.  Where  such  pockets  are  small  in  extent 
the  fine  sand  may  be  removed  and  the  spaces  filled  with  concrete.  Where  the 
pockets  are  larger  it  may  be  necessary  to  carry  piers  through  them  to  a  better 
foundation-bed,  to  drive  piles,  or  to  resort  to  other  expedients. 

Fine  Dry  Sand  is  readily  converted  into  quicksand  by  the  addition  of  water, 
which  fact  should  be  carefully  borne  in  mind  in  considering  the  load  on  fine  sand, 
as  a  material  which  in  dry  weather  is  apparently  safe,  may  be,  in  wet  weather, 
an  extremely  dangerous  one.  It  is  frequently  stated  that  confined  quicksand 
is  a  perfectly  reliable  material  on  which  to  found  a  building.  While  this,  as  a 
theory,  cannot  be  controverted,  it  is  a  dangerous  assumption  to  act  on  because 
of  the  impossibility  of  providing  that  the  fine  sand  shall  be  always  confined. 

Variation  in  the  Size  of  Grains  of  Sand.  The  accompanying  diagram 
(Fig.  1)  shows  graphically  the  results  of  sieve- tests  on  characteristic  ^sands. 


138 


Foundations 


Chap.  2 


The  dash-line  curve  (i)  is  an  average,  giving  the  results  of  sieve-tests  on  several 
so-called  quicksands;  the  full-line  curve  (2)  gives  the  result  of  sieve-tests  on  a 
natural  sand  which  would  be  classed  as  a  good  building  sand;  the  dot-and-dash 
curve  (3)  gives  the  result  of  sieve-tests  on  a  fine  beach  sand  remarkable  for  the 


/ 

1 

iBX^^^f^'^^ — 

-></ 

"X' 

1 

\ 
\ 

^ — " — '         ..(ii.UQttviVii'irx.^ • 

■ ^(1)  Djtsh  curve    ^(3)  Do|b  and  dash  curv 

J->^. 

\ 

\ 

10  Mesh  20  30  50  80100200 

Fig.  1.     Graphical  Illustration  of  Results  of  Sieve-tests  on  Sands 

uniformity  of  the  size  of  its  grains.  For  purposes  of  comparison  and  in  order 
to  show  the  variation  in  sands  which  appear  to  be  substantially  the  same,  the 
dotted  curve  (4)  has  been  added.  This  shows  the  result  of  tests  on  a  bank  sand 
apparently  as  coarse  as  sand  (2),  but  containing  a  much  larger  percentage  of 
fine  particles  between  0.015  and  0.0055  in  in  diameter.  Fine  sand  frequently 
contains  a  considerable  proportion  of  clay.  A  chemical  analysis  of  a  so-called 
QUICKSAND  from  the  down-town  section  of  New  York  City,  reported  on  to  the 
writer  by  Dr.  C.  F.  McKenna,  is  as  follows: 

Mark:   "Commercial  Cable" 

Silica 73 .  76% 

Alumina  and  oxide  of  iron 18 .  52% 

Lime i .  60% 

Magnesia i .  48% 

Loss  on  ignition 2 .  26% 

A  rational  analysis  shows  the  following  composition: 

Quartz,  as  given 39 .38% 

Clay  and  mica,  as  given 23 .  94% 

Feldspathic  detritus 36 .  68% 

On  the  other  hand,  a  sample  of  extremely  fine  sand  from  Michigan,  of  which 
75%  passed  a  200-mesh  sieve,  appears  to  be  absolutely  pure  quartz. 

Clay.  When  pure,  clay  consists  of  hydrated  silica  of  alumina,  the  product 
of  decomposition  of  feldspar.  Ordinarily,  various  impurities  are  mixed  with  the 
clay,  so  that,  in  general,  clay  may  be  considered  a  mixture  of  hydrated  silica 
of  alumina  with  other  finely  divided  minerals.  Mixtures  of  clay  and  sand  are 
found,  varying  from  beds  of  nearly  pure  clay  to  beds  of  nearly  pure  sand,  and 
no  definite  classification  can  be  made. 

The  Effect  of  Moisture  on  Clay.  Clay  as  generally  found  in  excavations 
is  in  a  plastic  condition  due  to  the  presence  of  moisture,  the  amount  of  water 
present  varying  greatly.  On  drying,  the  clay  shrinks  in  volume  and  loses  its 
plasticity,  becoming  a  firm  and  coherent  mass  resembling  in  consistency  a  sun- 
drie4  brick.    Large  masses  of  clay  are  liable  to  crack  into  a  number  of  sma^U, 


Characteristics  of  the  Materials  of  Foundation-Beds         139 

fragments  during  the  process  of  drying,  as  the  result  of  the  shrinkage  in  volume. 
When  these  lumps  are  crushed  or  ground  the  clay  becomes  an  extremely  fine 
or  impalpable  powder.  The  loss  in  volume  due  to  the  change  in  the  condition 
of  the  clay  from  a  moist,  plastic  state  to  a  thoroughly  air-dried  condition  may 
amount  to  from  io%  to  20%  of  the  original  volume.  Compact,  moist  clay  is 
impervious  to  water  in  the  sense  that  water  cannot  pass  through  it  as  it  would 
through  porous  sand;  but  when  clay  is  exposed  to  water  the  clay  gradually 
absorbs  the  water,  so  that  eventually  the  entire  mass  becomes  saturated  and 
softened  by  the  water. 

Clay  as  a  Foundation-Bed.  Clay  is  not  a  reliable  material  on  which  to 
found  a  building;  first,  because  of  the  plasticity  of  the  clay  when  wet,  and 
secondly,  because  of  its  tendency  to  shrink  on  losing  its  contained  moisture. 
The  plasticity  of  clay  increases  with  the  percentage  of  contained  water,  so  that 
a  firm,  hard  clay  may  be  converted  into  a  Hquid  puddle  by  being  agitated  in  the 
presence  of  a  sufiicient  amount  of  water.  The  plasticity  is  also  increased  by 
pressure,  as  is  shown  by  the  action  of  clay  in  a  brick-machine.  Clay,  in  a  founda- 
tion-bed under  moderate  pressure  imposed  on  it  by  the  footings  of  a  structure, 
frequently  develops  this  quality  of  plasticity,  the  clay  moving  out  from  be- 
neath the  footing  and  causing  serious  settlements  and  displacements  of  the 
footings.  This  movement  of  the  clay  may  be  a  local  movement,  as  referred  to 
each  footing,  in  which  case  the  clay  flows  from  beneath  the  footing  laterally 
toward  the  side  and  then  upward,  causing  the  surface  of  the  adjacent  ma- 
terial to  rise  and  to  form  so-called  bulges  or  waves.  If  this  motion  is  uniform 
from  the  center  toward  the  sides,  the  footing  may  settle  vertically,  but  more 
frequently  the  movement  will  not  be  symmetrical  and  the  footing  will  settle 
more  on  one  side  than  on  the  other.  Such  movements  of  the  clay  may  be  re- 
duced or  prevented  in  some  cases  by  the  simple  device  of  loading  the  surround- 
ing soil,  as,  for  example,  by  a  concrete  floor. 

Movements  of  Clay  Foundation-Beds.  The  movement  of  the  clay  may 
be  on  a  larger  scale,  amounting  to  a  general  flow  of  the  clay  underlying  the 
entire  building  toward  some  point  where  the  pressure  on  the  clay  is  less  than 
the  pressure  resulting  from  the  load  of  the  building.  Such  general  movements 
are  more  likely  to  happen  if  the  building  is  located  on  the  side  of  a  hill,  so  that 
the  clay  finds  some  outlet  at  a  point  below  the  level  of  the  footings.  It  fre- 
quently happens  that  adjoining  excavations  cause  settlements  to  buildings  at  a 
considerable  distance,  by  affording  an  outlet  to  a  bed  of  clay.  As  noted  else- 
where (pages  135  and  146),  beds  of  clay  resting  on  inclined  strata  of  rock  or 
other  material  are  liable  to  move  downward,  sometimes  with  a  slow,  almost 
imperceptible  movement,  and  at  other  times  forming  landslides  of  greater  ol 
less  magnitude. 

Protection  of  Clay  Foundation-Beds.  Where  the  foundation-bed  is  clay, 
or  sand  with  a  considerable  amount  of  clay,  it  is  advisable  to  protect  it  from 
water-action,  so  far  as  is  possible,  by  a  system  of  drains  surrounding  the  site 
of  the  building  and  by  diverting  the  surface-water  from  the  building:  Care 
should  be  taken  in  back-filling  around  exterior  walls  to  prevent  any  accumula- 
tion of  water  which  might  affect  the  material  under  the  footing.  The  neglect 
of  such  precaution  has  frequently  resulted  in  serious  settlements  during,  or 
inmiediately  after,  construction. 

Mud,  Silt,  Peat  and  Other  Unstable  Materials.  When  the  site  of  a 
structure  is  in  a  marsh  or  on  materials  which  are  not  capable  of  affording  a 
safe  foundation,  the  only  alternative  is  to  resort  to  the  use  of  wooden  piles, 
concrete  piles,  or  piers  sunk  to  an  underlying  and  firmer  strata.    Such  special 


140  Foundations  Chap.  2 

constructions  will  be  described  under  Subdivisions  27,  28  and  29,  which  consider 
wooden  piles,  concrete  piles  and  piers  sunk  by  the  coffer-dam  or  caisson 
methods. 

Filled  Ground.  All  artificial  fills  and  some  natural  fills  are  liable  to  a  more 
or  less  uniform  but  continuous  settlement  or  shrinkage  due  to  the  gradual  con- 
solidation of  the  material  of  which  the  fill  is  composed.  Where  the  fill  is  of  solid 
rock  this  consohdation  may  amount  to  little,  but  where  the  fill  is  of  earth,  and 
especially  where  it  is  of  mixed  materials,  the  shrinkage  will  not  only  be  large  in 
amount  but  will  continue  for  a  very  long  period.  For  example,  where  dirt 
has  been  thrown  on  top  of  a  rock-fill  each  rain-storm  will  wash  some  of  the  dirt 
into  the  voids  in  the  rock-fill,  and  this  action  will  be  continuous  until  all  of 
the  voids  are  filled  in.  Any  vegetable  matter,  or  other  matter  liable  to  decay 
and  shrinkage  in  volume,  will  increase  the  total  shrinkage  of  the  mass.  Cer- 
tain natural  deposits,  such  as  beds  of  peat  or  soils  containing  vegetable  matter, 
are  apt  to  shrink  in  volume  from  the  same  causes.  When  it  is  necessary  to 
found  a  building  on  such  material  it  is  inevitable  that  the  footings  will  settle 
with  the  mass,  notwithstanding  that  the  unit  load  on  the  foundation-bed  is  so 
small  as  to  be  negligible.  In  such  cases  the  settlements  may  be  vertical  and 
uniform;  but  if  the  depth  of  the  fill  under  one  part  of  the  building  is  greater 
than  the  depth  under  another  part,  the  settlements  will  not  be  uniform,  as  the 
shrinkage  in  the  fill  will,  in  general,  be  in  proportion  to  the  depth  of  the  fill. 
No  important  building  should  be  founded  on  such  material  and,  wherever 
possible,  the  footings  should  be  carried  down  through  the  filled-in  material  to 
some  more  reliable  underlying  stratum. 

8.   Allowable  Loads  on  Materials  of  Foundation-Beds 

General  Considerations.  Owing  to  the  infinite  number  of  variations  in  the. 
materials  encountered  and  the  conditions  affecting  the  reliability  of  such  mate- 
rials, no  general  or  definite  rule  can  be  given,  and  every  case  should  be  carefully 
investigated  before  determining  the  allowable  unit  load  on  the  foundation-bed. 
If  the  material  and  conditions  are  uniform  over  the  entire  site  of  the  building 
a  uniform  unit  load  may  be  used,  but  in  practice  it  is  frequently  found  that 
entirely  different  conditions  exist  under  different  portions  of  the  same  building 
and  in  such  cases  great  care  must  be  exercised  in  determining  the  unit  loads. 
For  instance,  one  section  of  a  building  may  rest  on  rock  and  another  section  on 
a  light  compressible  soil  or  on  a  clay  of  doubtful  stability.  In  such  cases  the 
unit  load  on  the  compressible  soil  or  on  the  clay  must  be  reduced  as  much  as 
possible  so  as  to  reduce  the  differences  in  settlements  between  the  two  sections 
of  the  building  to  a  minimum.  If  the  entire  building  were  on  a  compressible 
soil  a  very  considerable  settlement  might  be  allowable,  provided  it  was  uniform; 
but  in  this  particular  case  it  is  known  beforehand  that  the  part  of  the  building 
on  rock  will  not  settle  at  all  and  that  any  settlements  of  other  parts  of  the 
building  must  be  considered  as  unequal  settlements,  and,  as  such,  liable  to  pro- 
duce cracks  and  distortions  in  the  building.  It  is  also  important  to  remember 
that  a  certain  unit  load  on  compressible  soil  may  be  safe,  in  that  the  soil  will 
ultimately  safely  support  that  load;  but  the  use  of  that  load  would  nevertheless 
be  inadvisable  on  account  of  the  excessive  settlements.  In  this  connection  it 
may  be  said  that  a  considerable  settlement,  if  uniform,  in  a  detached  building 
may  be  a  matter  of  no  importance;  but  that  where  a  building  is  to  be  con- 
structed in  contact  with  adjoining  buildings  or  where  additions  are  to  be  made 
to  an  existing  building,  the  total  amount  of  settlement  becomes  a  matter  of 
prime  importance.    These  and  other  considerations,  such  as  the  character  of 


Allowable  Loads  on  Materials  of  Foundation-Beds  141 

the  proposed  building  and  of  the  material  composing  it,  should  be  borne  in 
mind  in  selecting  the  unit  load  for  any  given  foundation-bed,  irrespective  of  the 
allowed  pressure  as  given  by  building  codes  or  by  examples  quoted  in  this  chapter. 
Safe  Loads  on  Rock.  The  safe  unit  load  on  rock  may  often  amount  to 
more  than  the  crushing  strength  of  brickwork  or  stone  masonry,  and  in  nearly 
all  cases  any  material  worthy  of  the  name  of  rock  is  capable  of  supporting  from 
15  to  30  tons  per  sq  ft. 

Safe  Loads  on  Sand,  Gravel  and  Boulders.  When  compact  and  con- 
fined laterally  these  materials  are  capable  of  supporting  10  tons  per  sq  ft  with- 
out appreciable  settlement.  It  rarely  happens,  however,  that  it  is  advisable  to 
load  such  materials  with  more  than  5  tons  per  square  foot. . 

Safe  Loads  on  Loose  Sand.  By  loose  sand  is  meant  sand  which  has 
not  been  thoroughly  compacted  and  which  may  settle  by  its  own  weight  inde- 
pendently of  a  superimposed  load.  All  such  materials  should  be  tested  and 
the  unit  load  reduced  in  accordance  with  the  result  of  such  tests. 

Loads  on  Fine  Sand  or  Quicksand.  It  is  probable  that  fine  sand,  if 
absolutely  confined,  will  sustain  as  heavy  a  load  as  coarse  sand,  but  in  view  of 
the  fact  that  if  afforded  the  slightest  opportunity  it  is  liable  to  lateral  displace- 
ment, it  is  inadvisable  to  found  any  structure  on  such  material.  When  it  is 
imperative  to  place  the  footings  on  such  material  the  unit  load  should  be  reduced 
as  much  as  possible  and  preferably  to  less  than  2  tons  per  sq  ft,  and  great  care 
should  be  taken  to  connect  all  footings  with  a  continuous  layer  of  concrete  so 
as  to  prevent  any  flow  of  material  into  the  cellar-excavation..  Care  should 
be  taken,  also,  that  any  sumps,  pump-pits,  drainage-arrangements  and  sewerr 
connections  for  the  building  do  not  permit  the  escape  of  any  quicksand- 
Safe  Loads  on  Hard-pan  and  certain  cemented  sands  partaking  of  the 
nature  of  hard-pan  may  approximate  rock  in  hardness  and  reliability.  Such 
materials,  however,  are  liable  to  soften  if  exposed  to  water.  If  these  materials, 
when  uncovered,  are  dry,  experiments  should  be  made  to  determine  how  they 
behave  when  wet,  and  if  the  level  of  the  water  in  the  ground  is  liable  to  change 
so  as  to  reach  the  layer  of  hard-pan,  the  load  should  be  correspondingly  reduced. 
Cemented  hard-pan  containing  gravel  has  been  frequently  loaded  with  more 
than  10  tons  per  sq  ft.  '  Care  should  be  taken,  however,  to  determine  that 
the  layer  of  hard-pan  is  continuous  to  a  solid  substratum,  as  it  frequently  happens 
that  layers  of  hard-pan  and  fine  sand  or  clay  are  deposited  alternately.  • 

Safe  Loads  on  Clay.  Ordinary  clay  should  not  be  loaded  with  more  than 
2  tons  per  sq  ft.  If  soft  and  plastic,  a  load  of  2  tons  per  sq  ft  may  produce 
inadmissible  settlements.  Clay  containing  so  large  a  percentage  of  sand  as  to 
lose  its  plasticity  has  been  loaded  with  from  4  to  6  tons  per  sq  ft  without  undue 
settlements,  and  sand  or  gravel  containing  sufficient  clay  to  act  as  a  cementing 
material  will  partake  of  the  qualities  of  hard-pan.  In  general,  however,  clay 
is  the  most  dangerous  of  all  the  materials  on  which  structures  are  founded  and 
the  unit  load  should  be  reduced  to  a  minimum  and  every  precaution  taken  to 
prevent  the  flow  of  material.  Undue  reliance  should  not  be  placed  upon  load- 
ing-tests of  clayey  soils.  It  is  probable  that  a  loading  on  a  large  area  which 
will  produce  a  movement  of  the  clay  will  on  a  small  area  have  no  effect,  so  that 
it  is  unsafe  to  rely  upon  the  results  of  a  test-load  applied  to  an  area  smaller  than 
the  actual  supporting  areas  to  be  used.  From  the  experience  gained  in  the 
construction  of  large  buildings  in  Chicago  which  were  floated  on  clay,  the 
allowable  unit  load  has  been  generally  reduced  to  2  tons  per  sq  ft  and,  in 
the  writer's  experience,  a  load  of  less  than  2  tons  per  sq  ft  on  clay  has  pro- 
duced settlements  varying  from  nothing  to  J2  in._ 


142  Foundations  Chap.  2 

9.  Unit  Loads  on  Foundation-Beds  Allowed  by  Building  Codes 

Variations  in  Building  Codes.  Table  I  gives  an  outline  of  the  requirements 
of  dififerent  cities  as  to  the  allowable  unit  loads  on  different  materials,  as 
contained  in  their  respective  building  codes  or  regulations.  While  the 
allowed  loads  given  may  in  some  cases  be  based  upon  actual  experience  in  the 
respective  localities,  it  is  more  Ukely  that  they  are  based  upon  the  individual 
experience  of  the  authors  of  the  codes,  or  are  copied  from  other  codes.  The 
architect  should,  therefore,  not  place  too  much  reUance  on  the  unit  loads  allowed 
by  the  codes,  but  should  investigate  each  case  and  determine  for  himself  the 
proper  allowance  to  be  made.  • 

Special  Requireijients  of  Some  Building  Codes.  *  The  Boston  code  pro- 
vides that  "the  footing  shall  not  overload  the  material  on  which  it* rests." 

The  New  Orleans  code  limits  the  maximum  load  to  i  400  lb  per  sq  ft,  the  entire 
city  being  on  an  alluvial-delta  formation. 

The  Buffalo  code  limits  the  load  on  soil  to  3H  tons  per  sq  ft;  if  the  soil  is  other 
than  hard  clay  or  gravel  the  supporting  areas  "shall  be  extended  as  directed." 

The  Cincinnati  code  limits  the  load  on  soils  inferior  to  those  listed,  to  i  ton 
per  sq  ft. 

10.   Investigation  of  the  Site 

General  Considerations.  To  determine  the  character  of  the  materials  which 
will  be  encountered  at  the  level  of  a  foundation-bed,  the  architect  should  first 
get  as  definite  information  as  possible  from  others  as  to  their  experience  in  mak- 
ing excavations  and  erecting  buildings  in  that  vicinity.  In  some  localities  the 
subsoil  conditions  are  uniform  over  large  areas,  while  in  other  localities  impor- 
tant variations  may  occur  within  the  limits  of  a  city  lot.  Abrupt  changes  in 
surface-topography,  changes  in  the  character  of  the  surface-soil  or  in  the  native 
vegetation,  proximity  to  old  or  existing  water-courses  are  suggestive  of  sub- 
surface irregularities.  In  such  cases,  and  in  all  cases  where  there  is  any  doubt 
as  to  subsurface  conditions,  a  sufficient  number  of  exploratory  borings  or  test- 
pits  should  be  made  to  determine  the  facts.  This  exploratory  v/ork  should  go 
below  the  level  of  the  proposed  footings,  should  determine  the  ground-water 
level  and  insure  that  no  unsuspected  layer  of  quicksand  or  other  unsuitable 
material  underlies  the  foundation-bed.  The  methods  in  use  for  such  explora- 
tions are  as  follows: 

Testing  in  an  Open  Pit.  For  shallow  work  an  open  pit  is  the  most  sat- 
isfactory method  as  it  allows  actual  inspection  of  the  undisturbed  material  over  a 
considerable  area.  If  the  excavation  is  in  firm  material,  no  sheet-piling  or  other 
protection  may  be  required;  but  if  in  flowing  material,  or  if  carried  deeper 
than  adjoining  footings,  timber  sheeting  or  steel  sheeting  should  be  employed. 
If  the  excavation  is  carried  no  deeper  than  the  proposed  footing-level,  the  under- 
lying material  should  be  tested  by  one  of  the  methods  hereinafter  described. 

Testing  with  Steel  Bars.  A  steel  bar  with  a  pointed  end  or  a  steel  pipe 
provided  with  a  steel  point  is  driven  to  the  required  depth  by  a  maul  or  by  a 
falling  weight.  While  no  samples  can  be  obtained  by  this  crude  method,  it 
may  determine  the  ground-water  level,  and  a  little  practice  will  enable  one  to 
distinguish  sandy  from  clayey  soils  by  the  sound  given  out  when  the  bar  is 
twisted.  The  difficulty  of  driving  is  a  rough  index  of  the  degree  of  the  com- 
pressibility of  the  soil.  It  should  be  remembered,  however,  that  any  dry 
material  will  afford  considerable  resistance  to  the  bar  and  that  a  small  boulder 
will  stop  it;  so  that  not  much  reliance  can  be  placed  on  a  report  that  the  BAR 

DROVE  HARD  Or  that  it  REACHED  ROCK. 

•  As  codes  change,  quotations  must  be  verified. 


Investigation  of  tiie  Site 


143 


Table  I.     Loads  in  Tons  per  Square  Foot  on  Foundation-Beds  Allowed 
by  Building  Codes* 


Character  of  foundation-bed 

4 
s 

.2 

s 

-t-J 

O 

"> 
'B 

-b 

0 
^ 

^ 

g 

^ 

d 

d 

a 
c 

c 
0 

6 

03 

d 
a 

1 

6 

1 

J5 

Alluvial  soils 

Vz 

>^ 

3 

I 

Firm  dry  loam 

3 

I 

2-3 

I 

21/2 

3 

I 

Soft  clay     

I 
2 

Ordinary  clay 

2 

Good  solid  natural  clay 

Clay  in  thick  beds,  always  dry 

4 
2 

Clay  in  thick  beds,  moderately  dry 
Dry  clay 

3 

3 
4 

3 

4 

{ 

3h 

2-3 
t8 
3-4 

\ 

4 

iK' 

21/2 
4 

3 
4 

3 

4 

Hard  clay 

4 

Dry  hard  clay 

4 

Soft  wet  clay  and  sand 

2 

2 

Ordinary  clay  and  sand  together 

in  layers;  wet  and  springy 

Moderately  dry  clay  and  sand 

2 

2 

2 

3 

2 

Stratified  clay  and  stone 

4 

V2 

3'i 

I 

Soft  wet  sand 

Wet  sand      

I 

Fine  sand  firm  and  dry 

3 

3 

2-3 

4 

2^ 

3 

3 

2 

Fine  sand,  compact  and  well  ce- 
mented 

4 

3 

Coarse  compact  sand 

4 

4 

Very  firm  coarse  sand 

4 

4 

3-4 

4 

4 

4 

2 

Stiff  gravel 

4 

4 

6 

3-4 
t8 

4 

4 

3H 

5 
8 

Compact  sand  and  gravel,  well  ce- 

6 

Gravel  and  coarse  sand,  well  ce- 
mented 

8 

8 

Hard-pan  ' 

o-iS 

Hard  shale,  unexposed 

8 
8 

10 
20 

Rock 

ti5 

8 

*  Some  values  may  change  with  the  changes  in  building  codes, 
t  In  caissons. 


144  Foundations  Chap.  2 

Testing  with  Post-Hole  Diggers.  For  shallow  explorations  in  easily  ex- 
cavated material,  the  ordinary  post-hole  digger  used  for  fence-posts,  or  the 
longer  and  larger  ones  used  for  telegraph-poles,  can  be  used  to  depths  of  from 
6  to  8  ft. 

Testing  with  Augers.  In  clay  or  similar  material  a  single  or  double-twist 
carpenter's  auger  welded  to  a  long  rod,  or  the  so-called  pod-auger  may  give 
satisfactory  samples.  In  gravel  or  loose  and  sandy  material,  the  sides  of  the 
hole  fall  in,  clogging  the  operation  and  destroying  the  samples. 

Testing  by  Dry-Pipe  Borings.  A  pod-auger  or  the  above-described 
carpenter's  auger  can  be  used  inside  a  casing-pipe.  The  pipe  should  be 
driven  so  as  to  keep  close  to  the  bottom  of  the  hole  made  by  the  auger.  The 
pipe  prevents  the  material  falling  from  the  sides  of  the  hole  and  the  auger  ex- 
cavates and  loosens  the  material  ahead  of  the  pipe  and  facilitates  driving.  The 
above  methods  are  not  generally  successful  for  deep  holes  or  where  gravel, 
boulders  or  compact  material  interferes  with  driving  the  pipe. 

Testing  with  Wash-Pipes.  For  test-borings  over  lo  ft  in  depth  the  method 
in  most  frequent  use  is  the  wash-pipe  method.  In  this  method  a  wrought-iron 
or  steel  pipe  known  as  the  casing-pipe  or  drive-pipe  is  driven  .into  the  earth  in 
much  the  same  way  as  in  the  dry-pipe  method,  but  the  driving  of  the  pipe  is 
facilitated  by  the  use  of  a  jet  of  water.  The  lower  end  of  the  casing-pipe  is 
provided  with  a  hollow  shoe  or  reinforcement,  slightl}^  larger  in  outside  diameter 
than  the  casing.  This  serves  to  protect  the  pipe  from  injury  in  driving  through 
gravel  or  hard-pan,  and  forms  a  hole  slightly  larger  than  the  diameter  of  the 
casing.  The  upi^er  end  of  the  drive-pipe  is  protected  from  injury  by  an  annular 
drive-head  which  has  a  threaded  part  fitting  the  thread  on  the  casing-pii>e  and 
a  central  hole  to  admit  the  jet-pipe.  The  jet-pipe  is  small  enough  to  permit 
It  to  freely  enter  the  casing-pipe.  The  lower  end  is  contracted  so  as  to  produce 
a  jet-action.  The  upper  end  is  connected  with  a  water-supply  which  must  be 
under  considerable  pressure.  The  driving-mechanism  consists  of  a  cast-iron 
weight  with  a  central  vertical  hole  large  enough  to  admit  the  wash-pipe,  and 
stationary  verticals  supix>rting  a  block-and-fall  and  an  arrangement  which 
releases  the  weight  when  it  has  reached  a  predetermined  height.  With  this 
arrangement,  water  is  continuously  pumped  through  the  jet-pipe,  the  length  of 
which  is  regulated  so  that  the  jet-action  loosens  the  material  immedFately  below 
or  AHEAD  of  the  casing.  Some  of  the  jetting  water  returns  to  the  surface  out- 
side of  the  casing  and  thus  lubricates  the  surface  in  contact  with  the  outside 
material.  Another  part  of  the  water  returns  to  the  surface  in  the  annular 
space  between  the  wash-pipe  and  the  casing,  carrying  with  it  particles  of  the 
material  loosened  by  the  jet.  As  the  jet  loosens  and  washes  away  the  material 
immediately  below  the  casing,  the  latter  is  driven  deeper  by  repeated  blows  of 
the  ram,  the  driving  and  washing  being  carried  on  at  the  same  time.  The 
operation  is  thus  continuous  until  the  top  of  the  casing  comes  close  to  the  sur- 
face of  the  ground,  when  the  hammer  drive-head  and  hose-connection  are  re- 
moved to  permit  additional  lengths  of  pipe  to  be  added  to  the  casing  and  wash- 
pipes,  after  which  the  hose-connection,  drive-head  and  hammer  are  replaced 
and  the  operation  is  resumed. 

Borings  can  be  made  by  this  method  to  great  depths  in  sand,  clay  or  other 
suitable  material.  Samples  of  the  material  encountered  are  obtained  by  settle- 
ment from  the  water  returning  between  the  jet-pipe  and  wash-pipe.  These 
samples  are  not  accurate  samples  as  the  water  separates  the  materials.  The 
finer  particles  do  not  settle  readily  and  the  large  and  heavy  particles  may  not 
be  brought  up  at  all.  It  is  evident  that  such  samples  do  not  give  any  index 
as  to  the  solidity  of  the  original  deposits.    If  large  gravel,  hard-pan  or  boulders 


Loading-Tests  145 

are  encountered  there  will  be  great  difBculty  in  forcing  the  casing  past  such 
obstructions.  In  such  cases  a  drill-rod  is  sometimes  substituted  for  the  jet 
and  the  obstruction  broken  up  into  small  pieces  or  pushed  to  one  side;  but  in 
either  case  it  is  difficult  to  get  any  sample  or  real  indication  of  the  character 
of  the  obstruction.  If  solid  rock  or  large  boulders  are  encountered,  no  further 
progress  can  be  made  with  the  casing  and  no  sample  can  be  obtained  by  this 
method.  Resort  must  then  be  had  to  one  of  the  core-boring  methods  described 
hereafter,  to  determine  the  character  of  the  obstruction  encountered. 

Testing  by  Core-Borings.  These  borings  can  be  made  through  rock  or 
boulders  and  accurate  samples  obtained.  In  all  core-boring  methods  the  hole 
is  made  by  rotating  a  pipe-like  tool  which  makes  an  annular  cut  in  the  rock 
and  leaves  a  cylindrical  core  which  is  afterwards  detached  and  brought  to  the 
surface  by  a  gripping-tool  called  the  core-lifter.  The  cutting  is  done  in 
different  ways. 

Diamond  Bits  are  annular  rings  fitted  on  the  lower  end  of  the  hollow  pipe 
used  as  the  rotating  drill-rod  and  furnished  with  a  number  of  small  diamonds 
arranged  so  as  to  form  cutting-edges,  which,  when  rotated  in  contact  with  the 
rock,  gradually  wear  away  the  required  annular  space.  The  diamonds  employed 
are  known  as  bort,  black  diamonds,  or  carbons,  and  their  only  resemblance 
to  the  stones  used  by  jewelers  is  the  necessary  hardness.  The  carbons  ara 
skillfully  secured  in  a  soft  metal  bed,  in  sockets  drilled  in  the  bit,  and  they  pro- 
ject below  the  bit  and  also  sufficiently  inside  and  outside  to  insure  the  cutting 
of  a  groove  large  enough  to  provide  clearance  for  the  bit  and  the  attached  drill- 
rod  or  pipe. 

Shot-Drills.  The  same  result  is  arrived  at  by  the  shot-drill  method,  by 
wliich  particles  of  chilled  cast  iron  called  shot  are  used  as  the  abrasive  or  cutting- 
agent.  The  shot  is  poured  loose  into  the  hole  and  forced  against  the  rock  by 
the  rotating  bit. 

Efficiency  of  Drill-Methods.  Both  of  the  drill-methods  mentioned  are  ex- 
pensive, but  as  they  are  the  only  methods  which  will  give  an  accurate  sample 
in  rock,  one  or  the  other  must  be  employed  where  the  accurate  determination 
of  rock  is  necessary.  If  the  core  corresponds  to  the  known  underlying  rock- 
formation  and  the  rock  is  continuous  for  a  length  of  from  8  to  20  ft,  it  is  safe 
to  assume  that  solid  rock  has  been  reached.  If,  however,  the  core  is  of  differ- 
ent rock  from  the  known  underlying  formation,  the  probability  is  that  a  boulder 
has  been  encountered.  If  the  core  is  not  continuous  it  may  indicate  that 
there  are  seams  in  the  rock  or  that  there  are  detached  rock-masses.  The  above- 
described  methods  are  used  after  the  overlying  earth  has  been  penetrated  by 
one  of  the  pipe-sinking  methods  previously  described. 

The  Results  of  Pipe-Borings  are  frequently  misleading  and  misinterpreted, 
and  great  care  should  be  taken  to  compare  the  samples  with  samples  obtained 
from  other  borings  where  the  exact  character  of  the  materials  tested  is  known. 

11.   Loading-Tests 

General  Considerations.  Loading-tests  of  the  materials  forming  the  foun- 
dation-bed are  made  to  assist  in  determining  its  safe  bearing  capacity.  It  is  not 
known  to  what  extent  the  supporting  power  of  a  given  soil  varies  with  the  area 
subjected  to  the  unit  load,  and  tests  on  small  areas  are  not  a  safe  guide  for  the 
safe  load  on  large  areas.  On  account  of  the  expense  involved,  tests  on  large 
areas  are  rarely  made,  the  usual  test  being  on  an  area  of  about  i  sq  ft.  The 
test  should  be  made  on  an  undisturbed  portion  of  the  foundation-bed,  leveled 
to  receive  the  test-load,  and  for  a  space  around  the  area  tested,  so  that  the 


146  Foundations  Chap.  2 

adjoining  material  is  not  reinforced  or  surcharged  by  a  bank  of  unexcavated 
material.  The  load  should  be  applied  with  the  least  possible  jar  or  movement 
of  the  surface  in  contact  with  the  material  of  the  foundation-bed. 

Explanation  of  Methods.  A  convenient  arrangement  for  this  purpose 
consists  of  a  vertical  timber  or  post  carrying  a  platform  to  receive  the  test-load, 
and  having  four  horizontal  guys  at  the  top  to  keep  the  post  in  a  vertical  position. 
The  bottom  of  the  post,  forming  the  loading-area  should  be  approximately  12  by 
12  in  and  its  exact  area  should  be  known.  The  platform,  sufficiently  strong 
to  support  the  load  to  be  applied,  should  be  concentric  with  the  post  and  as 
close  to  the  bottom  of  the  post  as  practicable.  The  load  may  be  pig  iron,  cement 
or  sand  in  bags,  or  any  other  convenient  material.  The  guys  should  be  not  less 
than  four  in  number,  should  be  attached  to  the  top  of  the  post  and  should  lead 
horizontally  so  as  not  to  pull  up  or  down  on  it.  Levels  should  be  read  to  a 
point  on  the  post  above  or  below  the  load,  as  may  be  most  convenient.  The 
load  should  be  applied  gradually  and  with  the  least  possible  jar,  care  being  taken, 
also,  to  keep  the  loading  uniform  on  opposite  sides  of  the  post,  which  should  be 
always  vertical.  Levels  should  be  taken  at  frequent  intervals  during  the  applica- 
tion of  the  load.  The  level  observed  when  the  platform  is  first  in  position  may 
be  taken  as  zero  and  successive  settlements  referred  to  it.  When  the  proposed 
unit  load  has  been  reached,  no  additional  load  should  be  added  until  no  further 
settlement  is  observed.  After  this,  first  50  and  later  100%  overload  may  be 
added  and  the  total  and  periodic  settlements  observed.  If  the  settlement  under 
a  test-load  of  twice  the  proposed  load  is  not  excessive,  the  test  is  considered  satis- 
factory. 

12.   Topographical  and  Special  Conditions 

Excavations  over  Inclined  Strata.  In  case  the  site  of  a  proposed  building 
is  on  a  slope,  and  especially  if  the  slope  is  steep,  there  may  be  danger  from  a 
slip  of  the  material  forming  the  foundation-bed.  (See,  also,  page  135.)  This 
may  occur  if  there  is  an  inclined  plane  of  separation  between  layers  of  the  under- 
lying rock,  or  between  the  rock-surface  and  the  material  overlying  the  rock, 
or  if  inclined  strata  or  beds  of  clay  occur  below  the  foundation-bed.  Slips  in 
such  locations  are  the  more  likely  to  occur  if  water  is  present,  as  the  water 
increases  the  weight  of  the  soil  and  also  reduces  the  coefficient  of  friction 
against  sliding.  Such  conditions  are  frequently  indicated  by  the  appearance  of 
springs  or  springy  ground  below  the  site.  Where  the  base  of  the  slope  reaches 
a  stream  or  river  there  may  be  danger  from  the  washing  away  of  banks  which 
have  been  supporting  the  side  slopes  of  the  valley.  In  the  case  of  deep  valleys 
with  steep  clay  banks,  or  in  any  location  where  landslides  have  been  known  to 
occur,  great  care  should  be  taken  to  extend  the  footings  to  a  bed  that  will  not 
be  affected  by  any  landslide.  It  sometimes  happens  that  there  is  a  slow,  con- 
tinuous and  general  movement  of  the  material  forming  the  side  slope  of  a  valley 
toward  the  center  of  the  valley;  but  such  conditions  are  rare,  fortunately,  as,  in 
general,  no  adequate  protection  is  possible.  In  certain  limestone  formations 
there  is  danger  from  natural  caves  formed  in  the  limestone  by  the  action  of 
water. 

Excavations  Near  Navigable  Waters.  When  buildings  are  located  near 
navigable  waters,  it  not  infrequently  happens  that  dredging-operations  at  a 
considerable  distance  induce  a  flow  of  fine  sand  or  clay  from  strata  underlying 
the  adjoining  banks.  This  has  occurred  where  the  existence  of  such  strata 
was  not  suspected.  This  danger  is  especially  to  be  guarded  against  in  marshy 
localities  adjoining  waters  which  are,  or  may  be,  used  as  navigable  streams,  or 
in  locations  near  the  water-front  where  it  is  Ukely  that  docks  will  be  constructed, 


Topographical  and  Special  Conditions  147 

Damage  from  Adjoining  Excavations.  Common  and  statute  laws  make 
general  provision  for  the  protection  of  property-owners  against  damage  result- 
ing from' the  acts  of  others  in  making  such  excavations;  but  an  owner  has  usu- 
ally no  control  over  such  operations,  whether  on  adjoining  properties  or  streets, 
and  in  general  will  prefer  the  assurance  of  safety  to  the  possibility  of  damage 
to  his  building  and  the  expense  and  uncertainty  of  a  lawsuit.  While  it  is  not 
always  possible  to  guard  fully  against  the  effects  of  adjoining  excavations,  and 
while  the  expense  of  so  doing  is  not  always  justifiable,  due  consideration  should 
be  given  to  the  matter.     The  following  suggestions,  therefore,  may  be  of  value. 

Depth  of  Adjoining  Excavations.  Footings  adjacent  to  property-lines 
or  situated  where  there  is  a  probability  of  future  additions  to  a  building,  or 
footings  of  a  building  which  adjoins  property  liable  to  become  the  site  of  building- 
operations,  should  go  down  at  least  as  deep  as  the  maximum  probable  depth  of 
the  adjacent  work.  In  estimating  these  probabilities,  the  character  of  the  loca- 
tion should  be  taken  into  account.  In  medium-priced  residential  sections 
footings  are  rarely  carried  much  deeper  than  lo  ft,  a  sufficient  depth  for  a  cellar 
of  medium  height  below  grade.  In  high-priced  residential  sections  it  is  not  un- 
usual to  have  both  a  basement  and  a  cellar,  in  which  case  a  depth  of  cellar 
below  grade  up  to  20  ft  may  be  expected.  Cellars  for  residences  are  rarely 
carried  below  10  ft,  if  in  reaching  that  depth  the  excavation  goes  below  the 
water-level.  In  fact,  a  high  water-level  discourages  deep  excavation,  not  only 
on  account  of  the  increased  difficulty  and  expense  of  excavation  but  also  on 
account  of  the  expense  of  waterproofing.  In  business  sections,  especially  in 
sections  of  high  ground-rents,  there  is  an  increasing  tendency  toward  deep 
cellars,  especially  in  boiler-rooms,  where  clear  heights  of  20  ft  and  over  are  de- 
sirable for  modern  water-tube  boilers.  The  basements  are  frequently  rentable 
at  high  figures  for  restaurants,  vaults,  stores,  etc.,  so  that  in  many  instances  the 
entire  mechanical  equipment  of  the  building  is  housed  below  the  basement  in  a 
subbasement  and  boiler-pit,  the  excavation  for  which  extends  down  at  least 
30  ft  and  in  special  cases  60  ft  below  the  curb;  and  this  notwithstanding  the 
fact  that  the  water-level  may  be  only  from  10  to  20  ft  below  the  curb. 

Sewers  and  Trenches  as  Affecting  Foundations.  In  cities  and  towns 
consideration  should  be  given  to  the  possibility  of  the  construction  of  trenches 
in  the  streets.  For  the  majority  of  localities  it  will  be  sufficient  to  consider 
the  probable  depth  of  a  sewer  of  the  proper  depth  to  serve  the  street.  In  other 
localities  it  will  be  necessary  to  consider  the  broader  question  as  to  the  proba- 
bility of  deeper  excavations  for  trunk  sewers,  subways,  etc.  As  such  construc- 
tions are  controlled  by  broad  topographical  considerations,  no  general  rules  can 
be  given  and  the  local  city  engineer  should  be  consulted. 

Foundations  Near  Mines,  Shafts,  Wells,  Etc.  In  mining-districts  local 
authorities  should  be  consulted  as  to  danger  from  the  caving  of  old  mine- 
workings.  No  adequate  provision  can  be  made  in  the  foundation  against 
such  widespread  caving  or  subsidence  as  may  result  from  mining-operations. 
In  some  cases,  successive  falls  of  rock-fragments  from  the  roof  may  gradually 
fill  the  voids  left  by  the  mining-operations,  as  the  loosely  piled  fragments  of  the 
roof  will  occupy  more  space  as  fill  than  they  did  as  part  of  the  solid  roof-mass. 
It  sometimes  happens  that  where  the  original  working  is  deep,  progressive 
falling  of  the  roof  fills  all  voids,  and  no  surface-settlements  result.  In  other 
cases  the  overburden  may  settle  as  a  solid  mass,  causing  a  settlement  at  the 
surface  equal  to  the  thickness  of  the  old  working.  Precautionary  measures  may 
involve  the  filling  in  of  the  workings,  a  subject  outside  the  limits  of  this  chapter. 
In  the  case  of  an  important  building  a  local  mining  engineer  should  be  consulted 
or,  if  pessibbi  the  location  of  the  building  changed  to  a  safer  site.    Mining* 


148  Foundations  Chap.  2 

SHAFTS,  DEEP  WELLS,  SHAFTS  FOR  TUNNELS,  etc.,  may  causc  disturbances  of 
the  soil,  but  in  such  cases  the  settlement  is  generally  concentrated  around  the 
shaft  or  well,  and  buildings  at  a  reasonable  distance  are  slightly  affected,  if  at  all. 

Foundations  Near  Tunnels  and  Trenches  for  Railroads  and  Subways. 

In  large  cities  the  necessities  of  transportation  are  increasingly  calling  for  con- 
struction of  underground  railroads,  tunnels  and  subways.  Such  constructions 
are  generally  planned  to  follow  streets.  Railroad  tunnels  for  trunk  lines  can 
be  expected  to  follow  direct  lines  to  centrally  located  stations  or  terminals  along 
routes  which  avoid,  as  far  as  possible,  difficulties  of  construction,  condemnation 
of  real  estate  and  damage  to  high-priced  properties.  The  depth  of  excavation 
will  generally  be  as  shallow  as  practicable.  Where  the  tunnel  has  to  dip  to  pass 
underneath  some  obstruction,  the  approach-grades  will  probably  be  at  the  max- 
imum or  limiting  grade  of  the  particular  section. 

Relation  of  Subways  to  Foundations  of  the  Most  Important  Build- 
ings. In  subway-construction  for  rapid-transit  passenger  service,  the  lines 
can  be  operated  on  sharper  curves  and  with  steeper  grades  than  would  be  used 
in  the  case  of  a  trunk-line  railroad.  This  permits  the  lines  to  follow  closely 
the  lines  of  the  city  streets.  For  traffic-considerations  the  locations  will,  in 
general,  follow  the  principal  arteries  of  surface  traffic,  and  stations  will,  in  gen- 
eral, be  located  at  intersections  of  important  streets,  where  there  is  the  greatest 
congestion  of  population.  As  such  conditions  are  caused  by  the  existence  of 
trade-centers,  and  call  for  the  construction  of  high  buildings,  it  may  readily  be 
seen  that  the  heaviest  and  most  important  buildings  are  most  likely  to  have 
their  foundations  affected  by  the  construction  of  a  subway  in  their  immediate 
vicinity.  Where  there  is  reason  to  apprehend  the  construction  of  such  sub- 
ways or  TUNNELS,  information  should  be  sought  as  to  the  probable  depth  of 
the  excavation,  the  depth  at  which  water  is  encountered,  the  character  of  the 
material,  the  probable  width  of  the  construction  as  affecting  the  use  of  sidewalk 
vaults,  and  the  method  to  be  employed  in  making  excavations.  Where  the 
excavations  for  such  tunnels  and  subways  have  been  carried  below  the  levels 
of  the  footings  of  adjoining  buildings,  as  in  Baltimore,  Boston,  Brooklyn,  Chicago 
and  New  York  City,  buildings  along  the  routes  have  been  seriously  affected. 
Such  results  have  not  been  limited  to  any  particular  methods  used  in  the  con- 
struction of  the  tunnels,  as  even  where  the  excavations  were  wholly,  or  partly, 
in  rock,  serious  damage  has  been  done. 

13.   Loads  Coming  on  the  Footings 

The  Loads  to  be  Considered  in  the  design  of  the  footings  of  a  structure 
are: 

(i)  The  Dead  Loads,  or  the  loads  due  to  the  actual  weight  of  the  completed 
structure,  ready  for  occupancy. 

(2)  The  Live  Loads,  or  the  loads  due  to  the  occupancy  of  the  building  and  also 
to  the  weight  of  snow  on  the  roof. 

(3)  The  Wind-Loads,  or  the  vertical  components  of  stresses  in  the  structure, 
produced  by  wind-pressure. 

(i)  The  Dead  Load.  The  dead  load  of  any  structure  can  be  accurately 
calculated.  If  the  structure  is  properly  designed  the  part  of  the  dead  load 
supported  by  each  element  of  the  foundation  can  be  definitely  stated.  The  total 
dead  load  becomes  effective  as  soon  as  the  building  is  completed,  and  remains 
constant  thereafter  unless  additions  or  alterations  are  made  to  or  in  the  struc- 
ture. 


Loads  Coming  on  the  Footings  1^9 

(2)  The  Live  Load.  The  live  load  of  any  structure  is  the  sum  of  the  roof- 
loads  and  floor-loads.  In  designing  the  roof  and  floors  the  calculations  for 
strength  are  based  on  an  assumed  unit  load  which  should  be  the  maximum  load, 
consistent  with  the  probable  use  of  the  structure,  to  which  any  portion  of  the 
roof  or  floor  may  ever  be  subjected.  The  assumed  live  load  is,  therefore,  prob- 
ably greater  than  the  average  load  for  the  entire  area  of  a  floor  or  the  entire 
area  of  the  roof.  Moreover,  as  it  is  improbable  that  conditions  of  maximum 
loading  will  ever  occur  simultaneously  on  the  roof  and  on  all  of  the  several 
floors,  it  is  probable  that  the  maximum  load  on  the  footings  will  be  less  than  the 
sum  of  maximum  loads  on  the  roof  and  on  the  several  floors.  " 

The  Minimum  Live  Load  for  an  unloaded  building  is  zero. 

The  Actual  Live  Load  will  vary  from  zero  to  a  maximum,  which  maximum 
will  generally  be  less  than  the  total  assumed  Hve  load. 

The  Ratio  of  the  Probable  Maximum  Live  Load  to  the  Assumed  Live  Load 
varies  in  different  buildings,  so  that  no  table  or  general  rule  can  be  given. 

The  Probable  Maximum  Live  Load.  As  it  is  important  to  know,  approxi- 
mately at  least,  the  maximum  live  loads  to  which  the  footings  will  be  subjected, 
and  as  this  maximum  may  be  only  a  fraction  of  the  assumed  live  loads,  the 
architect  should  make  a  careful  study  of  the  conditions  of  loading  to  which  the 
building  will  probably  be  subjected  and  estimate  the  probable  maximum  live 
load  for  the  entire  building. 

Data  for  Estimating  Live  Loads.  (See,  also,  Chapter  XXI,  pages  718 
to  721.)  In  estimating  the  probable  maximum  live  loads  for  different  uses,  the 
following  notes  may  be  of  value.  In  certain  buildings  the  assumed  unit  load- 
ing on  the  roof  and  on  parts  of  each  floor  may  be  reached  at  various  times, 
but  it  is  unlikely  that  the  maximum  loading  of  all  parts  of  the  building  will 
occur  at  the  same  time.  In  buildings  cf  many  stories  the  probability  of  having 
maximum  loads  on  all  of  the  floors  at  the  same  time  decreases  with  the  number 
of  stories. 

Ordinary  Household  and  Office-Furniture  weighs  from  5  to  10  lb  per  sq  ft  of 
space  occupied.  While  safes,  bookcases  or  filing-cases  may  produce  local  load- 
ings of  from  10  to  100  lb  per  sq  ft,  the  average  load  on  office-floors  rarely  reaches 
10  lb  per  sq  ft. 

Residences,  Apartments  and  Parts  of  Hotels  not  used  for  public  assembhes 
are  rarely  loaded  with  more  than  5  lb  per  sq  ft  of  floor-area. 

Retail  and  Wholesale  Stores  require  a  large  percentage  of  the  floor-area  for 
the  use  of  salespeople  and  customers,  and  not  over  50%  of  the  floor-area  is  used 
for  the  storage  of  stock.  In  estimating  the  weight  of  miscellaneous  stocks,  an 
average  between  the  lightest  and  heaviest  classes  should  be  taken  for  the  weight 
per  cubic  foot,  and  also,  in  figuring  the  total  space  occupied  by  stock,  an  average 
should  be  taken  between  the  maximum  and  minimum  amount  of  stock  carried. 
In  RETAIL  DRY-GOODS  STORES  the  floor-load  for  the  entire  building  may  amount 
to  not  more  than  25  lb  per  sq  ft,  but  in  wholesale  stores,  and  especially  in 
grocery  and  hardware  stores,  the  average  load  may  greatly  exceed  this  figure. 

In  Workshops,  Loft-Buildings  and  Buildings  for  Manufacturing,  the  actual 
live  loads  will,  of  course,  vary  with  the  class  of  material  handled  and  the  weight 
of  the  machinery  used,  and  no  general  estimate  can  be  made.  Where  the  char- 
acter of  the  occupancy  to  be  expected  is  known  it  is  possible  to  make  a  close 
approximation  of  the  weights  of  machinery,  fixtures  and  average  stock  on  each 
floor. 

Storehouses.  In  buildings  used,  in  whole  or  in  part,  for  storage  purposes 
a  floor  may  be  used  for  light,  bulky  materials  which,  when  stowed  so  as  to  leav« 


150  Foundations  Chap.  2 

gangways  and  working-spaces,  will  give  a  resultant  load  much  below  the  as- 
sumed load.  On  the  other  hand,  the  heaviest  materials  may  be  compactly 
piled  from  floor  to  ceiling  in  defiance  of  building  regulations,  posted  notices  and 
common  sense.  Raw  materials  or  crated  or  baled  materials  can  be  packed 
closer  than  miscellaneous  articles,  and  are  therefore  liable  to  increase  the  loads. 

The  'Ratio  of  the  Total  Probable  Maximum  Live  Load  to  the  Total  Assumed 
Live  Load  having  been  determined  for  the  entire  building,  the  probable  maximum 
live  load  for  any  element  of  the  footing  may  be  readily  obtained  by  multiplying 
the  assumed  or  calculated  live  load  for  that  element  by  this  ratio. 

(3)  The  Wind-Load  is  generally  calculated  on  the  assumption  that  the  wind 
may  exert  a  uniform  pressure,  frequently  taken  at  30  lb  per  sq  ft,  on  the  entire 
external  area  of  any  side  of  the  building.  This  assumption  makes  no  deduction 
for  the  protecting  influences  of  adjoining  buildings.  In  a  building  of  any  size  it 
is  improbable  that  the  maximum  pressure  will  be  reached  over  the  entire  exposed 
area  at  the  same  instant  of  time,  and  consequently,  if  the  assumed  pressure 
represents  the  maximum  pressure,  the  average,  at  any  time,  will  be  less  than 
the  calculated  total. 

General  Efifect  of  Wind-Pressure.  The  horizontal  pressure  of  the  wind  tends 
to  increase  the  load  on  footings  on  the  leaward  side  of  the  building  and  to  de- 
crease the  load  on  footings  on  the  windward  side.  In  many  buildings  diagonal 
bracing,  called  wind-bracing,  or  other  special  construction,  is  used  to  prevent 
the  building  from  being  deformed  by  the  wind-pressure  and  to  convert  the  hori- 
zontal stresses  due  to  the  wind-pressure  into  vertical  components,  acting  along 
defined  lines  of  support,  that  is,  into  either  uplifts  or  loads  on  certain  walls, 
piers  or  columns.  Where  the  uplift  on  any  element  of  the  structure  is  less  than 
the  dead  load  on  the  same  element,  the  upHft  is  ignored.  Where  the  vertical 
component  increases  the  compression  in  any  element  it  is  called  the  wind-load  in 
THAT  ELEMENT  of  Construction  and  on  the  corresponding  footing.  The  design 
is  generally  based  upon  concentrating  all  of  the  wind-load  on  certain  external 
footings.  If,  on  account  of  the  general  rigidity  of  the  building,  or  on  account  of 
any  other  reason,  the  wind- stresses  reach  footings  not  designed  to  receive  wind- 
loads,  the  amounts  figured  on  the  external  footings  will  be  reduced  correspond- 
ingly. It  is  probable  that  the  maximum  effect  of  the  wind  results  from  a  series 
of  impulses  of  short  duration  and  that  the  effect  of  such  pulsations  may  be 
partially  overcome  by  the  inertia  and  elasticity  of  the  buildings;  so  that  the 
resultant  load  reaching  the  footing  may  be  only  a  part  of  the  theoretical  load  for 
the  instant  during  which  the  maximum  pressure  is  exerted.  (See,  also.  Chapter 
XXIX,  Wind-Bracing  of  Tall  Buildings.) 

The  Probable  Maximum  Wind-Load  acting  on  the  footing  is,  therefore,  less 
than  the  theoretical  load  due  to  the  maximum  wind-pressure.  If  the  assumed 
wind-load  represents  approximately  the  maximum  wind-pressure,  as  recorded 
by  a  wind-gauge,  it  would  appear  safe  to  assume  that  only  50%  of  the  assumed 
wind-load  would  act  to  produce  a  settlement  in  the  footings  of  a  building. 
Some  authors  recommend  that  in  proportioning  footings  all  wind-loads  be 
ignored;  but  this,  especially  in  the  case  of  high  and  narrow  buildings,  is  mani- 
festly improper.  The  minimum  wind-load  is  negative,  being  actually  an  uplift 
from  which  the  load  may  vary  to  the  maximum,  but  the  maximum  will  be 
reached  only  at  rare  intervals  and  will  endure  for  a  short  period  only. 

The  Combined  Wind-Load  and  Live  Load.  It  is  improbable  that  the  maxi- 
mum wind-load  and  the  maximum  live  load  will  occur  at  the  same  time,  which 
consideration  should  be  borne  in  mind  when  the  estimate  is  being  made  as  to 
the  effective  wind-load. 


Assumed  Loads  Specified  by  Building  Codes 


151 


14.   Assumed  Loads  Specified  by  Building  Codes^ 

Table  II.     Requirements  of  Building  Codes  for  Assumed  Loads  for  OflBce- 
Buildings 


City 


Requirements 


Atlanta,  Ga., 


Boston,  Mass. , 


Buffalo.  N.Y.... 


Minneapolis,  Minn., 


Richmond,  Va.*.  .  . 
St.  Louis,  Mo.*.  .  .  . 


St.  Paul,  Minn.. 


Cincinnati,  O.. 


Chicago,  111. . 


New  York  City*., 
Cleveland,  O 


Live  load,  75  lb  per  sq  ft  above  ist  floor;  150  lb  per  sq  ft  on 

ist  floor 
Footings  designed  for  dead  load  and  60%  of  live  load  and 

wind-load 

Live  load,  100  lb  per  sq  ft.  Wind-load,  30  lb  per  sq  ft  where 
erected  in  open  spaces;  in  built-up  districts,  25  lb  at  the 
loth  story,  2^1j  lb  more  for  each  succeeding  upper  story,, 
up  to  a  maximum  of  35  lb  to  the  14th  story  and  above 

Live  load,  70  lb  per  sq  ft.  Wind-load,  30  lb  per  sq  ft.  Foun- 
dations designed  for  the  acting  average  loads  in  the  com- 
pleted and  occupied  building  and  not  the  theoretical  or 
occasional  loads 

Live  load,  75  lb  per  sq  ft  above  the  first  floor;  100  lb  for  first 
floor.  Wind-load,  30  lb  per  sq  ft.  Roof  and  top  floor,  full 
live  load.  For  each  succeeding  lower  floor,  a  reduction 
of  5%  until  50%  is  reached,  such  reduction  being  used  for 
the  remaining  floors 

Foundations  designed  for  60%  of  the  live  load 

Live  load,  70  lb  per  sq  ft;  first  floor,  150  lb.  Loads  carried 
by  the  soil,  total  dead  load  and  10  lb  per  sq  ft  of  all  the 
floor-area.     Wind-load,  30  lb  per  sq  ft 

Live  load,  60  lb  per  sq  ft  above  the  first  floor.  First  floor, 
125  lb.  Wind-load,  30  lb.  Roof  and  top  floor,  full  load; 
for  each  lower  floor,  a  reduction  of  5%  until  50%  of  the  full 
live  load  is  reached,  when  such  reduced  load  shall  be  used 
•  for  the  remaining  floors.  Footings  designed  for  dead  load 
and  live  load 

Live  load,  50  lb  per  sq  ft  above  first  floor;  100  lb  for  first 
floor.  Live  load  reduced  by  5%  for  each  floor  below  the 
top  until  20%  is  reached,  when  such  reduced  loads  shall 
be  used  for  remaining  floors.  Wind-load,  20  lb  per  sq  ft 
above  surrounding  buildings 

Live  load,  50  lb  per  sq  ft.  50%  of  the  live  load  used  for 
piles.  Piers  designed  for  85%  of  live  load  on  top  floor 
and  reduced  by  5%  for  each  lower  floor  until  50%  is 
reached,  when  such  reduced  loads  shall  be  used  for  the 
remaining  floors.     Wind-load  20_lb  per  sq  ft 

Footings  designed  for  60%  of  the  live  load 

Live  load  60  lb  per  sq  ft  in  offices  proper.  100  lb  per  sq  ft  in 
halls,  lobbies,  etc.  Footings  for  walls  designed  for  50% 
of  live  load.  Free-standing  columns  designed  for  80% 
of  loo-lb  load  and  75%  of  60-lb  load.  Wind-load  30  lb  per 
sq  ft  for  free-standing  structures  in  built-up  districts; 
25  lb  per  sq  ft  at  the  loth  story  and  2y2  lb  less  for  each 
lower  story,  and  2\^  lb  more  for  each  higher  story,  until 
35  lb  is  reached  ____________^ 


*  Codes  are  constantly  changing.  Richmond's  new  code  gives  floor-loads;  St.  Louis 
has  changed  some  values;  New  York  City's  new  code  gives  floor-load  values  different 
from  those  of  the  former  code. 


152  Foundations  Chap.  2 

Reduction  in  Assumed  Loads.  The  building  codes  of  various  cities  con- 
tain rules  governing  the  assumptions  to  be  made  as  to  live  loads  and  wind-loads, 
and  these  rules  generally  provide  for  some  reduction  in  the  assumed  loads. 
Generally,  it  will  be  found  possible  to  meet  these  requirements  and  at  the  same 
time  arrange  for  the  proper  proportioning  of  the  supporting  areas.  Table  II, 
page  151,  gives  briefly  the  requirements  of  the  building  codes  of  several  cities,  as 
to  assumed  loads  for  office-buildings. 

15.   Proportioning  the  Supporting  Areas  for  Equal  Settlement 

The  Minimum  Areas  of  Support.  The  actual  dead  loads  and  the  assumed 
live  loads  and  wind-loads  for  each  linear  foot  of  wall  and  for  each  column,  pier, 
or  other  supporting  element  of  the  building  down  to  the  level  of  the  footings 
having  been  calculated,  a  foundation-plan  should  be  prepared  giving  the  amount 
and  center  of  action  of  all  loads.  For  safety  under  the  worst  possible  combina- 
tion of  loads,,  each  footing  should  be  ample  to  support  the  total  of  the  dead  loads, 
live  loads  and  wind-loads  coming  on  it.  The  minimum  areas  of  support  for 
any  footing  are  obtained  by  dividing  the  total  of  the  dead  loads,  live  loads  and 
wind-loads  by  the  safe  supporting  power  of  the  foundation-bed.  If  the 
foundation-bed  is  rock,  or  can  be  considered  as  incompressible  under  the  unit 
load,  the  minimum  areas  so  obtained  may  be  used  for  the  footings.  On  com- 
pressible materials,  or  generally  on  all  materials  other  than  rock,  the  use  of 
these  minimum  areas  will  not  result  in  uniform  settlements  owing  to  the  fact 
that  the  actual  live  loads  and  wind-loads  are  not  consistent  with  the  assumed 
live  loads  and  wind-loads. 

The  Actual  Loads  on  the  Footings.  In.accordance  with  what  has  been 
previously  said,  let  us  assume  that  the  dead  load  is  constant,  and  that  for  a 
building  under  consideration  the  probable  maximum  live  load  is  50%  of  the 
assumed  hvc  load,  that  the  probable  maximum  wind-load  is  40%  .of  the  assumed 
wind-load,  and  that  on  the  completion  of  the  building,  for  a  short  period,  the 
live  loads  and  wind-loads  reduce  to  zero.  The  actual  loads  on  the  footings 
would  then  be: 

(i)  Upon  completion  of  the  building,  the  dead  load  only; 

(2)  Under  the  maximum  load  due  to  occupancy  and  to  snow  on  the  roof, 
the  dead  load  plus  50%  of  the  assumed  live  load; 

,(3)  When  loaded  as  in  (2)  and  subject,  in  addition,  to  the  maximum  prob- 
able wind-action, 

(a)  The  footings  on  the  leaward  side  of  the  building  will  sustain  the  total 

dead  load,  plus  50%  of  the  assumed  live  load,  plus  40%  of  the  as- 
sumed wind-load; 

(b)  The  footings  on  the  windward  side  of  a  building  will  sustain  the  total 

dead  load,  plus  50%  of  the  assumed  Uve  load,  minus  40%  of  the  as- 
sumed uplift; 

(c)  Other  footings  will  support  the  total  dead  load,  plus  50%  of  the  as- 

sumed live  load,  plus  zero  wind-load; 
(4)  Intermediate  conditions  as  to  live  loads  and  wind-loads  will  produce 
loadi/igs  intermediate  between  (i)  and  (3). 

Variations  in  Unit  Loads  on  Foundation-Beds.  With  such  known  varia- 
tions it  is,  therefore,  impossible  to  proportion  the  supporting  areas  so  that  the 
unit  load  on  the  foundation-bed  shall  be  uniform  at  all  times.  If  the  support- 
ing areas  are  proportioned  in  the  ratio  of  the  dead  load  only,  the  building,  on 
completion,  and  before  occupancy,  will  uniformly  load  the  supporting  areas, 
and  at  that  time  all  of  the  footings  should  show,  equal  settlements;  but  subse- 


Proportioning  the  Supporting  Areas  for  Equal  Settlement     153 

quently,  when  the  supporting  areas  have  been  subjected  to  the  full  effects  of  the 
live  loads  and  wind-loads,  certain  supporting  areas,  having  a  high  percentage 
of  live  loads,  or  of  live  loads  and  wind-loads,  will  be  subject  to  a  higher  unit 
load,  and  the  corresponding  footings  will  consequently  settle  more  than  other 
footings  supporting  a  low  percentage  of  live  loads,  or  Hve  loads  and  wind- 
loads. 

Non-Uniformity  in  Footing-Settlements.  If,  on  the  other  hand,  the  sup- 
porting areas  are  proportioned  on  the  basis  of  the  dead  loads,  plus  the  maximum 
live  loads,  plus  the  maximum  wind-loads,  even  if  the  maximum  loads  are  the 

PROBABLE  ACTUAL  MAXIMUM  LOADS,  and  not  the  FICTITIOUS  ASSUMED  LOADS,  it  is 

inevitable  that  upon  the  completion  of  the  building  and  before  occupancy,  the 
supporting  areas  having  a  lower  percentage  of  Uve  loads  and  wind-loads  will 
have  a  higher  unit  load,  and  the  corresponding  footings  will  have  settled  more 
than  other  footings  supporting  a  high  percentage  of  hve  loads  and  wind-loads. 
On  this  basis,  the  footings  will  not  come  to  a  uniform  settlement  until  they 
have  been  subjected  to  the  maximum  live  loads  and  wind-loads. 

I  Arbitrary  Rules  for  Proportioning  Supporting  Areas.  Various  arbi- 
trary RULES  have  been  recommended  for  the  proportioning  of  the  supporting 
areas  to  secure  equal  settlements.  These  rules  generally  provide  for  a  reduc- 
tion in  the  assumed  live  loads  and  wind-loads,  but  do  not  take  into  consideration 
the  fact  that  a  large  proportion  of  the  total  settlement  of  certain  footings  may 
take  place  subsequently  to  the  completion  of  the  building  and  after  other  foot- 
ings may  have  reached  practically  their  full  settlement. 

Rational  Rule  for  Proportioning  Supporting  Areas.  The  rule  herein- 
after recommended  provides  not  only  for  a  reduction  of  the  assumed  loads  on 
a  more  rational  basis,  but  also  fof^the  proportioning  of  the  footings  for  the  mean 
load,  instead  of  for  the  ultimate  load,  and  it  is  believed  that  the  resulting  settle^ 
ments  will  be  as  nearly  uniform  as  possible.  The  rule  is  based  on  the  propor- 
tioning of  the  footings  in  accordance  with  the  loads  which  will  act  on  the 
footings  at  the  time  when  all  of  the  dead  loads  and  one-half  of  the  probable 
maximum  live  loads  and  wind-loads  exist.  The  reason  for  taking  one-half  of 
the  probable  maximum  wind-loads  and  live  loads  is  that  these  loads  vary  from 
zero  to  a  maximum,  the  average  being  one-half  of  the  maximum. 

Provision  for  Variations  in  Loads.  On  the  completion  of  the  building 
and  before  the  live  loads  or  wind-loads  have  gone  on  the  footings,  the  settle- 
ments will  not  be  uniform,  because  areas  designed  for  a  high  percentage  of  live 
loads  and  wind-loads  will  have  much  less  than  their  average  load  and  will  there- 
fore have  settled  less  than  footings  having  a  low  percentage  of  live  loads  and  wind- 
loads.  When  these  same  footings  have  been  subjected  to  the  maximum  probable 
live  loads  and  wind-loads,  the  settlements  will  again  be  unequal,  because  .the 
areas  have  been  proportioned  for  only  one-half  of  the  probable  maximum  live 
loads  and  wind-loads;  but  the  footings  which  originally  were  the  highest  will 
now  be  the  lowest.  The  inevitable  movement  due  to  the  variation  in  the  live 
loads  and  wind-loads  will  be  equally  divided,  one-half  of  the  settlement  being 
required  to  bring  the  footing  to  the  level  of  a  footing  having  the  dead  loads  only, 
and  the  other  half  of  the  settlement  carrying  it  an  equal  distance  below  the  same 
footing.  In  other  words,  the  method  provides  for  the  least  possible  variation 
between  footings  having  different  proportions  of  live  loads  and  wind-loads. 

The  Mean  Load.  For  lack  of  a  better  name,  the  loads  taken  for  the  pro- 
portioning ot  the  footings,  consisting  of  the  total  dead  loads,  one-half  of  the 
probable  maximum  live  loads  and  one-half  of  the  probable  wind-loads  coming 
on  each  footing,  will  be  called  the  mean  load. 


154  Foundations  Chap.  2 

The  Mean  Unit  Load.  The  areas  will  be  made  such  that  the  load  on  the 
foundation-bed  due  to  the  mean  loads  will  be  uniform,  and  this  uniform  load 
which,  in  general,  will  be  considerably  less  than  the  allowable  unit  load  on  the 
foundation-bed  will  be  called  the  mean  unit  load. 

I'he  Minimum  Unit  Load.  The  necessity  for  providing  for  the  worst 
possible  condition  of  loading  is  satisfied  if  the  supporting  area  for  all  footings 
is  sufficiently  large  to  support  the  total  of  the  dead  loads  and  the  assumed  live 
loads  and  wind-loads  at  the  allowable  unit  pressure.  The  resulting  areas  of 
support  are  the  minimum  areas,  and  any  change  in  these  areas  necessary  to 
make  them  proportionate  to  the  mean  loads  must  be  effected  by  increasing  some 
areas  rather  than  by  diminishing  any.  Any  mean  unit  load  which  would  give, 
when  divided  into  the  mean  loads,  areas,  aU  of  which  would  be  larger  than  the 
minimum  areas,  would  serve  as  the  mean  unit  load,  but  it  is  more  economical 
to  determine  the  lowest  possible  mean  unit  load  which,  when  applied  to 
the  mean  loads,  will  give  the  least  possible  increase  of  the  areas.  This  can  be 
done  by  determining  which  one  of  the  minimum  areas  carries  the  least  mean 
LOAD  PER  SQUARE  FOOT.  This  area  may  be  selected  by  calculating  the  mean 
load  on  each  of  the  minimum  areas,  or  more  simply,  by  comparing  the  table 
of  assumed  loads  and  a  table  giving  the  mean  loads,  and  noting  which  footing 
has  the  largest  percentage  of  reduction  between  the  assumed  load  and  the 
mean  load.  The  resulting  mean  load  on  this  footing  will  be  the  minimum  unit 
LO/\D  which  can  be  used  as  a  mean  unit  load. 

The  Method  Reduced  to  Rule.  The  method  can  be  reduced  to  rule  as 
follows: 

(i)  Prepare  a  table  giving  in  vertical  columns  or  table-divisions  for  each 
footing,  the  dead  loads,  the  assumed  live  loads,  the  assumed  wind-loads  and 
the  total  of  these  three  loads.    This  table  is  called  the  table  of  assumed  loads. 

(2)  Prepare  a  similar  table  giving  the  dead  loads,  one-half  of  the  maximum 
probable  live  loads,  one-half  the  maximum  probable  wind-loads  and  the  total 
of  these  three  loads.     This  table  will  be  called  the  table  of  mean  loads. 

(3)  By  a  comparison  of  the  two  tables,  find  the  supporting  area  which  has 
suffered  the  greatest  percentage  of  reduction  between  the  total  assumed  loads 
and  the  total  mean  loads  and  find  the  unit  load  resulting  from  the  mean  load  on 
this  area.    This  unit  load  will  be  called  the  mean  unit  load. 

(4)  Divide  the  total  mean  load  as  given  in  the  table  of  mean  loads  for  each 
footing  by  the  mean  unit  load.  The  result  will  be  the  required  area  of  sup- 
port. 

Short  Method  for  Determining  the  Mean  Unit  Load.  From  the  fore- 
going it  follows  that  the  mean  unit  load  can  be  obtained  more  directly  by  tlie  fol- 
lowing rule.  Find  the  supporting  area  which  has  suffered  the  largest  percentage 
of  reduction  between  the  total  assumed  load  and  the  total  mean  load  and  multi- 
ply the  allowable  unit  load  on  the  foundation-bed  by  the  ratio  obtained  by 
dividing  the  total  mean  load  by  the  total  assumed  load. 

Illustrative  Example.  The  following  example  is  figured  out  more  fully  than 
is  necessary  in  practice  in  order  to  fully  explain  the  method  and  also  to  compare 
the  method  with  other  methods  frequently  used  and  recommended.  Ordinarily 
the  wind-loads  on  a  building  of  the  size  and  type  assumed  in  the  example  would  be 
ignored,  but  they  have  been  considered  here  to  make  the  example  complete. 

A  factory-building  (Fig.  2)  is  to  have  four  floors  above  the  basement,  each 
capable  of  supporting  an  assumed  unit  load  of  200  lb  per  sq  ft.  The  load  on 
the  flat  roof  is  assumed  at  50  lb  per  sq  ft.  The  horizontal  wind-pressure  is  as- 
sumed as  a  uniform  pressure  of  40  lb  per  sq  ft,  on  the  sides  A  B  and  CD  only. 


Proportioning  the  Supporting  Areas  for  Equal  Settlement      155 


The  vertical  component  of  the  wind-pressure  is  to  be  taken  care  of  by  the  foot- 
ings of  the  side  walls.  There  is  also  an  inteiior  self-supporting  chimney  and 
ventilating  shaft  which  is  protected  from  the  wind  and  which  carries  no  floor- 
loads. 

The  foundation-bed  is  a  uniform,  sandy  material  which  is  expected  to  compress 
uniformly  and  at  the  rate  of  ^i  in  per  ton  of  load  per  sq  ft  of  supporting  area. 


D 


Ghini 

ey 

C 

JOl..i 

D 

D 


Col.5 


D 


Xgstnned  Load. 


PLAN  SECTION 

Fig.  2.     Foundation-plan  and  Section  of  Factory-building 


The  MAXIMUM  UNIT  LOAD  on  the  foundation-bed  is  taken  at  4  tons,  correspond- 
ing to  a  settlement  of  2  in  for  the  assumed  load.  The  calculated  dead  loads  of 
the  building,  including  all  construction  down  to  the  level  of  the  footings,  the 
summation  of  the  assumed  live  loads  and  the  vertical  components  of  the  assumed 
wind-loads  are  given  in  Table  III. 


Table  in.     Dead  Loads  and  Assumed  Live,  and  Wind-Loads 

Element  of  footing 

Division  i, 

dead  loads 

only, 

lb 

Division  2, 

assumed 

live  loads, 

lb 

Division  3, 

assumed 

wind-loads, 

lb 

Division  4, 
total  dead, 

live  and 

wind-loads, 

lb 

Side  walls  per  lin  ft 

Columns  i  and  5 

Columns  2,  3  and  4 

Chimney 

14000 
137  500 

90  000 
320  000 

8  400 
160  000 
340  000 

2  000 

24  400 
297  500 
430000 
320  000 

Table-columns  are  called  divisions  to  avoid  confusion  with  building-columns. 


156 


Foundations 


Chap.  2 


A  careful  study  of  the  probable  loading  of  the  building  shows  that  the  maximum 
live  loads  at  any  one  time  will  not  exceed  60%  of  the  total  assumed  live  loads, 
and  that  the  maximum  wind-loads  will  be  less  than  50%  of  the  assumed  wind- 
loads,  for  the  reason  that  the  assumed  wind-pressure  is  based  upon  the  highest 
recorded  pressure  on  a  Umited  area  in  an  exposed  situation,  whereas  the  pro- 
posed building  will  be  in  a  sheltered  situation.  Having,  therefore,  determined 
the  probable  maximum  live  loads  and  wind-loads  at  60%  and  50%  respectively 
of  the  assumed  loads,  the  so-called  mean  loads,  corresponding  to  loads  half-way 
*)etwe».n  the  minirnum  and  maximum  loads,  will  be  one-half  of  the  probable 
maximum  loads,  or  60%  X]^i=  30%  'of  the  assumed  Hve  loads  and  50%  X  I'i 
=  25%  of  the  assumed  wind-loads.  Table  IV  gives  the  dead  loads  and  the 
mean  live  loads  and  wind-loads  separately,  and  the  total  of  the  dead  loads  and 
mean  loads,  which  total  is  to  be  used  in  proportioning  the  areas  for  least  varia- 
tion in  settlement.    This  is  known  as  the  total  mean  load. 

Table  IV.     Dead  Loads,  Mean  Live  and  Wind-Loads  and  Total  Dead  and 
Mean  Loads 


Element  of  footing 

Division  5, 
dead  loads, 
unchanged, 

Division  6, 
one-half  of 
60%  of  as- 
sumed live 
loads,  lb 

Division  7, 
one-half  of 
50%  of  as- 
sumed wind- 
loads,  lb 

Division  8, 

total  mean 

loads,  lb 

- 

lb 

Side  walls  per  lin  ft  — 

Columns  i  and  5 

Columns  2,  3  and  4 

Chimney 

14000 
137500 

90  000 
320  000 

2520 

48  000 
102  000 

500 

17  020 
185  500 

192  000 
320  000 

Table-columns  are  called  divisions  to  avoid  confusion  with  building-columns. 


Comparing  the  two  tables  it  will  be  seen  that  the  interior  columns  of  the 
building,  columns  2,  3  and  4,  had  originally  the  largest  percentage  of  live  loads 
(no  wind-loads) ,  and  have  consequently  suffered  the  greatest  reduction  in  the 
amount  of  total  load.  The  minimum  areas  of  support  for  columns  2,  3  and  4, 
and  also  for  the  other  elements  of  the  footings,  are  obtained  by  dividing  the 
total  assumed  loads  given  in  division  4,  Table  III,  by  8000,  the  allowable 
unit  load  in  pounds  on  the  foundation-bed.  The  resulting  areas  are  given  in 
division  9,  Table  V.  No  reduction  can  be  made  in  these  areas  without  exceed- 
ing the  limitation  that  the  most  disadvantageous  combinations  of  loading,  how- 
ever improbable,  shall  not  exceed  the  safe  unit  load.  The  adjustment  of  the 
areas  to  the  probable  mean  loading,  as  given  in  Table  IV,  the  table  of  mean 
loads,  must  be  accomplished  solely  by  increasing  the  sizes  of  certain  footings. 

If  we  divide  the  total  mean  loads  in  division  8,  Table  IV,  by  the  minimum 
areas  given  in  division  9,  Table  V,  we  will  get  the  mean  load  per  sqQare  foot 
on  the  minimum  areas  for  each  element  of  the  footing.  The  results  given  in 
division  10,  Table  V,  show  that  the  meiin  load  for  columns  2,  3  and  4  is  only 
3  568  lb  per  sq  ft,  while  under  the  chimney  the  load  is  8  000  lb  per  sq  ft.  As 
no  reduction  in  area  is  permissible  it  is  necessary  to  increase  the  footings  under 
the  chimney,  side  walls  and  columns  i  and  5  until  the  mean  unit  load  corre- 
sponds to  the  mean  unit  load  for  columns  2,  3  and  5.  This  is  done  by  dividing 
the  mean  loads  given  in  division  8,  Table  IV,  by  3  568,  the  mean  unit  load  as 


Proportioning  the  Supporting  Areas  for  Equal  Settlement     157 

determined  for  columns  2,  3  and  4.     The  resulting  areas  are  given  in  division 
II,  Table  V,  and  are  the  areas  which  should  be  used. 

The  n^ethod  of  calculation  can  be  shortened  and  reduced  to  a  rule  as  followsi. 
Compare  Table  IV,  the  table  of  mean  loads,  with  Table  III,  the  table  of  assumed 
loads,  and  find  the  element  of  support  which  has  suffered  the  highest  percentage 
of  reduction  between  the  total  assumed  load  and  the  total  mean  load,  and  note 
the  corresponding  minimum  area  of  support  at  the  allowable  unit  load  on  the 
foundation-bed.  Divide  the  mean  load  for  the  same  element  of  support  by 
the  number  of  square  feet  in  the  minimum  area  of  support.  The  result  will  be 
the  unit  load  for  mean  settlement.  Then  divide  the  mean  loads  for  each  ele- 
ment of  support  by  the  mean  unit  load.  The  results  will  be  the  required  areas 
as  given  in  Table  V. 

Table  V.     Mean  Loads  on  Minimum  Areas  and  Areas  for  Mean  Loads 


Element  of  footing 


Side  walls  per  lin  ft 
Columns  i  and  5 .  . , 
Columns  2,  3  and  4 
Chimney , 


Division  9, 
minimum 

areas, 

sq  ft 


3.0s 
37-2 
53.8 
40.0 


Division  10, 

mean  loads  on 

minimum 

areas, 
lb  per  sq  ft 


5580 
4986 
3  568 


Division  11, 

areas  for  mean 

loads, 

sq  ft 


4-7 
51-9 
53.8 
89.7 


Table-columns  are  called  divisions  to  avoid  confusion  with  building-columns. 


Or  the  mean  unit  load  may  be  determined  by  multiplying  the  allowable  unit 
load  by  the  ratio  obtained  by  dividing  the  mean  load  for  the  element  of  sup- 
port having  suffered  the  highest  percentage  of  reduction  by  the  assumed  load 
for  the  same  element. 

Resulting  Settlements.  The  following  Tables  VI,  VII  and  VIII  show  the 
comparative  settlements  which  may  be  expected  if  the  supporting  areas  are 
proportioned  in  accordance  with  different  assumptions  as  to  load.  In  all  the 
tables  it  is  assumed  that  the  foundation-bed  will  settle  H  in  per  ton  of  load,  and 
that  the  total  assumed  load  will  never  load  the  foundation-bed  in  excess  of  4  tons 
per  sq  ft. 

In  Table  VI  the  footings  are  proportioned  in  the  ratio  of  the  dead  loads  only. 

In  Table  VII  the  footings  are  proportioned  in  the  ratio  of  the  total  assumed 

LOADS. 

In  Table  VIII  the  footings  are  proportioned  in  the  ratio  of  the  mean  loads. 

In  each  table,  division  i  gives  the  dead  load  coming  on  the  footings  on  the 
completion  of  the  building.  Division  2  gives  the  load  coming  on  the  footings 
when  the  building  is  subjected  to  the  maximum  probable  live  loads  and  wind- 
loads.  Division  3  gives  the  supporting  areas  in  accordance  with  the  assumed 
loading.  Division  4  gives  the  settlements  for  the  unloaded  building.  Divi- 
sion 5  gives  the  settlement  after  the  addition  of  the  maximum  probable  live 
loads  and  wind-loads. 

Explanation  of  Table  VI.  The  method  of  proportioning  the  areas  in  the 
ratio  of  dead  loads  only,  as  recommended  by  C.  C.  Schneider*  may,  in  the  form 
of  a  rule,  be  stated  as  follows: 

*  See  article  on  the  Structural  Design  of  Buildings,  Trans.  Am.  Soc.  C.  E.,  vol.  54, 
June  1905. 


158 


Foundations 


Chap. 2 


Compare  the  table-division  of  dead  loads,  Table  VI,  with  the  division  of 
assumed  live  loads,  find  the  element  of  support  which  has  the  highest  percentage 
of  live  loads  to  dead  Ipads,  and  note  the  corresponding  minimum  area  of  support 
at  the  allowable  unit  load  on  the  foundation-bed.  Divide  the  dead  load  for 
the  same  element  of  support  by  the  number  of  square  feet  in  this  minimum  area 
of  support,  and  the  result  will  be  the  unit  load  due  to  the  dead  load  only.  Then 
divide  the  dead  loads  for  all  other  elements  of  support  by  this  unit  load,  and 
the  results  will  be  the  areas  required.  Thus,  in  Table  VI,  it  is  seen  by  referring 
to  Table  III  that  columns  2,  3  and  4  have  the  greatest  percentage  of  Hve  load 
to  dead  load,  and  their  minimum  area  of  support,  as  in  Table  V,  is  53.8  sq  ft. 
Then,  90  000  -r-  53.8  =  i  675  lb,  the  unit  load  due  to  the  dead  load  only.  The 
area  for  columns  i  and  5  is  137  500  -^  i  675  =82.1  sq  ft.  The  process  is  simi- 
lar for  the  other  elements. 


Table  VI.     Footings  Proportioned 

in  the  Ratio  of  the  Dead  Loads  Only 

Probable  settlement  where  supper 
deaa 

tin?  areas  are  proportioned  in  the  ratio  of 
loads  only 

Element  of  footing 

Division  i 

Division  2 

Division  3 

Division  4 

Division  5 

Dead  loads 

only, 

lb 

Maximum 

probable 

loads, 

lb 

Areas, 
sq  ft 

Settlements 

Empty, 
in 

Loaded , 
in 

Side  walls  per  lin  ft 

Columns  i  and  5 

Columns  2,  3  and  4 

Chimney 

14  000 
137  Soo 

90  000 
320  000 

20  040 
233500 
294  000 
320  000 

8.3 

82.1 
53.8 
191. 0 

0.42 
0.42 
0.42 
0.42 

0.60 
0.71 
1.36 
0.42 

Maximum  variation,  em 

pty 

0.00 

0.94 

Maximum  variation,  loa 

ded 

Table-columns  are  called  divisions  to  avoid  confusion  with  building-columns. 


The  calculations  for  settlements  are  readily  made,  when  the  amount  of  com- 
pressibility of  the  foundation-bed  is  known,  by  multiplying  the  unit  load  on  the 
foundation-bed  of  each  element  of  support  by  the  amount  of  compressibility  of 
the  foundation-bed  per  unit  of  load.  Thus,  in  the  above  example  the  amount 
of  compressibility  is  given  as  V2  in  per  ton.  In  Table  VI  the  unit  loads,  due  to 
dead  loads  for  each  element  of  support,  are  the  same,  or  i  675  lb  =  0.838  tons 
per  sq  ft,  which,  multiplied  by  }^  =  0.42  in.  Similarly,  the  unit  loads  due  to 
maximum  probable  loads  for  each  element  of  support  are  determined,  and  these 
loads,  in  tons,  multiplied  by  one-half,  give  the  settlements  in  inches  as  given  in 
division  5  of  Table  VI. 

Explanation  of  Table  VII.  The  areas  given  in  Table  VII  are  obtained  by 
dividing  the  total  maximum  dead  loads,  live  loads  and  wind-loads  (Table  III) 
by  the  allowed  unit,  8  000  lb  per  sq  ft,  and  are  the  minimum  areas  given  in  Table 
V.  The  settlements  for  the  loaded  building  are  based  on  the  maximum  probable 
loads  as  given  in  division  2  of  Table  VII. 


Proportioning  the  Supporting  Areas  for  Equal  Settlement     15^ 
Table  VII.     Footings  Proportioned  in  the  Ratio  of  the  Total  Assumed  Loads 


Probable  settlement  where  supporting  areas  are  proportioned  in  the  ratio  of 
total  assumed  loads 

Element  of  footing 

Division  i 

Division  2 

Division  3 

Division  4 

Divisions 

Dead  loads 

only, 

lb 

Maximum 

probable 

loads, 

lb 

Areas, 
sq  ft 

Settlements 

Empty, 
in 

Loaded, 
in 

Side  walls  per  lin  ft 

Columns  i  and  5 

Columns  2,  3  and  4. . . . . 
Chimney . . 

14000 
137  500 

90  000 
320  000 

20  040 
233  500 
294  000 
320  000 

3.0s 
37.2 
53.8 
40.0 

I. IS 

0.92 
0.42 
2.00 

1.64 
1.57 
1.36 

2.00 

pty 

1.58 

0.64 

Maximum  variation,  loa 

ded 

Table-columns  are  called  divisions  to  avoid  confusion  with  building-columns. 
Table  VIII.     Footings  Proportioned  in  the  Ratio  of  the  Mean  Loads 


Probable  settlement  where  supporting  areas  are 
total  mean  loads 

proportioned  in  the  ratio  of 

Element  of  footing 

Division  i 

Division  2 

Division  3 

Division  4 

Division  s 

Dead  loads 

only, 

lb 

Maximum 

probable 

loads, 

lb 

Areas, 
sqft 

Settlements 

Empty, 
in 

Loaded, 
in 

Side  walls  per  lin  ft 

Columns  i  and  5 

14  000 
137  soo 

90  000 
320  000 

20040 
233  soo 
294  000 
320  000 

4-7 
SI. 9 
S3. 8 
89.7 

0.74 
0.66 
0.42 
0.89 

1.06 
1. 12 
1.36 
0.89 

Columns  2,  3  and  4 

Chimney 

Maximum  variation, 
Maximum  variation. 

em 
loa 

pty       

0.47 

0.47 

ded 

Table-columns  are  called  divisions  to  avoid  confusion  with  building-columns. 

Explanation  of  Table  VIII.  The  areas  in  Table  VIII  are  obtained  as 
already  explained  and  as  given  in  division  11,  Table  V,  and  the  methods  used 
in  determining  the  settlements  are  similar  to  those  used  for  the  preceding 
tables.  In  Table  VIII  it  will  be  noted  that  columns  2,  3  and  4  have  a  settle- 
ment of  1.36  —  0.42  =  0.94  in,  as  a  result  of  the  addition  of  the  live  loads  and 
wind-loads.  Half  of  this  settlement  is  required  to  bring  these  footings  down  to 
the  level  of  the  chimney-footing,  and  the  other  half  of  the  settlement  brings 


160  Foundations  Chap.  2 

them  below  the  chimney-footing.  There  is  no  way  to  prevent  this  settlement 
of  0.94  in,  but  its  effect  on  the  building  is  reduced  to  a  minimum  by  having  the 
settlement  of  the  footings  of  columns  2,  3  and  4  start  above  the  chimney-footing 
and  finish  below  it.  The  chimney-footing  does  not  change  its  elevation  after 
the  completion  of  the  building,  and  compared  with  it,  the  variation  in  level  of 
the  other  footings  is  the  minimum.  In  their  mean  position,  half-way  in  their 
movement,  these  other  footings  will  be  at  the  same  level  as  the  chimney-footing. 

16.   Determining  the  Supporting  Areas 

General  Requirements.  In  laying  out  the  areas  of  support  for  any  struc- 
ture it  should  be  borne  in  mind,  as  previousl}'  explained,  that  (i)  the  total  of 
the  dead  loads,  assumed  live  loads  and  assumed  wind-loads  should  not  load  the 
foundation-bed  in  excess  of  the  allowable  load  on  it;  (2)  when  the  foundation- 
bed  is  compressible  the  areas  of  support  should  be  calculat^^d  by  the  method  of 
mean  loads;  and  (3)  the  center  of  gravity  of  the  supporting  area  should  coincide 
with  the  center  of  action  of  the  load  to  be  supported.  To  these  may  be  added 
a  further  condition  that  (4)  economy  will  be  furthered  by  keeping  the  support- 
ing areas  simple  in  outline  and  by  arranging  each  area  as  compactly  as  possible 
around  the  center  of  the  load  to  be  supported. 

(i)  The  first  condition  is  necessary  in  order  to  provide  that  no  possible  con- 
dition of  loading  will  exceed  the  allowable  pressure  on  the  foundation-bed. 

(2)  The  second  condition  provides  for  making  the  settlements  of  different 
footings  as  nearly  equal  as  possible. 

(3)  The  third  condition  provides  that  the  settlements  of  each  footing  shall 
be  uniform,  that  is,  that  the  footing  shall  not  settle  out  of  level. 

(4)  The  fourth  condition  provides  for  economy  in  design  in  the  footing  itself 
and  for  economy  in  making  the  excavation  for  the  footing,  especially  in  the  case 
of  deep  excavations  requiring  sheathing  for  the  protection  of  their  sides. 

In  the  case  of  a  free-standing  structure,  the  total  load  of  which  is  not  in  excess 
of  the  supporting  capacity  of  the  entire  area  of  the  building  at  the  safe  unit 
load  on  the  foundation-bed,  it  will  generally  be  possible  to  arrange  simple  sup- 
IX)rting  areas  whose  centers  will  correspond  with  the  centers  of  the  loads.  The 
disposition  of  such  areas  is  considered  in  succeeding  paragraphs  in  the  discus- 
sions of  Concentric  Loading.  In  buildings  having  restricted  sites,  where 
walls  or  columns  are  placed  close  to  adjoining  property-lines,  it  will  frequently 
be  impossible  to  arrange  for  simple  concentric  loadings  and  necessary  to  use 
offset  footings,  cantilevers  or  other  devices  to  transfer  the  loads  to  supporting 
areas  located  on  the  property.  Such  supporting  areas  are  discussed  in  succeed- 
ing paragraphs  relating  to  Eccentric  Footings. 

Footings  with  a  Concentric  Load.  In  order  to  have  the  load  on  the 
foundation-bed  uniform  under  a  looting  it  is  necessary  that  the  cenier  of  grav- 
ity of  the  supporting  area  should  coincide  with  the  center  of  gravity  of  the  load, 
otherwise  the  area  is  said  to  be  eccentrically  loaded  and  the  resulting  load 
on  the  foundation-bed  will  not  be  uniform.  Any  variation  in  the  loading  of  a 
compressible  foundation-bed  under  a  footing  will  result  in  an  unequal  settlement 
of  the  footing  and  this  in  turn  will  result  in  unequal  stresses  in  the  wall,  pier,  or 
column  supported  by  the  area. 

Wall-Footings  with  Concentric  Load.  In  the  case  of  a  wall,  the  footing 
should  project  an  equal  distance  on  each  side  so  that  the  center  of  gravity  of 
the  supporting  area  will  coincide  with  the  center  of  gravity  of  the  wall  and  of 
the  loads  transmitted  by  the  wall.  The  width  of  the  supporting  area  should 
vary  with  the  load  on  the  wall,  irrespectively  of  any  change  in  the  thickness  of 
the  wall 


OT^ 


Determining  the  Supporting  Areas  161 

Footing  for  a  Concentric  Isolated  Load.  In  the  case  of  a  simple  con- 
centrated LOAD,  as,  for  example,  a  load  from  a  column  or  pier,  the  footing 
maj'  be  circular,  square,  rectangular,  or  irregular  in  outline,  but  the 
center  of  gravity  of  the  area  mu5t  coincide  with  the  center  of  gravity  of  the  load. 
Theoretically  the  circular  shape  gives  the  most  economical  footing,  as  the 
supporting  areas  extend  radially  the  least  possible  distance  from  the  center  or 
axis  of  the  load.  Where  deep  excavation  is  necessary  the  circular  form  may 
lend  itself  to  an  economical  method  of  excavation,  as,  for  example,  when  cylin- 
drical piers  are  sunk  by  the  pneumatic  method  or  by  dredging.  In  general, 
however,  for  ordinary  footings  the  rectangular  form  is  preferable,  in  that  it 
lends  itself  to  an  economical  arrangement  of  grillage- beams.  The  square  is 
the  most  economical  rectangle  as  the  sum  of 

the   bending    movements   in    the  grillage  and       A     Property-Line      S 

bolsters  is  reduced  to  a  minimum.  I 

w 

Elongated  Supporting  Areas.    When  the         J 

supporting  area  for  an  isolated  load  cannot  be       -^G^^      ^       i 

made  a  circle  or  a  square,  for  example,  when  ^     l*        l    T        ' 

the  square  or  the  circle  would  overlap  an  ad-    ^ig.    3.      Elongated    Supporting 

joining  property-line  or  interfere  with  an  ad-  Area.     Concentric  Load 

joining    supporting    area,    the    necessary    area 

may  frequently  be  made  rectangular  in  form,  as  ABDC  (Fig.  3),  having  a 

width  Wj    twice  the  distance  a  between  the  center  of  the  load  O  and  the 

limiting  line  yl  5. 

The  required  length  /  equals  the  required  area  divided  by  w  and  the  area 
should  be  centered  on  O,  that  is,  h  must  equal  h. 

Combinations  of  Simple  Areas.  Two  Adjacent  Isolated  Areas.  W' hen 
adjoining  supporting  areas  overlap  or  when,  for  other  reasons,  it  is  desirable  to 
combine  adjacent  footings,  the  best  arrangement  may  be  obtained  as  follows: 
Knowing  the  supporting  area  required  for  each  of  two  adjacent  concentrated 
loads  and  the  distance  between  the  centers  of  the  loads,  the  sum  of  the  two 
areas  should  be  divided  by  twice  the  distance  between  the  load-centers.  The 
quotient  will  be  the  width  or  the  dimension  of  the  required  rectangle  of  sup- 
port taken  at  right-angles  to  the  line  connecting  the  load-centers;  and  the 
other  dimension  of  the  rectangle  will  be  twice  the  distance  between  the  load- 
centers.  The  center  of  the  area  should  be  placed  so  as  to  coincide  with  the 
center  of  gravity  of  the  two  loads,  when  it  will  be  found  that  each  load  will 
be  concentric 'with  its  own  area  of  support.  Where  a  row  of  columns  requires 
areas  which  nearly  overlap,  the  combination  of  the  areas  frequently  results  in 
economy  in  excavation  and  form-work. 

Supporting  Area  for  a  Concentrated  Load  in  the  Line  of  a  Wall. 

If  one  or  more  concentrated  loads  are  carried  in  the  line  of  a  wall  the  additional 
supporting  areas  reciuired  for  such  concentrated  load  may  be  provided  in 
either  of  two  ways. 

(i)  If  the  concentrated  loads  rest  on  the  wall,  as,  for  example,  when  the  wall 
supports  the  ends  of  girders  and  when  the  conditions  are  such  that  the  con- 
centrated loads  are  distributed  along  given  lengths  of  it,  then,  all  that  is  neces- 
sary is  to  increase  the  width  of  the  footing  for  the  given  lengths  sufficiently  to 
provide  for  the  total  of  the  uniformly  distributed  and  concentrated  loads. 

(2)  If  a  concentrated  load  is  on  the  center  line  of  the  wall  but  cannot  be  dis- 
tributed by  the  wall,  as  when  a  considerable  load  is  carried  by  a  pier  or  column 
to  the  level  of  the  footings,  then  one-half  the  additional  area  for  the  concentrated 
load  should  be  placed  on  either  side  of  the  wall-footing,  so  that  a  line  connecting 
the  centers  of  the  two  areas  will  pass  through  the  center  of  the  load.    In  general, 


fe2 


Foundations 


Chap.  2 


T,     X.  ,i    1 


1  J  1 

Fig.  4.  Square  Supporting 
Area.  Wall  and  Concentric 
Isolated  Load 


k  is  desirable  that  the  additional  areas,  together  with  the  area  for  the  wall  lying 

between  them,   should  approximate  a  square.     Knowing  the  width  of  the 

footing  required  to  support  the  wall  and  the  additional  area  required  to  support 

the  concentrated  load,  the  length  of  the  side  of  the 

required  square  can  be  determined  by  the  following 

formula  (Fig.  4): 

Let  w  =  the  width  of  the  footing; 

A  =  the  area  required  to  support  the  concen- 
trated load; 
/=  the  side  of  the  square  which  will  support 
a  length  of  wall  equal  to  /,  and  also 
provide  an  additional  area  equal  to  ^4. 
Then 

Supporting  Area  for  Concentrated  Load  not  in  the  Center  Line  of  a 
WalL  The  same  additional  supporting  area  is  required  for  this  as  for  a  con- 
centrated load  on  the  center  line  of  a  .wall,  but  the  total  area  must  be  divided 
unequally  between  the  two  sides  of  the  wall-footing, 
the  larger  portion  being  placed  on  the  side  of  the 
eccentric  load.  The  simplest  way  to  determine  the 
location  of  the  supporting  areas  for  this  combination 
is  to  determine  the  size  of  the  required  square  as  if 
the  concentrated  load  were  concentric  with  the  center 
line  of  the  wall.  The  next  step  is  to  calculate  the 
load  due  to  the  wall  for  the  length  of  this  square  and 
determine  the  location  of  the  center  of  gravity  of  the 
\:ombined  loads,  that  is,  the  center  of  gravity  of  this 
tvall-load  and  the  concentrated  load.  The  center  of  the  supporting  area  is  then 
placed  concentrically  with  the  center  of  gravity  of  the  combined  loads.  In 
Fig.  5  let 

w  =  the  required  width  of  the  wall-footing; 

0=  the  concentrated  load; 

A  =  the  area  required  for  the  support  of  the  concentrated  load.    Then, 
as  before,  the  length  of  the  side  of  the  required  square  will  be 

The  center  of  gravity  of  the  wall-load  contained  between  the* lines  AD  and 
BC  is  at  g,  and  the  amount  of  the  load  is  evidently  the  load  per  foot  multiplied 
by  the  distance  AB=f.  Knowing  the  position  and 
amount  of  the  loads  at  0  and  g,  the  center  of  gravity 
of  the  combined  loads  is  determined,  say  at  G.  This 
fixes  the  center  for  the  square. 

Supporting  Area  for  a  Concentrated  Load  on 
the  End  of  a  Wall.  A  somewhat  different  treatment 
is  required  for  this,  but  the  supporting  area  may  be 
best  determined  as  follows  (Fig.  6):  Knowing  the 
width  w  of  the  footing  required  for  the  support  of  the 
wall,  the  additional  area  required  for  the  concentrated 
load  0  and  the  distance  p  from  the  center  of  the  concen- 
trated load  from  the  end  of  the  wall,  proceed  in  this  way.  Determine  the  square 
whose  area  corresponds  to  the  sum  of  the  areas  required  for  the  support  of 
the  concentrated  load  and  for  a  length  of  wall  equal  to  twice  the  projection  of  the 
wall  beyond  the  center  of  the  concentrated  load.    Plot  this  square  A  BCD  en  tne 


Fig.  5.  Square  Supporting 
Area.  Wall  and  Eccen- 
tric Isolated  Load 


L 

p 

■M 

J 

A 
K      E 

B 

s 

i 

1 
< 

H.  « 

R      H          C 
D 

3 

C 

'^      O 

L 

-•n 

Fig.  6.  Square  Support- 
ing Area.  Isolated  Load 
on  End  of  Wall 


Offset  Footings 


163 


foundation-plan  and  also  the  total  area  required  for  the  support  of  the  wall. 
The  square  A  BCD  includes  an  area  sufficient  for  the  support  of  the  concentrated 
load  and  for  a  section  of  the  wall  EFGH  corresponding  to  a  length  of  wall  equal 
to  twice  the  projection  p,  multiplied  by  the  width  of  the  footing.  It  is  evident 
that  the  area  KEHR  is  loaded  both  by  the  wall  and  the  concentrated  load;  in 
other  words,  that  the  square  A  BCD  is  too  small  by  the  amount  of  the  rectangle 
KEHR.  The  required  square  LMNO  will  be  approximately  the  square  which 
will  contain  the  original  area  A  BCD  plus  the  area  KEHR,  plus  twice  the  area 
JKRQ.  The  length  of  the  side  LM  =  MN  will  be  approximately  the  length 
of  the  original  square  plus  one-half  of  the  area  KEHR  divided  by  the  length 
of  the  original  square.  The  resulting  square  should  be  moved  from  the  posi- 
tion shown  on  the  drawing  so  that  its  center  coincides  with  the  center  of 
gravity  of  the  combined  concentrated  load  and  the  wall-load  back  as  far  as  the 
square  goes  on  the  wall.  A  further  approximation  may  be  necessary  where 
accuracy  is  required.  The  fmal  result  should  be  that  the  area  of  the  square 
LMNO  should  be  sufficient  to  support  the  concentrated  load  0  and  that  portion 
of  the  wall-load  JEGQ  resting  on  the  square,  and  that  the  center  of  gravity  of 
the  square  should  coincide  with  the  center  of  gravity  of  the  combined  loads. 


17.    Offset  Footings 

Supporting  Areas  for  Non-Concentric  Loads.  When  walls,  columns,  or 
piers  are  placed  close  to  property-lines  the  required  supporting  areas  cannot 
be  placed  concentrically  with  the  loads  without 
overlapping  the  property-lines.  In  such  cases 
recourse  must  be  had  to  some  method  which  will 
transfer  the  loads  to  supporting  areas  not  con- 
centric with  the  loads.  An  attempt  to  accomphsh 
this  result,  the  method  known  as  offsetting  the 
FOOTING  has  been  largely  used,  especially  for  side 
walls  adjoining  property-lines.  While  theoreti- 
cally faulty,  if  not  useless,  it  is  indisputable  that 
OFFSET  FOOTINGS  have  generally  served  the  pur- 
pose for  which  they  were  designed.  In  the  typical 
construction  a  cellar  wall  rests  on  a  course  of  con- 
crete or  of  flat  stones  forming  a  footing  course 
considerably  wider  than  the  wall,  the  projection 
being  entirely  on  one  side  of  the  wall.  The  load 
acting  on  one  side  of  the  center  of  the  footing 
loads  the  supporting  area  unequally.  The  vary- 
ing LOAD  on  the  supporting  area  can  be  calculated 
as  follows:    In  Fig.  7  let 

W  =  the  total  load  per  unit  of  length  coming  on  the  supporting  area; 
U  =  the  eccentricity  of  load,  that  is,  the  distance  between  the  center  of 

the  load  and  the  center  of  the  supporting  area; 
L  =  the  width  of  the  footing  =  the  width  of  the  supporting  area  =  AB; 
Ki=  the  unit  load,  or  pressure  on  the  foundation-bed  at  A,  the  edge  of 
the  footing  nearest  the  load;  ' 

K2  =  the  unit  load,  or  pressure  on  the  foundation-bed  at  B,  the  edge  of 
the  footing  farthest  from  the  load; 
y  =  any  ordinate,  from  A  to  B. 

Then  the  average  pressure  on  the  foundation-bed  will  evidently  be  W/L. 
The  pressure  at  A,  the  edge  nearest  to  the  point  of  application  of  the  load,  wiU 


Fig.  7.  Offset  Footing.  Vary- 
ing Pressure  on  Foundation- 
bed 


164 


Foundations 


Chap.  2 


be  Ki  =  W/L  (i  +  6  U/L),  or  the  maximum  lo.\d  will  equal  the  average  load 
plus  six  times  the  average  load  multiplied  by  the  ratio  of  the  eccentricity 
divided  by  the  width  of  the  footing. 

Similarly,  the  pressure  at  B,  the  edge  farthest  from  the  point  of  application 
of  the  load,  will  be  A'2  =  W/L  (1  —  6  U/L),  or  the  minimum  load  equals  the 
average  load  minus  six  times  the  average  load  multiplied  by  the  ratio  of  the 
eccentricity  divided  by  the  width  of  the  footing. 

When  the  eccentricity  equals  H  the  width,  the  pressure  at  B  becomes  zero. 
If  the  eccentricity  exceeds  H  the  width  there  will  be  an  uplift  at  B,  or  the  foot- 
ing will  have  a  tendency  to  overturn.  This  relation  is  generally  expressed  by 
saying  that  to  avoid  an  upward  reaction  the  center 
line  of  the  load  must  fall  within  the .  middle  third 
of  the  base. 

Load-Diagrams  for  Offset  Footings.  If  in  the 
diagram  (Fig.  8)  the  figure  A  DEC  represents  the 
load-diagram  on  the  foundation-bed  for  a  width  of 
footing  AD  and  the  load  ^C  is  the  maximum  per- 
missible load,  then  the  area  A  DEC  represents  the 
maximum  support  afforded  by  the  footing  AD.  If 
the  width  is  increased  until  the  load  falls  on  the  limit 
of  the  middle  third  or  to  the  width  AB,  then  the 
load  at  B  is  zero  and  the  support  is  represented  by  the  triangle  ABC,  the 
area  of  which  is  less  than  the  area  A  DEC.  Moreover,  if  the  width  of 
the  footing  is  reduced  until  its  center  is  concentric  with  the  load-center,  then 
the  load-diagram  becomes  AFGC,  the  area  of  which  is  greater  than  either  ABC 
or  A  DEC.  From  the  foregoing  it  is  evident  that  any  advantage  gained  by 
offsetting  the  footing  must  be  obtained  at  the  cost  of  concentrating  the  support 
given  to  the  wall  away  from  the  center  line  of  the  wall. 


I 


Q 


^B 


Fig.   8.     Pressure-diagrams 
for  Footings 


^  c 

1 

B 

! 

c 

D 

1 

:5 


G 

Fig.  9  Fig.  10  Fig.  11  Fig.  12 

Figs.  9,  10  and  11.     Eccentric  Loading  and  Tendencies  to  Failure  Due  to  Offset 

Footings;  Fig.  12.    Improved  Type  of  Construction 

Eccentric  Loading  Due  to  Offset  Footings.  In  Fig.  9,  representing  a 
simple  case  of  eccentric  loading  due  to  offset  footings,  the  load  on  the 
foundation-bed  at  E  is  perhaps  twice  the  average  load  and  at  F  about  zero. 
Tender  these  conditions  the  projecting  portion  of  the  footing  may  shear,  as  iadi- 


The  Use  of  Cantilevers  in  Foundations  165 

cated,  along  the  line  DG.  If  it  does  not  shear  and  if  there  is  any  settlement 
due  to  the  load,  the  settlement  will  be  unequal  and  the  footing  course  will  tend 
to  rotate  into  the  position  shown  in  Fig.  10.  The  entire  load  will  then  be  trans- 
mitted through  the  inner  lower  corner  D  of  the  cellar  wall,  rendering  the  wall 
unstable  and  developing  a  tendenc}^  to  move  in  the  direction  //, 

The  cellar  wall  may  successfully  resist  this  tendency  by  its  own  rigidity 
assisted  by  the  first-floor  beams  acting  as  ties  or  by  the  external  resistance 
afforded  by  an  abutting  wall  or  bank  of  earth,  or  it  may  partially  or  completely 
fail,  developing  a  horizontal  crack  as  indicated  in  Fig.  11  at  7. 

.In  this  figure  it  will  be  noted  that  the  base  of  the  wall  itself  is  offset.  This 
is  done  to  prevent  the  separate  rotation  o/  the  footing  course;  but  this  con- 
struction docs  not  diminish-  the  tendency  to  rotation  of  the  entire  base  of 
the  wall  and  to  the  formation  of  a  crack  at  /. 

An  improved  type  of  construction  is  illustrated  in  Fig.  12,  in  which  the  floor- 
beams  are  anchored  into  the  wall  and  the  cellar  wall  has  a  continuous  stepped 
batter  from  the  level  of  the  footing  up  to  the  level  of  the  beams.  The  beams 
should  evidently  be  arranged  as  tension-members,  should  run  across  the  build- 
ing and  should  be  anchored  in  the  opposite  wall.  While  this  method  may  have 
some  effect  it  is  of  doubtful  efficacy  and  should  never  be  used  for  piers. 

18.   The  Use  of  Cantilevers  in  Foundations* 

Application  of  the  Principle  of  the  Lever.  The  use  of  the  cantilever, 
in  transferring  a  load  to  a  supporting  area  not  concentric  with  the  load,  is  based 
upon  the  principle  of  the  lever  and  involves  a  girder  or  cantilever  connecting 
the  two  loads,  and  a  supporting  area  or  areas  the  center,  of  action  of  which 
lies  between  the  two  loads.  Part  or  all  of  the  load  on  one  side  counterbalances 
the  load  on  the  other  side  of  the  center  of  the  supporting  area. 

Illustrative  Example.  If  an  exterior  column  A  (Fig.  13)  carrying  a  load  of 
400  tons  and  requiring  100  sq  ft  of  supporting  area,  at  4  tons  per  sq  ft,  the  column- 
center  being  18  in  from  a  property-line  PP  which  forms  the  limit  of  the  building 
plot,  it  is  evidently  impractical  to  employ  a  concentric  footing  3  by  2>2)\^  ft  for 
its  support.  If,  however,  a  sufficient  counterweight  can  be  found  in  the  shape 
of  an  adjacent  interior  column-load,  as  at  B,  the  exterior  load  can  be  trans- 
ferred by  a  girder  or  cantilever  construction  CDEF  to  a  supporting  area  MN  •< 
lying  between  the  two  loads,  and  entirely  within  the  limits  of  the  property. 

In  Fig.  13  let  PP  represent  the  property-line,  A  the  center  of  the  load  on 
column  A,  and  B  the  center  of  the  load  on  column  B.  Let  the  load  on  A  be 
400  tons,  on  B,  200  tons  and  the  distance  AB  between  centers,  20  ft.  Assume 
that  a  rigid  girder  CDEF  supports  and  connects  the  two  columns.  If  now  a 
FULCRUM  or  point  of  support  G  is  provided  for  the  girder  at  some  point  between 
A  and  B,  the  load  on  that  point  can  be  readily  determined  from  the  principle 
OF  THE  LEVER  by  multiplying  the  load  on  A,  400  tons,  by  the  distance  AB^ 
20  ft,  and  dividing  the  product  by  the  distance  BG,  19  ft;  or,  the  load  ori 
G=  400  X  20/19  =  421  tons-f.  The  area  required  for  the  support  of  this  load, 
at  4  tons  per  sq  ft,  is  421/4  =  105H  sq  ft.  The  uplift  at  B,  or  the  part  of  the 
load  B  required  to  counterbalance  the  overhanging  load  A  is,  from  the  principle 
of  the  lever,  the  product  of  the  load  A  by  the  lever-arm  AG  divided  by  the  lever- 
arm  BG.  The  load  on  the  footing  for  B  is  the  difference  between  the  original 
load  and  the  uplift;  but  in  view  of  the  possibility  of  a  reduction  in  the  load  A, 
which  would  decrease  the  uplift  at  B,  it  is  well  to  provide  for  a  possible  increase 
in  the  load  B. 

*  See,  also.  Chapter  XIX,  pages  678  to  680,  for  an  example  of  a  Continuous  Girder  io 
Grillage  Foundation. 


166 


Foundations 


Chap.  2 


Determination  of  the  Area  of  Support.  In  determining  the  area  of 
SUPPORT  for  A,  having  assumed  one  dimension  of  the  supporting  area  to  be 
twice  the  distance  GP,  or  say  5  ft,  the  other  dimension  will  be  105 H  sq  ft/s  =  21 
ft  H  in.    If  the  length  21  ft  H  in,  as  determined,  is  found  to  be  excessive,  then 


2^ 


Fig.  13.     Cantilever  Foundation-construction 


the  point  G  must  be  moved  to  the  left  and  the  corresponding  length  of  the  sup- 
porting area  must  be  determined  as  before.  When  the  length  of  the  supporting 
area  for  the  fulcrum  of  the  cantilever  is  limited,  so  that  the  length  parallel  to 
the  prop)erty-line  is  fixed,  the  width  of  the  area  can  be  determined  experimentally 
or  by  the  use  of  the  formula 

X=  (L+u)  -  V(L  +  m)2-  2  WL/IS 
in  which 

L  =  the  distance  between  centers  of  the  two  loads; 
W  =  the  load  nearest  to  the  property-line; 
!  /  =  the  length  of  the  supporting  area; 
5  =  the  unit  load  on  the  supporting  area;   and 

u  =  the  distance  between  the  center  of  action  of  the  load  to  be  cantilevered 
and  the  edge  of  the  supporting  area  nearest  to  the  property-line. 

If  the  position  of  the  center  of  gravity  of  the  load  A  combined  with  that 
part  of  the  load  on  B  which  is  borne  by  the  cantilever  is  determined,  it  will  be 
found  to  coincide  with  the  fulcrum  or  point  of  support  G  of  the  cantilever,  thus 
demonstrating  that  the  use  of  the  cantilever  provides  a  means  of  combining 
two  loads  so  that  their  center  of  gravity  falls  on  the  center  of  a  supporting  area 
not  concentric  with  either  load. 

The  Grillage  Fulcrum.  Of  course  in  practice  the  knife-edge  fulcrum 
shown  in  the  diagram  is  not  used.  The  bottom  flange  of  the  girder  forming 
the  cantilever  rests  on  the  distributing  grillage  directly,  as  is  shown  in  Fig.  14, 
which  may  be  considered  a  typical  arrangement. 

The  Girdering-Method  for  Two  Equal  Loads.  When  it  is  desirable  to 
support  two  or  more  adjacent  concentrated  loads  on  a  single  supporting  area 


The  Use  of  Cantilevers  in  Foundations 


167 


the  method  called  girdering  is  employed.  In  the  case  of  two  concentrated 
loads,  let  A  and  B  (Fig.  15)  represent  two  columns.  Let  Wi  represent  the  load 
on  A  and  W2  represent  the  load  on  B.  Let  D  represent  the  distance  between 
the  centers  of  the  two  loads.  Let  G  represent  the  center  of  gravity  of  the  com- 
bined loads.  Let  r  represent  the  allowable  unit  load  on  the  foundation-bed. 
The  required  area  of  support  will  be  {Wi  +  W2)/r.    This  area  may  be  of  any 


^     ^ 


+ 


^  i     >  1     11     I  -I     I  ' 


+ 


Fig.  14.     Cantilever  Foundation.     Grillage  Fulcrum 


desired  shape,  provided  that  its  center  of  gravity  coincides  with  the  center  of 
gravity  of  the  combined  loads  at  G.  In  general,  however,  the  most  economical 
arrangement  will  result  when  each  load  is  as  nearly  as  possible  over  the  center  of 
gravity  of  its  own  required  area.  If,  however,  this  is  impracticable,  as  for 
example,  when  either  column  is  near  a  property-line  or  an  adjoining  footing,  it 
will  be  necessary  to  distribute  the  loads  of  both  columns  over  the  area  lying  be- 
tween the  two  columns.  In  the  case  of  two  columns  equally  loaded,  as  in 
Fig.  15,  the  distance  u,  from  the  center  of  column  A  to  the  property-line  PP, 
determines  the  maximum  allowable  extension  beyond  column  A.  The  dimen- 
sions of  the  area  are  obtained  by  making  the  length  L  of  the  footing  equal  to 


168 


Foundations 


Chap.  2 


the  distance  D  between  the  columns  plus  twice  the  extension  u.    Knowing  the 
length  of  the  required  area  the  width  w  is  determined  by  simple  division. 

The  Girdering-Method  for  Two  Unequal  Loads.  In  the  case  of  columns 
not  equally  loaded,  the  supporting  area  may  be  a  trapezoid,  as  in  Fig.  16, 
the  center  of  gravity  of  which  must  coincide  with  the  center  of  gravity  of  the 
loads.     Knowing  the  sum  and  distance  apart  of  the  loads  and  the  area  for  their 


+ 


V  A    I'.'.j    l.'i    I  .'J    f  J    r,'  J    I     .11     i    VM 

G 


"\  \":\  I'  "I  i"N  I'  i  \\'\  t;'  ^  I,. "I  I  \  \:  .i  \  .'j  jn 


'r^U-^ 


-u—>\? 


Fig.  15.    Girdering-method  of  Foundations.    Two  Equal  Loads 


support,  and  fixing  the  total  length  L  of  the  footing  in  accordance  with  the 
requirements  tLi.:,t  the  footing  shall  not  project  beyond  the  line  PP,  the  widths 
of  the  footing  at  tiie  small  and  large  end,  a  and  b  respectively,  can  be  determined 
as  follows:  Let  B  represent  the  distance  from  the  small  end  of  the  trapezoid 
to  the  center  of  gravity  of  the  two  loads  and  let  A  represent  the  area  of  the 
trapezoid.    Then 

h  =2A/L{sB/L-i) 
a  =  2A/L{2  -sB/L) 
A  =  {a  -^  b)L/2     and    a  +  b  =  2A/L 

For  practical  reasons  the  distance  d  should  be  made  as  small  as  possible. 


Stresses  in  Footing  Courses 


169 


Cantilevering  an  Exterior  Wall.  In  the  case  of  a  wall  the  same  principles 
apply,  but  the  cantilevering  etlect  must  be  distributed  along  the  length  of  the 
wall.  This  can  be  accomplished  by  placing  a  girder  under  the  wall,  the  girder 
in  turn  resting  on  the  cantilever,  or  by  using  a  number  of  cantilevers  arranged 


ITTr^TTTTITTP 

Fig.  16.     Girdering-method  of  Foundations.     Two  Unequal  Loads 

in  fan  shape  and  radiating  from  the  interior  load-center.     In  narrow  building^ 
the  cantilevers  may  run  from  wall  to  wall. 

Double  Cantilevering.  The  considerations  controlling  the  design  of  the 
supporting  areas  required  are  the  same  as  outhned  in  the  preceding  paragraphs. 

19.   Stresses  in  Footing  Courses 

Size  and  Form  of  Footing  Courses.  The  footing  courses  of  all  walls  and 
piers  should  be  larger  than  the  superimposed  construction  in  order  to  secure 
STABILITY  AGAINST  OVERTURNING  and  to  reduce  the  UNIT  LOAD  on  the  founda^j 
tion-bed.  When  the  change  in  size  is  accomplished  abruptly  as  when  a  wall 
rests  on  a  grillage  or  a  slab  of  plain  or  reinforced  concrete  the  footing  is  called 
a  SPREAD  FOOTING.    When  the  base  of  the  wall  is  thickened  by  meaiis  of  o£fset 


170  Foundations  Chap.  2 

courses  so  that  its  bottom  course  is  substantially  as  large  as  the  footing  course 
the  construction  is  known  as  a  stepped  footing.  It  is  evident  that  no  hard 
and  fast  Hne  can  be  drawn  between  the  two  classes.  Whatever  the  form  of  the 
footing  is  it  must  be  strong  enough  to  distribute  the  more  or  less  concentrated 
load  coming  on  it,  into  a  uniform  pressure  or  load  on  the  foundation-bed. 

The  Unit  Loads  of  Footing  Courses.  If  the  load  on  the  upper  surface 
of  a  footing  course  is  uniformly  distributed  the  intensity  of  the  load,  or  in  other 
words  the  unit  load  on  the  sooting,  is  obtained  by  dividing  the  total  load  by 
the  area  of  the  base  of  the  wall,  pier,  or  other  construction  at  that  level.  The 
load  on  the  foundation-bed  should  be  uniformly  distributed  and  in  fact,  if 
the  foundation-bed  is  compressible  and  the  load  concentric  with  the  supporting 
area,  it  may  safely  be  assumed  as  uniform,  since  a  compressible  material  will 
adjust  itself  until  the  loading  at  different  points  is  substantially  uniform.  The 
unit  load  on  the  foundation-bed  is  evidently  the  total  load  divided  by  the  sup- 
porting area.  If  the  area  of  the  footing  course  varies  between  the  top  and  bot- 
tom of  the  footing  the  intensity  of  the  load  will  vary,  and  if  uniformly  distributed, 
the  unit  load  at  any  level  is  obtained  by  dividing  the  total  load  by  the  area  of 
the  footing  at  that  level. 

The  Weight  of  the  Footing  Itself.  This  is  generally  so  small  when  com- 
pared with  the  superimposed  loads  that  it  may  be  ignored  without  serious  error. 
The  Transmitting  of  Loads  by  Footings.  If  we  neglect  the  weight  of 
the  footing  we  can  consider  the  footing  course  as  transmitting  the  imposed  load 
to  the  foundation-bed  or  as  being  subject  to  two  equal  loads;  one,  the  super- 
imposed LOAD,  more  or  less  concentrated  on  the  center  line  of  the  footing  and 
acting  downward;  the  other,  the  reaction  due  to  the  loading  of  the  foundation- 
bed,  uniformly  distributed  over  the  supporting  area  and  acting  upward.  These 
loads  or  forces  being  equal  and  opposite  in  direction,  the  stresses  developed  in 
the  footings  are  due  to  the  differences  in  the  distribution  of  these  loads,  and 
the  footing  courses  simply  act  to  convert  concentrated  into  distributed  loads. 
Manner  of  Failure  of  Footings.  A  footing  rriay 
fail  in  several  ways:  (i)  by  shearing;  (2)  by  direct 
crushing;  (3)  by  spreading;  and  (4)  by  bending 
or  rupture. 
_B  (i)  Failure  of  Footings  by  Shearing.  This  is 
illustrated  in  Fig.  17,  showing  a  wall  the  weight  of 
which  has  caused  it  to  shear  along  the  lines  EG 
and  FH. 
Fig.  17.  Failure  of  Footing  ^^^  ^^^^^  tending  to  cause  SHEAR  is  the  weight  due 
by  Shearing  ^^  ^^^^  ^^^^  ^^^^  ^^^  reaction  of  the  foundation-bed  act- 

ing on  the  under  side  of  the  section  EFGII.     Since  the 
load  is  supposed  to  be  uniformly  distributed  this  is  equivalent  to  the  product 
of  the  area  corresponding  to  the  width  CD  minus  the  width  Gil  times  the  length 
of  the  wall  considered,  by  the  unit  loading  on  the  foundation-bed. 
For  a  I -ft  length  of  wall  the  force  causing  shear,  S,  is 

S=Wil--w)/l 

in  which  W  =  the  load  due  to  wall  per  foot  of  length  in  pounds; 
/  =  the  width  of  footing; 
w  =  the  width  of  base  of  wall. 
Or,  since 

W/l  =  C/  =  the  unit  load  on  the  foundation-bed  in  pounds  per  square  foot, 


ZL 


E5 


HI 


G 


Stresses  in  Footing  Courses 


171 


Since  U  is  in  terms  of  feet,  /  and  w  also  must  be  in  feet.  The  resistance  to  shear, 
R,  under  the  conditions  illustrated  in  Fig.  17,  taken  for  a  i-ft  length  b  of  the 
wall,  is  determined  by  the  equation 

R=2XdXbXf 

in  which  /=  the  safe  resistance  of  the  material  to  shear,  in  pounds  per 

square  inch; 
d  =  the  depth  of  the  footing  in  inches;  and 
b  =  the  length  of  wall  considered  =  12  in. 
Placing  S  =  R,  we  have 

2dbf=^Uil-w)0 
Or,  since  (/  —  iv)/2  =  the  projection  of  the  footing  ^ 

UP  =  12  dj 
The  depth  of  the  footing,  therefore,  must  net  be  less  than 

d=UP/l2f 

in  which  P  is  in  feet. 

Shear  in  Footings  of  Piers  and  Columns.  Failure  by  shear  is  most  likely 
to  occur  in  footings  for  piers  and  columns.  The  force  tending  to  cause 
SHEAR  is  the  total  load  on  the  column  or  pier  less  the  reaction  of  the  foundation- 
bed  on  the  area  immediately  under  the  column-base.  The  resistance  offered  is 
determined  by  multiplying  the  perimeter  of  the  column-base  by  the  depth  of  the 
footing  and  by  the  allowable  unit  shear.  When  the  area  of  the  column-base 
is  small,  the  entire  load  may  be  taken  as  producing  shear.  When  reinforced 
concrete  is  used  for  the  footing,  there  must  be  a  sufficient  number  of  stirrups  to 
take  care  of  the  shear.  (See  Chapters  XXIV  and  XXV.)  Where  steel  beams 
are  employ  d  the  cross-section  of  the  beams  must  be  sufficient  to  take  care  of 
the  shear,  otherwise  additional  web-plates  should  be  added,  as  is  explained  in 
Chapters  XV  and  XX. 

(2)  Failure  of  Footings  by  Direct  Crushing.  The  failure  of  footings 
by  DIRECT  CRUSHING  of  the  materials  composing  the  footings  rarely,  if  ever, 
occurs.  Where,  however,  the  concentrated  load,  due  to  a  pier  or  column,  is 
distributed  by  beams  or  girders  which  have  thin  webs,  the  webs  may  fail  by 
BUCKLING.  Such  beams  or  gird- 
ers should  have  their  webs  re- 
inforced by  vertical  stiffeners 
or  by  additional  web-plates,  and 
the  spaces  between  the  beams 
or  girders  should  be  filled  with 
concrete  or  grout.  Where  the 
load  transmitted  by  the  column- 
base  exceeds  the  safe  unit  load 
on  the  material  of  the  footing 
the  area  of  the  column-base  may 
be  increased,  or  a  block  of  granite 
may  be  interposed  between  the 
concrete  or  masonrj^  footing  and 
the  base  of  the  columns.  In 
this  case,  however,  such  granite 
blocks  should  be  considered  as  a  footing  course  and  designed  to  resist  bend- 
ing, by  formulas  hereinafter  given. 

(3)  Failure  of  Footings  by  Spreading.  Failure  of  the  footings  by  spread- 
ing may  occur  under  walls  or  piers,  as  shown  in  Fig.  18,  especially  when  the 


Fig.  18.    Failure  of  Footing  by  Spreading 


172 


Foundations 


Chap.  2 


foundation-bed  is  of  clay  or  other  yielding  material,  which  has,  under  the  load 
of  the  footing,  a  tendency  to  flow  along  the  lines  indicated  by  arrows  in  the 
figure.  This  tendency  should  be  provided  against  by  making  the  bottom  layer 
continuous  and  adequate  to  resist  the  tension.  Vertical  joints,  such  as  are 
made  in  footings  composed  of  masonry,  are  sources  of  weakness,  and  should  be 
avoided.  The  tendency  to  spread  is  greatest  in  footings  having  a  spread  which 
is  wide  compared  with  the  width  of  the  superimposed  wall  or  other  construction. 
The  writer  knows  of  at  least  one  important  footing  which  has  failed  in  tliis  way, 
the  cracks  in  general  following  the  joints  of  the  masonry  substantially  as  shown 
in  Fig.  18. 

(4)  Failure  of  Footings  by  Bending  or  Rupture.  A  footing  may  fail  by 
bending  or  RUPTURi;^as  a  beam  or  girder.  In  the  case  of  a  wall,  if  the  foot- 
ing bends,  as  shown  in  Fig.  19,  the  concentration  of  the  load  on  the  lower  edges 


E 

F         B 

A 

1 

1 

1 

I 

F         B 

rt             E 

^s 

^^W 

c 

D 

Fig.  19  Fig.  20  Fig.  21 

Figs.  19,  20  and  21.      Failures  of  Footings  by  Bending 

of  the  wall,  as  at  E  and  F  may  cause  the  base  of  the  wall  to  fail.  This  possibility 
should  be  borne  in  mind  in  designing  footings  where  the  load  on  the  wall  ap- 
proaches the  allowable  unit  load  for  the  material  composing  it,  and  especially 
where  the  width  of  the  footing  is  much  greater  than  its  own  width.  If  the 
footing  fails  by  rupture  the  rupture  may  occur  either  under  the  center  line  of 
the  wall,  as  in  Fig.  20,  or  at  points  close  to  the  outer  edge  of  the  wall  as  in 
Fig.  21.  Fig.  20  illustrates  the  objection  to  using  a  footing  course  composed 
of.  masonry  o-  stones  which  do  not  extend  the  full  width  of  the  footing.  The 
joints  in  such  construction  prevent  the  footing  course  from  acting  in  tension 
and  the  footing  as  a  whole  from  acting  as  a  beam. 


H 


<-ii;f 


20.   Methods  of  Calculating  Bending-Stresses  in  Wall-Footings 

Assumptions  Made  in  Determining  Bending-Stresses  in  Footings. 
Two  methods  for  the  calculation  of  the  bending- 
stresses  in  footing  courses  are  in  general  use. 
Both  are  based  upon  the  assumption  that  the 
REACTION  of  the  foundation-bed  is  uniform;  but 
the  methods  differ  in  the  assumption  made  as  to 
how  the  footing  course  and  the  base  of  the  super- 
A  E|    4  pt  If  B     structure  act.     Neither  assumption  can  be  held  to 

L- W >      be  wholly  correct. 

The  First  Method  of  Determining  Bending- 
Stresses  in  Footings.  This  method  is  based  upon 
the  assumption  that  the  pressure  of  the  wall  on  the 
footing  is  uniform  over  the  area  and  remains  so  at  all 
times. 

If,  in  Fig.  22,  ABCI^  represents  a  footing  course  supporting  a  centrally  located 
waU  EFGH,  and  U 


O 

I 

I 


-t- 


H 


Fig.  22.  Bending-Stresses  in 
Footings.    First  Method 


Methods  of  Calculating  Bending-Stresses  in  Wall-Footings       173 

W  =  the  load  of  the  wall  in  pounds  per  linear  foot; 
w  =  the  width  of  the  wall  in  feet; 
and  /  =  the  width  of  the  footing  in  feet; 

then 

Yz  {I  —w)  =  the  projection  AE  or  FB, 
and  W/l  =  [/  =  the  unit  load  per  square  foot  on  the  foundation-bed. 

Considering  the  forces  acting  on  the  right  of  the  center  line  of  the  wall  for  a 
i-ft  length  of  wall,  it  is  evident  that  the  uplift  on  the  half-footing  OD  will  equal 
^A  W  and  that  its  center  of  action  will  lie  half-way  between  O  and  D,  or  at  a 
distance  H  /  from  the  center  line  00;  and,  similarly,  that  the  load  due  to  one- 
half  the  wall  will  be  H  W  and  that  its  center  of  action  will  be  at  a  distance 
H  w  from  the  center  line  00.    The  resulting  moments  will  be 

Mi  =  HWXHl=  H  Wl 
and 

Mz  =  H  WXHw  =  H  Ww 

and  as  these  two  moments  act  in  opposite  directions,  the  resultant  moment 
tending  to  produce  bending  in  the  footing  will  be  the  difference  between  the  two, 
or  the  bending  moment  at  the  center  line  OO  is 

Mq  =  Ml  -  Ml 
or 

3f  0  =  H  W  {l-w) 
Or,  since 

W/l  =  U     and     H  {l—w)  =  P,  the  projection. 

Equation  (i)  may  be  written  in  either  of  the  forms 

•      Mq  =  \^U  {l-w)l     ) 
or  Ma^MWP  )  ^'^ 

The  Error  Involved  in  this  first  method  ir,  due  to  the  assumption  that  the 
pressure  on  the  upper  surface  of  the  footing  remains  uniformly  distributed, 
as  if  the  base  of  the  wall  acted  as  a  fluid,  in  which  case  the  distribution  of  the 
load  would  remain  constant  and  the  formula  would  be  correct.  But  the  base 
of  the  wall  is  not  a  fluid,  but  a  solid  which  will  resist  deformation.  If,  as  in 
Fig.  19,  the  footing  course  A  BCD  deflects  and  the  base  of  the  wall  is  assumed 
to  be  incompressible,  the  entire  load  of  the  wall  will  be  communicated  to  the 
footing  through  the  edges  E  and  F.  While  such  a  concentration  is,  of  course, 
impossible  (as  the  edges  E  and  F  will  crush  or  com- 
press  until  a  considerable  area  of  the  base  of  the  ] 

wall  is  in  contact  with  the  footing)  the  result  is  that 
the  weight  of  the  wall  is  concentrated  near  the  outer 
edges  of  its  base.  Equation  (i)  gives  results  which 
are  too  large;  but  as  it  errs  on  the  side  of  safety,  it 
is  recommended  for  general  use. 

The  Second  Method  of  Determining  Bending 


I 
I 

<-^/^| — * 
I 

I 
I 


-Z- 


-H 


Stresses  in  Footings,  also  in  common  use,  takes  J      j^^J 

into  consideration  only  the  projecting  portion  of  the  0 

footing  as  follows:  ^  Fig.  23.  Bending-stresses  in 

If  in  Fig.  23  ACBD  represents  a  footmg  course      Footings.    Second  Method 
supporting   a   centrally  located   wall  EFGH,  and  if 

we  use  the  notation  of  the  preceding  method,  then,  if  we  assume  that  the 
footing  acts  as  a  fixed  beam  and  the  projections  AE  and  FB  as  cantilevers 
rigidly  supported  by  the  wall,  and  denote  the  projection  of  the  footing  on  either 


174  Foundations  Chap.  2 

side  of  the  wall  by  P,  the  reaction  of  the  foundation-bed  on  this  projecting 
portion  P,  per  unit  length  of  wall,  will  be  PU.  The  center  of  action  of  this 
force  will  be  at  a  distance  H  P  from  E  or  F  and  its  moment  at  E  or  F  will  be 

M  =  PUxHP  =  ]^iUP^ 
or,  since 

P  =  Vi  (/  -  w) 
the  value  of  M  may  be  given  in  the  form 

Af  =  HU{l-wy  (2) 

The  Error  Involved  in  this  second  method  is  due  to  the  assumption  that  the 
uplift  on  the  projection  P  can  be  resisted  by  the  extreme  outer  edge  of  the  base 
of  the  wall.  If  the  uplift  on  the  projecting  part  is  concentrated  on  the  edge, 
then  the  edge  must  either  compress  or  fail  by  crushing,  which,  in  either  case, 
would  throw  the  center  of  support  for  the  cantilever  back  from  the  edge  of  the 
wall;  and  this  is  contrary  to  the  assumption  used  in  calculating  the  moment. 
This  method  takes  into  consideration  only  the  intensity  of  the  reaction  or  uplift 
and  the  length  of  the  projection,  and  is  known  as  the  projection -method. 

Comparison  of  Results.  Comparing  the  results  of  the  two  methods,  it  will 
be  seen  that  the  load  cannot  act  at  the  two  edges  E  and  F  as  assumed  in  Equa- 
tion (2),  nor  ordinarily  can  it  be  uniformly  distributed  as  assumed  in  Equation 
(i),  but  that  the  intensity  of  the  load  per  unit  of  area  will  vary,  being  a 
MINIMUM  at  the  center  and  a  maximum  near  the  edges  of  the  base  of  the  wall. 
The  exact  positions  of  the  centers  of  action  are  affected  by  various  consider- 
ations which  cannot  be  fully  discussed  in  this  chapter. 

New  Formula  for  Determining  Bending  Moments  in  Footings.  The 
writer  has  devised  a  formula  which  gives  values  for  the  bending  moment  M 
half-way  between  the  values  given  by  Equations  (i)  and  (2),  and  which  closely 
corresponds  to  the  assumption  that,  considering  the  forces  on  either  side  of  the 
center  of  the  wall,  the  center  of  action  of  the  half-load  of  the  wall  is  at  the 
center  of  the  half-wall,  when  the  projection  equals  zero,  and,  as  the  projection 
increases,  moves  toward  a  position  which  is  two-thirds  of  the  distance  from  the 
center  of  the  wall  to  its  edge.    This  formula  may  be  expressed  as  follows: 

M^HU{l-w){l-H'w)  (3) 

Or,  substituting  the  value  of  U  in  terms  of  W, 

M  =  HW{l-w)ij-w/2l) 

Weight  and  Pressure-Units.  In  practice  IF,  the  weight  due  to  the  wall,  is 
generally  given  in  pounds  per  linear  foot  of  wall,  and  the  allowable  pressure  on 
the  foundation-bed,  while  frequently  given  in  tons  per  square  foot,  should  be 
reduced  to  pounds  per  square  foot. 

The  Required  Width  of  the  Footing  in  feet  is  obtained  by  dividing  the  weight 
of  the  wall  in  pounds  per  linear  foot  of  wall  by  the  allowable  unit  load  on  the 
foundation-bed  expressed  in  pounds  per  square  foot. 

Moment -Units.  The  moment  tending  to  produce  rupture  may  be  calculatec 
in  foot-pounds  or  inch-pounds.  If  in  Equations  (i),  (2)  and  (3)  the  dimensions 
/,  w  and  P  are  in  feet  and  U  is  in  pounds  per  square  foot,  the  resulting  bending 
moment  will  be  in  foot-pounds  per  linear  foot  of  wall.  As  the  moment  of  resist- 
ance is  generally  stated  in  inch-pounds  it  is  more  convenient  to  have  the  max- 
imum bending  moment  or  moment  of  rupture*  in  inch-pounds.  Thus,  for 
Equation  (i) 

•  In  the  flexure-formula  the  moment  of  resistance  is  m»de  equal  to  the  bending 
moment  at  any  cross-section  of  the  footing,  and  the  maximum  bending  moment  19 
sometimes  called  the  moment  of  rupture* 


Methods  of  Calculating  Bending-Stresses  in  Wall-Footings      175 

M  (in  inch-pounds  per  foot  of  wall)  =  12  M  in  foot-pounds, 
or  M  (in  inch-pounds)  =  yzU  {l  —  w)l  (i)' 

Equation  (2)  in  the  same  way  becomes 

M  (in  inch- pounds)  =  y^  U  {I-  w)^  (2)' 

Or,  using  the  more  convenient  form, 

M  =  H  UP^ 
if  we  express  the  projection  P  in  inches,  instead  of  in  feet,  we  will  have 

M  (in  inch-pounds  per  foot  of  wall)  =  1^4  UP^ 
Similarly,  Equation  (3)  becomes 

M  (in  inch-pounds  per  foot  of  wall)  =  y2U  {l  —  w)  (l  —  H  w).  (3)' 

Until  Equations  (3)  or  (3)'  are  more  generally  accepted,  an  engineer  or  designer 
will  avoid  criticism  and  be  perfectly  safe  in  using  Equation  (i),  and  in  the  follow- 
ing pages  the  writer  will  use  Equations  (i)  or  (i)'  unless  the  contrary  is  stated. 

(l.)(3)(2) 


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Sir 

fi 

' 

1 

I 

J 

i 

\ 

5 

6 

J 

8 

9 

I  in  terra  of  to 
Fig.  24.     Graphical  Comparison  of  Bending  Moments  in  Footings 

Example.  The  following  is  an  example  illustrating  the  application  of  the 
foregoing  formulas: 

A  24-in  wall  transmits  to  the  footing  42  000  lb  per  linear  foot  of  wall.     The 
allowable  unit  load  on  the  foundation-bed  is  3  600  lb  per  sq  ft.     What  is  the 
width  and  required  moment  of  resistance  *  of  the  footing? 
42  000/3  600  =  iiYz  ft 

*  In  the  flexure-formula  the  moment  of  resistance  is  made  equal  to  the  bending 
moment  at  any  cross-section  of  the  footing,  and  the  maximum  bending  ,n3^0JBe;^t,JB 
sometip^es  called  the  moment  of  rupture.  noisaaJjs 


176  Foundations  Chap.  2 

Then,  by  Equation  (i),  we  have 

If  =  H  X  3  600  (iiH  -  2)  11^^  -  50  750  ft-lb 
If  Equation  (2)  is  used,  we  have 

Jlf  =  ^^  X  3  600  (11^^  -  2)2  =  42  050  ft-lb 
and  by  Equation  (3) 

M  =1^X3600(11^^-2)  (ii^i-i)  =  46  400  ft-lb 

Comparing  the  results  we  see  that  the  moment  by  Equation  (3)  is  the  average 
of  the  moments  by  Equations  (i)  and  (2). 

Graphical  Comparison  of  Bending  Moments  in  Footings.  Fig.  24  is 
a  graphical  comparison  of  the  moments  for  varying  ratios  of  /  to  w  calculated 
by  Equations  (i),  (2)  and  (3)  on  the  assumption  that 

w  =  the  width  of  wall  =  i  ft; 

U  =  the  unit  load  on  the  foundation-bed  =  i  000  lb  per  sq  ft;  and 

r  =  l/w. 

The  load  on  the  wall,  in  pounds,  for  any  value  of  /,  is  i  000  /. 

Comparing  the  curves  of  Equations  (i)  and  (2)  it  will  be  seen  that  the  results 
are  widely  apart,  the  percentage  of  variation  being  highest  in  the  case  of  small 
projections.  When  /  is  less  than  twice  w,  or  in  other  words,  when  the  projection 
is  less  than  one-half  the  width  of  the  wall,  Equation  (2)  gives  moments  less  than 
half  the  moments  given  by  Equation  (i).  Equation  (2)  may  be  used  for  small 
projections.  Equation  (i)  gives  results  which  are  too  large,  especially  where 
the  projections  are  sm  ill.  Equation  (3),  giving  results  half-way  between  those 
of  Equations  (i)  and  (2)  and  in  accordance  with  a  reasonable  hypothesis,  would 
appear  to  be  preferable,  but  is  not  in  accordance  with  present  practice. 

21.   Bending  Moments  in  Footings  of  Columns  and  Piers ;  ' 

General  Statement  of  the  Problem.  Fig.  25  represents  in  plan  a  pier  or 
column  resting  on  a  footing  which  projects   on  four  sides.     The  base  of  the 

c         n  n         rr       column  or  pier  is  represented  by  A  BCD,  and  the 

footing  and  its  area  of  support  by  EFGH.  That 
part  of  the  footing  included  in  the  areas  MNOF  and 
QRST  can  be  considered  as  acting  in  the  same  way 
as  projecting  footings  under  a  wall,  but  the  uplift  on 
the  four  corners  EQMA,  etc.,  on  which  no  superim- 
posed wall-load  is  imposed,  also  causes  bending 
moments.  [ 

,  ^ 1 ij: f^  Different  Theories.     There  are  several  theories, 

.        t  c  \  more  or  less  complicated  and  unsatisfactory,  as  to 

'■footing  with  Four^qTal     I'"^*''  ^^""  ON  THE  FOUR  CORNER-AREAS  should 

Projections  "^   determmed.     The    discussion   01    these    theories 

would  be  out  of  place  in  this  chapter.  In  a  square 
footing,  the  projection  is  not  over  one-half  the  width  of  the  superimposed 
base,  the  four  corner-areas  will  not  aggregate  over  25%  of  the  total 
area  of  the  footing,  and  it  may  then  be  assumed  that  the  bending  moment 
is  the  same  as  if  the  base  of  the  column  or  pier  extended  like  a  wall  across 
the  entire  footing,  as  is  shown  in  Fig.  26.  To  insure  these  conditions,  when  the 
projection  of  the  footing  exceeds  \i  w,  and  in  all  cases  when  the  footing  is  not 
homogeneous,  as  when  a  grillage  of  steel  is  used,  the  load  of  the  column  must 
be  distributed  over  the  width  of  the  footing  by  a  girder  or  bolster  or  by  an 
extension  of  the  column-base.    In  case  the  footing  is  in  several  layers,  each 


A, 



B 

C 

0 

.   0-— , 


Bending  Moments  in  Footings  of  Columns  and  Piers         177 


B 


1       1 

1      1 
1       1 
1      1 
1       1 

D 


D 


B 


layer  must  extend  the  full  width  of  the  underlying  layer.  With  such  construc- 
tion it  is  evident  that  the  bending  moment  will  be  the  same  as  if  the  girder  or 
BOLSTER  were  a  wall  and  Equation  Ci)  will  be  applicable. 

Bending  Moments  in  Column-Footings.  For  column-footings  Equation 
(i)  can  be  used,  taking  the  total  load  in  place  of  the  load  per  foot,  and  the  result 
will  then  be  the  total  bending  . 
moment.  — 

Example.  A  column  carrying 
96  tons  is  to  be  supported  on  a 
square  concrete  slab.  The  cast- 
iron  column-base  is  2  ft  square. 
The  allowable  pressure  on  the 
foundation-bed  is  6  tons  per 
sq  ft.  What  is  the  maximum 
BENDING  MOMENT  in  the  slab? 

The  area  of  support  =  96/6  =  p^g^  26.  Column-footing  Treated  Like  Wall-footing 
16  sq  ft  =  4  by  4  ft.  The  pro- 
jection is  H  (4  —  2)  =1  ft,  or  one-half  the  width  of  the  base,  and  by  the  fore- 
going rule  we  can  calculate  the  bending  moment  as  if  the  base  of  the  column 
extended  in  one  direction  across  the  footing.  Applying  a  convenient  form  of 
Equation  (i) 

1/  =  H  X  192  000  lb  (4  -  2)  =  48  000  ft-lb,  or  576  000  in-lb 

The  footing  must  therefore  be  of  sufficient  depth  to  resist  this  bending 
moment. 

'  If  in  this  example  the  allowable  unit  pressure  on  the  foundation-bed  is  2  tons 
instead  of  6  tons  per.  sq  ft  the  supporting  area  and  the  area  of  the  bottom  con- 
crete footing  course  will  be  96/2  =  48  sq  ft.  If  the  footing  course  can  be  a 
square  its  dimensions  will  be,  with  sufficient  exactness,  7  by  7  ft.  By  the  rule 
given,  since  the  projection  exceeds  one-half  the  width  of  the  base,  there  should 
be  a  BOLSTER  extending  across  the  footing.  The  bolster  will  be,  therefore,  7  ft 
long  and  may  properly  be  composed  of  two  or  more  steel  beams.  The  cast-iron 
base  may  be  dispensed  with,  in  which  case  the  base  of  the  column  will  be  pro- 
vided with  a  steel  base  or  with  flange-angles.  Let  us  assume  that  the  column- 
base  is  I  ft  6  in  square  and  the  width  of  the  bolster  2  ft.  i-si 

The  bending  moment  in  the  bolster  is  determined,  then,  by  Equation  (i)^ 
using  iH  ft,  the  width  of  the  column-base,  for  w,  and  7  ft,  the  length  of  the 
bolster,  for  /. 

M  =  HX  192  oco  (7  —  ij'^)  =  132 000  ft-lb  =  I  584 000  in-lb 

The  bendfng  moment  in  the  slab  is  determined  in  the  same  way  by  Equation  (i), 

using  2  ft,  the  width  of  the  bolster,  for  w,  and  7  ft,  the  length  of  the  slab,  for  /. 

M  =  li  x"i92  00c  (7  —  2)  =  120  000  ft-lb  =  I  440  000  in-lb. 

Footings  Other  Than  Square  in  Plan.  In  case  it  is  necessary  to  use  some 
other  shape  than  a  square  for  the  supporting  area  the  resulting  moments  in 
the  slab  and  bolster  will  vary  from  those  calculated  above.  If  in  the  foregoing 
example  the  supporting  area,  for  any  reason,  is  necessarily  made  6  by  8  ft,  giving 
48  sq  ft  as  the  required  area,  and  if  the  bolster  is  parallel  with  the  6-ft  side,  the 
moment  in  the  bolster  will  be 

M  =  HX  192  000  (6 -  iM)  =  108 000  ft-lb  =  I  296 000  in-lb 
and  the  moment  in  the  slab  will  be 

M  =  %x  192 000  (8 -  2)  =  144 000  ft-lb  =  I  728 000  in-lb 


178  Foundations  Cliap.  2 

or,  the  moment  in  the  bolster  is  less  and  the  moment  in  the  slab  is  greater  than 
in  the  case  of  the  7  by  7-ft  supix>rting  area.  If  the  bolster  runs  parallel  with 
the  long  side,  the  moments  will  be,  for  the  bolster, 

M  =  HX  192  000  (8  -  iH)  =  156  000  ft-lb 
and  for  the  slab, 

M  =  Hx  192  000  (6  —  2)  =  96  000  ft-lb 

In  footings  having  more  than  two  layers,  each  layer  must  be  investigated 
separately,  using./  for  the  length  of  the  layer  which  is  being  determined  and  w 
for  the  width  of  the  superimposed  layer. 

Compound  Footings.  In  compound  footings  where,  for  example,  a  wall 
and  a  column  or  two  or  more  columns  are  supported  by  a  single  footing,  or 
where  loads  are  cantilevered,  the  loads  will  in  general  be  distributed  to  the  sup- 
porting area  by  girders  or  cantilevers.  The  shears  and  bending  moments 
of  such  girders  or  cantilevers  must  be  determined  for  each  case  by  the  methods 
used  in  the  calculations  of  beams  and  girders  in  Chapters  XV  and  XX. 

22,    Design  of  the  Footings 

Materials  used  for  Footings.  To  possess  the  required  strength  the  safe 
MOMENT  OF  RESISTANCE  of  the  footing  must  be  at  least  equal  to  the  moment 
OF  rupture,  calculated  as  explained  in  the  preceding  paragraphs.  Masonry, 
whether  of  brickwork  or  stone,  is  not  generally  suitable  for  any  but  the  light- 
est buildings,  as  its  tensional  strength  is  low.  Concrete,  plain  or  reinforced, 
or  grillages  of  steel  embedded  in  concrete,  are  generally  employed.  (See  Chap- 
ter III  for  footings  for  light  buildings.) 

Footings  of  Homogeneous  Slabs.  If  the  footing  is  composed  of  a  slab 
OF  homogeneous  material,  as  a  block  of  granite  or  other  reliable  building  stone, 
or  a  single  layer  of  concrete,  the  moment  of  resistance  is,  by  the  well-known 
flexure-formula  for  rectangular  cross-sections,  Mr  =  H  bd^  S  (see  Chapters  X, 
XV  and  XVI)  in  which 

d  =  the  depth  or  thickness  of  the  footing,  in  inches; 
b  =  the  breadth  of  the  footing,  in  inches; 

S  =  the  allowable  unit  tensile  stress  of  the  material,  in  pounds  per  square 
inch; 
Mr  =  the  moment  of  resistance. 

Placing  M,  the  moment  of  the  forces  tending  to  cause  rupture,  equal  to  Mr, 
for  a  length  of  wall  equal  to  i  foot  we  have  , 

fc=  12  in 

and  d-'  =  Vz  M/S  (4) 

Substituting  in  Equation  (4)  the  value  for  M  in  inch-pounds  as  determined  by 
formulas  (i),  (2)  and  (3)  and  a  value  for  S  as  given  in  the  followmg  paragraph, 
the  required  depth  d  can  be  determined. 

Safe  Tensional  Strength  for  Materials  in  Footings.  The  values  of  5, 
the  allowable  unit  tensile  stress,  for  concrete  or  stone  must  include  a  high 
factor  of  safety,  as  experiments  show  wide  variations  in  the  tensional  strength 
and  in  the  modulus  of  rupture  or  flexural  strength  of  such  materials. 
The  following  values  for  S  in  pounds  per  square  inch  include  a  factor  of  safety 
of  from  8  to  10  and  should  not  be  exceeded.  (See,  alsO;  Table  III,  page  628, 
Chapter  XVI.) 


Design  of  the  Footings  179 

r      -  .  5  in  lbs  per  sq  in 

For  brickwork  or  masonry  in  lime  mortar from      o  to    lo 

For  brickwork  or  masonry  in  cement  mortar.  ...*..  from    lo  to    40 

For  concrete,  1:3:6 from    15  to    25 

For  concrete,  i  :  2y2.  :  5 from    20  to    40 

For  concrete,  1:2:4 from    30  to    50 

For  sandstone  or  limestone  in  monolithic  blocks.  . . .  from    75  to  150 

For  granite  in  monolithic  blocks from  100  to  250 

Example  of  Concrete-Footing  Design.     Concrete  Cast  as  a  Unit.     A  concrete 
tooting  course  4  ft  wide  supports  a  wall  2  ft  thick.     The  load  on  the  foundation* 
bed  is  28  000  lb  per  lin  ft  of  wall,  or  7  oco  lb  per  sq  ft.     Assuming  a  value  for  5 
a  35  lb  per  sq  in,  what  is  the  required  depth  for  the  concrete  footing  course? 
The  moment  of  rupture  from  one  form  of  Equation  (i)'  is 

'       M  =  Vi  W  (/  -  w),     or    %  X  i8  coo  (4  -  2)  =  84  000  in-lb 
Substituting  in  Equation  (4) 

d>  =  Vi  X  84  000/35  =  I  200,     or    J  =  35  in 
By  Equation  (2)'  the  moment  of  rupture  is 

M  =  1/^4  f/P^  =  1.^4  X  7  000  X  12  X  12  =  42  oco  in-lb 
ind 

</2  =  H  X  42  000/35  =  600,     or    ff  =  24  in  + 

The  depth  determined  by  Equations  (i)  or  (i)',  as  previously  noted,  errs  on 
the  side  of  safety.  The  result  by  Equations  (2)  or  (2)'  conforms  more  nearly 
Arith  usual  practice,  and  as  the  projection  is  small  compared  with  the  width  of 
:he  wall,  it  may  be  used,  or  an  intermediate  value,  as  determined  by  Equations 
vo)  or  (3)',  may  be  considered  amply  safe. 

Stepped  Footings.  If  the  concrete  footing  is  cast  in  one  uninterrupted 
operation  so  as  to  act  as  a  single  girder  for  its  entire  depth,  a  considerable 
>aving  of  material  may  be  effected  by  forming  steps, 
is  shown  in  Fig.  27.  If  the  steps  are  of  equal 
leight  the  total  projection  should  be  equally  divided 
Detween  the  steps.  If  the  footing  is  cast  in  several 
ayers,  or  if  a  granite  slab  is  superimposed  on  a  bed 
)f  concrete,  then  each  layer  must  be  figured  separately 
md  the  width  of  the  superimposed  layer  used  in  place 
)f  w,  the  width  of  the  wall. 

Caution  in  Design  of  Footings  of  Several 
Layers.  Equation  (2)  should  not  be  used  where 
:he  footing  consists  of  several  layers,  as  the  error 
iue  to  the  erroneous  assumption  is  cumulative  and 
vould  result  in  a  serious  concentration  on  the  outer 
idges  of  the  upper  layers. 

-,  ,,_^.  ,„  ,^  ^       .       Fig.  27.     Concrete  Steppe«^ 

Example    of    Footmgs   of    Several   Layers.     In  the  Wall-footing 

:ase  of  footings  cast  in  separate  layers  the  calculations 

ihould  be  made  as  follows:  Let  h  =  the  length  of  the  footing  having  a 
noment,  M.     From  Equation  (i),  reduced  to  inch- pounds, 

,        2M 

3W 

Having  d^ded  on  the  depth  of  each  layer,  say  15  in,  and  a  value  of  S,  say 
JS  lb,  for  concrete,  then,  from  the  flexure-formula,  M  =  Mr=HXi2XiS* 


180 


Foundations 


Chap.  2 


X  35  =  15  750  in-lb,  which,  substituted  in  the  above  equation,  will  give  the  value 
of  /i,  or  the  length  of  the  top  course.  Having  determined  /i,  the  length  of  the 
second  course,  k,  is  found  in  the  same  way,  using  h  for  w,  and  so  on  until  the 
required  width  of  the  footing  is  reached.  The  dimensions  /  and  w  are  to  be 
taken  in  feet. 

Comparison  of  Unit  and  Separate-Layer  Footings.  Footings  made  in 
separate  layers  are  very  uneconomical  in  the  amount  of  material  required,  when 
compared  with  those  cast  in  one  operation.  If  the  footing  in  the  previous 
example  is  designed  on  the  separate-layer  basis  and  the  courses  assumed  to  be 
15  in  thick,  their  lengths  are  as  follows: 

2  M 

^1  -  ~^  +  '^  =  1(2  X  IS  750)/ (3  X  28  000)]  +  2  =  2.375  ft 

3  yV 

Also 

/2=  2.75  ft,     h  =  3.125  it,    /4  =  3.50  ft     and    /s  =  3-^75  ft 

As  h  is  nearly  4  ft,  the  required  length,  it  may  be  made  so  by  increasing  the 
thickness  of  the  bottom  course  to  16  in.  The  total  thickness  of  the  footing  is 
therefore  (4  X  15  in)  +  16  in  =  76  in  instead  of  35  in,  as  previously  determined 
by  Equation  (i)  for  the  footing  cast  as  a  imit. 

3.0 


2.6 

a.4 

2.2 

2.0 

^1.8 

^1.6 

2  1.4 


1.0 


„_ 

1 

\ 

\ 

\ 

\ 

V 

\ 

\ 

^ 

y 

\ 

\ 

\ 

y 

\ 

\ 

\ 

\ 

\ 

s. 

^ 

\ 

V 

Sy 

s 

\ 

Vy 

X 

\ 

>y 

s 

X 

si' 

y            V 

\ 

^^^0 

y 

\^ 

N, 

\ 

\ 

^ 

^ 

-^..^ 

*l 

s 

N 

\ 

""'V) 

^ 

■*■ 

■ — J 

^'.. 



"•^-^ 

J«^ 

^"" — 

- 

"~ 





4000       6000        8000       lOOOO     12  000     14  000     IGOOO     18  000     20000 
Bearing  per  square  foot 
Fig.  28.     Diagram  Showing  Ratio  of  Projection  to  Depth  of  Footings 

Rule-of-Thumb    Methods    for    Projections    and    Steps   in   Footings. 

Various  arbitrary  rules  are  in  use  which  purport  to  give  for  different  materials 
of  construction  so-called  safe  projections  for  given  depths  of  footing  or  to 
give  the  safe  ratio  between  the  projection  and  the  depth  of  a  footing.  These 
rules  ignore  the  fact  that  the  uplift  varies  and  they  are  entirely  unreliable,  al- 
though such  rules-of-thumb- are  often  incorporated  in  the  building  codes  of 
cities.     (See  Chapter  III,  page  224.) 

Example.     The  safe  projection  for  offsets  in  brickwork  is  frequently  given 
in  building  codes  and  in  text-books  as  3  in  jfor  a  double  course  of  bricks  or  foc 


Steel  Grillages  in  Foundations  181 

a  depth  of  about  5  inches,  the  corresponding  ratio  being  0.6.  If  we  assume  the 
value  of  S  for  brickwork  at  20  lb  per  sq  in,  this  offset  will  be  safe  when  the  up- 
lift is  less  than  2  666  lb  per  sq  ft,  but  not  safe  when  the  uplift  is  over  2  666  lb 
per  sq  ft. 

Ratio  of  Projection  to  Depth  of  Footing.  For  footings  of  homogeneous 
material,  however,  having  a  small  projection  and  where  Formula  (2)  can  be  used 
safely,  it  is  possible  to  calculate  a  so-called  safe  ratio  of  projection  for  a 
given  unit  load.  From  Equation  (2)'  and  Equation  (4),  derived  from  the 
formula  for  the  moment  of  resistance  for  beams  of  homogeneous -material  and 
rectangular  cross-section,  the  following  formula  may  be  derived: 

p/d^V^ss/u  (5) 

in  which  all  dimensions  are  in  inches,  S  in  pounds  per  square  inch,  and  U  in 
pounds  per  square  foot.  The  quantity  p/d  is  the  ratio  of  the  projection  to  the 
depth  of  the  beam  or  footing.  For  a  given  value  of  5  the  ratio  will  vary  in- 
versely as  the  square  root  of  U. 

The  diagram  (Fig.  28)  shows  curves  for  different  values  of  S  and  U  from  which 
the  ratio  of  projection  to  depth  of  footing  may  be  taken.  Thus,  for  a  concrete 
footing  for  which  the  allowable  unit  stress,  S,  in  tension  is,  say  30  lb  per  sq 
in,  if  the  load,  U,  on  the  foundation-bed  is  3  000  lb  per  sq  ft,  the  allowable  pro- 
jection will  be  0.69  times  the  depth  of  the  footing  course.  If  the  concrete  is 
12  in  thick,  the  allowable  offset  will  be  8.3  in.  Conversely,  for  a  given  offset, 
say  12  in,  when  the  unit  load  is  3  000  lb  and  5  =  30  lb  as  before,  the  required 
depth  will  be  1.45  times  the  offset. 

23.   Steel  Grillages  in  Foundations* 

Advantages  in  the  Use  of  Steel-Beam  Grillages.  When  it  is  desirable 
to  avoid  the  deep  excavation  required  for  concrete  or  masonry  footings,  and 
when  the  load  of  a  wall  has  to  be  distributed  over  a  wide  area  of  support,  steel 
rails  or  steel  beams  are  frequently  advantageously  used  to  give  the  required 
moment  of  resistance  with  a  minimum  of  depth.  Steel  beams  are  generally 
cheaper  and  preferable  to  rails,  although  second-hand  rails  have  frequently  been 
used  as  an  expedient. 

Preparing  the  Bed  and  Setting  the  Beams.  The  foundation-bed  should 
be  first  covered  with  a  layer  of  concrete  not  less  than  6  in  in  thickness  and  so 
mixed  and  compacted  as  to  be  as  nearly  impervious  to  moisture  as  possible. 
The  beams  should  be  placed  on  this  layer,  the  upper  surfaces  brought  to  a  line 
and  the  lower  flanges  carefully  grouted  so  as  to  secure  an  even  bearing.  Sub- 
sequently, concrete  should  be  placed  between  and  around  the  beams  so  as  to 
permanently  protect  them. 

Requirements  for  Steel  Grillages.  In  determining  the  number  and  size 
of  the  beams  for  any  given  footing  the  following  points  should  be  considered: 

(i)  The  beams  must  resist  the  maximum  bending  moment,  and  this  without 
undue  deflection. 

(2)  The  beams  must  resist  the  shearing-stresses,  the  meeting  of  which 
requirement  ordinarily  provides  against  crushing. 

(3)  The  beams  must  not  be  spaced  so  far  apart  that  there  is  danger  of  the 
concrete  filling  between  the  beams  failing  to  distribute  the  load. 

(4)  The  beams  must  not  be  spaced  so  near  together  as  to  prevent  the  placing 
of  concrete  between  them.  The  clear  space  between  the  flanges  of  the  top  layer 
should  preferably  be  not  less  than  2  in  and  should  be  somewhat  more  for  the 
lower  layers. 

•  See  pages  678  to  680  for  an  example  of  a  continuous  girder  in  grillage  foundation. 


182 


Foundations 


Chap.  2 


(5)  Where  the  bending  moment  is  the  governing  feature,  of  two  beams  of 
equal  weight,  the  deeper  beam  should  be  used.  Thus,  if  the  required  section- 
modulus  is  147,  a  20-in  80-lb  beam  might  be  used;  but  a  24-in  80-lb  beam  is 
stiff er  and  stronger  in  bending. 

(6)  Where  the  shear  is  the  governing  feature,  of  two  beams  of  equal  weights, 
the  smaller  beam  is  the  stronger.  Thus,  the  she.vring  value  of  a  20-in  80-lb 
beam  is  greater  than  that  of  a  24-in  80-lb  beam  and  is  nearly  equivalent  to  that 
of  a  24-in  90-lb  beam.  However,  on  account  of  the  greater  stiffness  of  the 
deeper  beam  it  is  sometimes  advisable  to  use  it  even  though  the  cost  is  increased. 

Spacing  of  Beams  in  Grillage.  Table  IX  gives  the  limiting  spacing  for 
steel  beams,  based  upon  the  safe  capacity  of  the  concrete  filling  acting  as  a 
beam,  for  loads  of  from  i  to  6  tons  per  sq  ft.  Since,  however,  in  such  small 
spans  there  is  considerable  arching  effect,  the  concrete  will  safely  distribute 
the  load  on  larger  spans  than  those  given  in  the  table,  provided  a  sufficient 
number  of  tic-rods  of  proper  size  are  used  to  take  up  the  thrust  of  the  arches. 


Table  IX.     The  Limiting  Spacing  for  Steel  Beams  Used  With  Concrete  Filling 


Depths 

of 
beams 

Spa. 

ling  of  beams  for  the  following  pressures  per  square 

foot 

I 

ton 

2  tons 

3  tons 

4  tons 

5  tons 

6  tons 

in 

ft 

in 

ft     in 

ft     in 

ft     in 

ft     in 

ft     in 

6 

I 

3 

0      II 

0      10 

0        9 

0        8 

o        7 

7 
8 

I 
I 

6 
8 

I         I 
I        3 

0  II 

1  I 

0       10 
0      II 

0        9 
0      10 

0        8 
0        9 

9 

10 

I 
2 

II 
I 

I        5 
I        6 

I        2 
I        4 

I        0 
I        2 

0  II 

1  I 

0  10 

1  0 

12 
IS 
18 

2 
3 
3 

S 

0 
8 

1  10 

2  3 
2        8 

I        6 

1  10 

2  3 

I         4 
I        8 
I       II 

I         3 
I        6 
I        9 

I        2 
I        5 

I        8 

20 

4 

0 

2         II 

2       s 

2         2 

I       II 

I         JO 

24 

4 

9 

3        6 

2       II 

2        7 

2        4 

2        2 

The  Design  of  a  Wall-Footing  of  steel  beams  is  illustrated  by  the  follow- 
ing example:  A  24-in  wall  carries  42  000  lb  per  lin  ft.  What  should  be  the  size 
and  spacing  of  steel  beams  to  distribute  the  load  over  the  foundation-bed  at 
3  600  lb  per  sq  ft?  The  required  width  of  the  footing  is  42  000/3  600  =  11  f t 
8  in  and  the  bending  moment  by  Equation  (3)  is  556  800  in-lb  per  lin  ft  of 
wall.  The  amount  of  shear,  by  the  formula  given  on  page  170,  isS  =W  (I  —  'w)/l, 
or  34  800  lb.  As  the  beams  are  in  double  shear  the  single  shear  per  linear  foot 
of  wall  is  17  400  lb.  The  required  section-modulus  per  linear  foot  of  wall  is  ob- 
tained by  dividing  the  bending  moment  by  the  allowed  fiber-stress  in  the  steel, 
or  556  800/16  000  (assumed  fiber-stress)  =  34.8.  By  referring  to  Table  IV, 
page  355,  giving  the  section-moduli  of  steel  beams  we  find  that  a  12-in  3ii'^-lb 
beam  has  a  section-modulus  of  36.  To  satisfy  the  condition  of  bending,  the 
beams  must  not  be  spaced  more  than  36/34.8=  1.03  ft,  center  to  center.  To 
satisfy  the  condition  of  web-crippling  due  to  direct  compression,  the  unit  com- 
pressive stress  must  not  exceed  the  value  of  Sh,  Table  II,  page  575,  which, 
for  a  i2-in  3iV^-lb  beam,  is  13  060  lb  per  sq  in.  The  area  of  the  beam  resisting 
compression  is  the  length  over  which  the  load  is  distributed,  times  the  web* 
thickness.    Some  authorities  consider  that  the  load  is  distributed  over  a  length 


Steel  Grillages  in  Foundations 


183 


equal  to  the  loaded  portion  of  the  beam  plus  one-half  the  depth  of  the  beam, 
but  in  this  and  the  following  example  the  length  of  only  the  loaded  portion  is 
taken.  In  this  case  the  area  is  therefore  24  x  0.35  =  8.4  sq  in.  If  the  beams 
are  spaced  1.03  ft  on  centers  the  unit  direct  compression  is  42  000  x  1.03/8.4  = 
5  150  lb,  which  is  well  within  the  allowed  stress  given  by  Table  II,  page  575. 
To  satisfy  the  condition  of  web-crippling  due  to  shear,  the '  shearing-stress  must  ' 
not  exceed  the  value  as  derived  from  the  formula  for  allowable  shear.  (See, 
in  Chapter  XV,  paragraphs  and  foot-notes  relating  to  Buckling  of  Beam- Webs 
and  to  the  illustrative  Example  15  in  that  chapter.)  The  approximate,  allowed, 
unit  shearing  value  may  be  obtained  by  dividing  the  value  of  Sb  (Table  II, 
page  575)  by  the  factor  F,  the  values  of  which  are  given  in  Table  TX  A, 
following.  For  example,  for  a  12-in  3iH-lb  beam  this  shearing  value  =  13  060/, 
165  =  7915  lb  per  sq  in.  The  shearing  capacity  of  the  beam  is  obtained  by 
multiplying  this  unit  stress  by  the  depth  of  beam  times  the  web-thickness,  or 
7915X  I2X  0.35  =  $$  240  lb,  or  much  more  than  required.  Only  one  of  the 
conditions  of  web-crippling  need  be  considered  by  applying  the  following  rule: 
If  the  shear  divided  by  the  depth  of  the  beam  is  greater  than  the  total  load 
divided  by  the  product  of  the  distance  (over  which  the  load  is  distributed)  by 
the  factor  F,  investigate  for  shear;  if  otherwise,  investigate  for  direct  compres- 
sion. This  rule  may  also  be  expressed  as  follows:  According  as  {I  —  'w)/l  is  greater 
or  less  than  2  D/w'F,  investigate  for  shear  or  for  compression.  Here  /  =  length 
of  beam,  lu  =  loaded  portion  of  beam,  D  =  depth  of  beam,  w'  =  length  of  beam, 
over  which  the  load  is  assumed  to  be  distributed  (often  taken  =  w  +  HD)  and 
F  =  the  factor  for  the  given  beam  obtained  from  Table  IX  A.  All  dimensions 
must  be  taken  in  the  same  unit.  If,  instead  of  the  12-in  beams,  15-in  42-lb 
beams,  having  a  section-modulus  of  58.9  are  used,  the  spacing  will  be  58.9/34.8 
=  1.7  ft  nearly,  say  i  ft  8  in.  By  referring  to  Table  IX,  page  182,  it  is  seen 
that  the  spacing  of  the  beams  is  well  within  the  safe  limit  of  the  concicte  and  no 
tie-rods  are  theoretically  necessary.  It  is  preferable,  however,  to  use  at  least 
one  row  of  tie-rods. 

Table  IX  A.     Values  of  Factor  F*  for  Shearing  Values  for  Various  Beams 


r 

Beams 

For  standard- 
weight  beams 

For  heavy- 
weight beams 

12-in  beam 
15-in  beam 
1 8- in  beam 
20-in  bearrt 
24-in  beam 

1.65 
1. 71 
1.76 
1.77 
1. 91 

1. 52 

1.50 
1.58 
1.62 

1.67 

*  The  factors,  F,  which  have  been  deduced  to  be  used  in  connection  with  Sb,  Table  II, 
pages  574-5,  to  give  the  safe  unit  shearing  value  based  on  web-crippling,  will  help  greatly 
in  investigations  of  shears  in  case  tables  of  safe  shears  are  not  obtainable.  It  is  to  be 
noted,  however,  that  the  values  derived  from  the  use  of  F  are  approximate  only,  as  this 
factor  is  a  little  different  for  every  beam;  and  to  give  its  value  for  every  beam  would 
require  as  much  space  as  complete  tables  of  safe  shears.  The  values  of  F  are  not  given 
for  the  new  sections  of  light  beams  as  they  are  not  usually  good  sections  for  grillages. 
It  may  be  mentioned  that  the  standard  weight  for  each  size  of  beam  for  which  F  is  given 
is  always  the  next  weight  higher  than  the  minimum  weight  given  in  Table  II,  j)ages  574-5, 
except  for  the  20-in  beams,  for  which  the  minimum  weight,  65  lb,  is  also  the  standard 
weight.  The  rule  given  above  for  detefmining  whether  web-crippling  based  on  shear  or 
on  direct  compression  is  the  determining  condition  eliminates  one  of  the  calculations  to 
be  made  in  investigatiug  grillages. 


184  Foundations  Chap.  2 

The  Design  of  a  Column-Footing  of  steel  beams  is  illustrated  by  the 
following  example:  A  column  carries  576  tons.  The  allowable  pressure  on  the 
foundation-bed  is  3  tons  per  sq  ft.  What  should  be  the  arrangement,  number 
and  size  of  the  steel  beams  composing  the  grillage?  The  required  area  of  sup- 
port  =  576/3  =  192  sq  ft.  In  order  to  make  the  problem  as  general  as  possible 
let  it  be  supposed  that  practical  considerations  limit  the  width  of  the  footing  to 
12  ft.  The  dimensions  of  the  concrete  mat  on  which  the  lower  layer  of  beams 
rests  will  be  12  by  16  ft.  By  referring  to  the  diagram  (Fig.  28)  we  find  that  if 
the  mat  is  made  12  in  thick  an  offset  of  6  in  is  permissible.  The  dimensions 
of  the  lower  layer  of  beams  will  therefore  be  11  by  15  ft.  A  suitable  grillage  for 
the  given  conditions  may  be  designed  of  two  or  of  three  layers.  If  two  layers 
are  used  the  length  of  the  top  beams  will  be  11  ft.  Assuming  the  column-base 
=  30  in,  the  loaded  portion  =  qVz  ft,  and  by  Formula  (i),  the  bending  moment  * 
=  H  X  I  152  000  lb  X  (11  —  2^)  X  12  X  H  =  14  688  000  in-lb,  from  which  the 
required  section-modulus  (at  16  000-lb  maximum  fiber-stress)  =  918.  By  re- 
ferring to  Table  IV,  Chapter  X,  five  24-in  90-lb  beams  have  a  section-modulus 
of  932.5  and  consequently  satisfy  the  condition  of  bending.  By  applying  the 
rule  given  in  the  preceding  paragraph  for  the  design  of  a  wall-footing,  to  see  if 
web-crippling  due  to  shear  or  to  compression  is  to  be  investigated,  {I  —  w)/l  = 
0.773  and  2  D/w'F  =  0.958,  which,  being  greater  than  0.773,  shows  that  the  beams 
should  be  investigated  for  web-crippling  due  to  compression,  by  the  method 
explained  in  the  previous  example.  It  will  be  found  that  the  five  24-in  90-lb 
beams  also  satisfy  this  condition  and  will  therefore  be  used.  Their  flange- 
width  is  about  7H  in,  so  they  should  be  spaced  about  9'/^  in  on  centers,  requir- 
ing the  length  of  the  column-base  to  be  about  3  ft  9  in.  The  calculation  for 
the  lower  layer  is  similar,  the  length  of  the  beams  being  15  ft  and  the  loaded 
portion,  3  ft  9'in.  It  is  rarely  necessary  to  investigate  the  lower  layer  for  web- 
crippling,  the  condition  of  bending,  except  for  the  top  layer,  being  usually  the 
governing  feature.  If,  owing  to  conditions  of  bending,  it  is  not  practicable  to 
make  the  beams  of  the  top  layer  sufficiently  long  to  extend  across  the  required 
width  of  the  concrete  mat,  it  is  then  necessary  to  make  the  grillage  of  three 
layers.  The  calculation  for  a  three-layer  grillage  for  the  same  problem  as  the 
preceding  is  as  follows: 

Calculation  of  the  Top  Layer.  For  web-crippling  due  to  compression, 
I  152  000  \h  =  Sb  X  w'  X  t  X  n,  where  Sb  =  the  allowable  unit  stress,  w'  =  the 
length  of  beam  over  which  the  load  is  assumed  to  be  distributed,  /  =  the  web- 
thickness  and  n  =  the  number  of  beams.  Referring  to  Table  II,  Chapter  XV, 
and  assuming  a  20-in  75-lb  beam  to  be  used,  Sb  =  13  660  lb  per  sq  in  and  /  = 
0.649  in.  Taking  w'  =  30  in  (the  width  of  the  column-base),  13  660  x  30  X 
0.649  =  265  960  lb  and  the  value  for  five  beams  is  i  329  800  lb,  which  is  more 
than  enough.  But  it  is  found  that  five  20-in  70-lb  beams  would  not  be  suffi- 
cient. It  will  be  economical  to  make  these  beams  of  the  greatest  length  for  which 
they  will  resist  bending.  The  section-modulus  of  one  beam  is  126.9;  ^.nd  the 
total  Mr  =  5  X  126.9  X  16  000  (assumed  fiber-stress).  This  may  be  determined, 
also,  by  Formula  (i)  in  which  M  =  H  WP.  From  these  equations  the  projec- 
tion P  =  35H  in,  and  the  length  of  the  beams  is  therefore  (2  X  35H)  +  30  (the 
width  of  the  base)  =  100V2  in,  or  approximately  8  ft  4  in.  By  applying  the 
foregoing  rule  to  see  if  web-crippling  due  to  shc^r  must  be  considered, 
(100— 3o)/ioo=  0.7  which  is  less  than  40/(30  x  1.62)  =  0.82,  and  the  shear 
need  not  be  investigated. 

*  It  is  to  be  noted  that  the  bending  moment  is  the  same  as  for  a  beam  uniformly  loaded 
with  576  tons  on  a  span  of  Sy-i  ft,  (/  —  w),  and  that  the  number  and  size  of  the  required 
beams,  as  far  as  bending  is  concerned,  may  be  taken  from  the  tables  giving  the  safe  loads 
of  beams.     See  Table  IV,  Chapter  XV. 


Steel  Grillages  in  Foundations 


185 


ililiiiilLli 


The  width  of  the  flanges  of  these  beams  is  nearly  6H  in,  so  that  they  should 
be  spaced  from  8V^  to  9  in,  thus  making  the  required  length  of  column- base 
about  3  ft  6  in. 

Calculation  of  the  Second  Layer.  Since  the  length  of  the  top  layer  is  limited 
to  8  ft  4  in  and  the  width  of  the  lowest  layer  is  11  ft,  it  will  be  necessary  to  have 
an  intermediate  layer.  This 
will  cover  the  area  given  by 
the  length  of  beams  of  the  top 
layer  and  the  width  of  the 
lower  layer,  or  8  ft  4  in  by  11 
ft.  The  beams  will  of  course 
be  at  right-angles  to  those  of 
the  top  layer,  so  their  length 
will  be  II  ft,  and  they  are  to 
be  so  spaced  as  not  to  exceed 
8  ft  4  in.  Since  the  width  of 
the  top  course  is  3H  ft,  their 
projection  is  (ii  ft—  3]^  it)/ 2 
=  3%  ft,  the  amount  of  single 
shear  is  i  152  000  X  3.75/1 1  = 
392  720  lb  and  the  bending 
moment  is  H  X  i  152  000  X  45 
in=  12  960  000  in-lb.  Using 
16  000  lb  as  the  fiber-stress  the 
required  section-modulus  is 
810.  By  referring  to  Table 
IV,  Chapter  X,  for  section- 
moduli  and  determining  the 
maximum  shear  as  above  ex- 
plained, we  find  that  ten  15-in 
60-lb  beams  will  have  a  total 
section-modulus  of  812,  and 
they  will  also  be  ample  for 
shear.  Furthermore,  ten 
beams  spaced  to  cover  a  width 
of  8  ft  4  in  will  give  a  spacing, 
center  to  center  of  beams,  of 
about  10  in,  which  is  sufficient. 
It  would  be  better,  however, 
to  use  ten  18-in  55-lb  beams. 

Calculation  of  the  Bottom 
Layer.  Taking  the  effective 
width  of  the  middle  layer  as 
8  ft,  the  projection  of  the 
beams  is  (15  ft  —  8  ft)/2  =  sVz 
ft.  Then  similarly  to  the 
above,  the  shear  =  268  800  lb. 

M  =  12  096  000   in-lb,   from 


qr  Ml f • 
iLlliill 

'     '  n' 

1  1  f  \  t  \  I 

[  "i  ('  ]  \  \  [ 

"1    )f'\    1    J    L   1 

. 

1    1    I    1    L   J    t               — 

—             J    1/  J    1"  1    1^  j 

1    i  t    i    i   t   J     • 

L\  iM  1.1  r 

^    J  1   l^.  J   I  1 

"              .  '  1 

Fig.  29.     Steel-beam  Grillage  Column-footing 


which  the  section-modulus  =  756,  and  thirteen  15-in  42-lb  beams,  spaced  loH 
in  on  centers,  will  be  required,  or  two  15-in  60-lb  beams  and  ten  15-in  42-lb 
beams  may  be  used,  increasing  the  spacing  between  the  beams.  In  this  case 
the  heavy  beams  should  be  placed  nearest  to  the  center  of  the  footing.  This 
grillage  is  illustrated  in  Fig.  29. 


t86  Foundations  Chap.  2 

24.   Reinforced-Concrete  Footings 

Advantages  and  Disadvantages.     Reinforced  concrete  has  in  recent  years 
been  largely  used  for  footings.     The  arguments  in  favor  of  its  use  are: 
(i)  Low  cost  of  the  footing-construction; 

(2)  Reduction  in  the  amount  of  excavation  required; 

(3)  Convenience,  as  compared  with  the  use  of  steel-beam  grillages,  in  that 
the  reinforcing-steel  is  readily  obtainable,  can  be  cut  to  length  on  the  work  and 
handled  without  derricks. 

The  objections  urged  are: 

(i)  Danger  of  defective  workmanship,  as  the  strength  of  the  footing  depends 
upon  the  proper  mixing  and  placing  of  the  concrete,  the  proper  placing  of  the 
reinforcement  and  the  complete  union  of  the  concrete  with  the  reinforcement. 
The  danger  of  defective  workmanship  is  increased  by  reason  of  the  usual  difficul- 
ties of  foundation- work,  in  that  water  and  mud  are  generally  present  and  the 
difficulty  of  careful  work  and  inspection  is  greater. 

(2)  Danger  of  the  deterioration  of  the  steel  reinforcement  either  by  rusting 
or  by  electrolysis.  This  danger  is  increased  by  the  presence  of  moisture  and  by 
the  relatively  small  cross-section  of  the  reinforcing-bars.  In  this  connection 
it  is  well  to  remember  that  in  reinforced-concrete  girders  as  usually  designed 
the  concrete  on  the  tension  side  is  stressed  beyond  its  elastic  limit,  as  a  result  of 
which,  numerous  fine  cracks  are  developed  under  the  figured  load. 

Use  of  Reinforced  Concrete  for  Foundations.  From  the  foregoing  it  is 
apparent  that  great  care  should  be  used  in  connection  with  reinforced  concrete 
in  foundations,  especially  as  any  defect  is  difficult  to  detect  or  repair.  Rein- 
forced concrete  is  used  not  only  for  so-called  mats  or  slabs  but  is  frequently 
used  for  distributing-girders,  bolsters  and  even  for  cantilevers.  The 
author's  preference  is  against  reinforced  concrete  for  foundations  for  important 
structures. 

The  Methods  Used  in  Calculating  the  Strength  of  Reinforced-Con- 
crete Slabs,  Girders,  etc.,  are  explained  in  Chapters  XXIV  and  XXV,  The 
stresses  coming  on  the  reinforced-concrete  construction  are  to  be  determined 
in  the  same  way  as  explained  for  footings  of  other  materials. 

25.   Timber  Footings  for  Temporary  Buildings 

Timber  Footings.  For  buildings  of  moderate  height  timber  may  be  used 
to  give  the  necessary  spread  to  the  footings,  provided  water  is  always  present. 
The  footings  should  be  built  by  covering  the  bottom  of  the  trenches,  which 
should  be  perfectly  level,  with  2-in  planks  laid  close  together  and  longitudinally 
with  the  wall.  Across  these  planks  heavy  timbers  should  be  laid,  spaced  about 
12  in  on  centers,  the  size  of  the  timbers  being  proportioned  to  the  transverse 
stress.  On  top  of  these  timbers  again  should  be  spiked  a  floor  of  3-in  planks 
of  the  same  width  as  the  masonry  footings  which  are  laid  upon  it.  A  section 
of  such  a  footing  is  shown  in  Fig.  30.  All  of  the  timber-work  must  be  kept 
below  low-water  mark,  and  the  space  between  the  transverse  timbers  should  be 
filled  with  sand,  broken  stone,  or  concrete.  The  best,  woods  for  such  founda- 
tions are  oak,  long-leaf  yellow  pine  and  Norway  pine.  Many  of  the  old  build- 
ings in  Chicago  rest  on  timber  footings. 

Calculations  for  the  Sizes  of  the  Cross-Timbers.  The  sizes  of  the  trans- 
verse timbers  should  be  computed  by  the  following  formula: 

Breadth  m  mches  =  ~ -. » 


Timber  Footings  for  Temporary  Buildings 


187 


w  representing  the  bearing  resistance  of  the  foundation-bed  in  pounds  per  square 
foot,  p  the  projection  of  the  transverse  timbers  beyond  the  3-in  planks,  in  feet, 
5  the  distance  on  centers  of  the  timbers  in  feet,  and  d  the  assumed  depth  of  the 
beam  in  inches.  A  is  the  constant  for  strength.*  The  values  recommended  for 
it  are  67  for  long-leaf  yellow  pine  and  white  oak,  44  for  Norway  pine,  and  39  for 
common  white  pine  or  spruce,  all  increased  from  30  to  40%  for  temporary  build- 
ings.    (See  Table  II,  page  628.) 


Fig.  30.    Spread  Footing  of  Timber 


Example.  The  side  walls  of  a  given  building  impose  on  the  foundation  a 
pressure  of  20  000  lb  per  lin  ft;  the  soil  will  only  support,  without  excessive 
settlement,  2  000  lb  per  sq  ft.  It  is  decided  for  economy  to  build  the  footings  as 
shown  in  Fig.  30,  using  long-leaf  yellow-pine  timber.  What  should  be  the  size 
of  the  transverse  timbers? 

Solution.  Dividing  the  total  pressure  per  linear  foot  by  2  000  lb,  we  have 
10  ft  for  the  width  of  the  footings.  The  masonry  footing  we  will  make  of  granite 
or  other  hard  stone,  4  ft  wide,  and  solidly  bedded  on  the  planks  in  Portland, 
cement  mortar.  The  projection  p  of  the  transverse  beams  will  then  be  3  ft. 
We  will  space  the  beams  12  in  on  centers,  so  that  ^=1,  and  will  assume  10  in 
for  the  depth  of  the  beams.    Then,  by  the  formula. 


the  breadth  in  inches  = 


2  X  2000  X  9  X  I 
100  X  90 


and  we  should  use  4-  by  lo-in  timbers,  spaced  12  in  on  centers.  If  spruce  timber 
were  used  we  should  substitute  55  for  90,  and  the  result  would  be  6H  in.  (See 
note,  page  628,  for  ^4  increased  from  30  to  40%.) 

Foundations  for  Temporary  Buildings.  W^en  temporary  buildings  are 
to  be  built  on  a  compressible  soil,  the  foundations  may,  in  some  parts  of  the 
country,  be  constructed  more  cheaply  of  timber  than  of  any  other  material,  and 
in  such  cases  the  durability  of  the  timber  need  not  be  considered,  as  when  it  is 
sound  it  will  last  two  or  three  years  in  almost  any  place,  if  thorough  ventilation 
is  provided.  The  World's  Fair  buildings  at  Chicago  (1893)  were,  as  a  rule, 
supported  on  timber  platforms,  proportioned  so  that  the  maximum  load  on  the 
soil  would  not  exceed  i}4  tons  per  sq  ft.  Only  in  a  few  places  over  mud-holes 
were  pile  foundations  used. 

*  The  values  given  to  the  term  A  of  the  formula  vary  In  different  building  codes. 


188  Foundations  Chap.  2 

26.   General  Conditions  Affecting  Foundations  and  Footings 

General  Considerations.  Where  the  footings  of  a  building  rest  on  wet  sand, 
or  on  clay,  it  is  important  that  any  movement  of  the  material  forming  the 
foundation-bed  be  prevented  if  possible.  In  many  cases  it  is  advisable  to  con- 
nect all  footings  with  a  concrete  floor  to  prevent  any  uplift  of  the  foundation- 
bed  between  the  footings.  Where  unequal  settlement  is  apprehended  it  is 
inadvisable  to  have  long  columns  firmly  attached  to  the  footings,  as  any  unequal 
settlement  of  the  footings  develops  a  bending-stress  in  the  column;  such 
bending-stresses,  in  the  case  of  long  columns,  may  become  extremely  serious, 
resulting  possibly  in  the  rupture  or  distortion  of  the  columns.  In  such  cases  it 
has  even  been  proposed  to  design  the  bases  of  the  columns  with  ball-and-socket 
joints  which  would  allow  unequal  settlement  of  the  footings  without  distortion 
or  bending  of  the  columns.  Such  connections,  however,  could  not  be  generally 
used  because  of  the  necessity  of  bracing  the  structure  against  the  horizontal 
pressure  of  the  wind,  but  they  would  be  entirely  practicable  in  the  case  of  long 
interior  columns. 

The  Minimum  Depth  of  Footings  is  limited  by  the  depth  of  the  cellar, 
by  the  requirements  of  the  cellar  as  to  whether  part  of  the  footings  can  project 
above  the  cellar-floor  level,  and  by  the  depth  of  the  footing  itself.  The  minimum 
depth  will  be  advantageously  exceeded  if,  by  a  slight  increase  in  depth,  a  material 
capable  of  sustaining  a  higher  unit  load  is  found  on  which  to  rest  the  footings; 
or  if,  as  explained  in  previous  articles  of  th's  chapter,  greater  security  is  afforded 
by  locating  the  footing  at  a  greater  depth.  These  considerations  will  influence 
the  design  of  a  footing  and  in  all  cases  should  be  taken  into  consideration.  In 
some  cases  it  may  be  cheaper  to  abandon  the  use  of  a  spread  footing  of  any  type 
and  resort  to  piles  or  masonry  construction  going  to  rock  or  to  some  other 
solid  substratum.  Where  there  is  any  question  on  this  point,  careful  comparison 
should  be  made  of  the  advantages  and  costs  of  the  two  methods.  In  general, 
however,  it  will  be  cheaper  to  spread  footings  immediately  below  the  cellar- 
excavation  level  than  to  employ  any  of  the  various  deep-foundation  methods. 

Deep  Foundations  are  necessary  when  the  material  at  the  level  at  which 
SPREAD  footings  would  Ordinarily  be  constructed  is  not  suitable,  or  in  case  it 
is  desirable  for  any  reason  to  carry  the  foundations  of  the  building  down  to  an 
underlying  stratum  of  greater  supporting  power.  Recourse  must  then  be  had 
to  one  or  more  of  the  following  expedients: 

(i)  Wooden  piles; 

(2)  Concrete  piles; 

(3)  Piers  or  walls  constructed  in  pits  or  trenches,  or  by  other  methods,  and 
going  down  to  the  required  depth  to  reach  a  solid  stratum. 

27.   Wooden-Pile  Foundations 

The  Use  of  Wooden  Piles.  When  it  is  required  to  build  upon  a  compres- 
sible soil  that  is  constantly  saturated  with  water  and  of  considerable  depth,  the 
most  practicable  method  of  obtaining  a  solid  and  enduring  foundation  for 
buildings  of  moderate  height  is  by  driving  wooden  piles.  Many  buildings  in 
the  city  of  Boston,  Mass.,  and  several  tall  oflice-buildings  of  New  York  City 
and  Chicago,  rest  on  wooden  piles,  and  they  are  extensively  used  for  supporting 
buildings,  grain-elevators,  etc.,  erected  along  the  water-front  of  coast  and  lake 
cities.  The  durability  of  wooden  piles  in  ground  constantly  saturated  with 
water  is  beyond  question,  as  they  have  been  found  in  a  perfectly  sound  condir 
tion  after  the  lapse  of  from  six  to  seventeen  centuries. 


Wooden-Pile  Foundations 


189 


Municipal  Requirements.  The  laws  of  Boston  require  that  wooden  piles 
ihall  be  capped  with  block-granite  levelers  or  with  Portland-cement  concrete, 
ind  that  the  spacing  shall  not  exceed  3  ft  between  centers.  The  laws  of  Chicago 
equirc  that  wooden  piles  shall  be  driven  to  rock  or  hard-pan  and  capped  with 
,Tillage  of  timber,  concrete,  or  steel,  or  a  combination  of  these.  The  laws  of 
^ew  York  specify  a  minimum  diameter  of  5  inches  and  a  maximum  spacing  of 
J  feet  between  centers. 

The  Maximum  Loads  Allowed  on  "Wooden  Piles  in  various  cities  are  as 
follows:  Atlanta,  20  tons;  Philadelphia,  20  tons;  Buffalo,  25  tons;  Minneapolis, 
20  tout;  Richmond,  25  tons;  St.  Louis,  as  many  tons  as  the  piles  will  safely 
iupport;  Chicago,  25  tons;  Louisville,  20  tons;  St.  Paul,  25  tons;  New  York, 
20  tons;  Portland,  Ore.,  25  tons;  Cleveland,  25  tons.  Most  of  the  above  cities 
ilso  limit  the  allowed  load  by  Wellington's  formula  which  is  hereinafter  given 
m  page  193,  under  the  heading,  Bearing-Power  of  Piles. 

Kinds  of  Wood  Used  for  Piles.  Wooden  piles  are  made  from  the  trunks 
ol  trees  and  should  be  as  straight  as  possible  and  not  less  than  5  in  in  diameter 
a,t  the  small  end  for  light  buildings,  or  8  in  for  heavy  buildings.  The  woods 
generally  used  for  piles  are  spruce,  hemlock,  white  pine,  Norway  pine,  long-leaf 
and  short-leaf  yellow  pine,  pitch-pine,  cypress,  Douglas  fir,  and  occasionally  oak, 
hickory,  elm,  black  gum  and  basswood.  There  does  not  appear  to  be  much 
difference  in  the  woods  as  to 
durability  under  water,  but  the 
tougher  and  stronger  woods  are 
to  be  preferred,  especially  where 
the  piles  are  to  be  driven  to 
hard-pan  and  heavily  loaded. 

Preparing     Wooden    Piles 
for  Driving.     The  piles  should 

be     PREPARED    FOR    DRIVING    by 

cutting  off  all  limbs  close  to  the 
trunk  and  sawing  the  ends 
square.  It  is  probably  better 
to  remove  the  bark,  although 
piles  are  more  often  driven  with 
the  bark  on,  and  it  is  doubtful  if 
the  bark  makes  much  difference 
one  way  or  the  other.  For 
driving  in  soft  and  silty  soils, 
experience  has  shown  that  the 
piles  drive  better  with  a  square 
point.  When  the  penetration  is 
less  than  6  in  at  each  blow  the 
top  of  the  pile  should  be  pro- 
tected from  BROOMING  by  put- 
ting on  an  iron  ring,  about  i  in 
less  in  diameter  than  the  head  of 
the  pile,  and  from  2H  to  3  in 
wide  by  %  in  thick.  The  head  should  be  chamfered  to  iit  the  ring.  When 
driven  into  compact  soil,  such  as  sand,  gravel,  or  stiff  clay,  the  point  of 
the  pile  should  be  shod  with  iron  or  steel.  The  method  shown  at  A,  Fig.  31, 
answers  very  well  for  all  but  very  hard  soils,  and  for  these  a  cast  conical  point 
about  5  in  in  diameter,  secured  by  a  long  dowel,  with  a  ring  around  the  end 
of  the  pile,  as  shown  at  B,  makes  the  best  shoe.     Piles  that  are  to  be  driven  in  or 


ri 


''B 


Points   of  Wooden  Piles   Prepared 
Driving 


for 


190  Foundations  Chap.  2  j 

exposed  to  salt  water  should  be  thoroughly  impregnated  with  creosote,  dead  oil,  i 
or  coal-tar,  or  some  mineral  poison  to  protect  them  from  the  teredo  or  ship-  | 
WORM,  which  will  completely  honeycomb  an  ordinary  pile  in  three  or  four  years.  | 

Driving  Wooden  Piles  with  the  Drop-Hammer.    The  piles  should  alwa5rs  i 
be  driven  to  an  even  bearing,  which  is  determined  by  the  penetration  under ! 
the  last  four  or  five  blows  of  the  hammer.    The  usual  method  of  driving  piles  ] 
for  the  support  of  buildings  js  by  a  succession  of  blows  given  with  a  block  of 
cast  iron  or  steel,  called  the  hammer,  which  slides  up  and  down  between  the  t 
uprights  of  a  machine  called  a  pile-driver.    The  machine  is  placed  over  the  ! 
pile,  so  that  the  hammer  descends  fairly  on  its  head,  the  piles  always  being 
driven  with  the  small  end  dowru     The  hammer  is  generally  raised  by  steam-power  i 
and  is  dropped  either  automatically  or  by  hand.     The  usual  weight  of  the 
hammers  used  for  driving  piles  for  building  foundations  is  from  i  500  to  2  500  lb, 
and  the  fall  varies  from  5  to  20  ft,  the  last  blows  being  given  with  a  short  fall.  , 
Occasionally,  hammers  weighing  up  to  4  000  pounds  and  over  are  used. 

Driving  Wooden  Piles  with  the  Steam-Hammer.  Steam-hammers* 
are  to  a  considerable  extent  taking  the  place  of  the  ordinary  drop-hammers  in 
large  cities,  as  they  will  drive  many  more  piles  in  a  day,  and  with  less  damage 
to  the  piles.  The  steam-hammer  delivers  short,  quick  blows,  from  sixty  to 
seventy  to  the  minute,  and  seems  to  jar  the  piles  down,  the  short  interval  be- 
tween the  blows  not  giving  time  for  the  soil  to  settle  around  them.f  In  driv- 
ing piles  care  should  be  taken  to  keep  them  plumb,  and  when  the  penetration 
becomes  small,  the  fall  should  be  reduced  to  about  5  ft,  the  blows  being  given  in 
rapid  succession.  Whenever  a  pile  refuses  to  sink  under  several  blows,  before 
reaching  the  average  depth,  it  should  be  cut  off  and  another  pile  driven  beside  it. 
When  several  piles  have  been  driven  to  a  depth  of  20  ft  or  more  and  refuse  to 
sink  more  than  H  in  under  five  blows  of  a  i  200-pound  hammer  falling  15  ft,  it 
is  useless  to  try  them  further,  as  the  additional  blows  only  result  in  brooming 
and  crushing  the  heads  and  points  of  the  piles,  and  splitting  and  crushing  the 
intermediate  portions  to  an  unknown  extent. 

Spacing  Wooden  Piles.  Piles  should  be  spaced  not  less  than  2  ft  nor  more 
than  3  ft,  on  centers,  unless  iron,  wooden,  or  reinforced-concrete  grillage  is 
used.  When  long  piles  are  driven  closer  than  2  ft  on  centers  there  is  danger  that 
they  may  force  each  other  up  from  their  solid  bed  on  the  bearing  stratum. 
Driving  the  piles  close  together  also  breaks  up  the  ground  and  diminishes  the 
bearing  power.  When  three  rows  of  piles  are  used  the  most  satisfactory  spac- 
ing is  2  ft  6  in  on  centers  across  the  trench  and  3  ft  on  centers  longitudinally, 
provided  this  number  of  piles  will  carry  the  weight  of  the  building.  If  they 
will  not,  then  the  piles  must  be  spaced  closer  together  longitudinally,  or  another 
row  of  piles  driven;  but  in  no  case  should  the  piles  be  less  than  2  ft  apart  on 
centers,  unless  driven  by  means  of  a  water-jet.  The  number  of  piles  under  the 
different  portions  of  the  building  should  be  proportioned  to  the  weight  which 
they  are  to  support,  so  that  each  pile  will  receive  very  nearly  the  same  load. 

Capping  Wooden  Piles.  The  tops  of  the  piles  should  invariably  be  cut 
off  at  or  a  little  below  low  water-mark,  otherwise  they  will  soon  commence  to 
decay.  They  should  then  be  capped,  either  with  large  stone  blocks,  or  concrete, 
or  with  timber  or  steel  grillage. 

Granite  Capping.  Wooden  piles  are  sometimes  capped  with  block-granite 
LEVELERS  which  rest  directly  on  the  tops  of  the  piles.     If  the  stone  does  not  fit 

*  See  Table  XI,  page  204. 

t  The  5  000  piles,  averaging  48  ft  in  net  length,  under  the  Chicago  Post  Office  were 
driven  with  a  steam-hammer  weighing  4  400  lb  and  delivering  60  blows  per  minute. 


W  ooden-Pile  Foundations 


191 


r 


;he  surface  of  the  pile,  or  a  pile  is  a  little  low,  it  is  wedged  up  with  oak  or  stone 
//edges.  In  capping  with  stone  a  section  of  the  foundation  should  be  laid  out 
m  the  drawings  showing  the  arrangement  of  the  capping  stones.  A  single 
^tone  may  rest  on  one,  two,  or  three,  but  not  oii  four  piles,  nor  on  three  piles  in 
1  straight  line,  as  in  the  two  last-mentioned  , 
::ases  it  is  practically  impossible  to  make  the 
stones  bear  evenly.  Fig.  32  shows  the  best 
arrangement  of  the  capping  for  three  rows  of 
piles.  Under  dwellings  and  light  buildings  the 
piles  are  often  driven  in  two  rows,  staggered,  in 
which  case  each  stone  should  rest  on  three  piles. 
After  the  piles  are  capped,  large  footing  stones, 
extending  in  single  pieces  across  the  wall,  shouW 
be  laid  in  cement  mortar  on  the  capping.  Fig. 
33  shows  a  partial  piling-plan,  with  the  arrange- 
ment .  of  the  capping  stones,  of  the  Boston 
Chamber  of  Commerce  Building.  It  may  be 
seen  that  most  of  the  stones  rest  on  three  piles, 
and  a  very  few  on  two  piles. 


'^^yj 


r 


^-^-2  3^^<-2  3^V> 


Fig.    32.    Stone    Capping    for 
Three  Rows  of  Wooden  Piles 


Concrete  Capping.  In  many  buildings  a  very 
;ommon  method  of  capping  is  to  excavate  to  a 
depth  of  I  ft  below  the  tops  of  the  piles  and  i  ft 
Dutside  of  them  and  to  fill  the  space  thus 
excavated  solid  with  Portland-cement  concrete, 
deposited  in  layers  and  well  rammed.  After  the 
concrete  is  brought  level  with  the  tops  of  the 
piles  additional  layers  are  deposited  over  the 
whole  width  of  the  foundation  until  the  concrete 
attains  a  depth  of  i8  in  above  the  piles.  On  this  foundation  brick  or  stone 
footings  are  laid  as  on  solid  earth.  If  long  bars  of  twisted  steel,  about  %  in 
square  in  cross-section  are  embedded  in  the  concrete  about  3  in  above  the 
tops  of  the  piles,  the  construction  makes,  in  the  opinion  of  the  author,  the  best 
form  of  capping,  the  twisted  bars  giving  great  transverse  strength  to  the  concrete. 

Timber-Grillage  Capping.  The  pile  foundations  of  many  buildings  have 
heavy  timber  grillages  bolted  to  the  tops  of  the  piles  and  stone  or  concrete  foot- 
ings laid  on  top  of  the  grillages.  The  tirnbers  for  the  grillages  should  be  at  least 
10  by  10  in  in  cross-section,  and  should  have  sufficient  transverse  strength  to 
sustain  the  load  from  center  to  center  of  piles,  using  a  low  fiber-stress.  They 
should  be  laid  longitudinally  on  top  of  the  piles  and  fastened  to  them  by  means 
of  DRIFT-BOLTS,  which  are  plain  bars  of  iron,  either  round  or  square  in  section, 
and  driven  into  holes  about  20%  smaller  in  section  than  the  bolts  themselves. 
Round  or  square  bars  i  in  in  section  are  generally  used,  the  holes  being  bored 
by  a  -M-in  auger  for  the  round  bolts  and  by  a  %-in  auger  for  the  square  bolts. 
The  bolts  should  enter  the  piles  at  least  i  ft.  It  heavy  stone  or  concrete  footings 
are  used  and  the  space  between  the  piles  and  timbers  is  filled  with  concrete  level 
with  the  tops  of  the  timbers,  no  more  timbering  is  required;  but  if  the  lootings 
are  made  of  small  stones  and  no  concrete  is  used,  a  solid  floor  of  cross-timbers, 
at  least  6  in  thick  for  heavy  buildings,  should  be  laid  on  top  of  the  longitudinal 
capping  and  drift-bolted  to  them.  Where  timber  grillage  is  used  it  should,  of 
course,  be  kept  entirely  below  the  lowest  recorded  water-line,  as  otherwise  it 
will  rot  and  allowjthe  building  to  settle.  It  has  been  proved  conclusively, 
however,  that  any  kind  of  sound  timber  will  last  practically  forever  if  completely 
immersed  in  water. 


192 


Foundations 


The  Advantages  of  Timber  Grillage  are  that  it  is  easily  laid  and  effectually) 
holds  the  tops  of  the  piles  in  place.  It  also  tends  to  distribute  the  pressure 
3venly  over  the  piles,  as  the  transverse  strength  of  the  timber  will  help  to  caYry 


o  oro 
0  b  |o 


Fig.  33.    Piling-plan,  Chamber  of  Commerce  Building,  Boston,  Mass. 

the  load  over  a  single  pile,  which  for  some  reason  may  not  have  the  same  bearing 
capacity  as  the  others.  Steel  beams,  embedded  in  concrete,  are  sometimes  used 
to  distribute  the  weight  over  piles,  but  some  other  form  of  construction  can 
generally  be  employed  at  less  expense  and  with  equally  good  results.* 

*  For  a  description  of  the  pile  foundations  and  capping  of  the  Chicago  Post  Office,  see 
Freitag's  Architectural  Engineering,  pages  350  to  352. 


Wooden- Pile  Foundations  193 

Specifications  for  Wooden-Pile  Foundations.  This  contractor  is  to  firr- 
nish  and  drive  the  piles  indicated  on  sheet  No.  i. 

The  piles  are  to  be  of  sound  spruce  (hemlock,  long-leaf  yellow  pine)  perfectly- 
straight  from  end  to  end,  trimmed  close,  and  cut  off  square  to  the  axis  at  both 
ends. 

They  are  to  be  not  less  than  6  in  in  diameter  at  the  small,  end,  lo  in  at  the 
large  end,  when  cut  off,  and  of  sufficient  length  to  reach  solid  bottom,  the  neces- 
sary length  of  piles  to  be  determined  by  driving  test-piles  in  different  parts  of 
the  foundation. 

All  piles  are  to  be  driven  vertically,  in  the  exact  positions  shown  by  the  plan, 
until  they  do  not  move  more  than  5  in  under  the  last  five  blows  of  a  hammer 
weighing  2  000  lb  and  falling  20  ft.  All  split  or  shattered  piles  are  to  be  re- 
moved if  possible  and  a  good  one  driven  in  place  of  each  imperfect  one.  In 
cases  where  such  piles  cannot  be  removed  an  additional  pile  is  to  be  driven  for 
each  imperfect  one.  If  the  piles  show  a  tendency  to  broom,  they  are  to  be 
bound  with  wrought-iron  rings,  2\^  in  wide  and  y2  in  thick. 

All  piles,  when  driven  to  the  required  depth,  are  to  be  sawed  off  square  for  a 
horizontal  bearing  at  the  grade  indicated  on  the  drawings. 

The  Bearing  Power  of  Piles.  In  regard  to  their  use  for  supporting  build- 
ings, piles  may  be  divided  into  two  classes:  (i)  Those  which  are  driven  to 
ROCK  or  HARD-PAN,  that  is,  firm  gravel  or  clay  and  (2)  those  which  do  not 
reach  hard-pan. 

(i)  A  pile  belonging  to  this  class  when  driven  through  a  soil  that  is  sufficiently 
firm  to  brace  the  pile  at  every  point,  may  be  computed  to  sustain  a  load  equal 
to  the  safe  resistance  to  crushing  on  the  least  cross-section.  If  the  surrounding 
soil  is  plastic  the  bearing  power  of  the  pile  will  be  its  safe  load  computed  as  a 
column,  having  a  length  equal  to  the  length  of  the  pile  when  capped.  Test- 
piles  driven  on  the  site  of  the  Chicago  Public  Library  Building,  through  27  ft 
of  soft,  plastic  clay,  23  ft  of  tough,  compact  clay  and  2  ft  into  hard-pan,  sus- 
tained a  load  of  50.7  tons  per  pile  for  two  weeks  without  apparent  settlement. 
There  are  many  instances  where  piles  driven  to  the  depth  of  20  ft  in  hard  clay 
sustain  from  20  to  40  tons,  and  a  few  instances  where  they  sustain  up  to  80  tons 
per  pile. 

(2)  A  pile  belonging  to  this  class  depends  for  its  bearing  power  upon  the 
FRICTION,  COHESION  and  buoyancy  of  the  soil  into  which  it  is  driven.  The 
safe  load  for  such  piles  is  usually  determined  by  the  average  penetration  of 
the  pile  under  the  last  four  or  five  blows  of  the  hammer.  Several  engineers 
have  formulated  rules  for  determining  the  safe  loads  for  piles  of  this  class,  but 
there  are  so  many  conditions  that  modify  the  amount  of  the  penetration,  and 
its  exact  determination,  and  so  many  varying  conditions  of  driving  and  of 
soil,  that  it  is  considered  impossible  to  formulate  any  rule  that  can  be  considered 
entirely  satisfactory  for  all  the  conditions  under  which  such  piles  are  driven. 

The  Engineering  News  Formula.  The  formula  generally  used  by  engineers 
was  derived  by  M.  A.  WelHngton,  and  is  often  referred  to  as  the  Engineering 
News  formula: 

The  safe  load  in  tons  =  2  wh/  {S  +  1) 
in  which 

w  =  the  weight  of  the  hammer  in  tons; 
h  =  the  height  of  fall  of  the  hammer  in  feet; 

6*  =  the  penetration  in  inches  under  the  last  blow  or  the  average  under 
the  last  five  blows. 

When  loads  are  based  on  this  formula  the  piles  should  be  driven  until  the  pene- 
tration does  not  exceed  the  limit  assumed,  or  if  this  is  found  to  be  impracticably 


194 


Foundations 


Chap.  2 


new  calculations  must  be  made  based  on  the  smallest  average  penetration  that 
can  be  obtained,  and  a  greater  number  of  piles  used.  In  localities  where  piling 
is  commonly  used  for  foundations,  the  least  penetration  that  can  be  obtained 
within  practical  limits  of  length  of  pile  can  generally  be  ascertained  by  observa- 
tion, or  by  consulting  somebody  who  is  experienced  in  driving  piles.  The  longer 
the  pile  the  less,  as  a  rule,  will  be  the  final  set  or  penetration.  Where  there  is  no 
experience  to  guide  one  it  will  be  necessary  to  drive  a  few  piles  to  determine 
the  length  of  pile  required,  or  the  least  set  for  a  given  length  of  pile.  Some 
piles  will  have  to  be  driven  further  than  others  to  bring  them  to  bearings  of 
equal  resistance.  When  the  piles  are  to  be  loaded  to  more  than  50%  of  the 
assumed  safe  load,  the  final  set  of  each  pile  should  be  carefully  measured  by  an 
inspector,  the  broom  and  splintees  being  removed  from  the  head  of  the  pile 
for  the  last  blow. 

Safe  Loads  for  Piles.  Table  X,  computed  by  the  above  forniula,  gives  the 
safe  loads  for  different  penetrations,  under  different  falls  of  a  hammer  weighing 
I  ton.  For  a  hammer  of  different  weight  multiply  the  safe  load  in  the  table 
by  the  actual  weight  of  the  hammer  in  tons.  Thus,  for  a  hammer  weighing 
I  000  lb,  the  values  in  the  table  should  be  multiplied  by  3'^  and  for  a  i  500-lb 
hammer,  by  %. 

Table  X.     Safe  Loads  in  Tons  for  Piles 

For  hammer  weighing  i  ton 


Penetration 
of  pile  in 
inches 

Height  of  the  fall  of  the  hammer  in  feet 

3 

4 

5 

6 

8 

10 

12 

19.4 
16.1 
13.8 
12.0 
10.7 
9.6 
8.8 
8.0 
6.9 
6.0 
5-3 
4.8 
4.0 
3.4 

14 

16 

18 

-9.1 
24.0 
20.7 
18.0 
16.1 
14.4 
13.1 
12.0 
10.3 
9.0 
8.0 
7.2 
6.0 
5.1 

20 

25 

30 

0.25 

0.50 
0.75 
1. 00 
1.25 
1.50 
1. 75 
2.00 
2.50 
3.00 
3.50 
4.00 
5. 00 
6.00 

4.8 
4.0 
3.4 
3.0 

6.4 
5.3 
4.6 
4.0 
3.6 
3.2 

8.1 
6.7 
5.7 
S.o 
4.5 
4.0 
3.6 
3.3 

1:1 

6.9 
6.0 

5.4 
4.8 
4.4 
4.0 
3.4 
3.0 

12.9 
10.7 
9.2 
8.0 
7.1 
6.4 
5.8 
5.3 
4.6 
4.0 
3.6 
3.2 

16. 1 
13.3 
11.5 

lO.O 

8.9 
8  0 
7.3 
6.7 
5.7 
5.0 
4.4 
4.0 
3.3 

22.5 
18.7 

16. 1 
14.0 
12.5 

11. 2 
10.2 

9-3 
8.0 
7.0 
6.2 
5.6 
4.7 
4.0 

25.8 
21.3 
18.4 
16.0 
14.3 
12.8 
II. 7 
10.7 
91 
8.0 
7.1 
6.4 
5.3 
4.6 

32.3 
26.6 
23.0 
20.0 
17.9 
16.0 
14.6 
13.3 
II. 4 
10. 0 
8.9 
8.0 
6.7 
5.7 

33.3 
28.8 
25.0 
22.3 
20.0 
18.2 
16.7 
14.3 
12. 5 
II. I 
10.0 
8.3 
7.1 

34. 5 
30  0 
26.7 
24.0 
21.9 
20.0 
17. 1 
15-0 
13.3 
12.0 

lO.O 

8.6 

Example  of  Computations  for  Pile  Foundation.  Suppose  that  from  the 
observations  of  the  pile-driving  for  an  adjacent  building  it  is  found  that  piles 
driven  from  20  to  30  ft  take  a  set  of  i  in  under  a  i  200-lb  hammer  falling  20  ft, 
and  that  additional  blows  result  in  about  the  same  set. 

From  Table  X  we  find  that  the  safe  load  for  a  fall  of  20  ft  and  a  penetj 
tion  of  I  in  is  20  tons.  Multiplying  by  the  weight  of  the  hammer  in  tons, 
we  have  12  tons  as  the  safe  load  per  pile.  Suppose  that  the  total  load  oil 
lin  ft  of  footing  is  13  tons.  As  we  must  have  at  least  two  rows  of  piles,  and' 
each  two  piles  will  support  24  tons,  it  follows  that  the  spacing  of  the  piles 
longitudinally  should  be  24/13  =  i  ft  10  in.  As  this  is  too  close,  we  should  use 
three  rows  of  piles,  spaced  2  ft  apart  laterally,  and  the  longitudinal  spacing 


'ofl 


Wooden-Pile  Foundations  195 

wouid  then  be  36/13  =  2  ft  9  in.  The  width  of  the  capping  would  be  about 
5  ft.  If  the  load  on  the  piles  under  the  interior  columns,  for  example,  is  105.8 
tons,  this,  divided  by  12,  the  safe  load  for  one  pile,  gives  nine  piles,  or  three  rows 
of  three  piles  each,  which  should  be  spaced  2  ft  6  in  apart,  each  way. 

Some  Actual  Loads  on  Wooden  Piles.  The  following  examples  of  the 
actual  loads  supported  by  piles,  under  well-known  buildings,  and  of  loads  which 
piles  have  borne  for  a  short  time  without  settlement,  should  be  of  value  when 
designing  pile  foundations. 

Boston.  At  the  Southern  Railroad  Station  three  piles  were  loaded  with 
about  60  tons  of  pig  iron,  20  tons  per  pile,  without  settlement.  The  allowed 
load  was  10  tons  per  pile. 

Piles  12  in  in  diameter  at  the  butt  and  6  in  at  the  point,  driven  31  ft  into  hard, 
blue  clay  near  Haymarket  Square,  failed  to  show  movement  under  30  tons, 
the  ultimate  load  being  probably  60  tons.*  Other  piles  driven  17.9  ft  sustained 
a  load  of  31  tons  each.  The  average  penetration  under  the  last  ten  blows  of  a 
I  710-lb  hammer  faUing  from  9  to  12  ft  varied  from  0.4  to  0.95  in  per  blow  for 
fifteen  piles. 

Piles  25  ft  long  under  the  Chamber  of  Commerce  Building  penetrated  about 
3  in  under  the  last  blow  of  a  2  000-lb  hammer  falUng  about  15  ft. 

Chicago.  In  the  Public  Library  Building  the  piles  were  proportioned  to 
30  tons  each  and  were  tested  to  50.7  tons  without  settlement. 

In  the  Schiller  Building  the  estimated  load  was  55  tons  per  pile;  the  building 
settled  from  iH  to  2H  in. 

In  the  Passenger  Station  of  the  Northern  Pacific  Railroad,  at  Harrison  Street, 
piles  50  ft  long  were  designed  to  carry  25  tons  each  and  did  so  without  per- 
ceptible settlement. 

The  Art  Institute  Building,  parts  of  the  Stock  Exchange  Building  and  also 
a  large  number  of  warehouses  and  other  buildings  on  the  banks  of  the  river 
rest  on  piles. 

New  York  City.  The  Ivins  (Park  Row)  Building  is  supported  by  about 
3  500  14-in  spruce  piles,  arranged  in  clusters  of  fifty  or  sixty,  for  single  columns, 
and  a  corresponding  number  under  piers  supporting  two  or  more  columns. 
The  piles  were  driven  to  refusal  of  i  in  under  a  20-ft  fall  of  a  2  000-lb  hammer. 
The  material  is  fine,  dense  sand  to  a  depth  of  over  90  ft.  But  few  piles  could  be 
driven  more  than  15  or  20  ft.     The  average  maximum  load  per  pile  is  9  tons.f 

The  American  Tract  Society's  Building  is  supported  on  piles. 

Brooklyn.  Piles  under  the  Government  Graving  Dock,  driven"  32  ft,  on 
the  average,  into  fine  sand  mixed  with  fine  mica  and  a  Httle  vegetable  loam,  are 
supposed  to  sustain  from  10  to  15  tons  each. 

New  Orleans.  Piles  driven  from  25  to  40  ft  into  a  soft  alluvial  soil  carry 
safely  from  15  to  25  tons,  with  a  factor  of  safety  of  from  6  to  8.  J 

The  Cost  of  Driving  Wooden  Piles.  §  The  cost  of  driving  piles  naturally  varies 
with  the  character  of  the  soil,  and  the  conditions  under  which  they  are  driven. 

New  York  City.  A  2  500-lb  drop-hammer  drove  4  piles  per  day  of  10  hours, 
with  a  steam-hammer,  13  piles  per  day  were  driven,  for  the  same  foundation. 
The  piles  were  70  ft  long,  8  in  in  diam  at  the  point  and  15  in  at  the  head. 

The  average  cost  of  driving  800  piles  with  the  steam-hammer  was  $2  each.  In 
New  York  Harbor  i  800  piles  were  driven  by  a  steam-hammer,  from  24  to  26  ft 
into  gravel  and  hard-pan,  at  a  cost  of  80  cts  each. 

*  Horace  J.  Howe,  American  Architect,  June  ii,  1898. 

t  For  a  description  of  this  foundation,  see  the  Engineering  Record  of  July  23,  1898. 

t  W.  M.  Patton. 

§  These  prices  are  now  (1920)  considerably  higher. 


196  Foundations  Chap.  2 

Chicago.  Forty  Norway-pine  piles  were  driven  by  a  firm  of  contractors 
IS  ft  deep  every  ten  hours  at  a  cost,  for  driving,  of  55  cts  each.  Another  firm 
drove  from  60  to  65  piles,  each  45  ft  long  and  15  ft  deep,  into  hard  sand  each  day 
at  a  cost  of  about  30  cts  each.     In  both  cases  steam-hammers  were  used.* 

Boston.  Spruce  piles  from  30  to  45  ft  long  cost  from  $3  to  $5,  in  place. 
Long-leaf  yellow  pine  piles,  as  long  as  70  ft,  cost  about  $15  apiece  for  the  piles 
themselves,  and  $2  or  more  each  for  the  driving.  Oak  piles  from  40  to  50  ft 
long  cost  from  $8  to  $10  each,  in  place. f 

Some  Other  References  to  Wooden  Piles  and  Pile-Driving.  A  very 
valuable  paper  on  "Some  Instances  of  Piles  and  Pile-Driving,  New  and  Old," 
by  Horace  J.  Howe,  was  published  in  the  American  Architect  and  Biulding  News, 
commencing  June  11,  1898.  The  paper  records  a  great  many  tests  and  gives 
several  formulas  and  many  experiences  of  distinguished  engineers.  Part  I  of 
Building  Construction  and  Superintendence,  by  F.  E.  Kidder,  gives  additional 
information  in  regard  to  pile  foundations  and  experiments  on  the  bearing  power 
of  piles.  Much  valuable  information  on  piles  is  given  in  "A  Practical  Treatise 
on  Foundations, "  by  W.  M.  Patton.  The  recent  Engineers'  Handbooks,  also, 
should  be  consulted  for  additional  data. 

28.   Concrete-Pile  Foundations 

Durability  of  Wooden  and  Concrete  Piles,  Concrete  piles,  either  plain 
or  reinforced,  possess  many  advantages  over  wooden  piles  and,  in  general,  can 
be'used  in  all  places  where  wooden  piles  can  be  driven.  Concrete  piles,  com- 
pared with  wooden  piles,  have  primarily  the  advantage  of  greater  permanence. 
Timber  piles,  kept  constantly  wet  and  protected  from  the  action  of  the  torredo 
or  other  destructive  influences,  may  be  practically  everlasting,  but  cannot  be 
counted  upon  above  water  level;  whereas  concrete  piles  should  be  proof  against 
all  deteriorating  actions,  whether  wet  or  dry,  except  the  action  of  freezing  on 
wet  concrete. 

Strength  of  Wooden  and  Concrete  Piles.  Concrete  piles  without  rein- 
forcement, if  made  of  good  concrete,  should  have  nearly  the  same  crushing 
STRENGTH  per  squarc  inch  as  ordinary  yellow-pine  piles,  and  with  properly 
placed  reinforcement  concrete  piles  should  ha,ve  a  much  higher  crushing  strength 
per  square  inch  than  timber  piles.  Moreover,  timber  piles  do  not  have  uni- 
form CROSS-SECTIONS.  For  instance,  a  slender  timber  pile  40  ft  in  length  and 
12  in  in  diameter  at  the  butt,  is  probably  not  over  6  in  in  diameter  at  the  point. 
In  direct  compression  the  load  on  a  point-bearing  pile  of  the  above  dimensions 
is  limited  to  the  safe  load  on  the  point  of  the  pile,  where  it  is  6  in  in  diameter; 
and  a  cylindrical  concrete  pile,  12  in  in  diameter  and  under  similar  conditions, 
will  have  a  cross-section  of  113  sq  in  at  all  points,  compared  with  the  cross- 
section  of  28  sq  in  at  the  point  of  the  timber  pile.  Moreover,  if  we  consider 
both  piles  as  long  columns,  it  must  be  borne  in  mind  that  a  timber  pile  may  not 
be  straight  and  that  it  may,  therefore,  be  subject  to  stresses  and  deformations 
due  to  eccentric  loading,  which  are  avoided  in  a  straight,  concrete  pile. 

Reinforced-Concrete  Piles.  In  practice  concrete  piles  are  generally  rein- 
forced, and  if  a  pile  is  to  be  considered  as  a  long  column  the  reinforcement  may 
be  increased  at  the  center,  so  as  to  provide  for  stresses  due  to  handling  and  to 
its  acting  as  a  long  column.  The  concrete  piles  may  be  formed  complete, 
above  ground,  in  which  case  they  may  be  straight  or  tapered,  with  square,  cir- 
•ular  or  other  cross-sections.     The  reinforcement  may  consist  of  a  number  of 

*  American  Architect,  June  4,  1898,  page  78. 

t  George  B.  Francis,  in  American  Architect,  July  23,  1898. 


Concrete-Pile  Foundations  197 

Vertical  rods  generally  disposed  symmetrically  around  the  axis  of  the  pile.  The 
vertical  rods  should  be  connected  by  horizontal  wiring  or  by  spiral  reinforcement. 
As  before  stated,  the  reinforcement  may  be  increased  at  the  central  section  so 
as  to  provide  against  stresses  due  to  the  use  of  the  pile  as  a  long  column,  in 
which  case  the  additional  reinforcement  should  be  placed  near  the  periphery 
of  the  cross-section. 

Types  of  Concrete-Pile  Reinforcement.  There  arc  many  types  of  rein- 
forcement, one  method  even  employing  a  woven-wire  fabric  which  is  laid  out 
flat  on  a  table  and  covered  with  a  thin  layer  of  concrete,  the  entire  mat  comprising 
the  wire  fabric  and  the  concrete  being  then  rolled  into  a  solid  cylindrical  form 
which,  when  set,  forms  the  finished  pile.  The  concrete  piles  may  be  formed  in 
PLACE  by  any  one  of  several  different  methods. 

The  Raymond  System  of  Concrete  Piling.  In  this  system  of  concrete 
piling  a  permanent  form  is  provided  for  each  pile.  The  Raymond  system 
consists  of  a  collapsible  steel  mandrel  or  core,  tapering  from  8  in  in  diameter 
at  the  point  at  the  rate  of  0.4  in  per  foot  in  length,  until  in  a  length  of  37  ft> 
the  cUameter  equals  23.2  in.  Upon  this  expanded  mandrel  or  core  is  placed 
a  spirally  reinforced  sheet-metal  shell,  the  reinforcement  of  which  is  grooved 
into  the  metal  on  3-in  centers  the  entire  length  of  the  core  or  pile.  This  rein- 
forcement imparts  rigidity  and  stiffness  to  the  shell,  renders  it  capable  of  with- 
standing very  severe  soil-pressure  and  prevents  admixture  of  foreign  substances 
into  the  green  concrete.  The  combined  mandrel  and  shell  is  driven  into  the 
ground  to  a  proper  refusal;  the  mandrel  is  then  collapsed  and  withdrawn  from 
the  shell,  leaving  the  shell  permanently  in  the  ground;  and  the  interior  of  the 
shell  or  form  is  then  inspected,  and  when  perfect  from  tip  to  top,  is  tilled  with 
green  concrete.  Thus  the  pile  is  completed.  The  extreme  taper  of  the  shell, 
combined  with  the  friction  between  the  shell  and  the  surrounding  soil,  increases 
the  carrying  capacity  of  the  pile.  The  safe  load  on  a  Raymond  pile  varies 
from  25  to  30  tons. 

The  Simplex  Method  of  Forming  Concrete  Piles  in  Place.  The  Simplex 
Method  differs  from  the  Raymond  method  and  may  be  briefly  described  as 
follows:  A  steel  pipe,  generally  cylindrical  in  form,  of  the  required-  size  and 
length  and  fitted  with  a  detachable  cast-iron  conical  driving-point,  is  driven  into 
the  ground  to  the  required  depth;  the  pipe  is  then  partially  filled  with  concrete. 
A  piston-like  plunger,  smaller  in  diameter  than  the  inside  diameter  of  the 
pipe,  is  then  placed  on  the  concrete  and  the  pipe  is  partially  withdrawn,  leaving 
the  driving-point  and  part  of  the  superimposed  concrete  in  the  ground.  This 
operation  is  repeated  until  the  pile  is  built  up  to  the  required  height.  In  cer- 
tain materials,  instead  of  using  a  detachable  driving-point,  the  driving-point 
consists  of  two  jaws  hinged  to  the  lower  end  of  the  pipe,  so  arranged  that  while 
during  the  driving  they  form  a  driving-point,  when  the  pipe  is  withdrawn  they 
open  and  form  an  extension  of  the  cylindrical  pipe.  In  other  words,  the  jaws 
are  formed  of  steel  plates  previously  bent  to  the  same  radius  as  the  radius  of 
the  pipe  and  so  hinged  that  when  they  are  in  their  open-position  the  plates 
forming  the  jaws  constitute  an  extension  of  the  cylindrical  surface  of  the  pipe. 
It  is  evident  that  plain  reinforcing-bars  can  be  placed  in  position  before  concrete 
is  put  into  the  pipe. 

Caution  for  Concrete  Piles  Built  in  Place.  Care  should  be  taken  in  design- 
ing and  placing  the  reinforcing  for  all  concrete  piles  built  in  place,  that  the 
subsequent  placing  of  the  concrete  does  not  throw  the  reinforcement  out  of 
position  and  that  all  voids  between  the  reinforcement  and  the  shell  are  com- 
pletely filled. 


198  Foundations  Chap.  2 

The  Pedestal  Pile  is  designed  to  give  an  enlarged  cross-section  at  the 
base  of  the  pile.  The  method  is  similar  to  that  of  the  Raymond  method,  the 
increase  in  diameter  being  obtained  as  follows:  After  the  pipe  has  been  driven, 
the  driving-core  is  withdrawn  and  the  pipe  partially  filled  with  concrete.  Then 
the  concrete  in  the  pipe  is  rammed,  forcing  the  concrete  out  of  the  pipe  and  com- 
pressing the  material  below  the  pipe,  so  that  the  concrete  is  forced  into  the  soil. 
A  repetition  of  this  operation  results  in  forming  a  base  or  mushroom  below  the 
pipe  larger  in  diameter  than  the  diameter  of  the  pipe.  Finally  the  pipe  is  with- 
drawn, the  filling  and  ramming-operations  continuing  meanwliile,  until  the  pile 
is  carried  up  to  the  required  height. 

Composite  Piles.  Protected  piles,  for  use  in  localities  where  the  torredo 
affects  the  life  of  timber  piles  under  water,  are  composed  of  timber  piles  with 
concrete  coatings  held  in  position  by  steel  reinforcements  in  the  shape  of  expanded 
metal  or  wire  netting.  Such  piles  are  to  be  considered  as  timber  piles  rather 
than  as  concrete  piles. 

Timber  Piles  with  Concrete  Caps.  In  some  localities  where  the  permanent 
water-level  is  considerably  below  the  level  of  the  required  excavation,  timber 
piles  have  been  driven  with  a  follower,  the  follower  consisting  of  a  steel  pipe 
or  cylindrical  shell.  When  the  head  of  the  pile  is  driven  to  a  safe  distance 
below  low  water  the  pipe-follower  is  filled  with  concrete  and  withdrawn, 
leaving  the  concrete  pier  resting  on  a  timber  pile.  This  composite  pile  would 
appear  to  possess  the  advantage  of  combining  the  cheapness  of  a  timber  pile 
below  the  water-level  with  the  permanency  of  a  concrete  pile  above  the  water- 
level.  Great  care,  however,  should  be  used  in  adopting  this  method  on  account 
of  the  difficulty  of  securing  proper  connection  between  the  concrete  and  the 
wooden  pile. 

The  Methods  used  in  Driving  Built-up  Piles  are  practically  the  same 
as  are  used  in  driving  wooden  piles,  except  that  a  cushion  of  wood,  rope,  or 
other  material  is  placed  on  the  head  of  the  pile  to  be  driven  to  cushion  the  blow 
of  the  hammer.  Steam-driven  or  air-driven  reciprocating  hammers  are  pref- 
erable to  the  ordinary  drop-hammers.  In  stiff  materials  the  use  of  a  water- 
jet  is  advisable  and,  in  fact,  in  many  cases  indispensable.  In  lifting  concrete 
piles  use  is  made  of  a  special  sling  which  is  attached  to  a  pile  at  two  points,  each 
point  one-quarter  of  the  length  of  the  pile  from  the  end.  The  sling  should  have 
a  spreader  so  that  the  stress  due  to  the  oblique  pull  of  the  chain-sling  is 
takea  up  by  the  spreader  rather  than  by  the  pile. 

The  Casting  of  Concrete  Piles.  Concrete  piles  should  be  cast  in  one 
piece  by  a  continuous  operation  so  that  there  will  be  no  plane  of  weakness 
formed  between  partially  set  concrete  and  fresh  concrete.  They  may  be  cast 
either  in  a  vertical  position,  in  forms,  or  in  a  horizontal  position.  Square-sec- 
tion concrete  piles  have  been  cast  in  a  horizontal  position  and  side-forms,  only, 
used,  the  previously  cast  concrete  pile,  protected  by  paper,  forming  the  bottom 
form.  In  some  cases,  where  it  is  intended  to  use  a  water-jet  in  sinking  a  pile, 
the  latter  is  cast  around  an  iron  pipe  which  is  afterwards  used  for  the  water- 
jet.  In  general,  however,  this  is  dispensed  with  and  an  external  detachable 
pipe  used  for  the  water-jet. 

Incidental  Advantages  of  Concrete  Piles.  In  many  cases,  where  concrete 
piles  are  more  expensive  than  timber  piles,  the  saving  in  excavation  and  foot- 
ings more  than  offsets  the  increased  cost.  For  example,  if  the  excavation  for 
the  cellar  of  a  building  does  not  go  down  to  water-level,  the  use  of  timber  piles 
will  necessitate  excavating  down  to  a  point  below  water-level  in  order  that  the 
piles  may  be  cut  off  low  enough  to  keep  their  heads  always  wet.    Concrete 


Concrete-Pile  Foundations  199 

piles,  however,  can  be  driven  from  the  level  of  the  bottom  of  the  cellar-excava- 
tion, and  this  additional  excavation  and  the  necessary  construction  between 
the  excavation-level  and  the  level  of  the  cut-off  for  the  timber  piles  thus  avoided. 
Moreover,  as  one  concrete  pile  may  have  a  supporting  power  equal  to  the 
supporting  power  of  four  wooden  piles,  the  size  of  the  footings  will  be  much 
smaller  with  concrete  piles  than  with  wooden  piles. 

Comparison  of  Wooden  and  Concrete  Piles  under  Piers.  The  footings 
for  a  column  or  pier  24  in  sq  in  section,  requiring  for  its  support,  say,  sixteen 
wooden  piles,  spaced  2  ft  6  in  from  center  to  center,  will  be,  allowing  for  sUght 
[inequalities  in  driving,  approximately  10  ft  square,  the  projections  being  4  ft 
beyond  the  size  of  the  base.  Such  a  footing  will  ordinarily  require  a  steel 
grillage  or  reinforced-concrete  base,  or,  if  made  of  ordinary  concrete,  will  be  of 
very  considerable  depth;  whereas,  if  four  concrete  piles,  placed  3  ft  from  center 
to  center,  are  used,  instead  of  wooden  piles,  the  area  of  the  base  will  be  a  little 
Dver  4  ft  square  and  the  projection  will  be  only  i  ft.  A  suitable  footing  would 
consist  of  a  reinforced-concrete  cap  not  over  2  ft  in  thickness.  The  saving  in 
cost  of  excavation,  concrete  and  steel  in  the  footing  is  all  in  favor  of  the  use 
3f  concrete  piles. 

Concrete  Piles  under  Walls.  In  the  case  of  a  continuous  wall,  where  the 
load  per  linear  foot  of  wall  is  not  great,  a  single  row  of  concrete  piles  is  often 
mfficient  to  support  the  weight  of  the  wall.  In  such  cases,  the  piles  should 
not  be  placed  in  straight  hues  but  should  be  staggered,  and  a  sufficient  footing 
ihould  be  constructed  connecting  the  heads  of  the  piles,  so  as  to  afford  stability 
to  the  wall. 

The  Method  Employed  in  Calculating  Reinforcement  for  Concrete 
Piles  is  the  same  as  that  employed  in  calculating  ordinary  reinforced-concrete 
:olumns,  the  only  difference  being  that  where  a  pile  is  not  point-bearing,  but  is 
dependent  on  the  surrounding  material  for  its  support,  it  need  not  be  considered 
I  LONG  COLUMN.  PoiNT-BEARiNG  PILES  deriving  their  support  from  some 
solid  material  on  which  their  lower  extremity  rests,  must  be  considered  as  long 
rOLUMNS,  on  the  assumption  that  the  material  surrounding  the  piles  may  fail 
to  support  them.  In  the  case  of  friction-piles,  depending  for  their  support 
.ipon  the  surrounding  material,  this  assumption  cannot  be  made,  as  any  failure 
Df  the  material  will  involve  a  settlement  of  the  pile.  It  should  be  borne  in  mind 
that  any  structure  supported  on  piles  supported  by  skin-friction  is  dependent 
"or  its  stability  upon  the  continued  supporting  power  of  the  material  surround- 
ng  the  piles.  In  many  cases  buildings  resting  on  piles  driven  into  soft  ground 
lave  settled  as  the  result  of  the  consolidation  and  settlement  of  the  material 
surrounding  the  piles,  notwithstanding  the  fact  that  the  piles  when  driven  were 
imply  able  to  support  the  loads  for  which  they  were  designed. 

Iron-Pipe  Piles  with  Concrete  or  Reinforced-Concrete  Filling  have  been 
I  in  place  of  wooden  or  concrete  piles,  especially  in  underpinning- work. 
The  objection  to  the  use  of  such  piles  is  that  the  iron  pipe  forming  the  external 
hell  may  rust,  in  which  case  the  strength  of  the  pile  is  reduced  to  the  strength 
)f  the  concrete  filling  and  the  reinforcement  contained  therein.  The  writer 
Delieves  that  they  should  not  be  used  for  permanent  work. 

Loads  Allowed  on  Concrete  Piles.  The  building  laws  of  most  cities 
illow  on  concrete  piles  from  350  to  500  lb  per  sq  in  on  the  concrete  plus  from 
3  000  to  7  500  lb  per  sq  in  on  the  vertical  reinforcement.  On  this  statement 
t  would  appear  possible  to  design  a  short  concrete  pile  12  in  square,  on  which 
the  allowed  load  would  be  100  tons,  and  it  is  possible  that  such  a  pile,  tested 
IS  a  SHORT  column,  would  develop  in  a  testing-machine  a  strength  justifying 


200  Foundations  '  Chap^ 

the  use  of  such  construction;  but,  bearing  in  mind  that  the  character  of  tn 
support  for  the  base  of  such  a  column  is  underground  and  cannot  be  inspected, 
and  bearing  in  mind  also  the  uncertainties  attending  the  manufacture  of  the 
pile,  it  is  evident  that  it  would  be  improper  to  load  a  pile  to  this  extent  in  practice. 
It  would,  however,  be  considered  good  practice  to  load  concrete  piles  up  to  one- 
third  of  a  test-load  applied  to  not  less  than  3%  of  the  piles  used.  In  ordinary 
practice,  reinforced-concrete  piles  are  loaded  up  to  500  lb  per  sq  in  of  cross-sec-_ 
tion. 


29.   Foundation  Piers  and  Foundation  Walls 


•i^ff 


Foundation  Piers  and  Walls  as  distinguished  from  ordinary  cellar  pie 
and  WALLS,  extend  from  the  level  of  the  underside  of  the  cellar-floor  to  rock  or 
other  solid  foundation-bed.  (See  page  129,  Subdivision  i,  and  also  Chapter 
III,  pages  228-9.)  In  general,  such  piers  and  walls  are  composed  of  concrete 
and  are  of  such  dimensions  that  the  safe  unit  loads  on  the  concrete  forming 
them  are  not  exceeded.  If  the  foundation-bed  is  rock,  compact  hard-pan,  or 
gravel,  there  need  be  little  or  no  enlargement  of  the  base  of  the  pier  or  wall,  as 
the  safe  unit  loads  on  such  natural  foundation-beds  are  generally  equal  to  the 
safe  unit  loads  on  the  concrete  forming  the  body  of  the  pier  or  wall.  The  design 
of  such  piers  and  walls  is  therefore  an  entirely  simple  matter  governed  by  the 
principles  already  outlined,  and  by  certain  considerations  mentioned  hereafter. 

The  Methods  used  in  the  Construction  of  Foundation  Piers  and 
Walls  are,  however,  necessarily  varied  to  suit  different  materials  and  to  meet 
different  conditions  encountered,  and  the  design  of  a  pier  necessarily  differs  with 
different  methods- of  construction.  For  example,  if  the  construction  is  to  be 
executed  by  means  of  the  ordinary  sheet-piling  method,  piers  and  walls  will 
have  in  general  rectangular  outlines.  But  if  the  Chicago  method  or  the  pneu- 
matic CAISSON  is  employed,  it  will  generally  be  cheaper  to  use  piers  having  a 
circular  cross-section  and  the  support  for  walls  may  be  a  succession  of  cylinders 
rather  than  continuous  walls.  The  detailing  of  the  concrete  structure  consti- 
tuting the  piers  or  walls  is  simple  after  a  determination  is  made  of  the  methods 
by  which  the  construction  is  to  be  put  in  place.  This  subject  is  discussed  in  the 
following  chapter-subdivision,  Methods  of  Excavating  for  Foundations.        ^^_ 

30.    Methods  of  Excavating  for  Foundations  ^" 

Simple  and  Complex  Excavations.  Excavations  in  earth  for  footings  of 
walls  and  piers  may  vary  from  simple  trenches  and  pits  of  the  required  sizes 
and  depths  to  accommodate  the  footings,  up  to  deep  subaqueous  excavations 
requiring  all  the  resources  of  engineering  skill. 

The  Sides  of  Excavations.  If  the  earth  is  firm  and  the  depth  not  excessive 
the  sides  of  the  excavation  may  be  self-supporting,  in  which  case  the  excavation 
may  be  made  the  neat  size  of  the  footing  and  the  sides  of  the  excavation  may 
take  the  place  of  forms  for  the  concrete  deposited  to  form  the  footing.  Where 
the  excavation  is  deep,  and  especially  where  the  earth  is  not  firm,  the  sides  of 
the  excavation  must  be  sloped  or,  if  made  vertical,  must  be  supported  by  bracing 
or  by  some  form  of  sheet-piling.  Where  the  excavation  is  over  8  ft  in  depth  it 
will  generally  be  cheaper  to  support  the  sides  of  the  excavation  than  to  slope 
them.  Where  the  excavation  adjoins  a  property-line  it  will  generally  be  inad- 
visable to  slope  the  excavation  on  account  of  damage  to  the  adjoining  property, 
and  in  such  cases  it  will  be  necessary  to  use  sheeting,  even  if  sloping  the  earth 
would  be  cheaper. 


-m- 

Ill*l? 

iipppii 

y 

Methods  of  Excavating  for  Foundations  201 

Bracing  in  many  cases  will  serve  to  support  the  sides  of  the  excavation  with- 
out the  necessity  of  close  sheeting.  The  bracing  may  consist  simply  of  short 
pieces  of  plank  placed  against  opposite  sides  of  the  excavation  and  held  in 
position  by  horizontal  timber  struts  secured  by  wedges;  or,  especially  in 
narrow  trenches,  some  form  of 

an    EXTENSIBLE    SEWER-BRACE 

may  be  used.  Fig.  34  repre- 
sents a  usual  form  of  ex- 
tensible BRACE.  Generally, 
however,  the  sides  of  an  ex- 
cavation will  not  stand  with  a 
vertical  face,  even  if  braced  in 
this  manner,  for  any  length  of  Fig.  34.  Extensible  Brace  for  Narrow  Excavations 
time,  and  if   the   material   is 

loose  sand  or  soft  clay,  such  bracing  is  entirely  inadequate.  In  such  cases, 
and  in  fact  generally,  some  form  of  continuous  sheet-piling  must  be 
employed. 

Ordinary  Wooden  Sheet-Piling  consists  of  a  continuous  line  of  vertical 
planks  held  against  the  sides  of  the  excavation  by  horizontal  timbers  known  as 
WALES,  WALING  or  BREAST-TIMBERS,  these  wales,  or  breast-timbers  being  in  turn 
supported  either  by  cross-braces  extending  across  the  excavation  to  an  oppo- 
site wall  or  side  of  the  excavation,  or  by  inclined  struts  known  as  shores  or 
;  pushers,  extending  to  the  bottom  of  the  excavation  where  heels  or  inclined 
platforms  are  sunk  in  the  undisturbed  material  to  afford  points  of  support. 

Earth-Pressure  on  Sheet-Piling.  The  load  on  the  sheeting  due  to  the 
sarth-pressure  may  be  calculated  on  the  assumptions  made  for  the  design  of 
iETAiNiNG-WALLS,  but  the  thickness  of  the  sheeting  planks,  the  sizes  and  spacing 
Df  the  breast-pieces  and  braces,  if  figured  on  this  basis,  will  in  general  exceed  the 
dzes  constantly  used  with  success  and  safety  in  such  work.  The  probable  reason 
"or  this  is  that  an  earth  bank,  when  steadied  and  in  part  supported  by  the  sheet- 
ng,  does  not,  for  a  considerable  time,  lose  the  cohesion  between  its  particles 
latural  to  most  earth  banks  in  their  original  and  undisturbed  state.  Or,  in 
)ther  words,  under  these  conditions  no  real  angle  of  friction  is  developed  in 
he  earth-mass.  Local  experience  and  practice  should  be  consulted  and  will 
'cnerally  serve  as  a  guide.  Earth  banks  apparently  similar  will,  however,  act 
cry  differently  and  no  general  rule  can  be  given.  It  should  be  borne  in  mind 
hat  the  earth  composing  a  bank  should  be,  as  far  as  possible,  protected  from 
ar,  from  the  action  of  water  and  from  alternating  freezing  and  thawing;  and 
hat  permanent  work  should  be  completed  as  rapidly  as  possible  so  as  to 
\  oid  the  deteriorating  effects  of  time  and  exposure  on  the  structure  of  the 
>ank. 
The  Thickness  of  the  Sheeting  Planks  required  may  be  calculated  on  the 
ssumption  that  the  earth  bank  is  composed  of  loose  material  having  a  definite 
ngle  of  slope  and  coefficient  of  friction;  but  practically,  under  favorable 
onditions,  2-in  planks  may  be  used  for  a  depth  of  drive  of  i6  ft,  3-in  planks  up 

0  24  ft  and  4-in  planks  up  to  32  ft;  and  timbers,  8  by  12  in,  have  been  driven 

1  favorable  material  to  a  depth  of  over  40  ft. 
Depths  and  Numbers  of  Drives.     Ordinarily  the  depth  to  which  a  plank 

an  be  driven  is  limited  by  its  ability  to  resist  the  shock  due  to  driving,  and  in 
nfavorable  material  a  plank  may  become  shattered  before  it  is  driven  to  the 
bove-quoted  depths.  If  the  required  depth  cannot  be  reached  by  the  first  planks 
r  drive,  a  second,  and  sometimes  a  third  and  fourth  set  of  planks  are  employed, 
^s  the  breast-pieces  supporting  the  first  line  of  planks  must  remain  in  place. 


302 


Foundations 


Chap.fl 
he  breasF 


the  planks  in  the  second  set  or  drive  have  to  be  placed  inside  of  the  breast^ 
pieces,  thus  reducing  the  size  of  the  excavation  by  the  amount  of  the  necessary 
offset.'  Where  more  than  one  drive  is  required  the  first  drive  should  be  started 
at  a  sufficient  distance  outside  to  allow  the  planks  forming  the  second  or  the 
second  and  third  drives  to  be  placed  outside  of  the  required  area  for  the  bot- 
tom of  the  excavation. 

Cutting  and  Fitting  Sheeting  Planks.  The  sheeting  planks  may  be 
SQUARE-EDGED  where  there  is  no  water  or  fine  loose  sand,  but  where  water 
or  running  sand  is  to  be  excluded  the  planks  should  be  tongued  and 
GROOVED,  or  SPLiNED.  The  use  of  tongued  and  grooved  planks  has  the 
additional  advantage  that  the   planks  are  more  readily  kept  in  Hne.     It  is 


O) 


Fig.  35.     Small  Power-hammer 
for  Driving  Sheeting  Planks 


Fig.  36.    Large-size  Power-ham- 
mer and  Sheeting  Planks 


usual  to  cut  the  bottom  edge  of  each  plank  on  a  shght  angle,  so  that  m  driv 
it  is  WEDGED  against  the  preceding  plank.  The  top  of  each  plank  may  be  fitted 
to  receive  an  iron  driving-cap;  or,  if  this  is  not  used,  the  upper  corners  of  the 
plank  should  be  cut  off  so  that  the  effect  of  the  blows  will  be  coiij:entrated 
along  its  vertical  axis,  and  the  tendency  of  the  plank  to  split,  due  to  a  blow 
on  one  corner,  thus  diminished. 

The  Means  Employed  for  Driving  the  Sheeting  vary  with  the  depth 
and  the  size  of  the  sheeting.  For  small  jobs  and  for  moderate  depths  of 
drive,  the  primitive  method  of  driving  by  hand  with  ringed  wooden  mauls 
still  prevails.  For  work  involving  a  considerable  amount  of  driving,  and  in  all 
cases  for  long  drives,  power-hammers  driven  either  by  steam  or  compressed  air 
are  preferably  employed.  A  small-sized  power-hammer  (Fig.  35)  resembles  a 
STEAM-DRILL  and  may  be  handled  by  two  or  three  men  without  any  special  lif  tmg- 


Methods  of  Excavating  for  Foundations 


203 


appliances.  The  larger  sizes  of  power-hammers  (Figs.  36  and  37)  are  practically 
small,  power,  pile-driving  hammers  arranged  with  a  special  driving-head  to 
fit  the  sheeting  employed.  Such  hammers  are  handled  by  derricks  or  are 
carried  in  a  frame  similar  to  .a  pile-driver  frame.  Ordinary  drop-hammers 
are  sometimes  used,  but  are  not  as  advantageous  as  the  reciprocating  power- 
hammilRS,  as  the  blow  struck  by  the  drop-hammer 
shatters  the  plank,  while  the  frequent  light  blows 
of  the  power-hammer  tend  to  keep  the  planks  and 
the  adjacent  material  in  motion  and  accomplish  the 
required  work  with  less  damage  to  the  sheet-piling. 
The  weights  and  dimensions  of  several  types  of  pile- 
driving  hammers  are  given  in  Table  XI,  page  204. 

Manner  of  Driving  Sheeting  Piles.  In  prac- 
tice, a  shallow  excavation  is  first  made  to  the 
proper  line  for  the  outside  of  the  sheeting  planks. 
The  top  breast-timber  is  temporarily  secured  in 
place  and  the  lower  end  of  the  planks  placed  be- 
tween this  timber  and  the  bank.  If  the  planks 
are  long,  temporary  top  guides  or  stay-braces  are 
arranged  so  as  to  keep  the  planks  vertical  until 
they  have  been  driven  well  into  the  ground  and 
guided  by  the  permanent  breast-pieces.  The 
planks  are  then  driven  as  the  excavation  pro- 
gresses, each  plank  being  driven  a  few  inches  in 
turn.  As  the  driving  goes  on  the  material  under 
the  lower  edge  of  the  planks  is  loosened  with  a 
shovel  or  with  a  crowbar,  the  operation  being  so 
conducted  that  the  planks  are  held  true  to  line. 
The  horizontal  breast-timbers  and  their  braces  are 
placed  in  position  as  the  excavation  progresses. 
If  inclined  braces  are  to  be  used  the  excavation 'in 
the  center  is  taken  out  first,  leaving  a  sloping  bank 
against  the  sides  of  the  excavation.  This  permits 
of  the  placing  of  the  inclined  braces  and  of  the  \ 
heels  for  their  points  of  support  before  there  is  any 
danger  to  the  bank.  After  the  first  breast-piece 
and  its  inclined  brace  are  set  in  place,  the  second 
and  subsequent  breast-pieces  and  braces  are  put  in 
as  the  excavation  proceeds, 

Sheet-Piling  for  Excavations  Below  Water- 
Level.     These    excavations     may    be    made    by 

the  sheet-piling  method  if  there  is  not  too  much  water  and  if  water  can 
be  drained  out  of  the  material  without  inducing  a  flow  of  sand  or  clay  below 
the  bottom  of  the  sheet-piling.  In  some  cases,  where  unfavorable  conditions 
exist,  but  where  there  is  an  underlying  stratum  of  impervious  material,  it  is 
possible  to  drive  the  sheeting  in  advance  of  the  excavation,  so  that  the  bottom 
of  the  sheeting  makes  a  tight  joint  with  the  impervious  stratum,  cutting  off  the 
flaw  of  water  and  material.  Where  a  considerable  amount  of  water  finds  its 
way  into  the  excavation,  the  water  must  be  led  to  a  sump  or  depression  from 
which  it  is  ejected  by  means  of  a  pump  or  a  steam-syphon.  Where  the  founda- 
tion-bed is  below  water-level  and  the  material  is  sand,  clay,  or  other  material 
which  would  be  softened  by  the  action  of  the»water,  it  should  be  protected  by 
having  the  sump  at  a  considerable  distance  from  the  area  to  be  used  for  the  sup- 


Fig.  37.  Large-size  Power- 
hammer  for  Driving  Sheet- 
ing Planks 


204 


Foundations 


Chap.  2 


Table  XI.     Weights  and  Dimensions  of  Pile-Driving  Hammeis 


6 

Dimensions 
over  all 

Cylinder 

tes 

11 

§ 

i^ 

1 

^ 

« 

o 

1 

1 

^ 

3 
? 

Q 

B 

o 

CO 

3.6 

c/2  ^ 

o  3 

'o 

'in 

o  rt 

en 

lb 

lb 

m 

in     in 

in 

in 

cult 

m 

in 

m 

Duty,  size  of  piles 
or  piling  ham- 
mer will  drive 


Warrington  Steam  Pile-Hammers 
Manufactured  by  Vulcan  Iron  Works,  Chicago,  111. 


i6  coo 
9850 
6500 
3800 

1350 
800 1 


•16K2 
13K2 
loH 

8 

4 

4 


II vy  concrete  piles 
18"  sq  or  rd  piles 
14"  sq  or  rd  piles 
10"  sq  or  rd  piles 
4"Xi2"  sheeting 
3''Xi2''  sheeting 


Cram  Steam  Pile-Hammers 
Manufactured  by  A.  F.  Bartlett  &  Co.,  Saginaw,  Mich. 


8  400 
5500 
4  200 
I  000 


2^ 

27 

2 

20 

iH 

20 

m 

12 

8H|i8''  sq  or  rd  piles 
8H  14"  sq  or  rd  piles 
8H  10"  sq  or  rd  piles 
5HI  4"X  12"  sheeting 


U 
Manufactured  by 


nion  Pile-Hammers 

Union  Iron  Works,  Hoboken,  N.  J. 


0 

12  100 

I 

8000 

2 

5S0O 

3 

4500 

4 

2500 

5 

I  400 

6 

850 

7 

365 

1550 
548 
890 
663 
363 
214 
129 

70 


100 

so 

750 

2 

28 

8H 

no 

30 

600 

iVz 

28 

8K2 

130 

18 

300 

ili 

25 

6V2 

135 

15 

200 

iH 

23 

sV^ 

150 

10 

150 

I 

20 

aVi 

200 

8 

100 

I 

17 

4'/2 

250. 

5 

60 

H 

14 

3^/^ 

300 

3 

40 

H 

10 

3H 

!  Hvy  concrete  piles 

!  18''  sq  or  rd  piles 

!  ia"  sq  or  rd  piles 

!  10"  sq  or  rd  piles 

6"Xi2"  sheeting 

4"Xi2"  sheeting 

"X 12"  sheeting 

"X6"  sheeting 


Goubert  Steel-Pile  Driving- Hammer 
Manufactured  by  A.  A.  Goubert,  New  York,  N.  Y. 


5  000 

3400 

950 


I  500 
800 
200 


17 
14 


8 

14 

ISO 

SO 

6H 

10 

160 

2S 

4 

8 

200 

ID 

24 

81/4 

\^.     22 

6H 

\i    .... 

18"  sq  or  rd  piles 
12"  sq  or  rd  piles 
4"  sheeting 


New  Monarch  Steam  Pile-Hammer 
Manufactured  by  Henry  J.  McCoy  Co.,  New  York,  N.  Y. 


18"  sq  or  rd  piles 
14"  sq  or  rd  piles 
6"Xi2"  sheeting 
3"Xi2"  sheeting 


I 

7  000 

I  Soo 

90 

24 

24 

9 

I2K> 

I2S 

35 

600 

2 

24 

814 

2 

4600 

850 

72 

20 

20 

7H 

II 

ISO 

20 

300 

iy> 

20 

SH 

3 

2800 

450 

S4 

18 

18 

4H 

7 

17s 

IS 

150 

I 

18 

8H 

4 

800 

I2S 

48 

14 

14 

3H 

6 

250 

10 

6S 

'H 

McKiernan-Terry  Pile-Hammers 
Manufactured  by  McKiernan-Terry  Drill  Co.,  New  York,  N.  Y. 


9 

7  SOO 

I  500 

77 

21 

27H 

IS 

12 

200 

60 

600 

2 

21 

6K2 

7 

S  000 

800 

67 

21 

22H 

1 2 1/2 

10 

22s 

35 

350 

1H2 

21 

6^A 

5 

I  soo 

200 

S6 

II 

14^4 

7 

8H 

300 

20 

200 

iH 

II 

A'A 

3 

640 

68 

54 

9 

9K> 

3M 

5^4 

300 

IS 

ISO 

I 

9 

3H 

I 

I4S 

21 

42 

8 

6^ 

2H 

m 

500 

ID 

100 

H 

8 

2H 

18''  sq  or  rd  piles 
14"  sq  or  rd  piles 
4"Xi2"  sheeting 
3"Xi2"  sheeting 
2"Xio"  sheeting 


Ingersoll-Rand  Sheet  Pile-Driver 
Manufactured  by  Ir^gersoU-Rand  Co.,  New  York,  N.  Y. 


Gi|  I  20o|    20o|  SoIiiHlii     I  4     I  7HI300  I  10  |iio  |iM|....|...|  4''Xi2''  sheeting 


Methods  of  Excavating  for  Foundations  205 

port  of  the  footing.  This  may  be  accomplished  by  making  the  area  to  be  sheeted 
and  excavated  large  enough  to  accommodate  the  sump  outside  of  the  support- 
ing area,  or  by  sinking  a  separate  excavation  to  be  used  exclusively  as  a  sump; 
or  the  same  result  may  in  some  cases  be  accomplished  by  the  use  of  drive- 
wells,  driven  to  a  point  below  the  level  of  the  footing  in  which  continued 
pumping  may  reduce  the  level  of  the  water  to  a  point  below  the  footing.  Care 
also  should  be  taken,  when  the  level  for  the  footing  is  reached,  to  prevent  the 
foundation-bed  from  being  disturbed  and  softened  by  unnecessary  tramping 
of  workmen  over  the  surface  of  the  excavation. 

The  foundation-bed  should  be  left  as  nearly  as  possible  in  its  original  or 
natural  condition. 

Steel  Sheeting  has  been  largely  employed  recently  in  place  of  wooden  sheet- 
ing. It  has  the  advantage  that  it  can  be  driven  in  advance  of  the  excavation, 
thereby  reducing  the  likelihood  of  any  flow  of  material  under  the  sheeting.  It 
also  has  the  advantages  of  affording  greater  strength  for  a  given  thickness  of 
sheeting,  of  being  driven  to  a  greater  depth,  and  in  many  cases  of  being  with- 
drawn and  used  over  again.  As  generally  manufactured,  it  has  the  further 
advantage  of  being  interlocking,  so  that  there  is  less  danger  of  its  getting  out 
of  line  and  leaving  openings  between  adjacent  pieces. 

All  of  these  advantages  have  been  considered  by  engineers  in  using  steel 
instead  of  wooden  sheeting. 

The  Use  of  Steel  Sheeting.  The  fundamental  idea  of  steel  sheeting  is  not 
new,  as  cast-iron  sheet-piling  was  used  in  England  as  far  back  as  1822  and 
various  combinations  of  steel  plates  have  been  used  in  coffer-dams.  The  general 
use  of  steel  sheeting  started  in  this  country  in  1899  when  Luther  P.  Friestedt 
drove  experimental  interlocking  channel-bar  sections.  Since  that  time  it 
has  come  into  general  use,  and  with  its  aid  many  excavations  have  been  made 
with  steel  sheet-piling  which  would  have  been  impracticable  with  timber 
sheeting. 

Earth-Pressure  on  Steel  Sheeting.  In  using  steel  sheeting,  it  should 
be  borne  in  mind  that  the  earth-pressure  coming  on  the  steel  sheeting  is  the 
same  as  the  earth-pressure  coming  on  timber  sheeting,  and  the  breast-pieces 
and  braces  should  be  as  strong  as  in  the  case  of  timber  sheeting.  Certain  forms 
or  sections  of  steel  sheeting  offer  considerable  resistance  to  bending  due  to  the 
lateral  earth-pressure.  With  such  forms  the  horizontal  breast-pieces  may  be 
spaced  farther  apart  than  with  ordinary  timber  sheeting  or  steel  sheeting  not 
having  this  property;  but  the  strength  of  the  breast-pieces  and  of  their  braces 
must  be  sufficient  to  take  up  the  entire  load  coming  on  the  sheeting,  irrespective 
of  the  spacing  between  such  breast-pieces,  for  in  case  there  is  a  failure  in  these 
the  entire  sheeting  will  fail. 

Different  Forms  of  Steel  Sheeting.  Various  types  of  steel  sheeting 
are  on  the  market.  In  making  a  selection  between  different  forms  of  sheeting, 
the  character  of  the  material  to  be  encountered  should  be  borne  in  mind,  as  the 
simpler,  more  compact  sections  will  penetrate  hard  or  gravelly  soils  with  less 
danger  of  deformation  than  the  more  complicated  sections  made  up  of  thin 
plates  and  shapes.  The  various  companies  manufacturing  different  forms  of 
sheet-piling  publish  catalogues  containing  data  as  to  the  weight  and  also  giving 
the  properties  of  the  different  sections.  These  catalogues  may  be  obtained  from 
the  manufacturers,  but  for  convenience  illustrations  of  some  of  the  principal 
sections,  with  their  dimensions  and  weights  and  other  details,  are  given  in  the 
following  pages. 

There  are  other  types  of  steel  sheeting  than  those  shown  m  Figs.  38  to  44* 


206 


Foundations 


Chap.  2 


S^^^"'^ 


Fig.  38.    Lackawanna  Steel  Sheet-piling 


Lackawanna  Steel  Sheet-Piling* 

Composition  and  Dimensions  of  Sections 


Sections 

Per  linear  foot, 
lb 

Per  sqiiare  foot, 
lb 

Straight-web,  H  in  thick 

12.54 
37.187 
42.5 

40.83 
60 

21. s 

35 

40 

35 

48 

Straight-web,  %  in  thick 

Straight-web,  Yi  in  thick 

Arched-web,  14  in  long 

Arched-web,  15  in  long 

This  piling  is  adapted  to  straight  or  circular  work. 

._  •  Manufactured  by  the  Lackawanna  Steel  Company. 


Methods  of  Excavating  for  Foundations 


h 1 

Fig.  39.     United  States  Steel  Sheet-piling 


207 


United  States  Steel  Sheet-Piling  * 
Composition  and  Dimensions  of  Sections 


Size 

Web 

in 

b 
in 

h/2 

in 

12H  in,  38  lb 

9 

13H 
9H 

9  in,  16  lb 

This  piling  is  adapted  to  straight  or  circular  work. 

*  Manufactured  by  the  Carnegie  Steel  Company. 


.h.T^ii. m^^rJ 

Fig.  40.    Friestedt  Interlocking  Channel-bar  Piling 


Friestedt  Interlocking  Channel-Bar  Piling  • 

Composition  and  Dimensions  of  Sections 


Channels 

Zees 

h/2, 

in 

No. 

Description 

In 

Lbs  per  ft 

In 

Lbs  per  ft 

I 

10  in,  28  lb 

10 

IS 

zMXM 

4.8 

9 

2 

10  in,  34  lb 

10 

20 

MXM 

4.8 

9 

3 

12  in,  34  lb 

12 

20.5 

3-)iX% 

8.6 

10^^ 

4 

12  in,  39  lb 

12 

2S 

3HX?i 

8.6 

10^^ 

5 

15  in,  39  lb 

15 

33 

A\^X% 

9.2 

13H 

6 

15  in,  45  lb 

IS 

40 

A%X% 

9.2 

13H 

Manufactured  by  the  Carnegie  Steel  Company. 


208 


Foundations 


Chap.  2 


,,^>;v^^^^^?^^^^^^^/M^/^/^M, 


Fig.  41.     Standard  Sheet-piling 

Standard  Sheet-Piling  * 
Composition  and  Dimensions  of  Sections 


Size, 

Weight  per 

No. 

square  foot, 

A 

B 

C 

D 

in 

lb 

I 

12X5 

35. o 

12 

3.94 

5 

0.34 

2 

I2XS 

36.25 

12 

3.97 

5 

0.37 

3 

ISX6 

37.20 

15 

4.75 

6 

0.37 

4 

15X6 

39.75 

15 

4.81 

6 

0.44 

5 

15X6 

42.25 

15 

4-87 

6 

0.50 

An  interlocking  bar  is  wedged  to  each  beam  at  the  mill  and  the  two  pieces  are  driven 
kS  a  unit. 

*  Manufactured  by  the  Jones  &  Laughlin  Steel  Company. 


Fig.  42.     Spring-lock  Sheet-piling 


Spring-Lock  Sheet-Piling  * 
Composition  and  Dimensions  of  Sections 

Distance,  A 

15  U  in 

19U  in 

2zy\  in 

^6-in  plate.weight  per  square  foot,  in  pounds . 
H-in  plate,  weight  per  square  foot,  in  pounds. . 

17 

20 

14^2 

17 

13H 
16 

Plates  may  be  obtained  curved  to  any  radius  for  circular  work. 
*  Manufactured  by  the  Mitchell-Tappen  Company. 


—  A- 


Fig.  43.     Slip-joint  Sheet-piling 

Slip- Joint  Steel  Sheet-Piling  * 

Composition  and  Dimensions  of  Sections 


Distance,  A 

6  in 

gin 

12  in 

IS  in 

No.  14-gauge,  weight  per  square  foot,  in  pounds. 
No.  16-gauge,  weight  per  square  foot,  in  pounds. 

5.4 
4.3 

5.8 

4.0 

5.7 
3.9 

5.6 

Manufactured  by  the  Mitchell-Tappen  Company. 


Methods  of  Excavating  for  Foundations  209 


Fig.  44.     Wemlinger  Steel  Sheet-piling 

Wemlinger  Steel  Sheet-Piling* 

Composition  and  Dimensions  of  Sections 


No 

I 

2 

3 

4 

5 

6 

7 

8 

9 

10 

Depth  of  corrugation 

2 

Me 

12 

5 

2 
12 

7-5 

2 

H 

12 

8.5 

2V2 

12 
8 

2K2 

H 
12 

9-5 

2I/2 

12 

11-5 

2K> 

Me 
12 
13.5 

4 

3/1 6 
18 
15 

4 

H 
18 
19 

4 

Mo 
18 

23. 5 

1 

Thickness 

Width,  center  to  center  of  lap. .... . 

Weight  per  square  foot  in  pounds .  . 

The  dimensions  given  are  in  inches. 

*  Manufactured  by  the  Wemlinger  Steel  Piling  Company. 

The  Poling-Board  or  Chicago  Method  is  a  special  method  of  excavation 
in  general  use  in  Chicago  and  in  occasional  use  elsewhere  for  excavations  which 
go  to  a  great  depth  in  clay  or  in  other  suitable  material.  It  has  the  advan- 
tage over  the  ordinary  sheet-piling  method  that  the  lining  of  the  excavation  is 
not  driven.  The  method  is  not  generally  used  for  trenches  or  for  square  ex- 
cavations as  a  circular  excavation  is  more  readily  handled.  The  success  of  the 
method  depends  entirely  upon  the  character  of  the  material  to  be  encountered, 
as  the  excavation  is  first  made  and  the  sides  of  the  excavation  afterwards 
supported.  The  method  in  detail  for  a  circular  excavation  for  a  pier-foun- 
dation may  be  described  as  follows: 

(i)  A  circular  excavation  slightly  in  excess  of  the  size  required  for  the  pier 
is  carried  down  to  a  depth  of  5  ft,  great  care  being  taken  to  have  the  sides  of 
the  excavation  vertical  and  true  to  the  circle. 

(2)  Vertical  planks  called  lagging-pieces,  5  ft  in  length  and  slightly  beveled 
on  their  edges  so  that  each  piece  may  be  considered  as  a  stave  with  radial  joints 
corresponding  to  the  size  of  the  required  circle,  are  set  in  place  against  the  walls 
of  the  excavation.  These  planks  are  held  in  place  by  two  or  more  steel  rings, 
generally  made  in  quadrants,  so  that  they  may  be  conveniently  handled  and 
bolted  together.  The  planks  are  wedged  firmly  against  the  walls  of  the  excava- 
tion by  means  of  wooden  wedges  driven  between  the  planks  and  the  iron  rings. 

(3)  As  soon  as  the  first  set  of  lagging  is  compFete,  the  excavation  is  carried 
down  for  another  section,  5  ft  in  depth,  and  another  section  of  lagging  is  put  in 
place  and  secured  in  the  same  manner. 

Depth  and  Character  of  Excavations  in  the  Poling-Board  Method.  In  the 
manner  described  above  the  excavation  may  be  carried  down  for  an  indefinite 
distance,  a  depth  of  100  ft  having  frequently  been  attained.  In  many  cases 
the  bottom  of  the  excavation  is  belled  out  to  a  larger  diameter  than  the  ex- 
cavation for  the  main  shaft  of  the  pier  with  the  object  of  reducing  the  load  of 
the  foundation-bed  to  a  unit  load  less  than  the  safe  unit  load  on  the  main  shaft  of 
the  pier.  This  method  is  not  adapted  for  running  sand  nor  for  clay  that  is  not 
solid  enough  to  stand  with  vertical  sides  during  the  necessary  interval  between 
making  the  excavation  and  placing  the  lagging.  In  some  cases  where  a  stratum 
of  quicksand  has  been  encountered,  the  excavation  has  been  carried  past  it 


210  Foundations  Chap.  2 

by  the  use  of  a  cylindrical  shell  of  steel,  forced  by  jacks  through  it  to  an  under- 
lying impervious  layer  of  clay;  but  in  general  this  method  is  dependent  for  its 
success  upon  a  continuous  body  of  impervious  material. 

The  Open-Caisson  Method  or  Well-Curb  Method  is  used  for  piers  to  be 
carried  to  a  considerable  depth,  and  has  advantages  over  the  sheet-piling  method 
in  certain  materials.  It  is  a  development  of  the  old  method  used  in  sinking 
masonry  wells  and,  in  its  modern  form,  consists  of  a  structure  which  eventually 
forms  part  of  the  pier  itself  and  which  is  arranged  with  an  open  chamber  at  its 
base  in  which  men  may  excavate  the  material  under  the  structure  and  allow  it 
to  settle  as  the  excavation  proceeds.  It  is  evident  that  a  central  opening  or 
shaft  must  be  left  in  the  structure  to  permit  of  the  passage  of  men  and  material. 

Details  of  the  Open-Caisson  Method.  In  detail,  the  method  may  be  described 
as  follows:  First  a  curb  or  cutting-edge  of  timber  or  steel,  following  the  out- 
line of  the  pier,  is  constructed  on  the  surface  of  the  ground.  The  outer  face 
of  this  curb  is  generally  vertical  and  is  protected  with  a  steel  plate  which  ex- 
tends below  the  main  section  of  the  curb,  so  as  to  form  a  cutting-edge  or  sharp 
downward  projection  serving  to  penetrate  the  soil  slightly  in  advance  of  the 
excavation.  On  this  curb  a  wall  of  timber,  concrete,  or  masonry  is  constructed, 
inside  of  which  the  so-called  working-chamber  affords  room  for  the  workmen 
to  be  employed  in  excavating.  Above  the  working-chamber  the  walls  may  con- 
tinue to  a  height  corresponding  to  the  required  height  of  the  pier,  leaving  the 
central  space  to  be  filled  in  after  the  required  depth  is  reached;  or  a  roof  may 
be  built  over  the  working-chamber  and  the  entire  cross-section  of  the  pier  filled 
with  concrete  or  masonry  excepting  only  a  small  central  opening  large  enough  to 
accommodate  a  hoisting-tub  or  bucket  and  to  permit  of  the  ingress  and  egress 
of  the  men  employed  in  sinking  the  construction.  In  practice,  the  excavation 
is  started  before  the  pier-structure  is  carried  up  to  its  final  height,  after  which 
the  excavation  and  the  building  up  of  the  pier  progresses  simultaneously,  the 
constantly  increasing  weight  of  the  structure  aiding  the  sinking  of  the  pier. 
When  the  excavation  has  reached  rock  or  a  firm  substratum,  further  excava- 
tion is  stopp)ed  and  the  working-chamber  and  the  central  opening  are  packed 
full  of  concrete,  leaving  finally  a  complete  pier-structure  extending  from  the 
rock  to  the  proper  level  to  receive  the  steel  grillage  or  other  construction  com- 
ing on  the  pier. 

Advantages  of  the  Open-Caisson  Method.  This  method  of  construction  has 
the  advantages  that  the  workmen  at  all  times  are  protected,  that  obstructions, 
such  as  boulders  or  logs,  may  be  removed  from  under  the  cutting-edge,  and 
that  when  rock  is  encountered,  ample  opportunity  is  afforded  for  the  proper 
preparation  of  the  rock-surface  to  receive  the  final  concrete  filling.  If  a  moderate 
amount  of  water  is  encountered,  not  accompanied  by  a  flow  of  material,  it  can 
generally  be  taken  care  of  by  means  of  pumps. 

Dredged  Wells  are  similar  to  the  open  caissons  described  in  the  previous 
paragraphs  and  are  used  v/here  large  quantities  of  water  are  encountered.  The 
construction  of  the  piers  is  similar  to  that  of  the  piers  used  in  the  open-caisson 
method;  but  the  central  shaft  and  working-chamber  are  designed  to  permit 
of  the  use  of  a  clam-shell  dredge  or  other  form  of  dredge,  and  the  water  is 
allowed  to  rise  to  its  natural  level  in  the  working-chamber  and  shaft.  This 
method  can  be  used  to  advantage  when  a  considerable  amount  of  water-bearing 
sand  or  other  material  is  found  overlying  level  rock  or  other  firm  foundation- 
bed.  When  the  dredging  and  the  sinking  of  the  pier-structure  have  been  carried 
down  to  the  hard  underlying  strata  it  is  sometimes  possible  to  pump  out  the 
water.  If  this  is  not  practicable  the  bottom  may  be  prepared  by  divers  for  the 
reception  of  the  concrete  filling,  and  the  concrete  may  be  deposited  through  water, 


Methods  of  Excavating  for  Foundations  211 

care  being  taken  to  use  some  special  arrangement  to  protect  the  concrete  from 
being  injured  by  loss  of  its  cement-content,  in  the  process  of  deposition. 

The  Well-Digger's  Method  is  also  occasionally  used  in  making  pit-excava- 
tions under  walls  or  in  cramped  locations.  By  this  method  the  sides  of  the 
excavation  are  supported  by  planks  placed  horizontally.  The  method  of  plac- 
ing the  planks  is  as  follows:  A  shallow  excavation,  the  depth  of  a  plank, 
is  made  by  ordinary  methods,  and  a  set,  consisting  of  four  planks  fitting  the 
four  sides  of  the  excavation,  is  secured  in  place.  Before  proceeding  with  the 
general  excavation  of  the  pit  a  trench  is  dug  directly  alongside  and  underneath 
one  of  the  side  planks  of  the  first  set.  As  soon  as  this  trench  is  deep  enough  to 
accommodate  the  planks  for  the  second  set,  the  side  of  the  trench  under  the 
plank  already  in  place  is  cut  to  a  vertical  face,  the  plank  placed  in  position  and 
the  loose  earth  temporarily  back-filled  against  it.  As  soon  as  the  four  planks 
forming  the  second  set  have  been  put  in  place  by  this  method,  the  two  side 
planks  are  wedged  against  the  bank,  the  end-planks  being  used  as  struts.  The 
end-planks  are  wedged  into  position  and  nailed  or  cleated  to  the  side  planks 
forming  a  pressure-resisting  frame  supporting  the  side  of  the  excavation. 
A  continuation  of  this  method  enables  the  excavation  to  be  carried  on  indefi- 
nitely, provided  there  is  no  flow  of  water  or  run  of  material  causing  an  inflow 
of  material  into  the  excavation. 

The  Pneumatic-Caisson  Method.  Where  piers  or  foundation  walls  have 
to  be  carried  to  a  considerable  depth  through  water-bearing  materials,  and  espe- 
cially where  large  bodies  of  quicksand  are  encountered,  the  pneumatic-caisson 
METHOD  must  be  resorted  to.  This  method  is  based  upon  the  principle  of  a 
DIVING-BELL  and  may  be  briefly  described  as  follows:  The  construction  of  the 
pier  is  similar  to  the  piers  previously  described  as  used  in  the  open-caisson  and 
dredged-well  construction,  except  that  the  working-chamber  and  shaft  are  made 
air-tight  and  connected  with  a  device  called  an  air-lock,  so  that  compressed  air 
may  be  introduced  into  the  working-chamber.  The  object  of  the  compressed 
air  is  to  prevent  water  entering  into  the  working-chamber.  This  is  accomplished 
in  accordance  with  the  well-known  principle  of  the  diving-bell  by  having 
the  compressed  air  constantly  kept  at  a  pressure  which  will  counterbalance  the 
water-pressure  at  the  level  of  the  cutting-edge  of  the  working-chamber.  The 
pressure  of  the  air  evidently  must  vary  with  the  depth  of  the  cutting-edge  below 
water-level.  A  column  of  water  i  in  square  in  cross-section  weighs  .43 H  lb  per 
vertical  ft,  and  it  will  therefore  be  counterbalanced  by  an  air-pressure  of  .43H 
lb  per  sq  in  over  the  normal  air-pressure.  If  the  column  of  water  is  30  ft  in 
height,  it  will  weigh  thirty  times  .43 H  lb,  or  will  be  counterbalanced  by  an  air- 
pressure  of  13  lb  per  sq  in  above  the  atmospheric  pressure. 

The  Maximum  Air-Pressure  in  the  Pneumatic  Caisson  in  which  men  can  work 
for  short  periods  is  about  43  lb  per  sq  in  above  atmospheric  pressure,  correspond- 
ing to  a  depth  below  water-level  of  about  100  ft.  At  this  depth  the  work  is 
carried  on  in  shifts  of  from  two  to  three  hours  duration,  and  great  care  must 
be  exercised  in  coming  out  of  the  air-pressure.  The  physiological  effects  of 
compressed  air  are  often  serious;  pains  in  the  joints,  damage  to  the  ear-drums 
resulting  in  deafness,  and  the  so-called  caisson-disease  render  work  at  high 
pressure  extremely  hazardous. 

The  Air-Lock  Used  in  Connection  with  the  Pneumatic  Caisson  is  a  device  for 
the  purpose  of  retaining  the  air  in  the  caisson  and  at  the  same  time  permitting 
the  passage  of  men  and  material  in  and  out.  It  consists  essentially  of  a  metallic 
AIR-TIGHT  chamber  or  SHELL  connected  to  the  working-chamber  either  directly 
or  to  an  air-tight  lining  or  extension  of  the  central  shaft-opening.  This  air- 
chamber  has  two  doors,  oae  at  the  bottom,  opening  downward  into  the  shaft 


212  Foundations  Chap.  2 

and  the  other  in  the  upper  head  of  the  air-lock  chamber,  also  opening  down- 
ward and  afifording  a  direct  connection  to  the  open  air.  In  the  operation  of  an 
air-lock  one  of  these  two  doors  must  at  all  times  be  closed  so  as  to  prevent  the 
free  escape  of  air  through  the  air-lock.  If  the  bottom  door  is  closed,  it  will  be 
held  firmly  to  its  seat  by  the  uplift  of  the  compressed  air  in  the  shaft,  which  is 
at  all  times  in  direct  communication  with  the  working-chamber.  If,  under  these 
conditions,  the  upper  door  is  open,  the  interior  of  the  air-lock  will  be  in  direct 
communication  with  the  open  air  and  the  air  contained  in  the  lock  will  evidently 
be  at  atmospheric  pressure.  Workmen  and  materials  may  then  enter  the  air- 
lock. In  order  to  pass  into  the  shaft  and  working-chamber,  it  is  necessary, 
first,  to  close  the  upper  door,  and  secondly,  to  shift  the  so-called  equalizing 
VALVE  and  admit  compressed  air  into  the  space  between  the  two  doors,  until 
the  air-pressure  is  brought  up  to  the  air-pressure  in  the  working-chamber  and 
shaft.  Pressure  on  the  upper  side  of  the  lower  door  will  then  equal  the  pressure 
on  the  lower  side  and  the  lower  door  may  be  opened,  the  upper  door  being  firmly 
held  against  its  seat  by  the  compressed  air  in  the  air-lock.  As  soon  as  the  lower 
door  opens,  the  men  and  material  may  be  passed  into  the  shaft  and  working- 
chamber.  In  coming  out  the  operations  are  reversed;  men  and  material  enter 
the  air-lock  through  the  open  lower  door,  the  lower  door  is  closed  and  held  tightly 
against  its  seat,  and  the  equalizing  valve  is  shifted,  affording  a  connection  be- 
tween the  interior  of  the  air-lock  and  the  external  air.  The  compressed  air 
escapes  through  the  equalizing  valve,  reducing  the  pressure  in  the  air-lock  to 
atmospheric  pressure,  and  the  upper  door  has  atmospheric  pressure  on  both 
sides  of  it.  It  may  then  be  opened,  giving  free  connection  with  the  outside  air. 
The  Design  of  Pneumatic  Caissons.  The  first  consideration  is,  of  course,  to 
have  the  final  structure  a  permanent  and  sufficient  pier  to  carry  the  load  to  be 
imposed  upon  it.  To  this  end  the  cross-section  of  the  pier  at  all  points  from  top 
to  bottom  should  be  capable  of  carrying  safely  the  maximum  load.  As  the 
cross-section  of  the  pier  is  generally,  in  the  finished  pier,  composed  of  solid  con- 
crete, the  cross-section  will  be  determined  by  the  allowable  load  on  the  concrete. 
For  piers  the  cross-section  will  generally  be  square  or  circular;  for  walls  the 
caisson  will  generally  be  not  less  than  6  ft  in  width,  as  it  is  difficult  to  sink 
caissons  having  a  width  less  than  6  ft.  If  the  caisson  is  to  be  carried  to  solid 
rock,  the  bearing  on  the  rock  need  be  no  larger  than  the  cross-section  of  the 
concrete  pier;  but  if  the  excavation  does  not  go  to  rock,  it  is  frequently  desir- 
able to  BELL  OUT  the  base  of  the  pier  so  as  to  reduce  the  loading  on  the  founda- 
tion bed  to  a  unit  load  less  than  that  allowable  on  concrete.  The  operation  of 
BELLING  OUT  is  difficult  in  some  materials;  in  a  compact  material  it  can  be  gen- 
erally accomplished  without  serious  difficulty. 

Piers  Sunk  by  the  Pneumatic-Caisson*  Method  may  be  constructed  of  various 
combinations  of  materials.  The  side  walls  and  roof  of  the  working-chamber 
were  formerly  frequently  constructed  of  timber.  In  many  cases  they  are  now 
formed  of  steel;  but  in  recent  designs  the  working-chamber  is  generally  formed 
of  reinforced  concrete,  the  only  structural  steel  used  being  an  angle  or  a  plate 
and  angle  composing  the  cutting-edge.  The  outside  of  the  caisson  is  preferably 
made  vertical.  The  superimposed  pier  is  generally  of  the  same  size  as  the  work- 
ing-chamber, at  least  it  is  generally  so  in  piers  sunk  for  buildings. 

A  Typical  Design  for  a  Caisson  Built  of  Reinforced  Concrete  is  given  in  Fig.  45, 
in  which  AB  h  the  angle-iron  and  plate  forming  the  so-called  cutting-edge 
and  C  is  the  working-chamber  formed  by  the  side  walls  DE  and  DE  and  by 
the  roof  £E.  The  concrete  side  walls  are  reinforced  with  steel  rods  attached  to 
the  cutting-edge,  and  extending  upward  into  the  body  of  the  pier,  and  the  roof 
and  body  of  the  pier  are  reinforced  to  take  care  of  stresses  due  to  construe- 


Methods  of  Excavating  for  Foundations 


213 


tion  and  sinking.  In  building  up  the  working-chamber,  the  interior  forms  are 
arranged  so  as  to  support  the  concrete  which  makes  the  roof.  These  are  sub- 
sequently removed.  The  exterior  forms  may  constitute  a  permanent  part  of  the 
structure,  in  which  case  they  are  called  a  coffer-dam,  or  they  may  be  removed 
as  soon  as  the  concrete  has  sufficiently  set.  At  the  center  of  the  pier  an  open- 
ing is  left  to  serve  as  the 
SHAFT  or  opening  connecting 
the  working-chamber  with  the 
AIR-LOCK.  The  sides  of  this 
opening  or  of  the  upper  part 
of  it,  only,  are  lined  with  an 

AIR-TIGHT     STEEL    SHELL.      To 

the  upper  end  of  the  steel 
shell  the  air-lock  is  connected. 
If  the  height  of  the  pier  does 
not  exceed  40  ft  the  construc- 
tion of  it  may  be  completed 
before  the  excavation  is  com- 
menced. Generally,  however, 
the  construction  of  the  pier  is 
stopped  as  soon  as  the  work- 
ing-chamber and  from  5  to  10 
ft  of  the  superimposed  pier 
has  been  constructed;  then 
sufficient  excavation  is  done, 
without  the  use  of  compressed 
air,  to  carry  the  cutting-edge 
down  to  water-level.  This  is 
called  DITCHING  the  caisson 
and  is  done  so  that  the  caisson 
will  have  some  slight  latepal 
support  from  the  soil  before 
the  construction  is  carried  up 
high  enough  to  make  it  top- 
heavy.  When  the  entire  pier 
or  the  first  section  is  finished, 
excavation  is  resumed  and  the 
whole  structure  is  sunk  as  the 
excavation  progresses,  care  be- 
ing taken  to  remove  any 
obstruction  from  beneath  the 
cutting-edge.  During  the  progress  of  sinking  compressed  air  is  conducted  to 
the  working-chamber  through  the  supply-pipe  G,  the  excavated  material  being 
hoisted  through  the  shaft  F.  The  shaft  F  is  fitted  with  a  ladder  for  the  use 
of  the  workmen. 

Details  of  Caisson-Sinking  and  Filling.  In  sinking  the  caisson  and  super- 
imposed pier,  care  must  be  taken  to  maintain  it  in  a  vertical  position.  This 
end  may  be  accomplished  in  large  caissons  by  means  of  the  excavation  itself. 
In  case  one  side  of  the  caisson  is  high  the  excavation  on  that  side  will  be  carried 
somewhat  in  advance  of  the  excavation  on  the  low  side,  and  the  material  under 
the  cutting-edge  of  the  high  side  will  be  removed  while  a  bank  of  material  is 
kept  under  the  cutting-edge  of  the  low  side.  These  methods,  however,  are  of 
little  avail  when  the  caisson  is  narrow.  In  such  cases  that  part  of  the  caisson 
which  is  above  ground  is  held  in  position  by  guides  or  other  devices;  but  it 


Reinforced-concrete 


214 


Foundations 


Chap.  2 


frequently  happens  that  the  caisson  in  its  final  condition  is  considerably  out  of 
its  correct  location  and  considerably  out  of  plumb.  In  general,  therefore,  the 
size  of  the  caisson  should  be  made  larger  than  the  minimum  size  necessary,  in 
order  to  allow  for  errors  in  its  final  location.  When  the  caisson  has  reached  the 
required  depth  the  foundation-bed  is  prepared  for  the  reception  of  the  concrete 
filling  and  the  working-chamber  filled  with  it,  care  being  taken  that  it  completely 
fills  all  voids  and  is  in  perfect  contact  with  the  roof.  Finally,  the  air-lock  and 
the  steel  Uning  of  the  shaft  are  removed  and  the  shaft-opening  filled  with  con- 
crete to  the  proper  level  to  receive  the  grillage  or  other  construction  forming 
the  base  of  the  column  which  is  to  rest  on  the  caisson. 

The  Height  of  Caisson-Piers.  The  height  of  a  pier  cannot  be  exactly 
fixed  until  it  is  known  to  what  depth  the  caisson  must  sink  in  order  to  reach 
the  foundation-bed.  If  the  rock  is  found  at  a  greater  depth  than  anticipated, 
additional  height  is  added  to  the  top  of  the  pier  after  the  caisson  is  in  its  final 
position;  but  if,  on  the  other  hand,  the  rock  is  found  unexpectedly  high,  the 
top  of  the  pier  will  have  to  be  cut  off.  If  the  finished  elevation  of  the  pier  is  to 
be  below  the  level  of  -the  general  excavation,  it  is  usual  to  extend  the  exterior 
surface  of  the  pier  to  the  required  height  by  means  of  a  tem.porary  chamber- 
structure  called  a  coffer-dam,  the  height  of  which  corresponds  to  the  depth  of 
the  finished  surface  below  the  level  of  the  general  excavation.  Inside  of  this 
COFFER-DAM  some  STEEL  GRILLAGES  may  conveniently  be  set. 

The  Freezing  Process  for  Excavations.  This  method  has  sometimes 
been  employed  in  making  excavations.  In  this  country  its  use  has  been  limited 
to  one  or  two  mining-shafts,  but  in  Germany  it  has  been  resorted  to  in  making 
excavations  for  building-foundations.  The  method  consists  in  driving  steel 
pipes  into  the  ground.  These  pipes  are  closed  at  the  bottom  and  at  the  top 
are  connected  to  smaller  pipes  through  which  brine,  at  an  extremely  low  tem- 
jxjrature,  is  made  to  circulate.  The  refrigerating  effect  results  in  freezing  the 
water  contained  in  the  soil,  converting  quicksand  to  a  frozen  mass  resembhng 
soft  sandstone.  When:  the  freezing  has  progressed  sufficiently  to  form  a  solid 
wall  or  coflfer-dam  around  the  excavation,  the  material  inside  the  frozen  wall 
may  be  excavated.  This  method  has  the  advantage,  theoretically,  of  being 
applicable  to  excavations  of  any  depth.  There  are  many  precautions  necessary, 
and  for  the  present,  at  any  rate,  it  should  only  be  considered  as  a  possibility. 

31.   Protection  of  Adjoining  Structures 

General  Considerations.  The  common  law  provides  that  any  person  mak- 
ing an  excavation  is  responsible  for  resulting  damage  to  adjoining  property. 
Statute  laws  as  embodied  in  the  building  codes  of  different  cities  may  modify 
or  limit  this  responsibility,  but  in  general,  excavations  should  be  made  in  such 
a  manner  as  to  cause  the  least  possible  damage  to  surrounding  property.  Where 
there  are  no  adjoining  structures  it  is  generally  sufficient  to  slope  the  sides  of  the 
excavation  so  as  to  prevent  the  sliding  of  material  into  the  excavation,  or,  at 
least,  to  sheet-pile  and  brace  the  sides  of  the  excavation;  but  where  the  excava- 
tion is  to  be  made  alongside  of  an  existing  structure,  and  carried  below  the 
footings  of  such  structure,  it  is  necessary  to  take  special  measures  for  its  protec- 
tion. Such  work  is  described  as  shoring,  underpinning  and  protecting  ad- 
joining STRUCTURES,  and  may  involve  the  carrying  of  the  weight  of  part  or  all 
of  the  buildings  on  temporary  supports,  the  removal  of  the  old  footings  and 
the  construction  of  new  footings  at  lower  elevations. 

Shoring.  When  the  excavation  for  the  new  building  does  not  go  much 
below  the  adjoining  footings  and  when  the  material  is  fairly  solid,  it  may  suflBce 
to  transfer  a  portigu  of  the  load  of  the  wall  to  temporary  footings.    This  may  be 


Protection  of  Adjoining  Structures 


215 


accomplished  by  means  of  heavy  inclined  posts  called  shores,  arranged  to  act 
as  INCLINED  COLUMNS  OF  STRUTS.  Each  Shore  consists  of  a  post,  the  lower 
end  of  which  rests  on  a  platform,  generally  consisting  of  planks  and  timbers 
arranged  so  as  to  form  a  temporary  spread  footing.  This  platform  should  be 
placed  at  a  depth  which  will  insure  that  subsequent  operations  will  not  under- 
mine it.  The  upper  end  of  the  post  fits  into  a  hole  or  niche  cut  into  the  wall 
to  be  supported.  The  post  itself  may  be  a  timber  with  a  square  cross-section, 
usually  12  by  12  in,  and  of  the  required  length.  Provision  is  made,  between  the 
platform  and  the  lower  end  of  the  post,  for  wedges  or  jacks,  so  that  when 
operated  their  lifting  effect  transfers  part  of  the  weight  of  the  wall  from  its 
footing  to  the  temporary  foundation  or  platform.  During  this  operation  all 
parts  of  the  temix)rary  structure  are  in  compression  and  brought  into  bearing, 
and  the  material  under  the  platform  is  compressed  and  solidified  as  much  as 
possible. 

Kinds  of  Shores.  If  the  shore  is  to  act  preferably  for  lifting  only,  it  is 
kept  as  nearly  vertical  as  possible  and  is  known  as  a  lifting  shore.  If  it  is 
to  act  preferably  to  combine  a  horizontal  pushing  action  with  the  lifting 
action,  it  is  placed  at  a  considerable  angle  from  the  vertical  and  is  then  known 
as  a  pushing  shore  or  steadying  shore.  In  arranging  such  shores  care 
should  be  taken  to  have  the  niche  cut  close  to  a  floor-level  of  the  building  to  be 
shored,  as  otherwise  the  horizontal  component  of  the  thrust  of  the  shores  might 
buckle  the  wall. 

Numbers  and  Sizes  of  Shores.  Where  a  wall  is  light,  a  number  of  smaller 
shores  should  be  used  in  preference  to  a  few  large  ones.  Where  a  wall  is  high, 
two  or  more  shores  of  varying 
lengths  may  be  used,  and  these 
may  conveniently  be  placed  in  the 
same  vertical  plane  and  rest 
on     the     same 


O^ 


^ 


platform. 

Wedges  and 
Screw-jacks. 

In  transferring 
the  load  of  a 
wall  from  its 
own  footing  to 
the  temporary 
platform,  use  is 
made  of  wooden 


Fig.  46.     Standard    orsteel  wedges, 

lype     01     bteel    screw- TACKS 

Screw-jack  hydraulic       ^^^'  ^^'    ^^^^'^^^^  Type  of  Steel  Screw-jack 

jacks;  or,  wedges  and  jacks  may  be  used  in  combination.  Wooden  wedges 
should  be  made  of  hard  wood  and  are  generally  arranged  in  pairs,  both 
wedges  being  driven  at  the  same  time.  The  lifting  effect  of  such  wooden 
wedges  is  powerful,  but  where  a  considerable  settlement  of  the  temporary 
foundation  is  anticipated,  it  is  more  convenient  to  use  screw-jacks,  as  they 
can  take  up  a  considerably  settlement. 

Materials  and  Types  of  Screw-jacks.  The  screw-jacks  usually  manu- 
factured for  this  purpose  are  made  of  cast  iron  and  have  rough  threads,  with 
too  coarse  a  pitch  to  have  much  lifting  effect.  Screw-jacks  of  a  better  kind  are 
made  of  steel  and  have  a  machine-thread  of  small  pitch.  Such  jacks  can  be 
obtained  capable  of  hfting  weights  up  to  100  tons.    Figs.  46  and  47  represent 


216 


Foundations 


Chap.  2 


standard  forms  of  screw-jacks.  When  a  single  screw-jack  i.s  used  in  connec- 
tion with  a  post  or  shore,  a  hole  to  receive  the  threaded  portion  of  the  jack 
is  bored  in  the  end  of  the  timber  used  for  the  shore,  the  end  being  squared  to 
receive  the  nut.  Such  an  arrangement  is  called  a  pump  and  is  illustrated  in 
Fig.  48.  When  a  lifting  effect  greater  than  that  exerted  by  a  single  jack  is  re- 
quired, the  jacks  are  arranged  in  pairs  in  connection  with  a  short  timber  or  cross- 


Fig.  48.  Pump,  or 
Screw-jack  let  into 
End  of  Shore 


Shore,    Screw-jacks    and 
head 


Timber    Crosa- 


HEAD.  Such  an  arrangement  is  illustrated  in  Fig.  49.  It  has  the  advantage 
that  after  operating  the  jacks,  blocking  and  wedges  can  be  placed  between  the 
platform-timbers  and  the  cross-head  so  that  the  post  resting  on  the  cross-head 
has  a  direct  and  solid  bearing  on  the  platform.  By  this  method  the  load  of  the 
wall  can  be  thrown  on  the  platform  by  the  jacks  and  after  the  blocking  and  wedg- 
ing is  in  position  the  jacks  can  be  removed. 

Hydraulic  Jacks.  Where  excessively  heavy  loads  are  to  be  lifted,  hydraulic 
JACKS  may  be  used  in  place  of  screw-jacks  but  an  objection  to  them  is  that  they 
are  liable  to  slack  back  under  the  load.  While  the  load,  therefore,  should 
not  be  permanently  supported  on  hydraulic  jacks,  they  may  be  used  to  take  the 
load  temporarily  while  the  blocking  and  wedging  are  being  placed  between  the 
cross-head  and  the  temporary  footing.  In  this  way  an  indefinite  number  of 
shores  may  be  set  and  taken  care  of  with  a  single  pair  of  hydraulic  jacks. 

Example  of  Shoring.  Fig.  50  shows  the  method  jised  in  shoring  the  orna- 
mental front  wall  of  a  heavy  building,  advantage  having  been  taken  of  the  nu- 
merous deep  margin-drafts  shown  in  the  section.  In  order  to  avoid  the  necessity 
of  cutting  niches  for  the  tops  of  the  shores,  nine  hardwood  blocks,  a,  a,  etc., 
were  fitted  to  the  margin-draft  grooves  in  the  masonry.  Nine  similar  blocks, 
bt  b,  etc.,  were  gained  into  and  bolted  to  the  vertical  timber  VV,  space  being 


Protection  of  Adjoining  Structures 


217 


L 


Wl 


± 


tvc^ 


J 


T 


6 


3= 

3= 


^ 


Fig.  50.     Shoring  an. Ornamented  Wall 

left  between  the  a  blocks  and  the  b  blocks  for  adjusting  wedges  w,  w,  etc.  Three 
headpieces,  Ti,  T2  and  Ts  were  keyed  and  bolted  to  VV  and  transmitted  to  it 
the  uplift  of  the  three  shores,  Si,  S2  and  Ss.  Each  shore  had  a  60- ton  screw-jack 
at  its  base.  Each  shore  is  shown  fitted  with  a  pump  or  detached  extension- 
piece  arranged  for  the  screw-jack. 


218 


Foundations 


Chap.  2 


Needling.  Needles  or  girders  are  employed  when  part  or  all  of  the  weight 
of  the  wall  has  to  be  carried,  as  when  the  old  footing  is  to  be  removed  and  the 
wall  UNDERPINNED  or  Carried  down  to  a  new  footing  at  a  greater  depth. 

Example  of  Needling  and  Underpinning.  Fig.  51  represents  a  typical  case  of 
UNDERPINNING,  the  Several  operations  being  as  follows: 

(i)  The  General  Excavation  is  carried  down  to  within  a  few  inches  of  the 
bottom  of  the  footing  BB  under  the  wall  W. 

(2)  The  Pit  DDDD,  properly  braced  and  protected  by  sheet  piling,  is  sunk 
to  approximately  the  level  of  the  proposed  excavation,  this  pit  being  placed 
at  a  safe  distance  from  the  existing  wall.     In  good  material  it  may  be  safe  to 


Fig.  51.     Wall-needling  and  Underpinning 


have  this  pit  approach  to  within  a  few  feet  of  the  footing  course  of  the  wall,  but 
in  material  which  is  liable  to  run  it  should  not  approach  the  wall  closer  than 
its  depth.  No  hard  and  fast  rule  can  be  given,  and  in  every  case  great  care 
should  be  taken  to  prevent  any  movement  of  the  material  from  under  the  ad- 
joining footing. 

(3)  The  Platforms.  On  the  bottom  of  this  pit-excavation,  a  platform  FF 
is  placed,  generally  composed  of  heavy  timbers  resting  on  a  base  of  heavy 
planks^  and  acting  as  a  support  for  the  outer  end  of  the  needle.  During  the 
construction  of  this  pit  a  similar  pit  may  be  dug  on  the  inside  of  the  wall  to  pro- 
vide for  the  support  of  the  inside  end  of  the  needle;  but  as  this  involves  the 
destruction  of  the  cellar-floor  the  method  of  procedure  inside  the  building  is 
generally  different  from  this.  If  the  material  is  solid  it  is  sometimes  sufficient 
to  place  the  platform  for  the  support  of  the  inside  end  of  the  needle  directly 
on  the  cellar-floor  and  at  such  a  distance  from  the  wall  that  the  necessary 
excavation  for  the  new  footing  will  not  disturb  it;  or  the  platform  may  be 
placed  on  the  cellar-floor  and  a  line  of  sheeting  LL,  properly  braced,  so  placed 
that  the  excavation  can  be  made  for  the  new  footing.  This  is  generally  sufficient 
to  prevent  any  serious  settlement  of  the  temporary  platform  for  the  inside  end 
of  the  needle. 


Protection  of  Adjoining  Structures 


219 


(4)  The  Insertion  of  the  Needles.  Having  provided  a  support  for  each  end 
of  the  NEEDLE  it  only  remains  to  cut  a  hole  through  the  wall,  as  at  ^,  insert  the 
needle  GG,  put  the  post  and  blocking  MN  under  the  outside  end  of  the  needle, 
and  the  blocking  and  jacks  under  the  inside  end.  The  post  MN  may  be  fitted 
with  wedges  as  shown  at  K,  or  with  one  or  more  screw-jacks.  The  needle  GG 
may  consist  of  one  or  more  heavy  timbers  or  one  or  more  steel  I  beams.  In  any 
case,  the  load  to  come  on  this  needle  should  be  figured  and  its  strength  made 
ample  to  safely  support  such  load.  As  soon  as  the  weight  of  the  wall  W  is 
transferred  to  the  needles  and  to  the  temporary  platforms  prepared  to  receive 
the  load,  that  part  of  the  wall  which  is  below  the  needles  and  all  of  the  foot- 
ing may  be  removed  and  all  of  the  excavation  for  the  new  footing  made. 


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Fig.  52.    Needling  a  Brick  Wall 


Needling  a  Brick  Wall.  Fig.  52  shows  the  elevation  of  a  brick  wall  sup- 
ported by  NEEDLES.  If  the  needles  are  carrying  the  entire  weight  of  the  wall,  it 
is  evident  that  at  the  level  of  their  upper  surfaces  the  entire  weight  will  be 
transferred  through  those  parts  of  the  wall  which  are  immediately  above  them, 
and  that  above  these  points  the  material  composing  the  wall  will  corbel  out 
in  both  directions  as  indicated  in  Fig.  52  by  the  heavy  zigzag  fines  A  AAA  A. 
All  of  the  wall  below  this  line  will  be  supported  simply  by  cohesion  to  the  part 
of  the  wall  above  it.  An  experienced  man  can  determine  the  location  of  this 
line  by  the  sound  given  by  the  wall  on  being  struck  by  a  hammer.  All  of  the 
wall  below  this  line  is  hanging  and  liable  to  fall  as  soon  as  the  support  given  by 


220 


Foundations 


Chap.  2 


the  footing  is  removed.  The  hanging  parts  of  the  wall  may  be  removed  or  sus- 
pended by  rods  and  chains  to  the  needles.  If  they  are  not  so  suspended  a 
crack  will  form  along  the  line  AAA  A  A. 

Transferring  the  Load  to  the  New  Underpinning.  As  soon  as  the  new 
footing  has  been  put  in  place  and  the  new  wall  carried  up  ready  to  receive  the 
old  wall,  provision  must  be  made  for  reversing  the  operation,  that  is,  for 
transferring  the  load  onto  the  new  underpinning  wall  and  footing.  This  is 
generally  done  by  means  of  a  number  of  granite  blocks  set  in  pairs  between 
the  needles  and  fitted  with  steel  wedges.  After  setting  these  blocks,  the  space 
between  the  base  of  the  old  wall  and  the  top  of  the  upper  wedging  block  is  filled 

in  with  brickwork,  the 
mortar  in  the  last  joints 
being  compacted  by  means 
of  pieces  of  slate  driven 
in  so  as  to  wedge  the 
mortar  between  the  bricks. 
This  brickwork  should  be 
laid  up  in  Portland-cement 
mortar  so  as  to  reduce  the 
time  of  setting.  As  soon 
as  it  is  sufficiently  set,  the 
wedges  are  driven  home  so 
as  to  throw  at  least  a  por- 
tion of  the  weight  of  the 
wall  on  the  new  footing. 
As  a  result  of  this  it  fre- 
quently happens  that  this 
footing  settles,  the  load 
being  restored  to  the 
needles.  This  necessitates 
continued  driving  on  the 
wedges  until  it  has  reached 
its  final  settlement,  which 
will  be  evidenced  by  a  lift- 
ing of  the  wall  sufficient  to 
partially  relieve  the  stress 
in  the  needles  and  by  the 
fact  that  the  wedges  re- 
main tight. 

Removal  of  the 
Needles,  etc.  As  soon 
as  the  entire  weight  of  the 
wall  has  been  transferred 
to  the  footing  and  the  footing  has  demonstrated  that  it  is  capable  of  sup- 
porting the  weight  of  the  wall  without  further  settlement,  all  of  the  temporary 
work,  including  the  needles,  can  be  removed,  the  needle-holes  bricked  up  and 
the  repairs  made  to  the  cellar  of  the  adjoining  building. 

The  Figure-Four  Method  of  Needling.  In  certain  cases  it  is  impractical 
to  employ  a  needle-beam  projecting  on  both  sides  of  the  wall,  as  for  example 
when  the  occupancy  of  the  adjoining  building  is  such  as  to  make  it  impractical 
to  have  a  needle-beam  projecting  into  the  cellar  space.  In  such  cases  the  so- 
called  figure-four  Needle  has  been  employed  (Fig.  53).  In  this  case  the 
needle -.4 -8  acts  as  a  cantilever.     Part  of  the  load  of  the  wall  is  carried  by  the 


Fig.  53.    The  Figure-four  Method  of  Needling 


Protection  of  Adjoining  Structures 


221 


inclined  shore  C  and  another  equal  or  nearly  equal  part  is  carried  by  the  needle 
at  B,  the  needle-beam  AB  being  really  balanced  on  the  block  dd. 

Spring-Needles.  Fig.  54  shows  a  method  frequently  employed,  known  as 
the  SPRING-NEEDLE  METHOD.  In  this  case  the  needle  engages  with  the  wall  to 
be  supported  and  also  with  an  adjoining  wall.  A  temporary  platform  is  placed 
as  close  to  the  wall  to  be  supported,  W^  as  is  practicable.    The  uplift  of  the 


Fig.  54.     The  Spring-needle  Method  of  Underpinning 


jack  tending  to  lift  the  needle-beam  acts  on  both  walls,  but  on  account  of  its 
being  located  nearer  to  the  wall  to  be  lifted,  a  large  proportion  of  its  effect  is 
exerted  thereon. 

Pipes  or  Cylinders  for  Underpinning  are  frequently  used  for  the  support 
of  a  wall  and  have  many  advantages,  as  they  not  only  afford  a  support  for  the 
footing  through  the  operations  affecting  the  stability  of  the  wall,  but  also  form 
a  permanent  support.  The  operation  in  brief  is  as  follows:  A  hole  or  niche  is 
cut  in  the  wall  and  footing  to  be  supported,  of  sufficient  size  to  permit  the  intro- 
duction of  a  section  of  steel  pipe,  in  such  manner  that  the  center  of  the  pipe 
will  come  below  the  center  of  the  wall  to  be  supported,  the  height  being  sufficient 
to  accommodate  a  section  of  pipe  and  also  the  means  employed  to  drive  it. 
The  pipe  may  be  driven  (i)  by  hydraulic  jacks  or  by  screw-jacks,  placed 
between  the  top  of  the  pipe  and  the  wall  itself,  as  by  the  patented  Breuchaud 
method;  (2)  it  may  be  driven  by  means  of  a  power-hammer  driven  either  by 
steam  or  compressed  air;  or  (3)  in  some  cases,  where  the  material  is  fine  sand  or 
clay,  the  pipe  may  be  jetted  or  the  jet-method  may  be  used  in  combination 
with  either  jacks  or  power-hammers.  In  any  case  the  first  section  of  pipe  is 
driven  into  the  ground  and  additional  sections  are  added  until  the  lower  end  of 
the  pipe  encounters  rock  or  some  material  possessing  sufficient  stability  to  insure 
the  required  support.  The  material  entering  the  pipe  is  removed  by  a  water- 
jet  or  by  other  means  and  the  space  filled  with  concrete.  As  soon  as  the  con- 
crete has  set  sufficiently  the  pipe  is  capped  with  a  special  casting  on  which  short 
steel  I  beams  are  arranged  to  distribute  the  support  of  the  pipe  over  a  consider- 
able part  of  the  base  of  the  wall  to  be  supported.     These  I  beams  correspond 


222  Foundations  Chap.  2 

to  the  wedging  blocks  used  in  the  ordinary  methods  before  described.  Pro- 
vision is  frequently  made  for  steel  wedges  between  the  cap  and  the  base  of  the 
steel  beam,  but  it  is  generally  found  sufficient  to  thoroughly  grout  in  the  space 
between  the  base  of  the  wall  and  the  steel  beams  after  the  niche  itself  has  been 
bricked  up. 

Cylinders  for  Underpinning  Very  Heavy  Walls.  The  description  m  the 
preceding  paragraph  is  intended  to  cover  the  use  of  pipes  varying  in  size  from 
6  to  2o-in  in  diameter,  according  to  the  load  to  be  carried.  In  the  case  of  exces- 
sively heavy  walls,  cast-iron  cylinders  are  used  in  place  of  steel  pipes.  These 
cylinders  are  arranged  in  sections,  each  section  making  a  water-tight  joint  with 
the  preceding  section,  and  are  generally  used  where  water  is  encountered  and 
where  it  is  necessary  to  carry  down  the  underpinning  to  rock  at  great  depths. 
Under  such  conditions  these  cylinders  are  sunk  by  the  pneumatic-caisson 
METHOD.  Such  cylinders  have  been  sunk  to  a  depth  of  70  ft  below  water-level 
and  have  been  designed  to  carry  as  much  as  400  tons. 


Footings  for  Light  Buildings  223 


CHAPTER  III 

MASONRY  WALLS.    FOOTINGS  FOR  LIGHT  BUILDINGS.* 
CEMENTS  AND  CONCRETES 

By 
THOMAS   NOLAN 

PROFESSOR    OF    ARCHITECTURAL    CONSTRUCTION,    UNIVERSITY   OF   PENNSYLVANIA 

1.   Footings  for  Light  Buildings 

Footing  Courses  in  General,  f  Every  foundation  or  bearing  wall  overlying 
anything  except  solid  rock  should  rest  on  a  footing  or  base  projecting  beyond 
the  wall  on  each  side.  On  wet  or  very  compressible  soils  these  footings  may  be 
built  of  steel  beams  or  of  reinforced  concrete,  as  described  in  Chapter  II,  but 
on  reasonably  firm  soils  and  for  buildings  of  moderate  size  and  weight  the  foot- 
ings are  generally  of  concrete,  stone,  or  brick.  Footings  answer  two  important 
purposes: 

(i)  By  distributing  the  weight  of  a  structure  over  a  larger  area  of  bearing 
surface,  the  pressure  per  square  foot  on  the  foundation-bed  is  diminished  and 
the  tendency  to  vertical  settlement  correspondingly  lessened. 

(2)  By  increasing  the  area  of  the  base  of  a  wall,  footings  add  to  its  stability 
and  form  a  protection  against  the  danger  of  the  work  being  thrown  out  of 
plumb  by  any  forces  that  may  act  on  it.  Nearly  every  building  law  requires 
that  every  foundation  wall  or  pier  and  every  cellar  or  basement  wall  or  pier 
shall  have  a  footing  at  least  1 2  in  wider,  that  is,  6  in  on  each  side,  than  the  thick- 
ness of  the  wall  or  pier,  and  this  may  be  considered  as  the  minimum  projection, 
except  in  rare  instances  where  there  may  be  a  special  reason  for  making  it  less. 
On  firm  soils  and  for  comparatively  light  buildings  a  projection  of  6  in  on  each 
side  of  a  wall  will  generally  reduce  the  unit  pressure,  that  is,  the  pressure  per 
square  foot,  to  the  safe  resistance  of  the  soil,  but  it  is  always  wise  to  proportion 
the  footings  to  a  uniform  unit  pressure,  as  explained  in  Chapter  II,  Subdivision 
8.  To  have  any  useful  effect,  footings  must  be  well  bedded  and  have  sufficient 
transverse  strength  to  resist  the  upward  reactions  on  the  projections. 

Stone  Footings  for  Walls  with  Ordinary  Loads.  Stone  cellar  walls  and 
basement  walls  generally  have  stone  footings,  although  if  the  walls  are  heavily 
loaded  a  bottom  footing  of  coarse  concrete  is  advisable  under  the  stone  footing. 
If  practicable,  stone  footings  should  consist  of  stones  having  a  width  equal  to 
that  of  the  footing.  If  impracticable  to  obtain  stones  of  this  size,  then  two 
stones  should  be  used,  meeting  under  the  middle  line  of  the  wall.  In  any  event 
each  footing  course  should  extend  inside  of  the  course  above,  a  distance  equal  to 
at  least  one  and  one-half  times  the  projection,  otherwise  the  stones  will  not 
properly  transmit  the  loads  and  reactions  and  the  footing  courses  will  tend  to 
open  at  the  joints,  as  in  Fig.  1. 

*  For  a  complete  discussion  of  foundations  in  general  and  the  mechanical  principles 
involved  in  their  strength  and  stability,  for  walls,  piers,  etc.,  below  the  basement  or 
cellar  floor,  see  Chapter  II. 

t  For  a  complete  discussion  of  footing  courses  for  heavy  buildings  and  of  the  theories 
of  the  stresses  developed  in  offset,  projecting,  or  cantilever  footings,  see  Chapter  II. 
especially  Subdivisions  17  to  23. 


224  Masonry  Walls.     Cements  and  Concretes  Chap.  3 

Stone  footings  should  be  of  hard,  strong  and  durable  stones,  always  laid  on 
their  natural  bed  and  solidly  bedded  in  mortar.  As  a  general  rule,  for  light 
buildings,  and  where  the  loads  per  unit  of  foundation-bed  are  much  less  than 

the  allowable  pressure,  the  thickness  of  each 
course  is  made  about  equal  to  its  projection 
beyond  the  course  above.  The  most  com- 
mon defect  in  large-stone  footings  is  that 
the  stones  are  not  properly  bedded,  as  it  is 
more  difficult  to  bed  a  large  stone  than  a 
small  one.  The  stones  should  be  laid  in  a 
thick  bed  of  mortar  and  worked  sidewise  with 
a  bar  until  firmly  settled  in  place. 

Offsets  in  Masonry  Footings.*  The 
projections  of  the  footing  courses  beyond 
the  wall,  or  beyond  the  courses  above,  must 


r 

/  Joint  //I 


^y>^^. 


Fig.    1.    Stone  Footing.    Openings    be   carefully   considered    whatever  the   ma- 
at  Joints  terial  of  the  footmgs.     If  the  projection  of 

the  footing  or  offset  of  the  courses  is  too 
great  for  the  strength  of  the  stone,  brick,  or  concrete,  the  footing  will  crack, 
as  shown  in  Fig.  2.  The  proper  offset  for  each  course  depends  upon  the 
vertical  load,  the  transverse  strength  of  the  material, 
the  resisting  power  of  the  foundation-bed  and  the 
thickness  of  the  course. t 

Tables  for  Offsets  for  Masonry  Footing 
Courses.!  As  stated  in  Chapter  II,  in  the  discus- 
sion of  the  design  of  stepped  footings,   there  are        V-* — i 

rule-of-thumb  methods  giving  so-called  safe  projec-        . X 1 — . 

tions  for  given  depths  of  footings  or  giving  the  ratios        V 1 — . 

between  the  projections  and  the  depths  of  the  courses.        ,^,  ^_..^    ,X>-  ->^^'x"^*^ 
Tables  of  offsets  for  footing  courses  of  different  ma-   p.      Z^r^^  k  *'  F    t* 
terials  have  been  computed  from  the  flexure-formula       (^^^  Excessive  Offsets 
apphed  to  the  projecting  footing  courses  considered  as 

CANTILEVER  BEAMS  uniformly  loaded  by  the  upward  pressures  on  the  under  side. 
Although  these  tables,  so  computed,  are  incorporated  in  some  building  codes, 
they  cannot  be  safely  used  without  numerous  restrictions,  exceptions  and  modi- 
fications, and  hence  they  are,  in  general,  unreliable  and  of  use  only  as  approxi- 
mations. As  these  tables  are  still  inserted  in  engineers'  and  architects'  hand- 
books, the  table  of  offsets  for  masonry  footing  courses,  in  a  revised  form,  is  re- 
tained in  this  chapter  with  the  recommendation  that  for  footings  of  several 
offsets  it  be  used  with  caution  and  that  for  such  footings  the  methods  explained 
in  Chapter  II  be  used  when  greater  accuracy  of  results  is  required. 

Notes  Regarding  Use  of  Table  I.  The  values  in  Table  I  are  computed 
from  the  formula  l=Md  VSf/wJ  which  is  derived  from  the  flexure-formula 
for  a  uniformly  loaded  cantilever  beam,  and  slightly  changed  to  make  the 
numerical  coefficient  of  the  second  member  of  the  equation  the  value  shown. § 
In  this  equation,  /  =  the  maximum  allowed  offset  of  the  footing  course  in  inches, 
d  =i  the  thickness  of  the  footing  course  in  inches,  S^  =  the  modulus  of  rupture 

*  See  Offset  Footings,  Chapter  II,  especially  Subdivisions  17  and  22. 

t  See  Chapter  II,  Subdivision  22,  for  a  complete  discussion  of  the  principles  involved 
in  the  design  of  projecting  footings,  ratio  of  projection  to  depth  of  footing,  etc.,  for  homo- 
geneous slabs,  separate-layer  footings,  etc. 

X  See  Chapter  II,  Subdivision  22,  page  180. 

§  See,  also,  formula  in  Chapter  II,  Subdivision  22. 


Foe  tings  for  Light  Buildings 


225 


Table  I.    Approximate  Values  of  Offsets  for  Masonry  Footing  Courses  in 
Terms  of  the  Thickness  of  the  Course 

The  values  are  computed  with  a  factor  of  safety  of  lo. 


Material  of  the  footings 


5y  in 

pounds 

per  square 

inch 


w  in  tons  per 
square  foot 


North  River  Bluestone  (ordinary  run) 

Granite  (average) 

Limestone  (average) ^ 

Sandstone  (average) 

Brickwork  (good  bricks  in  natural-cement  mortar, 

I  :  2,  60  daj'^s  old) 

Brickwork  (hard-burned  bricks  in  Portland-cement 

mortar,  i  :  3,  60  days  old) 

Concrete  (Portland  cement,  i  :  2  :  4,  i  month  old) . 
Concrete  (Portland  cement,  i  :  2  :  4,  6  months  old) 


3000 
1850 
I  375 
I  375 

125 

400 
300 
400 


4.1 
32 

2.8 


1.6 
1-3 
1.5 


2.9 
2.2 
2.0 
2.0 

o."5 

I.I 
0.9 
I.I 


2.0 
1.6 
1-4 
1.4 


0.7 
0.6 
0.7 


of  the  materials  in  pounds  per  square  inch,  w  =  the  determined  or  assumed 
pressure  on  the  bottom  surface  of  the  footing  course  considered,  in  tons  of  2  000 
lb  per  sq  ft,  and  /  =  the  factor  of  safety  used.  The  table  gives  the  values  of  l/d 
for  three  unit  pressures  w.  For  example,  if  w  is  taken  at  2  tons  per  sq  ft,  then 
for  Umestone  or  sandstone  footings  l/d  =  1 .4,  and  if  d,  the  thickness  of  the 
footing  course,  is  12  in,  the  offset  or  projection  should  be  16  or  17  in.  The 
values  given  in  the  tal)le  for  Sf,  the  modulus  of  rupture  for  the  materials,  differ 
very  slightly  from  those  given  in  Subdivision  22  of  Chapter  II,  in  Table  I  of 
Chapter  XV  and  in  Table  III  of  Chapter  XVI.  If  results  are  required  based 
upon  different  fiber-stresses,  upon  a  different  factor  of  safety,  or  upon  different 
pressures  per  square  foot,  the  formula  may  be  used  instead  of  the  table.  It 
should  always  be  borne  in  mind  that  as  each  footing  course  transmits  the  entire 
weight  of  the  wall  and  its  load,  the  pressure  will  be  greater  per  square  foot  on 
the  upper  courses,  and  that  the  offsets  should  be  made  proportionately  less; 
and  that  the  values  in  Table  I,  when  applied  to  stone-masonry  footings,  are 
really  valid  for  the  lower  offset  only,  and  then  only  when  the  footing  is  built 
of  stones  the  thickness  of  which  is  equal  to  the  thickness  of  the  course,  which 
have  a  projection  of  less  than  half  their  length,  and  which  are  well  bedded  in 
cement  mortar. 

Concrete  Footings.*  For  buildings  of  great  weight,  except  the  very  heaviest, 
and  especially  for  those  built  on  a  clay  soil,  concrete  generally  makes  the  best 
footing,  and  it  is  even  preferable  to  and  generally  cheaper  than  large  slabs  of 
stone.  When  the  concrete  is  properly  made  and  used,  it  attains  a  strength 
equal  to  that  of  most  stones,  and  under  walls,  being  devoid  of  joints,  it  is  like 
a  CONTINUOUS  BEAM,  having  sufficient  strength  to  span  any  soft  spots  that 
happen  to  be  in  the  foundation-bed.  When  deposited  in  thin  layers  and  well 
rammed,  concrete  becomes  firmly  bedded  on  the  bottom  of  the  trenches,  so  that 
there  is  no  possible  chance  for  settlement  except  that  due  to  the  compression  of 
the  soil. 

*  For  an  example  of  concrete-footing  design,  see  Chapter  II,  Subdivision  22.  For 
reinforced -concrete-footing  design,  see  C^hapter  II,  Subdivision  24.  See,  also,  Chapter 
XXV,  paragraphs  relating  to  footings,  pages  978  to  982. 


226 


Masonry  Walls.     Cements  and  Concretes 


Chap.  3 


Preparing  the  Trenches.  For  footings,  concrete  made  with  Portland 
cement  is  preferable,  and  it  should  have  a  thickness  of  at  least  8  in,  even  under 
light  buildings;  and  for  buildings  of  more  than  two  stories,  a  thickness  of  at 
least  12  in.  On  firm  soils,  such  as  hard  clay,  the  trenches  should  be  accurately 
dug  and  trimmed  to  the  exact  width  of  the  footings,  so  that  the  concrete  will 
fill  them.  When  the  foundation-bed  is  of  loose  gravel  or  sand  it  is  generally 
necessary  to  set  up  planks  to  confine  the  concrete  and  form  the  sides  of  the 
footings.  These  planks  may  be  held  in  place  by  stakes;  they  should  be  left 
in  place  until  the  concrete  has  become  hard,  which  generally  requires  from  two 
to  four  days,  after  which  they  may  be  pulled  up  and  dirt  filled  in  against  the 
concrete.  The  proportions  and  manner  of  mixing  concrete  are  described  in  the 
latter  part  of  this  chapter. 

Depositing  the  Concrete.  Concrete  should  be  used  as  soon 'as  mixed  and 
should  always  be  deposited  in  layers,  which  as  a  rule  should  not  exceed  6  in  in 
thickness,  especially  for  the  first  layer.  On  small  jobs  where  the  work  is  done 
by  hand'  the  concrete  is  usually  carried  to  the  trenches  in  wheel-barrows  and 
dumped  into  the  trenches.  The  height  from  which  the  concrete  is  dumped, 
however,  should  not  exceed  4  ft  above  the  bottom  of  the  trench,  because  when  it 
falls  from  a  greater  height  the  heavy  particles  are  apt  to  separate  from  the 
lighter  ones.  As  soon  as  the  concrete  has  been  deposited  in  the  trenches,  it 
should  be  leveled  off  and  then  tamped  with  a  wooden  rammer  weighing  about 
20  lb,  until  the  water  in  the  concrete  is  brought  to  the  surface.  Concrete  should 
not  be  permitted  to  dry  too  quickly,  and  if  twenty-four  hours  elapse  between 
the  deposits  of  the  successive  layers,  the  top  of  each  layer  should  be  sprinkled 
before  the  next  is  put  in  place.  For  buildings  over  five  stories  high,  it  Is  a  good 
idea  to  place  a  stone  footing  course  above  the  concrete  footing,  if  suitable  stones 
for  the  purpose  can  be  obtained. 

Brick  Footings.  Where  the  foundation  walls  are  of  brick,  the  footings  are 
usually  brick  or  concrete.     For  interior  walls  on  dry  ground,  and  in  many 


1  BRICK 


1I-BRICKS 


WmM 


Mi 


Fig.  3.     Brick  Footing.    Wall 
One  Brick  Thick 


Fig.    4.     Brick  Footing.     Wall  One  and 
One-half  Bricks  Thick 


localities  for  outside  walls,  brick  footings  are  fully  as  good  as  stone  footings, 
provided  good,  hard  bricks  are  used  and  the  footings  are  properly  built.  Brick 
footings  should  always  start  with  a  double  course  on  the  foundation-bed  and 
then  be  laid  in  single  course  for  ordinary  footings,  the  outside  ot  the  work  being 
laid  all  headers,  as  in  the  accompanying  illustrations,  and  no  course  projecting 
more  than  one-fourth  the  length  of  a  brick  beyond  the  one  above  it,  except  in 
the  case  of  an  8-in  or  9-in  wall.  For  brick  footings  under  high  or  heavily  loaded 
walls,  each  projecting  course  should  be  made  double,  the  header-course  above 
and  the  stretcher-course  below.    Figs.  3,  4,  5  and  6  show  footings  for  walls 


Footings  for  Light  Buildings 


227 


2  BRICKS 


varying  from  one  brick  to  three  bricks  in  thickness.  The  bricks  used  for  foot- 
ings should  be  the  hardest  and  soundest  that  can  be  obtained,  should  be  laid  in 
cement  mortar  and  should  be  either  grouted  or  thoroughly  slushed  up,  so  that 
every  joint  shall  be  entirely  filled  with  mortar.  The  writer  favors  grouting 
for  brick  footings,  that  is,  the 
using  of  a  thin  mortar  to  fill  the 
inside  joints,  as  he  has  always 
found  that  it  gives  very  satisfac- 
tory results.  The  bottom  course 
of  the  footing  should  always  be 
laid  in  a  bed  of  mortar  spread 
on  the  bottom  of  the  trench 
after  the  latter  has  been  care- 
fully leveled.  All  bricks  laid  in 
warm  or  dry  weather  should  be 
thoroughly  wet  before  laying,  for, 
if  laid  dry,  they  rob  the  mortar 
of  a  large  percentage  of  the  mois- 
ture it  contains,  greatly  weakenin; 


hi^rSMM^MB 


...^^  J  , 


Fig 


Brick  Footing.     Wall  Two  Bricks  Thick 


the  adhesion  and  strength  of  the  mortar. 
Careful  attention  should  be  given  to  the  laying  of  the  footing  courses  of 
buildings,  as  upon  them  the  stability  of  the  work  largely  depends.  If  the 
bottom  courses  are  not  solidly  bedded,  if  any  rents  or  voids  are  left  in  the 
beds  of  the  masonry,  or  if  the  materials  themselves  are  unsound  or  badly 


3  BRICKS 


^m. 


^^^^^^^^^^ 


%g&i 


Fig.  6.    Brick  Footing.    Wall  Three  Bricks  Thick 


put  together,  defects  in  the  superstructure  are  almost  sure  to  show  them- 
selves sooner  or  later,  and  almost  always  at  a  period  when  remedial  efforts  are 
difficult  and  expensive. 

Inverted  Arches.*  In  a  few  buildings  in  which  the  external  walls  are 
divided  into  piers  with  wide  openings  between  them,  and  in  which  the  support- 
ing power  of  the  soil  is  not  more  than  2  or  3  tons  per  sq  ft,  it  was  thought  desir- 
able to  connect  the  bases  of  the  piers  by  means  of  inverted  arches,  for  the  pur- 
pose of  distributing  the  weight  of  the  piers  over  the  whole  length  of  the  footings. 
Examples  of  inverted-arch  footings  are  shown  in  Figs.  7  f  and  8,t  which  represent 
respectively  the  construction  employed  in  the  Drexel  Building  in  Philadelphia 

*  For  an  example  worked  out  in  full,  showing  the  method  of  proportioning  inverted 
arches,  see  Chapter  III,  Building  Construction  and  Superintendence,  Part  I,  Masons* 
Work,  by  F.  E.  Kidder. 

t  From  the  Engineering  Record,  May,  1899,  and  Nov.,  1890. 


$2$ 


Masonry  Walls.     Cements  and  Concretes  Chap.  3 


and  the  World  Building  in  New  York  City.  Unless  the  piers  are  about  equally 
loaded,  however,  it  is  generally  impossible  to  distribute  the  weight  evenly,  and 
if  the  arches  extend  to  an  angle  of  the  building,  the  end-arch  must  be  provided 
with  ties  of  sufficient  strength  to  resist  the  thrust  of  the  arch,  as  otherwise  it 
may  push  out  the  corner-pier.  It  is  usually  better  to  build  the  piers  with  sepa- 
rate footings,  projecting  equally  on  all  sides  of  the  pier,  and  each  proportioned 


Fig.    7.     Inverted-arch   Footing.     Drexel         Fig.    8.     Inverted-arch    Footing.    World 
Building,  Philadelphia  Building,  New  York 

to  the  load  supported.  The  intermediate  wall  may  be  supported  by  steel  beams 
or  by  arches.  About  the  only  advantage  over  ordinary  masonry  footings 
possessed  by  inverted  arches  is  in  the  resulting  shallower  foundations. 

The  following,  relating  to  inverted  arches,  is  taken  from  the  New  York  build- 
ing law:  "If,  in  place  of  a  continuous  foundation  wall,  isolated  piers  are  to  be 
built  to  support  the  superstructure,  where  the  nature  of  the  ground  and  the 
character  of  the  building  make  it  necessary,  in  the  opinion  of  the  Commissioner 
of  Buildings  having  jurisdiction,  inverted  arches  resting  on  a  proper  bed  of 
concrete,  both  designed  to  transmit  with  safety  the  superimposed  loads,  shall 
be  turned  between  the  piers.  The  thrust  of  the  outer  piers  shall  be  taken  up 
by  suitable  wrought-iron  or  steel  rods  and  plates."     (Law  of  1906.) 


3.   Cellar  Walls  and  Basement  Walls 

Definitions.  These  terms  are  generally  applied  to  walls  which  are  below 
the  surface  of  the  ground  or  below  the  water-table  or  first-floor  beams, 
which  support  the  superstructure  and  which  go  down  to  the  foundation  walls, 
properly  so  called.  (See  Chapter  II,  Divisions  i  and  29.)  Walls  whose  chief 
office  is  to  withhold  a  bank  of  earth,  such  as  the  walls  around  areas,  are  called 
RETAINING- WALLS.     (For  retaining-walls,  see  Chapter  IV.) 

Materials  for  Cellar  and  Basement  Walls.  These  walls  may  be  built  of 
brick,  stone  or  concrete.  Brick  is  suitable  only  in  very  dry  soils  or  for  a  party 
wall  with  a  cellar  or  basement  on  each  side  of  it.  Portland-cement  concrete 
is  an  excellent  material  for  foundation  walls,  and  is  being  more  extensively 
used  in  their  construction  every  year.  The  concrete  may  be  filled  in  between 
wooden  forms,  which  hold  it  in  place  until  it  has  set,  or  concrete  blocks  molded 
so  as  to  form  a  solid  wall  may  be  used.    If  poured  concrete  is  used  the  forms 


Walls  of  the  Superstructure 


229 


should  be  removed  as  soon  as  the  concrete  has  set  and  the  walls  should  be 
sprinkled  once  or  twice  a  day,  if  the  weather  is  dry,  so  that  the  concrete  will  not 
dry  too  quickly  Good  hard  ledge-stone,  especially  if  it  comes  from  the  quarry 
with  flat  beds,  makes  not  only  a  strong  wall  but,  if  well  built,  one  that  will  stand 
the  effects  of  moisture  and  the  pressure  of  the  earth  much  better  than  a  brick 
wall.  Between  a  good  stone  wall  and  a  wall  of  Portland-cement  concrete, 
there  is  probably  not  much  choice,  except  perhaps  in  the  matter  of  expense,  the 
relative  cost  of  stonework  and  concrete  varying  in  different  localities.  A  wall 
built  of  soft  stones,  or  stones  that  are  very  irregular  in  shape,  with  no  flat  surfaces, 
is  greatly  inferior  to  a  concrete  wall,  or  even  to  a  wall  of  good  hard  bricks,  and 
should  be  used  only  for  dwellings  or  light  buildings.  Stone  walls  should  never 
be  less  than  i8  in  thick,  and  should  be  well  bonded,  with  full  and  three-quarter 
headers,  and  all  spaces  between  the  stones  should  be  filled  solid  with  mortar 
and  broken  stones  or  spalls.  The  mortar  for  stonework  should  be  made  of 
cement  and  sharp  and  rather  coarse  sand.  The  outside  walls  of  cellars 
and  basements  should  be  plastered. smooth  on  the  outside  with  i  :  2,  or  i  :  iH 
cement  mortar,  from  Vi  to  %  in  thick.  In  heavy-clay  soils  it  is  a  good  idea  to 
batter  the  walls  on  the  outside,  making  them  from  6  in  to  i  ft  thicker  at  the 
bottom  than  at  the  top. 

Thickness  of  Cellar  and  Basement  Walls.  This  is  usually  governed  by 
that  of  the  walls  above,  and  also  by  the  depth  of  the  wall.  Nearly  all  building 
regulations  require  that  the  thickness  of  the  cellar  and  basement  wall,  to  the 
depth  of  12  ft  below  the  grade-line,  shall  be  4  in  greater  than  the  thickness  of  the 
wall  above  for  brick,  and  8  in  greater  for  stone,  and  that  for  every  additional 
10  ft  or  part  thereof  in  depth,  the  thickness  shall  be  increased  4  in.  In  all  large 
cities  the  thickness  of  the  walls  of  buildings  is  controlled  by  law.  For  buildings 
in  which  the  thickness  of  the  walls  is  not  so  governed,  the  following  table  will 
serve  as  a  guide: 

Table  II.    Thickness  of  Cellar  and  Basement  Walls 


Height  of  building 

Dwellings,  hotels, 
etc. 

Warehouses 

Brick, 
in 

Stone, 
in 

Brick, 
in 

Stone, 
in 

Two  stories  

12  or  16 
16 
20 
24 
28 

20 
20 
24 
28 
32 

16 
20 
24 
24 
28 

20 
24 
28 
28 
32 

Three  stories 

Four  stories     

Six  stories                  . .                

3.   Walls  of  the  Superstructure 

Brick  and  Stone  Walls,  Very  little  is  known  regarding  the  stability  of 
walls  of  buildings  beyond  what  has  been  gained  by  practical  experience.  The 
only  stresses  in  any  horizontal  sections  of  such  walls,  which  can  be  determined 
with  any  accuracy,  are  the  direct  weight  of  the  walls  above  and  the  pressure 
due  to  the  floors  and  roof.  In  most  walls,  however,  there  is  a  tendency  to 
buckle,  to  overcome  which  it  is  necessary  to  make  them  thicker  than  would 
be  required  to  resist  the  direct  crushing  stress.  The  resistance  to  fire  should 
also  be  taken  into  account  in  deciding  upon  the  thickness  of  any  given  wall. 


230  Masonry  Walls.    Cements  and  Concretes  Chap.  3 

The  strength  of  a  wall  depends  also  very  much  upon  the  quality  of  the  materials 
used  and  upon  the  way  in  which  the  wall  is  built.  A  wall  bonded  every  12  in 
in  height,  and  with  every  joint  slushed  full  with  good  rich  mortar,  is  as  strong 
as  a  poorly  built  wall  4  in  thicker.  Walls  laid  with  cement  mortar  are  also 
much  stronger  than  those  laid  with  lime  mortar,  and  a  brick  wall  built  with 
bricks  that  have  been  well  wet  just  before  laying  is  very  much  stronger  than  one 
built  with  dry  bricks. 

Thickness  of  External  Walls.  In  nearly  all  the  larger  cities  oC  the  country 
the  minimum  thickness  of  the  walls  is  prescribed  by  law  or  ordinan':e,  and  as 
these  requirements  are  generally  ample  they  arc  commonly  adhered  to  by  archi- 
tects when  designing  brick  buildings.  Table  III  *  gives  the  thickness  of  brick 
walls  required  for  mercantile  buildings  in  representative  cities  of  different 
sections  of  the  United  States,  and  allords  about  as  good  a  guide  as  one  can 
have,  because  the  values  given,  as  a  rule,  represent  the  judgment  of  well- 
qualified  and  experienced  persons.  Walls  for  dwellings  arc  generally  per- 
mitted to  be  4  in  less  in  thickness  than:  for  warehouses,  although  in  some 
cities  little  or  no  distinction  is  made  between  business  blocks  and  dwellings. 

Table  IV  gives  the  thickness  required  for  the  brick  walls  of  dwellings,  tene- 
ments, hotels  and  office-buildings  t  in  Chicago.  The  thickness  given  is  the  mini- 
mum that  should  be  allowed  for  the  walls  of  such  buildings,  unless  certain 
special  conditions  exist.  For  modifications  for  different  classes  of  buildings  see 
the  building  code.  In  St.  Louis  the  two  upper  stories  of  dwellings  are  required 
to  be  13  in,  the  next  two  below,  18  in,  the  next  two  22  in,  and  the  next  two  26  in 
thick. 

In  compiling  Table  III  the  top  of  the  second  floor  was  taken  at  19  ft  above 
the  sidewalk,  and  the  height  of  the  other  stories  at  13  ft  4  in,  including  the 
thickness  of  the  floor,  as  the  New  York  and  Boston  laws  and  the  laws  of  some 
other  cities  give  the  height  of  the  walls  in  feet  instead  of  in  stories.  W'hen  the 
height  of  stories  exceeds  these  measurements  the  thickness  of  the  walls  in  some 
cases  will  have'  to  be  increased.  The  Chicago  ordinance  (1916)  specifies  that 
"where  12-in  walls  are  used,  the  story-heights  shall  not  exceed  18  ft,  where  i6-in 
walls  are  used,  the  story-heights  shall  not  exceed  24  ft,  and  where  20-in  walls 
are  used,  the  story-heights  shall  not  exceed  30  ft." 

General  Rule  for  Thickness  of  Walls.  Although  there  are  great  dilTer- 
ences  in  the  thickness  given  in  Table  III,  more  indeed  than  there  should  be, 
a  general  rule  might  be  formulated  from  it,  for  mercantile  buildings  over 
four  stories  in  height,  which  would  be  somewhat  as  follows: 

For  bricks  equal  to  those  used  in  Boston  or  Chicago,  make  the  thickness  of 
the  three  upper  stories  16  in,  of  the  next  three  below  20  in,  the  next  three  24  in 
and  the  next  three  28  in.  For  a  poorer  quafity  of  material  make  only  the  two 
upper  stories  16  in  thick,  the  next  three  20  in,  and  so  on  down.  In  buildings  less 
than  five  stories  in  height  the  top  story  may  be  12  in  thick. 

In  determining  the  thickness  of  walls  the  following  general  principles  should 
be  recognized: 

(i)  That  walls  of  warehouses  and  mercantile  buildings  should  be  heavier 
than  those  used  for  living  or  oflBce  purposes. 

•  Since  this  table  was  compiled,  some  provisions  of  some  laws  have  been  changed,  but 
the  requirements  relating  to  the  thicknesses  of  walls  vary  but  little  from  those  given. 
As  building  laws  of  different  cities  are  amended  from  time  to  time,  architects  and  builders 
must  be  guided  by  the  code  in  force  in  the  city  in  which  a  building  is  to  be  erected.  The 
table  represents  the  average  requirements  and  is  useful  for  comparative  purposes  and  as 
a  guide  for  those  building  outside  of  cities,  or  where  no  special  building  laws  are  in  force. 

t  For  other  than  steel  skeleton  construction. 


Walls  of  the  Superstructure  2 

Table  III.*     Thickness  in  Inches  of  Walls  for  Mercantile  Buildings  and. 
Except  in  Chicago,  for  All  Buildings  Over.  Five  Stories  in  Height 


Height  and  location  of  building 

Stories 

ISt 

2d 

3d 

4th 

5th 

6th 

7th 

8th 

Two 
stories 

Three 
stories 

Four 
stories 

Five 
stories 

Six 
stories 

Seven 
stories 

Eight 
stories 

f  Boston 

i6 

12 
12 
12 
I8 

13 
17 
13 

20 

i6 
i6 
i6 
i8 
17 
17 
13 

2C 

i6 

20 

i6 

22 
21 
17 
I8 

20 
20 
20 
20 
22 
21 
21 
I8 

2-1 
24 
20 
20 
26 
26 
21 
22 

24 

28 
20 
20 
26 
26 
22 

28 

32 

24 
24 

30 
30 

22 

12 
12 
12 
12 
13 
13 
13 
13 

i6 
i6 

12 
T2 
I8 
17 

17 
13 

i6 
i6 
i6 
i6 
i8 
17 
17 
i8 

20 

i6 

20 

i6 

22 
21 

17 
I8 

20 
20 
20 
20 
22 
21 
21 
I8 

20 
24 
20 
20 
26 
21 
22 

24 
28 
24 
20 
26 
26 
22 

'  New  York 

Chicago 

Minneapolis 

St.  Louis 

Denver 

San  Francisco 

New  Orleans 

( Boston 

i6 

12 
12 
12 
13 
13 
13 
13 

i6 
i6 
i6 

12 

18 
17 
17 
13 

20 

i6 
i6 
i6 
i8 
17 
17 
i8 

20 
20 
20 

i6 

22 

21 
17 
i8 

20 
24 
20 
20 
22 
21 
I8 

20 
24 
20 
20 
26 
21 
22 

New  York. 

Chicago 

Minneapolis 

St.  Louis 

Denver         

San  Francisco 

New  Orleans 

f  Boston       

i6 

12 
12 
12 
13 

13 
13 
13 

20 

i6 
i6 

12 

i8 
17 
17 
13 

20 
20 

i6 
i6 
i8 
17 
17 
i8 

20 
20 
20 

i6 

22 
21 
l8 

20 

24 
20 
20 
22 
21 

i8 

New  York 

Chicago       

Mirneaoolis 

St.  Louis 

Denver , 

San  Francisco 

New  Orleans 

f  Boston 

i6 
i6 
i6 

12 

13 
13 
13 
13 

20 

i6 
i6 
i6 
I8 
17 
17 
13 

20 
20 
l6 

i6 
i8 
17 
i8 

20 
20 
20 
l6 
22 
21 
18 

New  York 

Chicago 

St.  Louis 

San  Francisco       

New  Orleans 

f  Boston       

i6 
i6 
i6 

12 

13 
13 
13 
13 

20 

i6 
i6 
i6 
i8 
17 
13 

20 
20 

i6 
i6 
i8 
17 
i8 

New  York  

Chicago       

Minneapolis            .... 

Denver                  

New  Orleans 

Boston 

i6 
i6 
i6 

12 

13 
17 
13 

20 

i6 
i6 
i6 
i8 
17 
13 

i6 
i6 
i6 

12 

13 

T.7 

x3 

New  York 

Chicap:o. 

St.  Louis        

New  Orleans 

Boston 

New  York 

Chicago  

Minneapolis 

Denver     

New  Orleans 

*  See  paragraphs  and  foot-note  on  page  230. 


232 


Masonry  Walls.     Cements  and  Concretes 


Chap.  3 


Table  III  (Continued).*    Thickness  in  Inches  of  Walls  for  Mercantile 

Buildings  and,  Except  in  Chicago,  for  all  Buildings  Over 

Five  Stories  in  Height 


Height  and  location  of 
building 


Nine 
stories 


Ten 
stories 


Eleven 
stories 


Twelve 
stories 


Boston .. 

New  York. . 

Chicago 

Minneapolis. 

St.  Louis 

Denver 


Boston 

New  York. . 

Chicago 

Minneapolis^ 

St,  Louis 

Denver 


Boston 

New  York. 

Chicago 

St.  Louis.. . 
Denver . . . . 


Boston 

New  York. 
Chicago. . . . 
St.  Louis. . . 
Denver.  . . . 


Stories 


ist     2d     3d     4th    5th   6th   7th   8th    9th  loth  nth  12th 


26 


26 


*  See  footnote  on  page  230. 

Table  IV.f    Thickness  of  Enclosing  Walls  for  Residences,  Tenements, 
Hotels  and  Office-Buildings,  t    Chicago  Building  Ordinance  (1916) 


Number  of  stories 

Base- 
ment 

Stories 

1st 

2d 

3d 

4th 

Sth 

6th 

7th 

8th 

9th 

lOth 

iithi2th 

Basement  and .  .  . 

One-story 

Two-story 

Three-story 

Four-story 

Five-story 

Six-story 

Seven-story 

Eight-story 

Nine-story 

Ten -story 

Eleven-story. . .  . 
Twelve-story.  .  . 

12 
16 
16 
20 
24 
24 
24 
24 
28 
28 
28 
32 

12 
12 

16 
20 
20 
20 
20 
24 
24 
28 
28 
28 

12 
12 
16 
20 
20 
20 
24 
24 
28 
28 
28 

12 
16 
16 
20 
20 
20 
24 
24 
24 
28 

12 

16 
16 
20 
20 
20 
24 
24 
24 

16 
16 
16 
20 
20 
24 
24 
24 

16 
16 
16 
20 
20 
20 
24 

16 
16 
16 
20 
20 
20 

16 
16 
16 

20 
20 

16 
16 
16 

20 

16 
16 
16 

16 
16 

16 

t  These  thicknesses  are  allowed  when  certain  requirements  are  fulfilled  in  regard  to 
lengths  of  walls,  heights  of  stories,  etc.  For  these,  modifying  restrictions  and  for  the 
classifications  of  buildings  in  regard  to  their  uses  the  building  laws  must  be  consulted. 
The  table  is  inserted  in  this  form  as  a  useful  general  guide  and  as  an  illustration  of  the 
average  contemporary  practice.  For  modifications  for  different  classes  of  buildings,  see 
code. 

1  For  other  than  steel  skeleton  construction. 


Walls  of  the  Superstructure  233 

(2)  That  high  stories  and  clear  spans  exceeding  25  ft  require  thicker 
walls. 

(3)  That  the  length  of  a  wall  is  a  source  of  weakness,  and  that  the  thickness 
should  be  increased  4  in  for  every  25  ft  over  100  or  125  ft  in  length.  In  New 
York  the  thicknesses  given  in  the  table  must  be  increased  for  buildings  exceed- 
ing 105  ft  in  depth  on  the  lot.  In  Western  cities  the  tables  are  compiled  for 
warehouses  125  ft  in  depth,  as  that  is  the  usual  depth  of  lots  in  those 
cities. 

(4)  That  walls  with  over  33%  of  openings  should  be  increased  in  thickness, 
(s)  That  partition  walls  may  be  4  in  less  in  thickness  than  the  outside  walls 

if  not  over  60  ft  long,  but  that  no  partition  should  be  less  than  8  in  thick. 

Walls  Faced  with  Ashlar.  "Bearing  walls  faced  with  ashlar  shall  be  at  least 
16  in  thick.  Ashlar  shall  not  be  included  in  reckoning  the  thickness  of  walls 
unless  it  is  either  at  least  8  in  thick  or  alternately  4  in  and  8  in  to  allow  at  least 
a  4-in  bond.  Ashlar  not  having  at  least  a  4-in  bond  in  alternate  courses  must  be 
tied  to  the  backing  by  metal  anchors,  one  to  each  block,  3  ft  or  less  long  and 
two  to  each  block  over  3  ft  long."  * 

Stone  Walls  should  generally  be  4  in  thicker  than  required  for  brick 
walls. 

Hollow  Walls.  Hollow  walls  are  undoubtedly  desirable  for  dwellings,  and 
might  well  be  used  for  other  buildings  not  more  than  four  or  five  stories  in  height, 
on  account  of  the  security  afforded  from  the  weather.  Owing  to  the  fact  that 
they  are  usually  more  expensive  than  solid  walls  and  occupy  more  space,  they 
are  not  very  extensively  used  in  this  country. 

The  Boston  building  law  requires  that  vaulted  walls  shall  contain,  exclusive 
of  withes,  the  same  amount  of  material  as  is  required  for  solid  walls,  and  the 
masonry  on  the  inside  of  the  air-space  in  walls  over  two  stories  in  height  shall 
be  not  less  than  8  in  thick,  and  the  parts  on  either  side  shall  be  securely  tied 
together  with  ties  not  more  than  2  ft  apart  in  each  direction. 

Walls  of  Concrete  Blocks.  Blocks  made  of  Portland-cement  concrete,  and 
formed  in  molds,  are  frequently  used  for  building  walls  and  partitions  that  are 
comparatively  thin  and  bear  light  loads.  Patents  have  been  taken  out  on 
different  forms  of  blocks  and  on  machines  or  processes  for  making  the  same, 
and  many  buildings  have  been  erected  with  walls  built  of  these  blocks.  Most  of 
the  blocks  are  molded  so  as  to  form  hollow  walls.  Block  construction  of  this 
kind  has  an  advantage  over  poured  walls,  in  that  the  blocks  are  thoroughly 
seasoned  before  they  are  set  and  hence  no  provision  is  required  for  expansion  or 
contraction.  For  the  thin,  light  walls  above  mentioned  the  concrete-block 
construction  is  better  adapted  than  solid  concrete.  The  expense  of  forms  is 
avoided  and  also  the  tendency  to  crack  and  to  leave  an  unsatisfactory  surface- 
finish.  Concrete  blocks  may  be  substituted  for  any  ordinary  stone  or  brick 
masonry.  Building  laws  usually  require  the  thickness  of  walls  of  hollow  con- 
crete blocks  to  be  not  less  than  that  required  for  brick  walls.  They  should  not 
be  used  in  party  walls.     (See,  also.  Chapter  XXIII,  Subdivision  2.) 

Walls  of  Hollow  Tiles.  Hollow  tiles  are  used  for  the  external  walls  of 
dwellings  and  sometimes  for  factories  in  some  locations  and  under  certain 
restrictions.  For  example,  the  building  laws  (19 13)  of  the  District  of  Columbia 
allow  approved  hollow  tiles,  not  less  than  12  in  in  thickness,  to  be  used  for  the 

•  Boston  Building  Law,  in  force  in  1915. 


234  Masonry  Walls.     Cejnents  and  Concretes  Chap.  3 

external  walls  of  dwellings  located  not  less  than  3  ft  from  the  side  or  party  line 
of  the  lot.  The  Philadelphia  laws  do  not  allow  the  use  of  hollow  tiles  for  any 
external  wall  or  heavy  bearing  partition.  As  far  as  fire-resistance  is  concerned, 
construction  of  hollow  tiles  is,  of  course,  superior  to  wooden  construction,  and  its 
use  is  increasing,  the  outside  walls  being  usually  covered  with  cement  or  stucco, 
although  occasionally  left  with  the  finished  texture  of  the  tile  surface.  The 
reason  hollow  tiles  are  prohibited  by  building  ordinances  for  certain  uses  is 
because  when. heated  and  then  suddenly  cooled  by  water  they  are  apt  to  crack, 
from  the  sudden  contraction.  Recent  conflagrations  have  shown  that  hard- 
burned  terra-cotta  will  crack  and  fall  to  pieces  under  severe  heat  alone.  (See, 
also,  Chapter  XXllI,  Subdivision  2.) 

Party  Walls.  There  is  much  diversity  in  building  regulations  regarding 
the  thickness  of  party  walls,  although  thty  all  agree  in  that  such  walls  should 
never  be  less  than  12  in  thick.  About  one-half  of  the  laws  require  that  party 
walls  shall  be  of  the  same  thickness  as  external  walls;  the  remainder  are  about 
equally  divided  between  making  the  party  walls  4  in  thicker  or  thinner  than 
for  independent  side  walls.  When  the  walls  are  proportioned  by  the  rule 
pieviously  given  the  author  believes  that  the  thickness  of  the  party  walls  should 
be  increased  4  in  in  each  story.  The  floor-load  on  party  walls  is  obviously 
twice  that  on  side  walls,  and  the  necessity  for  thorough  fire-protection  is 
greater  in  the  case  of  party  walls  than  in  other  walls. 

Enclosing  Walls  for  Steel,  Skeleton  Construction.  In  buildings  of  the 
skeleton  type  the  outer  masonry  walls  are  usually  supported  either  in  every 
story  or  every  other  story  by  the  steel  framework,  and  carry  nothing  but  their 
own  weight.  Such  walls  may,  therefore,  be  considered  as  only  one  or  two 
stories  high,  and  are  usually  made  only  12  in  thick  for  the  whole  height  of  a 
twelve-story  or  fifteen-story  building.  For  skeleton  construction,  the 
Chicago  ordinance  allows  enclosing  walls  of  i2-in  thickness  for  all  stories. 
The  former  New  York  City  code*  required  the  use  of  12-in  enclosing  walls  for  75 
ft  of  the  uppermost  height  thereof,  or  to  the  nearest  tier  of  beams  to  that  measure- 
ment, and  4  in  additional  thickness  for  every  lower  60-ft  section  or  to  the  near- 
est tier  of  beams  to  such  vertical  measurement,  down  to  the  tier  of  beams  near- 
est to  the  curb-level.  But,  on  account  of  the  severity  of  some  of  the  require- 
ments as  applied  to  very  high  buildings  of  skeleton  construction,  permission 
was  frequently  given  by  the  Commissioners  of  Buildings,  who  were  empowered 
to  modify  the  building  laws  within  certain  Hmits,  to  reduce  the  thicknesses 
of  certain  walls  for  very  high  buildings,  according  to  the  peculiar  circumstances 
of  each  case,  without  endangering  the  strength  and  safety  of  the  building. 
A  few  of  the  earlier  tall  buildings  were  built  with  self-sustaining  walls, 
starting  from  the  foundation,  while  columns  were  introduced  merely  to  support 
the  floors  and  to  give  additional  stiffness.  ''The  World  Building,  New  York 
City,  erected  in  1890,  is  an  extreme  example  of  high-building  construction, 
with  self-sustaining  walls.  The  main  roof  is  191  ft  above  the  street-level, 
making  thirteen  main  stories,  above  which  is  a  dome  containing  six  stories,  in 
all,  a  height  of  275  ft  above  the  street.  The  self-sustaining  walls  are  built  of 
sandstone,  brick  and  terra-cotta,  the  thickness  increasing  from  2  ft  at  the  top 
to  as  much  as  1 1  ft  4  in  near  the  bottom,  where  the  walls  are  ofTset  to  a  concrete 
footing  IS  ft  wide.  The  walls  are  vertical  on  the  outside  faces,  the  thickness 
being  varied  by  inside  offsets,  so  that  the  columns  are  recessed  into  the  walls 
at  the  bottom,  but  emerge  and  are  some  distance  clear  of  the  walls  at  the  top."t 

•  The  revised  Code,  1916-17,  allows  12-in  curtain  walls  in  skeleton  buildings  the  entire 
height  of  building,  when  supported  on  girders  in  each  story.  This  practice  is  followed 
by  about  fifty  other  cities. 

t  From  Architectural  Engineering,  by  J,  K,  Freitag. 


Natural  Cements  235 

4.     Natural  Cements  and  Mortars* 

Properties  and  Uses  of  Natural  Cements.  The  first  hydraulic  cements 
used  in  this  country  were  natural  cements,  manufactured  by  the  calcination 
of  argillaceous  limestone  containing  sufficient  silica,  alumina  and  iron  oxide  to 
confer  hydraulic  properties  when  the  burned  rock  was  pulverized  and  gauged 
with  water.  These  natural  cements  were  very  widely  manufactured  and  used 
until  recent  years,  when  they  have  been  practically  completely  replaced  by 
Portland  cement.  Natural  cements  vary  in  color  from  light  yellow  to  dark 
brown  according  to  the  content  of  oxide  of  iron,  and  in  distinction  to  Portland 
cements  they  are  not  uniform  in  their  composition  or  behavior.  The  chemical 
composition  and  physical  characteristics  of  various  natural  cements  vary  within 
wide  limits,  not  only  between  cements  manufactured  in  different  mills,  but  be- 
tween the  products  of  the  same  mill  at  different  times.  Natural  cements  set 
more  rapidly  than  Portland  cements  and  are  slower  in  developing  strength. 
The  production  of  natural  cement  in  the  United  States  for  1913  was  800000 
barrels,  while  during  the  same  year  the  production  of  Portland  cement  was 
82  000  000  barrels;  from  which  it  is  seen  that  the  natural-cement  industry  is 
relatively  almost  extinct.  Natural  cement  may  be  used  in  massive  masonry 
where  weight  rather  than  strength  is  the  essential  feature.  It  is  used,  also, 
for  certain  special  purposes,  such  as  in  the  manufacture  of  safes  and  in  certain 
industries  where  a  quick-setting  cement  is  necessary.  Where  economy  is  the 
governing  factor,  a  comparison  m2Ly  be  made  between  the  use  of  natural  cement 
and  a  leaner  mixture  of  Portland  cement  that  will  develop  the  same  strength. 

Weight.  The  specifications  of  the  American  Society  for  Testing  Materials 
require  that  a  bag  of  natural  cement  shall  contain  94  lb,  net,  of  cement,  and  that 
each  barrel  of  natural  cement  shall  contain  three  bags  of  this  net  weight. 

Strength.  A  natural-cement  mortar,  in  order  to  comply  with  the  require- 
ments of  the  standard  specifications  of  the  American  Society  for  Testing  Ma- 
terials, must  show  a  tensile  strength,  for  the  neat  cement,  of  at  least  150  lb 
per  sq  in,  when  one  week  old,  and  250  lb  at  the  end  of  28  days;  or,  when  mixed 
with  three  parts  of  standard  Ottawa  sand,  50  lb  at  the  end  of  one  week,  and  125 
lb  at  the  end  of  28  days.  The  strength  of  i  :  2  natural-cement  mortar  is  about 
equal  to  that  of  i  :  4  Portland-cement  mortar. 

Proportions  of  Natural  Cement  and  Sand  for  Mortar  and  Concrete. 
For  mortar  for  rubble-stone  masonwork  and  ordinary  brickwork,  one  part  of 
natural  cement  may  be  mixed  with  three  parts  of  sand,  by  measure. 

Hydraulic  Lime.  A  product  closely  related  to  natural  cement  is  hydraulic 
LIME.  This  is  manufactured  in  the  same  way  as  natural  cement,  but  the  rock 
used  contains  sufficient  Hme  to  permit  it  to  slake  like  quicklime.  When  the 
resulting  product  is  pulverized,  it  sets  and  hardens  as  an  hydraulic  cement. 
Hydraulic  limes  arc  largely  manufactured  in  Europe,  and  especially  in  France, 
and  Belgium,  but  in  the  United  States  they  have  been  manufactured  only  in  a 
few  localities.  This  is  due  to  the  fact  that  while  rock  of  suitable  composition 
is  widely  found,  the  impurities  are  not  uniformly  distributed  through  it,  but  are 
found  in  layers  or  seams  which  prevent  the  material  from  being  uniformly 
burned.  The  portion  of  the  rock  immediately  adjacent  to  and  including  the. 
seam  of  impurities  overburns,  frequently  melting  like  a  slag,  while  the  purer 
portions  consist  simply  of  quicklime;  and  while  the  resulting  mass  slakes  partly,, 
the  product  when  pulverized  is  unreliable  as  a  cement. 

*  Practical  data  relating  to  Cements,  Limes  and  Plasters  were  furnished  the  Editor  by 
the  Charles  Warner  Company  of  Wilmington,  Del.  For  Limes  and  Plasters,  see  Part 
III,  pages  1548  to  1558. 


236  Masonry  Walls.     Cements  and  Concretes  Chap.  3 

Grappier  Cement  is  a  by-product  produced  during  the  calcination  of  hy- 
draulic \AllE. 

La  Farge  Cement  is  an  imported  non-staining  grappier  cement.  It 
develops  nearly  the  same  strength  as  the  Portland  cements. 

5.     Artificial  Cements  and  Mortars 

The  Artificial  Cements  used  in  the  United  States  include  Portland  tement 
and  Puzzolan  or  slag  cement. 

Portland  Cement.  The  principal  artificial  cement  in  this  country  to-day 
is  Portland  cement.  It  is  manufactured  from  two  raw  materials  which  are 
ground  to  extreme  fineness  to  secure  an  intimate  mix  before  burning,  aiid  it 
is  from  this  fact  that  it  derives  its  name,  artificial  cement.  These  ma- 
terials must  be  so  proportioned  that  in  the  finished  cement,  silica,  alumina,  iron 
oxide  and  lime  will  be  present  in  a  certain  ratio  which  must  be  maintained 
within  close  limits.  In  the  Lehigh  Valley  region  of  Pennsylvania,  in  which 
are  located  some  of  the  leading  Portland-cement  mills  of  the  United  Stales,  the 
raw  materials  used  are  limestone  and  cement-rock.  The  cement-rock  is  an  im- 
pure hmestone  carrying  argillaceous  or  clay-matter.  In  order  to  bring  the  lime- 
content  up  to  the  required  percentage,  it  is  usually  found  necessary  in  this 
region  to  add  limestone.  In  other  districts  the  raw  materials  used  are  lime- 
stone and  clay,  limestone  and  shale,  marl  and  clay  and  also  blast-furnace  slag 
and  Hmestone.  The  product  from  the  last-mentioned  mixture  should  not  be 
confused  with  the  common  slag  cement  or  Puzzolan  cement,  as  the  slag  is  simply 
used  as  a  raw  material  supplying  silica,  alumina,  iron  oxide  and  lime;  and  with 
the  exception  of  the  use  of  slag  to  furnish  these  ingredients,  the  process  of  manu- 
facture and  the  properties  are  substantially  the  same  as  for  the  other  Portland 
cements.  The  raw  mix  in  a  Portland  cement  mill  is  analyzed  at  most  mills 
several  times  each  hour  to  keep  the  composition  of  the  cement  within  the  proper 
Umits.  The  raw  material,  which  is  pulverized  as  fine  as  the  finished  cement,  is 
burned  in  rotary  kilns,  the  fuel  used  in  most  instances  being  powdered  coaL 
From  the  kiln  it  issues  in  the  form  of  clinker,  the  name  given  to  the  semivit- 
rified  product.  After  cooling,  calcium  sulphate  in  the  form  of  gypsum  is 
added  to  control  the  set  and  the  product  is  pulverized  and  packed  for  shipment. 
The  manufacture  and  properties  of  Portland  cement  have  been  made  the  subject 
of  careful  study  by  the  American  Society  for  Testing  Materials  and  by  the 
American  Society  of  Civil  Engineers.  The  result  of  this  study  is  embodied  in 
the  standard  specifications  of  the  American  Society  for  Testing  Materi^ds,  ex- 
tracts from  which  are  given  in  the  paragraphs  following.  These  si>ecilications 
furnish  a  reliable  guide  for  the  acceptance  or  rejection  of  any  shipment  of  ce- 
ment and  have  been  very  widely  adopted  by  the  leading  architects  and  engineers 
of  this  country.  These  specifications  do  not  stipulate  that  l^ortland  cement  shall 
consist  of  any  one  particular  composition,  but  in  this  respect  confine  themselves 
to  the  Hmitation  of  the  magnesia  (MgO)  and  anhydrous  sulphuric  acid  (SO3)  con- 
tent. The  reason  for  this  is  that  with  different  raw  materials  it  is  found  neces- 
sary to  vary  the  composition  of  the  cement  to  obtain  the  correct  physical 
properties  in  the  finished  material.  Different  cements  which  satisfy  the  require- 
ments of  these  standard  specifications  are  generally  considered  satisfactory  ce- 
ments for  use,  although  the  composition  of  one  may  vary  in  some  particulars 
from  that  of  another.  The  chemical  composition  of  a  good  brand  of  Port- 
land cement  is  about  as  follows:  Lime,  62;  silica,  23;  alumina,  8;  and  impurities, 
such  as  iron  oxide,  magnesia,  und  sulphuric  acid,  7. 

Standard  Specifications  for  Portland  Cement.*  The  following  extracts 
give  the  most  important  requirements  for  Portland  cement: 

•  From  the  Standard  Specifications  and  Tests  for  Portland  Cement,  revised,  1916  (ef- 
fective, January  i,  1917),  by  the  American  Society  for  Testing  Materials. 


Artificial  Cements  237 

(i)  Definition.  Portland  cement  is  the  product  obtained  by  finely  pulveriz- 
ing clinker  produced  by  calcining  to  incipient  fusion  an  intimate  and  properly  pro- 
portioned mixture  of  argillaceous  and  calcareous  materials,  with  no  additions  sub- 
sequent to  calcination  excepting  water  and  calcined  or  uncalcined  gypsum.  (2) 
Chemical  Limits.    The  foUqwing  limits  shall  not  be  exceeded: 

Loss  on  ignition,  per  cent 4 .  00 

Insoluble  residue,  per  cent 0.85 

Sulphuric  anhydride  (SO3),  per  cent 2 .00 

Magnesia  (MgO),  per  cent .*.   5 .00 

(3)  Specific  Gravity.  The  specific  gravity  of  cement  shall  be  not  less  than 
3.10  (3.07  for  white  Portland  cement).  Should  the  test  of  cement  as  received  fall 
below  this  requirement  a  second  test  may  be  made  upon  an  ignited  sample.  The 
specific-gravity  test  will  not  be  made  unless  specifically  ordered.  (4)  Fineness. 
The  residue  on  a  standard  No.  200  sieve  shall  not  exceed  22  per  cent  by  weight. 
(5)  Soundness.  A  pat  of  neat  cement  shall  remain  firm  and  hard,  and  show  no 
signs  of  distortion,  cracking,  checking,  or  disintegration  in  the  steam  test  for 
soundness.  (6)  Time  of  Setting.  The  cement  shall  not  develop  initial  set  in 
less  than  45  minutes  when  the  Vicat  needle  is  used,  or  60  minutes  when  the 
Gilmore  needle  is  used.  Final  set  shall  be  attained  within  10  hours.  (7)  Tensile 
Strength.  The  average  tensile  strength  in  pounds  per  square  inch  of  not  less 
than  three  standard  mortar  briquettes  composed  of  i  part  cement  and  3  parts 
standard  sand,  by  weight,  shall  be  equal  to  or  higher  than  the  following: 


Age  at  test, 
days 

Storage  of  briquettes 

Tensile 

strength, 

lb  per  sq  in 

7 
28 

I  day  in  moist  air,    6  days  in  water 

I  day  in  moist  air,  27- days  in  water 

200 
300 

(8)  The  average  tensile  strength  of  standard  mortar  at  28  days  shall  be  higher 
than  the  strength  at  7  days.  (9)  Packages  and  Marking.  The  cement  shall 
be  delivered  in  suitable  bags  or  barrels  with  the  brand  and  name  of  the  manu- 
facturer plainly  marked  thereon,  unless  shipped  in  bulk.  A  bag  shall  contain 
94  lb  net.  A  barrel  shall  contain  376  lb  net.  (10)  Storage.  The  cement  shall 
be  stored  in  such  a  manner  as  to  permit  easy  access  for  proper  inspection  and 
identification  of  each  shipment,  and  in  a  suitable  weather-tight  building  which 
will  protect  the  cement  from  dampness.  (11)  Inspection.  Every  facility  shall 
be  provided  the  purchaser  for  careful  sampling  and  inspection  at  either  the  mill 
or  at  the  site  of  the  work,  as  may  be  specified  by  the  purchaser.  At  least  10  days 
from  the  time  of  sampling  shall  be  allowed  for  the  completion  of  the  7-diay  test, 
and  at  least  31  days  shall  be  allowed  for  the  completion  of  the  28-day  test.  The 
cement  shall  be  tested  in  accordance  with  the  methods  hereinafter  prescribed. 
The  28-day  test  shall  be  waived  only  when  specifically  so  ordered.  (12)  Rejec- 
tion. The  cement  may  be  rejected  if  it  fails  to  meet  any  of  the  requirements  of 
these  specifications. 

Sections  (13)  to  (15),  also,  relate  to  Rejection.  (See  complete  Specification.) 
Puzzolan  or  Slag  Cements  are  not  used  extensively  and  never  in  important 
work.  Their  manufacture  and  properties  may  be  briefiy  described  as  follows: 
Blast-furnace  basic  slag  is  granulated  by  running  it  in  a  molten  condition  into 
water.  This  accomplishes  two  objects.  The  slag  is  broken  up  into  fine  particles 
and  the  sudden  chilling  enhances  its  hydraulic  properties.  These  particles 
are  dried  and  ground  with  hydrated  lime,  in  the  proportion  of  from  15  to  25% 
of  hydrated  lime  and  from  75  to  85%  of  granulated  slag.  Such  cement,  known 
as  slag  cement,  is  slow-setting  and  slow-hardening,  and  does  not  develop  as 


238  Masonry  Walls.     Cements  and  Concretes  Chap.  3 

much  strength  as  natural  or  Portland  cement.  Slag  cements  are  characterized 
by  their  light  Hlac  color,  their  extreme  fineness  and  their  low  specific  gravity. 
They  are  considered  unreliable  for  use  except  for  foundation- work  under  ground 
where  they  are  not  exposed  to  air  or  running  water. 

Stainless  Cements.  Any  ordinary  Portland  or  natural  cement  will  stain 
limestones,  some  porous  marbles,  some  granites  and  some  other  light-colored 
stones.  The  best  non-staining  material  is  hme,  that  is,  lime  free  from  excess  of 
iron  oxide.  There  are  some  Portland  cements,  however,  which  are  called  non- 
staining  CEMENT^,  and  where  care  is  used  in  their  manufacture  and  they  are 
free  or  comparatively  free  from  iron  oxide,  they  cause  no  trouble.  Among 
the  non-staining  cements  which  have  been  extensively  used  for  masonry  on 
which  staining  would  be  objectionable,  is  La  Farge  Cement,  before  mentioned. 
It  is  made  at  Teil,  France,  is  light-colored  and  contains  a  small  percentage  of 
iron  and  soluble  salts.  There  are  other  non-staining  cements  on  the  market. 
For  setting  stones,  and  in  order  to  retard  the  setting  of  the  cement  until  the 
stones  are  well  bedded,  i  part  by  volume  of  lime-paste  is  usually  mixed  with 
4  parts  of  the  cement. 

Cost  of  Portland  Cement.*  Portland  cement  can  now  (1915)  be  purchased 
in  this  country  at  prices  ranging  from  90  cents  to  $2.50  per  barrel,  free  on  board 
cars  at  the  mills.  The  cost  of  the  sacks  and  the  freight  are  extra.  The  retail 
price  for  single  barrels  varies  from  about  $2.00  to  $2.50  per  barrel.  As  a  rule, 
the  cost  of  cement  in  carload  lots  is  about  85  cts  per  bbl  at  the  mills.  An  extra 
charge  of  10  cts  per  bbl  for  bags  is  made  when  the  cement  is  delivered  in  paper 
bags.  The  extra  charge  is  40  cts,  if  dehvered  in  cloth,  but  the  mills  refund  this 
40  cts  when  the  bags  are  returned  in  good  condition.  There  is  a  charge  of  40 
cts  when  the  cement  is  furnished  in  wooden  barrels  and  no  allowance  is  made 
for  barrels  returned.  It  is  generally  cheaper  in  the  end  to  buy  the  cement  in 
cloth  bags  and  return  the  empty  bags.  For  about  500  miles,  the  freight- 
charges  are  about  40  cts  per  bbl  of  cement,  making  the  total  cost  per  bbl  for 
this  distance  $1.25,  when  purchased  in  cloth  bags  and  when  the  40  cts  per  bag 
are  refunded.  Testing  costs  from  3  to  5  cts  per  bbl,  or  from  $5  to  $6  per 
carload.  Unloading  and  storing  near  the  station  cost  about  3  cts  per  -bbl,  and 
about  2  cts  per  bbl  are  usually  added  to  the  costs  to  allow  for  handling  and 
returning  empty  sacks,  and  freight-charges  for  and  damage  to  same.  Teaming 
costs  about  5  cts  per  bbl  per  mile.  The  total  cost,  therefore,  according  to 
these  average  costs,  is  about  $1.38  per  bbl  for  the  cement  ready  for  use  for 
mortar  or  concrete.  (For  Cost  of  Concrete,  see  page  249;  also  foot-note  for  same.) 

Water  Required  in  Mixing  Cement  Mortar.  Good  Portland  cement 
requires  relatively  little  water  to  make  a  good  mortar.  Neat  cement  will  take 
from  20  to  22%  (by  weight)  of  water  to  produce  the  normal  consistency,  a 
quick-setting  cement  requiring  more  water  than  one  that  is  slow-setting.  If  a 
greater  quantity  of  water  is  required,  it  indicates  the  presence  of  an  excess  of 
free  hme.  When  sand  is  mixed  with  cement,  in  the  proportion  of  3  to  i,  not 
more  than  from  9  to  12^%  (by  weight)  of  water  will  be  required.  Natural 
cements  and  slag  cements  require  more  water  than  do  Portland  cements.  Too 
much  water  drowns  the  cement,  retards  the  setting  and  weakens  the  mortar. 
Cements  can  also  be  weakened  or  even  spoiled  by  a  deficiency  of  water. 

Portland-Cement  Mortar.     For  first-class  mortar  not  more  than  3  bbl  of 

sand  should  be  added  to  i  bbl  of  cement.     For  rubble  stonework  under  ordinary 

conditions  a  mortar  composed  of  4  parts  of  sand  to  i  of  cement  will  answer  every 

purpose,  and  be  much  stronger  than  lime  mortar.    For  the  top  surface  of  floors 

♦  See  foot-note,  page  249. 


Cement  Mortars  239 

and  walks,  from  i  to  i  H  parts  of  sand  may  be  mixed  with  i  part  of  cement. 
I  to  3  Portland-cement  mortar  has  about  the  same  strength  at  the  end  of  one 
year  as  r  to  i  natural-cement  mortar.  Mortar  made  with  fine  sand  requires  a 
much  larger  quantity  of  cement  to  obtain  a  given  strength  than  mortar  made  with 
coarse  sand.    (See  page  276  for  ideal  mortar  with  hydrated  lime  for  brickwork.) 

Effects  of  Low  Temperatures  and  Freezing  on  Cement  Mortars.    The 

rate  of  setting  and  hardening  of  cement  mortar  is  greatly  affected  by  the  temper- 
ature, and  the  exposure  and  loading  of  new  work  often  depends  upon  the  pre- 
vailing temperature.  The  freezing  of  natural-cement  mortars  should  be  en- 
tirely avoided  as  it  seriously  injures  them.  Although  freezing  greatly  retards 
the  hardening  of  Portland-cement  mortars  and  concretes,  it  does  not  appear 
to  injure  them.  Thin  coats  of  mortar,  such  as  plaster,  and  troweled  surfaces 
or  those  on  which  free  moisture  is  formed  should  not  be  applied  in  freezing 
weather  as  they  are  apt  to  scale.  In  general,  it  is  undesirable  to  work  with 
mortar  or  concrete  in  freezing  weather,  as  the  difficulties  of  properly  mixing 
and  placing  the  materials  are  then  increased;  it  must  be  admitted,  however, 
that  successful  work  with  Portland-cement  mortar  and  concrete  has  been  done 
in  temperatures  considerably  below  freezing. 

The  Effect  of  Salt  in  Mortar.  When  salt  is  added  to  the  water  of  mix- 
ture, the  freezing-point  is  lowered,  and,  within  certain  limits,  the  freezing  of 
the  mortar  or  concrete  is  prevented.  1  he  ultimate  strength  of  mortar  does  not 
appear  to  be  reduced  when  the  amount  of  salt  does  not  exceed  10%.  Tetmajer 
gives  the  amount  of  salt  required  to  lower  the  freezing-temperature  as  equal  to 
1%  of  the  weight  of  the  water  per  degree  F.  below  32''.  The  rule  for  the  pro- 
portion of  salt  used  in  the  works  at  Woolwich  Arsenal,  is  said  to  have  been  as 
follows:  ''Dissolve  i  lb  of  rock-salt  in  18  gal  of  water  when  the  temperature  is 
at  :i>2°  ¥.,  and  add  3  oz  of  salt  for  every  three  degrees  of  lower  temperature." 

Effect  of  Hot  Water  and  of  Soda.  Hot  water  hastens  the  setting  of 
Portland-cement  mortar,  and  2  lb  of  carbonate  of  soda  in  i  gal  of  water,  boiled 
and  mixed  in  mortar,  hastens  the  setting  and  lessens  the  danger  of  freezing. 

Quantity  of  Mortar  required  for  Masonry  and  Plastering,*  "One  bbl 
of  Portland  cement  and  3  bbl  of  sand,  thoroughly  and  properly  mixed,  will 
make  3H  bbl,  or  12  cu  ft  of  good  strong  mortar.  This  will  be  sufficient  to  lay 
up  lYz  cu  yd  of  rough  stone,  or  about  750  bricks,  with  from  \i  to  5^-in  joints, 
or  cover  125  sq  ft  of  surface,  i  in  thick,  or  250  sq  ft,  Yi  in  thick." 

"One  bbl  of  natural  cement  and  2  bbl  of  lime,  mixed  with  about  Yi  bbl  of 
water,  will  make  8  cu  ft  of  mortar,  sufficient  to  lay  522  common  bricks,  with 
from  Y^  to  %-m  joints,  or  about  i  cu  yd  of  rough  rubble. " 

For  the  top  coat  of  walks  or  floors,  i  bbl  of  Portland  cement  and  i  of  sand 
will  cover  from  75  to  80  sq  ft,  Yi  in  thick,  or  from  50  to  56  sq  ft;  %  in  thick. 

One  bbl  of  Portland  cement  and  lYi  bbl  of  sand  will  cover  from  no  to  120  sq 
ft  of  floor,  Y  in  thick,  or  from  75  to  80  sq  ft,  %  in  thick. 

The  Mixing  of  Mortar.  Mortar  may  be  mixed  by  hand  or  by  mechanical 
mixers,  the  latter  being  preferable  for  the  mixing  of  large  quantities.  When 
the  mixing  is  by  hand,  it  should  be  done  on  platforms  made  water-tight  to  pre- 
vent the  loss  of  cement.  The  cement  and  sand  should  be  mixed  dry  in  small 
batches  and  in  the  proportions  required,  the  platform  being  clean.  W'ater  is 
added  and  the  whole  mass  remixed  until  it  is  homogeneous  and  leaves  the  mixing 
hoe  clean  when  drawn  out.  Mortar  should  never  be  retempered  after  it  has 
begun  to  set. 

*  These  figures  can  be  considered  as  approximate  only,  as  the  amount  of  mortar  will 
vary  on  different  jobs. 


240  Masonry  Walls.     Cements  and  Concretes  Chap.  3 

Adhesive  Strength  of  Portland  Cement,  Sulphur  and  Lead  for  Anchor- 
ing  Bolts.*  "Fourteen  holes  were  drilled  in  a  ledge  of  solid  limestone,  seven 
of  them  being  i%  and  seven  iH  in  in  diameter,  and  all  being  3^2  ft  deep.  Seven 
%  and  seven  i-in  bolts  were  prepared  with  thread  and  nut  on  one  end  and  with 
the  other  end  plain  but  ragged  for  a  length  of  sVi  ft. 

*'Four  were  anchored  with  sulphur,  four  with  lead  and  six  with  cement, 
mixed  neat.  Half  the  number  of  the  %-m  and  i-in  bolts  being  thus  anchored  with 
each  of  the  three  materials,  all  stood  until  the  cement  was  two  weeks  old. 
Then  a  lever  was  rigged  and  the  bolts  pulled,  with  the  following  results. 

"Sulphur:  Three  bolts  out  of  four  developed  their  full  strength  16000  and 
31  000  lb.  One  I-in  bolt  failed  by  drawing  out,  under  12  000  lb.  Lead:  Three 
bolts  out  of  four  developed  their  full  strength,  as  above.  One  r-in  bolt 
pulled  out,  under  13  000  lb.  Cement:  Five  of  the  bolts  out  of  six  broke  with- 
out pulling  out.  One  i-in  bolt  began  to  yield  in  the  cement  at  26  000  lb,  but 
sustained  the  load  a  few  seconds  before  it  broke. 

"While  this  experiment  demonstrated  the  superiority  of  cement,  both  as  to 
strength  and  ease  of  application,  it  did  not  give  the  strength  per  square  inch  of 
area.  To  determine  this,  four  specimens  of  limestone  were  prepared,  each 
10  in  wide,  18  in  long  and  12  in  thick,  two  of  them  having  1^4-in  holes,  and  two 
of  them  2>4-in  holes  drilled  in  them.  Into  the  small  holes  .i-in  bolts  were 
cemented,  one  of  them  being  perfectly  plain  round  iron,  and  the  other  having  a 
thread  cut  on  the  portion  which  was  embedded  in  the  cement.  Into  the  2%-in 
holes  were  cemented  2-in  bolts  similarly  treated,  and  the  four  sp^^cimens  were 
allowed  to  stand  13  days  before  completing  the  experiment.  At  the  end  of  this 
time  they  were  put  into  a  standard  testing-machine  and  pulled.  The  plain  i-in 
bolt  began  to  yield  at  20000  lb  and  the  threaded  one  at  21  000  lb.  The  2-in 
plain  bolt  began  to  yield  at  34  000  lb  and  the  threaded  one  at  32  000  lb,  the 
force  in  all  cases  being  very  slowly  applied.  The  pump  was  then  run  at  a  greater 
speed,  and  the  stones  holding  the  2-in  bolts  split  at  67  000  lb  in  the  case  of  the 
smooth  one  and  at  50  000  lb  in  the  case  of  the  threaded  one. 

"It  is  thus  seen  that  for  anchoring  bolts  in  stone,  cement  is  more  reliable, 
stronger  and  easier  of  application  than  either  lead  or  sulphur,  and  that  its  re- 
sistance is  from  400  to  500  lb  per  sq  in  of  surface  expensed.  It  is  also  a  well- 
ascertained  fact  that  it  preserves  iron  rather  than  corrodes  it.  The  cement 
used  throughout  the  experiment  was  an  English  Portland  cement. " 

6.   Concrete  t  « 

Properties  and  Uses  of  Concrete.^  There  is  probably  no  material  that  is 
so  enduring  or  better  adapted  for  foundations,  walks  and  basement  floors,  etc., 
than  cement  concrete,  and  for  certain  classes  of  buildings  it  is  used  with  ad- 
vantage for  the  walls,  floors  and  interior  supports.  There  are  now  thousands  of 
buildings  in  this  and  other  countries  in  which  all  of  the  structural  portions  are 
formed  of  reinforced  concrete,  and  the  use  of  Portland-cement  concrete  for  a 

*  The  test  of  these  materials  is  reported  in  the  American  Architect,  page  105,  vol. 
xxiv. 

t  The  subject  of  concrete  in  general,  including  plain  or  mass-concrete  and  reinforced 
concrete,  is  to-day  so  important,  and  the  available  data  so  vast  in  amount  that  only  those 
brief  statements  of  general  principles  and  of  the  best  engineering  practice  that  are  the  most 
important  for  the  architect  and  builder  to  know  can  be  included  in  a  handbook  of  this 
kind.  For  full  treatments  of  the  subject,  the  readers  are  referred  to  the  numerous  recent 
treatises,  tests,  proceedings  of  engineering  societies,  etc. 

X  For  reinforced  Concrete,  see  Chapter  XXIV;  for  Concrete  Foundations,  Chapter  II; 
ior  Reinforced-Concrete  Factory  Construction,  Chapter  XXV;  and  for  Strength  of  Con- 
crete, Chapter  V.    See,  also.  Chapter  XXIII,  pages  817  and  843. 


Concrete  241 

great  variety  of  purposes  is  rapidly  extending,  due  to  the  reduced  price  of 
Portland  cement,  and  to  a  better  appreciation  and  understanding  of  its  proper- 
ties and  merits.  Concrete  may  be  defined  as  an  artificial  stone,  made  by 
uniting  cement,  water  and  what  is  called  an  aggregate,  consisting  of  small  and 
large  particles  of  sand  or  screenings  and  gravel  or  broken  stone;  and  when 
made  with  good  Portland  cement,  in  proper  proportions,  it  becomes  so  hard 
and  strong  that  when  pieces  of  it  are  broken,  the  line  of  fracture  often  passes 
through  the  particles  of  stone,  showing  that  the  adhesion  of  the  cement  to  the 
stone  is  greater  than  the  cohesive  strength  of  the  stone  itself. 

The  Aggregates.*  "Extreme  care  should  be  exercised  in  selecting  the  aggre- 
gates for  mortar  and  concrete,  and  careful  tests  made  of  the  materials  for  the 
purpose  of  determining  their  qualities  and  the  grading  necessary  to  secure 
maximum  density  or  a  minimum  percentage  of  voids.  A  convenient  coefficient 
of  density  is  the  ratio  of  the  sum  of  the  volumes  of  materials  contained  in  a 
unit  volume  to  the  total  unit  volume.     (See,  also,  pages  908  and  909.) 

"  (i)  Fine  Aggregates  should  consist  of  sand,  crushed  stone,  or  gravel  screen- 
ings, graded  from  fine  to  coarse  and  passing  when  dry  a  screen  having  ^-in  diam 
holes;  it  preferably  should  be  of  siliceous  material,  and  should  be  clean,  coarse, 
free  from  dust,  soft  particles,  vegetable  loam  or  other  deleterious  matter,  and 
not  more  than  6%  should  pass  a  sieve  having  100  meshes  per  hn  in.  Fine  aggre- 
gates should  always  be  tested.  Pine  aggregates  should  be  of  such  quality 
that  mortar  composed  of  one  part  Portland  cement  and  three  parts  fine  aggre- 
gate by  weight  when  made  into  briquettes  will  show  a  tensile  strength  at  least 
equal  to  the  strength  of  i  13  mortar  of  the  same  consistency  made  with  the 
same  cement  and  standard  Ottawa  sand.  This  is  a  natural  sand  obtained  at 
Ottawa,  111.,  passing  a  screen  having  20  meshes  and  retained  on  a  screen  having 
30  meshes  per  lin  in.  It  is  prepared  and  furnished  by  the  Ottawa  Silica  Com- 
pany, for  2  cts  per  lb,  free  on  board  cars,  at  Ottawa,  111.,  under  the  direction  of 
the  Special  Committee  on  Uniform  Tests  of  Cement  of  the  American  Society 
of  Civil  Engineers.  If  the  aggregate  be  of  poorer  quality  the  proportion  of 
cement  should  be  increased  in  the  mortar  to  secure  the  desired  strength.  If 
the  strength  developed  by  the  aggregate  in  the  i  :  3  mortar  is  less  than  70%  of 
the  strength  of  the  Ottawa-sand  mortar,  the  material  should  be  rejected.  To 
avoid  the  removal  of  any  coating  on  the  grains,  which  may  affect  the  strength, 
bank  sands  should  not  be  dried  before  being  made  into  mortar,  but  should  con- 
tain natural  moisture.  The  percentage  of  moisture  may  be  determined  upon  a 
separate  sample  for  correcting  weight.  From  10  to  40%  more  water  may  be 
required  in  mixing  bank  or  artificial  sands  than  for  standard  Ottawa  sand  to 
produce  the  same  consistency. 

**  (2)  Coarse  Aggregates  should  consist  of  crushed  stone  or  gravel  which  is 
retained  on  a  screen  having  yi-in  diam  holes  and  graded  from  the  smallest  to 
the  largest  particles;  they  should  be  clean,  hard,  durable  and  free  from  all 
deleterious  matter.  Aggregates  containing  dust  and  soft,  flat  or  elongated 
particles  should  be  excluded  from  important  structures." 

Any  kind  of  stone  is  suitable  for  the  coarse  aggregate  which  has  such  strength 
that  the  strength  of  the  concrete  is  not  limited  by  the  strength  of  the  stone. 
Great  strength  is  of  little  advantage  beyond  this  minimum.  The  stones  gener- 
ally employed  are  granites,  traps  and  limestones.    Shales  and  sandstones  of 

*  Most  of  the  matter  of  this  paragraph,  and  of  following  paragraphs  relating  to  concrete, 
consists  of  data  and  conclusions  formulated  by  the  joint  committees  of  the  Am.  5oc.  C.  E., 
Am.  Soc.  for  Test.  Mats.,  Am.  Ry.  Eng.  and  Maint.  of  Way  Asso.,  and  Asso.  of  Am. 
Portland  Cement  Manfrs.  In  regard  to  Aggregates,  etc.,  see,  also,  the  same  subjects  in 
Chapter  XXIV,  pages  908  and  909,  and  foot-notes  on  page  908  in  that  chapter. 


242  Masonry  Walls.     Cements  and  Concretes  Chap.  3 

deficient  strength  should  be  tested  before  use.  Screened  gravel  generally  makes 
a  good  coarse  aggregate.  "  The  maximum  size  of  the  coarse  aggregate  is  governed 
by  the  character  of  the  construction.  For  reinforced  concrete  and  for  small 
masses  of  unreinforced  concrete,  the  aggregate  must  be  small  enough  to  produce 
with  the  mortar  a  homogeneous  concrete  of  viscous  consistency  which  will  pass 
readily  between  and  easily  surround  the  reinforcement  and  fill  all  parts  of  the 
forms.  For  concrete  in  large  masses  the  size  of  the  coarse  aggregate  may  be 
increased,  as  a  large  aggregate  produces  a.  stronger  concrete  than  a  fine  one, 
although  it  should  be  noted  that  the  danger  of  separation  from  the  mortar 
becomes  greater  as  the  size  of  the  coarse  aggregate  increases." 

The  use  to  be  made  of  the  concrete  determines  the  maximum  size  of  the  coarse 
aggregate.  When  used  in  mass-concrete  construction,  such  as  heavy  walls, 
the  maximum  size  may  run  up  to  2^^  and  3  in  with  good  results.  For  reinforced 
work  and  thin  walls,  however,  it  is  necessary  to  reduce  the  maximum  size  to  i 
in  or  less.  It  has  been  found  that  the  following  are  the  maximum  sizes  for  the 
coarse  aggregate  of  plain  or  mass-concrete  in  the  best  practice:  for  foundations, 
2y2  in;  for  abutments,  2  in;  for  arch-rings,  iH  in;  and  for  copings,  thin  walls, 
etc.,  I  in. 

"Cinder  concrete  should  not  be  used  foi'  reinforced-concrete  structures.  It 
may  be  allowable  in  mass  for  very  light  loads  or  for  fire-protection  purposes. 
The  cinders  used  should  be  composed  of  hard,  clean,  vitreous  clinkers,  free  from 
sulphides,  unburned  coal,  or  ashes.     (See,  also,  page  909.) 

"  Water  for  Mixing  Concrete.  The  water  used  in  mixing  concrete  should 
be  free  from  oil,  acid,  alkalies,  or  organic  matter. " 

Preparing  and  Placing  Mortar  and  Concrete.  "  (i)  Proportions.*  The 
materials  to  be  used  in  concrete  should  be  carefully  selected,  of  uniform  quality, 
and  proportioned  with  a  view  to  securing  as  nearly  as  possible  a  maximum 
density. 

"(a)  Unit  of  Measure.  The  unit  of  measure  should  be  the  cubic  foot.  A 
bag  of  cement,  containing  94  lb,  net,  should  be  considered  the  equivalent  of  i 
cu  ft.  The  measurement  of  the  fine  and  coarse  aggregates  should  be  by  loose 
volume. 

"(b)  Relation  of  Fine  and  Coarse  Aggregates.  The  fine  and  coarse  aggre- 
gates should  be  used  in  such  relative  proportions  as  will  insure  maximum  den- 
sity. In  unimportant  work  it  is  sufficient  to  do  this  by  individual  judgment, 
using  correspondingly  higher  proportions  of  cement;  for  important  work  these 
proportions  should  be  carefully  determined  by  density-experiments  and  the 
sizing  of  the  fine  and  coarse  aggregates  should  be  uniformly  maintained  or  the 
proportions  changed  to  meet  the  var>dng  sizes. 

"  (c)  Relation  of  Cement  and  Aggregates.  For  reinforced-concrete  con- 
struction, one  part  of  cement  to  a  total  of  six  parts  of  fine  and  coarse  aggre- 
gates, rheasured  separately,  should  generally  be  used.  For  columns,  richer 
mixtures  are  generally  preferable,  and  in  massive  masonry  or  rubble  concrete 
a  mixture  of  i  :  9  or  even  1:12  may  be  used.  These  proportions  should  be 
determined  by  the  strength  or  the  wearing-qualities  required  in  the  construc- 
tion at  the  critical  period  of  its  use.  Experienced  judgment  based  on  individual 
observation  and  tests  of  similar  conditions  in  similar  localities  is  an  excellent 
guide  as  to  the  proper  proportions  for  any  particular  case.  For. all  important 
construction,  advance  tests  should  be  made  of  concrete,  of  the  materials,  pro- 
portions and  consistency  to  be  used  in  the  work.  These  tests  should  be  made 
under  laboratory  conditions  to  obtain  uniformity  in  mixing,  proportioning  and 

*  See,  also,  in  Chapter  XXIV,  paragraphs  relating  to  these  subjects  on  page  910, 
and  ,foa«,-note  relating  to  the  same,  on  page  908  of  that  chapter. 


Concrete  243 

storage,  and  in  case  the  results  do  not  conform  to  the  requirements  of  the  work, 
aggregates  of  a  better  quality  should  be  chosen  or  richer  proportions  used  to 
obtain  the  desired  results." 

Professor  Turneaure  of  the  University  of  Wisconsin  gives  the  following  as 
the  proportions  of  cement,  sand  and  coarse  aggregate  generally  used  for  various 
classes  of  work: 

For   reinforced   columns   and   structural    parts 

requiring  extra  strength from  i :  i  :  2  to  i  :  i  J-^  :  3 

For  buildings,   thin  walls,   reinforced  concrete, 

tanks  and  impervious  construction from  i  :  2  :  4  to  i  :  2H  :  4H 

For  structures  requiring  great  strength  rather 

than  mass from  i  :  2^-^  :  5  to  i  :  3  :  6 

For    structures    requiring    mass    rather    than 

strength,  foundations,  etc from  i  :  3  :  6  to  i  :  4  :  8      ' 

"  (2)  Mixing  Concrete.  The  ingredients  of  concrete  should  be  thoroughly 
mixed  and  the  mixing  should  continue  until  the  cement  is  uniformly  distributed 
and  the  mass  is  uniform  in  color  and  homogeneous.  As  the  maximum  density 
and  greatest  strength  of  a  given  mixture  depend  largely  on  thorough  and  com- 
plete mixing,  it  is  essential  that  the  work  of  mixing  should  receive  special  atten- 
tion* and  care.  Inasmuch  as  it  is  difhcult  to  determine,  by  visual  inspection, 
whether  the  concrete  is  uniformly  mixed,  especially  where  limestone  or  aggre- 
gates having  the  color  of  cement  are  used,  it  is  essential  that  the  mixing  should 
occupy  a  dcfuiite  period  of  time.  The  minimum  time  will  depend  on  whethef 
the  mixing  is  done  by  machine  or  hand.      * 

"(a)  Measuring  Ingredients.  Methods  of  measurement  of  the  proportions 
of  the  various  ingredients  should  be  used  \#hich  will  secure  separate  and  uni- 
form measurements  of  cement,  fine  aggregate,  coarse  aggregate  and  water  at 
all  times. 

"(b)  Machine-Mixing.  When  the  conditions  will  permit,  a  machine-mixer 
of  a  type  which  insures  the  uniform  proportioning  of  the  materials  throughout 
the  mass  should  be  used,  as  a  more  uniform  consistency  can  be  thus  obtained. 
The  mixing  should  continue  for  a  minimum  time  of  at  least  one  minute  after 
all  the  ingredients  are  assembled  in  the  mixer. 

"  (c)  Hand-Mixing.  When  it  is  necessary  to  mix  by  hand,  the  mixing  should 
be  on  a  water-tight  platform  and  especial  preca'utions  should  be  taken  to  turn 
all  the  ingredients  together  at  least  six  times  and  until  they  are  homogeneous  in 
appearance  and  color." 

"The  most  satisfactory  method  *  of  mixing  concrete  by  hand  is  to  first  prepare 
for  the  mixing  of  the  materials,  a  tight  floor  of  planks,  or,  better  still,  of  sheet 
iron  with  the  edges  turned  up  about  2  in.  Upon  this  platform  should  first  be 
spread  the  sand,  and  upon  this  the  cement.  The  two  should  then  be  thoroughly 
and  immediately  mixed  by  means  of  shovels  or  hoes  until  of  an  even  color. 
Enough  water  should  be  added  to  make  a  thin  mortar  wliich  is  then  spread 
again.  The  gravel,  if  used,  should  then  be  added, 'and  then  the  broken  stone. 
Gravel  and  stone  should  be  first  thoroughly  wet,  if  originally  dry.  The  mass 
should  be  turned  until  all  the  ingredients  are  thoroughly  incorporated  and  all 
the  stone  and  gravel  covered  with  mortar,  this  requiring  from  four  to  six  turn- 
ings." 

"  (d)  Consistency.  The  materials  should  be  mixed  wet  enough  to  result  in  a 
concrete  of  such  a  consistency  that  it  will  flow  into  the  forms  and  about  the  metal 
reinforcement  when  used,  and  which,  at  the  same  time,  can  be  conveyed  from 

•  This  paragraph  is  condensed  from  several  recent  specifications. 


244  Masonry  Walls.    Cements  and  Concretes  Chap.  3 

the  mixer  to  the  forms  without  separation  of  the  coarse  aggregate  from  the 
mortar. 

"(e)  Retempering.  Mortar  or  concrete  should  not  be  remixed  with  water 
after  it  has  partly  set." 

(3)  Placing  Concrete,  "(a)  Methods.  Concrete  after  the  completion  of 
the  mixing  should  be  handled  rapidly,  and  in  as  small  masses  as  is  practicable, 
from  the  place  of  mixing  to  the  place  of  final  deposit,  and  under  no  circum- 
stances should  concrete  be  used  that  has  partly  set.  A  slow-setting  cement 
should  be  used  when  a  long  time  is  likely  to  occur  between  mixing  and  placing. 
Concrete  should  be  deposited  in  such  a  manner  as  will  permit  the  most  thorough 
compacting,  such  as  can  be  obtained  by  working  with  a  straight  shovel  or  shcing 
tool  kept  moving  up  and  down  until  all  the  ingredients  have  settled  in  their 
proper  places  by  gravity  and  the  surplus  water  has  been  forced  to  the  surface. 
Special  care  should  be  exercised  to  prevent  the  formation  of  laitance,*  which 
hardens  very  slowly  and  forms  a  poor  surface  on  which  to  deposit  fresh  concrete. 
All  LAITANCE  should  be  removed.  When  suspended  work  is  resumed,  con- 
crete previously  placed  should  be  roughened,  thoroughly  cleansed  of  foreign 
material  and  laitance,  thoroughly  wetted  and  then  slushed  with  a  mortar  con- 
sisting of  one  part  Portland  cement  and  not  more  than  two  parts  fine  aggregate. 
The  faces  of  concrete  exposed  to  premature  drying  should  be  kept  wet  for  a 
period  of  at  least  seven  days." 

"(b)  Mixing  and  Depositing  Concrete  in  Freezing  Weather.  Concrete 
should  not  be  mixed  or  deposited  at  a  freezing  temperature,  unless  special  pre- 
cautions are  taken  to  avoid  the  use  of  materials  covered  with  ice-crystals  or 
containing  frost,  and  to  provide  means  to  prevent  the  concrete  from  freezing 
after  being  placed  in  position  and  until  it  has  thoroughly  hardened.  As  the 
coarse  aggregate  forms  the  greater^  portion  of  the  concrete,  it  is  particularly 
important  that  this  material  be  heated  to  well  above  the  freezing-point. 

"(c)  Rubble  Concrete.  Where  the  concrete  is  to  be  deposited  in  massive 
work,  its  value  may  be  improved  and  its  cost  materially  reduced  by  the  use  of 
clean  stones  thoroughly  embedded  in  the  concrete  and  as  near  together  as  is 
possible  while  still  entirely  surrounded  by  concrete. 

"  (d)  Depositing  Concrete  Under  Water.  In  placing  concrete  under  water  it 
is  essential  to  maintain  still  water  at  the  place  of  deposit.  The  use  of  TREMiES,t 
properly  designed  and  operated,  is  a  satisfactory  method  of  placing  concrete 
through  water.  The  concrete  should  be  mixed  very  wet  (more  so  than  is  or- 
dinarily permissible)  so  that  it  will  flow  readily  through  the  tremies  and  into 
the  places  with  practically  a  level  surface.  The  coarse  aggregate  should  be 
smaller  than  ordinarily  used,  and  never  more  than  i  in  in  diameter.  The  use  of 
gravel  facilitates  mixing  and  assists  the  flow  of  concrete  through  the  tremies. 
The  mouth  of  the  tremie  should  be  buried  in  the  concrete  so  that  it  is  at  all 
times  entirely  sealed  and  the  surrounding  water  prevented  from  forcing  itself 
into  the  tremie;  the  concrete  will  then  discharge  without  coming  in  contact 
with  the  water.  The  tremie  should  be  suspended  so  that  it  can  be  lowered 
quickly  when  it  is  necessary  either  to  choke  off  or  prevent  a  too  rapid  flow;  the 

*  Laitance  is  a  whitish,  gelatinous  substance  of  about  the  same  composition  as  cement 
but  with  little  tendency  to  harden.  It  accompanies  a  disintegration  of  some  of  the 
cement  from  the  surface  of  concrete  which  is  exposed  to  the  action  of  water  in  which  it 
is  deposited.  The  con6rete  is  thus  weakened  and  the  laitance,  also,  weakens  the  bond 
between  old  and  new  material  and  should  be  removed  before  fresh  concrete  is  placed. 

t  A  tremie  is  a  round  or  square  box  or  tube  of  wood  or  plate  iron  open  at  the  top  and 
bottom.  The  diameter  varies  from  12  to  24  in.  The  tremie  rests  in  the  deposited  con- 
crete, extends  above  the  water-level  and  is  kept  full  of  concrete,  which  escapes  at  the 
bottom  as  the  tube  is  shifted  over  the  surface. 


Concrete  245 

lateral  flow  should  preferably  be  not  over  15  ft.  The  flow  should  be  continuous 
in  order  to  produce  a  monolithic  mass  and  to  prevent  the  formation  of  laitance 
in  the  interior.  In  large  structures  it  may  be  necessary  to  divide  the  mass  of 
concrete  into  several  small  compartments  or  units,  filling  one  at  a  time.  With 
proper  care  it  is  possible  in  this  manner  to  obtain  as  good  results  under  water  as 
in  the  air. " 

Forms  for  Concrete.  "Forms  should  be  substantial  and  unyielding,  so  that 
the  concrete  will  conform  to  the  designed  dimensions  and  contours,  and  should 
be  tight  in  order  to  prevent  the  leakage  of  mortar.  The  time  for  removal  of  forms 
is  one  of  the  most  important  considerations  in  the  erection  of  a  structure  of  con- 
crete or  reinforced  concrete.  Care  should  be  taken  to  inspect  the  concrete  and 
ascertain  its  hardness  before  removing  the  forms.  So  many  conditions  affect 
the  hardening  of  concrete,  that  the  proper  time  for  the  removal  of  the  forms 
should  be  decided  by  some  competent  and  responsible  person,  especially  where 
the  atmospheric  conditions  are  unfavorable.  It  may  be -stated,  in  a  general 
way,  that  forms  should  remain  in  place  longer  for  reinforced  concrete  than  for 
plain  or  massive  concrete,  and  that  the  forms  for  floors,  beams  and  similar  hori- 
zontal structures  should  remain  in  place  much  longei  than  for  vertical  walls. 
When  the  concrete  gives  a  distinctive  ring  under  the  blow  of  a  hammer,  it  is 
generally  an  indication  that  it  has  hardened  sufficiently  to  permit  the  removal 
of  the  forms  with  safety.  If,  however,  the  temperature  is  such  that  there  is 
any  possibility  that  the  concrete  is  frozen,  this  test  is  not  a  safe  rehance,  as 
frozen  concrete  may  appear  to  be  very  hard." 

Shrinkage  of  Concrete  and  Temperature-Changes.  "Shrinkage  of  con- 
crete, due  to  hardening  and  contraction  from  temperature-changes,  causes 
cracks,  the  size  of  which  depends  on  the  extent  of  the  mass.  The  resulting 
stresses  are  important  in  monolithic  construction  and  should  be  considered  care- 
fully by  the  designer;  they  cannot  be  counteracted  successfully,  but  the  effects 
can  be  minimized.  Large  cracks  produced  by  quick  hardening  or  wide  ranges 
of  temperature  can  be  broken  up  to  some  extent  into  small  cracks  by  placing 
reinforcement  in  the  concrete;  in  long  continuous  lengths  of  concrete,  it  is 
better  to  provide  shrinkage-joints  at  points  in  the  structure  where  they  will  do 
little  or  no  harm.  Reinforcement  is  of  assistance  and  permits  longer  distances 
between  shrinkage-joints  than  when  no  reinforcement  is  used.  Small  masses  or 
thin  bodies  of  concrete  should  not  be  joined  to  larger  or  thicker  masses  without 
providing  for  shrinkage  at  such  points.  Fillets  similar  to  those  used  in  metal 
castings,  but  of  larger  dimensions,  for  gradually  reducing  from  the  thicker  to 
the  thinner  body,  are  of  advantage.  Shrinkage-cracks  are  likely  to  occur  at 
points  where  fresh  concrete  is  joined  to  that  which  is  set,  and  hence  in  placing 
the  concrete,  construction-joints  should  be  made  on  horizontal  and  vertical 
lines,  and,  if  possible,  at  points  where  joints  would  naturally  occur  in  dimen- 
sion-stone masonry." 

Effect  of  Heat  on  Concrete  Fireproofing.*  "The  actual  fire-tests  of 
concrete  and  reinforced  concrete  have  been  limited,  but  experience,  together 
with  the  results  of  tests  thus  far  made,  indicates  that  concrete,  on  account  of 
its  low  rate  of  heat-conductivity  and  the  fact  that  it  is  incombustible,  may  be 
used  safely  for  fireproofing  purposes.  The  dehydration  of  concrete  probably 
begins  at  about  500°  F.  and  is  completed  at  about  900°  F.;  but  experience  indi- 
cates that  the  volatilization  of  the  water  absorbs  heat  from  the  surrounding  mass, 
which,  together  with  the  resistance  of  the  air-cells,  tends  to  increase  the  heat- 
resistance  of  the  concrete,  so  that  the  process  of  dehydration  is  very  much  re- 

*  See,  also,  Chapter  XXITI,  page  817. 


246  Masonry  Walls.    Cenlents  and  Concretes  Chap.  3 

tarded.  The  concrete  that  is  actually  affected  by  fire  remains  in  position  and 
affords  protection  to  the  concrete  beneath  it.  The  thickness  of  the  protective 
coating  required  depends  on  the  probable  duration  of  a  fire  which  is  Hkely  to 
occur  in  the  structure  and  should  be  based  on  the  rate  of  heat-conductivity. 
The  question  of  the  conductivity  of  concrete  is  one  which  requires  further  study 
and  investigation  before  a  definite  rate  for  different  classes  of  concrete  can  be 
fully  established.  However,  for  ordinary  conditions  it  is  recommended  that 
the  metal  in  girders  and  columns  be  protected  by  a  minimum  of  2  in  of  con- 
crete; that  the  metal  in  beams  be  protected  by  a  minimum  of  iVi  in  of  concrete, 
and  the  metal  in  floor-slabs  be  protected  by  a  minimum  of  i  in  of  concrete. 
It  is  recommended  that  in  monolithic  concrete  columns,  the  concrete  to  a  depth 
of  iVi  in  be  considered  as  protective  covering  and  not  included  in  the  effective 
section.  It  is  recommended  that  the  corners  of  columns,  girders  and  beams  be 
beveled  or  rounded,  as  a  sharp  corner  is  more  seriously  affected  by  fire  than  a 
round  one. " 

Waterproofing  Concrete.  "Many  expedients  have  been  used  to  render 
concrete  impervious  to  water  under  normal  conditions,  and  also  under  pressure- 
conditions  that  exist  in  reservoirs,  dams  and  conduits  of  various  kinds.  Expe- 
rience shows,  however,  that  where  mortar  or  concrete  is  proportioned  to  obtain 
the  greatest  practicable  density  and  is  mixed  to  a  rather  wet  consistency,  t^e 
resulting  mortar  or  concrete  is  impervious  under  moderate  pressure.  A  con- 
crete of  dry  consistency  is  more  or  less  pervious  to  water,  and  compounds  of 
various  kinds  have  been  mixed  with  the  concrete,  or  applied  as  a  wash  to  the 
surface  for  the  purpose  of  making  it  water-tight.  Many  of  these  compounds 
are  of  but  temporary  value,  and  in  time  lose  their  power  of  imparting  imperme- 
ability to  the  concrete.  In  the  case  of  subways,  long  retaining-walls  and  reser- 
voirs, provided  the  concrete  itself  is  impervious,  cracks  may  be  so  reduced  by 
horizontal  and  vertical  reinforcement  properly  proportioned  and  located,  that 
they  are  too  minute  to  permit  leakage  or  are  soon  closed  by  infiltration  of  silt. 
Coal-tar  preparations  applied  either  as  a  mastic  or  as  a  coating  on  felt  or  cloth- 
fabric  are  used  for  waterproofing,  and  should  be  proof  against  injury  by  liquids 
or  gases.  For  retaining-walls  and  similar  walls  in  direct  contact  with  the 
earth,  the  application  of  one  or  two  coatings  of  hot  coal-tar  pitch  to  the  thor- 
oughly dried  surface  of  concrete  is  an  efficient  method  of  preventing  the  pene- 
tration of  moisture  from  the  earth. "  (See,  also,  Waterproofing  for  Founda- 
tions, Part  III. 

Surface-Finish  of  Concrete.  "Concrete  is  a  material  of  an  individual  type 
and  should  not  be  used  in  imitation  of  other  structural  materials.  One  of  the 
important  problems  connected  with  its  use  is  the  character  of  the  finish  of 
exposed  surfaces.  The  finish  of  the  surface  should  be  determined  before  the 
concrete  is  placed,  and  the  work  conducted  so  as  to  make  possible  the  finish 
desired.  For  many  forms  of  construction  the  natural  surface  of  the  concrete 
is  unobjectionable;  but  frequently  the  marks  of  the  boards  and  the  flat,  dead 
surface  are  displeasing,  thus  making  some  special  treatment  desirable.  A 
treatment  of  the  surface  either  by  scrubbing  it  while  green  or  by  tooling  it  after 
it  is  hard,  which  removes  the  film  of  mortar  and  brings  the  aggregates  of  the 
concrete  into  relief,  is  frequently  used  to  remove  the  form-markings,  break  the 
monotonous  appearance  of  the  surface,  and  make  it  more  pleasing.  The  plaster- 
ing of  surfaces  should  be  avoided,  for  even  if  carefully  done,  the  plaster  is  likely 
to  peel  off  under  the  action  of  frost  or  temperature-changes. " 

Design  of  Massive  Concrete.  "In  the  design  of  massive  or  plain  concrete, 
no  account  should  be  taken  of  the  tensile  strength  of  the  material,  and  sections 
Should  usuaUy  be  proportioned,  so  as  to  avoid  tensile  stresses,  except  in  slight 


Concrete 


247 


amounts,  to  resist  indirect  stresses.  This  will  generally  be  accomplished,  in 
the  case  of  rectangular  shapes,  if  the  line  of  pressure  is  kept  within  the  middle 
third  of  the  section,  but  in  very  large  structures,  such  as  high  masonry  dams,  a 
more  exact  analysis  may  be  required.  Structures  of  massive  concrete  are  able 
to  resist  unbalanced  lateral  forces  by  reason  of  their  weight;  hence  the  element 
of  weight  rather  than  strength  often  determines  the  design.  A  relatively  cheap 
and  weak  concrete,  therefore,  will  often  be  suitable  for  massive  concrete  struc- 
tures. It  is  desirable  generally  to  provide  joints  at  intervals  to  localize  the 
effect  of  contraction.  Massive  concrete  is  suitable  for  dams,  retaining-walls, 
and  piers  and  short  columns  in  which  the  ratio  of  length  to  least  width  is  rela- 
tively small.  Under  ordinary  conditions  this  ratio  should  not  exceed  six.  It 
is  also  suitable  for  arches  of  moderate  span,  where  the  conditions  as  to  founda- 
tions are  favorable." 

Quantities  of  Materials  Required  per  Cubic  Yard  of  Concrete.*  The 
following  tables  give  the  quantities  of  Portland  cement  required  to  make  i  cu  yd 
of  mortar  and  the  quantities  of  cement,  sand  and  stone  required  to  make  i  cu 
yd  of  concrete.     They  are  based  upon  formulas  deduced  by  Halbert  P.  Gillette. 


Barrels  of  Portland  Cement  per  Cubic  Yard  of  Mortar 

Voids  in  sand,  35%,  i  bbl  of  cement  yielding  3.65  cu  ft  of  cement  paste 


Proportion  of  cement  to 
sand 

I  to  I 

I  to  l]-2 

I  to  2 

I  to  21-2 

I  to  3 

I  to  4 

Barrel  specified  to  be  3.5  cu  ft 
Barrel  specified  to  be  3.8  cu  ft 
Barrel  specified  to  be  4.0  cu  ft 
Barrel  specified  to  be  4.4  cu  ft 

bbl 
4.22 
4.09 
4.00 
3.81 

bbl 

3-49 
3.33 
3.24 
3-07 

bbl 

2.97 
2.81 
2.73 
2.57 

bbl 

2.57 
2.45 
2.36 
2.27 

bbl. 
2.28 
2.16 
2.08 
2.00 

bbl 
1.76 
1.62 
1.54 
1.40 

Cubic  yard  of  sand  per  cu 
yd  of  mortar 

0.6 

0.7 

0.8 

0.9 

I.O 

1.0 

Barrels  of  Portland  Cement  per  Cubic  Yard  of  Mortar 

Voids  in  sand,  45%,  i  bbl  of  cement  yielding  3.4  cu  ft  of  cement  paste 


Proportion  of  cement  to 
sand 


Barrel  specified  to  be  3-5  cu  ft 
Barrel  specified  to  be  3.8  cu  ft 
Barrel  specified  to  be  4.0  cu  ft 
Barrel  specified  to  be  4.4  cu  ft 


Cubic  yard  of  sand  per  cu 
yd  of  mortar 


I  to  I 

I  to  iK' 

I  to  2 

I  to  2y> 

I  to  3 

I  to  4 

bbl 

bbl 

bbl 

bbl 

bbl 

bbl 

4.62 

3.80 

3.25 

2.84 

2.35 

1.76 

432 

3.61 

3.10 

2.72 

2.16 

1.62 

4.19 

346 

3-00 

2.64 

2.05 

1.54 

3.94 

3.34 

2.90 

2.57 

1.86 

1.40 

0.6 

0.8 

09 

1.0 

1.0 

1.0 

"In  using  these  tables  remember  that  the  proportion  of  cement  to  sand  is 
by  volume  and  not  by  weight.  If  the  specifications  state  that  a  barrel  of  cement 
shall  be  considered  to  hold  4  cu  ft,  for  example,  and  that  the  mortar  shall  be 

*  Quoted,  by  permission,  from  the  Handbook  of  Cost  Data  for  Contractors  and  En- 
gineers, by  Halbert  P.  Gillette,  published  by  The  Myron  C.  Clark  Publishing  Company, 
Chicago.Ill.  See  1914  revised  edition,  pages  538  to  540.  This  handbook  contains  com- 
plete and  voluminous  data  on  quantities,  costs,  etc.,  of  building  materials  and  operations. 


248 


Masonry  Walls.     Cements  and  Concretes 


Chap.  3 


I  part  cement  to  2  parts  sand,  then  i  bbl  of  cement  is  mixed  with  8  cu  ft  of  sand, 
regardless  of  what  is  the  actual  size  of  the  barrel,  and  regardless  of  how  much 
cement  paste  can  be  made  with  a  barrel  of  cement.  If  the  specifications  fail  to 
state  what  the  size  of  a  barrel  will  be,  then  the  contractor  is  left  to  guess. 

"If  the  specifications  call  for  proportions  by  weight,  assume  a  Portland  ce- 
ment barrel  to  contain  380  lb  of  cement,  and  test  the  actual  weight  of  a  cubic 
foot  of  the  sand  to  be  used.  Sand  varies  extremely  in  weight,  due  both  to  the 
variation  in  the  per  cent  of  voids,  and  to  the  variation  in  the  kind  of  minerals 
of  which  the  sand  is  composed.  A  quartz  sand  having  35%  voids  weighs  107  lb 
per  cu  ft;  but  a  quartz  sand  having  45%  voids  weighs  only  91  lb  per  cu  ft.  If 
the  weight  of  the  sand  must  be  guessed  at,  assume  100  lb  per  cu  ft.  If  the 
specifications  require  a  mixture  of  i  part  of  cement  to  2  parts  of  sand,  by  weight, 
we  will  have  380  lb  (or  i  bbl)  of  cement  mixed  with  2  times  380,  or  760  lb  of 
sand;  and  if  the  sand  weighs  90  lb  per  cu  ft,  we  shall  have  760  divided  by  90,  or 
8.44  cu  ft  of  sand  to  every  barrel  of  cement.  In  order  to  use  the  tables  above 
given,  we  may  specify  our  own  size  of  barrel;  let  us  say  4  cu  ft;  then,  8.44  divided 
by  4  gives  2.n  parts  of  sand  by  volume  to  i  part  of  cement.  Without  material 
error  we  may  call  this  a  i  to  2  mortar,  and  use  the  tables,  remembering  that  our 
barrel  is  now  *  specified  to  be'  4  cu  ft.  If  we  have  a  brand  of  cement  that  yields 
3.4  cu  ft  of  paste  per  bbl  and  sand  having  45%  voids,  we  find  that  approximately 
3  bbl  of  cement  per  cu  yd  of  mortar  will  be  required. 

"It  should  "be  evident  from  the  foregoing  discussions  that  no  table  can  be 
made,  and  no  rule  can  be  formulated  that  will  yield  accurate  results  unless  the 
brand  of  cement  is  tested  and  the  percentage  of  voids  in  the  sand  determined. 
This  being  so,  the  sensible  plan  is  to  use  the  tables  merely  as  a  rough  guide, 
and,  where  the  quantity  of  cement  to  be  used  is  very  large,  to  make  a  few  batches 
of  mortar,  using  the  available  brands  of  cement  and  sand  in  the  proportions 
specified.  Ten  dollars  spent  in  this  way  may  save  a  thousand,  even  on  a  com- 
paratively small  job,  by  showing  what  cement  and  sand  to  select." 


Ingredients  in  One  Cubic  Yard  of  Concrete  * 

Sand-voids,  40%;  stone-voids,  45%;   Portland-cement  barrel  yielding  3.65  cu  ft 
paste.     Barrel  specified  to  be  3.8  cu  ft 


Proportions  by  volume 

I  :2:4 

I  :2:s 

1:2:6 

i:2i/^:5 

1:21/2:6 

I  :3:4 

Barrels  cement  per  cu  yd 
concrete 

1.46 
0.41 
0.82 

1.30 
0.36 
0.90 

1. 18 
0.33 
1. 00 

113 

0.40 
0.80 

1. 00 
0.3s 
0.84 

I-25 
0.53 
0.71 

Cubic  yard  sand  per  cu  yd 
concrete 

Cubic  yard  stone  per  cu  yd 
concrete 

Proportions  by  volume 

I  :3:5 

1:3:6 

1:3:7 

1:4:7 

1:4:8 

I  :4:9 

Barrels  cement  per  cu   yd 
concrete 

1. 13 

0.48 
0.80 

1.05 

0.44 
0.88 

0.96 
0.40 
0.93 

0.82 
0.46 
0.80 

0.77 
0.43 
0.86 

0.73 
0.41 
0.92 

Cubic  yard  sand  per  cu  yd 
concrete 

Cubic  yard  stone  per  cu  yd 
concrete 

*  This  table  is  to  be  used  where  cement  is  measured  packed  in  the  barrel,  for  thft 
ordinary  barrel  holds  3.8  cu  ft. 


Concrete 


249 


"It  will  be  seen  that  the  above  table  can  be  condensed  into  the  following: 
"Rule.  Add  together  the  number  of  parts  and  divide  this  sum  into  ten,  the 
quotient  will  be,  approximately,  the  number  of  barrels  of  cement  per  cubic  yard. 
"Thus  for  a  I  12:5  concrete,  the  sum  of  the  parts  is  i  plus  2  plus  5,  which  is 
8;  then  10  divided  by  8  is  1.25  bbl,  which  is  approximately  equal  to  the  1.30  bbl 
given  in  the  table.  Neither  this  rule  nor  this  table  is  applicable  if  a  different 
size  of  cement-barrel  is  specified,  or  if  the  voids  in  the  sand  or  stone  differ  mate- 
rially from  40%  and  45%  respectively.  There  are  such  innumerable  com- 
binations of  varying  voids,  and  varying  sizes  of  barrels,  that  the  author  does 
not  deem  it  worth  while  to  give  other  tables. " 

Ingredients  in  One  Cubic  Yard  of  Concrete  * 

Sand-voids,  40%;  stone-voids,  45%;   Portland-cement  barrel  yielding  3.65  cu  ft  of 
paste.     Barrel  specified  to  be  4.4  cu  ft 


Proportions  by  volume 

I  :  2  ;  4 

1:2:5 

I  :2:6 

I  •.2Y2.  '.$ 

1:21/2:6 

1:3:4 

Barrels   cement   per  cu    yd 
concrete 

Cubic  yard  sand  per  cu  yd 
concrete 

Cubic  yard  stone  per  cu  yd 
concrete 

1.30 

0.42 
0.84 

1. 16 
0.38 
0.9s 

1. 00 
0.33 

1. 00 

1.07 
0.44 
0.88 

0.96 
0.40 
0.9s 

1.08 
0.53 
0.71 

Proportions  by  volume 

1:3:5 

1:3:6 

1:3:7 

1:4:7 

1:4:8 

I  :4:9 

Barrels   cement   per  cu   yd 
concrete 

0.96 
0.47 
0.78 

0.90 
0.44 
0.88 

0.82 
0.40 
0.93 

0.75 
0.49 
0.86 

0.68 
0.44 
0.88 

0.64 
0.42 
0.95 

Cubic  yard  sand  per  cu  yd 
concrete 

Cubic  yard  stone  per  cu  yd 
concrete 

Cost  of  Concrete. t  (For  Cost  of  Cement,  see  page  238.)  The  average 
cost  of  sand  may  be  taken  at  30  cts  per  cu  yd  to  cover  digging  and  loading,  but 
when  washed  or  screened  the  cost  averages  between  40  and  55  cts  per  cu  yd. 
Hauling  and  freight-charges  generally  raise  the  cost  of  sand,  ready  to  unload  at 
the  site,  to  from  90  cts  to  $1.10  per  cu  yd,  and  about  15  cts  per  yd  additional 
must  be  added,  if  unloaded  from  cars.  Gravel  costs  from  $1.20  to  $1.40  per  cu 
yd,  unloaded  at  the  job,  and  crushed  stone  from  $1.45  to  $1.60.  These  prices 
are,  of  course,  average  prices  only,  and  include  moderate-haul  teaming  and  un- 
loading. For  hand-mixing  and  placing  of  soft  concrete,  and  spreading  without 
any  ramming,  the  labor-cost  varies  from  90  cts  to  $1.30  per  cu  yd.  This  is 
for  handling  in  barrows  materials  that  are  conveniently  at  hand.  This  cost 
will  be  much  higher  for  dry  concrete,  and  hand-mixing  costs  may  reach  $2  or 
$3  per  cu  yd.  For  machine-mixing  alone  and  with  machines  taking  four  bags 
to  the  batch,  the  cost  of  mixing  may  be  even  as  low  as  50  or  60  cts  per  cu  yd. 
For  placing  alone,  the  cost  is  about  75  cts  per  cu  yd;  this  includes  wheeling  the 
concrete,  dumping  it  in  place  and  spreading  and  spading  it  into  forms.  This 
cost  could  be  almost  doubled  where  unusual  care  had  to  be  exercised  to  obtain 
a  good  surface  and  where  there  was  an  extra  amount  of  spading.     The  costs 

*  This  table  is  to  be  used  when  the  cement  is  measured  loose,  after  dumping  it  into 
a  box,  for  under  such  conditions  a  barrel  of  cement  yields  4.4  cu  ft  of  loose  cement. 

t  War-conditions  changed  many  costs.  Values  given  are  retained  temporarily  for  pur- 
poses of  comparison. 


250  Masonry  Walls.     Cements  and  Concretes  Chap.  3 

are  reduced  for  heavy  mass-concrete,  and  have  been  as  low  as  50  or  60  cts  per 
cu  yd  for  machine-mixing  and  placing  together,  by  mixer  and  derrick  or  by 
tracks  and  cars.  The  following  approximate  schedule  *  of  labor-costs  for  mix- 
ing and  placing  concrete  is  given  by  L.  li.  Allen  of  the  Aberthaw  Construc- 
tion Company,  in  Professor  Hool's  excellent  treatise: 

For  footings $1 .  50  per  cu  yd 

For  floor-slabs  not  exceeding  4H  in  in  thickness $1 .60  per  cu  yd 

For  floor-slabs  exceeding  5  in  in  thickness $1 .00  per  cu  yd 

For  columns  and  thin  walls $i .  50  per  cu  yd 

For  walls  exceeding  18  in  in  thickness $1 .00  per  cu  yd 

For  dams  and  thick  retaining-walls $0.70  per  cu  yd 

For  the  unit  cost  due  to  the  cost  of  the  tools,  plant  and  supplies,  $1  may  be 
taken  as  an  average  for  jobs  requiring  from  4  000  to  10  000  cu  yd  of  concrete. 
It  varies,  of  course,  with  the  character  and  magnitude  of  the  work.  The  cost 
for  this  item  is  reduced  in  larger  jobs,  falling  to  80  or  even  70  cts  per  cu  yd; 
and  it  is  increased  in  operations  of  less  magnitude  to  from  $1  to  $1.50  per  cu  yd, 
for,  say,  3  000  cu  yd  of  concrete.  When  the  amount  of  concrete  required  is  as 
small  as  600  or  7cx)  cu  yd,  hand-mixing  is  generally  more  economical  than 
machine-mixing.  Mr,  Allen  summarizes  *  the  cost  of  i  cu  yd  of  concrete  for  a 
building  requiring  5  000  cu  yd  of  reinforced-concrete  work  in  floors  and  columns 
as  follows,  the  cost  of  forms  and  steel  and  finishing  of  the  surface  not  being 
included: 

Cement,  t%  bbl,  at  $1.38  per  bbl $2 .30 

Sand,  3'^  cu  yd,  at  $1  per  cu  yd 0.50 

Stone,  1.35  tons,  at  $1.40  per  ton 1.89 

Labor,  per  cu  yd 1.35 

Plant,  per  cu  yd i .  00 

Total,  per  cu  yd $7 .  04 

In  this  summary  the  exact  theoretical  proportions  or  quantities  of  cement, 
sand  and  stone  required  for  i  cu  yd  of  concrete,  and  deduced  from  formulas, 
are  not  adhered  to,  the  author  stating  that  the  exact  theoretical  proportions  are 
the  net  quantities  of  the  materials  determined  by  careful  experiment,  that 
"conditions  on  actual  construction  work  do  not  approach  those  of  laboratory 
work  and  that  there  is  always  a  considerable  waste  of  cement,  sand  and  stone." 
In  view  of  these  facts,  he  states  that,  "when  estimating  quantities,  it  is  not  safe 
to  allow  less  than  the  following  amounts  of  cement  for  different  proportions 
of  mix: 

I  :  il'i  :  S  niix 2 .  00  bbl  per  cu  yd 

1:2      14  mix 1 .  66  bbl  per  cu  yd 

I  :  21^^  :  5  mix i .  40  bbl  per  cu  yd 

1:3      :  6  mix i .  20  bbl  per  cu  yd  " 

It  is  customary  to  allow  H  cu  yd  of  sand  and  i  cu  yd  of  crushed  stone,  to 
I  cu  yd  of  concrete,  and  to  estimate  the  weight  of  crushed  stone  at  100  lb  per 
cu  ft. 

The  Weight  of  Concrete  varies  from  no  to  155  lb  per  cu  ft,  according  to 
the  material  used.  Concrete  of  the  usual  proportions  weighs  from  140  to  150  lb 
per  cu  ft.  Trap-rock  concrete  weighs  from  148  to  155;  limestone  or  gravel 
concrete,  from  142  to  148;  and  cinder  concrete  from  80  to  115  lb  per  cu  ft. 

*  Reinforced  Concrete  Construction,  by  George  A.  Hool,  McGraw-Hill  Book  Companyt 
New  York. 


Concrete  251 

The  Strength  of  Concrete.    See  Chapter  V. 

Earlier  Examples  of  Portland-Cement  Concrete.  From  the  foregoing  it 
is  seen  that  for  foundation- work  to-day,  mass-concrete  varies  in  proportions 
from  ai:3:6toai:4:8  mix.  Some  of  the  earher  examples  are  added  for 
comparison. 

Foundations  of  the  United  States  Naval  Observatory,  Georgetown,  D.  C.r 
I  part  cement,  2i/i  sand,  3  gravel,  5  broken  stone,  (i  bbl  of  cement,  380  lb, 
made  1.18  yd  of  concrete.) 

Foundations  of  the  Cathedral  of  St.  John  the  Divine,  New  York:  i  part 
Portland  cement,  2  parts  sand,  3  parts  quartz  gravel  of  pieces  from  ij^i  to  2  in 
in  diameter.     (17  cx)o  bbl  of  cement  made  11  000  yd  of  concrete.) 

Manhattan  Life  Insurance  Building,  New  York,  filling  of  caissons:  i  part 
Alsen  Portland  cement,  2  parts  sand,  4  parts  broken  stone. 

Johnston  Building  (15  stories),  New  York,  filling  of  caissons:  i  part  Portland 
cement,  3  parts  sand,  7  parts  stone,  finished  on  top  for  brickwork  with  i  part 
cement  and  3  parts  gravel. 

Professor  Baker  states  that  the  concrete  foundations  under  the  Washington 
Monument  were  made  of  i  part  Portland  cement,  2  parts  sand,  3  parts  gravel 
and  4  parts  broken  stone,  and  that  this  mixture  stood,  when  six  months  old,  a 
load  of  2  000  lb  per  sq  in,  or  144  tons  per  sq  ft. 


25? 


Retaining-Walls,  Breast-Walls  and  Vault- Walls       Chap.  4 


CHAPTER  IV 

KETAINING-WALLS,   BREAST-WALLS  AND 
VAULT-WALLS 

By 
GRENVILLE  TEMPLE  SNELLING 

MEMBER  OF   AMERICAN   INSTITUTE   OF   ARCHITECTS 

1.    Mechanical  Principles  Involved 

General  Principles.  Before  discussing  more  in  detail  the  problems  relating 
to  masonry  structures,  in  which,  if  improperly  constructed,  a  tendency  to  slide 
or  overturn  on  their  bases  may  be  developed,  a  familiarity  with  what  are  known 
as  the  THEOREM  OF  FRICTION  and  the  theorem  of  the  middle  third  will  be 
of  assistance  in  comprehending  the  methods  indicated  for  rendering  such  struc- 
tures stable. 

Theorem  of  Friction.  If  a  body  rests  on  an  inclined  plane  it  will  remain 
stationary   until   the   angle   <f>,   that   the   plane  makes  'with    the   horizontal, 


Body  on  Inclined  Plane. 


Fig.  4 
Graphical  Representation  of  Forces 


becomes  so  great  that  the  friction  developed  between  the  surfaces  of  the  body 
and  the  plane  is  no  longer  sufficient  to  prevent  the  body  from  sliding  down 
the  plane  (Fig.  1). 

Assume  the  body  ////  resting  on  the  plane  EF.    The  weight,  W,  of  this  body 
is  shown  graphically  by  the  line  AB,  applied  at  its  center  of  gravity  A  (Fig.  2). 


Mechanical  Principles  Involved 


263 


This  weight  can  be  resolved  into  two  component  forces,  one,  AC,  normal  to  the 
inclined  plane  and  the  other,  AD,  parallel  to  it.  It  is  the  parallel  or  tangential 
force  which  tends  to  pull  the  body  down  the  plane  and  which  is  resisted  by  the 
friction  developed  between  the  two  surfaces.  The  friction  developed  between 
any  two  surfaces  in  contact  depends  upon  the  nature  of  the  materials  of  which 
they  are  composed  and  the  intensity  of  the  forces  pressing  them  together;  and 
it  resists  the  tendency  to  slide  only  up  to  a  certain  point.  As  the  angle  <f>, 
which  the  inclined  plane  makes  with  the  horizontal,  increases,  the  tangential 
component  T,  of  the  weight  W,  increases,  until  it  becomes  greater  than  the 
frictional  resistance,  and  the  body  moves  down  the  plane  (Fig.  3).  From 
trigonometry, 

T=Wsm(l> 
N  =  Wcos<l>,     or,     r  =  i\^tan0 

There  is  evidently  a  position  of  the  plane,  intermediate  between  the  positions 
shown  in  Figs.  1  and  3,  in  which  the  component  force  T  is  just  balanced  by  the 
friction  and  in  which  the  body  remains  at  rest  although  just  on  the  point  of 
sHding  (Fig.  4).  If  the  angle  which  the  inclined  plane  makes  with  the  hori- 
zontal, at  the  moment  when  the  body  is  just  about  to  slide,  be  designated  by  </>, 
the  friction  developed  between  the  two  surfaces  will  be  equal  to  N  tan  0,  since, 
when  the  angle  of  inclination  of  the  plane  to  the  horizontal  is  (f>,  the  tangential 
component  of  the  weight  just  balances  the  friction.  From  the  equation  T  =  N 
tan  <t>  it  is  evident  that  the  friction  is  directly  proportional  to  N  and  to  tan  <f>. 
Tan  (f)  is  then  known  as  the  coefficient  of  friction  and  </>  as  the  angle  of 
REPOSE,  or,  in  the  case  of  stone  s\irfaces,  it  is  often  known  as  the  angle  of 
friction. 

The  following  Table  I  gives  the  average  values  of  these  constants  as  deter- 
mined by  experiment. 

Table  I.    Coefficients  and  Angles  of  Friction 


Kind  of  surface 

Coefficient  of 
friction,  tan  0 

Angle  of 
friction,  0 

Granite,  limestone  and  marble: 
Soft  dressed  upon  soft  dressed 

0.70 
0.55 
0.65 

0  65 
0.60 
0.50 
0.50 
0.33 
0.40 
0.60 
0.40 
0.30 

35°  00' 
28    50 
33    00 

33    00 
31     00 
26    46 
26    40 
18     20 
21     50 
31     00 
21     50 
16    40 

Hard  dressed  upon  hard  dressed 

Hard  dressed  upon  soft  dressed 

Stone,  brick  or  concrete i 
Masonry  upon  masonry 

Masonry  upon  wood  (with  the  grain) 

Masonry  upon  wood  (across  the  grain) 

Masonry  upon  dry  clay 

Masonry  upon  wet  or  moist  clay 

Masonry  upon  sand 

Masonry  upon  gravel 

Soft  stone  upon  steel  or  iron 

Hard  stone  upon  steel  or  iron    

In  this  discussion  only  the  weight  AB  (Figs.  2,  3  and  4),  of  the  body  has  been 
considered;  but  the  body  might  be  subjected  to  the  action  of  other  forces  be- 
sides the  force  of  gravity,  in  which  case  these  other  forces  would  be  combined 
with  the  weight  in  order  to  find  the  resultant,  this  resultant  being  again  resolved 
into  a  tangential  and  a  normal  component.     Since  the  angle  BAC  is  equal  to  the 


254 


Retaining-Walls,  Breast-Walls  and  Vault-Walls      Chap.  4 


angle  PEG  (Figs.  2,  3  and  4),  given  a  certain  normal  pressure  exerted  by  the 
body  on  the  plane,  the  amount  of  the  tangential  pressure  T  depends  upon  the 
angle  PEG.  The  problem  in  actual  practice  reduces  itself  to  so  arranging  the 
conditions  that  no  matter  what  the  position  of  the  plane  may  be,  the  angle  </>, 
which  the  resultant  W,  makes  with  the  normal  N,  to  the  plane,  will  not  be  greater 
than  the  angle  of  friction  or  repose. 

;"  Theorem  of  the  Middle  Third.  When  any  surface  is  subjected  to  pres- 
sure from  the  action  of  any  force  or  forces,  this  total  pressure  may  be  con- 
sidered as  a  SYSTEM   OF   AN  INFINITE   NUMBER  OF  PARALLEL  FORCES,  equal   or 

unequal  in  intensity.  These  forces  will  have  a  resultant,  whose  magnitude, 
DIRECTION  and  point  of  APPLICATION  can  be  determined,  either  graphically,  or 
by  moments,  as  explained  in  Chapter  VI.  The  determination  of  these  three 
elements  of  this  resultant  force  may  at  times  become  of  the  utmost  importance 
to  the  engineer. 

Pressure  of  this  nature  is  technically  known  as  the  stress  to  which  the  sur- 
face in  question  is  subjected.  (See  Chapter  I.)  When  the  intensity  of  a 
stress  is  not  the  same  at  different  points  of  a  surface,  it  is  called  a  varying 
stress,  while  if,  on  the  contrary,  its  intensity  remains  the  same  at  every  point 
of  the  surface,  it  is  called  a  uniform  stress. 

When  a  stress  varies  it  may  do  so  in  one  or  two  ways.  It  ma}^  vary  uni- 
formly, that  is  to  say,  in  a  uniform  manner,  following  some  definite  law  of 
variation,  so  that,  knowing  this  law,  its  intensity  may  be  determined  for  any 
given  point  of  the  surface;  or  non-uniformly,  following  no  law.  When  a 
stress  varies  in  the  former  manner  it  is  called  a  uniformly  varying  stress 
This  is  the  case  most  frequently  met  with  in  engineering  problems. 


Resultant  of  the  stresses 


Fig.  5.    Resultant  within  Middle  Third 


Fig.  6.    Resultant  at  Middle' Third 


In  dealing  with  isolated  forces,  such  as  concentrated  loads  on  a  beam,  we 
are  usually  interested  in  determining  the  magnitude  and  point  of  application 
of  the  resultant  of  these  forces.  When,  however,  the  question  is  one  of  stress, 
or  of  an  unlimited  number  of  forces,  the  problem  that  usually  presents  istelf 
is  one  in  which  the  resultant  is  known,  in  magnitude,  direction  and  point  of 
application,  and  in  which  it  is  required  to  determine  the  distribution  of  the 
stress  to  which  the  surface  is  subjected.  Or,  in  actual  practice,  it  is  required 
to  so  arrange  the  parts  of  the  structure  that  this  resultant  shall  have  such  a  mag- 
nitude, direction  and  point  of  application  that  the  stress  to  which  the  surface 
under  consideration  is  subjected  shall  not  exceed  certain  limits  of  safety, 
determined  beforehand  by  experience.  For  example,  when  the  resultant  of  a 
known  amount  of  pressure  or  stress  acts  at  the  center  of  gravity  of  the  sur- 
face subjected  to  the  stress,  this  stress  is  uniformly  distributed  over  the 
surface. 


Retaining- Walls 


255 


Resultant  of  the  stresses 


When  the  resultant  acts  at  a  distance  of  two-thirds  the  total  width  of  the 
surface  from  one  edge  or  boundary  line  of  the  surface,  and  at  one-third  the 
width  from  the  other  edge,  the  stress  is  uniformly  varying;  and  its  in- 
tensity at  the  edge  farthest  from 
the  point  of  application  of  the 
resultant  is  zero  and  at  the  other 
edge  a  maximum  or  twice  the  average 
stress.  When,  however,  the  total 
amount  of  the  stress  remaining  the 
same,  the  point  of  application  of 
the  resultant  is  at  a  greater  distance 
from  one  edge  than  two-thirds  the 
total  width  of  the  surface,  a  certain 
part  of  the  surface  adjacent  to  the 
edge  furthest  from  the  resultant  is 
subjected  to  a  stress  of  a  contrary 
NATURE  to  that  distributed  over 
the  rest  of  the  area;  that  is  to  say,  if  the  stress  to  which  the  major  part  of  the 
surface  is  subject  is  a  compressive  stress,  the  stress  acting  on  the  remainder  of 
the  surface  is  a  tensile  stress.  The  stresses  in  a  surface  resulting  from  three 
different  positions  of  the  resultant  force  may  be  illustrated  graphically,  as  shown 
in  Figs.  5,  6  and  7.     (See,  also.  Chapter  XXXI,  pages  1225  and  1234.) 

2.   Retaining-Walls 

Definitions.  A  Retaining-Wall  is  a  wall  built  to  resist  the  pressure  of 
earth,  sand,  or  other  filling  or  backing  deposited  behind  it  after  it  is  built,  as 
distinguished  from  a  breast-wall  or  face-wall,  which  is  a  similar  structure 
built  to  prevent  the  fall  of  earth  which  is  in  its  undisturbed,  natural  position, 
but  from  which  part  has  been  excavated,  leaving  a  vertical  or  inclined  face.  Fig 
8  is  an  illustration  of  the  two  kinds  of  wall. 


Fig.  7.     Resultant  beyond  Middle  Third 


Retaining-wall  and  Breast-wall 


Theories  of  Retaining-Walls.  A  great  deal  has  been  written  on  the  theory  . 
OF  retaining-walls,  and  many  theories,  involving  elaborate  calculations  for 
determining  the  conjugate  pressures  in  the  earth-backing  behind  the  wall, 
have  been  developed  for  computing  the  thrust  which  a  bank  of  earth  exerts 
against  such  a  wall,  and  for  determining  the  form  of  wall  which  offers  the  great- 
est resistance  with  the  least  amount  of  material.  There  are  so  many  condi- 
tions, however,  upon  which  the  thrust  exerted  by  the  backing  depends,  such  as 
the  cohesion  of  the  earth,  the  dryness  of  the  material,  the  mode  of  backing  up 
the  wall,  etc.,  that  in  practice  it  is  impossible  to  determine  the  exact  thrust  which 
will  be  exerted  against  a  wall  of  a  given  height.  It  is  necessary,  therefore,  in 
designing  retaining-walls,  to  be  guided  by  experience  rather  than  by  theory. 
As  the  theories  of  retaining-walls  are  so  vague  and  unsatisfactory,  we  shall  not 


256 


Retaining-Walls,  Breast- Walls  and  Vault-Walls      Chap.  4 


include  any  in  this  work,  but  offer,  rather,  such  suggestions,  rules  and  cautions 
as  have  been  established  by  practice  and  experience.  A  construction  sug- 
gested from  empirical  data,  which  has  been  found  to  work  well  in  practice,  for 
determining  the  thrust  of  the  earth-backing  and  the  dimensions  of  the 
WALL  to  properly  resist  this  thrust,  is  given  on  page  257. 

In  designing  a  retaining-wall  the  backing  as  well  as  the  wall  itself  must  be 
carefully  considered.  The  tendency  of  the  backing  to  slip  is  very  much 
less  when  the  material  is  in  a  dry  state  than  when  it  is  saturated  with  water, 
and  hence  every  precaution  should  be  taken  to  secure  good  drainage.  Besides 
surface-drainage,  there  should  be  openings  left  in  the  wall  for  the  water  which 
may  accumulate  behind  it  to  escape. 

The  manner  in  which  the  material  is  filled  against  the  wall,  also,  affects  the 
stability  of  the  backing.  If  the  ground  is  made  irregular,  with  steppings,  as 
shown  in  Pig.  8,  and  the  earth  well  rammed  in  layers  inclined  down  from 
the  wall,  the  pressure  will  be  very  trifling,  provided  that  attention  is  paid  to 
drainage.  If,  on  the  other  hand,  the  earth  is  tipped  in  the  usual  manner,  in 
layers  sloping  down  towards  the  wall,  almost  the  full  pressure  of  the  earth 
will  be  exerted  against  it,  and  it  must  be  made  strong  enough  to  withstand 
such  pressure. 

Slopes  of  Repose  and  Angles  of  Repose.  Cases  may  occur  in  practice  in 
which  the  conditions  are  not  such  as  are  shown  in  Fig.  8,  which  shows  only  a 
limited  amount  of  fill  or  new  material  put  in  behind  the  wall  on  top  of  the 
original  slope  of  the  grade;  cases  in  which,  on  the  contrary,  the  wall  has  been 
built  on  the  natural  surface  of  the  ground  with  a  view  to  creating  an  entirely 
new  terrace  or  embankment  and  where  all  the  material  back  of  the  wall  is  new. 

All  of  this  material  does  not  beat  upon  the  wall  and  tend  to  overturn  it,  for 
sand  or  loose  earth  taken  from  an  excavation  and  deposited  on  the  surface  of 
the  ground  does  not  spread  itself  out  like  a  liquid  but  piles  up  in  a  mound.  This 
PILING  UP  is  due  to  the  friction  developed  between  the  separate  particles  as 
they  slide  one  over  the  other  while  being  dumped.  This  phenomenon  is  observed 
in  the  action  of  any  solid  material  broken  up  into  separate  particles;  and  although 
the  SLOPE  OF  THE  SIDES  of  such  a  mound  varies  with  different  materials,  it  is, 
in  general,  the  same  for  the  same  material.  The  angle  of  this  slope  is  known  as 
the  ANGLE  OF  NATURAL  SLOPE  of  the  material.  This  angle  for  the  materials  gen- 
erally used  for  fill  is  given  in  the  following  Table  II. 


Table  11.     Slopes  of  Repose,  Angles  of  Repose  and  Weights  of  Loose 
Materials 


Kind  of  earth 


Slope  of 
repose* 


Angle  of 
repose 


Weight  in 
lb  per  cu  ft 


Sand,  clean 

Sand  and  clay 

Clay,  dry 

Clay,  damp,  plastic 

Gravel,  clean 

Gravel  and  clay 

Gravel,  sand  and  clay  . 

Soil 

Soft  rotten  rock 

Hard  rotten  rock 

Bituminous  cinders. . . 
Anthracite  ashes 


1.5  to  I 
1.33  to  I 
1.33  to  I 

2         to  I 

1.33  to  I 
1.33  to  I 
1.33  to  I 
1.33  to  I 
1.33  to  I 
I  to  I 
I  to  I 
I        to  I 


33"  41' 

36  53 

36  53 

26  34 

36  53 

36  53 

36  53 

36  53 

36  53 

45  00 

45  00 


90 
100 
100 
100 
100 
100 
100 
100 
no 
100 
65 
30 


*  The  slope  is  that  of  horizontal  to  vertical  projection. 


Retaining-Walls  257 

Pressures  on  Retaining-Walls.  Even  under  the  conditions  shown  in  Fig.  8, 
Dnly  a  part  of  the  fiUed-in  material  will  exert  a  pressure  on  the  wall.  It  would 
be  natural  to  suppose  that  the  part  of  the  fill  exerting  pressure  on  the  wall 
would  be  determined  by  the  angle  of  natural  slope,  all  material  from  a 
natural  horizontal  grade  up  to  this  angle  being  able  to  take  care  of  itself,  and 
all  the  material  above  the  angle  needing  the  wall  to  hold  it  in  place.  Experi- 
ment shows  that  this  is  not  strictly  true,  for  as  the  earth  settles  into  place  certain 
forces  of  internal  elasticity  and  tendencies  toward  a  state  of  equilibrium 
come  into  play  creating  internal  stresses  which  produce  the  conjugate 
pressures  already  referred  to.  The  exact  determination  of  these  internal 
STRESSES  demands  relatively  complicated  calculations  which  would  be  out  oi 
place  in  a  book  of  this  character.  The  construction  given  in  the  following 
paragraphs  for  determining  the  slope  of  the  cleavage-plane,  between  that 
part  of  the  backing  which  sustains  itself  and  the  triangular  fill  which  actually 
bears  on  the  wall,  is  sufficiently  accurate,  however,  for  all  practical  purposes. 

The  Slope  of  the  Cleavage-Plane.  The  following  construction  (Figs.  9 
and  10),  based  upon  empirical  data,  for  determining  first,  the  prism  of  earth 


Fig.  9.     Method  of  Determining  the  Prism  of  Earth 

which  exerts  pressure  on  the  back  of  the  wall  and  secondly,  the  proper  dimen- 
sions for  the  wall,  has  been  found  to  work  well  in  practice,  when  certain  neces- 
sary precautions  are  taken.  These  include  proper  drainage  behind  the  wall, 
proper  ramming  of  the  fill  and  eflScient  bracing  of  the  wall  during  its  construc- 
tion. 

In  the  calculations  to  determine  the  pressure  of  the  earth  and  the  weight  of 
the  wall,  a  shce  i  ft  thick  is  first  considered.  Then  the  area  of  the  triangle 
ABE  is  proportional  to  the  volume  and  weight  of  the  slice  of  earth  causing 
pressure  on  the  wall,  and  as  the  area  "of  the  cross-section  of  the  wall  is  propor- 
tional to  the  volume  and  weight  of  the  shce  of  the  wall  itself. 

To  determine  the  prism  of  earth  which  exerts  pressure  against  the  back  of 
the  wall,  decide  first  upon  the  batter  to  be  given  to  the  back  of  the  wall.  In 
this  case  it  made  8o°  with  the  horizontal,  an  angle  slightly  greater  than  that 
advised  by  Trautwine.  Draw  BH  (Fig.  9),  making  an  angle  ABH,  equal  to 
2  0,  with  the  back  of  the  wall;  continue  this  Une  until  it  meets  at  H  the  slope 
of  the  surface  of  the  earth  back  of  the  wall,  prolonged.  From  A,  the  top  of  the 
wall,  draw  A  J  parallel  to  BF  the  natural  slope  of  the  fill.  This  has  been  taken 
at  35°,  as  a  fair  average  value.  Erect  a  perpendicular  from  the  middle  of  JB, 
?.nd  with  any  point,  0,  as  a  center,  on  this  perpendicular,  describe  an  arc  passing 


258 


Retaining-Walls,  Breast-Walls  and  Vault- Walls       Chap.  4 


through  J  and  B.  Draw  HO  and  bisect  it,  and  with  0'  as  a  center  and  00'  as 
a  radius,  describe  the  arc  cutting  the  arc  J  KB  at  K.  Again,  with  a  radius  HK 
and  with  H  as  center,  describe  the  arc  KL,  and  finally,  from  L,  draw  LE  parallel 
CO  J  A .    The  intersection  of  this  line  with  the  surface  of  the  ground  locates  the 


Fig.  10.    Method  of  Determining  Dimensions  of  Retaining-wall 


point  E.  The  line  EB  is  the  line  of  the  cleavage-plane  which  separates  the 
part  of  the  backing  which  bears  against  the  wall  from  the  part  which  exerts  no 
lateral  pressure. 

Having  found  the  dimensions  of  the  volume  of  earth,  the  thrust  of  which 
must  be  resisted  by  the  wall,  the  next  step  is  to  determine  what  the  dimensions 
OF  the  wall  should  be  to.  properly  resist  this  thrust.  Usually  one  or  two  trials 
are  necessary  before  the  proper  solution  of  the  problem  is  found.  In  the  ex- 
ample given,  a  preliminary  trial  was  made  with  a  thickness  at  the  base  of  4  ft. 
This  construction  is  shown  with  the  green  lines  (Fig.  10). 

After  drawing  the  triangle  representing  the  base  of  the  prism  of  earth,  find 
its  center  of  gravity,  G  (Chap.  VI).  From  this  point  draw  two  normals,  one  to 
the  back  of  the  wall  and  the  other  to  the  line  of  the  cleavage-plane.  Draw 
the  two  lines,  GM  and  GN,  making  angles  <t>  with  these  normals.  Lay  off  ver- 
tically from  the  center  of  gravity,  at  any  convenient  scale  of  so  many  square 


Retaining-Walls  259 

inches  to  the  linear  inch,  the  area  of  the  triangle  of  the  base  of  the  prism,  the 
area,  as  already  explained,  being  proportional  to  the  volume  of  the  prism  and 
its  weight.  Resolve  this  weight-line  along  the  two  hnes  GM  and  GN  (Chap.  . 
VI).  This  will  give  the  magnitude  and  direction  of  the  thrust  or  pressure 
of  the  earth  against  the  wall.  Apply  this  pressure  at  a  point  on  the  back  of  the 
wall  one-third  of  the  distance  from  the  bottom,  as  shown  by  the  arrow.  This 
is  the  force  which  may  tend  to  overturn  the  wall  and  which  tends  to  make  it 
SLIDE  along  the  base.    (See  Fig.  6.) 

To  resist  these  overturning  and  sliding-tendenctes,  the  weight  of  the  wall 
combined  with  the  pressure  of  the  earth  behind  it  should  produce  a  resultant 
which  satisfies  the  following  conditions.  First,  its  magnitude  should  not 
be  great  enough  to  cause  a  unit  pressure  on  the  foundation-bed  greater  than 
it  can  safely  bear;  secondly,  it  should  pass  within  the  middle  third  of  the  base 
so  that  the  stress  over  the  entire  area  of  the  base  will  be  a  compressive  stress; 
and  thirdly,  it  should  make  an  angle  with  a  normal  to  the  plane  of  the  founda- 
tion-bed not  greater  than  the  angle  of  friction  between  the  stone,  brickwork, 
concrete,  or  other  masonry  of  the  footings  and  the  sand,  clay,  or  rock  of  the  foun- 
dation-bed. 

In  order  to  determine  these  conditions,  the  center  of  gravity  of  the  cross- 
section  of  the  wall  must  be  detcr.nined  and  a  vertical  line  drawn  through  this 
point  until  it  intersects  the  line  of  the  earth-thrust  produced.  It  is  at  this 
intersection  of  the  lines  of  action  of  the  two  forces  that  their  resultant 
acts.  To  find  the  center  of  gravity  of  the  cross-section  of  the  wall,  the  method 
of  dividing  the  trapezoid  into  two  triangles  has  been  followed,  the  center  of 
gravity  of  each  triangle  being  found  and  these  two  points  being  joined  by  a  line. 
The  intersection  of  this  line  with  the  median  line  drawn  between  the  base  and 
the  top  of  the  wall  is  the  center  of  gravity  of  the  trapezoid.  In  this  example, 
for  convenience,  the  scale  used  for  the  composition  of  the  forces  of  the  pressure 
of  the  earth  and  the  v/cight  of  the  wall  is  one-half  the  scale  used  for  the 
resolution  of  the  forces  representing  the  weight  of  the  earth-prism. 

In  the  first  trial,  shown  by  the  green  lines,  the  first  and  third  conditions  neces- 
sary to  insure  stability  are  fulfilled;  but  the  second  is  not,  the  resultant  pass- 
ing outside  the  middle  third  of  the  base.  This  indicates,  theoretically,  a 
sUght  tensile  stress  or  a  tendency  for  the  joints  at  the  back  of  the  wall  to  open. 
Another  trial,  therefore,  is  shown  with  the  red  Hnes,  the  thickness  of  the  wall 
being  increased  as  shown  by  the  rectangle  CC'D'D.  In  this  second  trial  the 
weight  of  the  wall  is  necessarily  increased  while  the  earth-thrust  remains 
the  same.  As  in  this  case  the  resultant  passes  within  the  middle  third,  it  is 
concluded  that  a  wall  of  these  dimensions,  5  ft  base  by  10  ft  height  and  with 
an  80°  batter,  will  be  safe  and  will  properly  resist  the  thrust  of  the  earth- 
backing. 

Details  of  Construction.  Retaining-walls  are  generally  built  with  a  batter- 
ing, that  is,  a  sloping  face,  as  walls  of  this  form  are  the  strongest  for  a  given 
amount  of  material;  and  if  the  courses  are  inclined  down  towards  the  back,  the 
tendency  to  slide  on  each  other  will  be  resisted,  and  it  will  not  be  necessary  to 
depend  upon  the  adhesion  of  the  mortar.  The  importance  of  making  the  resist- 
ance independent  of  the  adhesion  of  the  mortar  is  obviously  very  great,  as  it 
wou)d  otherwise  be  necessary  to  delay  the  backing  up  of  the  wall  until  the  mortar 
had  thoroughly  set,  which  might  require  several  months. 

In  brickwork  it  is  advisable  to  let  every  third  or  fourth  course  below  the  frost- 
line  project  an  inch  or  two.  This  increases  the  friction  of  the  earth  against 
the  back  and  causes  the  resultant  of  the  forces  acting  behind  the  wall  to  become 
more  nearly  vertical,  and  to  fall  farther  within  the  base,  increasing  the  stabiUtyc, 


260 


Retaining-Walls,  Breast-Walls  and  Vaiilt-Walls       Chap.  4 


It  also  conduces  to  strength  to  make  the  courses  of  varying  heights  throughout 
the  thickness  of  the  wall,  and  to  have  some  of  the  stones,  especially  those  near 
the  back,  sufficiently  high  to  extend  through  two  or  three  courses.  By  this 
means  the  whole  masonry  becomes  more  effectually  interlocked  or  bonded 
together  as  one  mass  and  is  less  liable  to  bulge.  The  courses  of  masonry  are 
often  laid  with  their  beds  sloping  in,  as  in  Fig.  15,  to  overcome  the  tendency 
of  the  courses  to  slide  on  each  other. 

Where  the  ground  freezes  to  a  great  depth,  the  back  of  the  wall  should  be 
SLOPED  FORWARD  for  three  or  four  feet  below  its  top  surface,  as  at  OC  (Fig.  11), 


Fig.  11. 


Retaining-wall  for  Deep- 
freezing Earth 


Fig.  12.  Retaining-wall 
with  Rectangular  Cross- 
section 


-8-0 ^ 


Fig.  13.  Retaining- 
wall  with  Triangular 
Cross-section 


and  this  slope  should  be  quite  smooth,  so  as  to  lessen  the  hold  of  the  frost  and 
prevent  displacement. 

Figs.  12,  13,  14  and  15  show  the  approximate  relative  vertical  sectional 
AREAS  of  walls  of  different  shapes  that  would  be  required  to  resist  the  pressure 
of  a  bank  of  earth  12  ft  high.  The  first  three  examples  are  calculated  to  --^sist 
the  maximum  thrust  of  wet  earth,  while  the  last  shows 
the  modified  form  usually  adopted  in  practice. 

Notes   on  the    Thickness  of 

Retaining- Walls.     As   has  been 

stated,  about  the   only   practical 

rules  for   retaining-walls   are   the 

empirical    rules   based    upon    ex- 
perience and   tests.     Trautwine* 

gives  the  following  Table  III  for 

the    thickness    at    the    base    of 

vertical    retaining-walls    with    a 

sand    backing    deposited    in   the 

usual  manner.     The  first  column 

contains   the  vertical  height  CD 

(Fig.  16)  of  the  earth  as  compared 

with  the  vertical  height  of  the 
wall,  AB.  The  latter  is  assumed  to  be  i,  so  that  the  table  begins  with  a 
backing  of  the  same  height  as  the  wall.  These  vertical  walls  may  be  battered 
to  any  extent  not  exceeding  iH  in  to  i  ft,  or  i  in  8,  without  affecting  their 
stability  and  without  increasing  the  base. 

If  the  wall  is  built  as  in  Fig.  17,  with  the  ground  practically  level  with  the 
top,  the  top  of  the  wall  should  be  not  less  than  18  in  thick,  and  the  thicknesses 
at  a,  a,  etc.,  just  above  each  step,  should  be  from  one-third  to  two-fifths  of  the 

*  The  Civil  Engineer's  Pocket-Book,  John  C.  Trautwine. 


k~    70---^ 

Fig.  14.  Retaining-wall 
with  Triangular  Cross- 
section 


Fig.  15.  Retaining- 
wall  with  Stepped 
Back 


Retaining-Walls 

Table  III.     Proportions  of  Retaining-Walls 

(Thickness  of  wall  at  the  base  in  parts  of  the  height,  AB,  Fig.  16) 


261 


Total  height  of  the  earth 

Wall  of  cut 

Wall  of  rubble  or 

Wall  of  good. 

compared  with  the  height 
of  the  wall  above  ground 

stone  in  mortar 

brick,  good  mortar 

dry  rubble 

I 

0.35 

0.40 

0.50 

I.I 

0.42 

0.47 

0.57 

1.2 

0.46 

0.51 

0.61 

1.3 

0.49 

0.54 

0.64 

1.4 

o.si 

0.56 

0.66 

1.5 

0.52 

0.57 

0.67 

1.6 

0.54 

0.59 

0.69 

1.7 

0.55 

0.60 

0.70 

1.8 

0.56 

0.61 

0.71 

2 

0.58 

0.63 

0.73 

2.5 

0.60 

0.65 

0.7s 

3 

0.62 

0.67 

0.77 

4 

0.63 

0.68 

0.78 

6 

0.64 

0.69 

0.79 

14 

0.65 

0.70 

0.80 

25 

0.66 

0.71 

0.81 

or  more 

0.68 

0.73 

0.83 

height  from  the  top  of  the  wall  to  each  of  these  levels.  If  the  earth  is  banked 
above  the  top  of  the  wall,  the  thicknesses  should  be  increased  as  indicated  by 
the  table  given  above.  If  built  upon  ground  that  is  aflected  by  frost  or  sur- 
face-water, the  footings  should  be  carried  sufficiently  below  the  surface  of  the 
ground  at  the  base  to  insure  against  heaving  or  settling. 


Fig.    16. 


Retaining-wall    with    Raised    Sand 
Backing 


Fig.  17.  Retaining-wall  with  Stepped 
Back 


Rainforced-Concrete  Retaining-Walls.  With  the  constantly  increasing 
use  of  REINFORCED  CONCRETE  for  various  purposes,  there  has  come,  also,  the 
construction  of  retaining-walls  in  this  material.  Figs.  18,*  19  *  and  20  * 
show    three   designs   by    A.    L.    Johnson    for    retaining-walls    to    satisfy   the 

*  Plain  and  Reinforced  Concrete,  Taylor  and  Thompson. 


262 


Retaining-Walls,  Breast-Walls  and  Vault-Walls       Chap.  4 


requirements  of  banks  5,  10  and  20  ft  high.  The  wall  shown  in  Fig.  20  is 
reinforced  at  intervals  with  counterforts.  The  walls  themselves  in  Figs.  18 
and  19  act  as  caniilever  beams.  The  footings,  in  all  three  cases,  are 
,subjected   to   two   principal  external   forces,    the   resultant   of   the  resisting 


/I  "anchor-bolts 


Fig.    18.      Reinforced-concrete 
Retaining-wall,  5  ft  High 


Fig.  19.     Reinforced-concrete  Retaining-wall,  10 
ft  High 


upward  pressure  of  the  foundation-bed  and  the  resultant  of  the  down- 
ward pressures  of  the  fill.  In  Fig.  20  the  coping  acts  as  a  beam  fixed  at 
BOTH  ENDS,  with  a  span  equal  to  the  distance  between  the  counterforts, 
and  loaded  with  the  proper  proportion  of  the  load  due  to  the  pressure  of 
the  fill  behind  the  wall  and  transmitted  to  the  coping  by  the  wall.  The  wall 
itself  in  this  case  acts  as  a  ^'loor-slab  supported  on  all  four  sides  and  subjected 
to  an  approximately  evenly  distributed  load.  The  counterforts  arc  in  tension. 
The  MAXIMUM  BENDING  MOMENTS  for  thcsc  various  cases  can  be  determined 
(Chapter  IX)  and  the  necessary  dimensions  and  reinforcement  to  be  pro- 
vided decided  by  the  rules  given  in  Chapter  XXIV. 


3.   Breast-Walls 

Breast-Walls.  Where  the  ground  to  be  supported  is  firm,  and  the  strata  are 
horizontal,  the  ofBce  of  a  breast- wall  (Fig.  8)  is  more  to  protect  than  to  sustain 
the  earth.  It  should  be  borne  in  mind  that  a  trifling  force  skilfully  applied  to  un- 
broken ground  will  keep  in  its  place  a  mass  of  material,  which,  if  once  allowed  to 
move,  would  crush  a  heavy  wall.     Great  care,  therefore,  should  be  taken  not  to 


Vault-WaUs  263 

eipose  the  newly  opened  ground  to  the  influe^xe  of  air  and  water  longer  than  is 
requisite  for  sound  work,  and  to  avoid  leaving  the  smallest  space  for  motion 
between  the  back  of  the  wall  and  the  ground.  The  strength  of  a  l3reast-wall  must 
be  proportionately  increased  when  the  strata  to  be  supported  incline  down 


Fig.  20.     Reinforced-concrete  Retaining-wall  with  Counterforts  and  Apron 

towards  the  wall;  where  they  incline  down  from  it,  the  wall  need  be  httle  more 
than  a  thin  facing  to  protect  the  ground  from  disintegration.  The  preserva- 
tion of  the  NATURAL  DRAINAGE  is  One  of  the  most  important  points  to  be 
attended  to  in  the  erection  of  breast-walls,  as  upon  this  their  stabihty  in  a 
great  measure  depends.  No  rule  can  be  given  for  the  best  way  to  do  this;  it 
is  a  matter  for  attentive  consideration  in  each  particular  case. 


4.   Vault- WaUs 

Vault- Walls.  In  large  cities  it  is  customary  to  utilize  the  space  under  the 
sidewalk  for  storage  or  other  purposes.  This  necessitates  a  wall  at  the  curb- 
line  to  hold  back  the  earth  and  the  street-pressures  and  also  the  weight  of  the 
sidewalk.  Where  practicable  the  space  should  be  divided  by  partition-walls 
about  every  lo  ft,  and  when  this  is  done  the  outer  wall  may  be  advantageously 
built  of  hard  bricks  in  the  form  of  arches,  as  shown  in  Fig.  21.     The  thickness 


264 


Retaining-Walls,  Breast- Walls  and  Vault-Walls       Chap.  4 


of  the  arch  should  be  at  least  i6  in  for  a  depth  of  9  ft  and  the  rise  of  the 
arch  from  one-eighth  to  one-sixth  of  the  span.  If  partitions  are  not  practi- 
cable, each  sidewalk-beam  may 
be  supported  by  a  heavy  I-beam 
column,  with  either  flat  or  seg- 
mental arches  between,  of  either 
brick  or  concrete.  Fig.  22  * 
shows  a  detail  of  the  outer  walls 
of  the  vault  under  the  sidewalk 
around  the  Singer  building,  New 
York  City.  These  walls  consist 
of  a  core  formed  by  two-ring 
brick  arches  with  vertical  axes, 
built  between  the  flanges  of 
8-in  vertical  steel  I  beams 
spaced  about  5  ft  apart  and 
bedded  at  the  bottom  in  a  con- 
crete footing.  Their  tops  are 
joined  by  6-in  horizontal  I  beams  and  braced  laterally  by  the  sidewalk-beams, 
5  ft  apart.     The  arches  themselves  are  segmental,  with  a  rise  of  about  6.  in. 


Vault-wall  with  Partitions 


Fig.  22.     Vault-walls  of  Singer  Building,  New  York  City 

and  are  built  up  solid  against  an  8-in  outside  face-wall.  A  4-in  plain  curtain 
wall  is  built  inside  against  the  flanges  of  the  vertical  beams,  inclosing  seg- 
mental air-chambers  in  front  of  each  arch. 

*  From  The  Engineering  Record,  Feb.  26,  1898.   ' 


Crushing  Strength  of  Stonework,  Brickwork,  Bricks  265 


CHAPTER   V 

STRENGTH  OF  BRICK,   STONE,   MASS-CONCRETE  AND 
MASONRY 

By 
THOMAS   NOLAN 

PROFESSOR   OF   ARCHITECTURAL   CONSTRUCTIOI«f,    UNIVERSITY   OF   PENNSYLVANIA 

1.    Crushing  Strength  of  Stonework,  Brickwork,  Bricks,  etc. 

Stresses  in  Masonry.  By  the  term  strength  of  masonry  is  generally 
meant  its  resistance  to  a  direct  compressive  force  or  load,  and  this  is  the  only 
direct  stress  to  which  masonry  should  be  subjected.  Stone  lintels  and  footings 
may  be  subjected  to  a  transverse  or  bending  stress,  but  they  can  hardly  be 
included  in  the  term  masonry,  as  they  consist  of  single  pieces.  There  are  also 
tendencies  to  bend  and  to  split  apart  in  brick  walls  and  piers,  as  they  are  usually 
high  in  proportion  to  their  lateral  dimensions,  but  the  stresses  thus  developed 
cannot  be  accurately  determined  and  should  be  avoided  as  much  as  possible. 
It  is  impossible  to  fix  values  for  the  strength  of  brickwork  or  stonework  with 
anything  like  the  exactness  possible  for  wooden  or  steel  hiembers,  for  the  reason 
that  there  is  not  only  a  great  variation  in  the  strength  of  different  kinds  of 
brick  and  stone,  even  when  taken  from  the  same  kiln  or  quarry,  but  the  strength 
of  walls  and  piers  is  also  greatly  affected  by  the  kind  and  quality  of  the  mortar 
used,  the  way  in  which  the  work  is  built  and  bonded,  and  the  amount  of  moisture 
in  the  materials  when  they  are  laid.  All  that  can  be  done,  therefore,  is  to  give 
values  which  will  be  safe  for  the  different  kinds  of  masonry  built  in  the  usual 
manner. 

Working  Compressive  Strength  of  Masonry.  The  building  laws  of  most 
of  the  larger  cities  of  this  country  specify  the  maximum  loads  per  square  foot 
allowed  to  be  placed  upon  different  kinds  of  masonry,  and  these  laws  must  govern 
the  architects  in  such  cities.  When  there  is  no  restriction  of  this  kind.  Table  I 
gives  a  pretty  good  idea  of  the  maximum  loads  which  it  is  safe  to  put  upon  the 
different  kinds  of  work  mentioned.  Table  II  gives  the  maximum  safe  loads 
specified  in  the  building  laws  of  several  cities,  and  the  remaining  tables  of  the 
chapter  give  records  of  numerous  tests  made  to  determine  the  ultimate  com- 
pressive strengths  of  various  kinds  of  bricks,  building  stones,  mortars  and  con- 
cretes, and  are  of  value  in  determining  the  safe  loads  for  special  cases.  In 
determining  the  safe  compressive  resistance  of  masonry  from  tests  on  the  ulti- 
mate compressive  strength  of  work  of  the  same  kind,  a  factor  of  safety  of  at 
least  lo  should  be  allowed  for  piers  and  20  for  arches. 

Table  I.     Safe  Working  Loads  for  Masonry 

Brickwork  IN  Walls  or  Piers 

Tons  per  square  foot 

Eastern  Western 

Red  brick  in  lime  mortar 7  5 

Red  brick  in  hydraulic-lime  mortar ...  6 

Red  brick  in  natural-cement  mortar,  1:3 10  8 

Arch  or  pressed  bricks  in  lime  mortar 8  6 

Arch  or  pressed  bricks  in  natural-cement  mortar 12  9 

Arch  or  pressed  bricks  in  Portland-cement  mortar.  .. ,             15  12H 


266      Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry     Chap.  5 

Piers  exceeding  in  height  six  times  their  least  lateral  dimensions  should  be 
increased  4  in  in  lateral  dimensions  for  each  additional  6  ft. 

Stonework 

Tons  per 
square  foot 

Rubble  walls,  irregular  stones 3 

Rubble  walls,  coursed,  soft  stone 2\-2 

Rubble  walls,  coursed,  hard  stone 5  to  16 

Dimension-stone,  squared,  in  cement  mortar: 

Sandstone  and  limestone 10  to  20 

Granite 20  to  40 

Dressed  stone,  with  ?4-in  dressed  Joints,  in  Portland-cement  mortar: 

Granite 60 

Marble  or  limestone,  best 40 

Sandstone 30 

The  height  of  columns  should  not  exceed  eight  times  the  least  diameter,  unless 
the  least  diameter  is  sutficiently  greater  than  necessary  for  the  strength  of  the 
material  used. 

Concrete  * 

Portland-cement  mortar,  i  :  8,  6  months,  10  tons;   i  year,  15  to  20  tons 
Natural-cement  mortar,  i  :  6,  6  months,  3  tons;    i  year,  5  to  8  tons 

Hollow  tile 
Safe  loads  per  square  inch  of  effective  bearing  parts 

Hard  fire-clay  tiles 80  lb 

Hard  ordinary  clay  tiles 60  lb 

Porous  terra-cotta  tiles 40  lb 

Mortar 

In  K'-in  joints,  3  months  old 

Tons  per 
square  foot 

Portland-cement  mortar,  1:4 40 

Natural-cement  mortar,  1:3 13 

Lime  mortar,  best 8  to  10 

Best  Px>rt land-cement  mortar,  i  :  2,  in  H-ln.  joints  for  bedding 

iron  plates 70 

The  values  given  above  are  generally  very  conservative  The  leading  archi- 
tects and  engineers  of  Chicago  recommended  for  that  city  in  1908  the  follow- 
ing SAFE  WORKING  PRESSURES  for  brick  and  stone  masonry  and  concrete: 

Common  brick  of  crushing  strength  equal  to  i  800  lb  Lb  per  Tons  per 

per  sq  in:  sq  in  sq  ft 

In  lime  mortar 100  7H 

In  lime-and-cement  mortar 125  9 

In  natural-cement  mortar 150  loVr^ 

In  Portland-cement  mortar 175  l2^ 

*  See  pages  283  to  287. 


Crushing  Strength  of  Stonework,  Brickwork,  Bricks  267 

Select,  hard,  common  brick,  of  crushing  strength  equal         Lb  per     Tons  per 

to  2  500  lb  per  sq  in:  sq  in  sq  ft 

In  I  part  Portland  cement,  i  lime-paste  and  3  sand.  175  12Y5 

In  I  :  3  Portland-cement  mortar ...  200  14^^ 

Pressed  and  sewer-brick,  of  crushing  strength  equal  to 
5  000  lb  per  sq  in: 

In  I  :  3  Portland-cement  mortar. 250  18 

Paving  brick,  in  i  :  3  Portland-cement  mortar 350  251,^ 

Concrete,  natural  cement,  1:2:5 :....  150  10% 

Concrete,  Portland  cement,  1:3:6,  machine-mixed.  .  300  21% 

Concrete,  Portland  cement,  1:3:6,  hand-mixed 250  18 

Concrete,  Portland  cement,  1:2:4,  machine-mixed.  .  400  28H 

Concrete,  Portland  cement,  1:2  :  4,  hand-mixed 350  25 H 

Rubble,  uncoursed,  in  lime  mortar 60  4H 

Rubble,  uncoursed,  in  Portland-cement  mortar 100  yVi 

Rubble,  coursed,  in  lime  mortar 120  8% 

Rubble,  coursed,  in  Portland-cement  mortar. 200  14H 

Ashlar,  Hmestone,  in  Portland-cement  mortar 400  28H 

Ashlar,  granite,  in  Portland-cement  mortar 600  43  V^ 


Table  II.    Comparison  of  Building  Laws* 


Materials 


Granite,  cut • 

Marble  and  limestone,  cut 

Sandstone,  hard  cut 

Hard-burned  brick  in  Portland- 
cement  mortar 

Hard-burned  brick  in  natural- 
cement  mortar 

Hard-burnsd  brick  in  cement-and- 
lime  mortar 

Hard-burned  brick  in  lime  mortar 

Pressed  brick  in  Portland-cement 
mortar 

Pressed  brick  in  natural-cement 
mortar 

Rubble  stone  in  natural-cement 
mortar 

Portland-cement  concrete  in  foun- 
dations, I  :  2  14 

Natural-cement  concrete  in  foun- 
dations, I  :  2  :  4 


Bos- 

Buf- 

New- 

Chi- 

St. 

Phil- 
adel- 
phia, 

ton, 

falo, 

York, 

cago, 

Louis, 

191S 

1909 

1917 

1916 

1907 

1914 

Den 

ver. 
1898 


Allowable  pressures  in  tons  per  sq  ft 


60-72 
40 
30 


43-5C 
29 

18 

IS 

II  K2 


8t 
36 

15 


43 
29 
29 


18-28! 

loM!! 


*  See  important  notes  on  page  287  relating  to  various  building  laws  and  working  loads 
for  masonry,  etc. 

t  In  Portland-cement  mortar. 

t  In  Portland-cement  mortar,  lo;  in  lime-cement  mortar,  7. 

§  According   to   mixture. 

IJ  I  :  2  :  5  mixture. 

Brick  Piers.    As  a  rule  brickwork  is  subject  to  its  full  safe  resistance  only 
when  used  in  piers,  and  in  small  sections  of  walls,  under  bearing-plates.    In  the 


268      Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry     Chap.  5 

latter  case  but  a  few  courses  receive  the  full  load,  and  hence  a  greater  unit 
stress  may  be  allowed  than  for  piers.  Values  for  computing  the  area  of  bearing- 
plates  are  given  in  Chapter  XIII.  Aside  from  the  quaUty  of  the  work  and 
materials  the  two  elements  which  most  influence  the  strength  of  brick  piers 
are  the  ratio  of  height  to  least  lateral  dimension  and  the  method  of  bonding. 
When  the  height  of  a  brick  pier  exceeds  six  times  its  least  lateral  dimension  the 
load  per  square  foot  should  be  reduced  from  the  values  given  in  Table  I. 

Formulas  for  the   Safe  Strength  of  Brick  Piers  exceeding  six  diameters 

in  height.  From  the  records  of  numerous  tests  on  the  strength  of  brick  piers, 
from  some  formulas  published*  by  Ira  O.  Baker,  and  also  from  personal  obser- 
vation, Mr.  Kidder  deduced  the  following  formulas  for  the  maximum  working 
loads  for  first-class  brickwork  in  piers  whose  height  exceeds  six  times  the  least 
lateral  dimension. 

For  piers  laid  with  rich  lime  mortar: 

Safe  load  per  square  inch  =  i  lo  —  5  11 1 D  (i) 

For  piers  laid  with  i  :  2  natural-cement  mortar: 

Safe  load  per  square  inch  =  140  —  5H  B.ll>  (2) 

For  piers  laid  with  i  :  3  Portland-cement  mortar: 

Safe  load  per  square  inch  =  200  —  6  EJD  (3) 

H  representing  the  height  in  feet,  and  D  the  least  lateral  dimension  in  feet.f 

For  a  pier  20  ft  high  and  2  ft  square  these  formulas  will  reduce  the  safe  load 
to  4.3  tons  per  sq  ft  for  lime  mortar,  6.1  tons  for  natural-cement  mortar  and 
10  tons  for  Portland-cement  mortar.  No  pier  over  8  ft  high  should  be  less  than 
1 2  by  1 2  in  in  cross-section  and  when  from  6  to  8  ft  high  piers  should  be  at  least 
8  by  12  in  in  cross-section. 

The  following  is  the  Chicago  law  (1914):  "Isolated  piers  of  concrete,  brick 
or  masonry  shall  not  be  higher  than  six  times  their  smallest  dimensions  unless 
the  above  unit  stresses  |  are  reduced  according  to  the  following  formula: 

P  =  C(i.25-///2oZ))  (4) 

in  which  P  is  the  reduced  allowed  unit  load,  C  the  unit  stress  above  referred 
to,  E  the  height  of  the  pier  in  feet  and  D  the  least  dimension  of  the  pier  in  feet. 
No  pier  shall  exceed  in  height  twelve  times  the  least  dimension.  The  weight 
of  the  pier  shall  be  added  to  other  loads  in  computing  the  load  on  the  pier. " 

Brick  piers  intended  to  carry  more  than  50%  of  the  safe  loads  given  above 
should  not  be  built  in  freezing  weather  nor  with  dry  bricks.  Lime  mortar 
should  not  be  used  for  building  piers  that  are  to  receive  their  full  load  within 
three  months. 

Effect  of  Bond  on  the  Strength  of  Brickwork.  Brick  piers,  loaded  to 
the  point  of  destruction,  always  fail  by  the  splitting  and  bulging  out  of  the 

*  In  the  Brickbuilder,  April,  1898. 

t  For  piers  faced  with  pressed  bricks,  laid  with  joints  \i  in  or  less  in  thickness,  and 
backed  with  common  bricks  in  lime  mortar,  only  the  dimensions  of  the  backing  should  be 
considered  in  figuring  their  strength.  If  the  backing  is  laid  in  cement  mortar  and  the 
face-bricks  are  well  tied  to  the  backing,  the  full  section  of  the  pier  may  be  considered.  For 
piers  veneered  with  stone  or  terra-cotta,  4  in  thick,  only  the  strength  of  the  backing  should 
be  considered. 

\  These  are  in  general  the  "safe  working  pressures"  for  brickwork  previously  mentioned 
as  recommended  by  the  Chicago  architects  and  engineers  in  1908. 


Crushing  Strength  of  Stonework,  Brickwork,  Bricks  269 

piers  themselves,  and  not  by  direct  crushing  of  the  bricks  or  mortar,  showing 
that  piers  are  weakest  in  their  bond  and  in  the  tensile  or  transverse  strengths  of 
the  bricks.  It  is  very  important,  therefore,  to  have  the  brickwork  well  bonded, 
and  all  joints  filled  with  mortar  or  grouted.  The  strength  of  a  brick  pier  in- 
tended to  carry  an  extreme  load  would  probably  be  increased  by  bonding  fre- 
quently with  hoop-iron  in  addition  to  the  regular  brick-bond.* 

Bond-Stones  in  Brick  Piers.  Many  competent  architects  and  builders 
consider  that  the  strength  of  a  brick  pier  is  increased  by  inserting  bond-stones, 
from  5  to  8  in  in  thickness  and  the  full  size  of  the  pier  in  cross-section,  every  3  or 
4  ft  in  height. 

For  example,  the  Building  Laws  for  the  City  of  New  York  (1906)  require 
bond-stones  every  30  in  in  height,  and  at  least  4  in  in  thickness,  to  be  built  into 
brick  piers  which  contain  less  than  9  superficial  feet  of  section,  and  which  sup- 
port any  beam,  girder,  arch,  or  column  on  which  a  wall  rests,  or  lintel  spanning 
an  opening  over  10  ft  and  supporting  a  wall.  The  New  York  laws  allow  per- 
forated steel  or  cast-iron  plates  of  the  full  cross-section  of  the  pier  to  be  used 
instead  of  the  bond-stones.  On  the  other  hand,  there  are  many  first-class 
builders  who  consider  that  bond-stones  in  a  brick  pier  do  more  harm  than  good, 
and  the  author  is  of  the  opinion  that  this  is  generally  the  case.  The  Boston 
Building  Laws  do  not  require  intermediate  bond-stones.  If  bond-stones  are 
used,  they  should  be  bedded  so  as  to  bear  rather  more  heavily  on  the  inner 
portion  of  the  pier  than  on  the  outer  4  in,  for  unless  this  is  done  the  outer  shell 
will  take  most  of  the  load,  and  will  be  likely  to  bulge  away  from  the  core.  A 
pier  which  supports  a  girder  or  column  should  have  a  cap-stone  or  iron  plate  of 
suflScient  strength  to  distribute  the  pressure  over  the  entire  cross-section  of  the 
pier. 

Walls  Faced  with  Stone,  Terra-Cotta,  or  Cement  Blocks.  Brick  walls 
faced  with  blocks  or  ashlar  of  any  material  should  always  have  the  backing  laid 
in  cement  mortar  or  in  cement-and-Hme  mortar,  unless  the  backing  is  very 
thick,  that  is,  30  in  or  more.  The  aggregate  thickness  of  the  mortar  joints  in 
the  backing  is  so  much  greater  than  in  the  facing,  that  any  shrinkage  or  com- 
pression of  the  mortar  tends  to  throw  undue  weight  on  the  facing  and  to  sepa- 
rate it  from  the  backing.  Veneering  of  any  kind  should  be  tied  to  the  backing 
at  least  every  18  in  in  height.  The  Building  Ordinances  of  several  large  cities 
require  that  all  bearing  walls  faced  with  bricks  laid  in  running  bond,  and  all 
walls  faced  with  stone  ashlar  less  than  8  in  thick,  shall  be  of  such  thickness 
as  to  make  the  wall  independent  of  the  facing  conform  to  that  required  for 
unfaced  walls.  Ashlar  8  in  thick  and  bonded  into  the  backing  may  be  counted 
as  part  of  the  thickness  of  the  wall. 

Grouting.f  It  is  contended  by  persons  having  large  experience  in  building 
that  masonry  carefully  grouted,  when  the  temperature  is  not  lower  than  40°  F., 
will  give  the  most  efficient  result.  Many  of  the  largest  buildings  in  New  York 
City  have  grouted  walls.  The  Mersey  docks  and  warehouses  at  Liverpool, 
England,  one  of  the  greatest  pieces  of  masonry  in  the  world,  were  grouted 
throughout.  It  should  be  stated,  however,  that  there  are  many  engineers  and 
others  who  do  not  believe  in  grouting,  claiming  that  the  materials  tend  to 
separate  and  form  layers. 

Crushing  Height  of  Brick  and  Stone.  If  we  assume  that  the  weight  of 
brickwork  is  120  lb  per  cu  ft,  and  that  it  would  commence  to  crush  under  700  lb 

•  The  manner  in  which  brick  piers  fail  is  excellently  shown  by  illustratioos  on  page  79 
of  the  Brickbuilder  for  May,  1896. 

t  See  American  Architect,  July  2J,  1887,  page  11. 


270      Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry    Chap.  5 

per  sq  in,  then  a  wall  of  uniform  thickness  would  have  to  be  840  ft  high  before 
the  bottom  courses  would  commence  to  crush  from  the  weight  of  the  brickwork 
above.  Average  sandstones,  at  145  lb  per  cu  ft,  would  require  a  column  5  950  ft 
high  to  crush  the  bottom  stones,  and  an  average  granite,  at  165  lb  per  cu  ft, 
would  require  a  column  10  470  ft  high.  The  Merchants'  shot-tower  at  Balti- 
more is  246  ft  high,  and  its  base  sustains  a  pressure  of  6y2  tons  per  sq  ft,  the  tons 
being  long  tons  of  2  240  lb.  The  base  of  the  granite  pier  of  Saltash  Bridge  (by 
Brunei),  of  solid  masonry  to  the  height  of  96  ft,  and  supporting  the  ends  of  two 
iron  spans  of  455  ft  each,  sustains  ^y2  tons  per  sq  ft. 

Stone  Piers.  Piers  of  good  strong  building  stone  laid  in  courses  the  full 
cross-sections  of  the  piers,  with  the  top  and  bottom  courses  bedded  true  and 
even,  may  be  built  to  support  very  heavy  loads.  The  height  of  such  piers, 
however,  should  not  exceed  ten  times  the  least  lateral  dimension,  and  when  it 
exceeds  eight  times  the  thickness,  the  load  should  be  reduced.  The  joints 
should  not  exceed  %  in  in  thickness  and  should  be  spread  with  i  :  2  Portland- 
cement  mortar,  kept  back  i  in  from  the  face  of  the  pier  to  prevent  spalling  of 
the  edges.  A  test  of  the  strength  of  a  limestone  pier  12  in  square  is  described 
under  Marbles  and  Limestones,  in  this  chapter.  Rubble-work  should  not  be 
used  for  piers  whose  height  exceeds  five  times  the  least  dimension,  or  in  which 
the  latter  is  less  than  20  in. 

Records  of  Tests  on  the  Crushing  Resistance  of  Bricks.  Table  III 
gives  the  results  of  some  tests  on  bricks,  made  under  the  direction  of  Mr.  Kidder 
in  behalf  of  the  Massachusetts  Charitable  Mechanics'  Association. 


Table  III.    Ultimate  and  Cracking  Strengths  of  Bricks 


Kind  of  brick 


Size  of  test- 
specimen 


Area  of 
face. 


Com- 
menced 
to  crack 

under 

lb  per 
sq  in 


Net 
strength, 

lb  per 
sq  in 


Philadelphia  face-brick . 

Philadelphia  face-brick. 

Philadelphia  face-brick. 

Average 


Cambridge  brick  (Eastern) . 
Cambridge  brick  (Eastern) . 
Cambridge  brick  (Eastern) . 
Cambridge  brick  (Eastern) . 
Average 


Boston  Terra-Cotta  Co.'s  brick. 

Boston  Terra-Cotta  Co.'s  brick. 

Boston  Terra-Cotta  Co.'s  brick. 

Average 


New  England  pressed  brick. 
New  England  pressed  brick. 
New  England  pressed  brick. 
New  England  pressed  brick. 
Average 


Whole  brick 
Whole  brick 
Whole  brick 


Half  brick 
Whole  brick 
Half  brick 
Half  brick 


Half  brick 
Whole  brick 
Whole  brick 


Half  brick 
Half  brick 
Half  brick 
Half  brick 


33.7 
32.2 
34.03 


10.89 
25.77 
12.67 
13.43 


11.46 
25.60 
28.88 


12.9s 
13.2 
13.30 
13  45 


4303 
3400 
2879 
3527 

3670 
7760 
3  393 

3  797 
46SS 

II  518 

8593 
3530 
7880 

3862 
8  180 
2  480 

4  535 
4764 


6  062 
5831 
5862 
5918 

982s 
12  941 

11  681 
14  296 

12  186 

13  839 
II  406 

9  766 

11  670 

10  270 
13530 
13  082 
13  08s 

12  490 


Crushing  Strength  of  Stonework,  Brickwork,  Bricks  271 

The  specimens  were  tested  in  the  government  testing-machine  at  Watertown, 
Mass.,  and  great  care  was  exercised  to  make  the  tests  as  perfect  as  possible. 
As  the  parallel  plates  between  which  the  bricks  are  crushed  are  fixed  in  one  posi- 
tion, it  is  necessary  that  each  specimen  tested  should  have  perfectly  parallel 
faces.  The  bricks  which  were  tested  were  rubbed  on  a  revolving  bed  until  the 
top  and  bottom  faces  were  perfectly  true  and  parallel.  The  preparation  of  the 
bricks  in  this  way  required  a  great  deal  of  time  and  expense;  and  it  was  so  difficult 
to  prepare  some  of  the  harder  bricks  that  they  had  to  be  broken  and  only  one-half 
of  the  brick  prepared  at  a  time. 

The  Philadelphia  bricks  used  in  these  tests  were  obtained  from  a  Boston 
dealer,  and  were  fair  samples  of  what  is  known  in  Boston  as  Philadelphia  Face- 
Bricks.     They  were  very  soft  bricks. 

The  Cambridge  bricks  were  the  common  bricks,  such  as  are  made  around 
Boston.     They  are  about  the  same  as  the  Eastern  bricks. 

The  Boston  Terra-Cotta  Company's  bricks  were  manufactured  of  a  rather 
fine  clay,  and  were  such  as  are  often  used  for  face-bricks. 

The  New  England  pressed  bricks  were  hydraulic-pressed  bricks,  and  were 
almost  as  hard  as  iron. 

From  tests  made  on  the  same  machine  by  the  United  States  Government  in 
1884,  the  average  strength  of  three  (M.  W.  Sands)  Cambridge,  Mass.,  face- 
bricks  was  13  925  lb,  and  of  his  common  bricks,  18  337  lb  per  sq  in,  one  brick 
developing  the  enormous  strength  of  22  351  lb  per  sq  in.  This  was  a  very  hard- 
burned  brick.  Three  bricks  of  the  Bay  State  (Mass.)  manufacture  showed  an 
average  strength  of  11  400  lb  per  sq  in.  The  New  England  bricks  are  among 
the  hardest  and  strongest  in  the  country,  those  in  many  parts  of  the  West  not 
having  one-fourth  the  strength  given  above;  so  that  in  heavy  buildings,  where 
the  strength  of  the  bricks  to  be  used  is  not  known  by  actual  tests,  it  is  advisable 
to  have  the  bricks  tested.  Ira  O.  Baker  reported  some  tests  on  Illinois  bricks, 
made  on  the  100  000-pound  testing-machine  at  the  University  of  Illinois  in 
1888  and  1889,  which  give  for  the  crushing  strength  of  soft  bricks,  674  lb  per  sq  in, 
for  the  average  of  three  face-bricks,  3  070  lb  per  sq  in,  and  for  four  paving- 
bricks,  9  775  lb  per  sq  in.  In  nearly  all  makes  of  bricks  it  will  be  found  that  the 
face-bricks  are  not  as  strong  as  the  common  bricks. 

Tests  of  the  Strength  of  Brick  Piers  Laid  with  Various  Mortars.* 
These  tests  were  made  for  the  purpose  of  testing  the  strength  of  brick  piers 
laid  up  with  different  cement  mortars,  as  compared  with  those  laid  up  with 
ordinary  mortar.  The  bricks  used  in  the  piers  were  procured  at  M.  W.  Sands's 
brickyard,  Cambridge,  Mass.,  and  were  good  ordinary  bricks.  They  were- from 
the  same  lot  as  the  samples  of  common  bricks  described  above.  The  piers 
were  8  by  12  in  in  cross-section,  and  nine  courses,  or  about  22yz  in  high,  except- 
ing the  first,  which  was  but  eight  courses  high.  They  were  built  Nov.  29,  1881, 
in  one  of  the  storehouses  at  the  United  States  Arsenal  in  Watertown,  Mass.  In 
order  to  have  the  two  ends  of  the  piers  perfectly  parallel  surfaces,  a  coat  of  pure 
Portland  cement,  about  V*  in  thick,  was  put  on  the  top  of  each  pier  and  the  foot 
was  grouted  in  the  same  cement.  On  March  3,  1882,  three  months  and  five 
days  later,  the  tops  of  the  piers  were  dressed  to  plane  surfaces  at  right-angles 
to  the  sides  of  the  piers.  On  attempting  to  dress  the  lower  ends  of  the  piers, 
the  cement  grout  peeled  off,  and  it  was  necessary  to  remove  it  entirely  and  put 
on  a  layer  of  cement  similar  to  that  on  the  tops  of  the  piers.  This  was  allowed 
to  harden  for  one  month  and  sixteen  days,  when  the  piers  were  tested.  At  that 
time  the  piers  were  four  months  and  twenty-six  days  old.  As  the  piers  were 
built  in  cold  weather,  the  bricks  were  not  wet.     They  were  built  by  a  skilled 

*  Made  under  the  direction  of  F.  E.  Kidder. 


272      Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry     Chap.  5 

bricklayer  and  the  mortars  were  mixed  under  his  superintendence.  The  tests 
were  made  with  the  government  testing-machine  at  the  Arsenal.  The  follow- 
ing table  is  arranged  so  as  to  show  the  result  of  these  tests,  and  to  afford  a  ready 
means  of  comparison  of  the  strength  of  brickwork  with  different  mortars.  The 
piers  generally  failed  by  cracking  longitudinally,  and  some  of  the  bricks  were 
crushed.  The  Portland  cement  used  in  these  tests  was  made  by  Brooks,  Shoo- 
bridge  &  Company,  of  England.  Roman  cement  is  a  European  natural  cement, 
usually,  although  not  always,  containing  a  low  percentage  of  magnesia.  It 
sets  rapidly,  has  about  one-third  the  strength  of  true  Portland  cement  and  is 
much  weakened  by  the  addition  of  sand. 


Table  IV.     Tests  of  Piers  of  Common  Bricks  Laid  in  Different  Mortars 


Piers  8  by  12  in  in  section,  built  of  common 
bricks  in  common  mortar 


Lime  mortar 

Lime  mortar,  3  parts;  Portland  cement,  i 
part 

Lime  mortar,  3  parts;  Newark  and  Rosen- 
dale  cements,  i  part 

Lime  mortar,  3  parts;  Roman  cement,  i 
part 

Portland  cement,  i  part;  sand,  2  parts. . . . 

Newark  and  Rosendale  cements,  i  part; 
sand,  2  parts 

Roman  cement,  i  part;  sand,  2  parts 


Ultimate 
strength 
of  pier. 


lb 


ISO  000 

290  000 

24s  000 

195000 
240  000 

205  000 
185  000 


Pressure 
per  sq  in 

under 

which  pier 

commenced 

to  crack, 

lb 


833 

187s 

I  354 

I  041 
I  302 

708 

I  770 


Ultimate 
strength, 


lb  per  sq 
in 


1  562 
3  020 
2552 

2  030 
2  500 

2  135 

I  927 


As  the  actual  strength  of  brick  piers  is  a  very  important  consideration  in 
building-construction,  some  tests,  made  by  the  United  States  Government  at 
Watertown,  Mass.,  and  contained  in  the  report  of  the  tests  made  on  the  Govern- 
ment testing-machine  for  the  year  1884,  are  given  as  being  of  much  value. 
Three  kinds  of  bricks  were  represented  in  the  construction  of  the  piers,  and 
mortars  of  different  composition,  ranging  in  strength  from  lime  mortar  to  neat 
Portland-cement  mortar.  The  piers  ranged  in  cross-section  dimensions  from 
8  by  8  to  16  by  16  in,  and  in  height  from  16  in  to  10  ft.  They  were  tested  at 
the  age  of  from  18  to  24  months. 

Table  V  gives  the  results  obtained  and  memoranda  regarding  the  size  and 
character  of  the  piers. 

Table  VI  gives  the  results  obtained  from  tests  of  the  strength  of  brick  piers 
made  at  the  McGill  University,  Montreal,  laboratories,  in  March,  1897. 

Recent  Tests  of  Brick  Piers.*  Elaborate  tests  of  brick  piers,  with  valuable 
results,!  were  made  in  1908  by  A.  N.  Talbot  and  D.  A.  Abrams  at  the  Uni- 
versity of  Illinois  Experiment  Station.  Table  VII  is  a  summary  of  these  results. 
The  tests  were  made  on  sixteen  brick  piers,  the  lengths  of  which  varied  from 

*  See,  also,  results  of  important  tests  made  in  19 14  and  1915  at  Columbia  University, 
New  York,  by  J.  S.  Maqgregor. 

t  Bulletin  27,  University  of  Illinois  Engineering  E.xpcriment  Station,  Sept.  29, 1908 


Crushing  Strength  of  Stonework,  Brickwork,  Bricks  275 


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274      Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry     Chap. 


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Crushing  Strength  of  Stonework,  Brickwork,  Bricks  275 

Table  VI.     Tests  of  Brick  Piers,  McGill  University  Laboratories,  March,   1897 


Crushing 

strength, 

Dimensions  of 

Composition  of 

Kind  of  bricks 

lb  per  sq  in 

Age 

piers 

mortar 

At 
first 
crack 

Max- 
imum 
load 

8.1  by  8.1  in,  11.6 

I  Canadian  Port- 

Ordinary well- 

in  high;    joints 

land-cement 

burned    flat 

i  822 

I  234 

3  weeks 

Vs  in  thick 

mortar,  3  sand 

bricks 

8.1  by  8.1  in,  11.6 

I  German  Port- 

Ordinary well- 

in  high;    joints 

land-cement 

burned  fiat 

[  990 

I  230 

3  weeks 

\i  in  thick 

mortar,  3  sand 

bricks 

8.2  by  8.3  in,  10.5 

I  English    Port- 

La Prairie  pressed 

in  high;    joints 

land-cement 

bricks,    keyed 

[i  130 

I  524 

3  weeks 

V2  in  thick 

mortar,  3  sand 

on  one  side 

8.4  by  8.4  in,  10.75 

I  Belgian  Port- 

La Prairie  pressed 

in  high;    joints 

land-cement 

bricks,  keyed 

>i  204 

1985 

3  weeks 

H  in  thick 

mortar,  3  sand 

on  one  side 

Table  VII. 


Tests  of  Brick  Piers,  Made  at  the  University  of  Illinois 

The  amounts  given  are  average  values 


Characteristics  of  piers 


Average 
unit 
load 

lb  per 
sq  in 


Ratio  of 

strength 

of  pier 

to 
strength 
of  brick 


Ratio  of 
strength 

of  pier 

to 

strength 

of  first 
of  series 


Crushing 
strength 
of  6-in 
mortar- 
cubes 

lb  per 
sq  in 


Ratio  o^ 
strength 
of  pier 
to 
strength 
of  cubes 


Shale  building  bricks 


Well  laid,  i  :  3  Portland-    ) 
cement  mortar,  67  days  ) 

3363 

0.31 

(Stand-) 

1  ri  \ 

2870* 

1. 17 

Well   laid,    i  :  3    Portland- 

^ 

cement  mortar,  6  months. 

3950 

0.37 

1. 18 

Well   laid,    i  13    Portland- 

cement  mortar,  eccentri- 

cally loaded,  68  days 

2800 

0.26 

0.83 

Poorly  laid,  i  :  3  Portland- 

cement  mortar,  67  days. . . 

2  920 

0.27 

0.87 

2870* 

1.05 

Well   laid,   I  :  5    Portland- 

cement  mortar,  65  days. . . 

2225 

0.21 

0.66 

1 710 

1.30 

Well    laid,    i  :  3     natural- 

cement  mortar,  67  days. . . 

I  750 

0.16 

0.52 

305 

5. 75 

Well  laid,  I  :  2  lime  mortar. 

66  days 

I  450 

0.14 

0.43 

Underburned  clay  bricks 


Well    laid,    i  :  3   Portland- 
cement  mortar,  63  days. . . 


I  060 


o  27 


0.31 


2870* 


0.37 


old. 


Average  value  based  on  thirteen  tests  of  i  :  3  Portland-cement  mortar-cubes,  60  days 


276        Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry    Chap.  5 

lo  to  io>2  ft.  The  lateral  dimensions  were  i2>^  by  i2>^  in.  Two  grades 
of  bricks  were  used,  an  excellent  class  of  building  bricks  and  a  soft  grade  seler:ted 
as  representative  of  inferior  bricks.  Different  qualities  of  mortar  and  different 
grades  of  workmanship  were  employed.  Compression-tests  of  single  bricks 
gave  these  average  results.  For  hard,  shale  building  bricks,  bedded  in  plaster, 
crushing  strength,  flatwise,  lo  700  lb  per  sq  in;  modulus  of  rupture,  edgewise, 
6-in  span,  i  670  lb  per  sq  in.  For  soft  or  underburned  clay  bricks,  crushing 
strength,  flatwise,  3  900  lb  per  sq  in;  modulus  of  rupture,  480  lb  per  sq  in. 
The  Macgregor  tests  showed  that  maximum  strength  with  minimum  expense 
for  brickwork  is  obtained  with  mortar  made  of  yi  cu  ft  of  Portland  cement, 
^  cu  ft  of  hydrated  Hme  and  3  cu  ft  of  sand,  or  a  i :  i :  6  mixture. 

Tensional  Strength  of  Brickwork.     See  Chapter  II,  page  179. 

2.    Strength  of  Terra-Cotta  and  Terra-Cotta  Piers 

General  Properties  of  Terra-Cotta.  The  lightness  of  terra-cotta,  combined 
with  its  great  compressive  strength,  together  with  its  durability  and  indestructi- 
bility by  fire,  water,  frost,  etc.,  renders  it  an  especially  valuable  building  material. 
Terra-cotta  for  building  purposes,  whether  plain  or  ornamental,  is  generally 
made  of  hollow  blocks  formed  with  webs  to  give  extra  strength  and  keep  the 
work  true  while  drying.  This  is  necessary  because  good,  well-burned  terra- 
cotta cannot  safely  be  made  more  than  about  \Vi  in  thick,  whereas,  when  re- 
quired to  bond  with  brickwork,  it  must  be  at  least  4  in  thick.  When  extra 
strength  is  needed,  these  hollow  spaces  are  filled  with  concrete  or  brickwork, 
which  greatly  increases  the  crushing  strength  of  the  terra-cotta,  although  alone 
it  is  able  to  bear  a  very  heavy  weight.  "A  solid  cubical  block  of  terra-cotta 
has  borne  a  crushing-stress  of  more  than  500  tons." 

Crushing  Strength  of  Terra-Cotta  Blocks.  Some  exhaustive  experiments 
made  by  the  Royal  Institute  of  British  Architects  give  the  following  results  as 
the  crushing  strengths  of  terra-cotta  blocks: 

Crushing  weight 
per  cu  ft 

Solid  block  of  terra-cotta 523  tons 

Hollow  block  of  terra-cotta,  unfilled 186  tons 

Hollow  block  of  terra-cotta,  lightly  made  and  unfilled 80  tons 

Tests  of  terra-cotta  manufactured  by  a  New  York  Company,  which  were 
made  at  the  Stevens  Institute  of  Technology  in  April,  1888  gave  these  results: 

Crushing  weight      Crushing  weight 
per  cu  in  per  cu  ft 

Terra-cotta  block,  2-in  square,  red 6  840  lb     or     492  tons 

Terra-cotta  block,  2-in  square,  buff 6  236  lb     or     449  tons 

Terra-cotta  block,  2-in  square,  gray 5  126  lb     or     369  tons 

In  tests  for  the  New  York  Building  Department,  made  at  Columbia  University, 
dense  terra-cotta  blocks  developed  a  net  crushing  strength  of  4  721  lb  per  sq  in 
or  340  tons  per  sq  ft,  and  semiporous,  2  168  lb  per  sq  in  or  156  tons  per  sq  ft, 
these  results  being  in  each  case  the  averages  of  a  series  of  tests.      (See  page  815.) 

From  these  results,  the  writer  would  place  the  safe  working  strength  of  terra- 
cotta blocks  in  the  wall  at  5  tons  per  sq  ft  when  unfilled,  and  10  tons  per  sq  ft 
when  filled  sohd  with  brickwork  or  concrete. 


Strength  of  Terra-Cotta  and  Terra-Cotta  Piers 


277 


Tests  of  Terra-Cotta  Piers.  Tests  *  of  terra-cotta  block  piers  were  made 
about  the  same  time  (January,  1907,  and  January,  1908)  that  the  brick  piers 
referred  to  in  Table  Vll  were  made.  The  tests  were  made  on  terra-cotta  piers, 
the  lengths  of  which  varied  from  9  ft  9  in  to  12  ft  7%  in.  The  lateral  dimensions 
varied  from  SVz  by  S^i  in  to  17V2  by  ly^i  in.  "The  piers  were  built  and  tested 
in  two  lots,  an  interval  of  about  one  year  separating  the  times  of  making  the 
tests.  The  two  lots  of  piers  were  built  of  blocks  which  came  in  different  ship- 
ments.    The  cement  used  was  the  same  brand  in  both  years,  although  the  lots 


Table  VIII.     Tests  of  Terra-Cotta  Piers,  Made  at  -the  University  of  Illinois 

The  amounts  given  are  average  values.  The  table  gives  results  of  tests  of  piers  of 
second  shipment,  except  for  the  concave-end  blocks.  The  piers  recorded  in  this  table 
were  all  12  H  by  i2yi  in  by  9H  ft. 


Characteristics  of  piers 


Well  laid,  i  :  3  Portland-1 
cement  mortar ,  concentr i-  > 
cally  loaded 1 

Well  laid,  i  :  3  Portland- 
cement  mortar,  eccentri- 
cally loaded 

Poorly  laid,  1  :  3  Portland- 
cement  mortar,  concen- 
trically loaded 

Poorly  laid,  i  :3  Portland- 
cement  mortar,  eccentri- 
cally loaded 

Well  laid,  I  :  3  Portland- 
cement  mortar,  concen- 
trically loaded 

Well  laid  1  :  5  Portland- 
cement  mortar,  concen- 
trically loaded,  inferior 
unburned  blocks  t 

Blocks  with  concave  ends, 
I  :  2     Portland-cement 
mortar 


Average 
unit 
load 


lb  per 
sq  in 


4300* 


2  970 


Ratio  of 

strength 

of  pier 

to 

strength 

of  block, 

gross 

area 


0.83* 

0.65 
0,64 
0.60 


0.6s 


0.86 


Ratio  of 
strength 

of  pier 

to 

strength 

of  first 
of  series 


Stand-  "j 
ard  [ 
I . 00*  J 

0.81* 

o  76 

0.75 

0.71 

0.78 
0.69 


Crushing 
strength 
of  6-in 
mortar- 
cubes 

lb  per 
sq  in 


Ratio  of 
strength 
of  pier 
to 
strength 
of  cubes 


1.26* 


1.05 
1.06 
0.88 


Estimated. 


t  Blocks  of  good  quality,  but  undcrbumcd. 


were  different.  The  terra-cotta  block  piers  were  generally  made  in  sets  of  two. 
Each  set  was  constructed  and  loaded  similarly.  Three  of  the  piers  were  laid  up 
hurriedly  (poorly  laid);  the  remainder  were  built  with  the  usual  care  given  to 
such  work.  The  load  was  applied  to  the  piers  in  different  ways,  although  gen- 
erally apphed  continuously  to  failure."  Some  piers  were  loaded  eccentrically 
to  failure  and  one  was  loaded  both  concentrically  and  eccentrically,  but  the 
additional  eccentric  load  was  not  sufficient  to  cause  failure. 

*  See  Bulletin  No.  27,  University  of  Illinois  Engineering  Experiment  Station,  Sept.  29, 
1908. 


278      Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry     Chap.  5 

Comparison  of  Results  of  Tests  of  Brick  and  Terra-Cotta  Piers.     In 

the  tests  summarized  in  Tables  VII  and  VIII,  ''both  the  brick  piers  and  the 
terra-cotta  block  piers  gave  high  strengths  in  all  cases  where  strong  mortar  and 
care  in  building  were  used.  The  eftect  of  the  strength  of  the  mortar  was  appar- 
ent in  the  carrying  capacity  developed  in  the  piers,  smaller  loads  being  indi- 
cated for  piers  built  with  i  :  5  Portland-cement  mortar  than  for  those  with  i  :  3 
Portland-cement  mortar,  and  still  smaller  loads  for  those  with  i  :  2  lime  mortar. 
The  effect  of  the  quality  of  the  bricks  is  shown  in  the  piers  made  with  inferior 
bricks,  these  piers  carrying- only  31%  as  much  as  piers  built  with  the  better 
grade  of  bricks.  In  the  ease  of  the  terra-cotta  piers,  the  blocks  which  were 
culled  out  as  somewhat  inferior  gave  a  pier-strength  which  was  perhaps  30% 
less  than  the  piers  built  with  superior  blocks.  The  effect  of  the  attempt  to 
represent  hurried  or  careless  workmanship  in  two  brick  piers  and  in  three  terra- 
cotta block  piers  was  a  loss  in  strength  of  about  15%  and  25%  respectively. 

"In  the  well-built  brick  piers,  concentrically  loaded,  the- ratio  of  strength  of 
pier  to  compressive  strength  of  individual  brick  ranged  from  31  to  37%,  and 
in  the  underburned  clay-brick  pier  the  ratio  was  27%.  In  the  terra-cotta 
block  piers,  concentrically  loaded,  the  ratio  of  strength  of  pier  to  that  of  individ- 
ual block  was  74%  (an  incompleted  test)  and  83,  85  and  89%  for  the  others. 
The  higher  ratio  found  for  the  terra-cotta  block  piers  than  for  brick  piers  sug- 
gests that  the  ability  of  individual  pieces  to  resist  transverse  forces  is  an  ele- 
ment in  the  strength  of  the  completed  pier;  and  this  suggestion  may  have  an 
important  bearing  on  the  advantageous  size  of  the  component  blocks  which 
may  be  used  in  a  compression-piece  where  great  strength  is  required. 

"  The  strength  of  the  pier  is  greater  than  that  of  the  mortar-cubes  in  both 
brick  and  terra-cotta  block  piers,  except  the  soft-brick  piers,  which  had  bricks 
of  low  compressive  strength.  Both  the  strength  of  the  individual  bricks  or 
blocks  and  the  strength  of  the  mortar  affect  the  resistance  of  the  pier,  and  the 
relative  effect  of  the  two  depends  upon  the  character  of  the  materials.  It  is 
evident,  however,  that  the  better  the  individual  piece  the  more  important  it  is 
to  have  a  mortar  of  high  resisting  strength. 

"The  results  obtained  in  applying  the  loads  eccentrically  were  found  to  agree 
very  well  with  those  obtained  from  ordinary  analysis. 

"The  quality  of  workmanship  in  laying  up  such  columns  has  an  important 
bearing  upon  the  resisting  strength.  The  work  of  building  piers,  however,  is 
not  difficult  and  requires  only  ordinary  care.  Full  joints  and  an  even  bearing 
are  important,  and  the  ordinary  workman  ought  to  be  able  to  construct  piers 
of  great  strength.  In  the  tests  made  on  piers  intended  to  re;present  poor  or 
careless  workmanship,  the  decrease  in  strength  was  not  as  much  as  anticipated. 
However,  it  must  be  understood  that  careful  and  trustworthy  work  is  essential 
and  that  a  few  poor  joints  will  materially  reduce  the  strength  of  the  structure. 
Wherever  good  material  and  good  workmanship  are  insured  the  strength  of 
masonry  of  this  kind  may  be  utilized  with  advantage. " 

Strength  of  Terra-Cotta  Brackets  or  Consoles.  A  cornice-modillion 
made  by  the  Northwestern  Terra-Cotta  Company,  iiK'  in  high  at  the  wall-line, 
8  in  wide  on  the  face,  and  with  a  projection  of  2  ft,  was  built  into  a  wall  and  the 
upper  surface  loaded  with  2  tons  of  pig  iron  without  any  effect  upon  the  modilHon. 
Another  bracket,  53^2  in  high,  6  in  wide  and  with  a  14-in  projection,  made  in 
the  East,  broke  at  the  wall-line  under  2  650  lb,  while  a  duplicate  of  it  sustained 
2  400  lb  for  one  month  without  breaking.* 

The  Weight  of  Terra-Cotta.  The  weight  of  terra-cotta  in  solid  blocks  is 
120  or  122  lb  per  cu  ft.  When  made  in  hollow  blocks  iVz  in  thick  the  weight 
*  See  The  Brickbuilder,  Vol.  7,  page  142. 


Crushing  Strength  of  Building  Stones 


279 


varies  from  65  to  85  lb  per  cu  ft,  the  smaller  pieces  weighing  the  most.  For 
pieces  12  by  18  in  or  larger  on  the  face,  70  lb  per  cu  ft  will  probably  be  a  fair 
average.  The  tables  in  the  manufacturers'  catalogues  give  the  various  bearing- 
areas,  weights  per  square  foot,  thicknesses  of  parts,  sizes  of  blocks,  etc.,  for  por- 
ous and  semiporous  blocks  for  all  purposes. 

3.    Crushing  Strength  of  Building  Stones 

(i)  Sandstones 

Longmeadow,  Mass.,  Stone.*  Reddish-brown  sandstone,  two  blocks  about 
4  by  4  in  in  cross-section  and  8  in  in  height. 

Block  No.  I  commenced  to  crack  at  10  S33  lb  per  sq  in,  and  flew  from  the 
machine  in  fragments  at  13  596  lb  per  sq  in. 

Block  No.  2  commenced  to  crack  at  3  012  lb  per  sq  in  and  failed  completely 
at  9  121  lb  per  sq  in. 

Sandstone  from  Norcross  Brothers'  Quarries,  East  Longmeadow,  Mass., 
Soft  Saulsbury  Stone.*  Block  No.  i,  4  by  4  by  8  in  high,  commenced  to  crack 
at  8  250  lb  and  failed  at  8  812  lb  per  sq  in. 

Block  No.  2,  4  by  4  by  8  in  high,  commenced  to  crack  at  6  500  lb  and  failed 
at  8  092  lb  per  sq  in. 

Hard  Saulsbury  Stone.*'  Block  No.  i,  4  by  4  by  8  in  high  (about),  commenced 
to  crack  at  12  716  lb  and  failed  at  13  520  lb  per  sq  in. 

Block  No.  2,  same  size  as  No.  i,  commenced  to  crack  at  13  953  lb  and  failed 
at  14  650  lb  per  sq  in. 

Kibbe  Stone.*  Block  No.  i,  6  by  6  by  6  in,  commenced  to  crack  at  12  590  lb 
and  failed  at  12  619  lb  per  sq  in. 

Block  No.  2,  same  size  as  No.  i,  commenced  to  crack  at  12  185  lb  and  failed 
at  12  874  lb  persqin. 

Brown  Stone  from  the  Shaler  &  Hall  Quarry  Company,  Portland,  Conn.f 
The  results  of  the  tests  are  as  follows: 


Table  IX.     Crushing  Strength  of  Brown  Sandstone 


Dimensions 

Sectional 
area 

sq  in 

First 
crack 

lb 

Ultimate 
strength 

lb  per 
sq  in 

Classification 

Height 
in 

Compressed, 
surface 

in 

2.50 
2.50 
2.98 
2.95 
2.51 
2.48 

2.50 
2.48 
3.00 
2.98 
2.55 
2.48 

2.45 
2.47 
2.9s 
2.97 
2.53 
2.52 

6.13 
6.13 
8.85 
8.85 
6.45 
6.25 

84800 
81  700 
123  200 
122  000 
63850 
58  340 

13980 
13330 
13920 
15  020 
9900 
9330 

ist  quality 
I  St  quality 
2d  quality 
3d  quality 
Bridge 
Bridge 

Brown  Stone  from  the  Middlesex  Quarry  Company,  Portland,  Conn.f  Four 
nearly  cubical  blocks,  about  iM  in  square.  Pressure  per  square  inch  at  time  of 
failure:  No.  i,  10  928  lb;  No.  2,  10  322  lb;  No.  3,  8  252  lb  and  No.  4,  6  322  lb. 

*  These  tests  were  made  with  the  United  States  testing-machines  at  Watertown 
Arsenal,  Mass. 

t  From  tests  made  by  Colt's  Patent  Fire-arms  Manufacturing  Company. 

t  These  tests  were  made  with  the  United  States  testing-machines  at  Watertown 
Arsenal,  Mass. 


280       Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry    Chap.  5 

Red  Sandstone  *  from  Greenlee  &  Son's  Quarries  at  Manitou,  Col.  One 
specimen  failed  at  ii  ooo  lb  per  sq  in;  weight,  140  lb  per  cu  ft. 

Light-Red  Laminated  Sandstone,!  from  St.  Vrain  Canon,  Col.,  a  very  hard 
stone,  excellent  for  walks  and  foundations.  Crushing  strength  on  bed,  11  505 
lb  per  sq  in;   weight,  150  lb  per  cu  ft. 

Gray  Sandstone  f  (free-working)  from  Trinidad,  Col.  Crushing  strength, 
10  000  lb  per  sq  in;   weight,  145  lb  per  cu  ft. 

Gray  Sandstone  f  from  Fort  Collins,  Col.  (laminated  and  similar  in  quality 
to  the  St.  Vrain  stone).  Crushing  strength  on  bed,  11  700  lb  per  sq  in;  weight, 
140  lb  per  cu  ft.     One  ton  of  this  stone  measures  just  a  perch  in  the  wall. 

(2)  Granite 
Red  Granite -t  from  Platte  Canon,  Col.     Crushing  strength  per  square  inch, 
14  600  lb;  weight  per  cubic  foot,  164  lb. 

(3)  Lava  Stones 
Lava  Stone  from  the  Kerr  Quarries,  near  Salida,  Col.     Four  cubical  blocks. J 
The  results  of  the  tests  are  as  follows: 

Table  X.     Crushing  Strength  of  Lava  Stone 


Dimensions 

Sectional 
area 

sq  in 

First 
crack 

lb 

Ultimate  strength 

Height 
in 

Compressed 

surface 

in 

lb 

lb  per 
sq  in 

4.00 
4.00 
2.00 
1-99 

4.00 
4.00 
2.00 
1.99 

4.00 
4.00 
1-99 
1.99 

16.00 
16.00 
3.93 
3.96 

1 65  900 
174  100 
36400 
38  200 

165  000 
174  100 
37  100 
38200 

10369 
10  881 
9322 
9  646 

Lava  Stone,t  Curry's  Quarry,  Douglas  County,  Col.  Crushing  strength, 
10675  lb  per  sq  in;  weight,  119  lb  per  cu  ft.  Experience  has  shown  that  this 
stone  i?  not  suitable  for  piers,  or  where  any  great  strength  is  required,  as  it 
cracks  v  ary  easily. 

(4)  Marble  and  Limestone 

White  marble  quarried  at  Sutherland  Falls,  Vt.  Two  cubical  blocks  about 
6  in  square.  § 

Block  No.  I  commenced  to  crack  at  9  750  lb  per  sq  in  and  failed  suddenly  at 
II  250  lb  per  sq  in. 

Block  No.  2  did  not  crack  until  it  suddenly  gave  way  at  10  243  lb  per  sq  in. 

Test  of  a  Limestone  Pier.  A  pier  of  Lemont  limestone,  i  sq  ft  in  cross-section 
and  9  ft  in  height,  composed  of  seven  stones  with  bearing  surfaces  planed  per- 
fectly true  and  parallel  to  the  natural  bed  and  the  joints  washed  with  a  thin 
grout  of  the  best  English  Portland  cement,  was  tested  at  the  Watertown  Arsenal 
for  William  Sooy  Smith,  and  only  commenced  to  crack  when  the  full  power 
of  the  machine,  400  tons,  was  exerted. 

•  These  tests  were  made  with  the  United  States  testing-machines  at  Watertown 
Arsenal,  Mass. 

.t  From  tests  made  for  the  Board  of  Capitol  Managers  of  Colorado  by  State  Engineer 
E.  S.  Nettleton,  in  1885,  on  2-in  cubes. 

t  From  tests  made  by  the  Denver  Society  of  Civil  Engineers,  in  1884,  also  on  2-in 
cubes. 

§  Tested  at  the  United  States  Arsenal,  Watertown,  Mass. 


Crushing  Strength  of  Building  Stones 


281 


(S)  Bricks  and  Various  Stones 

Table  XI  gives  the  crushing  strength  of  various  kinds  of  bricks  and  building 
stones,  the  pressure  being  normal  to  the  plane  of  the  bed. 

Table  XI.     Crushing  Strength  of  Brick  and  Stone  * 

Pressure  at  right-angles  to  bed 


Kind  of  brick  or  stone 


Bricks: 

Common,  Massachusetts 

Common,  St.  Louis,  Mo 

Common,  Washington,  D.  C 

Paving,  Illinois ; 

Granites; 

Blue,  Fox  Island,  Me 

Gray,  Vinal  Haven,  Me 

Westerly,  R.  I 

Rockport  and  Quincy,  Mass 

Milford,  Conn 

Staten  Island,  N.  Y 

East  St.  Cloud,  Mmn 

Gunnison,  Col 

Red,  Platte  Canon,  Col. 

Limestones: 

Glens  Falls,  N.  Y 

Joliet,  111..,.,.. 

Bedford,  Ind 

Salem,  Ind. , 

Red  Wing,  Minn 

Stillwater,  Minn 

Sandstones: 

Dorchester,  N.  B.  (brown) 

Mary's  Point,  N.  B.  (fine  grain,  dark  brown) 

Connecticut  brown  stone, f  (on  bed) 

Longmeadow,  Mass.  (reddish  brown) 

Longmeadow,  Mass.  (average,  for  good  quality)  . 

Little  Falls,  N .  Y 

Medina,  N.  Y 

Potsdam,  N.  Y.  (red) 

Cleveland,  Ohio 

North  Amherst,  Ohio 

Berea,  Ohio 

Hummelstown,  Pa 

Fond  du  Lac,  Minn 

Fond  du  Lac,  Wis 

Manitou,  Col.  (light  red) 

St.  Vrain,  Col.  (hard  laminated) 

Marbles: 

Lee,  Mass 

Rutland,  Vt 

Montgomery  Co.,  Pa 

Colton,  Cal. ; 

Italy 

Flagging: 

North  River,  N.  Y 


Crushing 

strength, 

lb  per  sq  in 


10  GOO 

6417 

7370 

5  000  to  13  000 

1487s 
}  000  to  18  000 
15  000 
17  750 
22  600 

22  250 
28  000 

13  000 

14  600 

11  475 
12775 

5  000  to  10  000 
862s 

23  000 
10750 

9  ISO 

7700 
J  000  to  13  000 

J  000  to  14  000 

12  000 
98SO 

17  000 

5  000  to  42  000 

6800 

6  212 

\  000  to  10  000 

12  810 

8750 

6237 
)  000  to  II  000 

II 505 

22900 
10  746 
10  000 

17783 

12  is6 
1342s 


*  For  more  complete  tables  of  the  strength,  weight  and  composition  of  building  stones, 
see  new  data,  tables,  etc.  by  Professor  Thomas  Nolan  in  Kidder's  Building  Construction 
and  Suoerintendence,  Part  I,  Masons'  Work. 

\  This  stone  should  not  be  set  on  edge. 


282       Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry     Chap.  5 


(6)  Additional  Data  on  the  Strength  of  Building  G  tones 

Average  Data  for  Building  Stones  of  Good  Quality.  The  following  average 
relative  values*  are  given  by  R.  P.  Miller.f  Sandstone:  weight,  150  lb  per 
cu  ft;  specific  gravity,  2.40;  crushing  strength,  8  000  lb  per  sq  in;  shearing 
strength,  i  500  lb  per  sq  in;  modulus  of  rupture,  i  200  lb  per  sq  in;  modulus 
of  elasticity,  3000000  lb  per  sq  in.  Granite:  weight,  170;  specific  gravity, 
2.72;  crushing  strength,  15  000;  shearing  strength,  2  000;  modulus  of  rupture, 
1500;  modulus  of  elasticity,  7000000.  Limestone:  weight,  170;  specific 
gravity,  2.72;  crushing  strength,  6000;  shearing  strength,  1000;  modulus  of 
rupture,  i  200;  modulus  of  elasticity,  7000000.  Marble:  weight,  170;  spe- 
cific gravity,  2.72;  crushing  strength,  10  000;  shearing  strength,  1400;  mod- 
ulus of  rupture,  i  400;  modulus  of  elasticity,  8000000.  Slate:  weight,  175; 
specific  gravity,  2.80;  crushing  strength,  15  000;  modulus  of  rupture,  8  500; 
modulus  of  elasticity,  14  000  000.  Trap-Rock:  weight,  185;  specific  gravity, 
2.96;   crushing  strength,  20  000. 

The  following  average  relative  values  are  given  by  A.  I.  Frye.t  They  are 
the  results  of  tests  made  on  small  cubes  of  the  materials.  Sandstone:  crush- 
ing strength,  9  000  lb  per  sq  in;  Granite  and  Gneiss:  crushing  strength, 
17  733  lb  per  sq  in.  Limestones  and  Marbles:  crushing  strength,  14  445  lb 
sper  sq  in.  Slate:  crushing  strength,  10  000;  ultimate  tensional  strength, 
3  000;  modulus  of  rupture,  5  000  lb  per  sq  in. 

When  stones  are  not  tested,  Frye  recommends  the  following  average  values 
for  ultimate  strengths  to  be  used  in  determining  the  safe  stresses.  Sandstone: 
crushing  strength,  5  000;  ultimate  tensional  strength,  150;  modulus  of  rupture, 
I  200  lb  per  sq  in.  Granite  and  Gneiss:  crushing  strength,  12000;  mod- 
ulus of  rupture,  i  600  lb  per  sq  in.  Limestones  and  Marbles:  crushing 
strength,  8  000;  ultimate  tensional  strength,  800;  modulus  of  rupture,  i  500  lb 
per  sq  in. 

The  following  working  unit  stresses  in  pounds  per  square  inch  for  stone  slabs 
or  single  blocks  of  stone  are  recommended  by  W.  J.  Douglass. §  Sandstone: 
compression,  700;  tension  (direct  and  flexural),  75;  shear,  150.  Granite, 
Syenite  and  Gneiss:  compression  for  hard,  i  500;  for  medium,  i  200;  for 
soft,  I  000;  tension  (direct  and  flexural),  150;  shear,  200.  Limestone:  com- 
pression for  hard,  i  000;  for  medium,  800;  for  soft,  700;  tension  (direct  and 
flexural),  125;  shear,  150.  Marble:  compression  for  hard,  900;  for  soft,  700; 
tension  (direct  and  flexural),  125;  shear,  150.  Bluestone  Flagging:  compres- 
sion, I  500;   tension  (direct  and  flexural),  200. 


4.   Compressive  Strength  of  Mortars  and  Concretes 

The  Compressive  Strength  of  Lime  Mortar.  The  crushing  strength  of 
common  lime  mortar,  six  months  old  and  composed  of  i  part  lime  to  6  parts 
sand  by  measure,  varies  from  150  to  300  lb  per  sq  in  or  from  10.8  to  21.6  tons 
per  sq  ft.  Lime  mortar  alone  should  never  be  used  wher«  any  but  moderate 
loads  are  to  bear  upon  the  work,  nor  where  the  full  loading  is  to  be  applied  before 
the  mortar  has  had  time  to  harden. 

*  The  values  in  all  cases  are  as  follows:  weight,  in  lb  per  cu  ft;  strength,  modulus  of 
rupture  and  modulus  of  elasticity,  in  lb  per  sq  in. 

t  American  Civil  Engineers'  Pocket  Book  (1912),  page  357. 

t  Civil  Engineers'  Pocket-Book  (19 13),  page  511. 

§  American  Civil  Engineers'  Pocket  Book  (1912),  page  575. 


Compressive  Strength  of  Mortars  and  Concretes  283 

The  Compressive  Strength  of  Natural-Cement  Mortar.  The  crushing 
strength  *  of  natural-cement  mortar,  neat,  averaged,  for  7  days,  2  010;  for 
28  days,  2  689;  for  3  months,  3  646;  and  for  ^months,  5  052  lb  per  sq  in.  When 
mixed  with  2  parts  of  standard  quartz  sand,  the  mortar  averaged  in  crushing 
strength,  for  7  days,  940;    for  28  days,  i  390;    for  3  months,  i  730;    and  for 

6  months,  2  012  lb  per  sq  in.  For  2  years,  an  additional  increase  of  18%  and 
6%  may  be  assumed  for  the  neat  and  sanded  mortars,  respectively,  of  natural 
cement. 

The  Compressive  Strength  of  Portland-Cement  Mortar.  The  crushing 
strength*  of  Portland-cement  mortar,  neat,  averaged,  for  7  days,  5915;  for 
28  days,  7  041;  for  3  months,  7  347;  and  for  6  months,  9  760  lb  per  sq  in. 
When  mixed  with  3  parts  of  standard  quartz  sand,  the  mortar  averaged,  in 
crushing  strength,  for  7  days,  941;  for  28  days,  i  290;  for  3  months,  i  490; 
and  for  6  months,  i  529  lb  per  sq  in.  When  mixed  with  3  parts  of  Ottawa  sand, 
the  mortar  averaged,  in  crushing  strength,  for  7  days,  i  199;  for  28  days,  i  796; 
for  3  months,  i  887;  and  for  6  months,  2  181  lb  per  sq  in.  For  2  years,  an  . 
additional  increase  of  about  16%  and' 18%  may  be  assumed  for  the  neat  and 
sanded  mortars,  respectively,  of  Portland  cement. 

Relation  of  Compressive  to  Tensile  Strength  of  Mortars.  While  it 
may  be  stated  as  a  very  general  guide  that  the  compressive  strength  of  hy- 
draulic-cement mortars  is  from  six  to  ten  times  the  tensile  strength,  these  ratios 
are  variable  and  cannot  be  used  as  a  reliable  basis  for  calculations.  The  tensile, 
strength  of  Portland-cement  mortars,  under  normal  conditions,  increase^, 
rapidly  during  the  first  few  days,  the  rate  of  change  gradually, falling  off.     In-  / 

7  days  the  tensile  strength  is  generally  from  one-half  to  two-thirds  of  the  ulti- 
mate strength,  which  is  practically  reached  in  2  or  3  months.  The  compressive 
strength,  however,  continues  to  increase  with  age  and  the  rate  of  increase  varies 
according  to  a  somewhat  different  law. 

The  Compressive  Strength  of  Concrete.  There  are  many  reasons  for 
the  variations  in  the  values  of  the  compressive  strength  of  concrete  and  the 
principal  factors  are  (i)  the  quality  of  the  cement,  (2)  the  size  and  character 
of  the  aggregates,  (3)  the  quantity  of  the  cement  to  a  unit  volume  of  the  con- 
crete, (4)  the  manner  of  mixing,  (5)  the  density  of  the  mixture,  (6)  the  condi- 
tions under  which  it  seasons,  and  (7)  its  age;  and  of  these  various  conditions 
affecting  the  determination  of  the  compressive  strength  the  most  important 
are  generally  the  proportions  of  the  different  ingredients  of  the  mixture  and  its 
age.  Although  tables  of  average  values  of  ultimate  crushing  strengths  of  con- 
crete are  published  and  are  of  general  value,  they  may  be  misleading  unless 
considered  with  caution.  In  important  operations  it  is  advisable  to  have  the 
concrete  tested  and  to  adjust  by  trial  the  character  and  proportions  of  the  in- 
gredients until  the  required  strength  is  obtained. 

Form  of  Specimen  for  Compression-Tests.  For  compression-tests  of 
concrete  in  general,  4  to  12-in  cubes  of  the  mixture  have  been  the  standard 
forms  of  test-specimens;  but  since  the  advent  of  reinforced-concrete  construc- 
tion and  the  growth  of  the  importance  of  determining  the  elastic  properties  of 
concrete,  it  has  been  found  that  a  cylindrical  test-specimen  gives  more  definite 
results  than  a  cube.  A  common  shape  of  such  cylinder  is  one  in  which  the 
height  is  about  three  times  the  diameter,  and  the  cylinders  are  not  less  than 
6  by  18  in.  It  is  found  that  the  compressive  strengths  of  these  cylinders  of 
concrete  are  from  10  to  15%  less  than  those  of  the  cubes,  but  for  cylinders  of 

*  From  compression-tests  made  by  W.  P.  Taylor  on  cylindrical  specimens  i  in  in  height, 
about  iH  in  in  diameter  and  i  sq  in  in  cross-section. 


284       Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry     Chap.  5 

still  greater  slenderness  the  compressive  strengths  remain  about  constant  for 
heights  up  to  about  seven  diameters. 

Compression-Tests  on  Concrete  Cubes.  From  some  tests  made  in  1899 
for  the  Boston  Elevated  Railway  Company  at  the  Watertown  Arsenal,  on  T2-in 
cubes  of  concrete  made  with  five  brands  of  Portland  cement,  coarse,  sharp 
sand  and  broken  stone  up  to  2j'2-in  size,  having  49.5%  voids,  the  following 
average  values  of  the  compressive  strengths  were  obtained: 

Table  XII.     Compression-Tests  on  Concrete  Cubes 


Mixtures 

7  days 
lb  per  sq  in 

I  month 
lb  per  sq  in 

3  months 
lb  per  sq  in 

6  months 
lb  per  sq  in 

1:2:4 
1:3:6 

I  560 
I  310 

2400 
2  160 

2900 
2520 

3820 
3090 

Compression-Tests  on  Concrete-Cylinders.  For  cylindrical  test-speci- 
mens of  concrete,  made  under  reasonably  good  conditions  as  to  character  of 
materials  and  care  in  mixing,  an  average  compressive  strength  of  about  2  000 
lb  per  sq  in  is  usually  developed  in  a  i  :  2  :  4  Portland-cement  concrete  in  from 
I  to  2  months;  and  of  about  i  600  lb  per  sq  in  in  a  i  :  3  :  6  mixture.  When 
the  conditions  are  unusually  favorable  somewhat  higher  values  than  these  are 
obtained,  but  when  the  materials  and  workmanship  are  poor  the  ultimate  com- 
pressive stresses  are  lower. 

Increase  in  Compressive  Strength  of  Portland-Cement  Concrete.  In 
regard  to  the  increase  of  compressive  strength  of  Portland-cement  concrete 
with  age,  tests  show  that  the  ultimate  compressive  strength  is  nearly  reached  in 
60  days,  at  which  time  the  strength  varies  from  80  to  90%  of  its  value  in  i  year's 
time. 

Ultimate  Strengths  of  Natural-Cement  Concrete.  For  natural-cement 
concrete,  the  ultimate  compressive,  tensile  and  shearing  strengths  and  the  mod- 
ulus of  rupture  may  be  taken  at  about  one-half  the  corresponding  values  for 
Portland-cement  concrete,  unless  natural  cements  of  known  and  tested  values 
are  employed. 

Strength  of  Unreinforced  Concrete  Columns.  Short  concrete  columns, 
of  lengths  up  to  10  or  15  diameters,  develop  a  crushing  strength  of  from  10  to 


Table  XIII.     Compression-Tests  on  Unreinforced  Concrete  Columns 


Average  ulti- 

Kind of 

Average  age 

mate  compres- 

concrete 

sive  stress 

days 

lb  per  sq  in 

1:1:2 

60 

3600* 

i:iV^:3 

60 

2  270 

1:2:4 

60 

I  600 

I  :  21^^  :  5 

60 

I  200 

1:3:6 

60 

935 

I  :  3H  :  7 

60 

745 

1:4:8 

60 

600 

•  This  value  was  estimated  as  it  was  beyond  the  range  of  the  tests. 


Compressive  Strength  of  Concretes  285 

20%  less  than  that  for  short  prismatic  or  cylindrical  specimens.  In  Table  XIII 
are  the  results  obtained  by  A.  N.  Talbot  *  on  short,  round,  unreinforced  stone- 
concrete  columns,  12  in  in  diameter  and  10  ft  in  length.  A  wet-mixture  concrete 
was  used,  of  the  different  proportions  shown,  the  forms  were  removed  after 
10  days  and  the  columns  were  tested  through  60  days. 
The  values  given  in  the  table  were  deduced  from  the  straight-line  formula 

12  CXX) 

Ultimate  compressive  strength,  lb  per  sq  in  = —  —  400 

in  which  formula 

Sa  =  the  ratio  of  sand  to  cement 

St  =  the  ratio  of  stone  to  cement 
For  example,  in  the  1:3:6  mixture,  Sa  =  3  and  St  =  6 

Crushing  Strength  of  Concrete  Affected  by  Area  of  Bearing  Surface. 

Professor  Hool  states  f  that  if  a  load  is  applied  over  the  central  part,  only, 
of  the  bearing  surface  of  a  concrete  test-specimen  in  compression,  the.  unit  load 
will  be  greater  than  if  it  is  applied  over  the  entire  surface;  and  this  is  due  to  the 
fact  that  the  outer  parts  tend  to  assist  the  inner  part  to  resist  the  stress.  This 
was  shown  by  tests  made  on  some  of  the  12-in  concrete  cubes  used  in  the  tests 
made  for  the  Boston  Elevated  Railway  Company  and  referred  to  in  the  preced- 
ing paragraphs.  Thirty-six  of  these  concrete  cubes  were  crushed  by  applying 
the  load  over  the  entire  upper  bearing-surface  of  144  sq  in  and  an  equal  number 
of  similar  concrete  cubes  were  then  crushed  by  applying  the  stress  over  a  smallei 
area,  10  by  10  in,  or  100  sq  in.  After  this,  the  cubes  of  a  third  set  were  crushed 
by  the  application  of  the  stress  over  the  still  smaller  area,  8  by  SH  in,  or  66 
sq  in.  The  tests  of  the  second  set  gave  unit  crushing  strengths  12%  higher  than 
the  first,  and  those  of  the  third  set  unit  crushing  strengths  28%  higher  than 
the  first. 

Working  Stress  for  Bearing  on  Concrete.  "When  compression  is  applied 
to  a  surface  of  concrete  of  at  least  twice  the  loaded  area,  a  stress  of  32.5%  of 
the  compressive  strength  may  be  allowed,  "t 

Working  Stress  for  Axial  Compression  on  Concrete.  "For  concentric 
compression  on  a  plain  concrete  column  or  pier,  the  length  of  which  does  not 
exceed  12  diameters,  22.5  %  of  the  compressive  strength  may  be  allowed."  * 
(For  the  strength  of  reinforced-concrete  columns,  see  Chapter  XXIV,  page  945.) 

Recommended  Ultimate  Compressive  Strengths  of  Portland-Cement 
Concrete. I  Table  XIV,  of  ultimate  compressive  strengths  of  concrete  of 
different  mixtures  gives  the  values  recommended  by  the  American  Society  for 
Testing  Materials,  even  though  occasional  tests  show  higher  results.  The 
values  given  are  recommended  as  the  maximum  ultimate  unit  compressive 
strengths  that  should  be  used  in  design  and  on  which  the  permissible  working 
stresses  should  be  based  as  a  proper  percentage  of  the  same.  The  report  referred 
to  states,  also,  that  "in  selecting  the  permissible  working  stresses  to  be  allowed 
on  concrete,  we  should  be  guided  by  the  working  stresses  usually  allowed  for 
other  materials  of  construction,  so  that  all  structures  of  the  same  class,  but 
composed  of  different  materials,  may  have  approximately  the  same  degree  of 
safety. "  (For  working  stresses  for  concretes,  masonry,  etc.,  see  this  chapter, 
pages  265  to  276.) 

*  See  University  of  Illinois  Bulletin,  No.  20,  1907,  and  Engineering  News,  Sept.  26, 
1907. 

t  See  Reinforced  Concrete  Construction,  Vol  I.,  page  i8,  by  George  A.  Hool. 

t  Report  of  Committee  on  Concrete  and  Reinforced  Concrete,  of  the  American  Society 
for  Testing  Materials,  Nov,  20,  1912, 


280      Strength  of  Brick,  Stone,  Mass-Concrete  and  Masonry     Chap.  5 

Table  XIV.     Ultimate  Compressive  Strengths  of  Different  Mixtures  of 
Portland-Cement  Concretes 


Aggregates 

Mixtures 

1:1:2 

lb  per 

sq  in 

1  :iK'  :3 

lb  per 
sq  in 

1:2:4 

lb  per 
sq  in 

I  :  2H  :  5 

lb  per 

sq  in 

1:3:6 

lb  per 
sq  in 

3300 

3000 

2  200 
800 

2800 
2  500 

I  800 

700 

2  200 

2  000 

I  500 
600 

1800 

I  600 

I  200 
500 

I  400 
I  300 

1  boo 

400 

Gravel,  hard  limestone  and 
hard  sandstone 

Soft   limestone   and   sand- 
stone 

Cinders 

Effect  of  Consistency  on  the  Crushing  Strength  of  Concrete.  Concrete 
that  is  mixed  fairly  dry  and  tamped  until  the  moisture  is  brought  to  the  surface, 
develops  a  somewhat  greater  compressive  strength  than  concrete  mixed  with 
more  water.  From  a  large  number  of  tests  *  average  compressive  strengths  of 
wet,  plastic  and  dry  concretes  were  determined.  The  age  of  the  concrete  was 
1  year  and  8  months,  and  five  brands  of  cements  were  used.  The  mean  com- 
pressive strengths  were,  for  the  wet  concrete,  2  130;  for  the  plastic^  2  200; 
and  for  the  dry,  2  350  lb  per  sq  in. 

In  another  series  of  tests  f  greater  differences  appeared.  At  the  age  of  i 
month  the  mean  compressive  strengths  in  ix)unds  per  square  inch  were,  for  the 
wet  concrete:  granite,  3  155;  gravel,  2  300;  limestone,  4  195.  For  the  medium 
concrete:  granite,  4090;  gravel,  3  545;  limestone,  2  975.  For  the  damp  con- 
crete: granite,  4  520;  gravel,  4  610;  limestone,  4  365.  At  the  end  of  3  months 
the  values  for  the  granite  aggregates  were,  for  the  wet  concrete,  4  755;  for  the 
medium,  4  990;   and  for  the  damp,  5  445. 

Effect  of  Size  of  Stone  on  the  Compressive  Strength  of  Concretes.    It 

may  be  stated,  generally,  that  the  use  of  stones  of  a  maximum  size  consistent 
with  convenience  generally  results  in  a  maximum  compressive  strength  in  the 
concrete.  Stones  of  the  larger  sizes  are  generally  more  uniformly  graded  than 
the  smaller  stones,  and  consequently  grade  better  with  the  sand  and  give  greater 
strength.  From  tests  t  made  by  W.  B.  Fuller,  the  average  compressive  strengths, 
at  140  days,  of  i  :  9  concrete,  were,  for  maximum  size  of  stone  J-i  in,  i  000  lb 
per  sq  in;  for  i-in  stone,  i  150  lb  per  sq  in;  and  for  2^-in  stone,  i  400  lb  per 
sq  in. 

Comparison  of  Compressive  Strengths  of  Gravel  and  Stone  Concretes. 

Concretes  made  with  broken  stone  have,  gcnerall}'-,  a  somewhat  greater  com- 
pressive strength  than  those  made  with  gravel.  From  tests  made  by  E.  Candlot, 
the  average  compressive  strength  at  30  and  180  days,  of  concrete  made  with 
iH-in.  maximum-size  broken  stone,  was  20%  greater  than  that  of  concrete  made 
of  gravel  of  about  the  same  size,  the  percentage  of  voids  being  nearly  the  same, 
40%  voids  for  the  gravel  and  47.4%  voids  for  the  broken  stone.  The  average 
difference  at  12  months,  however,  was  reduced  to  9%. 

*  Made  for  G.  W.  Rafter.     See  "Tests  of  Metals,"  1898. 

t  Made  in  1908.     See  Bulletin  No.  344,  United  States  Geological  Survey. 

t  See  Trans.  Am.  Soc.  C.  E.,  Vol.  59,  1907. 


Building  Laws  for  Working  Loads  on  Masonry  287 

Effect  of  the  Strength  of  the  Aggregate  on  the  Compressive  Strength 
of  Concrete.  The  compressive  strength  of ,  trap-rocks,  granites  and  most 
limestones  is  relatively  so  great  that  it  cannot  reduce  the  strength  of  the  con- 
crete itself.  Some  sandstones,  however,  have  a  much  lower  average  compressive 
strength,  and  if  they  are  friable  and  soft  may  lower  relatively  the  final  strength 
of  the  concrete.  A  concrete  of  low  strength  results  from  using  cinders  for  the 
aggregate. 

Building  Laws  for  Working  Loads  on  Masonry.*  As  previously  mentioned 
(page  265)  the  building  codes  of  most  cities  specify  working  loads  to  be  used  for 
masonry  and  as  shown  in  Table  II  (page  267)  these  loads  vary  greatly.  It  is 
important,  therefore,  that  the  architect  should  be  acquainted  with  the  municipal 
code  by  which  the  construction  of  his  building  is  governed.  As  building  laws 
and  regulations  are  constantly  changing  this  information  should  be  obtained 
from  the  code  itself,  care  being  taken  that  the  latest  edition  and  all  supplements 
are  consulted.  A  few  requirements,  pecuHar  to  the  codes  in  which  they  are 
found,  will  be  cited. 

The  Chicago  code  (1916)  gives  for  eight  classes  of  brickwork  bearing  values 
ranging  from  100  lb  per  sq  in  for  common  brick  with  good  lime  mortar  to  350 
lb  per  sq  in  for  paving  brick  with  i  to  3  Portland-cement  mortar.  This  code 
discriminates  between  concrete  mixed  by  hand  and  by  machine,  values  of  from 
to  250  to  350  lb  per  sq  in  being  given  for  hand-mixed  concrete  and  from  300  to 
400  lb  per  sq  in  for  the  same  mixture  if  mixed  by  machine.  The  values  in  the 
Buffalo  code  are  exceptionally  low,  common  brick  laid  in  lime  mortar  being 
allowed  but  3  tons  and  concrete  in  foundations  but  4  tons  per  sq  ft.  The 
Louisville  code  introduces  values  for  "Louisville-cement  mortar."  The  practice 
of  stating  values  of  local  material  is  to  be  commended.  The  Denver  code  gives 
a  value  of  3  tons  per  sq  ft  on  common  brick  with  coal-dust  in  lime  mortar,  3  tons 
for  hollow  tile  in  cement  mortar  and  8  tons  for  terra-cotta,  solid,  in  cements 
The  Seattle  code  gives  for  the  allowable  compressive  stress  of  mass  concrete 
20%  of  its  compressive  strength  in  twenty-eight  days.  The  building  code  rec- 
ommended by  the  National  Board  of  Fire  Underwriters  is  followed  by  a  number 
of  cities.  This  code  includes  in  its  list  of  allowable  compression  values,  1000  lb 
per  sq  in  for  Portland-cement  grout,  neat,  and  1500  lb  per  sq  in  for  Portland- 
cement  grout,  neat,  not  over  yi  in  thick,  between  steel  members  in  foundations. 
For  natural-cement  concrete  values  are  given  of  125  lb  per  sq  in  for  a  i  :  2  :  4 
mixture  and  80  lb  per  sq  in  for  a  i  :  2  :  5  mixture.  The  average  ultimate  com- 
pressive strength  for  terra-cotta  blocks  designed  to  be  normally  laid  with  the 
cells  vertical,  and  which  are  tested  with  the  cells  in  that  position,  must  not  be 
less  than  1200  lb  per  sq  in.  The  allowable  working  stress  on  such  blocks  must 
not  exceed  120  lb  per  sq  in.  The  average  ultimate  compressive  strength  for 
terra-cotta  blocks  designed  to  be  normally  laid  with  the  cells  horizontal,  and 
which  are  tested  with  the  cells  in  that  position,  must  not  be  less  than  800  lb 
per  sq  in.  The  allowable  working  stress  on  such  blocks  must  not  exceed  80  lb 
per  sq  in.  Hollow  building  blocks  may  be  filled  solidly  with  Portland-cement 
concrete  or  cement  mortar  to  increase  the  stability  and  to  aid  in  distributing 
the  load,  but  the  allowable  working  stress  on  such  blocks  must  not  be  greatet 
than  that  permitted  for  unfilled  blocks. 

*  Condensed  from  valuable  data  from  Robins  Fleming.  See,  also,  pages  265  to  267 
and  Table  II,  page  267. 


288 


Forces  and  Moments 


Chap.  6 


CHAPTER   VI 
FORCES   AND   MOMENTS 

By 
MALVERD   A.   HOWE 

PROFESSOR   OF    CIVIL  ENGINEERING,    ROSE   POLYTECHNIC   INSTITUTE 

1.    Composition  and  Resolution  of  Forces 

Composition  and  Resolution  of  Forces.  Imagine  a  round  ball  placed  on  a 
plane,  frictionless  surface  at  A  (Fig.  1),  the  surface  being  perfectly  level,  so  that 
the  ball  has  no  tendency  to  move  until  some  force 
is  applied  to  it.  If,  now,  the  force,  F,  is  applied 
to  the  ball  in  the  direction  indicated  by  the  arrow, 
the  ball  will  move  in  that  direction.  If,  instead  of 
one  force  only,  two  forces,  P  ajid  Pi,  are  apphed  to 
the  ball,  it  will  not  move  in  the  direction  of  either 
of  the  forces,  but  will  move  in  the  direction  of  the 
RESULTANT  of  thcse  forces,  or  in  the  direction  Ab. 
If  the  magnitudes  of  the  forces  P  and  Pi  are 
indicated  by  the  lengths  of  the  lines,  then,  if  we 
complete  the  parallelogram  ABDC,  the  diagonal 
DA  represents  the  direction  and  magnitude  of  a 
single  force  which  has  the  same  effect  on  the  ball 
as  that  resulting  from  the  two  forces  P  and  Pi.  If,  in  addition  to  the  two 
forces  P  and  Pi,  the  third  force,  P2,  is  applied,  the  ball  will  move  in  the 
direction  of  the  resultant  of  all  three  forces,  and  this  resultant  is  obtained  by 
completing  the  parallelogram  ADEF,  of  which  the  resultant  DA  and  the  third 
force  Pi  are  two  adjacent  sides.  The  diagonal  R  of  this  second 
parallelogram  is  the  resultant  of  all  three  forces,  and  the  ball 
will  move  in  the  direction  Ae.  In  the  same  way  the  resultant 
of  any  number  of  forces  may  be  found.  Again,  suppose  a 
ball,  whose  weight  is  indicated  by  the  length  of  the  line  W 
(Fig.  2),  is  suspended  by  two  inclined  cords.  What  are  the 
magnitudes  of  the  pulls  or  stresses  which  are  developed  in  the 
cords  and  which  keep  the  ball  suspended  at  the  point  A? 
This  is  the  converse  of  the  last  case.  Instead  of  finding  the 
diagonal  or  the  resultant,  the  diagonal,  which  is  the  line  W,  is 
given,  and  the  sides  of  the  parallelogram  are  to  be  found.  To 
find  these  the  lines  representing  the  directions  of  P  and  Pi  are 
prolonged  and  from  B  lines  parallel  to  them  are  drawn  to 
complete  the  parallelogram.  Then  CA  is  the  required  mag- 
nitude of  the  stress  in  cord  P,  and  BC  of  that  in  cord  Pi.  Thus  one  force  may 
have  the  same  effect  as  many,  or  many  the  same  effect  as  one. 

Forces  Represented  by  Straight  Lines.  In  considering  the  action  of  forces, 
it  is  convenient  to  represent  them  graphically  by  straight  lines  with  arrow- 
heads, as  in  Fig.  3.  The  length  of  the  hne,  if  drawn  to  a  scale  of  pounds,  repre- 
sents the  MAGNITUDE  OF  THE  FORCE  in  pouuds;  the  position  of  the  line  indicates 


Fig.  1 .    Composition  of  Forces 


B 

Fig.  2.     Resolu- 
tion of  Forces 


Moments  of  Forces 


289 


Fig.  3.     Force  Represented 
by  a  Straight  Line 


Parallelogram  of 
Forces 


its  LINE  OF  action;   the  arrow-head  indicates  its  sense  or  the  direction  in  which 

it  acts;    and  the  point  A   its  point  of  application.      Thus  the  magnitude, 
direction  and  point  of  appli- 
cation are  indicated  and  the 
force    is    completely    repre- 
sented. 

Parallelogram  of  Forces. 
If  two  forces  applied  at  one 
point  are  represented  in  mag- 
nitude and  direction  by  two 

straight    lines   inclined  to  each  other,   their   resultant   is  the  diagonal   of  the 

PARALLELOGRAM  formed  on  those  lines.      Thus,  if  the  lines  AB  and  AC  (Fig.  4) 

represent  two  forces  acting  at  a  point  A,  to  find  the  force  which  will  have  the 

same  effect  as  the  two  forces,  the   parallelogram 

ABDC  is  completed  and  the  diagonal  AD  drawn. 

This  line   represents   the   resultant  of   the    two 

forces.     When  the  two  given  forces  act  at  right- 
angles  to  each  other,  the  magnitude  of  the  resultant 

is  equal   to   the   square  root  of   the   sum   of  the 

squares  of  the  magnitudes  of  the  other  two  forces. 
Triangle  of  Forces.     If  three  forces  acting  at 

a  point  are  represented  in  magnitude  and  direction 

by  the  sides  of  a  triangle  taken  in  order,  they  arc 

in  equilibrium.     Let  P,  Q  and  R  (Fig.  5)  represent 

three  forces  acting  at  the  point  0.     If  a  triangle 

can  be  drav/n,  like  that  shown  at  the  right  in  Fig. 

6,  having  sides  respectively  parallel  to  the  direc- 
tions of  the  forces  and  taken  in  the  same  order, 

the  forces  are  in  equilibrium.     If  such  a  triangle  cannot  be  drawn,  the  forces 

are  not  in  equilibrium. 

The  Polygon  of  Forces.     If  any  number  of  forces  acting  at  a  point  can 

be  represented  in  magnitude  and  direction   by  the  sides  of  a  polygon  taken 


Triangle  of  Forces 


in  order,  they  are  in   equihbrium. 
theorem. 


This  follows  directly  from  the  preceding 


2.   Moments  of  Forces 


Moments.  In  considering  the  stability  of  structures  and  the  strength  of 
materials,  we  are  often  obliged  to  take  into  consideration  the  moments  of 
the  forces  acting  on  a  structure  or  on  some  part  of  a  structure;  and  a  knowledge 
of  the  general  principles  of  moments  is  essential  to  the 
proper  understanding  of  these  subjects.  When  we  speak  of 
the  MOMENT  OF  A  FORCE,  we  must  have  in  mind  some  fixed 
point  or  line  with  respect  to  which  the  moment  is  taken. 
The  moment  of  a  force  with  respect  to  any  given  point,  or 
CENTER  OF  MOMENTS,  is  the  product  of  the  magnitude  of 
the  force  and  the  perpendicular  distance  from  the  point  to 
the  LINE  OF  ACTION  of  the  force;  or,  in  other  words,  the  mo- 
ment of  a  force  is  the  product  of  the  magnitude  of  the  force  by 
the  ARM  with  which  it  acts.  Thus  if  we  have  the  force  F  (Fig.  6).  and  wish  to 
determine  its  moment  with  respect  to  the  point  F,  we  determine  the  per- 
pendicular distance  Pa,  between  th?  point  and  the  line  of  action  of  the  force, 
and  multiply  it  by  the  magnitude  of  the  force.     For  example,  if  the  magnitude 


290 


Forces  and  Moments 


Chap.  6 


Fig.  7. 


Pi 


Algebraic  Sum  of  Unlike 
Parallel  Forces 


-B 


-h-^ — >: 


3- 


Fig.  8.     Algebraic  Sum  of   Mo- 
ments of  Unlike  Parallel  Forces 


B 


of  the  force  F  is  500  lb  and  the  distance  Pa  is  2  in,  the  moment  of  the  force 
with  respect  to  the  point  P  is  500  lb  X  2  in  =  i  cx50  in-lb.* 

Parallel  Forces.  If  any  body  is  in  a  state  of  rest  or  equilibrium  under  the 
action  of  parallel  forces,  the  sum  of  the  forces  acting  in  one  direction  equals  the 

sum  of  the  forces  acting  in  the  opposite 
direction.  Thus  if  we  have  the  parallel 
forces  Pi,  P^  P^  and  P^  acting  on  the  rod 
AB  (Fig.  7),  in  a  direction  opposite  to  that 
of  the  forces  Pi,  Pi  and  Pa,  then,  if  the  rod 
is  in  equilibrium,  the  sum  of  the  forces  P^, 
P2,  P3  and  P**  must  equal  the  sum  of  the 
forces  Pi,  P2  and  P3. 

Parallel  Forces  Opposite  in  Character. 
If  any  number  of  parallel  forces,  not  all 
acting  in  the  same  direction,  act  on  a  body, 
if  the  body  is  in  equilibrium,  the  sum  of  the 
moments  of  the  forces  tending  to  turn  the 
body  in  one  direction  about  any  given 
point  is  equal  to  the  sum  of  the  moments  of  the  forces  tending  to  turn  it  in 
the  opposite  direction.  Let  Pi,  P2  and  Fz  (Fig.  8)  represent  three  parallel 
forces  acting  on  the  rod  AB.  If  the  rod  is  in  equilibrium,  the  sum  of  the 
forces  F2  and  P3  is  equal  to  Pi.  Also,  if  we 
lake  the  end  of  the  rod,  A,  for  the  center  of 
moments,  the  moment  of  Pi  is  equal  to  the  sum 
of  the  moments  of  P2  and  P3  about  that  point, 
because  the  moment  of  Pi  measures  the  tend- 
ency to  turn  the  rod  clockwise,  and  the  sum 
of  the  moments  of  P2  and  P3  measure  the  tend- 
ency to  turn  the  rod  contra-clockwise,  and 
there  is  no  more  tendency  to  turn  the  rod  one 
way  than  the  other.  For  example,  let  the  mag- 
nitude of  forces  P2,  P3  each  be  represented  by  5 
force-units,  the  distance  Aa  by  2  length-anits 
and  the  distance  AB  hy  4  length-units.  The 
magnitude  of  the  force  Pi  must  equal  the  sum 
of  the  magnitudes  of  the  forces  P2  and  P3,  or  10  force-units,  and  its  moment 
with*  respect  to  any  point  in  the  plane  of  the  forces  must  equal  the  sum 
of  the  moments  of  P2  and  Fz  with  respect  to  the  same  point.  If  we  take  A  as 
the  center  of  moments,  the  moment  of  Pi  =  5  x  2  =  10,  and  of  P2  =  5  X  4  =  20. 
Their  sum  equals  30;  hence  the  moment  of  Pi  must  be  30.  Dividing  .the  mo- 
ment 30  by  the  force  Pi  =  10  force-units,  we  have  for  the  arm,  3  length-units;  or 
the  force  Pi  must  act  at  a  distance  of  3  units  from  A  to  keep  the  rod  in  equilib- 
rium. If  we  take  h  as  the  center  of  moments,  the  force  Pi  has  no  moment,  as 
the  length  of  its  lever-arm  is  zero;  and,  for  equilibrium,  the  moment  of  P2  about 
h  must  equal  the  moment  of  P3  about  the  same  point;  or,  as  in  this  case  the 
magnitudes  of  the  forces  P2  and  Fz  are  equal,  they  must  both  be  applied  at  the 
same  distance  from  b,  showing  that  b  must  be  half-way  between  a  and  B,  as  was 
demonstrated  before. 

Three  Parallel  Forces,  the  principle  op  the  lever.  This  principle  is 
based  upon  the  two  preceding  propositions  and  is  of  great  importance  and  con- 

*  The  expressions  pound-feet  and  pound-inches  are  often  given  to  these  products 
♦o  distinguish  them  from  foot-pounds  and  inch-pounds,  by  which  work  and  energy 
are  measured. 


Center  of  Gravity 


291 


venience.  If  a  body  is  in  equilibrium  under  the  action  of  three  parallel  forces 
acting  in  the  same  plane,  each  force  is  proportional  to  the  normal  distance  be- 
tween the  other  two.     Thus,  if,  as  in  Figs.  9,  10  and  1 1,  three  forces,  Pi,  Pt  and 


i 

\ 

? 

16 

A>'          C 

, 

6 

12 

Q 

( 

> 

5 

Pa 

p« 

Pi 

Fig.  9.     Principle  of  the  Lever 


Fig.  10.     Principle  of  the  Lever 


6 


Pa,  act  on  the  rod  AB,  in  order  that  it  may  be  in  equilibrium,  the  following 
relations  must  obtain  between  the  magnitudes  of  the  forces  and  the  distances 
between  their  points  of  application; 

Pi_     Pi^     Pi^ 
CB  ' AB  '  AC 

or  Pi:P2:Pz::CB:AB:AC 

This  is  the  case  of  the  common  lever  and  shows  the  method  of  determining 
what  weight  a  given  lever  will  raise.  The  proportion  is  also  true  for  any  ar- 
rangement of  the  forces  (as  shown  in  Figs.  9,  10  and  11),  provided,  of  course, 
the  forces  are  lettered  in  the  order  shown  in  the 
figures. 

For  example,  let  the  distance  ^C  be  6  in  and  the 
distance  CB,bc  12  in.  If  a  weight  of  500  lb  is 
applied  at  the  point  B,  how  much  will  it  raise  at 
the  other  end  and  what  support  will  be  required  at 
C  (Fig.  10)? 

Applying  the  rule  just  given,  we  have  the  pro- 
portion; 

Pa-.Pi-.iACiCB    or    500:  Pi::  6:  12 

Hence  Pi  =  i  000  lb;  or  500  lb  applied  at  B  will  Fig.  11.  Principle  of  the  Lever 
lift  I  000  lb  resting  on  or  suspended  at  A.     The 

supporting  force  at  C  must,  by  the  principles  of  parallel  forces  im 
EQUILIBRIUM,  be  cqual  to  the  sum  of  the  forces  Pi  and  Ps,  or  i  500  lb  in 
this  case. 

3.   Center  of  Gravity 

General  Principles.  The  lines  of  action  of  the  force  of  gravity  converge 
towards  the  center  of  the  earth;  but  the  distance  of  the  center  of  the  earth  from 
the  bodies  which  we  have  occasion  to  consider,  compared  with  the  size  of  those 
bodies,  is  so  great,  that  we  may  consider  the  lines  of  action  of  the  forces  as 
parallel.  The  number  of  the  forces  of  gravity  acting  upon  a  body  may  be  con- 
sidered as  equal  to  the  number  of  particles  composing  the  body.  The  center  of 
GRAVITY  of  a  body  may  be  defined  as  the  point  through  which  the  resultant  of 
the  parallel  forces  of  gravity,  acting  upon  the  body,  passes  for  every  position 
01  ine  body.     If  a  body  is  supported  at  its  center  of  gravity  and  turned  about 


Px 


292  Forces  and  Moments  Chap.  6 

that  point,  it  will  remain  in  equilibrium  in  all  px)sitions.  The  resultant  of  the 
parallel  forces  of  gravity  acting  upon  a  body  is  obviously  equal  to  the  weight 
OF  THE  body;  and  if  a  force,  equal  in  magnitude  to  the  resultant,  is  applied, 
acting  in  a  line  passing  through  the  center  of  gravity  of  the  body,  and  in  a 
direction  opposite  to  that  of  the  resultant,  the  body  will  be  in  equilibrium. 

Center  of  Gravity  of  a  Straight  Line.  The  word  line  here  means  a 
material  line  whose  transverse  section  is  very  small,  such  as  a  very  fine  wire. 
The  center  of  gravity  of  a  straight  line  or  rod  of  uniform  size  and  material  is 
at  its  middle  point.     This  proposition  is  too  evident  to  require  demonstration. 

The  Center  of  Gravity  of  the  Perimeter  of  a  Triangle  is  at  the  center 
of  the  circle  inscribed  in  the  triangle  formed  by  the  lines  joining  the  middle 
points  of  the  sides  of  the  given  triangle.  Thus, 
let  ABC  (Fig.  12)  be  the  given  triangle.  To  find 
the  center  of  gravity  of  its  perimeter,  find  the 
middle  points,  D,  E  and  F,  and  connect  them  by 
straight  lines.  The  center  of  the  circle  inscribed 
in  the  triangle  formed  by  these  lines  will  be  the 
center  of  gravity  sought. 

°  F  Center  of  Gravity  of  Symmetrical  Lines. 

Fig.  12.     Center  of  Gravity  of    The  center  of  gravity  of  a  line  which  is  sym- 
Perimeter  of  Triangle  metrical   with   reference   to   a   point   is  at   that 

point.  Thus 'the  center  of  gravity  of  the  cir- 
cumference of  a  circle  or  of  an  ellipse  is  at  the  geometrical  center  of  the  figures. 
The  center  of  gravity  of  the  perimeter  of  an  equilateral  triangle,  or  of  a 
regular  polygon,  is  at  the  center  of  the  inscribed  circle.  The  center  of  gravity  of 
the  perimeter  of  a  square,  rectangle,  or  parallelogram  is  at  the  intersection  of 
the  diagonals  of  those  figures. 

Center  of  Gravity  of  a  Surface.  A  surface  here  means  a  very  thin  plate 
or  shell.  If  a  surface  can  be  divided  by  a  line  into  two  symmetrical  halves,  the 
center  of  gravity  will  be  on  that  line;  if  it  can  thus  be  divided  by  two  lines,  the 
center  of  gravity  will  be  at  their  intersection. 

Center  of  Gravity  of  Regular  Figures.  The  center  of  gravity  of  the  sur- 
face of  a  circle  or  an  ellipse  is  at  the  geometrical  center  of  the. figure;  of  an 
equilateral  triangle  or  regular  polygon,  at  the  center  of  the  inscribed  circle;  of 
a  parallelogram,  at  the  intersection  of  the  diagonals;  of  the  surface  of  a  sphere, 
or  of  an  eUipsoid  of  revolution,  at  the  geometrical  center  of  the  body;  and  of 
the  convex  surface  of  a  right  cylinder,  at  the  middle  point  of  the  axis  of  the 
cylinder. 

Center  of  Gravity  of  Irregular  Figures.    Any  figure  bounded  by  straight 
lines  may  be  divided  into  rectangles  and  triangles,  and,  the  center  of  gravity 
of  each  part  being  found,  the  center  of  gravity  of  the  whole  figure  may  be  deter- 
mined by  treating  the  centers  of  gravity  of  the  separate  parts  as  particles  whose  • 
weights  are  proportional  to  the  areas  of  the  parts  they  represent.     (See  page  296.) 

Center  of  Gravity  of  Triangles.  To  find  the  center  of  gravity  of  a  tri- 
angle, draw  a  line  from  each  of  two  angles  to  the  middle  of  the  opix)site  side. 
The  intersection  of  the  two  lines  is  the  center  of  gravity. 

Center  of  Gravity  of  Quadrilaterals.  To  find  the  center  of  gravity  of  any 
quadrilateral,  draw  the  diagonals,  and  from  that  end  of  each  diagonal  which  is 
farthest  from  the  intersection,  lay  off,  toward  the  intersection,  the  length  of 
its  shorter  segment.    The  two  points  thus  formed,  together  with  the  point  ol 


Center  of  Gravity 


293 


intersection,  will  form  a  triangle  whose  center  of  gravity  is  that  of  the  quad- 
rilateral. Thus,  let  Fig.  13  be  a  quadri- 
lateral whose  center  of  gravity  is  to  be 
found.  Draw  the  diagonals  AD  and  BC, 
and  from  A  lay  oQ  AF  =  DE,  and  from  B 
lay  off  BH  =  CE.  From  E  draw  a  line  to 
the  middle  of  FH,  and  from  F  a  line  to  the 
middle  of  EH.  The  point  of  intersection 
of  these  two  lines  is  the  center  of  gravity 
of  the  quadrilateral.  This  is  a  method 
commonly  used  for  finding  the  centers  of 
gravity  of  the  voussoirs  of  an  arch. 

Table  of  Centers  of  Gravity.    Let  a 
be  a  line  drawn  from  the  vertex  of  a  figure 
to  the  middle  point  of  the  base,  and  D  the  distance  from  the  vertex  to  the  center 
of  gravity  of  the  figure.     Then  (Fig.  14) : 


Center     of     Gravity 
Quadrilateral 


In  an  isosceles  triangle ^  =  % 

In  a  segment  of  a  circle,  vertex  at  center  of  circle    D  = 


chord^ 


In  a  sector  of  a  circle,  vertex  at  center  of  circle     D  ■■ 
In  a  semicircle,  vertex  at  center  of  circle D 


12  X  area 

2  X  chord 

:  R  X '■ 

4R    3Xarc 


:    =    0.4244!? 

In  a  quadrant  of  a  circle D  =  %R 

In  a  semieliipse,  vertex  at  center  of  circle D  =  0.4244  a 

In  a  parabola,   vertex  at  intersection  of  axis 

with  curve D  =  %a 

In  a  cone  or  pyramid D  =  %a 


IsoBcxjles  Triangle 


Segment  of  Circle 


Sector  of  Circle 


Fig.  14.     Center  of  Gravity  of  Triangle,  Segment  and  Sector 


In  a  frustum  of  a  cone  or  pyramid,  let  h  =  the  height  of  the  complete  cone  or 
pyramid,  hi  =  the  height  of  the  frustum,  and  let 
P*W  the  vertex  be  at  the  apex  of  the  complete  cone 

or  pyramid;   then, 


e- 


B 


-e 

w 


D  = 


4  (A3  -  hi^) 


Fig. 


15.     Center  of  Gravity  of 
Two  Heavy  Particles 


Center  of  Gravity  of  Two  Heavy  Particles. 

Let  F  be  the  weight  of  a  particle  at  A  (Fig.  15), 
and  W  that  of  a  particle  at  C.  The  center  of 
gravity  is  at  some  point,  B,  on  the  line  joining  A 
and  C.  The  point  B  must  be  so  situated  that  if  the  two  particles  were  held 
together  by  a  stiff  wire  and  supported  at  B  by  a  force  equal  in  magnitude  to 
the  sum  of  P  and   W  they  would  be  in  equilibrium.     The  problem  then  is 


294 


Forces  and  Moments 


Chap.  6 


W2 

Fig.  16.     Center  f»f  Gravity 
of  Several  Heavy  Particles 


solved  by  the  principle  of  the  lever,  and  we  have  the  proportion  (see 
Three  Parallel  Forces.     The  Principle  of  the  Lever), 

P+W:  P::  AC:  BC 

If  W  =  P,  then  BC=  AB,  or  the  center  of  gravity  will  be  half- way  between  the 
two  particles.  This  problem  is  of  great  importance  and  has  many  practical 
appUcations. 

Center  of  Gravity  of  Several  Heavy  Particles.  Let  W\,  Wi,  Wz,  Wa 
and  \W  (Fig.  16)  be  the  weights  of  the  particles.  Join  W\  and  Wi  by  a  straight 
line  and  find  their  center  of  gravity  A,  as  in  the 
preceding  problem.  Join  A  with  Wz  and  find  the 
center  of  gravity  B,  which  will  be  the  center  of 
gravity  of  the  three  weights  Wi,  W2,  W3.  Proceed 
in  the  same  way  with  each  weight.  The  last  center 
of  gravity  found  will  be  the  center  of  gravity  of  all 
the  particles.  In  both  of  these  cases  the  lines  joining 
the  particles  are  supposed  to  be  horizontal  lines,  or 
else  the  horizontal  projections  of  the  straight  lines 
which  join  the  points. 

Center  of  Gravity  of  Compound  Sections 
Found  by  Moments.  To  determine  the  strength 
of  a  beam  having  an  unsymmetrical  cross-section,  it 
is  first  necessary  to  determine  the  distance  of  the  center  of  gravity  of  this  section 
from  the  upper  or  lower  surface  of  the  beam.  Various  other  computations, 
also,  involve  finding  the  center  of  gravity  of  an  irregular  figure,  so  that  the 
problem  is  one  of  practical  importance.  If  the  figure  of  which  the  center  of 
gravit}^  is  to  be  found  can  be  divided  into  parts  which  are  themselves  regular 
figures,  the  readiest  and  simplest  method  of  finding  the  distance  of  the  center 
of  gravity  from  one  edge  of  the  section  is  by 
means  of  moments.  To  explain  this  method 
assume  a  T-shaped  section  of  uniform  thick- 
nes?,  hinged  on  a  wire  XX,  as  in  Fig.  17. 
The  T  section  is  made  up  of  two  rectangles, 
one  forming  the  flange,  the  other  the  web. 
The  center  of  gravity  of  each  rectangle  is  at 
its  own  center  of  figure  and  may  be  readily 
found.  If  the  T  section  is  placed  horizon- 
tally, as  in  the  figure,  the  axis  XX  being 
fixed,  it  will   immediately,   by  the  force   of 

gravity,  revolve  about   the  axis  until  it  be-  '  -^ 

comes  vertical,  and  the  sum  of  the  moments  fig.    17.     Center    of    Gravity    of 
of    the    forces    causing    the     revolution     is      Compound  Sections  by  Moments 
A'  Xd'  -^  A"  X  d",     A '     representing     the 

weight  of  the  web  and  A"  the  weight  of  the  flange.  To  hold  the  T  section 
in  a  horizontal  position,  there  must  be  a  moment  of  some  force  acting  in  an 
opposite,  or  upward,  vertical  direction  and  just  equal  to  the  sum  of  the 
two  moments  causing  revolution  downwards.  If  the  force  A,  of  this  moment, 
tending  to  cause  revolution  upward,  is  equal  to  the  weight  of  the  entire  T  sec- 
tion, it  must  be  applied  at  the  center  of  gravity  of  the  entire  figure  to  make  its 
moment  just  equal  to  the  sum  of  the  moments  of  the  two  downward  forces. 


Center  of  Gravity 


295 


But  the  moment  oi  AhAxd,  therefore  d  is  the  distance  from  the  end  of  the  web, 
or  from  the  axis  XX,  to  the  center  of  gravity  of  the  entire  figure.  Therefore, 
since  Axd  =  A' X  d' -{- A"  X  d", 


J  = 


A'xd'-^A"xd" 


(i) 


d 


As  the  weight  of  any  homogeneous  material  of  uniform  thickness  is  proportional 
to  the  area,  A,  A'  and  A"  may  be  used  to  represent  areas  as  well  as  weights. 
Expressing  formula  (i)  as  a  rule,  we  have: 

Center  of  Gravity  of  Compound  Figures.  The  distance  of  the  center  of 
gravity  of  a  compound  figure  from  any  line  of  reference  is  equal  to  the  sum  of 
the  products,  obtained  by  multiplying  the  area  of  each  of  the  simple  parts  into 
which  the  compound  figure  is  divided  by  the  distances  of  its  center  of  gravity 
from  the  line  of  reference, 
divided  by  the  area  of  the 
entire  figure.  This  rule  ap- 
plies to  any  compound  figure. 
Example  I.  Assume  that 
the  T  section  shown  in  Fig. 
17  has  the  dimensions  in- 
dicated. Then  A'  equals  6, 
A"  equals  8,  and  A  equals  14 
sqin;  and  <i' equals  3  and  </" 
equals  6^/^  in.  The  sum  of 
the  products  of  yl'  by  d'  and 
A"  by  d"  is  18  +  52  or  70  sq  in  x  in,  and  this  divide.d  by  14  sq  in,  the  area 
of  the  entire  figure,  gives  5  in  for  the  distance  d.  The  distance  d  of  the  center 
of  gravity  from  the  top  of  the  webs,  in  each  of  the  figures  shown  in  Fig.  20, 
is  found  by  the  following  formula: 


d 


3- 


Fig.  18.  Center  of  Grav- 
ity of  Tees,  Angles, 
Channels,  etc. 


o 

Fig.  19.     Center  of  Grav- 
ity o[  Irregular  I  Sec- 
« tion 


area  of  the  web  or  webs  x  d'/2  +  area  of  flange  x  d" 
area  of  the  web  or  webs  +  area  of  flange 


(2) 


For  a  section  like  that  shown  in  Fig.  18,  in  which  A',  A"  and  A'"  represent  the 
areas  of  the  respective  rectangles,  the  distance  d  of  the  center  of  gravity  from 
the  top  may  be  found  by  the  formula 


A'  X  d'  +  A"  x  d"  +  A"'  X  d'" 
A'^A"  +  A"' 


is) 


Example  II.     To  show  the  application  of  the  rule  for  finding  the  center  of 
gravity  of  compound  figures,  take  the  one  shown  in  Fig.  19.    The  distance  d 


JL\U]iJWJUl]UU 


Fig.  20.     Center  of  Gravity  of  Irregular  Figures 

of  the  center  of  gravity  of  the  entire  figure  from  the  vertex  O  is  found  as  follows: 
The  area  of  the  triangle  is  36  sq  in  and  of  the  semicircle  56.5  sq  in.  From  the 
Table  of  Centers  of  Gravity  (page  293)  the  distance  of  the  center  of  gravity  of 
an  isosceles  triangle  from  the  vertex  is  two-thirds  its  height,  which  gives  4  in  as 


296 


Forces  and  Moments 


Chap.  6 


the  value  for  d'.     The  center  of  gravity  for  a  semicircle  is  0.4244  R  from  its 
base,  so  that  d"  equals  8.54  in.     Then, 

36X4+56.SX  8.54 


d=- 


36  +  56.5 


=  6.77  in 


This  method  of  finding  the  center  of  gravity  is  similar  to  that  explained  in 
Chapter  IX  for  finding  the  supporting  forces  or  reactions.  In  the  latter  case, 
however,  the  problem  is  to  find  the  balancing  forces  instead  of  the  lever-arms. 

Additional  Methods  of  Determining  Graphically  the  Center  of  Gravity 
of  Irregular  Plane  Figures.*  The  center  of  gravity  may  be  obtained  graph- 
ically by  means  of  the  force-polygon  and  the  equilibrium-polygon.  The 
figure  or  section  considered,  Fig.  21,  is  divided  into  parts  whose  centers  of 


Fig.  21. 


Center  of  Gravity  Determined 
Graphically. 


Fig.  22.     Center  of  Gravity   Determined 
Graphically.     Second  Method. 


gravity  can  be  located  and  areas  calculated.  The  force-polygon  (b)  and  equilib- 
rium-polygon (c)  are  drawn.  The  figure  (a)  is  divided  into  rectangles  and  tri- 
angles, A,  D,  C  and  D,  and  vertical  hnes  are  drawn  through  their  centers  of 
gravity.  In  (b)  the  vertical  lines  a,  b,  c  and  d  are  respectively  proportional  in 
length  to  the  areas  yl,  ^,  C  and  D  The  pole,  O,  is  located  by  the  intersection  of 
lines  drawn  at  angles  of  45°  from  the  extremities  of  the  line  abed.  The  rays 
I,  2,  3,4  and  5  are  drawn  from  o,  as  shown,  and  the  corresponding  parallel  Hnes 
drawn  in  {c).  (See  Figs.  3  and  5,  pages  299  and  300;  Figs.  12  to  17,  pages 
314  to  320;  and  page  345)  The  vertical  fine  through  Y,  produced  upwards, 
is  a  GRAVITY-AXIS  and  its  intersection  G  with  the  horizontal  gravity-axis  XX  is 
the  center  of  gravity  of  the  figure.  If  the  figure  is  not  symmetrical  about 
XX  a  second  gravity-axis  may  be  found  by  turning  the  figure  through  90"*  and 
repeating  the  construction.  The  intersection  of  the  two  gravity-axes  will  be  the 
center  of  gravity  of  the  figure.  Another  method  is  shown  in  Fig.  22.  Let 
the  centers  of  gravity  of  two  areas  A  and  B  be  at  the  points  Ca  and  C^  respect- 
ively. From  Ca  the  line  CaD  is  drawn  in  any  direction,  and  its  length  represents 
on  some  given  scale  the  area  A.  From  Cb  the  line  Ci)E  is  drawn  parallel  to  it 
and  its  length  on  the  same  scale  represents  the  area  B.  The  intersection  of  the 
line  joining  D  and  E  with  CaCb  is  at  the  center  of  gravity  of  the  areas  A  and  B. 
For  three  areas  A ,  B  and  C,  the  construction  can  be  repeated  by  considering  A 
and  .6  as  a  single  area;  and  so  on  for  any  number  of  areas. 

•  Condensed  from  data  by  Robins  Fleming. 


Stability  of  Piers  and  Buttresses 


297„ 


CHAPTER  VII 

STABILITY  OF  PIERS  AND  BUTTRESSES* 

By 
GRENVILLE  TEMPLE   SNELLING 

LATE    MEMBER    OF    AMERICAN    INSTITUTE    OF    ARCHITECTS 

Mechanical  Principles.  A  pier  or  buttress  may  be  considered  stable  when 
the  forces  acting  upon  it  do  not  cause  it  to  rotate  or  tip  over  nor  cause  any 
course  of  masonry  to  slide  on  its  bed;  some  parts,  however,  of  the  masonry  may 
be  crushed.  Wlien  a  pier  sustains  a  vertical  load  only,  it  might  be  con- 
sidered stable,  but  it  might  not  have  sufficient  strength.  It  is  only  when  the 
pier  receives  a  thrust,  as  from  a  rafter  or  an  arch,  that  its  stability  must  be  con- 
sidered. In  order  that  there  may  be  no  rotation, 
the  moment  of  the  thrust  (Chapter  VI)  against 
the  pier  about  any  point  in  its  outside  edge  must 
not  exceed  the  moment  of  the  weight  of  the 
pier  about  the  same  point. 

To  illustrate  let  us  consider  the  pier  shown  in 
Fig.  1.  Let  us  suppose  that  this  pier  receives  the 
foot  of  a  rafter  which  exerts  a  thrust  T  in  the 
direction  AB.  The  tendency  of  this  thrust  is  to 
cause  the  pier  to  rotate  about  the  outer  edge  b\, 
and  the  moment  of  the  thrust  about  this  point, 
which  is  the  measure  of  this  tendency  to  rotate, 
is  r  X  d'hi,  a'bi  being  the  lever-arm  of  the  moment. 
For  unstable  equilibrium,  only,  the  moment  of 

the  weight  of  the  pier  about  the  same  edge  must  just  equal  Tx  a'h.  The 
resultant  force  representing  the  weight  of  the  pier  acts  vertically  through  its 
center  of  gravity  which  in  this  case  is  equidistant  from  its  sides;  and  its  lever- 
arm  is  h\c,  or  one-half  its  thickness. 

Hence,  for  equilibrium  of  moments,  we  must  have  the  equation 
TXa'h=Wy.hxc 

But  in  this  condition  the  least  additional  thrust,  or  the  crushing  of  the  outer 
edge,  will  cause  the  pier  to  rotate;  hence,  for  safety,  we  must  use  some  factor 
OF  safety.  This  is  sometimes  done  by  making  the  moment  of  the  weight  equal 
to  that  of  the  thrust  when  referred  to  a  point  in  the  bottom  of  the  pier,  a  cer- 
tain distance  in  from  the  outer  edge.  This  distance  for  piers  or  buttresses  should 
not  be  less  than  one-fourth  the  thickness  of  the  pier. 

Representing  this  point  in  the  figure  by  b,  we  have  the  necessary  equation  for 
the  safe  stability  of  the  pier 

TXah^WXtU 

t  being  the  width  of  the  pier. 

We  cannot  from  this  equation  determine  the  dimensions  of  a  pier  to  resist  a 
given  thrust,  because  we  have  the  distance  ab,  I  and  W ,  all  unknown  quantities. 
Hence  we  must  first  assume  a  tentative  size  for  the  pier,  find  the  length  of  the 
line  ab,  and  see  if  the  moment  of  the  weight  of  the  pier  is  equal  to  the  mo- 
ment of  the  thrust.  If  it  is  not  we  must  assume  another  size  for  the  pier. 
In  point  of  fact  the  steps  of  the  problem  usually  present  themselves  in  the 
*  See,  {ilso,  Chapter  XXXI,  Section  2,  Vaults. 


Pier  with  Thrust 


298  Stability  of  Piers  and  Buttresses  Chap.  7 

inverse  order,  the  pier  or  buttress  being  given  and  the  determination  of  its 
stability  being  required.  The  size  of  the  pier  or  buttress  is  usually  first  deter- 
mined rather  from  the  architectural  exigencies  of  the  design  than  from  the 
engineering  requirements  for  the  stabiUty  of  the  structure.  If  upon  investiga- 
tion these  are  not  in  accord,  it  is  the  duty  of  the  designers  to  use  their  ingenuity 
in  seeing  that  both  conditions  are  fufilUed. 

The  Stability  of  Piers  and  Buttresses.    When  it  is  desired  to  determine 

if  a  given  pier  or  buttress  is  capable  of  resisting  a  given  thrust,  the  problem  can 

_    be   solved    graphically  in    the   following   manner.     Let 

^  '     A  BCD  (Fig.  2)  represent  a  pier  which  sustains  a  given 

A  y  thrust  T  at  B.    To  determine  whether  the  pier  will  safely 

B  sustain  this  thrust,  we  proceed  as  follows: 

Draw  the  indefinite  line  BX  in  the  direction  of  the 
thrust.  Through  the  center  of  gravity  of  the  pier,  which 
in  this  case  is  midway  between  /ID  and  BC,  draw  a  ver- 


1 

4 

w 

L 

' 

X-         V  tical  Hne  intersecting  the  line  of  the  thrust  at  e.     As 

Dj 'C  force  may  be  considered  to  act  anywhere  along  its  line  of 

action,  we  may  consider  that  the  thrust  and  the  weight 
act  at  the  point  e.  The  resultant  of  these  two  forces  is 
'  Det!rminatTon  of  obtained  by  laying  ofif  the  thrust  T  from  e  on  eX,  and  the 
Thrust  on  Pier  weight  of  the  pier  W,  from  e  on  eY,  both  to  the  same  scale 

of  so  many  pounds  to  the  inch,  completing  the  parallel- 
ogram and  drawing  the  diagonal.  If  this  diagonal,  prolonged,  cuts  the  base 
of  the  pier  at  less  than  one-third  the  width  of  the  base  from  the  outer 
edge,  the  pier  is  generally  considered  unstable  and  its  dimensions  are  changed. 
(See  Chapter  IV,  Theorem  of  the  Middle  Third.) 

The  Stability  of  Buttress  with  Offsets.  The  stability  of  a  pier  may  be 
increased  by  adding  to  its  weight  by  placing  some  heavy  material  on  top,  for 
example,  or  by  increasing  its  width  at  the  base  by  means  of  offsets,  as  in 
Fig.  3.  Figs.  3  and  4  show  the  method  of  determining  the  stability  of  a  but- 
tress with  offsets.  The  first  step  is  to  find  the  vertical  line  passing  through  the 
center  of  gravity  of  the  whole  pier.  This  is  best  done  by  dividing  the  buttress 
into  quadrilaterals,  as  A  BCD,  DEFG  and  GTIIK  (Fig.  3),  finding  the  center  of 
gravity  of  each  quadrilateral  by  either  the  method  of  diagonals  or  triangles  as 
explained  in  Chapter  VI,  and  then  measuring  the  perpendicular  distances  X\, 
X2,  X3  from  the  different  centers  of  gravity  to  the  hne  KI.  (See,  also,  Chapter 
VIII,  page  313)- 

Multiply  the  area  of  each  quadrilateral  by  the  distance  of  its  center  of  grav- 
ity from  the  hne  KI  and  add  together  the  areas  and  the  products.  Divide  the 
sum  of  the  products  by  the  sum  of  the  areas  and  the  result  will  be  the  distance 
of  the  center  of  gravity  of  the  whole  buttress  from  KI.  This  distance  we  denote 
by  Xo.  This  calculation  is  a  practical  application  of  the  theorem  in  mechanics 
that  the  moment  of  the  resultant  of  any  number  of  forces  about  a  given 
point  is  equal  to  the  sum  of  moments  of  the  individual  forces  about  that  point. 

Example  i.  Let  the  buttress  shown  in  Fig.  3  have  the  dimensions  shown. 
Then  the  areas  of  the  quadrilaterals  and  the  distances  from  their  centers  of 
gravity  to  KI  are  as  follows: 

First  area  X  Xi  =  33.25 
Second  area  X  ^2  =  67.85 
Third  area     X    Xz  =  54.45 


First  area 

= 

35  sq 

ft 

Xi  = 

0' 

.q5 

Second  area 

= 

23  sq 

ft 

X2  = 

2' 

.95 

Third  area 

= 

II  sq 

ft 

:^3  = 

4' 

•95 

Total  area,  6^  sq  ft  Total  moments,  1 55-55 


Stability  of  Piers  and  Buttresses 


290 


The  sum  of  the  moments  of  the  areas  is  155.55,  and  dividing  this  by  the  tota^ 
area,  we  have  2.25  as  the  distance  Xq.  Measuring  this  to  the  scale  of  the  draw- 
ing from  KI,  we  have  a  point  through  which  the  vertical  line  passing  through  the 
center  of  gravity  must  pass. 

This  line,  passing  through  the  center  of  gravity  of  the  buttress,  can  be  found 
GRAPHICALLY,  also,  by  the  method  of  the  equilibrium  polygon   (Fig.  3).     (See 


Fig.  3.     Buttress  with  Offsets 


-<    }i     ^     'A    ^   H    * 
Fig.  4.     Resultant  Thrust  on 
with  Offsets 


K 
Buttress 


pages  296  and  314  to  320.)  In  order  to  do  this,  lay  ofif  at  any  convenient 
scale,  beginning  at  some  convenient  point  M,  Mw  i,  w  i  w  2,  and  w  2  w  s,  the 
areas  of  the  various  quadrilaterals  composing  the  buttress.  Through  the  center 
of  gravity  of  each  quadrilateral  draw  a  vertical  (green)  line.  Draw  the  lines 
MO  and  w  s  0,  intersecting  at  some  conveniently  chosen  pole-point,  O. 
Draw  Ow  1  and  Ow  2.  Through  a,  where  MO  intersects  the  vertical 
(green)  line  drawn  through  the  center  of  gravity  of  the  first  quadrilateral^ 
draw  ab  parallel  to  Ow  i,  and  through  b,  where  ab  intersects  the  (green)  line 
through  the  center  of  gravity  of  the  second  quadrilateral,  draw  be  parallel  to 
Ow  2.  Finally  draw  cL  parallel  to  Ow  3.  Where  this  line  intersects  MO 
at  L  will  be  the  point  through  which  the  (heavy  red)  line,  passing  through  the 
center  of  gravity  of  the  buttress  takeii  as  a  whole,  should  be  drawn.    The  distance 


300 


Stability  of  Piers  and  Buttresses 


Chap.  7 


Xoy  measured  from  IK,  should  then  be  2.25  ft  or  very  nearly  this,  allowing  for 
slight  errors  of  drawing,  and  the  same  as  that  found  by  moments.     Fig.  5  shows 

the  same  method  of  determining  the  posi- 
tion of  the  center  of  gravity  of  a  buttress 
similar  to  the  one  illustrated  in  Fig.  9. 

After  this  line  is  found,  the  method 
of  determining  the  stabihty  of  the  pier 
is  the  same  as  that  given  for  the  pier  in 
Fig.  2  and  Fig.  4.  If  the  buttress  is 
more  than  one  foot  thick,  that  is,  at 
right-angles  to  the  plane  of  the  paper,  its 
cubic  contents  must  be  determined  in 
order  to  find  its  weight.  It  is  easier, 
however,  to  divide  the  total  thrust  by 
the  thickness  of  the  buttress.  This  gives 
the  thrust  per  foot  of  thickness  of  the 
buttress. 

The  Line  of  Pressure  or  Line  of 
Resistance.*  The  line  of  resistance 
or  the  LINE  OF  pressure  of  a  pier  or 
buttress   is    a    line   drawn   through   the 


Center  of  Gravity  of  Wall  and 
Buttress 

CENTER  OF  PRESSURE  of  each  joint.  The 
CENTER  OF  PRESSURE  of  any  joint  is  the 
point  in  which  the  resultant  of  the  forces 
acting  on  that  portion  of  the  pier  above 
the  joint  cuts  it.  The  Hne  of  pressure,  or 
of  resistance,  when  drawn  in  a  pier,  shows 
how  near  the  greatest  stress  on  any  joint 
comes  to  the  edges  of  that  joint.  It  can 
be  drawn  by  the  following  method. 

Let  A  BCD  (Fig.  6)  be  a  pier  whose  line 
OF  PRESSURE  we  wish  to  draw.  Let  T  be  the  thrust  against  the  pier.  First, 
divide  the  height  of  the  pier  into  several  parts,  each  2  or  3  feet  high,  as  shown 
by  the  horizontal  dotted  lines.     It  is  more  convenient  to  make  the  courses  or 

•  This  line  is  called,  interchangeably,  the  line  of  pressure,  the  Hne  of  resistance,  the 
resistance-line,  etc. 


Line  of  Pressure  in  Pier 


Stability  of  Piers  and  Buttresses 


301: 


parts  equal  in  height.  Prolong  the  line  of  the  thrust,  ^nd  draw  a  vert  cal 
line  through  the  center  of  gravity  of  the  pier,  intersecting  the  hne  of  thrust  at 
the  point  a.  From  a  lay  off  to  a  scale  the  thrust  T,  and  the  weights  of  the 
different  parts  of  the  pier,  commencing  with  the  weight  of  the  upper  portion. 
Thus  wi  represents  the  weight  of  the  portion  above  the  first  joint;  w^  repre- 
sents the  weight  of  the  second  part;  and  so  on.  The  sum  of  the  ^s  will 
represent  the  weight  of  the  whole  pier.  ^;,„^„oi 

Draw  a  parallelogram,  with  T  and  w,  for  its  two  sides.  Draw  the  diagonal 
and  produce  it  beyond  the  parallelogram,  if  necessary.  Its  point  of  mtersection 
with  the  first  joint  will  be  a  point  in  the  hne  of  pressure.  Draw  a  second  par- 
Xto^^^^^^^  ^1  +  I  for  its  two  sides.    Draw  the  diagonal  intersectmg 

the  second  joint  at  the  point  2.  Continue  in  this  way  with  the  rest  of  t^c  Partial 
weights,  the  last  diagonal  intersecting  the  base  AD, 
in  the  point  4.    Join  the  points  i,  2,  3  and  4.    The 


X,  =  r 

X2  =  2:95 


resulting  broken  line  C1234 
is  the  LINE  or  pressure  or 

LINE  OF  RESISTANCE. 

Wehavetakenthe  simplest 

case  as  an  example;  but  the 

same  principles  are  true  for 

any    case.     If    the    line    of 

/M^^M         pressure  of  the  pier  at  any 

/J  ^P 1  point  falls  at  a  distance  f rom- 

/\   YMm  the  outside  edge  of  the  joint 

less    than    one-third    the 

WIDTH   OF   the    joint,    the 

pier  is  generally  considered 

unsafe. 

The  Stability  of  a  Wall 
and  Buttress.  By  Mo- 
ments and  Graphical 
Method.  The  following 
example  illustrates  the  ap- 
plication of  these  principles. 
Example  2.  Let  Fig.  7 
represent  the  section  of  a 
side  wall  of  a  church,  with  a 
buttress  against  it.  Oppo- 
site the  buttress,  on  the 
inside  of  the  wall,  is  a  hammer-beam  truss,  which  we  will  suppose  exerts  an 
outward  thrust  on  the  wall  of  the  church,  amounting  to  about  9  600  lb.  We 
will  further  consider  that  the  resultant  of  the  thrust  acts  at  P,  and  at  an  angle 
of  60°  with  the  horizontal.  The  dimensions  of  the  wall  and  buttress  are  given 
in  Fig  8  The  buttress  is  2  ft  thick,  at  right-angles  with  the  plane  of  the^ 
paper  Has  the  buttress  the  proper  size  and  form  to  enable  the  wall  to  resist  ^ 
the  thrust  of  the  truss?  ,     ..  ^, 

The  first  point  to  decide  is  whether  or  not  the  line  of  pressure  cuts  the- 
joint  CD  at  a  safe  distance  in  from  C.  To  ascertain  this  we  must  determine 
the  position  of  the  center  of  gravity  of  the  wall  and  buttress  above  the  joint  CD 
(Fig  7)  One  way  to  determine  this  is  by  the  method  of  moments,  the 
MOMENTS  OF  THE  AREAS  being  taken  about  the  line  KM  as  an  axis  or  Ime  of 
reference  (Fig.  8),  as  already  explained.  The  distance  Xi  is.  of  ^ourse,^half  the 
thickness  of  the  wall  or  i  ft.    We  next  find  the  center  of  gravity  of  the  part 


\)l'0%2-m2-Q' 


.  7.     Stability  of  Wall 
and  Buttress 


Fig.  8 


,     Stability  of  Wall 
and  Buttress 


302  Stability  of  Piers  and  Buttresses  Chap.  7 

CEFG  (Fig.  8)  by  the  method  of  diagonals;  and  scaling  the  distance  A'2,  we  find 
it  to  be  2.95  ft. 

The  area  CEFG  =  /I2  =  10  sq  ft;    and  the  area  GIKL  =  Ai=  26  sq  ft.     Let 
A  =  the  total  area  above  CL. 
Then  we  have 

Xi  =  iit  ^i=26sqft  ^iXXi=26     sqftxft 

X2  =  2.95  ft        A2  =  10  sq  ft  A2X  X2=-  29.5  sq  ft  X  ft 

A  =36sqft  36)55.5  sqftxft 

Xo=i.5ft  ^^ 

Expressed  in  equations  of  moments  of  areas,  this  may  be  written  as  follows. 
A  representing  the  total  area  above  the  line  CL  (Fig.  8) : 

^XXo=(^iXXi)+(^2XX2) 
Hence, 

^  (^lXXi)  +  (^2XX2) 

The  center  of  gravity  is  at  a  distance  1.5  ft  from  the  line  ED  (Fig.  7).  In 
Fig.  7  measure  the  distance  Xo=  1.5  ft,  and  through  the  point  a  draw  a  vertical 
line  intersecting  the  Hne  of  the  thrust  prolonged  at  O.  If  the  thrust  is  9  600  lb, 
for  example,  for  a  buttress  2  ft  thick,  it  will  be  half  that,  or  4  800  lb,  for  a 
buttress  i  ft  thick.  We  will  call  the  weight  of  the  masonry  of  which  the  buttress 
and  wall  is  built,  150  lb  per  cu  ft.  Then  the  thrust  is  equivalent  to  4800/150  =32 
cu  ft  of  masonry.  Laying  this  off  to  a  scale  from  O,  in  the  direction  of  the 
thrust,  and  the  area  of  the  masonry,  36  sq  ft,  from  O  on  the  vertical  line,  com- 
pleting the  rectangle,  and  drawing  the  diagonal,  we  find  that  the  diagonal  cuts 
the  joint  CD  at  /,  within  the  limits  of  safety.  We  must  next  find  where  the 
LINE  OF  PRESSURE  cuts  the  base  AB.  - 

First,  determine  the  position  of  the  center  of  gravity  of  the  whole  figure. 
This  is  determined  by  finding,  as  explained  for  the  distances  Xi  and  X2,  the  dis- 
tances X2,  X3',  in  Fig.  8,  and  making  the  following  computation,  letting  A '  *= 
the  total  area  above  AM. 

Xi'=iit  ^i'  =  40sqft  ^iXXi  =  40       sqftXft 

X2'=2.98ft       /l2'=24sqft  ^2X^2=  71.52  sq  ft  X  ft 

^3' =4-95  ft       i43'=i2sqft  yls  X  X3  =  59.40  sq  ft  X  ft 


A'  =  76  sq  ft  76)170.92  sq  ft  X  ft 


Xo'=  2.25  ft 

This,  also,  may  be  expressed  in  equations  of  moments  of  areas,  as  explained 
for  the  part  above  the  line  CL. 

Then  from  the  line  EB  (Fig.  7)  lay  off  the  distance  Xo'  =2.25  ft,  and  draw 
through  d  a  vertical  line  intersecting  the  line  of  the  thrust  at  0'.  On  this  ver- 
tical line,  measure  down  from  0'  the  whole  area  76,  to  scale,  as  explained  above, 
and  from  the  lower  extremity  of  this  line  representing  the  area,  lay  off.  at  the 
proper  angle,  the  thrust  T=  32.  Draw  the  line  O'e,  intersecting  the  base  at  c. 
This  is  the  point  where  the  line  of  pressure  cuts  the  base;  and,  as  it  is  at 
a  safe  distance  in  from  A,  the  buttress  has  sufficient  stability.  If  there  were 
more  offsets,  we  should  proceed  in  the  same  way,  finding  where  the  line  of 
pressure  cuts  the  joint  at  the  top  of  each  offset.    The  reason  for  doing  this  Is 


Stability  of  Piers  and  Buttresses 


303 


because  the  line  of  pressure  might  cut  the  base  at  a  safe  distance  from  the 
outer  edge,  while  higher  up  it  might  come  outside  of  the  buttress  or  too  near 
the  outside  face,  thus  making  the  buttress  unstable.  The  method  given  in  these 
examples  is  appUcable  to  piers  of  any  shape  or  material.  If  the  line  of  pres- 
sure makes  an  angle  of  less  than  30°  with  any  horizontal  joint,  the  stones 
above  the  joint  may  slide  at  this  joint,  or  at  least  have  a  strong  tendency  to 
do  so.  Sliding  can  be  prevented  either  by  doweling,  or 
by  inclining  the  joints.  Such  conditions,  however,  are 
rare  in  architectural  construction. 

The  Stability  of  a  Wall  and  Buttress.     Graphical 
Method.     This  same  example,  which  has  been  solved  in 
the   foregoing   case  partly   by   moments   and   partly  by 
graphical  methods,  can  be  solved  entirely  by  graphical 
methods.     In  this  case  it  is  not  necessary  to  determine 
the  position  of  the  line  (the  heavy  red  lines  in  Figs.  3  and 
5)  passing  through  the  center  of  gravity  of  the  buttress 
taken  as  a  whole.     It  is  necessary,  only,  to   determine 
the  (red)  lines  passing  through  the  cen- 
ters of  gravity  of  the  various  trapezoids 
and  rectangles  into  which  it  has  been 
subdivided.     To  determine  the  position 
of  the  line  of  pressure  and  the  various 
CENTERS  OF  PRESSURE  on  the  different 
joints,  the  method  shown  in  Fig.  6  may 
be  used.     The   construction  shown  in 
that    figure,    in    which    the    complete 
parallelograms  of  the  forces  acting  at 
each  joint  are  drawn,  may  be  simplified. 
One-half  the  parallelogram,  only,  or  the 
triangle  OF  THE  FORCES  acting  at  each 
joint,   may  be    drawn    and   the  whole 
construction  placed  at  one  side  of  the 
figure  and  afterwards  transferred  to  the 
figure  itself  by  means  of  parallel  lines. 

Draw  the  joint-planes  FG,  EJ ,  CK 
and  BN  and  calculate  the  areas  of  the 
various  parts  of  the  wall  and  buttress, 
such  as  IKGF,  FGJE,  EJKC,  CKNB 
and  BNMA,  Fig.  9.  These  are  respec- 
tively 14  sq  ft,  6  sq  ft,  16  sq  ft,  10  sq  ft 
and  30  sq  ft.  Lay  off  these  areas  to  a 
scale  of  so  many  square  units  to  a  linear 
unit,  at  Pw  1,  w  1  w  2,  w  2  w  s,  w  3  w  4.  and  w  410  $,  along  the  line  KM,  begin- 
ning at  the  point  of  application  of  the  thrust.  Lay  off,  at  the  same  scale,  the 
thrust  OP  for  one  foot  of  thickness  of  the  wall,  and  let  this  thrust  be  4  800  lb. 
Draw  Ow  i,  Oiv  2,  Ow  3,  etc.  Then  Ow  i  will  be  the  resultant  of  the  thrust 
and  the  weight  of  the  buttress  above  the  joint  FG,  Ow  2  will  be  the  resultant  of 
this  last  resultant  and  the  weight  of  that  part  of  the  buttress  between  the  joints 
FG  and  EJ,  and  so  on  until  Ow  5  is  reached,  which  is  the  resultant  of  the  total 
weight  of  the  buttress  and  the  thrust  as  well  as  the  resultant  of  the  rectangle 
BNMA  and  the  previous  resultant.  Prolong  the  thrust  OP,  until  it  cuts  the 
first  (red)  line  through  the  center  of  gravity  of  the  first  rectangle  IKGF,  at  a. 
Through  this  point  draw  a  (green)  line  parallel  to  Ow  i  and  prolong  it  backward 


Line   of  Pressure 
Buttress 


in  Wall   and 


304  Stability  of  Piers  and  Buttresses  Chap.  7 

until  it  intersects  the  joint  FG  at  the  point  within  the  small  (red)  circle.  This 
determines  the  center  of  pressure  on  this  joint.  Next,  draw  ab  (green) 
parallel  to  Ow  2  and  prolong  it  backward  until  it  intersects  the  joint  EJ,  at  the 
CENTER  OF  PRESSURE  on  that  joint.  Repeat  this  operation  to  obtain  the 
centers  of  PRESSURE  OR  cach  successive  joint,  drawing  be,  cd  and  de  parallel 
respectively  to  Ow  3,  Ow  4  and  Ow  5. 

It  must  be  remembered,  however,  that  cd  does  not  have  to  be  prolonged  back- 
ward, as  it  cuts  the  joint  CK  below  and  to  the  left  of  the  line  passing  through 
the  center  of  gravity  of  EJKC.  Finally,  join  the  various  centers  of  pressure 
by  the  (red)  broken  line,  which  is  the  line  of  pressure  in  the  buttress.  As 
this  line  lies  within  the  middle  third  of  the  construction,  and  the  resultants  of 
the  pressures  on  the  various  joint-planes  do  not  make  with  the  normals  to  the 
joint-planes  angles  greater  than  the  angle  of  friction,  the  conditions  for 
stability  may  be  considered  to  be  satisfied. 


Arches  305 

CHAPTER  VIII 

THE  STABILITY  OF  MASONRY  ARCHES  * 

By 
GRENVILLE  TEMPLE   SNELLING 

LATE    MEMBER    OF    AMERICAN    INSTITUTE   OF    ARCHITECTS 

1.   Arches 

The  Lintel  and  the  Arch.  When  an  opening  is  made  in  a  masonry  wall 
it  is  necessary  to  provide  some  means  of  spanning  such  opening  to  support  the 
superimposed  masonry.  Two  methods  have  been  employed  by  constructors 
for  this  purpose.  The  first  involves  the  use  of  the  beam,  girder,  cap,  or  lintel, 
and  the  second  the  throwing  of  an  arch  from  one  side  of  the  opening  to  the 
other.  Lintels  are  made  of  various  materials,  as  wood,  stone,  reinforced  con- 
crete, cast  iron  and  steel,  and  have  cross-sections  of  different  shapes.  They 
are  placed  across  the  tops  of  the  openings  and  transfer  laterally  the  loads  above, 
causing  vertical  reactions,  only,  in  the  side  supports.  An  arch,  on  the 
contrary,  is  a  particular  arrangement  of  blocks  of  stone  or  other  material,  put 
together,  generally  along  a  curved  line,  in  such  a  way  that  they  resist  the  load 
by  a  balancing  of  certain  thrusts  and  counterthrusts.  An  arch  exerts  on 
its  supports  an  outward  thrust  as  well  as  a  vertical  pressure;  and  it  is 
this  outward  thrust  which  requires  that  the  arch  should  be  used  with  caution 
when  the  abutments  are  not  amply  large  and  strong.  The  mechanical  principles 
involved  in  the  spanning  of  an  opening  by  a  lintel  are  much  simpler  than 
those  of  the  arch  and,  historically,  the  lintel  very  considerably  antedates  the 
arch. 

Definitions.    Before  taking  up  the  principles  of  the  arch,  we  will  define  the 
principal  terms  relating  to  it.     The  distance  ec  (Fig.  1)  is  called  the  span  of  the 
arch;  at,  the  rise;  h,  the  crown;  the  lower  boundary 
line  eac,  the  soffit  or  intrados;  the  outer  boundary 
line,  the  back  or  extrados.     The  terms  soffit  and 
BACK  are  also  applied  to  the  entire  lower  and  upper 
curved  sufaces  of  the  whole  arch.     The  sides  of  the 
arch  which    are    seen    are  called  the  faces.    The 
blocks  of  which  the  arch  itself  is  composed  are  called 
VOUSSOIRS;  the  center  one,  X,  is  called  the  keystone;    p.      j      Diagram   of  See- 
and  the  lowest  ones,  SS,  the  springers.     In  seg-         '     "  mental  Arch 
MENTAL  arches,  or  those  of  which  the  intrados  is  not 

a  complete  semicircle,  the  springers  generally  rest  upon  two  stones,  as  RR,  which 
have  their  upper  surfaces  cut  to  receive  them;  these  stones  are  called  skewbacks. 
The  line  connecting  the  lower  edges  of  the  springers  is  called  the  springing- 
line;  the  sides  of  the  arch  are  called  the  haunches;  and  the  loads  in  the  tri- 
angular spaces,  between  the  haunches  and  a  horizontal  line  drawn  from  the 
crown,  are  called  the  spandrels.  The  blocks  of  masonry,  or  other  material, 
which  support  two  successive  arches,  are  called  piers;  and  the  extreme  blocks, 
which,  in  the  case  of  stone  bridges,  generally  support,  on  one  side,  embank- 
ments of  earth,  are  called  abutments.  A  pier  strong  enough  to  resist  the 
thrust  of  one  of  two  successive  arches,  in  case  the  other  one  falls  down,  is  some- 

*  See,  also,  Chapter  XXXI. 


306  The  Stability  of  Masonry  Arches  Chap.  8 

times  called  an  abutment-pier.  Besides  their  own  weight,  arches  usually  sup- 
port permanent  loads  or  surcharges  of  masonry  or  of  earth. 

Forms  of  Arches.  In  using  arches  in  architectural  constructions,  the 
FORMS  of  the  arches  are  generally  governed  by  the  style  of  the  building,  or  by 
a  limited  amount  of  space,  rather  than  by  engineering  considerations.  The 
problem,  therefore,  that  usually  presents  itself  to  the  architect  is  not  to  design 
the  form  and  dimensions  of  an  arch  that  will  most  economically  and,  from  an 
engineering  point  of  view,  efficiently  bear  its  load,  but  rather  to  determine  if 
an  arch  of  a  certain  form  and  of  certain  dimensions  will  be  stable  and  safe 
under  its  load.  The  semicircular  and  segmental  forms  of  arches  are  the 
best  as  regards  stability,  and  are  the  simplest  to  construct.  Elliptical  and 
three-centered  arches  are  not  as  strong  as  circular  arches,  and  should  only 
be  used  where  they  can  be  given  all  the  strength  desirable. 

The  Strength  of  an  Arch  depends  very  much  upon  the  care  with  which  it  is 
built  and  upon  the  quality  of  the  materials.  In  stone  arches,  special  care  should 
be  taken  to  cut  and  lay  the  beds  of  stones  accurately,  and  to  make  the  bed- 
joints  thin  and  close,  in  order  that  the  arches  may  be  stressed  as  little  as  possible 
in  settling.  To  insure  this,  arches  are  sometimes  built  dry,  grout  or  liquid 
mortar  being  afterwards  run  into  the  joints;  but  the  advantage  of  this  method 
is  doubtful. 

Brick  Arches.*  (See  Figs.  2,  3,  4  and  5.)  These  may  be  built  either  of 
wedge-shaped  bricks,  molded  or  rubbed  so  as  to  fit  to  the  radius  of  the  sofi5t, 


Fig.  4 
Brick  Arches 

or  of  bricks  of  common  shape.  The  former  method  is  undoubtedly  the  best,  as 
it  enables  the  bricks  to  be  thoroughly  bonded,  as  in  a  wall;  but,  as  it  involves 
considerable  expense  to  make  the  bricks  of  the  proper  shape,  it  is  very  sel- 
dom employed.  When  bricks  of  the  ordinary  shape  are  used,  they  are  ac- 
commodated to  the  curved  figure  of  the  arch  by  making  the  bed-joints  thinner 
towards  the  intrados  than  they  are  at  the  extrados;  or,  if  the  curvature  is  sharp, 
by  driving  thin  pieces  of  slate  into  the  outer  edges  of  those  joints;  and  different 
methods  are  followed  for  bonding  them. 

The  usual  method  is  to  build  the  arch  in  concentric  rings,  each  one-half  brick 
thick;  that  is,  to  lay  all  the  bricks  as  stretchers  and  depend  upon  the  tenac- 
ity of  the  mortar  for  the  connection  of  the  several  rings.  Brick  masonry  con- 
structed in  this  way  is  deficient  in  strength,  unless  the  bricks  are  laid  in  cement 
mortar  which  is  at  least  as  tenacious  as  themselves.  Another  way  is  to  intro- 
duce courses  of  headers  at  intervals,  and  to  connect  pairs  of  half-brick  rings 

*  For  illustrations  of  the  different  methods  o[  building  brick  arches,  see  Chapter  VII, 
Building  Construction  and  Superintendence,  Part  I,  Masons'  Work,  F.  E.  Kidder. 


Arches 


307 


together.  This  may  be  done  either  by  thickening  with  pieces  of  slate  the 
joints  of  the  outer  ring  of  a  pair  of  half-brick  rings,  so  that  there  will  be  the 
same  number  of  courses  of  stretchers  in  each  ring  between  two  courses  of 
headers;  or  by  placing  the  courses  of  headers  at  such  distances  apart,  that 
between  each  pair  of  them  there  will  be  one  course  of  stretchers  more  in  the 
outer  than  in  the  inner  ring.  The  former  method  is  best  suited  to  arches  of 
long  radius;  the  latter,  to  those  of  short  radius.  Hoop-iron  laid  around  the 
arch,  between  half-brick  rings,  as  well  as  longitudinally  and  radially,  is  very 
useful  for  strengthening  brick  arches.  The  bands  of  hoop-iron  which  traverse 
the  arch  radially  may  also  be  bent,  and  prolonged  into  the  bed-joints  of  the 
backing  and  spandrels.  By  the  aid  of  hoop-iron  bond,  Sir  Marc-Isambard 
Brunei  built  a  half-arch  of  bricks,  laid  in  strong  cement  mortar,  which  stood, 
projecting  from  its  abutment  Uke  a  bracket  to  the  distance  of  60  ft,  until  it  was 
destroyed  by  the  undermining  of  its  foundations. 

The  only  requirements  in  the  New  York  City  Building  Laws  for  brick  and 
stone  arches  is  that  "openings  for  doors  and  windows  in  all  buildings  shall  have 
good  and  sufficient  arches  of  stone,  brick,  or  terra-cotta,  well  built  and  keyed 
and  with  good  and  sufl&cient  abutments. " 

Rule  for  the  Radius  of  Brick  Arches.  A  good  rule  for  the  radius  of 
segmental  brick  arches  over  windows,  doors  and  other  small  openings  is  to 
make  the  radius  equal  to  the 

WIDTH     OF     THE     OPENING.      This 

gives  a  good  rise  to  the  arch  and 
a  pleasing  proportion.  In  com- 
mon brickwork,  when  no  par- 
ticular architectural  effect  is 
desired,  such  as  in  the  rowlock 
arches  thrown  over  the  openings 
in  cellar  walls,  a  rule  in  very 
common  use  is  to  make  the  rise 
of  the  arch  at  the  crown  an  inch 

in  height  for  every  FOOT  OF 

span. 

Segmental  Arches  with  Tie- 
Rods.  It  is  often  desirable  to 
span  openings  in  a  wall  by  means 
of  arches  when  there  are  not  a 
sufficient  number  of  abutments 
to    withstand     the     thrusts.     In 

cases  of  this  kind  each  arch  can  be  sprung  from  two  cast-iron  skewbacks,  held 
in  place  by  iron  rods,  as  is  shown  in  Fig.  6.  When  this  is  done,  it  is  necessary 
to  proportion  the  size  of  the  rods  to  the  thrust  of  the  arch.  The  horizontal 
THRUST  of  the  arch  may  be  very  closely  determined  by  the  following  formula; 

^^    .  ,    ,  load  on  arch  X  span 

Honzontal  thrust  = : 7—. — 7— - 

8  X  rise  of  arch  m  feet 

If  the  load  is  concentrated  at  the  center  of  the  arch,  the  thrust  will  be  twice 
that  given  by  this  formula. 

The  tensional  stress  in  the  rod  or  rods  will  equal  the  horizontal  thrusi 
of  the  arch  and  if  there  are  two  rods,  the  stress  in  each  will  be  one-half  the 
thrust.  If  there  are  three  rods,  then  each  must  resist  one-third  the  thrust. 
Knowing  the  stresses  in  the  rods,  the  size  of  each  may  b^  determined  from 
Table  II,  Chapter  XI. 


Fig.  6. 


Segmental  Brick  Arch,  Cast-iron  Skew- 
back  and  Wrought-iron  Tie-rod 


308  The  Stability  of  Masonry  Arches  Chap.  8 

Example  i.  Let  us  assume  that  a  brick  arch,  like  the  one  shown  in  Fig.  6, 
has  a  span  of  15  ft,  a  rise  at  the  center  of  i  ft  6  in,  and  that  it  supports  a  12-in 
brick  .wall.  The  weight  of  all  the  brick  masonry  above  the  arch  does  not  come 
upon  it.  Usually  only  an  equilateral  triangle  of  brickwork  is  considered, 
the  base  of  the  triangle  being  the  span.  Assume,  therefore,  an  equilateral  tri- 
angle the  sides  of  which  are  each  15  ft  long.  The  altitude  of  this  triangle  is 
about  12.6  ft  and  its  area  will  equal  15  ft  X  12.6  ft  X  H  =  94^  sq  ft.  If  the  wall 
is  12  in  thick  there  will  be  971^^  cu  ft  of  brickwork  within  this  triangle  of  the 
wall;  and  since  ordinary  brickwork  weighs  about  115  lb  per  cu  ft,  its  weight 
will  be  about  10  867  lb.     Substituting  these  values  in  the  formula, 

The  horizontal  thrust  =  — =13  584  lb 

o  X  i'5 

Looking  in  Table  II,  page  388,  it  appears  that  one  i  H-'m  or  two  i  '/^-in  plain, 
round,  wrought-iron  rods,  or  one  i3^^-in  or  two  M-in  round,  upset,  steel  rods 
should  be  used. 

Centers  for  Arches.  A  center  is  a  temporary  structure,  generally  of 
timber,  on  which  the  voussoirs  of  an  arch  are  supported  while  the  arch  is  being 
built.  It  consists  of  parallel  frames  or  ribs,  placed  at  convenient  distances 
apart,  curved  on  the  outside  to  a  line  parallel  to  that  of  the  soffit  of  the  arch, 
and  supporting  series  of  transverse  planks,  upon  which  the  arch-stones  rest. 
The  center  commonly  used  is  one  which  can  be  lowered,  or  struck  all  in  one 
piece,  by  driving  out  wedges  from  below  it,  so  as  to  remove  at  once  the  support 
from  every  point  of  the  arch.  The  center  of  an  arch  should  not  be  struck  until 
the  solid  part  of  the  backing  has  been  built  and  the  mortar  has  had  time  to 
set  and  harden;  and  when  an  arch  forms  one  of  a  series  of  arches  with  piers 
between  them,  no  center  should  be  struck  so  as  to  leave  a  pier  with  an  arch 
abutting  against  one  side  of  it  only,  unless  the  pier  has  sufficient  stability  to  act 
as  an  abutment.  When  possible,  the  striking  of  the  center  of  large  brick  arches 
should  be  delayed  for  two  or  three  months  after  the  arch  is  built,  and  during 
the  period  that  they  are  in  place  they  should  be  eased  from  time  to  time. 
This  is  done  by  easing  out  the  wedges  under  the  centers  a  Httle  at  a  time  so 
as  to  let  them  down  gradually  and  thus  adjust  any  slight  settling  or  shrinkage  of 
the  masonry  as  it  occurs. 

Mechanical  Principles  of  the  Arch.  In  designing  an  arch,  the  first  ques- 
tion to  be  settled  is  the  form  of  the  arch;  and  in  regard  to  this,  as  already  noted, 
there  is  generally  little  choice.  When  the  abutments  are  of  ample  size,  the  seg- 
mental arch  is  the  strongest;  but  when  it  is  necessary  to  make  the  abutments 
of  the  arch  as  small  as  possible,  the  semicircular  or  the  pointed  arch  should 
be  used. 

Depth  of  Keystone.  Having  decided  upon  the  form  of  the  arch,  the  depth 
OF  THE  arch-ring  must  next  be  decided.  This  is  generally  determined  by  com- 
puting the  required  depth  of  the  keystone  and  making  the  depth  of  the 
whole  ring  the  same  or  a  little  larger.  In  considering  the  strength  of  an  arch, 
the  depth  of  the  keystone  is  considered  to  be  only  the  distance  from  the  ex- 
trados  to  the  intrados  of  the  arch;  and  if  the  keystone  projects  above  the  arch- 
ring,  as  in  Fig.  1,  the  projection  is  considered  a  part  of  the  load  on  the  arch. 
There  are  several  rules  for  determining  the  depth  of  the  keystone,  but  all  are 
empirical;  and  they  dififer  so  greatly  that  it  is  difficult  to  recommend  any  par- 
ticular one. 

Rankine's  Formula  for  Depth  of  Keystone.  Professor  Rankine's  rule 
is  often  quoted,  and  gives  results  which  are  probably  true  enough  for  most 


Arches 


309 


arches.  It  applies  to  both  circular  and  elliptical  arches  and  is  as  follows. 
Take  a  mean  proportional  between  the  inside  radius  at  the  crown,  and  0.12  of 
a  foot  for  a  single  arch,  and  0.17  of  a  foot  for  an  arch  forming  one  of  a  series: 
Or, 


Depth  in  feet  of  keystone  for  single  arch         =  v  (o .  12  X  radius  at  crown) 
Depth  in  feet  of  keystone  for  arch  of  a  series  =  V  (o,  17  X  radius  at  crown) 

The  dimensions  given  by  this  formula  seem  to  agree  very  well  with  those 
generally  used  in  practice  in  arches  of  a  certain  kind.  The  formula,  however, 
gives  the  same  depth  of  keystone  for  spans  of  any  length,  provided  the  radius 
IS  the  same;  and  in  this  particular  it  would  seem  that  the  rule  is  not  satisfactory. 

Trautwine's  Formula  for  Depth  of  Keystone.  Trautwine,  from  calcu- 
lations made  for  a  large  number  of  arches,  deduced  a  formula  for  the  depth  of 
keystone,  which  seems  to  agree  with  theory  more  closely  than  Rankine's  formula. 
His  rule  is,  for  cut  stone, 

V  radius  +  half  span  | 


Depth  of  key  in  feet 


'{' 


+  0.2  ft 


For  SECOND-CLASS  work  this  depth  may  be  increased  about  one-eighth  part, 
or  for  BRICKWORK  or  fair  rubble,  about  one-third. 

Tables  for  Depths  of  Keystones.  Table  I  gives  a  few  examples  of  the 
DEPTHS  OF  THE  KEYSTONES  of  some  bridges,  together  with  the  depths  which 
would  be  required  by  Trautwine's  or  Rankine's  formula.  From  this  table  it 
is  seen  that  the  results  of  both  formulas  agree  very  well  with  dimensions  used 
in  actual  practice. 


Table  I.     Depths  of  Keystones  of  Some  Arches  of  Circular  Arc 


Name  or  location  of 
structure 


Span 


Rise 


Radius 


Actual 
depth 
of  key 


Calculated 
depth  of  key 


Traut- 
wine's 
Rule 


Ran- 
kine's 
Rule 


Engineer 


Cabin  John,  Washing- 
ton aqueduct 

Grosvenor  bridge 
Chester,  England. . . . 

Dora  Riparia,  Turin, 
Italy 

Tongueland,  England. 

Dean  bridge,  Scotland 
in  a  series 

Falls  bridge,  Phila- 
delphia &  Reading 
Railroad 

Chestnut  St.  bridge, 
Philadelphia,  brick 
in  cement 

Philadelphia  &  Read- 
ing Railroad ........ 

Philadelphia  &  Read- 
ing Railroad 


220.0 

200.0 

148.0 
118. o 

90.0 

78.0 

60.0 
440 
31.2 


57.25 
42.00 


18.00 
38.00 


25  00 

18.00 
8.00 
5.00 


134.25 

140.00 

160.10 
64.80 

48.90 

43-00 

34.00 
34.30 
26.80 


4.16 
4.00 


4.92 
3.50 


3.00 

2.50 
2.50 
I  66 


4. II 

4.0-/ 

4.03 
3-00 

2.62 

2.46 

2.20 
2.08 
1.83 


4.00 
4.10 


4.38 
2.79 


2.27 

2.00* 
2.02 
1.79 


Meigs 

Hartley 

Mosca 
Telford 

Telford 

Steele 

Kneass 

Steele 

Steele 


*  For  first-class  cut-stone  work. 


310 


The  Stability  of  Masonry  Arches 


Chap.  8 


Table  II*  gives  the  DEpms  of  keystones  for  arches  of  first-class  cut  stone, 
according  to  Trautwine's  P'ormula.  For  second-class  cut  stone,  add  about  one- 
eighth  part  and  for  fair  rubble  or  for  brickwork  about  one-third  part,  as  stated 
with  formula. 


Table  II.     Depths  of  Keystones  for  Arches  of  First-Class  Cut-Stone 
Masonry 


^.v  ihv/  V 

Vi  1      ■  ■•fJi. 

"     Rise,  in 

parts  of  the  span 

Span 

'   ,y,lt]<tlh>- 

.,.M-      .!  M 

\'i 

M 

H 

M 

H 

Ho 

ft 

ft 

ft 

ft 

ft 

ft 

ft 

ft 

2 

0.55 

0  56 

0.58 

0.60 

0.61 

0.64 

0.68 

4 

0.70 

0.72 

0.74 

0.76 

0  79 

0.83 

0.88 

6 

0  81 

0.83 

0.86 

0.89 

0.92 

0.97 

I  03 

8 

0  91 

0.93 

0.96 

1.00 

1.03 

1.09 

1. 16 

10 

0.99 

I  01 

1.04   . 

1.07 

I. II 

1. 18 

1.26 

15 

1. 17 

1. 19 

1.22 

1.26 

1.30 

1.40 

I  50 

20 

1.32 

I  35 

•  1.38 

1.43 

1.48 

1.59 

1.70 

25 

1.45 

1.48 

1.53 

1.58 

1.64 

I  76 

1.88 

30 

1.57 

1.60 

1.65 

1. 71 

1.78 

I  91 

2  04 

35 

1.68 

1.70 

1.76 

1.83 

1.90 

2  04 

2.19 

40 

1.78 

1. 81 

1.88 

i.<^^ 

2.03 

2.18 

2.33 

50 

1-97 

2.00 

2.08 

2.16 

2.25 

2.41 

2.58 

6o 

2:14 

2.18 

2.26 

2. 35 

2.44 

2.62 

2.80 

8o 

2.44 

2.49 

2.58 

2.68 

2.78 

2.98 

3.18 

100 

2.70 

2.75 

2.86 

2.97 

3.09 

3.32 

3.55 

120 

2.94 

2.99 

3.10 

3.22 

3.61 

3.88 

140 

3.16 

3.21 

3-33 

3.46 

3.60 

3.87 

4.15 

160 

3.36 

3.44 

3.58 

3.72 

3.87 

4.17 

180 

3.56 

3.63 

3.75 

3.90 

4.06 

4.38 

200 

3.74 

3.81 

3.95 

4.12 

4-29 

220 

3-91 

4  •  00    , 

4.13 

4.30 

4.48 

240 

4.07 

4.15 

4.30 

4.48 

260 

4.23 

4-31 

4.47 

4.66 

280 

4.38 

4.46 

4.63 

300 

4.53 

4.62 

4.80 

Example  2.  Having  decided  what  the  thickness  of  the  arch-ring  will  be  it 
remains  to  determine  whether  such  an  arch  would  be  stable  if  built.  The 
following  example  will  illustrate  the  method  of  determining  this. 

Consider  an  unloaded  semicircular  arch  of  20-ft  span. 

First,  to  find  the  depth  of  tlie  keystone,  we  will  use  Rankine's  Formula. 


Depth  of  key  =»  V  0.12  X  10  =  V1.2  =  i.i  ft 
Trautwine's  Formula  gives  nearly  the  same  result, 

T^      ,     ,  ,  V  lo-H  10 

Depth  of  key  « h  0.2  f t  =  1.3  ft 


<1 


But  if  we  should  compute  the  stability  of  a  20-ft  semicircular  arch  with  a 
keystone  1.3  ft  deep,  we  should  find  that  the  arch  is  very  unstable;  hence,  ir 
this  case,  we  cannot  use  the  formula  and  mv-st  act  upon  our  own  judgment 
In  the  opinion  of  the  author,  the  arch-ring  of  such  an  arch  should  be  at  leas 
2\(i  ft  deep  and  the  stability  of  the  arch  should  be  tested  for  that  thickness 
In  all  calculations  on  the  arch,  it  is-  customary  to  consider  it  i  ft  thick  a 

*  Taken  from  The  Civil  Engineer's  Pocket-Book,  John  C.  Trautwine. 


Arches 


311 


right-angles  to  its  face.  This  allows  the  areas  of  the  faces  to  be  substituted 
for  the  ACTUAL  weights  of  the  voussoirs  and  their  loads.  This  method  was 
used  in  the  discussion  of  Retaining- Walls,  Chapter  IV,  and  Piers  and  But- 
tresses, Chapter  VII.  Furthermore,  it  is  evident  that  if  an  arch  i  ft  thick  is 
stable,  any  number  of  arches  of  the  same  dimensions  built  alongside  of  it  would 
be  stable.  In  determining  the  stability  of  masonry  arches  it  is  also  customary 
to  neglect  any  increase  in  the  strength  of  the  arch  from  the  mortar  in  the  joints, 
or  in  other  words,  to  consider  the  arch  as  laid  up  dry. 

Graphic  Determination  of  the  Stability  of  Arches.  An  arch  has  already 
been  defined  as  a  particular  arrangement  of  blocks  of  stone  or  other  material, 
these  blocks  being  .called  the  vous- 
soirs. For  the  sake  of  simplicity 
consider  an  unloaded  arch.  In 
such  an  arch  each  voussoir  is  sub- 
jected to  the  action  of  three  forces, 
(i)  the  thrust  that  it  receives  from 
the  voussoir  next  above  it  in  the 
arch-ring,  (2)  the  force  of  gravitation, 
or  its  own  weight  and  (3)  the  reaction 
to  the  resultant  thrust.  The  first  two 
forces  combine  into  one  and  form 
the  thrust  that  this  voussoir  exerts  on  the  one  next  below  it  in  the  arch-ring 
(Fig.  7).  The  points  in  which  these  various  thrusts  cut  the  joints  are  called  the 
centers  of  pressure  of  the  joints,  while  the  line  joining  these  centers  of  pres- 
sure is  called  the  line  of  pressure  or  line  of  resistance.*  In  order  that  an 
arch  may  be  absolutely  stable,  this  line  of  resistance  must  fall  within  the  middle 
third  of  the  arch-ring.  (See  Theorem  of  the  Middle  Third,  Chapter  IV.)  If 
the  arch  is  stable  the  centers  of  pressure  on  the  various  joint-Hnes  are  within 
the  middle  third  of  the  voussoir-depths  and  the  angles  made  by  the  different 
thrusts  with  the  normals  to  the  joints  are  less  than  the  angle  of  friction  of 
the  material  of  which  the  arch  is  constructed.     If  these  conditions  are  not  ful- 


Thrust  from  voussoir. 
next  above 
Center  of  pressure 


Resultant  thrust 
on  voussoir  next  below 


•♦—Thrust  of  voussoir 


Fig.  7.«  Equilibrium  of  Forces  on  Voussoir 


Failure    of    Semicircular   Arch. 
Haunches  Sliding  Down 


Fig.  9.     Failure  of  Semicircular  Arch. 
Haunches  Sliding  Up 


filled  the  criteria  of  safety,  explained  in  Chapter  VII  in  the  discussion  of 
the  Stability  of  a  Buttress,  will  not  be  satisfied;  and  at  any  joint  where  these 
conditions  do  not  obtain,  the  voussoir  above  the  joint  will  tend  to  slide  along 
the  joint-plane  if  the  angle  made  by  the  thrust  with  a  normal  to  the  joint  is 
greater  than  the  angle  of  friction.  If  the  center  of  pressure  Ues  out.side  the 
middle  third,  there  will  be  a  tendency  for  the  voussoir  to  overturn.  When 
these  tendencies  reach  extreme  limits  actual  failure  may  occur.  Figures  8,  9, 
10  and  11  illustrate  some  of  the  ways  in  which  an  arch  may  fail,  Figs.  8  and  9, 

*  This  line  is  called,  interchangealily,  the  line  of  pressure,  the  line  of  resistance, 
tlie  RESIST.ANCE-LINE,  etc.      (See,  also,  Chapter  XXXI,  pages  1225  and  1234.) 


312  The  Stability  of  Masonry  Arches  Chap.  8 

showing  different  parts  of  the  masonry  sliding  on  the  joints  and  Figs.  10  and 
1 1  the  failures  caused  by  the  passing  of  the  Une  of  pressure  near  the  intrados  or 
extrados. 

Before  passing  to  the  actual  discussion  of  the  graphic  method  for  determining 
the  stability  of  arches,  a  consideration  of  the  action  of  the  stresses  developed 
in  a  construction  of  this  kind  will  assist  in  a  clearer  understanding  of  the  subject. 

Fig.  8  shows  how,  if  the  line  of  resistance  along  the  haunches  of  the  arch 
«\hould  turn  sharply  downward  and  in  so  doing  make  with  a  normal  to  one  of 
the  joints  an  angle  greater  than  the  angle  of  friction,  the  voussoirs  at  this  point 


Fig.  10.     Failure  of  Semicircular  Arch.  Fig.    11.     Failure   of    Poinled    Arch. 

Opening  of  Arch-ring  Opening  of  Arch-ring 

would  tend  to  slide  inward  on  their  joint-planes,  forcing  outward  the  voussoirs 
at  the  spring  and  crown  of  the  arch.  Fig.  9  shows  how  failure  of  the  arch  would 
occur  under  similar  conditions,  but  with  the  line  of  resistance  turning  sharply 
upward  instead  of  downward.  In  these  two  cases  it  is  conceivable  that,  al- 
though the  RESISTANT  THRUST  at  the  joint  where  failure  takes  place  makes  an 
angle  with  the  normal  greater  than  the  angle  of  friction,  its  point  of  application 
is  still  within  the  middle  third  of  the  joint. 

Figs.  10  and  11,  on  the  contrary,  illustrate  methods  of  failure  in  which,  al- 
though the  angle  made  by  the  thrust  may  be  such  as  to  cause  no  slipping  of  one 
joint  on  another,  its  point  of  application  is  suflSciently  outside  the  middle  third 
of  the  arch- ring  itself  at  the  crown  to  cause  overturning.  In  Fig.  10  the  line 
of  resistance  passes  high  up,  or  perhaps  entirely  outside  of  the  arch-ring,  in  the 
voussoirs  at  the  crown  of  the  arch  and  low  down  along  the  haunches.  In 
Fig.  11  exactly  contrary  conditions  exist. 

The  ten  ways  in  which  a  masonry  arch  may  fail  have  been  classified  as  follows:  * 
"  (i)  By  crushing  of  the  masonry;  (2)  By  sliding  of  one  voussoir  upon  another; 
(3)  By  one  voussoir  or  section  of  masonry  overturning  about  an  adjacent 
voussoir  or  section;  (4)  By  shearing  in  a  horizontal  or  vertical  plane,  this 
applying  to  solid  concrete  arches  and  not  to  voussoirs;  (5)  As  a  column  when 
the  ratio  of  the  unsupported  length  of  an  arch  to  its  least  width  is  greater  than 
twelve;  (6)  From  striking  the  centering  before  the  mortar  is  hard  or  when 
the  arch,  although  stable  under  the  full  load,  is  not  stable  under  its  weight 
alone;  (7)  By  striking  the  centering  or  loading  the  arch  during  construc- 
tion unsymmetrically;  (8)  By  settlement  of  the  foundations;  (9)  By  sliding 
upon  the  foundations;  (10)  By  overturning  about  any  point  in  the  pier  or 
abutment.  Methods  (8)  and  (9)  are  the  most  common  ways  of  failure.  All 
methods  of  failure,  however,  must  be  guarded  against  in  design." 

While  some  of  these  ways  of  failure  may  seem  other  than  those  illustrated 
in  the  foregoing  figures,  they  may  be  perhaps  more  properly  considered  causes 

*  W.  J.  Douglas  in  American  Civil  Engineering  Pocket-Book,  nage  625. 


Arches  313 

OF  FAILURE  than  WAYS  OF  FAILURE;  and  all,  with  the  exception  of  the  first, 
bring  about  a  position  of  the  line  of  resistance  in  the  arch-ring  which  causes 
failure  in  one  of  the  ways  noted. 

In  regard  to  the  method  of  failure  (i),  the  conditions  may  be  such  that  the 
loading,  although  symmetrical,  is  so«excessive  that  although  the  line  of  resistance 
remains  within  the  middle  third,  the  total  pressure  on  a  joint  is  sufficient  to 
CRUSH  THE  MATERIAL  of  which  the  arch  is  constructed.  Such  conditions,  how- 
ever, are  not  common. 

From  the  foregoing  discussion  it  is  evident  that  in  order  to  determine  whether 
or  not  a  given  arch  is  stable,  it  is  necessary  to  find  the  true  line  of  resistance 
corresponding  to  the  conditions  of  loading,  form  and  dimensions  of  that  par- 
ticular arch.  It  is  always  possible,  in  every  arch-ring,  to  pass  one  maximum 
and  one  minimum  line  of  resistance.  The  true  line  of  resistance  will  lie 
somewhere  between  these  two.  The  method  of  procedure,  therefore,  is  to  pass 
tentatively,  a  line  of  resistance,  either  a  maximum  or  a  minimum  one,  and  see 
if  it  remains  within  the  middle  third.  If  it  does  not,  as  it  may  not  be  the  true 
line  of  resistance,  it  does  not  mean  necessarily  that  the  arch  is  not  stable.  The 
next  step  then,  is  to  note  where  it  departs  farthest  from  the  middle  third,  and 
to  pass  a  second  line  of  resistance  through  the  same  point  on  the  crown-joint 
and  the  point  on  the  line  of  the  middle  third  where  the  original  line  departs 
farthest  from  the  middle  third.  If  this  second  line  of  resistance  remains  within 
the  middle  third  it  is  reasonable  to  assume  that  the  arch  is  stable.  In  these 
various  operations  it  is  only  necessary  to  consider  half  the  arch  when  the  loading 
is  symmetrical,  and  this  is  usually  the  case  in  architectural  problems.  The 
number  of  voussoirs,  also,  into  which  we  divide  the  half-arch,  is  immaterial 
and  the  joints  need  not  coincide  with  those  of  the  actual  arch. 

In  order  to  pass  a  line  of  resistance  through  an  arch-ring,  the  thrust  exerted 
by  the  other  half  at  the  crown-joint  on  the  half-arch  is  first  determined. 
This  thrust  is  then  combined  with  the  resultant  of  the  weight  of  the  first  voussoir 
and  its  load  to  determine  the  thrust  exerted  by  this  voussoir  on  the  one  next 
below  it,  and  this  thrust,  in  turn,  is  combined  in  the  same  way  with  the  resultant 
of  the  weight  and  the  load  of  the  second  voussoir,  and  so  on  down  to  the  spring- 
ing-joint,  for  each  succeeding  voussoir.  The  points  in  which  the  various  lines 
representing  the  thrusts  cut  the  joints  are  known  as  the  centers  of  pressure, 
and  the  fine  joining  them  is  the  line  of  pressure  or  line  of  resistance.  In 
performing  this  operation,  the  center  of  gravity  of  each  voussoir  as  well  as 
the  fine  passing  through  the  center  of  gravity  of  the  whole  half-arch  must  be 
located.  The  face  of  each  voussoir  may  be  considered  a  trapezoid,  and  any 
one  of  the  methods  for  finding  the  center  of  gravity  of  this  figure  may  be  used 
for  finding  the  center  of  gravity  of  each  voussoir.  The  method  of  dividing  the 
trapezoid  into  triangles  is  here  employed  and  is  shown  at  the  side  of  the  arch 
in  Fig,  12.  (See,  also,  in  Chapters  VI  and  VII.)  As  the  determination 
of  the  position  of  the  line  passing  through  the  center  of  gravity  of  the  half-arch 
is  the  problem  of  finding  the  resultant  of  a  system  of  parallel  forces,  the 
method  involving  the  drawing  of  the  equilibrium-polygon  may  be  used. 
The  most  convenient  way  to  determine  the  stability  of  an  arch  is  to  use  the 
GRAPHIC  method.  The  steps  in  this  method  are  outlined  in  the  preceding  para- 
graphs.    Each  of  the  operations  will  now  be  considered  in  detail. 

First  Step.  Draw  one-half  the  arch  to  as  large  a  scale  as  convenient,  and 
divide  it  into  voussoirs  of  equal  size.  In  the  example  shown  in  Fig.  12,  the 
arch-ring  is- divided  into  ten  voussoirs  of  equal  face-areas.  As  already  pointed 
out,  it  is  not  necessary  that  these  should  represent  the  actual  voussoirs  of  which 
the  arch  is  built.     Next,  the  face-area  of  each  of  these  voussoirs  is  to  be  foimd. 


314 


The  Stability  of  Masonry  Arches 


Chap.  8 


Method  of  finding  oentar 
gravity  of  vousaolr 


Where  the  arch-ring  is  divided  into  voussoirs  of  equal  size,  this  is  most  easily 
done  by  computing  the  total  area  of  the  arch-ring  and  dividing  this  total  area 
by  the  number  of  voussoirs.  The  formula  for  finding  the  area  of  one-half  the 
arch-ring  is  as  follows: 

Area  in  square  feet  =  ©7854  (''^  —  1^) 

In  this  formula  r  is  the  outside  radius  and  n  the  inside  radius  in  feet. 
In  this  problem,  for  example,  if  the 

Area  of  the  arch-ring  =  o  7854  (12.52  —  lo^)  =  44.2  sq  ft 

as  there  are  ten  equal  voussoirs,  the  area  of  each  voussoir  is  4.42  sq  ft.  Hav- 
ing  drawn  out  one-half  of  the  arch-ring,  divide  the  crown-joint  into  three  equal 

parts,  and  with  radii 
of  O'E  and  O'F  describe 
the  arcs  dividing  the 
arch-ring  into  thirds. 

Second  Step.  Choose 
the  points  E  and  H 
through  which  to  pass 

a  MINIMUM  LINE  OP  RE- 
SISTANCE. The  points 
F  and  G,  through  which 

a  MAXIMUM  LINE  OF  RE- 
SISTANCE can  be  passed, 
could  equally  well  have 
been  chosen.  It  should 
be  noted  that  an  un- 
loaded semicircular 
arch  is  more  apt  to  fail 
by  opening  at  the  in- 
trados  at  the  crown 
and  at  the  extrados  at 
the  haunch,  and  there- 


C   G  H 
Fig.  12 


Line  of  Pressure  in  Unloaded  Semicircular  Arch-ring    fore,  in  this  case,   the 

line  of  resistance  prob- 
ably passes  nearer  the  outer  third  at  the  crown  and  nearer  the  inner  third 
at  the  HAUNCH.  To  determine  this  minimum  line  of  resistance  the  minimum 
thrust,  applied  at  the  point  E  of  the  crown-joint,  must  first  be  determined. 

The  half-arch  is  in  equilibrium  under  the  action  of  three  forces:  (i)  the 
thrust  at  the  crown,  acting  horizontally,  applied  at  the  point  E  and  preventing 
the  half-arch  from  overturning  inward;  (2)  the  weight  of  the  half-arch 
considered  as  a  vertical  force,  acting  through  its  center  of  gravity  and  tending 
to  overturn  it  inwards  about  the  point  D;  and  (3)  A  force  equal  and  oppo- 
site TO  THE  RESULTANT  of  these  two  forces  and  passing  from  //  to  /.  /  is  the 
intersection  of  the  weight-line  through  the  center  of  gravity  of  the  half-arch, 
with  the  line  of  action  of  the  thrust  at  the  crown,  prolonged.  It  is  thus  possible 
to  construct  the  triangle  of  these  three  forces  and  determine  the  magnitudes 
of  the  thrusts,  when  the  position  of  the  weight-line  of  the  half-arch  is  deter- 
mined. It  is  first  necessary  to  draw  a  vertical  line  through  the  center  of  gravity 
of  each  voussoir.  The  center  of  gravity  of  one  of  the  voussoirs  may  be  found 
by  the  method  of  triangles,  as  shown  in  the  supplementary  figure  at  the  side 
of  the  arch-ring. 

Having  determined  the  positions  of  the  centers  of  gravity  of  the  voussoirs. 


Arches  315 

locate  them  on  the  voussoirs  as  shown.  From  the  point  E  (Fig.  12)  lay  off  verti- 
cally, to  a  scale  of  so  many  square  units  to  a  linear  unit,  the  area  of  each 
voussoir,  one  below  the  other,  commencing  with  the  top  voussoir.  The  length 
of  the  hne  EK  will  then  equal  the  total  area  of  the  arch-ring.  From  E  and 
K  (Fig.  12)  draw  45°  hnes  intersecting  at  O.  Draw  Ow  i,  Ow  2,  Ow  2>,  etc. 
Then  where  OE  intersects  the  first  vertical  line  through  the  center  of  gravity 
of  the  first  voussoir  at  a,  draw  a  line  parallel  to  Ow  i,  intersecting  the  second 
vertical  at  h.  Draw  he  parallel  to  Chv  2,  cd  parallel  to  Ow  3  and  so  on  to  k. 
Draw  kL  parallel  to  Ow  10  and  prolong  it  downward  until  it  intersects  EO  pro- 
longed, at  L.  A  vertical  line  drawn  through  L  will  pass  through  the  center  of 
gravity  of  the  half  arch-ring.  This  is  an  application  to  a  practical  problem  of 
the  method  of  finding,  by  the  equilibrium-polygon,  the  line  of  action  of  the 
resultant  of  a  system  of  parallel  forces.  The  weights  of  the  individual 
voussoirs  act  along  parallel  vertical  lines  and  the  weight  of  the  half-arch  is  their 
resultant  in  magnitude. 

Third  Step.  To  determine  the  thrust  at  the  crown  and  the  reaction 
AT  the  spring,  draw  a  horizontal  hne  through  E,  the  upper  part  of  the  middle 
third,  and  a  vertical  line  through  L,  the  two  lines  intersecting  at  /  (Fig.  12). 
For  the  arch  to  be  stable,  it  is,  in  general,  considered  necessary  for  the  line 
OF  resistance  to  pass  within  the  middle  third.  First,  assume  that  the  line 
of  pressure  or  resistance  starts  at  E  and  comes  out  at  H.  Draw  a  line  /// 
the  direction  of  the  hne  of  action  of  the  resultant  of  the  thrust  at  the  crowr^ 
and  the  weight  of  the  half-arch,  and  draw,  also,  a  horizontal  line  opposite  the 
point  w  ID,  between  N  and  M.  This  horizontal  line  MN  represents  the  magni- 
tude of  the  horizontal  thrust  at  the  crown,  for  INM  is  the  triangle  of  the 
three  forces  in  equilibrium,  the  thrust  at  the  crown,  the  weight  of  the 
half-arch  and  the  reaction  at  the  spring.  Draw  7£^  10  0^  parallel  to  ///,  and 
the  lines  O^w  1,  O^w  2,  O^w  3,  etc.  O^E,  equal  to  NM,  is  the  thrust  at  the 
crown,  and  w  10  0^,  equal  to  MI,  the  reaction  at  the  spring.  INM  and  EKO^' 
are  similar  triangles. 

Fourth  Step.  It  is  required  next,  to  determine  the  line  of  resistance 
through  the  arch-ring.  The  thrust  at  E  is  combined  with  the  weight  of  the 
first  voussoir;  their  resultant  is  found  and  in  turn  combined  with  the  weight  ot 
the  second  voussoir;  and  so  on  for  all  the  voussoirs.  The  intersections  of  these 
resultants  with  the  joint-lines  are  the  centers  of  pressure;  the  line  joining 
these  centers  of  pressure  is  the  line  of  resistance. 

These  resultants  could  be  determined  by  drawing  a  series  of  parallelo- 
grams .OF  FORCES  over  each  voussoir.  This  would  complicate  the  figure  and 
involve  unnecessary  labor.  It  is  found  more  convenient  to  draw  the  triangles 
OF  FORCES  one  after  the  other,  at  the  right-hand  side  of  the  figure  and  then 
transfer  the  results  thus  obtained  by  means  of  parallel  lines  to  the  figure 
Itself,  especially  as  the  weights  of  the  voussoirs  have  already  been  laid  off  along 
the  line  F.K,  at  Ew  1,  w  2,ws,w4,w  5,  etc. 

Then  from  the  point  where  O^E  prolonged  intersects  the  first  vertical  in 
voussoir  number  i,  draw  a  (green)  line  to  the  second  vertical,  parallel  to  O^wi; 
from  this  point,  a  (green)  line  to  the  third  vertical,  parallel  to  O^^w  2  and  so 
on.  The  last  line  should  pass  through  //.  Join  the  various  points,  where  these 
(green)  lines  cut  the  joints  at  the  centers  of  pressure,  by  the  broken  (red)  line. 
This  last  line  drawn  is  the  line  of  .resistance.  If  this  line  lies  entirely  within 
the  middle  third  of  the  arch-ring,  the  arch  may  be  considered  to  be  stable. 
But  suppose  that  the  line  of  resistance  passes  not  only  outside  of  the  middle 
third  but  also  outside  of  the  arch-ring  itself;  it  is  still  possible  that  the  arch 
is  not  unstable.     This  is  the  case  in  Fig.  12  and  we  will  next  determine  if  a 


316 


The  Stability  of  Masonry  Arches 


Chap.  8 


line  of  resistance  can  be  drawn  which  will  remain  within  the  limits  of  the  middle 
third  of  the  arch-ring. 

Fifth  Step.     The  Second  Trial.     Reproducing   the  condition  of    Fig.   12  in 
Fig.  13,  without  the  construction  Unes,  it  is  seen  that  the  line  of  resistance 

leaves  the  arch-ring  at  R  and 
j;^  enters  it  again  at  S,  while  it  is 
1^  furthest -from  it  at  U.  If,  at  U, 
"  a  perpendicular  is  erected  to  a 
straight  Une  joining  the  two 
points  R  and  5,  this  perpen- 
dicular line  VW,  called  the  line 
OF  FRACTURE,  will  be  approxi- 
mately the  trace  of  the  plane 
along  which,  with  the  line  of 
resistance  under  consideration, 
the  arch  will  tend  to  fail,  pre- 
sumedly by  TURNING  OVER  tO 
the  right  about  the  point  V. 
This  shows  that  the  thrust  at 
THE  CROWN,  assumed  to  be 
applied  at  the  point  E,  while  of 
sufficient  intensity  to  maintain 
equilibrium  about  //,  is  not  of 
sufficient  intensity  to  maintain 
equilibrium  about  V.  If  now  a 
SECOND  THRUST,  of  Sufficient 
intensity  to  maintain  equilibrium  about  V,  or  better,  about  X,  can  be  applied 
at  E  without  being  so  great  in  magnitude  that  it  will  overturn  the  arch 
outward  about  G,  or  some  other  point  on  the  outer  Hne  of  the  middle  third,  it 


C 
Fig. 


G  H    D 

13.     Line   of    Fracture   in    Unloaded 
circular  Arch-ring 


Spring-line 


C  G    H   D 
Fig.  14.     Second  Line  of  Pressure  in  Unloaded  Semicircular  Arch-ring 


is  reasonable  to  conclude  that  the  line  of  resistance  resulting  from  this  thrust  is 
very  nearly  the  true  line  of  resistance  in  the  arch-ring  and  that  the  arch 
is  stable. 

In  order  to  determine  this  new  lini?  of  resistance  the  new  thrust  at  thf 


Arches 


317 


CROWN  must  be  found  (Fig.  14).  The  preliminary  steps  required  for  this  are 
the  same  as  before  until  the  seventh  voussoir  is  reached.  This  is  divided  into 
two  voussoirs  by  the  line  VW  (Fig,  14),  one  being  w6  w6"^  and  the  other  the 
remainder  of  this  seventh  voussoir,  and  this  division  must  be  allowed  for  along 
the  load-line  EK,  at  wd  w6^.  The  line  w6  w6"'  represents  the  area  of  vous- 
soir 6**,  and  the  Hne  w6"  wy  the  area  of  the  remainder  of  the  seventh  voussoir. 
The  vertical  line  IL,  passing  through  the  center  of  gravity  of  that  part  of  the 
half-arch  above  the  line  VW,  is  found  by  prolonging  backwards  the  line  hg, 
parallel  to  0  wG  ^,  until  it  intersects  OE  at  L.  To  find  the  new  thrust  at  the 
CROWN  by  completing  the  triangle  of  forces  for  this  thrust  and  the  force 
equal  and  opposite  to  their  resultant,  the  inclined  (blue)  line  must  be  drawn 
through  the  point  X  and  the  horizontal  (blue)  line  through  w6°'.  The  new  thrust 
then  is  as  before  NM,  equal  to  O^E.  This  thrust  is  laid  off  at  O^E,  the  (green) 
lines  O^w  i,  O^w  2,  O^^w  3,  etc.,  being  drawn  as  before  and  the  new  line  of  re- 
sistance being  drawn  through  the  points  where  the  parallels  to  these  (green) 


C  G    H   D  O' 

Fig.  15.     Line  of  Pressure  in  Loaded  Semicircular  Arch-ring 


lines  cut  the  joints.  This  new  line  of  resistance,  if  drawn  correctly,  should 
pass  through  X.  It  Hes  within  the  middle  third,  except  for  a  short  distance  at 
the  springing,  and  hence  it  is  justifiable  to  consider  the  arch  stable.  If  it  had 
passed  outside  the  middle  third  to  any  great  extent,  in  this  second  trial,  this 
presumption  would  not  have  been  justified. 

This  discussion  explains  the  method  of  determining  the  stability  of  an  un- 
loaded semicircular  arch.  Such  cases  very  seldom  occur  in  practice,  but 
they  serve  to  illustrate  the  methods  which  apply  generally  to  all  other  cases. 
With  LOADED  arch-rings  there  is  slight  difference  in  the  method  of  determining 
the  position  of  the  center  of  gravity. 

Example  3.  A  loaded  or  surcharged  semicircular  arch  (Fig.  15)  will  be 
considered  next.  Assume  the  same  arch  shown  in  Figs.  12,  13  and  14,  and  sup- 
pose it  to  be  loaded  with  a  wall  of  masonry  of  the  same  thickness  and  weight 
per  square  foot  as  that  of  the  arch-ring,  the  upper  surface  of  the  wall  being  an 
inclined  plane,  i  ft  above  the  arch-ring  at  the  crown,  and  8  ft  above  it  at  the 
spring.     The  assumption  of  the  particular  load  in  this  case  is  a  purely  arbitrary 


318 


The  Stability  of  Masonry  Arches 


Chap.  8 


one  for  the  purpose  of  illustrating  the  method  of  solution.  The  determination 
of  the  ACTUAL  LOAD  that  comes  upon  an  arch  in  any  given  case  is  by  no  means 
easy,  so  numerous  are  the  uncertain  elements  that  affect  the  transmission  of 
this  load  to  the  arch- ring. 

The  customary  procedure  i.i  to  assume  that  the  load  is  itself  transmitted  to  the 
arch-ring  vertically  downward.  Each  voussoir  thus  receives  that  portion  of 
the  load  which  is  included  .between  two  vertical  lines  drawn  to  the  points  of 
intersection  of  the  joints  on  either  side  of  that  voussoir  with  the  extrados.  Hav- 
ing made  this  assumption  it  is  necessary  next  to  determine  how  much  of  the 
total  superimposed  masonry  bears  upon  the  arch-ring. 

It  is  a  matter  of  common  observation  that  if  an  opening  is  made  in  a  wall, 
especially  in  a  wall  that  has  stood  for  some  time,  the  major  portion  of  the  masonry 
above  this  opening  is  self-supporting,  limited  portions  only,  bounded  by  a  some- 
what irregular  line,  falling  down  into  the  opening,  as  shown  in  Fig.  16.     The 

profile  of  this  bounds; ry-line  depends  upon 
the  nature  of  the  material  of  which  the 
wall  is  constructed,  the  size  of  the  stones, 
bricks,  etc.,  the  character  of  the  bond 
and  the  quality  of  the  mortar.  This 
being  the  case,  all  the  masonry  above  an 
arch  should  not  be  considered  as  the 
load  on  it.  Some  authorities  recommend 
considering  as  the  proper  load,  for  brick- 
work, a  trlangular  part  of  the  wall, 
the  sides  of  which  triangle  have  an  in- 
clination to  the  horizontal  of  45°;  others 
assume  an  inclination  of  60°  (Fig.  16). 
(See,  also,  Chapter  XV,  page  612.)  The 
exact  determination  of  this  load  by 
mechanical  laws  is  difficult  if  not  impossible.  It  is  better  to  consider  each 
case  separately  and  by  a  careful  study  of  the  conditions  to  determine  as  closely 
as  possible  just  what  portion  of  the  weight  of  the  superimposed  masonry  is 
transmitted  to  the  arch.  Having  assumed  a  load  for  this  particular  arch-ring 
(Fig.  15),  the  procedure  is  as  follows: 

First  Step  of  Example  3.  This  involves  the  finding  of  the  center  of  gravity 
of  the  ARCH-RING  AND  LOAD  COMBINED.  Divide  the  arch-ring  into  five  voussoirs 
of  equal  size.  In  this  case  the  area  of  each  voussoir  is  equal  to  44.2  sq  ft  h-  5,  or 
8.8  sq  ft.  (See  under  First  Step,  Fig.  12,  preceding  example.)  The  surcharge 
or  load,  also,  is  divided  into  five  parts,  not  necessarily  equal,  by  drawing  ver- 
tical lines  to  the  points  of  intersection  of  the  joints  and  the  extrados.  The  ap- 
proximate area  of  each  one  of  these  surcharges  is  found  by  multiplying  half 
the  sum  of  the  lengths  of  the  two  parallel  vertical  sides  by  the  length  of  the 
horizontal  distance  between  them. 

The  positions  of  the  center  of  gravity  of  each  voussoir  and  of  the  center  of 
gravity  of  each  voussoir-surcharge  are  determined  as  in  the  preceding  example. 
The  CENTERS  OF  GRAVITY  of  these  SURCHARGES  can  be  found  by  dividing  each 
TRAPEZOIDAL  FIGURE  into  TRIANGLES  as  shown,  remembering  that  the  medial 
line  in  this  case  joins  the  middle  points  of  the  two  parallel  faces.  As, the  latter 
are  vertical,  the  medial  lines  approach  a  horizontal  direction.  This  construc- 
tion is  shown  on  surcharge  i",  Fig.  15.  Having  drawn  the  lines  of  action  of 
the  weights  of  the  various  voussoirs  and  of  their  loads  through  their  respective 
centers  of  gravity,  the  lines  of  action  of  the  combined  weight  of  each  voussoir 
and  its  load  must  be  found.    The  construction  for  this  operation  is  shown  at 


16.     Triangle    of    Loading 
Opening 


Arches  319 

the  left  of  Fig.  15.  The  method  used,  that  of  the  equilibrium-polygon, 
is  the  same  as  that  employed  in  the  previous  example  to  find  the  line  passing 
through  the  center  of  gravity  of  the  half-arch,  only  in  this  case  the  forces  are 
reduced  to  two.  Furthermore,  as  the  areas  of  the  various  voussoirs  are  equal 
it  is  possible  to  superimpose  the  different  force-diagrams,  one  over  the  other, 
and  so  save  considerable  labor.  Begin,  therefore,  by  laying  off  along  the  line 
RS  at  the  left  of  the  loaded  arch,  and  at  any  convenient  scale,  fw,  the  area 
(weight)  of  a  voussoir;  then  from  w,  in  turn,  the  distances  zy  i^,  w  2",  iv  3",  etc., 
,  representing  the  areas  of  the  successive  surcharges,  i*^,  2",  3^,  etc.,  always  at  the 
same  scale.  The  scale  to  be  employed  later  for  laying  off  the  combined  weights 
of  the  voussoirs  and  their  loads  along  the  line  AK  is  the  best  one  to  choose,  but 
the  difference  in  scales  is  not  important.  In  this  particular  instance  the  two 
points  i"  and  5"  coincide  because  the  two  areas  i'^  and  5"^,  although  of  different 
shapes,  are  each  equal  to  6.7  sq  ft.  This  is  a  mere  coincidence.  Next  draw 
/O"  and  4"  O"  at  45°  to  RS,  and  in  turn,  0"w,  0"i",  0"2«,  etc.  As  the  problem 
which  presents  itself  is  to  combine  the  weight  of  each  voussoir  with  its  individual 
surcharge,  and  as  the  weights  of  all  the  voussoirs  are  equal,  and,  furthermore, 
as  the  forces  which  are  to  be  combined  to  find  their  resultant  are  only  two,  the 
two  POLE-LINES  or  RAYS  0"f  and  0"w  in  the  force-diagram  serve  in  each  case, 
and  the  funicular  polygon  is  reduced  to  a  triangle.  Draw  gh,  ik,  Im,  np 
and  rs  parallel  to  0"w,  and  ///,  kii,  mv,  px  and  sy  parallel  to  0"f;  and  draw  gt, 
iu,  Iv,  nx  andry  parallel  respectively  to  0"i",  0"2°,  0"^'^,  O'V'  and  0"s^.  The 
points  /,  w,  V,  X  and  y  are  the  points  through  which  to  draw  the  heavy  (red) 
lines  of  action  of  the  combined  weights  of  the  voussoirs  and  their  surcharges. 

Having  found  and  drawn  these  lines,  the  procedure  for  finding  the  line  IN  is 
the  same  as  in  the  previous  example,  except  that  the  distances  Ewi  1°',  wi  i", 
wi  2",  etc.,  instead  of  being  equal  to  the  weights  of  the  voussoirs  alone,  are 
equal  to  the  combined  weights  of  each  voussoir  and  its  surcharge,  Ewi  i^,  being 
equal  to/i",  wi  i/^  to  wi  2"  being  equal  to/ 2",  etc. 

The  line  EO  is  drawn  at  45°  to  AO' ,  but  as  the  position  of  the  pole-point, 
0,  is  entirely  arbitrary,  the  line  Ow  5  s"  has  been  drawn  in  this  case  in  such  a 
way  that  0  falls  well  over  toward  the  left  of  the  figure,  thus  avoiding  a  certain 
amount  of  confusion  in  the  drawing  which  would  have  resulted  if  Oiv  5  5* 
had  made  an  angle  of  45°  with  ^0'.  The  lines  ah,  he,  A  and  de  are  drawn  respec- 
tively parallel  to  tvi  i"0,  wi  2^0,  etc.,  and  eL  is  produced  backward  parallel 
to  Ow  5  5"  until  it  intersects  EO  at  L,  which  is  the  point  through  which  the 
heavy  (red)  line  IN,  passing  through  the  center  of  gravity  of  the  whole  half-arch 
and  its  surcharge,  should  be  drawn.  A  vertical  line  drawn  through  L  will  pass 
through  the  center  of  gravity  of  the  arch-ring  and  its  load.  If  this  were  an  arch 
designed  for  a  building  and  if  the  only  abutments  possible  were  of  such  size  and 
form  that  it  was  essential  for  the  thrust  exerted  by  the  last  or  fifth  voussoir  on 
these  abutments  to  approach  more  nearly  the  vertical,  the  architectural  expedient 
of  increasing  slightly  the  weight  of  the  surcharge,  5*^,  on  this  voussoir  by  adding 
some  piece  of  ornament,  such  as  a  cartouche,  could  be  resorted  to.  A  case  of 
this  kind  in  actual  practice  is  the  archway  over  the  entrance  to  the  service-court- 
yard of  the  Grand  Opera  House  in  Paris,  where  the  pyramidal  stone  ornaments 
which  surmount  the  cornice  on  either  side  of  the  central  motive  were  added  after 
the  original  design  was  made,  with  this  end  in  view.  In  the  example  illustrated 
in  Fig.  15  {he  areas  of  the  faces  of  the  surcharges  are  shown  by  the  figures  on 
these  faces.  For  the  second  surcharge  from  the  crown,  for  example,  the  area 
is  8.1  sq  ft. 

Second  Step  of  Example  3.  This  involves  the  determination  of  the  thrust 
AT  THE  CROWN  and  the  line  of  resistance.     The  method  of  finding  this  thrust 


320 


The  Stability  of  Masonry  Arches 


Chap.  8 


Arches  321 

at  the  crown  is  similar  to  that  employed  in  the  previous  example.  In  that 
example,  however,  it  was  found  that  this  thrust,  appUed  at  E  and  determined 
by  assuming  //  as  the  point  of  application  of  the  reaction  at  the  spring,  produced 
a  line  of  resistance  which  fell  considerably  below  the  middle  third.  But  instead 
of  performing  the  operations  required  by  a  second  trial,  as  in  the  previous  exam- 
ple, the  expedient  is  tried  of  slightly  increasing  the  inclination  to  the  vertical 
of  the  (blue)  line  IM,  and  so  assuming  a  somewhat  greater  thrust  at  the 
CROWN.  As  the  line  of  resistance,  as  shown  in  Fig.  15,  passed  with  this  thrust 
departs  but  slightly  from  the  middle  third  near  the  springing,  we  are  justified 
in  assuming  that  this  arch  is  stable  under  the  given  conditions.  The  method 
used  for  this  example  may  be  used,  also,  for  a  semielliptical  arch. 

Example  4.  This  example  (Fig.  17)  illustrates  the  application  of  the  preced- 
ing methods,  with  some  variations,  to  the  determination  of  the  position  of  the 
center  of  gravity  of  a  loaded  segmental  arch,  the  thrusts  at  the  crown  and 
spring  and  the  line  of  pressure  or  resistance  through  the  arch-ring.  In  this  case, 
instead  of  dividing  the  arch-ring  into  a  certain  number  of  voussoirs  with  joints 
radiating  from  a  center  and  considering  the  surcharge  on  each  individual  voussoir, 
the  method  of  dividing  the  arch-ring  and  its  load  into  vertical  slices,  in  this 
case  two  feet  wide,  and  computing  the  areas  of  the  entire  slices  has  been  adopted. 
Having  computed  the  areas  of  the  slices,  including  in  each  case  the  combined 
areas  of  the  sliced  part  of  the  arch-ring  and  its  surcharge,  we  lay  them  off  in  order 
from  E,  to  a  convenient  scale,  and  then  proceed  as  in  the  previous  examples. 
The  remaining  steps  required  to  determine  the  thrusts  at  the  crown  and  at  the 
spring  and  the  line  of  resistance  are  also  the  same  as  explained  in  the  foregoing 
paragraphs.  In  a  flat  segmental  arch  there  is  practically  no  need  of  dividing 
the  arch-ring  into  voussoirs  by  joints  radiating  from  a  center,  in  order  to 
determine  its  stability.     Of  course,  when  built,  they  must  be  made  to  radiate. 

Fig.  17  shows  the  graphical  analysis  of  an  arch  of  40-ft  span  and  carrying 
a  load  i^Vz  ft  high  at  the  crown.  The  depth  of  the  arch-ring  is  2  ft  6  in.  It  is 
seen  that  the  line  of  resistance  lies  entirely  within  the  middle  third,  and  that 
the  arch  is  therefore  stable.  It  is  to  be  noted  that  the  hne  of  resistance  in  a 
segmental  arch  should  be  drawn  through  the  lower  or  inner  edge  of  the 
middle  third  at  the  springing.  It  is  to  be  noted,  also,  that  the  horizontal  thrust 
at  the  crown  and  the  thrust  T  against  the  supports  are  very  great  when  com- 
pared with  those  in  a  semicircular  arch;  and  hence,  although  the  segmental 
arch  is  the  stronger  of  the  two,  it  requires  much  heavier  abutments.  The  fore- 
going examples  serve  to  show  the  various  methods  of  determining  the  stability 
and  thrusts  of  any  arch  used  in  buildings. 


322 


Reactions  and  Bending  Moments  for  Beams  Chap.  9 


CHAPTER   IX 

EEACTIONS  AND  BENDING  MOMENTS  FOR  BEAMS 

By 
CHARLES   P.   WARREN 

LATE   ASSISTANT  PROFESSOR   OF   ARCHITECTURE,   COLUMBIA   UNIVERSITY 

1.     Reactions  for  Simple  Beams 

Definition  of  Reaction.  One  of  the  fundamental  principles  of  static  equilib- 
rium is  that  the  sum  of  all  the  forces  acting  upon  a  body  in  one  direction  must  be 
balanced  by  the  sum  of  another  set  of  forces  acting  in  the  opposite  direction. 
Therefore,  in  the  case  of  a  beam  or  girder,  the  loads  acting  downward  must  be 
balanced  by  an  equal  set  of  forces  at  the  supports,  acting  upward.  These  up- 
ward forces  are  called  thrusts,  or  reactions  and  in  computing  the  strength 
of  beams  one  of  the  first  steps  is  to  determine  them,  since  the  loads  are  usually 
given  in  intensity  and  position. 

The  Principle  of  Moments.  The  reactions  may  be  determined  by  the 
application  of  another  fundamental  principle  of  static  equilibrium  for  forces 
acting  in  the  same  plane.     The  algebraic  sum  of  the  moments  of  all  the  forces 


Fig.  1.     Simple  Beam.     One  Concentrated  Load 

taken  about  any  point  in  the  plane  in  which  they  act  must  be  zero.  The  moment 
of  a  force  about  a  point  is  the  product  of  the  magnitude  or  intensity  of  the  force 
by  the  perpendicular  distance  between  the  line  of  action  of  the  force  and  the 
point.  The  perpendicular  distance  is  called  the  lever-arm,  and  the  point 
the  center  of  moments.  Forces  acting  upward  are  considered  positive  and 
those  acting  downward  are  considered  negative.  The  center  of  moments  may 
be  taken  at  any  point  in  the  plane  of  action  of  the  forces,  but  it  is  more 
convenient  to  take  it  at  one  of  the  reactions.  For  example,  the  beam  in  Fig.  1 
supports  a  concentrated  load  P  at  the  distance  m  from  the  left  support.  To  find 
the  left  reaction  take  the  center  of  moments  at  the  right  reaction.  Then  the 
equation  of  moments  is 

Rd  -  Pn  =  o. 


from  which 


Ri  =  Pn/l 


(i) 


Reactions  for  Beams 


323 


In  like  manner,  to  find  ^2  the  center  of  moments  is  taken  at  Ri  and  the 
equation  of  moments  is 

R2I  -  Pm  ■■=  o,  from  which  Rt  =  Rmjl  (i)' 

From  the  first  principle  of  statics  mentioned,  R\-V  Ri.  must  equal  P;  hence,  as 
a  check,  Pn/l  +  Prnjl  =  P. 

Example  i.  Let  a  beam  15  ft  in  span  support  a  concentrated  load  of  700  lb» 
6  ft  from  the  left  end;  or,  P  =  700,  w  =  6  and  w  =  9.  Then,  from  Formula  (i), 
^1  =  700  X  9/15  =  420  lb.     Ri  =  700  X  6/15  =  280  lb  and  420  +  280  =  700  lb. 

For  a  concentrated  load  at  the  middle,  or  for  a  uniform  load  over  a  simple 
beam,  it  is  evic  ^nt  without  applying  the  conditions  of  equilibrium,  that  each 
reaction  is  one-naif  the  load,  for,  in  Formulas  (i)  and  (i)',  m  and  n  each  equal 
1/2  and  Ri  ana  R2  =  y2  P. 

For  any  number  of  concentrated  loads  (Fig.  2)  the  reactions  may  be  found  by 
adding  together  the  reactions  found  by  Formula  (i)  due  to  each  load  separately, 
or  they  may  be  computed  in  one  operation  by  the  following  formula: 


I 


-7l-„ 


Fig.  2.     Simple  Beam.     Three  Concentrated  Loads 

To  find  the  right  reaction,  the  center  of  moments  is  taken  at  the  left  support, 
and  the  equation  of  moments  is 


hence. 


RJ'  —  PlMi  —  PiMi  —  P3W3  =  o 

P\m\  -\-  P-imi  -f  Pzrm 


R2  = 


/ 


(2) 


In  like  manner,  to  find  Ri  the  center  of  moments  is  taken  at  R2  and  the  equa^ 
tion  of  moments  is 

Ril  —  Piui  —  P2W2  —  P3W3  =  o 
from  which 

Pim  -\-  P2W2  4-  Psm  ,  , 

i?,  = ^ (3) 

Example  2.  Suppose  the  beam  in  Fig.  2  is  20  ft  in  length.  Let  there  be 
three  concentrated  loads  of  500,  800  and  600  lb  placed  5,  9  and  12  ft  respectively 
from  the  left  support.  Then  /  =  20,  m\  =  5,  m2  =  9,  W3  =  12,  Pi  =  500,  Pa  =  800 
and  Pz=  600.     Substituting  in  Formulas  (2)  and  (3), 

500X5-1-800X9  +  600X12       „      ,, 

Rx= =  845  lb 

20 

„     500X15  +  800X11  +  600X8  ,, 

R^  = =  I  055  lb 


and 


500  -f  800  -(-  600  =  845  -f- 1  OSS  =  I  900  lb 


324 


Reactions  and  Bending  Moments  for  Beams        Chap.  9 


To  find  the  reactions  for  a  combination  of  uniformly  distributed  and  con- 
centrated loads,  to  each  of  the  reactions  obtained  by  Formulas  (i)  or  (2)  for  the 
concentrated  loads,  add  one-half  the  distributed  load.  Thus,  suppose  the 
20-ft  beam  in  this  example  weighs  40  lb  per  linear  ft.  This  is  considered  as  a 
uniformly  distributed  load  and  for  the  entire  beam  it  is  40  lb  X  20  =  800  lb. 
By  the  rule,  one-half  of  this  is  added  to  each  reaction,  so  that  the  total  reactions 
are,i?2  =  845  +  400  =  i  245  lb  andi?i=  i  055  +  400  =  i  455  lb. 

Example  3.  For  a  distributed  load  applied  over  only  a  part  of  the  span,  as  in 
Fig.  3,  assume  the  load  to  be  concentrated  at  the  middle  of  the  part  over 


m=4.5-' ^T* m=5.5- 

I 
__.-^__J 43i_ _,_ _3.. 


10  =  50  lbs.  per  ft. 


f?i 


Z  =  10 


Fig.  3.     Simple  Beam.     Distributed  Load  over  Part  of  Span 

which  it  acts  and  use  Formulas  (1)  and  (i)'.  For  example,  let  w  (Fig.  3)  equal  $0 
lb  per  linear  ft,  applied  for  a  distance  of  5  ft  over  the  beam.  Then  W,  the  total 
load,  is  50  lb  X  5  =  250  lb.  This  may  be  assumed  to  be  concentrated  at  its 
center,  4.5  ft  from  the  left  support.  Then  P  =  250,  m  =  4.5  and  m  =  5.5;  and 
from  Formulas  (i)  and  (i)', 

250X5.5  ,, 


and 


250X4-5  ,, 

A2=  =  T12.5  lb 


Therefore,  for  any  combination  of  concentrated  and  uniform  loads  distributed 
over  the  entire  beam,  or  over  only  part  of  it,  find  the  reactions  due  to  the  con- 
centrated loads  by  Formulas  (i)  or  (2),  and  to  them  add  the  reactions  due  to  the 
uniformly  distributed  loads. 


2.     Bending  Moments  in  Cantilever  and  Simple  Beams 

Definitions.  The  bending  moment  is  a  measure  of  the  tendencies  of  forces  to 
break  a  beam  by  bending  or  flexure.  Fig.  4  shows  the  manner  in  which  a 
simple  bearn,  supported  at  the  ends,  breaks  when  subjected  to  a  load  greater 
than  it  can  bear.  The  effect  of  a  load  upon  a  beam  is  to  cause  it  to  sag,  or 
bend.  The  bending  of  the  beam  shortens,  or  compresses,  the  upper  fibers  and 
Stretches,  or  elongates,  the  lower  fibers.     So  long  as  the  resistance  of  the  fibers 

*  See,  also.  Chapter  XV,  pages  555  to  563. 


Bending  Moments  in  Beams  for  Different  Kinds  of  Loading    325 

to  shortening,  or  compression,  and  to  stretching,  or  tension,  is  greater  than 
the  tendency  of  the  load  to  disrupt  them,  the  beam  carries  the  load;  but,  when 
the  load  causes  a  greater  tension,  or  compression,  on  the  fibers  than  they 
are  capable  of  resisting,  the  beam  breaks.  The  stretching  of  the  fibers  before 
breaking  allows  the  beam  to  bend;  hence,  the  name  bending  moment  has  been 
given  to  the  forces  causing  a  beam  to  bend  and  perhaps  ultimately  to  break. 


Fig.  4.     Manner  of  Rupture  of  Simple  Beam 

In  order  to  calculate  the  flexural  strength  of  a  beam,  it  is  necessary  to 
ascertain  the  nature  and  extent,  first,  of  the  external  forces  acting  to  break 
the  beam,  and  secondly  of  the  internal  forces  or  stresses  tending  to  resist 
rupture.*  The  external  forces  tending  to  break  the  beam  by  flexure  are  the 
downward  loads  and  the  upward  reactions.  Each  acts  with  a  leverage 
equal  to  the  perpendicular  distance  from  its  line  of  action  to  the  section  at 
which  the  beam  tends  to  break.  The  algebraic  sum  of  the  moments  of  these 
external  forces  on  the  left,  or  right,  of  any  section  is  called  the  bending  moment 
for  that  section,  since  it  is  the  momei^t  of  the  resultant  of  the  forces  which 
tends  to  bend  the  beam  at  that  section.  It  is  generally  designated  by  M.  Then, 
from  the  definition,  the  bending  moment  for  any  section  of  a  beam  resting  on 
two  supports  and  in  a  state  of  flexure  under  a  load  or  loads  is  If  =  the  moment 
of  either  reaction  minus  the  sum  of  the  moments  of  the  loads  between  that  reac- 
tion and  the  section.  The  moment  of  the  reaction  is  upward,  or  positive,  and 
the  moment  of  any  load  downward,  or 
negative,  if  the  part  of  the  beam  on  the  left 
of  the  section  is  considered. 


3.   Bending   Moments  in  Beams   for   Dif- 
ferent Kinds  of  Loading 

Case  I 

Beam  Fixed  at  One  End  and  Loaded  with  a 
Concentrated    Load    P,    Near    the    Free    End 

Fig.  5.     Cantilever  Beam.     Con- 
Maximum  bending  moment,  at  wall  =  Pxl       centrated  Load  near  Free  End 
Bending  moment  at  any  other  section  x  =  Fx 

Note.     If  /  is  in  feet,  the  bending  moment  will  be  in  foot-pounds;   if  /  is  in 
hiches,  the  bending  moment  will  be  in  inch-pounds. 


Case  II 

Beam  Fixed  at  One  End  and  Loaded  with  a  Uniformly  Distributed  Load  W, 
(Fig.  6.) 
Maximum  bending  moment,  at  wall  =  W  X  I/2 
At  any  other  section  x,  M  =  ■wxXx/2  =  WX-/2 
Note.     W  =  wl  and  w  =  the  load  per  unit  of  length. 
*  See  Chapter  X  for  a  discussion  of  these  internal  stresses  and  of  the  resisting  moment. 


326 


Reactions  and  Bending  Moments  for  Beams         Chap.  9 


Case  III 

Beam  Fixed  at  One  End  and  Loaded  with  Both  a  Concentrated  and  a  Unifonnly 
Distributed  Load  (Fig.  7). 

Maximum  bending  moment,  at  wall  =  Pxh+WX  I1/2 


^^^ 


^^ 


r*--aj--->i 


Fig.  6.     Cantilever  Beam.     Uni- 
formly Distributed  Load 


Fig.  7.     Cantilever  Beam.     Distrib- 
uted Load  and  Load  at  Free  End 


Case  IV 

Beam  Supported  at  Both  Ends  and  Loaded  with  a  Concentrated  Load  at  the 
Middle  (Fig.  8). 

Maximum  bending  moment,  under  the  load  =  FI/4 

P 


Fig.  8.     Simple  Beam.     Concentrated  Load  at  the  Middle 

Case  V  ' 

Beam   Supported  at    Both  Ends   and  Loaded   with  a  Uniformly  Distributed 
Load  W  (Fig.  9). 

Maximum  bending  moment,  at  the  middle  =  Wl/S 


Fig.  9.     Simple  Beam.     Uniformly  Distributed  Load 


Bending  Moments  in  Beams  for  Different  Kinds  of  Loading     327 

Case  VI 

Beam  Supported  at  Both  Ends  and  Loaded  with  a  Concentrated  Load  not  at  tho 
Middle  (Fig.  10). 

Maximum  bending  moment,  mider  the  load  =  Pmn/l 


r 


^-m-^ 


n- 


»P 


Fig.  10.     Simple  Beam.     Concentrated  Load  not  at  the  Middle 

Case  VII 

Beam  Supported  at  Both  Ends  and  Loaded  Symmetrically  with  Two  Equal 
Concentrated  Loads  (Fig.  11). 

Maximum  bending  moment  =  Pm  and  is  the  same  for  any  section  of  the  beam 
between  the  two  loads. 


Fig.  11.     Simple  Beam.     Two  Concentrated  Loads  Symmetrically  Placed 

From  these  examples  it  will  be  seen  that  all  the  quantities  which  enter  into 
the  computation  of  the  bending  moment  are  the  load,  the  span  and  the  distance 
of  the  point  of  application  of  the  load  from  the  center  of  moments. 


Case  Vin 

Beam  Supported  at  Both  Ends  and  Loaded  with  a  Distributed  Load  Over  Part 
of  the  Span  (Fig.  12). 

-n- 


Fig.  12.     Simple  Beam.     Distributed  Load  over  Part  of  Span 


If  assumed  under  the  center  of  the  load,  M*max  =  Wmn/l  —  TT/i/S 
When  m  and  n  are  equal  the  bending  moment  =WXI/a,  —W  X  /i/8 

*  This  is  only  approximately  correct  when  m  and  n  are  unequal.  For  the  exact  value, 
find  the  section  of  zero  shear;  the  maximum  bending  moment  will  be  at  that  section. 
(See,  also,  Example  5,  page  561.) 


328 


Reactions  and  Bending  Moments  for  Beams         Chap.  9 


Example  4.    In  Fig.  12  let  W  =  800  lb,  w  =»  8  ft,  «  =  1 2  ft,  /  =  20  ft  and  /i  -  8  ft. 
Then  the  bending  moment 

800  X8XI2  800X8  A      Q       .       ,u 

= =  3  840  —  800  =  3  040  ft-lb,     or     36  480  m-lb 

20  8 

Example  5.     In  Fig.  12  let  w  =  n  =  10  ft,  /  =  20  ft.  h=  4  it  and  IF  =  600  lb. 
Then  the  bending  moment 

600  X  20   600  X  4  .,  ,,  .  ,, 

= — - — ■=  3  000  —  300  =  2  700  it-lb,  or  32  400  m-lb 

4  8 

The  Bending    Moment  for    any  Case  Other  Than  the  Above  may  easily  be 
obtained  by  the  graphic  method,  which  will  now  be  explained. 

4.   Graphic  Method  of  Determining  Bending  Moments  in  Beams 
Beam  with  One  Concentrated  Load  (Fig.  13). 

The  BENDING  MOMENT  of  a  beam  supported  at  both  ends  and  loaded  with  one 
concentrated  load  may  be  determined  graphically,  as  follows: 

1  Let    P     be    the    load, 

I      ^~!F ^^ i  appHed  as  shown.     Then, 

by  the  rule  under  Case  VI, 

the       MAXIMUM       BENDING 

MOMENT  is  under  the  load 
and  =  Pmn/l 

Draw  the  beam,  with 
the  given  span,  accurately 
to  scale,  and  measure  down 
the  Hne  AB,  io  3.  scale  of 

FOOT-POUNDS  to  the  LINEAR 

INCH,  a  distance  equal 
to  the  bending  moment. 
Connect  B  with  each  end 


"^ig.  13. 


Bending-moment  Diagram. 
Load 


One  Concentrated 


of  the  beam.  To  find  the  bending  moment  at  any  other  point  of  the  beam, 
as  at  0,  draw  the  vertical  line  y  to  BC.  Its  length,  measured  to  the  same 
scale  to  which  AB  \%  drawn,  will  give  the  bending  moment  at  0.  The  figure 
DBCAD  is  called  the  bending-moment  diagram  and  the  hnes  BD  and  BC 
are  called  influence  lines  for  the  bending  moments. 


'I  wyO  h«. 


Fig.  14.     Bending-moment  Diagram.     Two  Concentrated  Loads 

Beam  with  Two  Concentrated  Loads  (Fig.  14). 

To  draw  the  bending-moment  diagram  for  a  beam  with  two  concentrated 
loads,  draw  the  doited  lines  ADD  and  ACD,  giving  the  bending-moment  dia- 


Graphic  Method  of  Determining  Bending  Moments  in  Beams    329 

GRAMS  for  each  load  separately.  EB  is  laid  out  to  scale,  equal  to  Ptnn/l  and 
FC  equal  to  Pirs/l 

The  bending  moment  at  the  point  E  is  equal  to  EB  (from  the  load  P)  +  Eb 
(from  the  load  Pi),  or  Af  =  EB  -{•  Eb  =  EBi;  and  at  F  the  bending  moment  is 
equal  to  FC  -\-  Fc=  FCu  The  bentding-moment  diagram:  for  both  loads  is 
ABiCiD  and  the  maximum  bending  moment  is,  in  this  particular  case,  the  hne 
FCi  measured  to  scale. 

Beam  with  Any  Number  of  Concentrated  Loads  (Fig.  16.) 

Proceed  as  in  the  last  case,  and  draw  the  bending-moment  diagram  for  each 
load     separately.      Make     AD  =  Ai  +  A2-\- A3,     BE  =  Bi -{■  B2  +  B3     and 


Fig.  15.     Bending-raoment  Diagram.     Three  Concentrated  Loads 

CF=Ci  +  C2-f  C3.  The  figure  IIDEFIFI  will  then  be  the  bending-mo- 
ment diagram  corresponding  to  all  the  loads.  The  bending-moment  diagram 
for  a  beam  with  any  number  of  concentrated  loads  may  be  drawn  in  the  same 
way. 

Beam  with  a  Uniformly  Distributed  Load  (Fig.  16). 

Draw  the  beam  with  the  given  span,  accurately  to  a  scale  as  before,  and  at 
the  middle  of  the  beam  draw  the  vertical  line  A  B,  to  a  scale  of  a  certain  number 
of  foot-pounds  to 
the  linear  inch, 
equal  to  Wl/S,  from 
Case  V,  W  represent- 
ing the  whole  distrib- 
uted load.  Connect 
the  points  C,  B,  Dhy 
a  PARABOLA  to  obtain 
the  bending-moment 

DIAGRAM.        To     find 

the  bending  moment 

at  any  point  a,  draw 

the  vertical  line  ab, 

measure    it    to    the 

same  scale  to  which  AB  h  drawn,  and  it  will  be  the  bending  moment  desired. 

Methods  for  drawing  the  parabola  will  be  found  in  Part  I,  page  79. 

Beam  Loaded  with  Both  Distributed  and  Concentrated  Loads  (Fig.  17). 

To  determine  the  bending  moments  in  this  case,  combine  the  bending-moment 
DIAGRAMS  for  the  concentrated  loads  and  for  the  distributed  load,  as  shown  in 


Fig.  16. 


Bending-moment  Diagram. 
Whole  Beam 


Distributed  Load  ovcif 


330 


Reactions  and  Bending  Moments  for  Beams         Chap.  9 


Bending-moment    Diagram. 
Concentrated  Loads 


Distributed     and 


Fig.  17.     The  bending  moment  at  any  section  of  the  beam  will  then  be  limited 
by  the  line  ABC  on  top  and  by  the  line  CDEFA  on  the  bottom;   and  the  max- 
imum BENDING  MOMENT  Will  be  the  longest  vertical  line  that  can  be  drawn 
n  between      these      two 

bounding  Hnes. 

For  example,  the 
bending  moment  at  X 
is  BE.     The   point  of 

MAXIMUM  BENDING  MO- 
MENT depends  upon  the 
position  of  the  concen- 
trated loads  and  the 
relative  magnitude  of 
the  distributed  load; 
it  may  or  may  not 
occur  at  the  middle  of 
the  beam  or  under  one 
of  the  concentrated 
loads. 

Example  6.  What 
is  the  greatest  bending 
moment  in  a  beam  of 

2o  ft  span  (Fig.  18),  loaded  with  a  distributed  load  of  8oo  lb,  a  concentrated  load  of 

500  lb  6  ft  from  one  end,  and  a  concentrated  load  of  600  lb  7  ft  from  the  other  end? 
Solution,     (i)  The  maximum  bending  moment  due  to  the  distributed  load, 

from  Case  V,  is  If //8,  or  800  X  20/8  =  2  000  ft-lb.     Lay  off  vertically  over  the 

middle  of    the  beam, 

and  at  any  convenient  -^         o  ■'^^•p^jT]^'  B~ 

scale,  say  4  000  ft-lb  to 

the     inch,    5i  =  2  000 

ft-lb,  and  draw  a  parab- 
ola through  the  points 

yl,    5    and    C.      (See 

page  79-) 

(2)  The  maximum 
bending  moment  for 
the  concentrated  load 
of  500  lb,  from  Case 
VI,  is  500  X  6  X  14/20, 
or  2  100  ft-lb.  Draw 
£2  =  2  100  ft-lb  to  the 
same  scale  as  5i,  and 
then  draw  the  lines 
ylEandCE. 

(3)  The  maximum  bending  moment  for  the  concentrated  load  of  600  lb,  In 
like  manner,  is  600  X  7  X  13/20,  or  2  730  ft-lb.  Draw  Z)3  =  2  730  ft-lb  and 
connect  D  with  A  and  C. 

(4)  Make  EH  equal  to  the  distance  from  2  to  4,  and  DG  to  the  distance  from 
3  to  5,  and  draw  AHGC. 

The  MAXIMUM  BENDING  MOMENT  Will  be  represented  by  the  longest  vertical 
Hue  which  can  be  drawn  between  the  parabola  ABC  and  the  broken  line  AHGC. 
In  this  example  the  longest  vertical  line  which  can  be  drawn  is  Xy,  and  it 
ihould  scale  5  645  ft-lb. 


Bending-moment     Diagram. 
Concentrated  Loads 


Distributed 


Beams  with  Triangular  Loading  and  with  Fixed  Ends  331 

The  position  of  the  line  Xy  is  determined  by  drawing  the  line  TT\  parallel 
to  II G  and  tangent  to  ABC.     Draw  Xy  vertically  through  point  of  tangency. 


5.   Reactions  and  Bending  Moments  for  Beams  with  Triangular  Loading 
and  for  Beams  Fixed  at  Both  Ends.* 

Beams  with  Triangular    Loading   have  reactions    and  bending  moments  as 
follows: 

Beam  Supported  at  Both  Ends,  Fig.  19  (a) 

End-reactions:  Ri  =  R2  =  14  W 

Bending  moment  at  any  px)int  =Wxi }4—2x'^/sl^) 

Maximum  bending  moment,  at  center  =  1^7/6 

Beam  Supported  at  Both  Ends,  Fig.  19  (b) 

End-reactions:  i?i  =H  W,  R2=  %W 

Bending  moment  at  any  point  ={Wx/s){i  —x^/l) 

Maximum  bending  moment  (at  x  =  0.58  /)  =  .128  Wl 

Cantilever  Beam,  Fig.  19  (c) 

Reaction:  Ri  =  W 

Bending  moment  at  any  point  =  Wx^/3  l^ 

Maximum  bending  moment  (at  i?i)    =  Wl/s 

Beams  of  Cases  IV,  V,  and  VI,  with  Fixed  Ends,  ^ig.  19.   Triangular  Load- 
have  reactions  and  bending  moments  as  follows:  '"^  ^'^  Beams 

Case  IV  A.     Beam  Fixed  at  Both  Ends,  with  a  Concentrated  Load  P  at  the 
Middle  (Fig.  8) 

End-reactions:  7?i  =  /?.,  =  H  Z' 

Maximum  positive  bending  moment,  under  the  load  =  Pl/8 
Maximum  negative  bending  moment,  at  ends  =  Pl/S 

Case  V  A.     Beam  Fixed  at  Both  Ends,  with  a  Uniformly  Distributed  Load  W 

(Fig.  9) 
End-reactions:  Ri  =  R^  =  i/^w 

Maximum  negative  bending  moment,  at  ends  =  Wl/ 12 

Maximum  positive  bending  moment,  at  center  =  Wl/24 

Case  VI  A.     Beam    Fixed    at    Both  Ends,  with    a    Concentrated    Load  P  at 
Distance  m  from  Left  End  and  Distance  //  from  Right  End    (Fig   IQ) 

End-reactions:    Ri  =  Pn^^  m  -f  n)/P;    R2  =  PmHs  n  +  m)/P 
Maximum  bending  moment,  negative ,  at  left  end,   M\  =  Pmn'^/l^ 

at  right  end,  M2  =  Pm  ^n/l  2 
Bending  moment  under  load,  positive  =  R^m  —  Mi 

*  From  notes  by  Robins  Fleming. 


332  Properties  of  Structural  Shapes,  etc.  Chap.  10 


CHAPTER  X 

PROPERTIES  OF   STRUCTURAL   SHAPES.     MOMENT  OF 
INERTIA,  MOMENT  OF  RESISTANCE,  SECTION- 
MODULUS  AND  RADIUS   OF   GYRATION 

By 
CHARLES   P.  WARREN 

LATE    ASSISTANT   PROFESSOR    OF   ARCHITECTURE..    COLUMBIA    UNIVERSITY 

1.   The  Properties  of  Cross-Sections 

The  Moment  of  Inertia.  The  strength  of  a  cross-section  to  resist  stresses, 
in  either  a  beam  or  a  column,  depends  not  only  upon  the  area  but  also  upon 
the  form  of  the  cross-section.  The  parts  of  the  cross-section  farthest  from  the 
neutral  axis,  which  always  passes  through  the  center  of  gravity  of  the  cross- 
section,  are  much  more  efficient  in  resisting  bending  stresses  than  those  parts 
adjacent  to  the  axis;  so  that  some  mathematical  expression  must  be  obtained 
that  will  represent  the  efficiency  of  the  entire  cross-section  to  resist  bending 
stresses  when  compared  with  that  of  any  other  cross-section.  This  expression  is 
called  the  Moment  of  Inertia  and  is  usually  designated  by  the  letter  I. 

The  Moment  of  Inertia  of  any  cross-section  may  be  defined  as  the  sum  of 
the  products  obtained  by  multiplying  each  of  the  elementary  areas  of  which  the 
section  is  composed  by  the  square  of  its  normal  distance  from  the  neutral  axis 
of  the  section. 

By  an  elementary  area  is  meant  an  area  smaller  than  any  dealt  with  in 
simple  mathematics,  and  it  is,  therefore,  impossible  to  find  an  exact  expression 
for  the  moment  of  inertia  of  a  cross-section  by  such  methods.  By  means  of  the 
calculus,  however,  exact  formulas  have  been  deduced  from  which  the  moments 
of  inertia  of  simple  geometrical  forms,  such  as  rectangles,  triangles,  circles,  etc., 
may  be  found,  with  respect  to  different  axes. 

The  NEUTRAL  AXIS  of  the  cross-section  of  a  beam,  girder,  column,  etc.,  which 
is  in  a  state  of  flexure,  is  the  line  on  which  there  is  neither  tension  nor  compres- 
sion in  the  fibers,  and  when  the  unit  stresses  do  not  exceed  the  elastic  limit  of 
the  material,  it  can  be  shown  that  this  neutral  axis  passes  through  the  center  of 
GRAVITY  of  the  cross-section.  The  normal  distance  of  the  extreme  fibers  from  the 
neutral  axis  is  usually  designated  by  the  letter  c  or  the  letter  y.  The  former  is 
used  in  the  notation  of  this  book. 

Since  for  all  sections  except  squares  and  cirdes,  there  are,  in  general,  two  neu- 
tral axes  corresponding  to  the  more  common  positions  cf  the  sections,  it  follows 
that  there  are  also  two  moments  of  inertia  commonly  used;  for  a  rectangle,  for 
example,  a  greatest  moment  of  inertia  about  an  axis  perpendicular  to  the 
long  side  and  a  least  moment  of  inertia  about  an  axis  perpendicular  to  the 
short  side.  The  moments  of  inertia  of  the  cross-sections  of  all  rolled  shapes 
have  been  calculated  and  are  tabulated  in  the  manufacturers'  handbooks.  Thus, 
for  example,  the  moments  of  inertia  of  the  cross-section  of  a  i2-in,  31.5-lb  I  beam, 
with  respect  to  axes  perpendicular  to  the  web  and  parallel  to  the  web,  are,  from 
Table  IV,  equal  to  215.8  and  9.5  biquadratic  inches  respectively.  Formulas  for 
calculating  the  moments  of  inertia  of  other  simple  sections  are  given  on  the 
following  pages. 


Properties  of  Structural  Shapes,  etc.  333 

The  Moment  of  Resistance.  In  Chapter  IX,  under  the  chapter-subdivi- 
sion treating  of  the  bending  moments  in  beams,  page  325,  it  was  stated  that 
in  order  to  calculate  the  flexural  strength  of  a  beam  it  is  necessary  to 
ascertain  the  nature  and  extent,  first,  of  the  external  forces  tending  to  break 
the  beam  by  flexure,  and,  secondly,  of  the  internal  forces  or  stresses  tending 
to  resist  rupture.  The  external  forces  cause  the  bending  moments,*  and  the 
internal  stresses  the  moments  of  resistance,  at  the  various  cross-sections  of 
a  beam. 

The  moment  of  resistance  or  the  resisting  moment  at  any  cross-section 
of  a  beam  is  the  algebraic  sum  of  all  the  moments  of  the  internal  horizontal 
stresses  in  that  section  with  reference  to  a  point  in  that  section.  It  is  usually 
represented  by  the  expression  Sljc,  in  which  S  is  the  horizontal  unit  stress, 
tensile  or  compressive,  as  the  case  may  be,  upon  the  fiber  most  remote  from  the 
neutral  axis  of  the  section,  and  called  the  fiber-stress;  /  is  the  moment  of 
inertia  of  the  area  of  the  section  with  reference  to  the  neutral  axis;  and  c 
is  the  shortest  distance  from  the  most  remote  fiber  to  that  axis.  Since,  for 
equilibrium  of  forces  and  stresses  at  any  cross-section  of  a  beam,  the  bending 
moment  equals  the  resisting  moment  for  that  section,  if  M  represents  the  bend- 
ing moment  we  have  the  equation 

M  =  Sl/c  (i) 

This  is  known  as  the  flexure  formula  and  is  universally  used  for  investi- 
gating the  flexural  strength  of  beams. 

The  Section-Modulus  or  Section-Factor.  That  expression  l/c  in  the  above 
formula  is  generally  known  as  the  section-modulus  or  section-factor. 
This  quantity  for  the  principal  rolled  sections  is  given  in  Tables  IV,  V,  VI,  VII, 
VIII,  XI,  XII,  XIII  and  XIV.  Corresponding  to  the  two  moments  of  inertia 
generally  used  for  all  sections  (except  for  squares  and  circles)  there  are  two 
section-moduH  also,  one  for  each  axis.  Thus,  the  section-modulus  of  the  12-ii^ 
31.5-lb  I  beam,  with  respect  to  a  neutral  axis  perpendicular  to  the  web,  is 
l/c  =  215.8/6  =  36;  and  for  the  axis  parallel  to  the  web,  it  is  l/c  =  9.5/2.5  =  3.8. 
For  other  shapes  the  section-modulus  may  be  found  by  dividing  the  moment  of 
inertia  by  the  normal  distance  of  the  extreme  fiber  from  the  neutral  axis. 

The  Radius  of  Gyration.  The  efifect  of  the  form  of  the  cross-section  of  a 
column  on  its  strength  is  determined  by  a  quantity  called  the  Raehus  of  Gyra- 
tion, which  is  as  necessary  in  the  determination  of  the  strength  of  a  column  as 
the  moment  of  inertia  is  in  the  determination  of  the  strength  of  a  beam.  It  is 
denoted  by  the  letter  r.  The  value  of  the  radius  of  gyration  for  any  section 
is  determined  by  the  formula 


r=Vl/A  (2) 

in  which  /  is  the  moment  of  inertia  of  the  section  and  A  the  section-area. 
The  radius  of  gyration  is  the  normal  distance  from  the  neutral  axis  to  the 
center  of  gyration,  and  the  center  of  gyration  of  a  section  is  the  point  where 
the  entire  area  might  be  concentrated  and  have  the  same  moment  of  inertia 
as  the  actual  distributed  area.  The  radius  of  gyration  of  a  section  is  a  distance 
and  it  is  always  less  than  the  distance,  c,  from  the  neutral  axis  to  the  remotest 
fiber.  For  the  two  moments  of  inertia  above  referred  to,  and  commonly  used, 
there  are  two  corresponding  radii  of  gyration.  The  least  of  these  is  the  one  to  be 
used  in  the  investigation  of  the  strength  of  a  column  as  it  is  referred  to  the  axis 
about  which  the  column  is  most  likely  to  fail      The  radii  of  gyration  of  the  rolled 

*  See  Chapter  IX,  page  325,  for  definition  of  "bending  moment," 


334 


Properties  of  Structural  Shapes,  etc. 


Chap.  10 


shapes  are  given  in  the  tables  of  the  properties  of  sections,  mentioned  above. 
For  the  12-in  31.5-lb  I  beam,  r  =  4.83  in  and  r'  =  i.oi  in.  The  radius  of  gyration 
of  any  other  section  may  be  found  by  Formula  (2). 

Formulas  for  the  moments  of  inertia,  radii  of  gyration  and  section-moduli 
of  the  principal  elementary  sections  are  given  on  the  following  pages.  In  the 
case  of  a  hollow  section  or  a  section  with  a  reentering  hollow  part,  the  moment 
of  inertia  of  the  hollow  part  is  to  be  subtracted  from  that  of  the  enclosing  area. 
JMoments  of  inertia  when  referred  to  the  same  axis  can  be  added  or  subtracted 
like  any  other  quantities  which  are  of  the  same  kind. 

2.   Areas,  Moments  of  Inertia,  Section-Moduli  and  Radii  of 
Gyration  of  Elementary  Sections 

J  =  the  moment  of  inertia 
Ijc  —  the  section-modulus 
r  =  the  radius  of  gyration 
A  =  the  area  of  the  section 

c  —  the  normal  distance  of  most  remote  fiber  from  neutral  axis 
The  position  of  axis  referred  to  in  each  case  is  represented  by  the  broken  line 


SQUARE 

Axis  of  moments  through 
center 


l._. 


"1 

-4 


u..—d----^ 


1  = 


d 

c  =  - 

'  2 

12 

/  _^ 

c  ~  6 


r  =  — ;=  =  0.288675  d 
V12 


SQUARE 
Axis  of  moments  on  base 

f"l \'l 

4 


i«— -d-— : 


A  =  d^ 
c=d 

3 

{_? 

c      3 

A 


r=  — ^  =  0.577350  i 


Properties  of  Structural  Shapes,  etc.', 


RECTANGLE 

Axis  of  moments  through 

center 


4-1 


_i 


—b---^ 


d 


b^ 


I  _bd^ 
c  ~   6 


r=  — ^  =o.  288675  i 
V12 


RECTANGLE 
Axis  of  moments  on  base 

t 

T 

1 

4 

1 

lJ___ 

--ii 

c=  d 

b^ 
3 

c        3 

r=~—  =  0.577350  </ 

V3 


HOLLOW  SQUARE 

Axis  of  moments  through 

center 


«-4.,-,, 

- 

^1 

^-__ 

..Jt 


^-■rd-—^ 


HOLLOW  RECTANGLE 

Axis  of  moments  through 

center 


I 


4 

^--Jj..—.. 


1<? 


I    r 


12 
c  6d 


^/d^±dl 

V         12 


A  =  bd  —  bidi 

d 

c=  - 

2 

bd^-bidi* 

12 

/     bd^-bidi^ 

c 


ed 


-\f; 


bd^-bidi^ 


2  (bd  —  bidi) 


336 


Properties  of  Structural  Shapes,  etc. 


Chap.  10 


HOLLOW  RECTANGLE  AND 

.     I   BEAM 
Axis  of  moments  through  center 


dl- 


RL 


/)-  -  -  -, 


UrJ. 


..t^. 


A  =  hd-  hdi 
d 

2 

bd^  -  hidi^ 

12 
/  bd^  -  bldl^ 


J  -  V 


6d 


a/    bd^-bidi^ 
'  V  i2{bd-hdi) 


TRIANGLE 

Axis  of  moments  through 
center  of  gravity 


b_d 

2 

i^ 
3 

"  36 
bj^ 
24 


=  0.235702  d 


TRIANGLE 
Axis  of  moments  on  base 

If' 


— >1 


7  = 


A  =  — 

2 

c  =  d 
bd^ 
12 

I  _bj^ 
c       12 


=   0.408248  (/ 


TRAPEZOID 

Axis  of  moments  through 
center  of  gravity 


't 


<- — 6- 


.4  = 


d{b  +  h) 


d{b+2by) 

"    Sib+bi) 


^^_d{bl^2b) 

Sib  +  bi) 
dHb^-}-4hbi  +  br') 
'  3(^{b  +  bi) 

C  12    (61    -f-  26) 

r  =  ^ V ^&'  -{-4bbiTb7) 

6  (6  +  6i) 


*  To  find  c  and  Ci,  see  Chapter  VI,  page  295. 


Properties  of  Structural  Shapes,  etc. 


337 


TRAPEZOID 
Axis  of  moments  on  base 


U 5 


A-- 
c- 
I-- 

I 

2 
=  d 

d'(b-\-3bi) 

12 

dUb^shi) 

c 

12 

'  tA+- 

iii 

T   SECTION  AND   CHANNEL 
Axis  of  moments  through  center 


of  gravity 


A  =  id  +  ti{b-l) 


t  <- 


^^---b >| 


|.4 


J?^,^      *      tdxy2d-{-ti{b-t){d-\iti) 
'        ^   = A 


/  = 


/c3+kl3-(6-/)(ci-/l)5 


■=v/| 


k — b- 


CIRCLE 

Axis  of  moments 
through  center 


ird^ 
A  =  —  =  0.785398^/2 

4 

d 

c=  - 

2 

I  =  -—  =  0.049087  d* 
64 

I       ^^' 

-  =  —  =  0.09817s  a' 

c       32 


HOLLOW   CIRCLE 

Axis  of  moments 
tlirough  center 


IT  (d^  -  di"^) 

A  =  -^^ ^  =  0.785398  id'-di') 

4 

c=  - 
2 

i  = :: — —  =  0.049087  (a*  —  rfi'*) 


64 
c  32  d 


=  0.098175 


{d*-di^) 


Vd^  +  di^ 


*  To  find  the  values  of  c  and  Ci,  see  Chapter  VI,  page  295. 


338 


Properties  of  Slructural  Shapes,  etc. 


Chap.  10 


CHANNEL 

Axis  of  moments  through 
center  of  gravity 


xM^zk 


::^- 


CROSS-SECTION 

Axis  of  moments  through 

center  of  gravity 


IRREGULAR  I   SHAPE 

Axis  of  moments  through 

center  of  gravity 

"} — v\ — ~ 


I  T 

i.i.J 


f 


cL 


-b— 


i- 


A  =■  tib  -]-2i{d-  k) 

^        2dH-^dxh^ 


2  A 


Ac- 


-W: 


A=td-^ti{h-t) 

d 
c=  - 

2 

td^  +  h^  {b  -  t) 

12 

I     Id^+hHb-t) 
c  6d 


UP  -  /l3  {b  -  t) 


V    12{td-\-tl{b-l)) 

A 

=  bh-\-d4^b,h 

r* 

td^^-  h'^ibi 

-0  +  h(b-t)(2d- 

h) 

td'i+ti^ib- 

2A 

-/)  -^n{bi-l)(2d- 

-h) 

/ 

6,C3-(6i- 

2.4 
/)X   (C-/l)3 

k,3 

+ 

3 

-(b-t)x(ci-ti) 

a 


*  To  find  c  and  ci,  see  Chapter  VI,  page  295. 

3.  Transferring  Moments  of  Inertia  to  Other  Parallel  Axes 
Explanation  of  Formula.  It  is  often  necessary  to  determine  the  moment 
of  inertia  with  respect  to  some  other  axis  than  the  one  passing  through  the 
center  of  gravity  of  the  section,  such,  for  example,  as  one  passing  through  the 
base  and  parallel  to  the  other.  Suppose  it  is  desired  to  find  the  moment  of  in- 
ertia of  a  rectangle  about  an  axis  passing  through  the  lower  base,  as  in  the 
second  figure  on  page  335.  It  may  be  demonstrated  by  the  principles  of 
mechanics  that  the  moment  of  inertia  of  any  section  with  respect  to  any  axis 
is  equal  to  the  moment  of  inertia  of  the  section  with  respect  to  a  parallel  axis 
through  the  center  of  gravity,  plus  the  product  of  the  area  of  the  section  multi- 
plied by  the  square  of  the  normal  distance  between  the  axes.  This  rule  may  be 
expressed  by  the  formula 

/i  =  /  +  ^A«  (3) 


Properties  of  Structural  Shapes,  etc. 


839 


in  which  /i  is  the  required  moment  of  inertia,  /  the  moment  of  inertia  of  the 
section  with  respect  to  the  axis  through  its  center  of  gravity  and  parallel  to  the 
given  axis,  A  the  area  of  the  section  and  h  the  normal  distance  between  the  axes. 
From  this  it  is  seen  that  the  moment  of  inertia  of  any  section-are^,  is  less  for 
an  axis  through  its  center  of  gravity  than  for  any  other  parallel  axis. 

For  example,  consider  the  rectangle  shown  on  page  335,  of  breadth  b  and 
depth  d,  the  /  of  which  is  known  to  be  bd^/ 12  for  an  axis  passing  through  the 
center  of  gravity  and  parallel  to  the  base.     Then,  for 
a  parallel  axis  through  the  base,  the  above  formula  \ 

gives: 


bd^       .,       d 
■■—  -{-bdxl 
12 


V- — 

I   ~    12 


4  3 


XI 


idn 


Fig.  1 


-N 


Moment  of  Inertia 
of  Cross-section  of  Steel 
Angle 


Thus  the  moment  of  inertia  of  the  cross-section 
of  the  steel  angle  shown  in  Fig.  1,  about  the  axis 
MN,  is  equal  to  the  moment  of  inertia  about  the 
axis  XX  plus  the  product  of  its  area  multiplied 
by  h^.  The  moments  of  inertia  for  the  sections  of 
the  standard  rolled  shapes  of  structural  steel  may 
be  found  from  the  tables  given  -in  this  chapter.  The 
distance  ci,  also,  may  be  found  from  the  same  tables; 
and  this  distance  subtracted  from  d  will  give  the 
distance  h  of  Formula  (3). 

Suppose,  for  example,  that  it  is  desired  to  find  the 
moment  of  inertia  of  the  cross-section  of  a  4  by  3 
by  Vz-'m  angle,  placed,  with  the  long  leg  horizontal, 
about  an  axis  MN,  12  in  from  the  back  (Fig.  1).  Turning  to  Table  XI,  the 
area  of  the  angle-section  =  3.25  sq  in.  /,  the  moment  of  inertia  of  the  angle- 
section  about  an  axis  2-2,  or  A^A^  of  Fig.  1,  parallel  to  the  long  leg  =  2.4,  a,  the 
distance  of  this  axis  from  the  back  of  the  long  leg  =  0.S3  in  and  h,  the  distance 
between  the  axes  =  {d—  ci)  =  12  —  0.83  in  =  11. 17  in.  Substituting  these  values 
in  Formula  (3) 

/i=  2.4  4- 3-25  X  11.17^=  2.4 +  405-50  =  407-9 

4.    Moments  of  Inertia  of  Compound  Sections 

The  Moment  of  Inertia  of  a  Compound  Section  made  up  of  a  number  of 
smaller  sections  may  be  found  by  the  same  formula,  Ii  =  I  -\-  Ah^.  Denote  the 
SUM  OF  THE  MOMENTS  OF  INERTIA  of  the  separate  sections  making  up  the  com- 
pound section,  with  respect  to  an  axis  through  the  center  of  gravity  of  that 
section,  by  S/i.     Formula  (3)  then  becomes 

XIi  =  ^{I  +  Ah')  (4) 

That  is,  to  find  the  moment  of  inertia  of  any  compound  section  made  up  of 
a  number  of  smaller  sections: 

(i)  Find  the  moment  of  inertia  of  each  of  the  smaller  sections  about  an  axis 
passing  through  its  own  center  of  gravity  and  parallel  to  the  neutral  axis  of  the 
compound  section; 

(2)  Multiply  the  area  of  each  of  the  smaller  sections  by  the  square  of  the  dis- 
tance between  its  center  of  gra\nty  and  the  center  of  gravity  of  the  whole  figure; 

(3)  Add  the  results  found  by  (i)  and  (2)  for  the  moment  of  inertia  of  the 
whole  figure. 

For  example,  consider  the  cast-iron  beam  or  lintel  shown  in  section  in  Fig.  2; 


340 


Properties  of  Structural  Shapes,  etc. 


Chap.  10 


(i)  /of  upper  ilange-section 
/  of  web-section 
/  of  lower  flange-section 
Total 

(2)  Ah"^  for  the  upper  flange 
Ah"^  for  the  web 
Ah^  for  the  lower  flange 
Total 


=  4XiVi2  =  M2 
=  1X183/12  =  5832/12 
=  16X1^12  =  1^2 
=  5852/12  =  487.6 

=  4X  (12.5)==  625 
=  18X32=  162 
=  16  X  (6.5)2  =676 
=  1463 


(3)  Total  of  (r)  and  (2)  =  487.6  +  i  463  =  /i  of  compound  section  =  i  950.6 

The  moment  of  inertia  of  the  cross-section  of  any  compound  beam,  therefore, 
can  generally  be  readily  found  by  using  the  tables  of  properties  of  sections  which 


^-i?-A 


\ 


¥^ 


-4-L 


II 


t 


-16- 


c 


^L 


) 


Zl___JL- 


Fig.  2.  Moment  of  Inertia 
of  Cross-section  of  Cast- 
iron  Lintel 

give  the  numerical  values  of  / 
for  the  various  rolled  shapes  of 
which  the  beam  is  composed, 
with  respect  to  the  axis  through 
the  center  of  gravity. 

The  Moment  of  Inertia  of 
a  Single-Web  Girder-Section. 
Consider,  for  example,  the  single- 
web  girder  shown  in  section  in 
Fig.  3,  and  made  up  of  one 
\^  by  24-in  web  and  four  4 
hy  3  by  H-in  flange-angles  with  the  long  legs  placed  horizontally.  Turn- 
ing to  Table  XI,  the  moment  of  inertia  of  the  cross-section  of  one  of 
these  angles  about  an  axis  XX  (2-2  "in  the  table)  parallel  to  the  long 
leg=  2.4,  a:nd  the  distance  of  this  axis  from  the  back  of  the  long  leg  {y  in  the 
table)  =  0.83  in;  hence  A,  the  distance  between  the  axis  of  the- angle-section 
and  the  axis  of  the  girder-section  =  12  —  0.83=  11. 17  in.  A,  from  the  table 
=  3,25  sq  in.  The  moment  of  inertia  of  the  cross-section  of  each  angle  about 
the  axis  of  the  girder,  therefore,  from  Formula  (3),  is  7i  =  2.4  -H  3.25  X  (11.17)2  =» 
407.9,  and  for  the  four  angles  =  1631.6.    Since  the  axis  of  the  cross-section  of 


Fig.  3.     Moment  of  Inertia  of  Cross-section 
of  Plate  Girder.     No  Flange-plates 


Properties  of  Structural  Shapes,  etc. 


341 


the  web-plate  is  coincident  with  the  axis  of  the  section  of  the  girder,  its 
moment  of  inertia  =  hd?l\2  =  HX  (24)3/12  =  576.  This  may  be  found 
directly  from  Table  I.  page  346,  Moments  of  Inertia  of  Rectangles.  The 
moment  of  inertia,  therefore,  of  the  section  of  the  compound  girder  =  163 1.6 
4-  576  =  2207.6. 

The  Moment  of  Inertia  of  a  Section  of  a  Compound  Girder  with 
Flange-Plates  is  found  in  the  same  way,  except  that  the  moments  of  inertia  of 
the  sections  of  the  flange-plates  with  respect  to  the  axis  of  the  girder-section 
must  be  added  to  the  moments  of  inertia  of  the  cross-sections  of  the  other 
members.  The  girder  in  Fig.  4  is  com- 
posed of  one  30  by  %-m  web-plate,  four 
5  by  4  by  ^le-in  angles,  with  the  longer 
legs  horizontal,  and  two  12  by  V^-in 
flange-plates. 

/(  =  /])  for  cross-section  of  web  (from 

Table  I,  page  346)  =  843.75 
h    for    each    angle-section  =  I  i-  Ah"^ 

(Formula  3) 

From  Table  XI,  for  each  flange-angle, 
/=  6.6,  A  =  4.75  and  the  perpendicular 
distance  from  center  of  gravity  to  back 
of  long  leg=  1..10  in.  Hence  A=  15  — 
1.10=  1390  in.  /i  =  6.6  +  4-75  X 
(13.90)2=924.35;    and   for  four  angles 

=  3  697.4.  /  for  the  cross-section  of 
each  flange-plate  =  12  X  i}AYl\2  =  0.125, 
^  =  3'^  X  12  =  6  s(i  in  and  /r  =  15  -f-  \i 

=  15.25  in.  For  each  flange-plate,  then, 
/i  =  0.125  -f  6  X  (15-25)^  =  1395-125; 
and  for  the  two  plates,  2  790.25.  The 
moment  of  inertia  for  the  cross-section 
of  the  whole  girder,  therefore,  with 
reference  to  the  horizontal  axis  passing 
through  the  center  of  gravity  of  the 
section  =  843.75  +  3  697.4+  2  790-25  = 
7331.4- 

It  will  be  noticed  that  the  moments 
of  inertia  of  the  cross-sections  of  the  flange-plates  and  angles  about  their  own 
neutral  axes  is  .so  small,  compared  with  their  moments  of  inertia  about  the 
neutral  axis  of  the  girder-section,  that  they  might  be  omitted  without  any 
appreciable  error.  Therefore,  in  calculating  the  moments  of  [^inertia  for  riveted 
girders,  it  is  the  custom  of  many  engineers  to  let  /i  =  Ah"^  for  flange-plate  and 
angle-sections.     In  that  case,  for  the  girder-section  in  Fig.  4, 


Fig.  4.  Moment  of  Inertia  of  Cross- 
section  of  Plate  Girder  with  Flange- 
plates 


/  for  web 

/i  for  angles  =  Ah"^ 

I\  for  flange-plates  =  Ah^ 


=  843.75 
=  3671.00 
=  2  790.00 


Moment  of  inertia  of  entire  girder-section  =  7  304.75 

The  Moment  of  Inertia  of  a  Section  of  a  Box  Girder.     Let  the  box 

girder  shown  in  I'ig.  5  be  composed  of  two  %  by  30-in  webs,  two  16  by  H-in 
flange-plates  and  four  4  by  3  by  Yi-ivi.  angles  with  the  long  legs  horizontal. 


342 


Properties  of  Structural  Shapes,  etc. 


Chap.  10 


i— 


Fig.  5.  Moment  of  Inertia  of 
Cross-section  of  Plate-and-angle 
Box  Girder 


/  for  each  Dange-plate  =  hd^/12  =  16  X  i}AYl\2  =  0.16;  A  =  Yz  X  16  in  =  8  sq  in 
and  A  =  15  +  H  =  15-25  in.  /i  =  /  +  vlA^  =  0.16  +  8  X  (15-25)'  =  1  860.64;  and 
for  the  two  flange-plates,  3  721.28.  /  for  each 
angle  =  2.4,  A  =  3.25  and  the  distance  from  the 
back  of  the  long  leg  to  an  axis  through  the 
center  of  gravity  of  the  angle,  parallel  to  the 
long  leg  =  0.83  in;  so  that  h=  15  —  0.83  =  14.17 
in.  /i  for  the  four  angles  is  (4  X  2.4)  -f  (4  X 
3.25)  X  (14-17)'  =  2  619.  /  for  each  web  (Table 
I,  page  346)  =  843.75  and  for  the  two  webs 
=  I  687.5.  The  mo- 
ment of  inertia,  there- 
fore, for  the  entire 
girder-section  = 
3  721.28  -f  2  619  + 
1687.5  =  8027.78. 

The  Moment  of 
Inertia  of  the  Sec- 
tion of  a  Channel 
Box  Column.  Fig. 
6  shows  the  cross- 
section  of  a  column 
made  up  of  two  lo-in 
15-lb  channels,  set 
6.33  in  apart,  back 
to  back,  and  two  \^  by  12-in  side  plates.  Let  it  be  required  to  find  the 
moment  of  inertia  of  the  section  about  the  two  axes  AB  and  CD. 

(i)  Find  the  moment  of  inertia  about  the  axis  AB.  /,  for  one  of  the  side 
plates  with  respect  to  an  axis  through  its  own  center  of  gravity  and  parallel  to 
AB=i2X{}Ay/i2  =  o.i2Sy  .^_ 

A  =  y-iXi  2-in  =  6  sq  in  and 
the  distance  of  its  center  of 
gravity  from  ^5  is  5.25  in. 
Therefore,  with  respect  to 
^5,/i  =  0.125  4-6  X  (5.25)' 
=  165.5.  The  moment  of 
inertia  of  a  lo-in  15-lb 
channel  with  respect  to  an 
axis  through  its  center  of 
gravity  and  perpendicular 
to  the  web  (Table  VIII, 
page  359)  =  66.9.  Hence 
the  moment  of  inertia  of 
the  whole  column-section 
with  respect  to  the  axis  AB 
=  (2X165.5) +(2X66.9) 
=  464.8. 

(2)  Find  the  moment  of 
inertia  about  the  axis  CD.  7,  for  one  of  the  side  plates  (Table  I,  page 
346)  =  72.  7,  for  one  of  the  channels  with  respect  to  an  axis  parallel  to  the 
web  =  2.30,  A  =  4.46  and  the  distance  of  the  center  of  gravity  from  the  back 
of  the  web  =  0.64  in,  approximately.  Hence  A  =  3.165 -f  0.64  =  3.8  in. 
7i  =2.30-1-  4.46  X  (38)2  =  66.7  and  the  moment  of  inertia  of  the  whole  column- 
section  with  respect  to  the  axis  CD=  (2  X  72)  +  (2  X  66.7)  =  277.4. 


-^:j- 


-}- 


r4 


Fig.  6.  Moment  of  Inertia 
of  Cross-section  of  Plate- 
and-channel  Box  Column 


45. 


jr 


IL. 


IT 


"C 


+2 


ifi" 


Fig.  7.     Moment  of  Inertia  of  Cross-section  of  Three- 
web  Plate-and-angle  Box  Column 


Properties  of  Structural  Shapes,  etc.  343 

The  Moment  of  Inertia  of  the  Section  of  a  Heavy  Plate-and-Angle 
Column.  Fig.  7  shows  the  cross-section  of  one  of  the  basement-columns  in 
the  Bankers'  Trust  Company  Building,  New  York  City.  It  is  made  up  of  six 
flange-plates,  each  27  by  H  in  section;  two  flange-plates,  each  27  by  iHe  in; 
four  flange-angles,  each  6  by  6  by  ^Me  in;  eight  outer  web-plates,  each  18  by 
iHein;  four  web-angles,  each  6  by  3^2  by  i-Me  in;  and  two  middle  web-plates 
each  18  by  Yie  in.  What  is  its  moment  of  inertia  of  the  entire  column-section 
with  respect  to  the  axis  AB? 

I  for  each  27  by  ^4-in  flange-plate  (Table  I)  =  i  230.19 

/  for  six  27  by  -^-in  flange-plates  =  i  230.19  X  6  =  7  381.14 

/  for  each  27  by  1  lie-in  flange-plate  (Table  T)   =  i  127.67 

/  for  two  27  by  iHs-in  flange-plates  =1  127.67  X  2  =  2  255.34 

/  for  both  flanges  9  G36.48 

For  the  flange-angles  (Table  XIT,  page  366)  the  area  of  a  6  by 
6  by  i^e-in  angle  =  10.37,  its  /  with  respect  to  an  axis  parallel  to 
AB  (Fig.  7)  and  passing  through  its  center  of  gravity  =  33.7  and 
the  distance  of  this  axis  from  the  back  of  the  leg  =  1.84  in.  Its  Ii 
with  respect  to  the  axis  ^J5  is  found  by  Formula  (3),  page  338, 
/i  =  I  -\-  Ah^.  h  =  13.5  —  (0.12  -h  4.16)  =  the  distance  from  the  axis 
AB  to  the  parallel  axis  through  the  center  of  gravity  of  the  angle 
=  9.22  in.    Hence,  substituting  in  Formula  (3), 

/i  =  33.7  +  10.37  X  (9.22)2  =  915.15 

I\  for  the  four  flange-angles  =915.15X4=  3  660.6c 

Each  outer  web  is  4  x  ^Me  in  =  2%  in  thick.  Hence  the  I  for 
each  outer  web  about  the  horizontal  axis  through  its  center  of 
gravity  =  18  X  (2.75)3/12  =  31.2.  A  =  18  by  2.75  in  =  49.5  sq  in. 
The  distance  from  its  center  of  gravity  to  the  axis  AB  is  13.5  —  (1.38 
+  1.84  -\-  4.16  -f  0.12)  =  6.01  or,  say  6  in. 

From  Formula  (3),  therefore,  I\  =  31.2  -}-  49.5  X  6^  =  i  813.2  and 
for  both  outer  webs  /i  =  i  813.2  X  2  =  3  626.4 

For  the  four  web-angles,  from  Table  XI,  page  363,  the  area  of  a 
6  by  ^M  by  ^Ms-in  angle  =  8.03,  its  /  with  respect  to  an  axis  through 
its  center  of  gravity  and  parallel  to  the  long  leg  =  6.9  and  the  dis- 
tance of  this  axis  from  the  back  of  the  long  leg  =  0.99  in.  h,  the 
horizontal  distance  between  the  two  axes  =  ^e  in,  or  0.5625  in 
•  (the  thickness  of  one  of  the  middle  web-plates)  -f-  0.99=  T.55  in, 
approximately.     Therefore,  for  one  web-angle,  from  Formula  (3), 

/i  =  6.9 -I- 8.03  X  (1.55)' =26.17 
and  for  the  four  angles,    /i  =  26.17  X  4  =  104.68 

The  middle  web-plates  are  together  Me  in  X  2  =  THin=  1.125 
inthick.     The/ (  = /i)  for  the  two  plates  is  18  X  (1.125)^12  =  2.14 

The  moment  of  inertia  of  the  entire  column-section  for  the  axis 
A  B  is,  therefore,  the  sum  of  these  moments  of  inertia  for  the  differ- 
ent parts: 

7i  for  the  eight  flange-plates  9  636.48 

I\  for  the  four  flange-angles  3  660.60 

1^1^.   I\  for  the  eight  outer  web-plates  3  626.40 

B|    /i  for  the  four  web-plates  104  68 

^ptt  /i  for  the  middle  web-plates  2.14 

K       The  moment  of  inertia  for  the  entire  section  17  030.3? 


344 


Properties  of  Structural  Shapes,  etc. 


Chap.  10 


5.   Radii  of  Gyration  of  Compound  Sections 

The  Radius  of  Gyration  of  any  Compound  Section  may  be  found  from 
Formula  (2),  page  333,  by  dividing  the  moment  of  inertia  of  the  section  by  the 
total  area  of  the  section  and  taking  the  square  root  of  the  quotient.  Thus, 
the  radii  of  gyration  of  the  channel-column  section  shown  in  Fig.  6,  about  the 
axes  A  B  and  CD,  are  found  as  follows:  xi  =  (the  sum  of  the  areas  of  two  \^  by 
i2-in  plates,  or  12  sq  in)  -f  (the  sum  of  the  areas  of  the  two  channels,  or  8.92 
sq  in)  =  20.92  sq  in.     /  about  AB  =  464.8  and  about  CD  =  277.4. 


Therefore,  f ,  with  respect  to  the  axis  A  B  = 


and  n,  with  respect  to  the  axis  CD  = 


=  4.71 


=  3.68 


Since  n  is  the  smaller,  iL  is  the  value  to  be  used  in  the  column-formula.  It  is 
to  be  noted  that  this  value  of  r  agrees  with  the  r  of  the  lo-in  channel-column  in 
Table  XXV,  on  page  533.  The  value  of  n  does  not,  however,  agree  exactly  with 
the  n  in  the  same  table,  the  variation  being  caused  by  a  difference  in  the  spacing 
of  the  channels,  back  to  back. 

The  Least  Radius  of  Gyration  of  a  Section  of  a  Plate-and-Angle 
Column.  As  another  example,  let  it  be  required  to  find  the  least  radius  of 
gyration  of  the  cross-section  of  the  plate-and- 
angle  column  shown  in  Fig.  8,  made  up  of  one 
^/i  by  i2-in  web-plate,  two  ^i  by  12-in  side  plates 
and  four  4  by  4  by  l^i-'m  angles. 

(i)  Find  the  moment  of  inertia  about  the  axis 
AB.  For  the  axis  AB,  I  for  each  one  of  the  side 
plates  with  respect  to  an  axis  through  its  own 
center  of  gravity  and  parallel  to  the  axis  A  B  = 
12  X  (^i)Vi2  =  C.05.  A  =  %X  12  =  4.5  sqinand 
h  =  6^6  in.  /i  =  0.05  -I-  4.5  X  (6fl6)2  =  172.33. 
/  for  each  one  of  the  angles  with  respect  to  an 
axis  through  its  center  of  gravity  and  parallel 
with  the  flange-leg  is  5.6,  A  =  3.75  and  the  dis- 
tance of  the  center  of  gravity  from  the  back  of. 
the  flange  of  the  angle  =  1.18.  Hence,  A  =  6  in 
—  1. 18  in  =  4.82  in  and  h  for  each  angle  =  5.6 
+  3-75  X  (4-82)2=  92.71.  /  for  the  web-plate  =« 
54.  The  moment  of  inertia  of  the  whole  column-section,  therefore,  about  the 
axis  AB  =  (2  X  172.33)  +  (4  X  92.71)  +  54  =  769.5c. 

(2)  Find  the  moment  of  inertia  about  the  axis  CD.  I  for  each  side  plate 
=  54.  /  for  each  angle  =5.6  and  A  for  each  angle  =  3.75.  The  -distance  of 
the  center  of  gravity  of  each  angle  from  the  back  of  the  flange  of  the  angle 
=  1. 18  in  and  hence,  h  =  1.18  in-f  y\&  in  =  1.36  in,  approximately,  h  for  each 
angle  =  5.6  +3.75  X  (1.36)2=12.54.  /  for  each  web-plate  =  0.05.  Themoment 
of  inertia  of  the  whole  column-section,  therefore,  about  the  axis  CD  =  (2  X  54)  + 
(4X  12.5.1) -h  0.05  =  158.21. 

Since  this  is  the  least  moment  of  inertia  the  least  radius  of  gyration  will  like- 
wise be  about  the  axis  CD.  The  area  of  the  cross-section  of  the  column  =  (4  X 
3.75,  the  area  of  the  angles)-}-  (3  X  45,  the  area  of  each  plate)  =  28.5.  f'=3 
158.21/28.S  =  5.55  and  r,  the  least  radius  of  gyration  =2.35. 


Fig.  8.  Least  Radius  of  Gyra- 
tion of  Cross-section  of  Plate- 
and -angle  Column 


Moment  of  Inertia  Determined  Graphically 


345 


The  Radius  of  Gyration  of  the  Cross-Section  of  a  Hollow  Rectangular 

Column.  As  another  example,  let  it  be  required  to  find  the  radius  of  gyration 
of  the  cross-section  of  a  hollow  rectangular  cast  iron  column  with  outside  dimen- 
sions 6  by  6  in  and  with  a  shell  H  in  thick.  (See  figures  and  formulas  for  hol- 
low squares  and  rectangles,  page  ^35.)  A  =  6"^  -  (5.5)2  =  36  -  30  25  =  5.75  sq  in. 
/  =  (b'P-bibi^)/j2  =  [64-  (5.5)Vi2  =  (i  296-  9io)/i2  =  386/12  =  32.2.  f2== 
32.2/5.75  =  5.6  and  r  =  2.37  in. 

The  radii  of  gyration  of  round-section  columns  and  square-section  columns, 
varying  from  2  to  20  in  in  diameter  and  of  metal  varying  from  H  to  2  in  thick, 
are  given  in  Tables  II  and  III,  see  pages  348  to  351.  For  example:  the  radius 
of  gyration  of  a  6  by  6-in  square-section  cast-iron  column  with  a  shell  J-i  in 
thick,  is,  from  Table  III,  2.35  in. 


6.    Graphical  Method  of  Determining  the  Moment  of  Inertia  of  Plane 
Figures  * 

The  Moment  of  Inertia  may  be  Determined  Graphically  as  follows: 
Divide  the  shape  in  question,  Fig.  9,t  into  strips  parallel  to  BC.  Through  the 
centers  of  gravity  of 
the  strips  draw  indef- 
inite hues  /i,  Jo,  etc. 
Along  a  line  ab  lay  off 
lengths/;,  /2,  etc.,  pro- 
portional respectively 
to  areas  /i,  fz,  etc. 
When  the  strips  are 
narrow  and  of  equal 
width,  each  strip  may 
be  assumed  propor- 
tional to  the  length  of 
the  strip  measured 
through  its  center  of 
gravity.  Through  a 
and  b  draw  lines  at 
45°  with  ab  to  deter- 
mine the  pole  0,  from 
which  the  rays  Od,  Oe, 
etc.  are  drawn.  Con-  Fig-  ^'  Graphical  Determination  of  Moments  of  Inertia  t 
struct  the  equilibrium-polygon  ^'.?/.  (See  page  296.)  A  line  sS  parallel  to 
BC  will  be  a  gravity- axis.  The  moment  of  inertia  about  this  axis  is  equal 
to  the  area  of  the  given  figure  ABC  multiplied  by  the  area  of  the  polygon  gsf. 
The  square  root  of  this  area  gsf  is  the  radius  of  gyration  of  the  figure  ABC 
with  regard  to  the  axis  sS.  A  graphic  method  especially  adopted  to  irregular 
figures  is  given  in  detail  in  Goodman's  Mechanics  Applied  to  Engineering.  See, 
also,  Merriman's  American  Civil  Engineers'  Handbook. 


*  From  notes  by  Robins  Fleming. 

t  Figure  from  Ott's  Graphic  Statics  (Clark's  Translation,  London,  1876). 
Church's  Notes  and  Examples  in  Mechanics. 


See,  also, 


346  Properlies  of  Structural  Shapes,  etc. 

Table  I.*     Moments  of  Inertia  of  Rectangles 

i 

^         Neutral  axis  through  center  and  normal  to  depth 


Depth 

in 
inches 

Widths  of  rectangles 

in  inches 

H 

Me 

H 

Me 

Vz 

Me 

% 

2 

O.I7 

0.21 

0.25 

0.29 

0.33 

0.38 

0.42 

3 

0.56 

0.70 

0.84 

0.98 

1. 13 

1.27 

1. 41 

4 

1-33 

1.67 

2.00 

2.33 

2.67 

3.00 

3.33 

5 

2.60 

3.26 

3.91 

4.56 

5.21 

5.86 

6.51 

6 

4. SO 

5.63 

6.75 

7.88 

9.00 

10.13 

11.25 

7 

7. IS 

8.93 

10.72 

12.51 

14.29 

16.08 

17.86 

8 

10.67 

13.33 

16.00 

18.67 

21.33 

24.00 

26.67 

9 

IS. 19 

18.98 

22.78 

26.58 

30.38 

34.17 

37.97 

lO 

20.83 

26.04 

31.25 

36.46 

41.67 

46.87 

52.08 

II 

27 -73 

34.66 

41.59 

48.53 

55.46 

62.39 

69.32 

12 

36.00 

4500 

54.00 

•  63  00 

72.00 

81.00 

90.00 

13 

45-77 

57.21 

68.66 

80.10 

91.54 

102.98 

114.43 

14 

57.17 

71.46 

85.7s 

100.04 

114.33 

128.63 

142.92 

IS 

70.31 

87.89 

105.47 

123.05 

140.63 

158.20 

175.78 

i6 

85.33 

106 . 67 

128.00 

149.33 

170.67 

102.00 

213  33 

17 

102.35 

127.94 

153  53 

179.12 

204.71  . 

230.30 

255.89 

18 

121.50 

151.88 

182.25 

212.63 

243.00 

273.38 

303.7s 

19 

20 

142.90 

178.62 

214.34 
250.00 

250.07 
291.67 

285.79 
333.33 

321.52 

375.00 

357-24 
416.67 

166.67 

208.33 

21 

192.94 

241.17 

289.41 

337.64 

385.88 

434.11 

482.34 

22 

221.83 

277.29 

332.75 

38S.21 

443.67 

499.13 

554.58 

23 

253.48 

316.8s 

380.22 

443.59 

506.96 

570.33 

633.70 

24 

288.00 

360.00 

432.00 

504.00 

576.00 

648.00 

720.00 

25 

325.52 

406 . 90 

488.28 

569.66 

651.04 

732.42 

813.80 

26 

366.17 

457.71 

549.2s 

640.79 

732.33 

823.88 

915.42 

27 

410.06 

512. 58 

615.09 

717.61 

820.13 

922.64 

1025.16 

28 

457.33 

571.67 

686.00 

800.33 

914.67 

1029 . 00 

1143.33 

29 

508.10 

635.13 

762.16 

889.18 

1016.21 

1143.23 

1270.26 

30 

562.50 

703.13 

843.7s 

984.38 

1125.00 

1265.63 

1406  25 

32 

682.67 

853 .33 

1024 . 00 

1194.67 

1365.33 

1536.00 

1706.67 

^ 

818.83 

1023.54 

1228.25 

1432.96 

1637.67 

1842.38 

2047.08 

36 

972.00 

1215.00 

1458.00 

1701.00 

1944.00 

2187.00 

2430 . 00 

38 

I143.17 

1428.96 

1714.75 

2000.54 

2286.33 

2572.13 

2857  92 

40 

1333.33 

1666.67 

2000.00 

2333.33 

2666.67 

3000.00 

3333.33 

42 

1543.50 

1929  38 

2315.25 

2701.13 

3087.00 

3472.88 

3858.75 

44 

1774.67 

2218.33 

2662 . 00 

3105.67 

3549.33 

3993.00 

4436.67 

46 

2027.83 

2534. 79 

3041.7s 

3548.71 

4055.67 

4562.63 

S069.58 

48 

2304.00 

2880.00 

3456.00 

4032.00 

4608 . 00 

5184.00 

5760.00 

SO 

2604.17 

3255.21 

3906.25 

4557.29 

5208.33 

5859.38 

6510.42 

S2 

2929.33 

3661.67 

4394.00 

5126.33 

5858.67 

6591  00 

7323.33 

54 

32B0.50 

4100.63 

4920.75 

5740.88 

6561.00 

7381 . 13 

8201 . 25 

S6 

3658.67 

4573.33 

5488.00 

6402.67 

7317.33 

8232 . 00 

9146.67 

58 

4064.83 

50S1.04 

6097.25 

7113.46 

8129.67 

9145.87 

10162.08 

6o 

4500.00 

5625.00 

6750.00 

7875.00 

9000 . 00 

10125.00 

11250.00 

*  This  table  may  be  used  in  computing  the  moments  of  inertia  of  plate  girders, 
columns  and  other  compound  sections  in  which  plates  are  used.  See  pages  341  and 
342. 


Properties  of  Structural  Shapes,  etc.  §47 

Table  I*  (Continued).     Moments  of  Inertia  of  Rectangles 


Neutral  axis  through  center  and  normal  to  depth 


Depth 

Widths  of  rectangles  in  inches 

inches 

iHe 

....  1  ,..> 

H 

1^6 

li 

iMe 

2 

3 

4 

0.46 
1. 55 
3.67 

0.50 
1.69 
4.00 

0.54 
1.83 
4-33 

0.58 
1.97 
4.67 

0.6: 

,  a. I] 

S-oc 

J                  0.67 
C                      2.25 
)                      5:33 

5 
6 
7 
8 
9 

7.16 
12.38 
19.65 
29.33 

41.77 

7.81 
13.50 
21.44 

32.00 
45. 56 

8.46 
14.63 
23.22 
34.67 
49.36 

9. II 
15.75 
25.01 
37.33 
53.16 

97' 
16. 8i 
26.8c 
40. a 
56.9! 

r            10.42 
i            18.00 
)            28.58 
)            42.67 
>            60.75 

10 

II 

12 

13 
14 

57.29 
76.26 
99.00 
125.87 
157.21 

62.50 
83.19 

108.00 
137.31 
171.50 

67.71 
96.12 
117.00 
148.75 
185.79 

72.92 
97.0s 
,    126.00 
160.20 
200.08 

78.1: 
103.9^ 
135.0c 
171.6^ 
214. 3i 

\            83.33 
\           110.92 

)                 144.  CX3 
[                 183.08 

5            228.67 

17 
i8 
19 

193.36 
234.67 
281.47 
334-13 
392.96 

210.94 
256.00 
307.06 
364.50 
428.69 

228.52 
277.33 
332.65 

394.88 
464.41 

246.09 
298.67 
358.24 
425.2s 
500.14 

263.6' 
320.  a 
383.8: 
455.6: 
535. 8( 

r          281.2s 
>          341.33 
\          409.42 
J          486.00 
)          571.58 

20 
21 
22 
23 
24 

458.33 
530.58 
610.04 

697.07 
792.00 

500.00 
578.81 
665.30 
760.44 
864.00 

541.67 
627.05 
720.96 
823.81 
936.00 

583.33 

675.28 
776.42 
887.18 
1008.00 

62s.  oc 
723.52 
831.8' 

950.55 
1080. oc 

)          666.67 

771.75 

r           887.33 

1013.92 

)          1152.00 

25 
26 

27 

28 
29 

895.18 
1006.96 
1127.67 
1257.67 
1397.29 

976.56 
1098.50 
1230.19 
1372.00 
1524  31 

1057. 94 
1190.04 
1332.70 
1486.33 
1651.34 

1139. 32 
1281.58 
14.35. 22 
1600.67 
1778.36 

1220.7c 
1373  i: 
1537.7: 
171S.0C 
1905.35 

}         1302.08 
\         1464.67 
5          1640.25 
)          1829.33 
}         2032.42 

30 

32 

34 
36 
38 

1546.88 
1877.33 
2251.79 
2673.00 
3143.71 

1687.50 
2048 . 60 
2456.50 
2916  00 
3429-.  50 

1828.13 
2218.67 
2661.21 
3159.00 
3715.29 

1968.75 
2389.33 
2865.92 
3402 . 00 
4001.08 

2109. 3J 

2560. oc 

3070.6: 
3645.0c 

4286. 8i 

5          2250.00 
)          2730.67 
5           3275.33 
)           3888.00 
i           4572.67 

40 

42 

44 
46 
48 

3666.67 
4244.63 
4880.33 
5576.54 
6336.00 

4000 . 00 
4630.50 
5324  00 
6083.50 
6912.00 

4333.33 
5016.38 
5767.67 
6590 . 46 
7488.00 

4666.67 
5402 . 25 
6211.33 
7097.42 
8064.00 

5000.0c 
5788. i: 
6655.  oc 
7604. 3^ 
8640.0c 

>           5333.33 
J           6174.00 
5           7098.67 
5           8111.33 
)           9216.00 

50 

52 

54 
56 
58 
6o 

7161.46 
8055.67 
9021.38 
10061.33 
11178.29 
12375.00 

7812.50 
8788.00 
9841 . 50 
10976.00 
12194.50 
13500.00 

8463.54 
9520.33 
10661.63 
11890.67 
13210.71 
14625.00 

9114.58 
10252.67 
11481.75 
12805.33 
14226.92 
15750.00 

9765.6. 
10985 .  oc 

I230I.8J 

13720.  oc 

15243.12 

16875.  oc 

J          10416.67 
)          11717.33 
I         13122.00 
)          14634.67 
I         16250.33 
)         18000.00 

*  This 

table  may 

be  used  in  cor 

npiiting  tl 

le  moments 

of  inertia 

of  plate  girders. 

columns  and  other  compound  sections  in  which  plates  are  used-    See  pages  341  and 
342. 


348  Properties  of  Structural  Shapes,  etc.  Chap.  10 

Table  II.*    Areas  and  Radii  of  Gyration  of  Hollow-Round  Sections 

""^  ^  Area  =  ~ — - — -  =  0.7854  {D^  -  rf*)  Bq  in 


Radius  of  gyration 


V£)2  +  <i2. 


Diam. 
D, 

inches 

A 
and 

Thickness  /  in  inches 

H 

5/16 

H 

H 

H 

H 

H 

I 

2 

2.37 
0.63 

1.66 
0.61 

3 

2.16 
0.98 

2.64 
0.96 

4 

2.9s 
1.33 

3.62 
1. 31 

4.27 
1.29 

5. 50 
1.25 

S 

3.73 
1.68 

4.60 
1.66 

5.45 
1.64 

7.07 
1.60 

8.59 
1.56 

10.01 
1.53 

6 

4.52 
2.03 

S.58 
2.01 

6.63 
1.99 

8.64 
1.95 

10.55 

1-91 

12.37 
1.88 

14.09 
1.84 

15.71 
1.80 

7 

5. 30 
2.39 

6.57 
2.37 

7.80 
2.35 

10.21 
2.30 

12.52 
2.27 

14.73 
2.23 

16.84 
2.19 

18.8s 
2. IS 

8 

6.09 
2.74 

7.55 
2.72 

8.98 
2.70 

11.78 
2.66 

14.48 
2.62 

17.08 
2.58 

19  59 
2.54 

21.99 
2.50 

9 

6.87 
3.09 

8.53 
3.07 

10.16 

3.  OS 

13.35 
3.01 

16.44 
2.97 

19.44 
2.93 

22.33 
2.89 

25.13 
2.85 

10 

7.66 
3. 45 

9.51 
3.43 

11.34 
3.41 

14.92 
3.36 

18.41 
3.32 

Vi 

25.08 
3.24 

28.27 
3.20 

:      II 

8.44 
3.80 

10.49 
3.78 

12.52 
3.76 

16.49 
3.72 

20.37 
3.67 

24.  IS 

3.63 

27.83 
3.59 

31.42 
3.55 

12 

9.23 
-4.16 

11.47 
4.13 

13.70 
4.H 

18.06 
4.07 

22.33 

4.03 

26.51 
3.99 

30.58 
3.95 

34.56 
3.91 

13 

10.01 
4.51 

12.46 
4.49 

14.87 
4.47 

19.63 

4.42 

24.30 
4.38 

28.86 
4.34 

33.33 

4.30 

37.70 
4.26 

14 

10.80 
4.86 

13.44 
4.84 

16.05 
4.82 

21.21 
4.78 

26.26 
4.73 

31.22 

4.69 

36.08 
4.65 

40.84 
4.61 

IS 

11.58 
5.22 

14.42 
5.19 

17.23 
5.17 

22.78 
5.13 

28.23  • 

5.09 

33.  S8 
5. 05 

38.83 

5.00 

43.98 
4.96 

16 

'' 

12.37 
5.57 

15.40 
5.55 

18.41 
5.53 

24.35 
5.48 

30.19 
5.44 

35. 93 

5.40 

41.58 
5.36 

47.12 
5.32 

17 

13.16 
5.92 

16.38 
5. 90 

19.59 

25.92 

32.15 
5.79 

38.29 
5.75 

44.33 
5.71 

SO.  27 
5.67 

18 

13.94 
6.28 

17.36 
6.25 

20.76 
6.23 

27.49 
6.19 

34.12 
6.15 

40.64 
6.10 

47.07 
6.06 

53.41 
6.02 

19 

'III 

t¥. 

21.94 
6.59 

29.06 
6.54 

36.08 
6.50 

43.00 
6.46 

49.82 
6.42 

56.5s 
6.37 

20 

IS. 51 
6.98 

19  33 
6.96 

23.12 
6.94 

30.63 
6.90 

38.04 
6.85 

45.36 
6.81 

52.57 
6.77 

59.69 
6.73 

♦  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 


Properties  of  Structural  Shapes,  etc. 


349 


Table  11  •  (Continued).    Areas  and  Radii  of  Gyration  of  Holiow-Round  Sectioat 

X  (£>2  -  </2) 


Area  = 


Radius  of  gyration 


=  0.7854  (£>2  _  rf2)  sq  In 


Diam. 

D, 
inches 

A 

and 

r 

Thickness  ( in  inches 

^% 

iH 

iH 

\\h. 

iH 

i3/4 

1^/i 

2 

2 

A 

r 

3 

A 

Y 

4 

A 
r 

5 

A 

r 

.  k 

6 

A 

r 

7 

A 
r 

20.76     . 
2.12 

22.58 
2.08 

8 

A 

r 

24.30 
2.46 

26.51 
2.43 

28.62 
2.39 

30.63 
2.36 

9 

A 

r 

27.83     . 
2.81 

50.43 
2.78 

32.94 
2.74 

35.34 

2.70 

37.65 
2.67 

39.86 
2.64 

10 

A    ' 

r 

31.37     . 
3.16 

J4.36 
3.13 

37.26 
3.09 

40.06 
3.0s 

42.76 
3.02 

45.36 
2.98 

47.86 
2.9s 

50.27 
2.92 

II 

A 
r 

34.90     . 
3.51 

58.29 
3.48 

41.58 
3.44 

44.77 
3.40 

47.86 
3.36 

50.8s 
3.33 

S3. 75 
3.29 

56.5s 
3.26 

12 

A 
r 

38.44     ^ 
3.87 

ti.22 
3.83 

45.90 
3.79 

49.48 
3.75 

52.97 
3.71 

56.3s 

59.64 
3.64 

62.83 
3.61 

13 

A 

r 

41.97     ^ 
4.22 

^6.14 
4.18 

50.22 
4.14 

54.19 
4.10 

58.07 
4.06 

61.85 
4.03 

65.53 
5.99 

69.12 
3.95 

14 

A 

r 

45.50     . 
4.57 

50.07 
4.53 

54.54 
4.49 

58.91 
4.45 

63.18 
4.41 

67.35 
4.38 

71.42 
4.34 

75.40 
4.30 

IS 

A  . 
r 

49-04      . 
4.92 

54.00 
4.88 

58.86 
4.84 

63.62 
4.80 

68.28 
4.76 

72.8s 
4.73 

77.31 
4.69 

81.68 
4.65 

16 

A 
r 

52.57      . 
5.27 

57.92 
5.23 

63.18 
5. 19 

68.33 
5.15 

73.39 
5. II 

78.34 
5.08 

83.20 
S.04 

87.97 
5.00 

17 

A 
r 

56.11      ( 
5.63 

51.85 
5.59 

67.50 
5-55 

73.04 
5.51 

78.49 
5.47 

83.84 
5.43 

89.09 
539 

94.25 
535 

18 

A 
r 

59.64      < 
5.98 

35.78 
5.94 

71.82 
5.90 

77.75 
5.86 

83.60 
5.82 

89.34 
5.78 

94.98 
S.74 

100.53 
5. 70 

19 

A 
r 

'63.18      ( 
6.33 

59.70 
6.29 

76.13 
6.25 

82.47 
6.21 

88.70 
6.17 

94.84 
6.13 

100.87 
6.09 

106.82 
6.0s 

20 

A 
r 

66.71      ' 
6.69 

^3.63 
6.64 

80.45 
6.60 

87.18 
6.56 

93.81 
6.52 

100.33 
6.48   . 

106.77 
6.44 

113. 10 
6.40 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


360  Properties  of  Structural  Shapes,  etc;  Chap.  10 

T^ible  m.*    Areas  and  Radii  of  Gyration  of  Hollow-Square  Sections 

Area  =  {D^  -  d^)  sq,  in 

Radius  of  gyration  =  V/- 


/Z)2  +  fiP. 


Side 
inches 

A 

and 
r 

Thickness 

in  inches 

H 

Me 

H 

\^ 

% 

H 

H 

1 

2 

A 

1.75 

2. II 

r 

0.72 

0.70 

3 

A 
r 

2.75 
1. 13 

3.36 
1. 10 

.... 

4 

A 
r 

3.75 
1.53 

4.61 
1.51 

5-44 
1.49 

7.00 
1.44 

5 

A 
r 

4.7s 
i.94 

5.86 
1.92 

6.94 

9.00 
1.85 

10.94 
1.80 

12.75 
1.76 

6 

A 
r 

5. 75 
2.35 

7. II 
2.33 

8.44 
2.30 

11.00 
2.25 

13.44 
2.21 

15-75 
2.17 

17 

2 

.94 
.12 

20.00 
2.08 

7     • 

A 
r 

6.75 
2.76 

8.36 
2.73 

9-94 
2.71 

13-00 
2.66 

IS.  94 
2.62 

18.75 
2.57 

21 

2 

.44 
■  53 

24.00 
2.48 

8 

A 
r 

7.75 
3.17 

9.61 
3.14 

11.44 
3.12 

15.00 
3.07 

18.44 
3.02 

21.7s 
2.98 

24 
2 

-94 
.93 

28. ©0 
2.89 

9 

A 
r 

8.75 
3.57 

10.86 
355 

12.94 
3. S3 

17.00 
3.48 

20.94 
3.43 

24.7s 
3.38 

28 
3 

-44 
.34 

32.00 
3.29 

10 

A 
r 

9.75 
3.98 

12. II 
3.96 

14.44 
3.93 

19.00 
3.88 

2344 
3.84 

27.7s 
3.79 

31 
3 

.94 
.74 

36.00 
3.70 

II 

A 
r 

10.75 
4.39 

13.36 

4.37 

IS.  94 
4.34 

21.00 
4-29 

25. 94 

4-24 

30.75 
4.20 

35 

4 

44 
15 

40.00 
4.10 

12 

A 
■  r 

11.75 
4.80 

14.61 
4.77 

17.44 
4. 75 

23-00 

4.70 

28.44 
4- 65 

33.75 
4.60 

38 
4 

'^ 

44.00 
4. SI 

13 

A 
r 

12.75 

5.21 

15.86 
5. 18 

V.l 

25.00 
5. 11 

30.94 
5.06 

36.7s 
5. 01 

42 
4 

U 

48.00 
4.92 

14 

A 
r 

13.75 
5.61 

17. II 
5.59 

20.44 

5.56 

27.00 

5.51 

33.44 

5. 47 

39.75 
5.42 

1 

94 
37 

52.00 
5-32 

IS 

A 
r 

14.75 
6.02 

18.36 
6.00 

21.94 

5-97 

29-00 
.    5.92 

35-94 
5-87 

42.7s 
5. 83 

49 
5 

44 
78 

56.00 
5. 73 

i6 

A 
r 

15.75 
6.43 

19.61 
6.41 

23.44 
6.38 

31.00 
6.33 

38.44 
6.28 

45.75 
6.23 

52 

6 

94 
19 

60.00 
6.14 

17 

A 
r 

16.75 
6.84 

20.36 
6.81 

24-94 
6.79 

33.00 
6.74 

40.94 
6.69 

48.75 
6.64 

56 
6 

44 
59 

64.00 
6.54 

i8 

A 

r 

17.75 
7.25 

22.11 
7.22 

26.44 
7.20 

35.00 
7.15 

43.44 
7.10 

51.75 
7.05 

59 
7 

94 
00 

68.00 
6.95 

19 

A 
r 

18.7s 
7.66 

23.36 
7.63 

27.94 
7.61 

37.00 
7.56 

45-94 
7. SI 

54.75 
7.46 

63 

7 

44 
41 

72.00 
7.36 

20 

A 
r 

19.7s 
8.06 

24.61 
8.04 

29.44 
8.01 

3900 
7.96 

48.44 
7.91 

57.75 
7.87 

66 
7 

94 
82 

76.00 
7.77 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Properties  of  Structural  Shapes,  etc.  351 

Table  ni  *  (Continued).   Areas  and  Radii  of  Gyration  of  Hollow-Square  Sections 

'mmm::"\  Area  -  (D«  -  rf2)  sq  in 


Radius  of  gyration  = 


1/ • — in 

V  12 


Side 
inches 

X 

Thickness  i  in  inches 

1 

Y 

iH 

iH 

1% 

i'/^ 

1% 

m 

iH 

2 

2 

A 

Y 

3 

A 
r 

4 

A 

Y 

•• 

5 

A 

Y 

6 

A 

Y 

7 

A        '. 

j6.44 

28.75 

Y 

2.44 

2.40 

8 

A 

Y 

JO.  94 
2.84 

33.75 
2.80 

36.44 
2.76 

39.00 
2.72 

9 

A 

Y 

J5.44 
3.2s 

38.75 
3.20 

41.94 
3.16 

45.00 
3.12 

47.94 
3.08 

50.75 
3.0s 

10 

A 

Y 

1;i^ 

43-75 
3-61 

47.44 
3.57 

51.00 
3.52 

54.44 
3.48 

57.7s 

3-44 

60.94 
3.40 

64.00 
3.37 

II 

A 

Y 

U.44 
4.06 

48.75 
4.01 

52.94 
3.97 

57.00 
3.93 

60.94 
3.88 

64.75 
3.84 

68.44 
3.80 

72.00 
3-76 

12 

A 

Y 

18.94 
4.46 

53.75 
4-42 

58.44 
4-37 

63.00 
4-33 

6744 
4.29 

71-75 
4-25 

75.94 
4.20 

80.00 
4.16 

13 

A 

Y 

53.44 
4.87 

58  75 
4.82 

63.94 
4.78 

69.00 

73.94 
4.69 

78.7s 
4.65 

83.44 
4.61 

88.00 
4.56 

4.74 

14 

A 

Y 

57-94 
5-28 

63-75 
5-23 

69.44 
5. 18 

75.00 
5-14 

80.44 
5.10 

85.75 
5.05 

90.94 
5.01 

96.00 
4-97 

15 

A 

Y 

52.44 
5.68 

68.75 
5.64 

74.94 
5.59 

81.00 
5.55 

86.94 
5.50 

92.75 
S.46 

98-44 
5.41 

104.00 
5.37 

i6 

A 

Y 

66.94 
6.09 

73  75 

6.04 

80.44 
6.00 

.     87.00 
5,95 

93.44 
5.91 

lii 

105.94 
5.82 

112.00 
5.77 

17 

A 

Y 

71.44 
6.50 

78.75 
6.45 

85.94 
6.40 

93.  CO 
6.36 

99-94 
6.31 

106.75 
6.27 

113.44 
6.23 

120.00 
6.18 

i8 

A 

Y 

75-94 
6.90 

83.75 
6.86 

91-44 
6.81 

1:?? 

106.44 
6.72 

113.75 
6.67 

'1;il 

128.00 
6.58 

19 

A 

Y 

80.44 
7-31 

88.75 
7.26 

96.94 
7.22 

105.00 
7.17 

112.94 
7.12 

120.75 
7.08 

128.44 
7.03 

136.00 
6.99 

20 

A 

Y 

84-94 

7-72 

'\l 

102 . 44 
7  62 

III. 00 
7.58 

119-44 
7.53 

127.75 
7.49 

135.94 
7.44 

144-00 
7.39 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


352 


Properties  of  Structural  Shapes,  etc. 


Chap.  10 


7.  Dimensions,  Moments  of  Inertia,  Radii  of   Gyration  and   Section- 
Moduli  of  Standard  Structural  Shapes 

Explanation  of  Tables.  As  in  using  structural -steel  shapes  the  choice  is 
practically  confined  to  such  shapes  as  are  rolled  by  the  mills,  it  is  essential  to 
have  at  hand  the  dimensions  and  properties  of  those  shapes  in  order  to  calcu- 
late the  necessary  sizes  to  meet  special  requirements  for  strength  and  practical 
conditions  of  economy  and  framing.  Since  1890  great  changes  have  been  made 
both  in  the  materials  and  in  the  shapes  of  the  standard  sections.  The  roUing- 
mills  which  manufacture  the  most  complete  assortment  of  structural  shapes  are 
those  of  the  Carnegie  Steel  Company,  the  Cambria  Steel  Company,  the  Jones 
&  Laughlin  Steel  Company  and  the  Bethlehem  Steel  Company.  In  general,  the 
products  of  these  mills,  especially  beams  and  channels,  are  respectively  similar 
in  shape.  This  is  particularly  true  of  the  shapes  rolled  by  the  first  three  of  the 
companies  named. 

The  standard  steel  beams  and  channels  considered  in  the  following  pages  are 
rolled  by  all  of  these  mills,  with  the  exception  of  those  of  the  Bethlehem  Steel 
Company.  With  a  few  exceptions  the  following  tables  of  properties  of  stand- 
ard structural  shapes  have  been  adopted  by  permission  from  the  Pocket 
Companion  of  the  Carnegie  Steel  Company.  It  may  be  well  to  state  that 
the  tables  of  properties  for  the  various  structural  shapes,  published  by  the 
companies  named  above,  do  not  agree  exactly,  even  for  the  same  weights, 
but  the  differences  are  not  of  practical  importance.  The  tables  of  the 
Cambria  Steel  Company  and  of  the  Carnegie  Steel  Company  for  beams  and 
channels  agree  more  closely.  As  angles  are  very  extensively  used  foi  a 
great  many  purposes,  the  properties  are  given  for  all  sizes  rolled  and  also  a 
table  showing  from  which  mills  the  different  sizes  may  be  obtained.  Natur- 
ally it  will  generally  be  advantageous  to  use  a  size  that  is  rolled  by  several 
mills. 

Tables  XV,  XVI  and  XVII  will  be  found  very  convenient  when  computing 
the  strength  of  struts  formed  of  pairs  of  angles,  and  Table  XVIII  when  com- 
puting the  same  for  pairs  of  channels. 

Standard  Steel  Beams  and  Channels.*      Common  Dimensions 


STRUCTURAL  BEAMS 

A.A.S.M.   STANDARD   SECTIONS 


^t 


n  =  minimum  web  »  t     ~~ 
R  =  minimum  web  -\-  o.io" 
r  =  Vio  minimum  web 
h  =  distance  between  flange-  fillets 
Slope  of  flange,  1:6=  i6%%  =  9°  27'  42" 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Properties  of  Structural  Shapes,  etc. 


353 


STRUCTURAL  CHANNELS 
A.A.S.M.   STANDARD  SECTIONS 


T 

n  =  minimum  web  =  / 
R  =  minimum  web  +0.10" 
r   =  Mo  minimum  web 
Slope  of  flange,  1:6=  16%%  =  9°  27'  42'' 


Dimensions  for  Structural  Beams  are  those  adopted  by  the  Association  of 
American  Steel  Manufacturers  and  apply  to  all  Structural  Beams,  except 
American  Standard  Sections  B  i,  B  2  and  B  3,  also  Sections  B  24  and  B  81. 

The  dimensions  of  the  Supplementary  Beams,  B  61  to  B  68,  inclusive, 
cannot  be  readily  reduced  to  formulas.     Slope  of  flange  is  i  :  11  =  5°  11' 40". 

Dimensions  for  Structural  Channels  are  those  adopted  by  the  Association 
of  American  Steel  Manufacturers  and  apply  to  all  Structural  Channels,  except 
Section  C  20,  the  13-in  sizes,  which  are  Car  Building  Channels. 


354 


Properties  of  Structural  Shapes,  etc. 
Table  IV.*     Properties  of  I-Beam  Sections 

|2^ 


Chap.  10 


Sec- 
tion- 
index 

Depth 

of 
beam 

Weight 
iK>t 

Area 
of 
sec- 
tion 

Width 

of 
flange 

Thick- 
ness of 
web 

Axis  I -I 

Axis  2-2 

/ 

r 

I-/C 

/ 

r 

I/c 

in 

lb 

sq  in 

in 

in 

in* 

in 

in3 

in* 

in 

in3 

B6i 

27 

90.0 

26.33 

9.000 

0.524 

2958.3 

10.60 

219. 1 

75.3 

1.69 

16.7 

B.4 

24 

1150 

IIO.O 

105.0 

33.98 
32.48 
30.98 

8.000 
7.938 
7.87s 

0.750 
0.688 
0.625 

2955. 5 
2883.5 
2811.5 

9.33 

9-42 

9.53 

246.3 
240.3 
234.3 

83.2 
81.0 
78.9 

1.57 
1.58 
1.60 

20.8 
20.4 
20.0 

B    I 

24 

100. 0 
950 
90.0 
85.0 
80.0 

29.41 
27.94 
26.47 
25.00 
23.32 

7.254 
7.193 
7.131 
7.070 
7.000 

0.754 
0.693 
0.631 
0.570 
0.500 

2379.6 
2309  0 
2238.4 
2167.8 
2087 . 2 

9.00 
9.09 
9.20 
9-31 
9.46 

198.3 
192.4 
186.5 
180.7 
173.9 

48.6 
47.1 

45.7 
44-4 
42.9 

1.28 
1.30 
1.31 
1-33 
1-36 

13-4 
13.1 
12.8 
12.6 
12.3 

B62 

24 

740 

21.70 

9.000 

0.476 

1950. I 

9.48 

162.5 

61.2 

1.68 

13.6 

B63 

21 

60.5 

17.68 

8.250 

0.428 

1235.5 

8.36 

117. 7 

43.5 

1-57 

10.6 

B    2 

20 

100. 0 
9S.O 
9.00 
85.0 
80.0 

29.^^1 
27.94 
26.47 
25.00 
23.73 

7.284 
7.210 
7.137 
7.063 
7.000 

0.884 
0.810 
0.737 
0.663 
0.600 

1655.6 
1606.6 
1557.6 
1508.5 
1466.3 

7.50 
7.58 
7.67 
7-77 
7.86 

165.6 
160.7 
155-8 
150.9 
146.6 

52.7 
50.8 
49 -o 
47.3 
45.8 

1-34 
1.35 
1.3© 
1.37 
1.39 

14.5 
14.1 
13.7 
13.4 
13.1 

B    3 

20 

7S.O 
70.0 
65.0 

22.06 
20.59 
19.08 

6.399 
6.325 
6.250 

0.649 
0.575 
0.500 

1268.8 
1219.8 
1169.5 

7.58 
7.70 
7.83 

126.9 
122.0 
117. 0 

30.3 
29.0 
27.9 

1.17 
1. 19 
I.  21 

9.5 
9. 2 
8.9 

B8r 

18 

90.0 
85.0 
80.0 
7S.O 

26.47 
25.00 
23.53 
22.05 

7 .  245 
7.163 
7.082 
7.000 

0.807 
0.725 
0.644 
0.562 

1 260 . 4 
1220.7 
1181 .0 
1141.3 

6.90 
6.99 
7.09 
7.19 

T40.0 
135-6 
131. 2 
126.8 

52. 0 
50.0 
48.1 
46.2 

1.40 
1.42 
1.43 
1.45 

14.4 
14.0 
13.6 
13.2 

B80 

18 

70.0 
65.0 
60.0 
SS.o 

20.59 
19.12 
17.65 
15.93 

6.259 
6.177 
6.095 
6.000 

0.719 
0.637 
0.555 
0.460 

921.2 
881.5 
841.8 
795-6 

6.60 
6.79 
6.91 
7.07 

102.4 
97-9 
93-5 
88.4 

24.6 

23.5 
22.4 

21.2 

1.09 
I. II 
1. 13 
1. 15 

1:1 

7.3 
7.1 

B64 

18 

48.0 

14.08 

7.500 

0.380 

737.1 

7.23 

81.9 

30.0 

1.46 

8.0 

B    S 

IS 

7S.O 
70.0 
65.0 
60.0 

22.06 
20.59 
19.12 
17.67 

6.292 
6.194 
6.096 
6.000 

0.882 
0.784 
0.686 
0.590 

691.2 
663 . 7 
636.1 
609.0 

5.60 
5.68 
5-77 
5.87 

92.2 
88.5 
84.8 

8l.2 

30.7 
29.0 
27.4 
26.0 

1. 18 

1. 19 
1.20 
I. 21 

9.8 
9.4 

1° 

B    7 

IS 

SS-O 
So.o 
450 
42.0 

16.18 
14.71 
13.24 
12.48 

5. 746 
S.648 
5.555 
S.soo 

0.656 
0.558 
0.460 
0.410 

511. 0 

483.4 
455-9 
441.8 

5.62 
5.73 
5.87 
5. 95 

68.1 
64.5 
60.8 
58.9 

17. I 
16.0 
151 
14.6 

1.02 
1.04 
1.07 
1.08 

5.9 
5.7 
5.4 
5.3 

B65 

15 

37.5 

10.91 

6.7SO 

0.332 

405.5 

6.10 

54. 1 

19.9 

1.35 

5.9 

Note.  The  [exponential  figures  used  with  /  and  I/c  denote  the  mathematical  "  dimen- 
sions" of  these  qualities,  that  is,  the  number  of  times  the  linear  unit  appears  as  a  factor 
in  the  quantities. 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Properties  of  Structural  Shapes,  etc.  355 

Table  IV*    (Continued).     Properties  of  I-Beaiu  Section 


-1 


Sec- 
tion- 
index 

Depth 

of 
beam 

Weight 
foot 

Area 

of 

section 

Width 

of 
flange 

Thick- 
ness of 
web 

Axis  I- 

[ 

Axis  2-2 

/ 

r 

I/c 
in3 

/ 

r 

in3 

in 

lb 

sq  in 

in 

in 

in« 

m 

in< 

in 
1.04 

III, 

1.08 

B    8 

12 

55-0 
50.0 
45-0 
40.0 

16.18 
14/1 
13   M 
11.84 

5. 611 
5.489 
5.366 
5.250 

0.821 
0.699 
0.576 
0.460 

321.0 
303.4 
285.7 
269.0 

4.45 
4.54 
4.65 

4.77 

53.5 
50.6 
47-6 
44.8 

17.5 
16. 1 
14-9 
13.8 

6.2 

.5-9  ; 

5-6    ; 
S.3    ' 

B    9 
B66 

12 
12 

35.0 
31.5 
28.0 

10.29 
9.26 

8.15 

5.086 
5.000 

0.436 
0.350 

228.3 
215.8 

4.71 
4.83 
4.95 

38.0 
36.0 
33.2 

10. 1 

9.5 
12.6. 

;  0.99 

I.OI 

1.24 

4-0   1 
3.8  ! 
,  4.2 

6.000 

0.284 

199.4 

Bii 

10 

40.0 
350 
30.0 
25.0 

11 .76 

10.39 

8.82 

7.37 

5.099 
4.952 
4.805 
4.660 

0.749 
c .  602 
0.455 
0.310 

158  7 
146.4 
134-2 
122.1 

3.67 
3-77 
3.90 
4.07 

31.7 
29.3 
26.8 
24.4 

Vs 

7.7 
6.9 

0.90 

0  91 

0.93 
0.97 

3  7 

3  4 
3.2 
3.0 

B67 

10 

22.25 

6.54 

5.500 

0.252 

113  6 

4.17 

22.7 

9.0 

1.17 

3.3 

B13 

9 

35.0 
30.0 
25.0 
21.0 

10.  29 
8.82 
7.35 
6.31 

4.772 
4.609 
4.446 
4.330 

0.732 
0.569 
0.406 
0.290 

III. 8 
101.  q 
91.9 
84.9 

3.29 
3.40 
3.54 
3.67 

24.8 
22.6 
20.4 
18.9 

1:1 

5.7 
5.2 

0.84 
0.85 
0.88 
0  90 

i.l 

2.5 
2.4 

B15 

8 

25-5 
23.0 
20.5 
18.0 

7.50 
6.76 
6.03 
5.33 

4.271 
4.179 
4.087 
4.000 

0.541 
0.449 
0.357 
0.270 

68.4 
64.5 
60.6 
56.9 

3.02 
3.09 
3.17 
3.27 

17  I 
16.1 
15.2 
14.2 

4.8 
4.4 
4.1 
3.8 

0.80 
0.81 
0.82 
0.84 

2.2 
2.1 
2  o- 
1-9 

B68 

8 

17.5 

5.12 

5.000 

0.220 

58  4 

3.38 

14.6 

6.2 

1. 10 

2-5 

B17 

7 

20.0 
17.5 
15.0 

5.88 
5. 15 
4.42 

3.868 
3.763 
3.660 

0.458 
0.353 
0.250 

42.2 
39.2 
36. ~ 

2.68 
2.76 
2.86 

12. 1 

11 .2 
10.4 

3.2 

2.9 
2.7 

0.74 
0.76 
0.78 

1-7 
1.6 
1.5 

B  19 

6 

17.25 
14.75 
12.25 

5.07 
4-34 
3.61 

3.575 
3.452 
3.330 

0.475 
0.352 
0.230 

26.2 
24.0 
21.8 

2.27 
2.35 
2.46 

8.7 
8.0 

7.3 

2.4 
2.1 
1.9 

0.68 
0.69 
0.72 

1.3 
1.2 
1 .1 

B21 

5 

14.75 
12.25 
9.75 

4.34 
2:87 

3.294 
3.147 
3.000 

0.504 
0.357 
0.210 

15.2 
13.6 
12. 1 

1.87 
1.94 
2.05 

6.1 

1-7 
1.5 
1.2 

0.63 
0.63 
0.65 

i.o 
0.92 
0.82 

B23 

4 

10.5 
9.5 
8.5 
7.5 

3.09 
2.79 
2.50 
2.21 

2.880 
2.807 
2 .  733 
2.660 

0.410 
0.337 
0.263 
0.190 

7.1 
6.8 
6.4 
6.0 

1.52 

1.55 
1.59 
1.64 

3.6 

3-4 
3.2 
3.0 

1 .0 
0.93 
0.85 
0.77 

0.57 
0.58 
0.58 
0.59 

0.70 
0.66 
0.63 
0.58 

B77 

3 

7.5 
6.5 
5-5 

2. 21 
1.63 

2.521 
2.423 
2.330 

0.361 
0.263 
0.170 

2.9 
2.7 
2.5 

I. IS 
1.19 
1.23 

1.9 
1.8 
1.7 

0.60 
O.S3 
0.46 

0.52 
O.S2 

O.S3 

0.48 
0.44 
0.40 

See  "Note"  with  table  on  preceding  page. 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


356 


Properties  of  Structural  Shapes,  etc. 
Table  V.*    Properties  of  H-Beam  Sections 


Chap.  10 


These  may  be  employed  as.  columns,  using  the  axis  2-^ 

Sec- 

Depth 
of 

Weight 

Area 
of 

Width 
of 

Thick- 

Axis i-i 

Axis  2-2 

per 

ness 

tion- 

beam 

foot 

seclrion 

flange 

of  web 

T 

r 

T/r. 

T 

r 

I/c 

index 

in* 

in 
1.87 

in3 
8.8 

in 

lb 

sqin 

in 

in 

in* 

in 

in3 

H4 

8 

34.0 

10.00 

8.0 

0.375 

IIS. 4 

3.40 

28.9 

3S.I 

H3 

6 

23.8 

7.00 

6.0 

0.313 

4S.I 

2.S4 

ISO 

14.7 

1.45 

4.9 

H  2 

5 

18.7 

5-50 

SO 

0.313 

23.8 

2.08 

9-5 

7.9 

1.20 

31 

Hi 

4 

13.6 

4.00 

4.0 

0.313 

10.7 

1.63 

5.3 

3.b 

0.95 

1.8 

See  "  Note  "  with  Table  IV,  page  354. 

♦  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Properties  of  Structural  Shapes,  etc.  357 

Table  VI.*    Properties  of  Bethlehem  I-Beam  Sections 


Depth 

of 
beam 

Weight 
per   . 
foot 

Area 

of 

section 

Thick- 
ness 

of 
web 

Width 

of 
flange 

Increase 
of  web 
and 
flange  for 
each  lb 
increase 
of  weight 

Neutral  axis 

perpendicular 

to  web  at  center 

Neutral 
axis  coin- 
cident with 
center  line 

of  web 

/ 

r 

I/c 

/ 

r 

in 

lb 

sq  in 

in 

in 

in 

in< 

in 

in3 

in* 

in 

30 

120.0 

35-30 

0.540 

10.500 

o.oio 

5239 .6 

12.18 

349-3 

165.0 

2.16 

28 

105.0 

30.88 

0.500 

10.000 

O.OII 

4014. I 

11.40 

286.7 

131 -5 

2.06 

26 

90.0 

26.49 

0.460 

9500 

O.OII 

2977.2 

10.60 

229.0 

101.2 

1.9s 

24 

84.0 

24.80 

0.460 

9-250 

0.012 

2381.9 

9.80 

198. 5 

91. 1 

1.92 

24 

83.0 

24  59 

0.520 

9-130 

0.012 

2240 . 9 

9.S5 

186.7 

78.0 

1.78 

24 

73.0 

21.47 

0.390 

9.000 

0.012 

2091.0 

987 

174.3 

74.4 

1.86 

20 

82.0 

24.17 

0.570 

8.890 

0.015 

1559-8 

8.03 

156.0 

79.9 

1.82 

20 

72.0 

21.37 

0.430 

8.750 

0.015 

1466.5 

8.28 

146.7 

75.9 

1.88 

20 

69.0 

20.26 

0.520 

8.145 

0.015 

1268.9 

7-91 

126.9 

51.2 

1.59 

20 

64.0 

18.86 

0.450 

8.075 

0.015 

1222. I 

8.05 

122.2 

49.8 

1.62 

20 

S90 

17.36 

0.375 

8.000 

0.015 

1172.2 

8.22 

117. 2 

48.3 

1.66 

18 

S90 

17.40 

0.49s 

7.675 

0,016 

883.3 

7.12 

98.1 

39.1 

I. SO 

18 

S4.0 

IS.  87 

0.410 

7.S90 

0.016 

842.0 

7.28 

93.6 

37.7 

1.54 

18 

52.0 

IS.  24 

0.375 

7 -555 

0.016 

825.0 

7-36 

917 

37.1 

1.56 

18 

48. 5 

14.2s 

0.320 

7-500 

0.016 

798.3 

7.48 

88.7 

36.2 

1. 59 

IS 

71.0 

20.95 

0.520 

7.500 

0.020 

796.2 

6.16 

106.2 

61.3 

1.71 

IS 

64.0 

18.81 

0.605 

7.195 

0.020 

664.9 

S.9S 

88.6 

41.9 

1.49 

IS 

S40 

15.88 

0.410 

7.000 

0.020 

610.0 

6.20 

81.3 

38.3 

1. 55 

15 

46.0 

13.52 

0.440 

6.810 

0.020 

484.8 

S.99 

64.6 

25.2 

1.36 

IS 

41.0 

12.02 

0.340 

6.710 

0.020 

456.7 

6.16 

60.9 

24.0 

1. 41 

IS 

38.0 

11.27 

0.290 

6.660 

0.020 

442.6 

6.27 

59.0 

23.4 

1.44 

12 

36.0 

10.61 
9.44 

0.310 
0.335 

6.300 
6.205 

0.025 
0.025 

269.2 
228.5 

5. 04 
4.92 

44.9 
38.1 

21.3 
16.0 

1.42 
1.30 

12 

32.0 

12 

28. 5 

8.42 

0.250 

6.120 

0.025 

216.2 

5.07 

36.0 

15.3 

1.35 

10 

28.5 

8.34 

0.390 

S.990 

0.029 

134.6 

4.02 

26.9 

12. 1 

1. 21 

10 

23. S 

6.94 

0.250 

5. 850 

0.029 

122.9 

4.21 

24.6 

II. 2 

1.27 

9 

24.0 

7.04 

0.365 

5-555 

0.033 

92.1 

3.62 

20. 5 

8.8 

1. 12 

9 

20.0 

6.01 

0.250 

5.440 

0.033 

85.1 

3.76 

18.9 

8.2 

1. 17 

8 

19s 

5. 78 

0.325 

5.325 

0.037 

60.6 

3.24 

IS. I 

6.7 

1.08 

8 

17. 5 

5.18 

0.250 

5.250 

0.037 

57.4 

3.33 

14.3 

6.4 

I. II 

See  "  Note  "  with  Table  IV,  page  354. 

•  Adapted  from  Catalogue  of  Structural  Shapes,  1909  Edition.  Bethlehem  St^ 
Company,  Bethlehem,  Pa. 


858  Properties  of  Structural  Shapes,  etc.  Chap.  10 

Table  Vn.*    Properties  of  Bethlehem  Girder-Beam  Sections 


Depth 

of 
beam 

Weight 
per 
foot 

Area 

of 

section 

Thick- 

ness  of 

web 

Width 

of 
flange 

Increase 

of  web 

and 

flange 

for  each 
pound 

increase 

of  weight 

Neutral  axis 

perpendicular 

to  web  at  center 

Neutral 
axis  coin- 
cident with 
center  line 
of  web 

I 

r 

I/c 

/ 

r 

in 

lb 

sq  in 

in 

in 

in 

in* 

in 

in» 

in* 

in 

30 
30 

300.0 

iSo.o 

58.71 
53- 00 

0.750 
0.690 

15.00 
13.00 

o.oio 
o.oio 

9150.6 
8194.5 

12.48 
12.43 

610.0 
546.3 

630.2 
433-3 

3.28 
3.86 

28 

38 

180.0 
165  0 

52.86 
48.47 

0.690 
0.660 

14:35 
12.50 

O.OII 
Q.OII 

7264.7 
6562.7 

11.72 
11.64 

518.9 
468.8 

533.3 
371  9 

3.18 

3.77 

36 
36 

i6o.o 
ISQO 

46.91 
43.94 

0.630 
0.630 

13.60 
12.00 

O.OII 
O.OII 

5620.8 
S153.9 

10.95 
10.83 

432.4 
396.5 

435.7 
314-6 

3.05 
2.68 

34 
24 

I4P.0 

130.0 

4116 
3S.38 

Q.600 
Q.530 

13.00 

12. QO 

0.013 

0.012 

4201.4 
3607.3 

10.10 

10.10 

350. 1 
300.6 

346.9 
249-4 

a. 90 
3.66 

30 
20 

140.0 

113. 0 

41.19 
33.81 

Q.640 
0.550 

13.50 
13.00 

o.ois 
o.ois 

3934.7 
3343.1 

8.44 
8.4S 

393. 5 
334.3 

348.9 
339.3 

291 
2.70 

l8 

92.0 

37-12 

0.480 

II. SO 

0.016 

IS9I.4 

7.66 

176.8 

183.6 

3.59 

IS 
15 
IS 

140.0 
104.0 
73- 0 

41.27 
30.50 
21.49 

0.800 
0,600 
0.430 

11.75 

11.25 

10.50 

0.020 
0.030 
0.020 

1593-7 

1320. I 
883.4 

6.31 

6.33 
6.41 

312.4 
162.7 

117. 8 

331.0 
313.0 
123.2 

3.83 
3.64 
3.39 

13 
13 

70.0 
SS.o 

20.58 
16.18 

0.460 
0.370 

10.00 

9-75 

0.02s 
0.035 

S38.8 
433.0 

5.13 
5.17 

89.8 
73.0 

114. 7 
81. 1 

3.36 

3.34 

10 

9 
8 

44.0 
38.0 

32. s 

12.95 

11.33 

9-54 

0.310 
0.300 
0.390 

9.00 
8.50 
8.00 

0.030 
0.033 
Q.G37 

344.3 
170.9 
114. 4 

4.34 
3.90 
346 

48.8 
38.0 
28.6 

57.3 
44.1 
32.9 

3.10 
1.98 

1.86 

8ee'« 

N6te  ♦•  ^ 

^th  Tal 

)le  IV.  page  354- 

•Ada 
Compan 

pted  fro 
y,  Beth 

m  Cata 
lehejn, 

logue  df 
Pa.     '-^ 

gtructu 

ral  Shape 

s.  1909 

Editic 

m.  Bel 

hleher 

a  Steel 

Properties  of  Structural  Shapes,  etc. 
Table  VIII.*    Properties  of  Channel-Sections 


359 


,___^ 

r^ 

0 

7 

[7= 

=»      ' 

-J 

d^ 

1 — 

1—1 
j 

•^           D 

t-» 

^ 

I 

Depth 
chan- 

Weight 
per 

Area 
of 

Width 
of 

Thick- 
ness of 

Axis  i-i 

Axis  2-2 

X 

" 

- 

nel 

foot 

tion 

flange 

web 

/ 

r 

I/c 

/ 

r 

I/c 

in 

df 

Df 

in 

lb 

sq  in 

in 

in 

in* 

in 

in3 

in* 

in 

in8 

55-0 

16.18 

3.818 

0.818 

430.2 

S^ 

57.4 

12.2 

0.87 

4.1 

0.82 

'8.53 

II. 9  > 

50.0 

14.71 

3.720 

0.720 

402.7 

S.23 

S3. 7 

n.2 

0.87 

3.8 

0.80 

«-7i 

I2.O0 

IS 

450 

13.24 

3.622 

0.622 

375.1 

5.32 

So.o 

10.3 

0.88 

3.6 

0.79 
0.78 

-8.92 
;9.i5 

12.23 

40. 0 

11.76 

3-524 

0.524 

347.5 

5.43 

46.3 

Vs 

0.89 

3.4 

12.42 

35.0 

10.29 

3.426 

0.426 

319.9 

5.58 

42.7 

0.91 

3.2 

0.79 

;9.43 

12.73 

33  0 

9-90 

a.  400 

0.400 

312.6 

5.62 

41.7 

8.2 

Q.91 

3.2 

o.n 

9-50 
!6.6o 

12.82 

40.0 

11.76 

3.418 

Q.758 

196.9 

4.09 

32.8 

6.6 

0.7S 

2.5 

o.n 

9.6i2 

35.0 

10.29 

3.296 

0.636 

179-3 

4.17 

59 

0.76 

2.3 

I'M 

6.81 

9.73 

12 

30.0 

8.82 

3.173 

O.S13 

l6l.7 

4.28 

26:9 

5.3 

0.77 

2.1 

7.07 

9.911 

25.0 

7.35 

3.050 

0.390 
Q.280 

144.0 

4.43 

24.0 

4.5 

0.79 

1.9 

0.68 

7.36 

10.21 

20.5 

6.03 

3.940 

128. 1 

4.61 

21.4 

3.9 

0.81 

1.7 

0.70 

7.67 

10.^ 

35. 0 

10.29 

3.183 

0.823 

iiS.S 

3.35 

23.1 

4.7 

0.67 

1.9 

0.70 

5.17 

8.00 

30.0 

8.82 

3.036 

Q.676 

103.2 

3.42 

20.7 

4.0 

0.67 

1.7 

0.65 

5.40 
S.67 

8.14 

10 

25-0 

7.35 

3.889 

0.529 

91.0 

3.52 

18.2 

3.4 

0.68 

1.5 

0.62 

S.28 

20.0 

5.88 

3.742 

0.382 

78.7 

3.66 

15.7 

2.9 

0.70 

1.3 

0.61 

S.97 

8.54 

ISO 

4.46 

2.600 

0.240 

66.9 

3.87 

13.4 

2.3 

0.72 

1.2 

0.64 

fe.33 

9.P2 

25.0 

7  35 

2.815 

0.615 

70.7 

3.10 

15.7 

3.0 

0.64 

1.4 

0.62 

'4.84 

7.43 

9 

20.0 

5.88 

2.652 

0.452 

60.8 

3.21 

13.5 

2.5 

0.65 

1.2 

o.ss 

:S.i2 

7 .8^9 

15.0 

4.41 

2.488 

0.288 

SO. 9 

3.40 

II. 3 

2.0 

0.67 

I.O 

0.S9 

S.49 

7.98 

13.25 

3.89 

2.430 

0.230 

47.3 

3.49 

10.5 

1.8 

0.67 

0.97 

0.61 

5. 63 

8.19 

21.25 

6.25 

2.622 

0.582 

47.8 

2.77 

II. 9 

2.3 

0.60 

I.I 

0.59 

4.23 

6,71 

18.75 

5.51 

2.530 

0.490 

43.8 

2.82 

no 

2.0 

0.60 

1.0 

0.S7 

4-38 

6.77 

8 

16.25 

4.78 

2.439 

0.399 

39.9 

2.89 

10. 0 

1.8 

0.61 

0.95  0.56 

4.54 

6.89 

13.75 

4.04 

2.347 

0.307 

36.0 

2.98 

9.0 

1.6 

0.62 

0.87I0.56I4.72 

7.07 

11.25 

3.35 

2.260 

0.220 

32.3 

3. II 

8.1 

1.3 

0.63 

o.79,o.58J4.94 

7-37 

19  75 

S.81 

2.513 

0.633 

33.2 

2.39 

9-5 

1.9 

0.56 

0.96 

0.583.48 

5.94 

17  25 

507 

2.408 

0.528 

30.2 

2.44 

8.6 

1.6 

0.57 

0.87 

0.563.64 

5.99 

7 

14.75 

4.34 

2.303 

0.423 

27.2 

2.50 

7.8 

1.4 

0.57 

0.79 

o.54'3-8o 

6.07 

12.25 

3.60 

2.198 

0.318 

24.2 

2.59 

6.9 

1.2 

0.58 

0.71 

0-53;3.99 

6.21 

9  75 

2.85 

2.090 

0.210 

21. 1 

2.72 

6.0 

0.98 

0.59 

0.63 

0.55 

4.22 

6.53 

15  5 

4  56 

2.283 

0.563 

19.5 

2.07 

6.5 

1.3 

0.53 

0.74 

0.55 

2.91 

5-23 

6 

13  0 

382 

2.160 

0.440 

17.3 

2.13 

58 

I.I 

0  53 

0.65  0.52 

3.09 

5-29 

10  5 

3.09 

2.038 

0.318 

15. 1 

2.21 

5.0 

0.88 

0  53 

0.57I0.50 

3.28 

5-42 

8.0 

2.38 

1.920 

0.200 

13.0 

2.34 

4.3 

0.70 

0.54 

0.500.52 

352 

5-71 

II. 5 

338 

2.037 

0.477 

10.4 

1.75 

4.2 

0.82 

0  49 

o.54'o.5i 

2.34 

4.51 

5 

9.0 

2  6s 

1.890 

0.330 

8.9 

1.83 

3.6 

0  64 

0.49 

0.45,0.48 

2.56 

4.62 

6.5 

I  95 

1.750 

0.190 

7-4 

1.95 

3.0 

0.48 

0.50 

0.38,0.49 

2.79 

4.87 

7-25 

2  13 

1.725 

0.325 

4.6 

1.46 

2.3 

0.44 

0.46 

0.35I0.46 

1.85 

3.84 

4 

6.25 

1.84 

1.652 

0.252 

4.2 

1.51 

2.1 

0.38 

0.45 

0.32 

0.46 

1.96 

3.93 

5. 25 

1.55 

I  580 

0.180 

3.8 

1.56 

1-9 

0.32 

0.45 

0.29 

0.46 

2.06 

4.04 

6.0 

1.76 

1.602 

0.362 

2.1 

1.08 

1.4 

0.31 

0.42 

0.27 

0.46 

1,07 

3.07 

3 

5-0 

1.47 

1.504 

0.264 

1.8 

1. 12 

1.2 

0.25 

0.42 

0.24 

0.44 

1. 19 

3-12 

4.0 

1. 19 

1. 410 

0.170 

1.6 

1. 17 

I.I 

0.20 

0.41 

0.21 

0.44 

1. 31 

3.22 

*  Rearranged  from  Pocket  Companion,  Carnegie  Steel   Company,  Pittsburgh,  Pa. 
See  "Note"  with  Table  IV,  pge  354. 

t  These  values  make  r  the  same  for  both  axes. 


360 


Properties  of  ^Structural  Shapes,  etc. 


Chap.  10 


Tftble  IX.*    Dimensions  of  Sections  and  Weights  of  Small  Grooved  Steel 
Channels 


Section- 

Si?eof 

Width  of 

Thickness  of 

Weight  per 

-'■• 

index 

section, 

flange. 

web. 

foot. 

in 

in 

in 

lb 

C-i«4 

2% 

me 

M 

2. 55 

C-165 

2H 

H 

Me 

2.09 

C-166 

2% 

iHe 

H 

1.63 

C-183 

2 

H 

H 

2.11 

C-184 

2 

Me 

Me 

1.68 

:'    '^^" 

C-18S 

2 

H 

H 

1.26 

C-190 

1% 

iHe 

Me 

1. 71 

iT' 

C-191 

iH 

H 

H 

1.33 

S 

C-193 

iM 

'H2 

^^2 

1.33 

C-I9S 

m 

H 

\^ 

0.96 

C-197 

m 

H 

Me 

1-47 

'  '  ■■', 

C-199 

iH 

H 

^^ 

0.93 

C-200 

iH 

Yie 

Me 

1. 12 

}{-' 

C-203 

I 

H 

^ 

0.83 

A 

C-207 

I 

^U 

H 

0.71 

C-213 

H 

Me 

H 

0.66 

■  i 

C-217 

H 

H 

H 

0.58 

C-219 

H 

H 

H 

0.54 

C-2JH 

H 

^2 

H2 

0.40 

C-aa3 

H 

Me 

H 

0.43 

•  IloUed  by  the  Jones  &  Laughlin  Steel  Company,  Pittsburgh,  Pa. 


Properties  of  Structural  Shapes,  etc. 


M 


Table  X.    Sizes  and  Makes  of  Rolled  Steel  Angles 

The  following  table  has  been  compiled  to  show  angles  of  various  sizes  rolled  by 
different  companies.  The  word  "all"  indicates  that  angles  of  the  sizes  mentioned  are 
rolled  by  all  the  companies  included  in  the  list.  The  abbreviations  refer  to  the 
following  companies:  Cam.,  Cambria  Steel  Company;  Car.,  Carnegie  Steel  Com- 
pany; J.  &  L.,  Jones  &  Laughlin  Steel  Company. 


Angles  with  unequal  legs 

Angles 

with  equal  legs 

Sizes  in  inches 

Companies 

Sizes  in  inches 

Companies 

8    X6 

Cam.  and  Car. 

8 

X8 

All 

8    X3H 

Car. 

6 

X6 

All 

7     XsVi 

All 

5 

XS 

All                        :       '] 

•ii 

6    X4 

All 

4\iX4l 

i 

Cam.                        , -J 

jF 

6    X3K2 

All 

4     X4 

AU                           ftvl 

5     X4 

All 

3l'^X3^/ 

i 

AU            ;;.s 

/ 

5    Xal'i 

All 

3HX3^ 

i  . 

J.&L. 

5     X3 

All 

3     X3 

AU 

4^/^X3 

Car.  and  J.  &  L. 

2%X25 

i 

Cam.  and  J.  &  L. 

!: 

4     X3J'i 

All 

2'/^X2^ 

i 

All 

4     X3 

All 

2^X2^ 

i 

Cam.  and  J.  &  L. 

33^^X3 

All 

2      X2 

All 

3^/2X2!^^ 

All 

iHXi^, 

i 

AU 

l 

3^X2 

J.&L. 

iJ'^Xi^/ 

i 

All 

{^ 

3HXi^^ 

J.&L. 

1%XI3/ 

i 

J.&L. 

i' 

3     X2K2 

All 

iMXi'/ 

i 

AU 

i 

3     X2 

All 

1^6  Xl? 

U 

J.&L. 

\ 

2>.^X2 

All 

I    Xi 

AU 

2l/^Xl% 

J.&L. 

HX  ? 

i 

J.  &  L. 

2Hxiy2 

Car.  and  J.  &  L. 

2i/iXiH 

Cam. 

■ 

% 

2MXIH 

J.&L. 

V 

2HX1H 

Car.  and  J.  &  L. 

t 

2      XlH 

Car.  and  J.  &  L. 

t 

2    XiH 

J.&L. 

s 

2    XiH 

Car. 

2      Xl 

J.&L. 

iHXiH 

J.&L. 

iHXi'A 

Car. 

iMXiH 

J.&L. 

ii'^XiH 

Car. 

iJ'^Xi 

J.&L. 

mx  n 

J.&L. 

I    X^He 

J.&L. 

I    X  H 

J.&L. 

362 


Properties  of  Structural  Shapes,  etc.  Chap.  10 

Table  XI.*     Properties  of  Angle-Sections.     Unequal  Legs. 


r-3 


;...jpo  i> 

.?iv/  r;  >i;4f)/,         Jl 

N 

■-'■ 

A  li.j;}>;>ji>' 

Axis 

i-i 

Axis  2-2 

Axis 

Weight 

Area 

3-3 

Size 

per 

of 

foot 

section 

I 

r 

I/c 

X 

I 

r 

I/c 

y 

^'inin 

in 

lb" 

sqin 

in* 

in 

in3 

in 

in* 

in 

in3 

in 

in 

8X6    Xi 

44.2   ; 

13.00 

80.8 

2.49 

15. 1 

2.65 

38.8 

1.73 

8.9 

1.65 

1.28 

8X6    X.^Me 

41.7 

12.25 

76.6 

2.50 

14.3 

2.63 

36.8 

1.73 

8.4 

1.63 

1.28 

8X6    XH 

39. i 

11.48. 

72.3 

.2.51 

13.4 

2.61 

34.9 

1.74 

7.9 

1. 61 

1.28 

8X6    XI 3/16 

36.5 

•10.72 

67.9 

2.52 

12.5 

2.59 

32.8 

1.75 

7.4 

1-59 

i.29 

8X6    XM    • 

33.8 

9-94 

63.4 

2.53 

II. 7 

2.56 

30.7 

1.76 

6.9 

1.56 

1.29 

8X6  .  X"/i6 

31.2 

9-15 

58.8 

2.54 

10.8 

2.54 

28.6 

1.77 

6.4 

1.54 

1.29 

8X6    XH   , 

28. 5 

8.36 

54.1 

2.54 

9-9 

2.52 

26.3 

1.77 

5.9 

1.52 

r.30 

8X6    X?i6 

25.7 

7.56 

49-3 

'2.55 

8.9 

2.50 

24.0 

1.78 

5.3 

1.50 

.r.30 

8X6    X\^ 

23.0 

6.75 

44.3 

2.56 

8.0 

2.47 

21.7 

1.79 

4.8 

1.47 

1.30 

8X6    XMe 

20.2   ' 

S-93 

39.2 

2.57 

7.1 

2.45 

19-3 

1.80 

4.2 

1. 45 

1.30 

8X3>^Xi 

35.7 

10.50 

66.2 

'2. SI 

13.7 

3.17 

7.8 

0.86 

3.0 

0.0? 
0.89 

0.73 

i8>«3HX-'-M6 

33.7 

990 

62.9 

2.52 

12.9 

3.14 

7-4 

0.87 

2.9 

C).73 

31  ..7 

;    Q-30 

59.4 

2.53 

12.2 

3.12 

7-1 

0.87 

2.7 

0.87 

0.73 

SXs^/^X^Me 

29.6 

8.68 

■55.9 

2.54 

II. 4 

3.10 

6.7 

0.88 

2.5 

0.8s 

0.73 

'  8X3^X3/4 

27.5 

8.06 

52.3 

^2.55 

10.6 

3.07 

6.3 

0.88 

2.3 

0.82 

0.73 

i  8X3ViXiM6 

2SJ3 

7.43 

48. 5 

2.56 

9-8 

3.05 

5.9 

0.89 

2.2 

0.80 

0.73 

;  8X3HXH 

23.2 

0.80 

44.7 

2.57 

9.0 

3.03 

S.4 

0.90 

2.0 

0.78 

0.74 

8X3HXri6 

21.0 

^•15 

40.8 

2.57 

8.2 

3.00 

5.0 

0.90 

1.8 

0.75 

0.74 

,  8X3^/^XH 

18.7 

^.50 

36.7 

2.58 

7.3 

2.98 

4.5 

o'.gi 

1.6 

0.73 

0.74 

1  8X31-^X^6 

16.5 

4.84 

32.5 

2.59 

6.4 

2.95 

4,1 

0.92 

1.5 

0.70 

0.74 

7X3HXI 

32.3 

Q.SO 
$•97 

45.4 

2.19 

10.6 

2v7^ 

■b'-3 

0.89 

•3.0 

0.96 

0.74 

7X3HXIM6 

30.5 

43.1 

2.19 

10. 0 

2.69 

7.2 

b.89 

'  2.8 

0.94 

0.74 

7X3^/^X7/^ 

28.7 

$.42 

40.8 

2.20 

9.4 

2.66 

6.8 

0.90 

2.6 

0.91 

Q.74 

1  iXz^AX^U 

26.8 

7.87 

38.4 

2.21 

8.8 

2.64 

6.5 

0.91 

-  2.5 

0.89 

D.74 

\  iXzViXH 

24.9 

7.31 
§•75 

36.0 

2.22 

8.2 

2.62 

6.1 

0.91 

i  2.3 

Q.87 

0.74 

1  7X31^^X11/16 

23.0 

33.5 

2.23 

7.6 

2.60 

5.7 

0.92 

2.1 

0.85 

0.74 

■  7X3HX)^ 

21.0 

fi7 

30.9 

2.24 

7.0 

2.57 

5-3 

0.93 

2.0 

0.82 

6.75 

;  ixz\^xy\% 

191 

3-59 

28.2 

2.25 

6.3 

2.55 

4.9 

0.^3 

1.8 

0.80 

0.75 

:  7X3^^X1^^ 

17.0 

5.00 

25.4 

2.25 

5.7 

2.53 

4.4 

0.94 

1.6 

oi.78 

0.75 

'  7X3V^XM6 

iS.o 

4.40 

22.6 

2.26 

5.0 

2.50 

4.0 

0.9s 

0.§0 

'  1.4 

0.7s 

0.76 

7X3HXH 

13.0 

4.80 

19.6 

2.27 

4.3 

2.48 

3.5 

!    ^-3 

,Q.73 

p.  76 

6X4    Xi 

30.6 

i.oo 

S.50 

30.8 

1.85 

8.0 

2.17 

10.8 

':l:<>9 

'3.8 

i^-X7 

b.85 

•  6X4    XI  Me 

28.9 

293 

1.86 

7.6 

2.14 

10.3 

i.io 

•    3.6 

-i.i^ 

b.85 

L6X4    Xli. 

27-2 

...JZ..8S.-. 

27.7 

1.86 

7^2 

2-12 

9..& 

^  I .  u 

3-A~ 

1.12 

_o,afi« 

6X4    XI  Me 

25.4 

7.47 

26.1 

1.87 

6.7 

2.10 

9.2 

I. II 

3.2 

I.IO 

0.86 

6X4    XH 

23.6 

6.94 

245 

1.88 

6.2 

2.08 

8.7 

1. 12 

3.0 

1.08 

0.86 

6X4    XI  He 

21.8 

6.40 

22.8 

1.89 

5.8 

2.06 

8.1 

1. 13 

2.8 

1.06 

0.86 

6X4    X^/i 

20.0 

5.86 

21. 1 

1.90 

5.3 

2.03 

7.5 

1. 13 

2.5 

1.03 

0.86 

6X4    XMe 

18. 1 

5.31 

19-3 

1.90 

4.8 

2.01 

6.9 

1. 14 

2.3 

1. 01 

0.87 

6X4     XH 

16.2 

4.75 

17.4 

1. 91 

4.3 

1-99 

6.3 

1. 15 

2.1 

0.99 

0.87 

6X4    XMe 

14.3 

4.18 

15.5 

1.92 

3.8 

1.96 

5.6 

1. 16 

1.8 

0.96 

0.87 

6X4    XH 

12.3 

3.61 

13. 5|   1.93 

3.3 

1.94 

4.9 

1. 17 

1.6 

0.94 

0.88 

See  "  Note  "  with  Table  IV,  page  354. 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh, 


Pa. 


Properties  of  Structural  Shapes,  etc. 


m 


Table  XI  *  (Continued).     Properties  of  Angle-Sections.     Uaequal  Le^g 
,1 


H! 

2^ 


i. 
tfc 


-r-3 


11  ^3 


Size 


6X3M2X1 

6X3'/2XiM6 

6X3V^X7/6 

6X3HXIM6 

6X3K2X% 

6X3'/2XiM6 

6X3HXH 

6X3V2Xri6 

6X3V2XK2 

6X3V'2XM6 

6X3V2X34 

6X3}'2X5/i6 

5X4  Xli 

5X4  X'Vis 

5X4  X3/i 

5X4  XI  He 

5X4  XH 

5X4  XMe 

5X4  XH 

5X4  XMo 

5X4  X3/^ 

5X3^/^X^4 

5X3V^XJM6 

5X3^/^X^4 

5X3l'^XiH6 

5X3M2XH 

5X3M2XM6 

5X3^/2X1/2 

5X3^2X^1 6 

5X3/2  X"H 

5X3HXM6 

5X3  X^Mo 

SX3  XH 

5X3  X^Vie 

5X3  X5^ 

5X3  X^ifl 

5X3  XH 

5X3  XMe 

5X3  X% 

5X3  XMa 


Weight 
per 
foot 


lb 


28.9 
27.3 
'25.7 
24.0 
22.4 
20.6 
18.9 
17. 1 
15.3 
13.5 
II. 7 
9.8 

24.2 
22.7 
21. 1 
19-5 
17.8 
16.2 
14.5 
12.8 

11. 0 

22.7 
21.3 
19-8 
18.3 
16.8 
15.2 
13.6 
12.0 
10.4 
8.7 

19.9 
18.5 

17. 1 
15.7 
14.3 
12.8 
II. 3 

9.8 
8.2 


Area 

of 

section 


8.50 
8.03 
7.55 
7.06 
6.56 
6.06 
5.55 
5.03 
4.50 
3.97 
3.42 
2.87 

711 
6.65 
6.19 
5-72 
5.23 
4.75 
4.25 
3.75 
3.23 

6.67 

6.25 
5.81 
5-37 
4.92 
4.47 
4.00 
3.53 
3.05 
2.56 

5:84 
5.44 
5.03 
4.61 
4.18 
3.75 
3-31 
2.86 
2.40 


Axis  i-i 


29.2 
,27.8 
26.4 
24.9 
23.3 
21.7 
20.1 
18.4 
16.6 
14.8 
12.9 

10,  Q 

16.4 
15.5 
14.0 
13.6 
12.6 

II. 6 
10.5 
9-3 
8.1 

15.7 
14.8 
13.9 
13.0 
12.0 

II. o 
lO.O 

8.9 
7.8 

6.6 

14.0 
13.2 
12.3 
II. 4 
10.4 
9-5 
8.4 
7.4 
6.3 


I/c 


1.89 


7.8 

7-4 

7.0 

6.6 

6.1 

5.6 

.90   5.2 

.91    4.7 

.92    4.2 

1.93!  3.7 

1.94  3-3 

1.95  2.7 

1.52  50 

1.53  4.7 


1.54 
1.54 
1.55 
1.55 
1.57 
1.58 
1. 59 

1.53 

1.54 

1.5 

1.56 

1.56 

1.57 

1.58 

1-59 

1.60 

1. 61 

1.55 
1.55 
1.56 
1.57 
1.58 
1.59 
1.60 
1. 61 
1. 61 


4.4 
4.1 
3-7 
3-4 
3-1 
2.7 
2.3 

4-9 

4.6 
4-3 
4.0 
3.7 
3  3 
3.0 
2.6 
2.3 
19 

45 
4.2 
3-9 
3-5 
3-2 
2.9 
2.6 
2.2 
1-9 


2.26 

2.24 

2.22 

2.20 

2.18 

2.15 

2.13 

2 

2.aS 

2.06 

2.04 

2.01 

1. 71 

1.6 

1.66 

1.64 

1.62 

1.60 

1.57 

1.55 

1.53 

1.79 
1.77 
1.75 
1.72 
1.70 
1.63 
1.66 
1.63 
1. 61 
1.59 

1.8 

1.8 

1.82 

1.80 

1.77 

1.75 

1.73 

1.70 

1.68 


Axis  2-2 


I/c 


0.92 
0.93 
0.93 
0.94 
0.94 
0.95 
0.96' 
0.96I 
0.971 
0.981 
0.99: 
1. 00 

1. 14 

1. 15 
1.15 

1. 16 

1. 17 

1. 18 
1. 18 
119 
1.20 

0.9') 
0.97 
0.9S 
0.98 
0.99 
1. 00 


1.02 
1.03 

0.80 
0.80 
0.81 
0.81 
0.82 
0.83 
0.84 
0.84 
0.85 


2.9 

1. 01 

2.7 

0.99 

2.6 

0.97 

2.4 

0.95 

2.3 

0.93 

2.1 

0.90 

1.9 

0.88 

1.8 

0.86 

1.6 

0.83 

1.4 

0.81 

1.2 

0.79 

I.O 

0.76 

3.3 

1. 21 

3.1 

1. 18 

2.9 

1. 16 

2.7 

1.14 

2.5 

1. 12 

2.3 

I.  10 

2.0 

1.07 

1.8 

1.05 

i.b 

1.03 

2.5 

1.04 

2.4 

1.02 

2.2 

1. 00 

2.1 

0.97 

19 

0.95 

1.7 

0.93 

1.6 

0.91 

1.4 

0.88 

1.2 

0.86 

1.0 

0.84 

1.7 

0.86 

1.6 

0.84 

1.5 

0.82 

1.4 

0.80 

1.3 

0.77 

I.I 

0.75 

1.0 

0.73 

0.8Q 

0.70 

0.75 

0.68 

See  "  Note  "  with  Table  IV,  page  354. 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


364 


Properties  of  Structural  Shapes,  etc. 


Chap. 


Table  XI*  (Continued).    Properties  of  Angle-Sections.     Unequal  Legs 


K 


1 
I 


:x: 


ii       ^3 


y 


I 

Weight 

Area 

Axis  i-i 

[  Axis  2-2 

Axis 
3-3 

Size 

foot 

of 

section 

I 

r 

I/c 

X 

I 

r 

1/c 

y 

fwm 

in 

lb 

sq  in 

in* 

in 

in3 

in 

in* 

in 

in3 

in 

in 

4^12X3    X^Me 

18.5 

5.43 

10.3 

1.38 

3.6 

1.65 

3.6 

0.81 

1-7 

0.90 

0.64 

4K2X3    XH 

17.3 

5. 06 

9-7 

1.39 

3.4 

1.63 

3.4 

0.82 

1.6 

0.88 

0.64 

4K2X3    XI  He 

16.0 

4.68 

91 

1.39 

3.1 

1.60 

3.2 

0.83 

1.5 

0.85 

0.64 

a\^X3    XH 

14.7 

4.30 

8.4 

1.40 

2.9 

1.58 

3.0 

0.83 

1.4 

0.83 

0.64 

4K2X3    XYie 

13.3 

3.90 

7.8 

1. 41 

2.6 

1.56 

2.8 

0.85 

1.3 

0.81 

0.64 

4K2X3    XH 

II. 9 

3.50 

7.0 

1.42 

2.4 

1. 54 

2.5 

0.85 

i-.i 

0.79 

0.65 

4}^iX3    XVie 

10.6 

3.09 

6.3 

1.43 

2.1 

1. 51 

2.3 

0.85 

1.0 

0.76 

0.65 

4K2X3    X% 

9.1 

2.67 

55 

1.44 

1.8 

1.49 

2.0 

0.86 

0.88 

0.74 

0.66 

4K2X3    XMc 

7.7 

2.25 

4.7 

1.44 

1.5 

1.47 

1.7 

0.87 

0.75 

0.72 

0.66 

4    X3'/^XiM6 

18.5 

5.43 

7.8 

1. 19 

2.9 

1.36 

5-5 

1. 01 

2.3 

1. 11 

0.72 

4    X3HX-)4 

17.3 

5.06 

7.3 

1.20    2.8 

1.34 

5.2 

1. 01 

2.1 

1.09 

0.72 

4     X3K2XIH6 

16.0 

4.68 

6.9 

1. 21    2.6 

1.32 

4.9 

1.02 

2.0 

1.07 

0.72 

4     X3HXH 

14.7 

4.30 

6.4 

1.22,  2.4 

1.29 

4.5 

1.03 

1.8 

1.04 

0.72 

4     X3K2XM6 

13.3 

3.90 

5-9 

1.23,    2.1 

1.27 

4.2 

1.03 

1.7 

1.02 

0.72 

4     X3HX3'^ 

II. 9 

3.50 

53 

I. 231   1.9 

1.25 

3.8 

1.04 

1.5 

1. 00 

0.72 

4     X3HX716 

10.6 

3.09 

4.8 

1.24 

1.7 

1.23 

3.4 

1.05 

1.3 

0.98 

0.72 

4     X3HXH 

9.1 

2.67 

4.2 

1.25 

1.5 

1. 21 

3.0 

1.06 

1.2 

0.96 

0.73 

4     X3}'^XM6 

7.7 

2.25 

3.6 

1.26 

1.3 

1. 18 

2.6 

1.07 

1.0 

0.93 

0.73 

4     X3     XI  Me 

17. 1 

5.03 

7.3 

1. 21 

2.9 

1.44 

3.5 

0.83 

1.7 

0.94 

0.64 

4     X3     XM 

16.0 

4.69 

6.9 

1.22 

2.7 

1.42 

3.3 

0.84 

1.6 

0.92 

C.64 

4     X3     X^Me 

14.8 

4.34 

6.5 

1.22 

2.5 

1.39 

3.1 

0.84 

1.5 

0.89 

0.64 

4    X3    X% 

13.6 

3.98 

6.0 

1.23 

2.3 

1.37 

2.9 

0.8s 

1.4 

0.87 

0.64 

4    X3    XMe 

12.4 

3.62 

5.6 

1.24 

2.1 

1.35 

2.7 

0.86 

1.2 

0.85 

0.64 

4    X3    XH 

II. I 

3.25 

5.0 

1.25 

1.9 

1.33 

2.4 

0.86 

I.I 

0.83 

0.64 

4    X3    XMe 

9.8 

2.87 

4.5 

1. 25 

1.7 

1.30 

2,2 

0.87 

1.0 

0.80 

0.64 

4     X3     XH 

8.5 

2.48 

4.0 

1.26 

1.5 

1.28 

1-9 

0.88 

0.87 

0.78 

0.64 

4    X3     XMe 

7.2 

2.09 

3.4 

1.27 

1.2 

1.26 

1.7 

0.89 

0.74 

0.76 

0.65 

4    X3     XH 

5.8 

1.69 

2.8 

1.28 

I.O 

1.24 

1.4 

0.89 

0.60 

0.74 

0.65 

3HX3    XiMe 

15.8 

4.62 

5.0 

1.04 

2.2 

1.23 

3.3 

0.85 

1.7 

0.98 

0.62 

3HX3    X)4 

14.7 

4.31 

4.7 

1.04 

2.1 

1. 21 

3.1 

0.85 

1.5 

0.96 

0.62 

3HX3    XI  He 

13.6 

4.00 

4.4 

1.05 

1-9 

I.I9 

.3.0 

0.86 

1.4 

0.94 

0.62 

3HX3    XH 

12.5 

3.67 

4.1 

1.06 

1.8 

1. 17 

2.8 

0.87 

1.3 

0.92 

0.62 

3HX3    XMe 

II. 4 

3.34 

3.8 

1.07 

1.6 

1. 15 

2.5 

0.87 

1.2 

0.90 

0.62 

3HX3    XH2 

10.2 

3.00 

3.5 

1.07 

1.5 

1. 13 

2.3 

0.88 

I.I 

0.88 

0.62 

3HX3     XHe 

9.1 

2.65 

3.1 

1.08 

1.3 

1. 10 

2.1 

0.89 

0.98 

0.85 

0.62 

3^/^X3     XH 

7.9 

2.30 

2.7 

1.09 

I.I 

1.08 

1.8 

0.90 

0.85 

0.83 

0.62 

3V^X3     XMe 

6.6 

1.93 

2.3 

1. 10 

0.96 

1.06 

1.6 

0.90 

0.72 

0.81 

0.63 

3ViX3    XH 

5.4 

1.56 

1-9 

I. II 

0.78 

1.04 

1.3 

0.91 

0.58 

0.79 

0.63 

3^/^X21/4X1  Me 

12.5 

3.6s 

4.1 

1.06 

1-9 

1.27 

1.7 

0.69 

0.99 

0.77 

0.53 

3HX2H2XH 

II. 5 

3.36 

3.8 

1.07 

1.7 

1.25 

1.6 

0.69 

0.92 

0.75 

0.53 

3HX2HXM6 

''10.4 

3.06 

3.6 

1.08 

1.6 

1.23 

1.5 

0.70 

0.84 

0.73 

0.53 

3l^X2HXH 

9-4 

2.75 

3.2 

1.09 

1.4 

1.20 

1.4 

0.70 

0.76 

0.70 

0.53 

3V4X2HXH6 

8.3 

2.43 

2.9 

1.09 

1.3 

1. 18 

1.2 

0.71 

0.68 

0.68 

0.54 

3l'4X2HXH 

7.2 

2. II 

2.6 

1. 10 

I.I 

1. 16 

I.I 

0.72 

0.59 

0.66 

0.54 

3HX2HXM6 

6.1 

1.78 

2.2 

I. II 

0.93 

1. 14 

0.94 

0.73 

0.50 

0.64 

0.54 

3HX2HXV4. 

4.9 

1.44 

1.8 

1. 12 

0.75 

I. II 

0.78 

0.74 

0.41 

0.61 

0.54 

See  "  Note  "  with  Table  IV,  page  354. 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Properties  of  Structural  Shapes,  etc. 


365 


Table  XI*  (Continued).     Properties  of  Angle-Sections.     Unequal  Legs 


->t 


Weight 

Area 

Axis  i-i 

Axis  2-2 

Axis 
3-3 

Size 

foot 

of 

section 

/ 

r 

I/c 

X 

I 

r 

I/c 

y 

in 

^-min 

in 

lb 

sq  in 

in4 

in 

in» 

in 

in\ 

in 

in3 

in 

3    X2HXM6 

9.5 

2.78 

2.3 

0.91 

1.2 

1.02 

1.4 

0.72 

0.82 

0.77 

0.52 

3    X2i/2Xi/i 

8.5 

2.50 

2.1 

0.91 

i.o 

1. 00 

1.3 

0.72 

0.74 

0.75 

0.52 

3     X2K2XM6 

7.6 

2.21 

1.9 

0.92 

0.93 

0.98 

1.2 

0.73 

0.66 

0.73 

0.52 

3      X2K2X3/^ 

6.6 

1.92 

1.7 

0.93 

0.81 

0.96 

1.0 

0.74 

0.58 

0.71 

0.52 

3     X2I/2XM6 

5.6 

1.62 

1.4 

0.94 

0.69 

0.93 

0.90 

0.74 

0.49 

0.68 

0.53 

3    X2i^iXH 

4-5 

1. 31 

1.2 

0.95 

0.56 

0.91 

0.74 

0.75 

0.40 

0.66 

0.53 

3    X2    XH 

7.7 

2.25 

1-9 

0.92 

I.O 

1.08 

0.67 

0.55 

0.47 

0.58 

0.43 

3    X2    XIU 

6.8 

2.00 

1-7 

0.93 

0.89 

1.06 

0.61 

0.55 

0.42 

0.56 

0.43 

3    X2     XVs 

5.9 

1.73 

1.5 

0.94 

0.78 

1.04 

0.54 

0.56 

0.37 

0.54 

0.43 

3    X2     XMo 

5.0 

1.47 

1.3 

0.95 

0.66 

1.02 

0.47 

0.57 

0.32 

0.52 

0.43 

3    X2    XK 

4.1 

1. 19 

I.I 

0.95 

0.54 

0.99 

0.39 

0.57 

0.2s 

0.49 

0.43 

21/2X2    XH 

6.8 

2.00 

I.I 

0.75 

0.70 

0.88 

0.64 

0.56 

0.46 

0.63 

0.42 

25.^X2    XVia 

6.1 

1.78 

I.O 

0.76 

0.62 

0.85 

0.58 

0.57 

0.41 

0.60 

0.42 

2l/^X2      X% 

5.3 

1.55 

0.91 

0.77 

0.55 

0.83 

0.51 

0.58 

0.36 

0.58 

0.42 

21/2X2    XM6 

4.5 

1. 31 

0.79 

0.78 

0.47 

0.81 

0.45 

0.58 

0.31 

0.56 

0.42 

2I/2X2    XH 

3.62 

1.06 

0.65 

0.78 

0.38 

0.79 

0.37 

0.59 

0.25 

0.54 

0.42 

2I/2X2    XVm 

2.7s 

0.81 

0.51 

0.79 

0.29 

0.76 

0.29 

0.60 

0.20 

0.51 

0.43 

2M2X2    XH 

1.86 

0.55 

0.35 

0.80 

0.20 

0.74 

0.20 

0.61 

0.13 

0.49 

0.43 

2l/4Xl3'^2XM6 

3.92 

1. 15 

0.71 

0.79 

0.44 

0.90 

0.19 

0.41 

0.17 

0.40 

0.32 

2l.^Xl'/2XH 

3.19 

0.94 

0.59 

0.79 

0.36 

0.88 

0.16 

0.41 

0.14 

0.38 

0.32 

2Hxiy2xyi6 

2.44 

0.72 

0.46 

0.80 

0.28 

0.85 

0.13 

0.42 

O.II 

0.35 

0.33 

2HXiy2XH 

5.6 

1.63 

0.7s 

0.68 

0.54 

0.86 

0.26 

0.40 

0.26 

0.48 

0.32 

2Hxiy2XVi6 

5.0 

1.45 

0.68 

0.69 

0.48 

0.83 

0.24 

0.41 

0.23 

0.46 

0.32 

2Hxiy2x% 

4.4 

1.27 

0.61 

0.69 

0.42 

0.81 

0.21 

0.41 

0.20 

0.44 

0.32 

2HXiViX^i6 

3.66 

1.07 

0.53 

0.70 

0.36 

0.79 

0.19 

0.42 

0.17 

0.42 

0.32 

2MXIK2XH 

2.98 

0.88 

0.44 

0.71 

0.30 

0.77 

0.16 

0.42 

0.14 

0.39 

0.32 

2HXIHXM6 

2.28 

0.67 

0.34 

0.72 

0.23 

0.75 

0.12 

0.43 

O.II 

0.37 

0.33 

2      Xl3'^2XH 

3.99 

1. 17 

0.43 

0.61 

0.34 

0.71 

0.21 

0.42 

0.20 

0.46 

0.32 

2      X1K2XM6 

3.39 

1. 00 

0.38 

0.62 

0.29 

0.69 

0.18 

0.42 

0.17 

0.44 

0.32 

2    XiHXH 

2.77 

o.8r 

0.32 

0.62 

0.24 

0.66 

0.15 

0.43 

O.I< 

0.41 

0.32 

2      X1K2XM6 

2.12 

0.62 

0.25 

0.63 

0.18 

0.64 

0.12 

0.44 

O.II 

0.39 

0.32 

2      XlK2Xj'i 

1.44 

0.42 

0.17 

0.64 

0.13 

0.62 

0.09 

0.45 

0.08 

0.37 

0.33 

2    XiHXH 

2.55 

0.75 

0.30 

0.63 

0.23 

0.71 

0.09 

0.34 

O.IO 

0.33 

0.27 

2      X1K4XM6 

1.96 

0.57 

0.23 

0.64 

0.18 

0.69 

0.07 

0.35 

0.08 

0.31 

0.27 

i3/4XiHXH 

2.34 

0.69 

0.20 

0.54 

0.18 

0.60 

0.09 

0.35 

O.IO 

0.35 

0.27 

i3/4XiV4XM6 

1.80 

0.53 

0.16 

0.55 

0.14 

0.58 

0.07 

0.36 

0.08 

0.33 

0.27 

i^4XiHXi/^ 

1.23 

0.36 

O.II 

0.56 

0.09 

0.56 

0.05 

0.37 

0.05 

0.31 

0.27 

1HXIHXM6 

2.59 

0.76 

0.16 

0.45 

0.16 

0.52 

O.IO 

0.35 

O.II 

0.40 

0.26 

IM2XIMXM 

2.13 

0.63 

0.13 

0.46 

0.13 

0.50 

o.c8 

0.36 

0.09 

0.38 

0.26 

iHXiHXMe 

1.64 

0.48 

O.IO 

0.46 

O.IO 

0.48 

0.07 

0.37 

0.07 

0.35 

0.26 

See  "  Note  "  with  Table  IV,  page  354. 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


366  Properties  of  Structural  Shapes,  etc.  Chap.  10 

Table  Xn.*    Properties  of  Angle-Sections.    Equal  Legs 


\ 


:~^'" 


Weight 

Area 

A 

xis  i-i  and  Axis  2 

-2 

Axis  3-3 

Size 

of      - 
section  • 

per 
foot 

I 

r 

J/c 

X 

rmin 

in 

lb 

sq  in 

in^ 

in 

inS 

in 

in 

8X8X1H 

56.9 

16.73 

98.0 

2.42 

17-5 

2.41 

1. 55 

8X8X1M6 

54.0 

15,87 

9i 

5 

2.43 

16.7 

2.39 

1.56 

8X8X1 

51.0 

15,00 

89 

0 

2.44 

IS. 8 

2.37 

1.56 

8X8X»M6 

48.1 

14,12 

84 

3 

2.44 

14.9 

2.34 

1.56 

8X8X7/^ 

45.0 

13.23 

79 

6 

2.45 

14.0 

2.32 

1.56 

8X8X^1  a 

42.0 

12.34 

74 

7 

2.46 

13. 1 

2.30 

1-57 

8X8X^4 

38.9 

11.44 

69 

7 

2.47 

12.2 

2.28 

1.57 

8X8X^18 

3S.8 

10.53 

64 

6 

2.48 

JI.3 

2. 23 

1.5a 

8X8XH 

32.7 

9.61 

59 

4 

2.49 

10.3 

a. 23 

1.58 

8X8X^6 

29.6 

8.68 

54 

I 

2.50 

11 

a. 21 

i-sa 

8X8XH 

26.4 

7.73 

48 

6 

2.51 

2.19 

1.5a 

6X6X1 

37.4 

11.00 

35.5 

1.80 

8.6 

1.86 

I.l6 

6X6X^^6 

3S.3 

10.37 

33.7 

1.80 

8.1 

1.84 

1. 16 

6X6X^/6 

•   33.1 

9-73 

31.9 

I.8i 

7.6 

1.82 

1. 17 

6X6X^^6 

31.0 

9.09 

30.1 

1.83 

7. a 

1. 80 

1. 17 

6X6X^4 

28.7 

8.44 

28.3 

1.83 

6.7 

1.78 

I  17 

6X6X1 H6 

26.S 

7.78 

26.2 

1.83 

6.3 

1.7S 

1. 17 

6X6XH 

24.2 

7.11 

24.2 

1.84 

5-7 

1.73 

1. 17 

6X6X916 

21.9 

6.43 

22.1 

1. 85 

S.I 

1. 71 

1. 18 

6X6x1/2 

19.6 

5-75 

19.9 

1.86 

4.6 

1.68 

1. 18 

6X6X^16 

17.2 

S.06 

17.7 

•  1.87 

4.1 

1.66 

1. 19 

6X6XH 

14.9 

4.36 

15.4 

1.88 

3.5 

1.64 

1. 19 

SXSXI 

30.6 

900 

19.6 

1.48 

5.8 

1. 61 

0.96 

5X5X1^6 

28.9 

8.50 

18.7 

1.48 

5.5 

1.59 

0.96 

5XSX^^ 

27.2 

7.93 

17.8 

1.49 

5.2 

1.57 

0.96 

SXsXme 

25. 4 

7.47 

16.8 

1.50 

4.9 

1.55 

0.97 

SXSXH 

23.6 

6.94 

15.7 

1.50 

4.5 

1.52 

0.97 

SXSX^VU 

21.8 

6.40 

14.7 

1. 51 

4.2 

1.50 

0.97 

SXSXH 

20.0 

5.86 

13.6 

1.52 

3.9 

1.43 

0.97 

SXsXVia 

18. 1 

5.31 

12.4 

1.53 

35 

1.46 

0.98 

SXSXH 

16.2 

4.7s 

II. 3 

1.54 

32 

1.43 

0.98 

5X5X^6 

14.3 

4.18 

10. 0 

1.55 

2.8 

1. 41 

0.98 

5X5XH 

12.3 

3.61 

8.7 

1.56 

2.4 

1.39 

0.99 

4X4XIM6 

19-9 

S.84 

8.1 

1. 18 

3.0 

1.29 

0.77 

4X4XM 

18.5 

5.44 

7.7 

1. 19 

2.8 

1.27 

0.77 

4X4X1  He 

17. 1 

5.03 

7.2 

1. 19 

2.6 

1.25 

0.77 

4X4XH 

15.7 

4.61 

6.7 

1.20 

2.4 

1.23 

0.77 

4X4X9i6 

14.3 

4.18 

6.1 

1. 21 

2.2 

1. 21 

0.78 

4X4X1/^ 

12.8 

3.7s 

5.6 

1.22 

2.0 

1. 18 

0.78 

4X4XM6 

II. 3 

3.31 

S.o 

1.23 

1.8 

1. 16 

0.78  . 

4X4XH 

9.8 

2.86 

4.4 

1.23 

1. 5 

1. 14 

0.79 

4X4XM6 

8.2 

2.40 

3.7 

1.24 

1.3 

1. 12 

0.79 

4X4XH 

6.6 

1.94 

3.0 

1.25 

i.o 

1.09 

0.79 

See  ' 


Note  "  with  Table  IV,  page  354. 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsbergh,  Pa, 


Properties  of  Structural  Shapes,  etc.  367 

Table  XII*  (Continued).    Properties  of  Angle-Sections.    Equal  Legs 


^ 


Weight 

Area 

Axis  i-i 

and  Axis  2 

-2 

Axis  3-3 

Size 

per 

of 

foot 

section 

I 

r 

I/c 

X 

ymin 

in 

lb 

sq  in 

in< 

in 

inS 

in 

in 

33'^X3K2X1^'16 

17. 1 

5.03 

5.3 

1.02 

2.3 

1. 17 

0.67 

3y2xmxH 

l6.o 

4.69 

S.o 

1.03 

2.1 

1.15 

0.67 

aHXaHx^Me 

14.8 

4.34 

4-7 

1.04 

2.0 

1. 12 

0.67 

aViXaJ'^xH 

13.6 

3.98 

4-3 

1.04 

1.8 

1. 10 

0.68 

3HX3K2X»/^6 

12.4 

3.62 

4.0 

I. OS 

1.6 

1.08 

0.68 

3y2Xiy2xy2 

II. I 

3.2s 

3.6 

1.06 

l.S 

1.06 

0.68 

3}'^X3K2XM6 

ti 

3.87 

3  3 

1.07 

1.3 

1.04 

0.68 

3VtX3'/2XH 

2.48 

a. 9 

1.07 

1.2 

1. 01 

0.69 

3VtX3K3XMQ 

7.3 

a. 09 

a. 5 

1.08 

0.98 

0.99 

0.69 

3'/2X3}'^XH 

5.8 

l:% 

a.o 

1.09 

0.79 

0.97 

0.69 

3    X3    XH 

J1.3 

a. 6 

0.88 

1.3 

0.98 

0.57 

3    X3    XMe 

10.4 

3.06 

2.4 

0.89 

1.3 

0.95 

0.58 

3    X3    X^^ 

It 

a. 75 

a. a 

0.90 

I.I 

0.93 

0.58 

3    X3    XMa 

3.43 

3.0 

0.91 

0.9s 

0.91 

o.s8 

3    X3    XH 

72 

2. II 

1.8 

0.91 

0.83 

0.89 

0.S8 

3    X3    XMa 

6.1 

1.78 

1. 5 

0.92 

0.71 

0.87 

0.59 

3    X3    XH 

4.9 

1.44 

J. 2 

0.93 

0.58 

0.84 

0.59 

2\^X2MX\'i 

7-7 

2.25 

1.2 

0-74 

0.73 

0.81 

0.47 

2MX2\iXlU 

6.8 

2.00 

i.i 

0.75 

o.6s 

0.78 

0.48 

2y2X2\^XH 

S.9 

1.73 

0.98 

0.75 

0.57 

0.76 

0.48 

2\hX2yixV\^ 

S.o 

1.47 

0.85 

0.76 

0.48 

0.74 

0.49 

2l/iX2>/^XH 

4. J 

1. 19 

0.70 

0.77 

0.39 

0.72 

0.49 

2HX2HXM6 

3.07 

0.90 

o.SS 

0.78 

0.30 

0.69 

0.49 

21/^X2^2X1/^ 

2.08 

0.61 

0.38 

0.79 

0.20 

0.67 

0.50 

2     X2     XTIe 

53 

1.56 

0.54 

0.59 

0.40 

0.66 

0.39 

2      X2      X3/i 

4.7 

1.36 

0.48 

0.59 

0.35 

0.64 

0.39 

2      X2      X5l6 

3.92 

I. IS 

0.42 

0.60 

0.30 

0.61 

0.39 

2      X2      XM 

3.19 

0.94 

0.35 

0.61 

0.2s 

0.59 

0.39 

2      X2      XMs 

2.44 

0.71 

0.28 

0.62 

0.19 

0.57 

0.40 

2      X2      XH 

1.6s 

0.48 

0.19 

0.63 

0.13 

0.55 

0.40 

i^XiMXMo 

4.6 

1.34 

0.35 

0.51 

0.30 

0.59 

0.33 

i3/4Xi3/4X^i 

3.99 

1. 17 

0.31 

0.51 

0  26 

0.57 

0.34 

i^XiMXMe 

3-39 

1. 00 

0.27 

0.52 

0.23 

0.55 

0.34 

iMXi%XH 

2.77 

0.81 

0.23 

0.53 

0.19 

0.53 

0.34 

lMXl3/4X3/i6 

2.12 

0.62 

0.18 

0.54 

0.14 

o.Si 

0.35 

i%Xi3/4XH 

1.44 

0.42 

0.13 

0  55 

O.IO 

0.48 

0.35 

ll/^XlK2X3/i 

3  35 

0.98 

0.19 

0.44 

0.19 

O.SI 

0.29 

iV^XiHXMe 

2.86 

0.84 

0.16 

0.44 

,0.16 

0.49 

0.29 

iHXiy2XH 

2.34 

0.69 

0.14 

0.45 

0.13 

0.47 

0.29 

iHXiHXria 

1.80 

0.53 

O.II 

0.46 

O.IO 

0.44 

0.29 

iHXii/^XH 

1.23 

0.36 

0.08 

0.46 

0.07 

0.42 

0.30 

iMXiHXMe 

2.33 

0.68 

0.09 

0.36 

O.II 

0.42 

0.24 

i^XiHXH 

1.92 

0.56 

0.08 

0.37 

0.09 

0.40 

0.24 

iMXiHX-Me 

1.48 

0.43 

0.06 

0.38 

0.07 

0.38 

0.24 

iHXiViXH 

1. 01 

0.30 

0.04 

0.38 

0.05 

0.3S 

0.25 

I    XI    XK 

1.49 

0.44 

0.04 

0.29 

0.06 

0.34 

0.19 

I      XI       XM6 

1. 16 

0.34 

0.03 

0.30 

0.04 

0.32 

0.19 

I    Xi    XH 

0.80 

0.23 

0.02 

0.31 

0.03 

0.30 

0.19 

See  "  Note  "  with  Table  IV,  page  354. 

?  From  Pocltet  Companionj  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


368  Properties  of  Structural  Shapes,  etc.  Chap.  10 

Table  Xin.*     Properties  of  T  Sections.     Flange  and  Stem  Equal 


iJ 


— 1 


Size 

Tir   •_i,+ 

Area 

Axis 

Flange 

Stem 

Minimum 
thickness 

per 
foot 

of 

sec- 
tion 

I 

r 

I/c 

X 

/ 

r 

I/c 

Flange 

Stem 

in 

in 

in 

in 

lb 

sqin 

in^ 

in 

in3 

in 

in< 

in 

in3 

6H 

6K2 

0.40 

0.4s 

19.8 

5. 80 

23-5 

2.01 

5.0 

1.76 

10. 1 

1.32 

3.1 

4 
4 

4 
4 

V2 

13.5 
10. 5 
II. 7 

3-97 
3.09 
3.44 

5.7 
4.5 
3.7 

1.20 
1. 21 
1.04 

2.0 
1.6 
i.S 

1. 18 
1. 13 
1.05 

2.8 
2.1 
1.9 

0.84 
0.83 
0.74 

1.4 
I.I 
I.I 

3 
3 

3V^2 

3 
3 

1.U 

3/i 

Me 

9.2 
9.9 

8.9 

2.68 
2.91 
2.59 

3.0 
2.3 
2.1 

1.05 
0.88 
0.89 

1.2 
I.I 

0.98 

1. 01 
0.93 
0.91 

1.4 
1.2 
1.0 

0.73 
0.64 
0.63 

0.81 
0.80 
0.70 

3 
3 

2\^ 

3 
3 

2\^ 

Me 

Me 

7.8 
6.7 
6.4 

2.27 
1-95 
i.87 

1.8 
1.6 

I.O 

0.90 
0.90 
0.74 

0.86 
0.74 
0.59 

0.88 
0.86 
0.76 

0.90 
0.75 
0.52 

0.63 
0.62 
0.53 

0.60 
0.50 
0.42 

2M 
2% 

2\h 
2M 

Me 
Vie 
H 

Me 
Me 

5.5 
4.9 
4.1 

1.60 
1.43 
1. 19 

0.88 
0.65 
0.52 

0.74 
0.67 
0.66 

0.50 
0.41 
0.32 

0.74 
0.68 
0.65 

0.44 
0.33 
0.25 

0.52 
0.48 
0.46 

0.35 
0.29 
0.22 

2 
2 

1% 

2 

2 

Me 
H 

Me 

4.3 

3.56 

3.09 

1.26 
1.05 
0.91 

0.44 
0.37 
0.23 

0.59 
0.59 
0.51 

0.31 
0.26 
0.19 

0.61 
0.59 
0.54 

0.23 
0.18 
0.12 

0.43 
0.42 
0.37 

0.23 
0.18 
0.14 

1^4 

H 
Me 

H 
Vie 

2.47 
1.94 
2.02 

0.73 
0.57 
0.59 

0.15 

O.II 

0.08 

0.45 
0.45 
0.37 

0.14 

O.II 
O.IO 

0.47 
0.44 
0.40 

0.08 
0.06 
0.05 

0.32 
0.32 
0.28 

O.IO 

0.08 
0.07 

Z 
I 

I 
I 

Me 
Me 

Me 
Me 

1. 59 
1.25 

0.89 

0.47 
0.37 
0.26 

0.06 
0.03 
0.02 

0.37 
0.29 
0.30 

0.07 
COS 
0.03 

0.38 
0.32 
0.29 

0.03 
0.02 

O.OI 

0.27 
0.22 
0.21 

0.05 
0.04 
0.02 

See  "Note"  with  Table  IV,  paf!;e  354. 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Properties  of  Structural  Shapes,  etc. 


369 


Table  XIV.*     Properties  of  T  Sections.     Flange  and  Stem  Unequal 

r 


^ 

Axis 

i-i 

Size 

Axis  2-2 

Weight 

Area 
of 

Minimum 

per 

" 

thickness 

foot 

sec- 

Flange 

Stem 

tion 

/ 

r 

I/c 

X 

in 

/ 

r 

I/c 

Flange 

Stem 

in 

in 

in 

in 

lb 

sq  in 

in* 

in 

in3 

in* 

in 

in' 

5 

3 

H 

1«%2 

II. 5 

3.37 

2.4 

0.84 

I.I 

0.76 

I3.9 

1. 10 

I..6 

5 

2^ 

Me 

10.9 

3.18 

1.5 

0.68 

0.78 

0.63 

4.1 

1. 14 

1.6 

A\^ 

3H 

Me 

iMe 

15.7 

4.60 

5.1 

1.05 

2.1 

I. II 

3.7 

0.90 

1.7 

4H    . 

3 

% 

3/^ 

9.8 

2.88 

2.1 

0.84 

0.91 

0.74 

3.0 

I  02 

1.3 

4H 

3 

Me 

Me 

8.4 

2.46 

1.8 

0.85 

0.78 

0.71 

2.5 

1. 01 

I.I 

4H 

iH 

% 

% 

9.2 

2.68 

12 

0.67 

0.63 

0.59 

3.0 

1.05 

1.3 

43^^ 

2H 

Me 

Me 

7.8 

2.29 

i.b 

0.68 

0.54 

0.57 

2.5 

1.05 

I.I 

4 

5 

3'^ 

1/^ 

15.3 

4.50 

10.8 

1-55 

3.1 

1.56 

2.8 

0.79 

1.4 

4 

5 

34 

3/i 

II.9 

3.49 

8.5 

1.56 

2.4 

1. 51 

2.1 

0.78 

I.I 

4 

4H 

^^ 

H 

14.4 

4.23 

7.9 

1.37 

2.5 

1.37 

2.8 

0.81 

1.4 

4 

4H 

% 

% 

II. 2 

3.29 

6.3 

1.39 

2.0 

1. 31 

2.1 

0.80 

I.I 

4 

3 

% 

H 

9.2 

2.68 

2.0 

0.86 

0.9c 

0.78 

2.1 

0.89 

I.I 

4 

3 

Me 

Me 

7.8 

2.29 

1.7 

0.87 

0.77 

0.75 

1.8 

0.88 

0.88 

4 

2l/i 

3/^ 

3/i 

8.5 

2.48 

1.2 

0.69 

0.62 

0.62 

2.1 

0.92 

i.o 

4 

2}.^2 

Me 

Me 

7.2 

2.12 

I.O 

0.69 

0.53 

0.60 

1.8 

0.91 

0.88 

4 

2 

% 

% 

1-^ 

2.27 

0.60 

0.52 

0.40 

0.48 

2.1 

0.96 

I.I 

4 

2 

Me 

Me 

6.7 

1.95 

0.53 

0.52 

0.34 

0.46 

1.8 

0.95 

0.88 

3V^ 

4 

Ki 

i/i 

12.6 

3.70 

5.5 

1. 21 

2.0 

1.24 

1-9 

0.72 

I.I 

3H 

4 

H 

^/^ 

9.8 

2.88 

4.3 

1.23 

1.5 

1 .19 

1.4 

0.70 

0.81 

3H 

3 

1/^ 

H 

10.8 

3.17 

2.4 

0.87 

I.I 

0.88 

1-9 

0.77 

I.I    . 

3H 

3 

% 

H 

8.5 

2.48 

1.9 

0.88 

0.89 

0.83 

1.4 

0.75 

0.81 

3}'^ 

3 

Me 

H 

7.5 

2.20 

1.8 

0.91 

0.85 

0.85 

1.2 

0.74 

0.68 

3 

4 

^/^ 

Vie 

II. 7 

3.44 
3.06 

5.2 

1.23 

1-9 

1.32 

1.2 

0.59 

0.81 

3 

4 

Me 

10.5 

4-7 

1.23 

1.7 

1.29 

I.I 

0.59 

0.70 

3 

4 

34 

%■ 

9-2 

2.68 

4.1 

1.24 

1.5 

1.27 

0.90 

0.58 

0.60 

3 

3H 

¥2 

H 

10.8 

3.17 

3.5 

1.06 

1.5 

1. 12 

1.2 

0.62 

0.80 

3 

SH 

Me 

Me 

9.7 

2.83 

3.2 

1.06 

1.3 

1. 10 

1.0 

0.60 

0.69 

3 

3H 

H 

H 

8.5 

2.48 

2.8 

1.07 

1.2 

1.07 

0.93 

0.61 

0.62 

3 

2H 

^■^ 

H 

7.1 

2.07 

I.I 

0.72 

0.60 

0.71 

0.89 

0.66 

0.59 

3  , 

2K2 

Me 

Me 

6.1 

1.77 

0.94 

0.73 

0.52 

0.68 

0.75 

0.65 

0.50 

2\i 

3 

H 

H 

7.1 

2.07 

1.7 

0.91 

0.84 

0.95 

0.53 

0.51 

0.42 

2K2 

3 

Me 

Via 

6.1 

1.77 

1.5 

0.92 

0.72 

0.92 

0.44 

0.50 

0.35 

2l/i 

iH 

Me 

Me 

2.87 

0.84 

0.08 

0.31 

0.09 

0.32 

0.29 

0.58 

0.23 

2 

iVz 

H 

M 

3.09 

0.91 

0.16 

0.42 

0.15 

•0.42 

0.18 

0.45 

0.18 

IH 

2 

Me 

Me 

2.45 

0.72 

0.27 

0.61 

0.19 

0.63 

0.06 

0.92 

0.08 

IH 

iH 

H 

H 

1. 25 

0.37 

0.05 

0.37 

0.05 

0.33 

0.04 

0.32 

0.05 

iH 

% 

No.  9 

H 

0.88 

0.26 

O.OI 

0.16 

O.OI 

0.16 

0.02 

0.31 

0.04 

See  "Note"  with  Table  IV,  page  354. 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


^^^  Properties  of  Structural  Shapes,  etc.  Chap.  10 

Table  XV.*     Properties  of  Double-Angle  Sections.     Equal  Legs 

ANGLES  PLACED  BACK  TO  BACK 


^ 


3! 


■y'^^ 


Single  angle 

Two 
angles 

Radii 

of  gyration,  r,  in 

inches 

Size, 
in 

Weight 

Area, 

Axis  i-i 

Axis  2-2 

per 
foot, 

sq  in 

In 

H-in 

3,i-in 

i/^-in 

54-in 

lb 

contact 

apart 

apart 

apart 

apart 

8    X8     XiH 

56.9 

33.46 

2.42 

3.42 

3.51 

3.55 

3.60 

3.69 

1^6 

42.0 

24.68 

2.46 

3.37 

3.46 

3.50 

3.55 

3.64 

\^ 

26.4 

15.51 

2.51 

3  33 

3.41 

3.45 

3.50 

3.59 

6    X6    Xi 

37.4 

22.00 

1.80 

2.59 

2.68 

2.72 

d.77 

2.87 

iMfi 

26.5 

15.56 

•1.83 

2.54 

2.63 

2.67 

2.71 

2.8?      i 

5    XS    Xi 

14.9 
30.6 

8.72 
18.00 

1.88 
1.48 

2.49 
2.19 

2.58 

2.62 

2.66 
^.38 

2.75 
2.47 

2.28 

2.33 

iHs 

21.8 

12.80 

1. 51 

2.13 

2.22 

2.26 

2.31 

2.4a 

^A 

12.3 

7.22 

1.56 

2.09 

2.17 

2.21 

2.26 

2.35 

4     X4     X^Me 

19-9 

11.68 

1. 18 

1.75 

1.85 

1.89 

1.94 

2.04 

Vx 

6.6 

3.88 

1. 25 

1.66 

1.75 

1.79 

1.84 

1.93 

3V^X3HX»3/i6 

17. 1 

10.06 

1.02 

1.55 

1.65 

1.70 

1.75 

1.85      1 

H 

5.8 

3.38 

1.09 

1.46 

1.55 

1.59 

I  64 

1.73      , 

3     X3    XH 

11.5 

6.72 

0.88 

1.32 

1. 41 

1.46 

i-Sr 

i.6i     \ 

H 

4.9 

2.88 

0.93 

I. 25 

.   1.34 

1.38 

1.43 

1.53     i 

2l/^X2HXH 

7-7 

4.50 

.0.74 

1.09 

1. 19 

1.24 

1.29 

1.39     ; 

H 

4.1 

2.38 

0.77 

1.05 

1. 14 

1. 19 

1.24 

1.34     i 

2    X2    YJA^ 

5.3 

3.12 

0.59 

0.88 

0.98 

1.03 

1.08 

1. 19     i 

M 

3.19 

»,i.88 

0.61 

0.85 

0.94 

0.99 

1.04 

1. 14 

This  table  and  the  two  following  are  employed  in  computing  the  safe  resistance  to 
compressive  stress  of  two  angles,  back  to  back,  used  as  struts  or  as  the  compression- 
chords  of  roof-trusses,  etc.,  by  the  following  rule: 

Obtain  from  the  compression-formula  in  use  the  allowed  stress  per  square  inch 
corresponding  to  the  ratio  of  slenderness  of  the  section,  and  multiply  that  value  by 
the  area.    The  result  will  be  the  allowable  compressive  stress. 

.  Example  i.  Section  given.  Required  the  safe  load  in  compression,  as  per  formula 
S  =  19  000  —  100  //r,  on  a  strut  composed  of  two  angles,  4  by  4  by  \i  in,  back  to  back, 
with  an  unsupported  length  of  9  ft. 

Area  of  section,  A  =  3. 88  sq  in;  least  radius  of  gyration,  r  =  1.25  in. 

Ratio  of  slenderness,  //r  =  9  X  12  -^  1.25  =  86.4. 

Allowed  unit  stress,  5  =  19  000  —  100  X  86.4  =  10  360  lb  per  sq  in. 

Safe  load,  AS  —  3.88  X  10  360  =»  40  200  lb. 

Example  2.  Stress  given.  Required  a  section  for  a  member  in  compression, 
12  ft  3  in  long,  made  of  two  angles  separated  by  ^^-in  gusset-plates,  to  resist  a  total 
stress  of  35  odo  lb;    ratio  of  slenderness  not  to  exceed  120. 

Assume  two  angles,  5  by  3  by  Me  in,  long  legs  back  to  back. 

Area  of  section,  A  =  4.80  sq  in;   least  radius  of  gyration,  r  =  1.26  in. 

Ratio  of  slenderness,  //r  =  12.25  X  12  -^  1.26  =  116. 7. 

Allowed  unit  stress,  5  =  19  000  —  loo  X  116.7  =  7  330  lb  per  sq  in. 

Safe  load,  AS  =  480  X  7  330  =  35  200  lb. 

In  the  first  case  the  least  radius  of  gyration  is  that  about  the  axis  r-i;  in  the  second 
case,  about  the  axis  2-2;  in  all  cases  the  least  radius  of  gyration  determines  the  ratio 
of  slenderness  and  therewith  the  allowed  safe  compressive  stress.  In  all  cases,  also, 
the  two  angles  are  to  be  secured  together  by  stay-rivets,  so  spaced  as  to  insure  that 
the  section  acts  as  a  unit.  The  ratio  of  slenderness  of  any  single  angle  between  ri  vets 
must  always  be  less  than  that  of  the  strut  or  compression-chord. 

•From  Pocket  Companion,  Carnegie  Stee^  Company,  Pittsburgh,  Pa» 


Properties  of  Structural  Shapes,  etc. 


371 


Table  XVI.^ 


Properties  of  Double-Angle  Sections.     Long  Legs  Vertical 

ANGLES  PLACED  BACK  TO  BACK 


hIkm^^4'' 


y- 


Single  angle 

Two 
angles 

Radii  of  gyration,  r,  in 

inches 

Size, 
in 

Weight 

per 

foot, 

lb 

Area, 
sq  in 

Axis  i-i 

Axis  2-2 

In    - 
contact 

H-in 
apart 

^6-in 
apart 

i/^-in 
apart 

M-in 
apart 

8     X6    Xi 

7/16 

44.2 
33.8 
20.2 

26.00 
19.88 
11.86 

2.49 
2.53 
2.57 

2.39 
2.35 
2.31 

2 
2 
2 

48 
44 
39 

2.52 
2.48 
2.43 

2.57 
2.52 
2.48 

2.66 
2.61 
2.56 

8    XsHXi 

H 

35.7 
27.5 
16.5 

21.00 
16.12 
9.68 

2.51 

2.55 
2.59 

1.26 
1.20 
I.  IS 

35 
29 
23 

1.40 
1.34 
1.28 

1. 45 
1.39 
1.32 

1.55 
1.49 
1. 41 

7   Xal'ixi 

3/8 

32.3 
23.0 
13.0 

19.00 
13  50 
7.60 

2  19 
2.23 
2.27 

1. 31 
1.25 
1.20 

40 
34 
28 

1.45 
1.39 
1.33 

1.50 
1.44 
1.37 

1.60 
1.53 
1.46 

6    X4    Xi 

30.6 
21.8 
12.3 

18.00 
12.80 
7.22 

1. 85 
1.89 
1.93 

1.60 
1.55 
1.50 

69 
63 

58 

1.74 
1.68 
1.62 

1.79 
1.73 
1.67 

1.89 
1.82 
1.76 

6  X3y2xi 

Mo 

28.9 
20.6 
9.8 

17.00 
12.12 
5.74 

1.85 
1.89 
1.9s 

1.37 
1. 31 

I. 25 

47 
41 
33 

1. 51 
1.45 
1.37 

1.56 
1.49 
1.42 

1.66 
1.60 
1.50 

5     X4     XVs 

24.2 
II. 0 

14.22 
6.46 

1.52 
1.59 

1.66 
1.58 

76 
66 

1.80 
1.70 

1.85 
1.75 

\% 

5   XaViX^/i 

M6 

22.7 
8.7 

13.34 
5.12 

1.53 
1. 61 

1.42 
1.33 

51 
41 

1.56 
1. 45 

1. 61 
1.50 

1. 71 
1.59 

5     X3     X^Vie 

19-9 

8,2 

11.68 
4.80 

1. 55 
i.6i 

1. 18 

1.09 

27 
17 

1.32 
1.22 

1.37 
1.26 

1.47 
1.35 

aVixz  xm<s 

Me 

18. 5 

1-1 

10.86 
4.50 

1.38 
1.44 

1. 21 
1. 13 

31 
22 

1.36 
1.26 

1. 41 
1.30 

1. 51 

1.40 

4     X3K2XIM6 
Me 

18. s 

7.7 

10.86 

4.50 

1. 19 
1.26 

1.50 
1.42 

59 
51 

1.64 
1.55 

1.69 
1.60 

1.79 
1.69 

4    X3     XI  Me 

17.1 
5.8 

10.06 
3.38 

1. 21 
1.28 

1.25 
1. 16 

35 

24 

1.40 
1.28 

1.45 
1.33 

1.55 
1.43 

3K2X3    X»M6 

15.8 
5  4 

9-24 
3.12 

1.04 
I. II 

1.30 
1.20 

40 
29 

1.45 
1.34 

1.50 
1.38 

1.60 
1.48 

3^^X2/2X1  He 

12. 5 

4-9 

7.30 
2.88 

1.06 
1. 12 

1.03 
0.95 

13 

04 

1. 18 

1.09 

1.23 
1. 13 

1.33 
1.23 

3    X2^iXMe 

9-5 
4  5 

5.56 
2.64 

0.91 
0.95 

1.05 
1. 00 

15 
09 

1.20 
1. 13 

1.25 
1. 18 

1.35 
1.28 

3      X2      XK2 

7  7 
41 

4.50 
2,38 

0.92 
0.95 

0.80 
0.74 

0 
0 

89 
84 

0.94 
0.88 

1. 00 
0.93 

1. 10 
1.03 

2^iX2      X^^ 

6.8 
362 

4.00 
2.12 

0.75 
0.78 

0,84 
0.80 

0 
0 

94 
89 

0.99 
0.93 

1.04 
0.98 

1. 15 
1.08 

» From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


372 


Properties  of  Structural  Shapes,  etc. 


Chap.  10 


Table  XVn.*    Properties  of  Double-Angle  Sections      Short  Legs  Vertical 

ANGLES   PLACED    BACK   TO   BACK 


\-Hto  % 


^TT^ 


Single  angle 

Two 
angles 

Radii  of  gyration,  r,  in 

inches 

Weight 

Area, 
sq  in 

Axis  2-2 

Size, 
in 

per 

foot, 

lb 

Axis  i-i 

In 
contact 

H-in 
apart 

3/^-in 
apart 

V2-in 
apart 

M-in 
apart 

8    X6    Xi 

H 

44.2 
33.8 
20.2 

26.00 
19.88 
11.86 

1.73 
1.76 
1.80 

3.64 
3.60 
3.55 

3.73 
3.69 
3.64 

3.78 
3.73 
3.68 

3.83 
3.78 
3.73 

It 

3.82 

8    X3HX1 

Vie 

35.7 

27. S 

16.5 

21.00 
16.12 
9.68 

0.86 
0.88 
0.92 

4.04 
3.99 
3.93 

4.14 
4.09 
4.02 

4.19 
4.13 

4.07 

4.24 
4.18 
4.12 

4.34 
4.28 
4.22 

7  xaV^xi 

32.3 
23.0 
13.0 

19.00 
13.50 
7.60 

0.89 
0.92 
0.96 

3.48 
3.42 
3.36 

3.58 
3.52 
3.46 

3.63 
3.57 
3.50 

3.68 
3.62 
3.55 

3.78 
3.72 
3.65 

6    X4    Xi 

30.6 
21.8 
12.3 

18.00 
12.80 
7.22 

1.09 
1. 13 
1. 17 

2.85 
2.79 
2.74 

2.95 
2.89 
2.83 

2.99 
2.93 
2.87 

3.04 
2.98 
2.92 

3.14 
3.08 
3.02 

6   XaV^Xi 

Me 

28.9 
20.6 
9.8 

17.00 
12.12 
5.74 

0.92 
0.95 
1. 00 

2.92 
2.87 
2.81 

3.02 
2.96 
2.90 

3.07 
3.01 
2.95 

3.12 
3.06 
3.00 

3.22 
3.16 

3.09 

5    X4    XH 

24- 2 
II. 0 

14.22 
6.46 

1. 14 
1.20 

2.29 
2.20 

2.38 
2.29 

2.43 
2.34 

2.48 
2.38 

2.58 
2.48 

5  X3y2XH 

Me 

22.7 
8.7 

13.34 
5.12 

0.96 
1.03 

2.36 
2.26 

2.4s 
2.35 

2. so 
2.39 

2.55 
2.44 

2.6s 
2.54 

5    X3    Xi-Me 
Me 

19.9 
8.2 

11.68 
4.80 

0.80 
0.85 

2.42 
2.33 

2.52 
2.42 

2.57 
2.47 

2.62 

2.S2 

2.72 
2.61 

^HX3    X^U 
Me 

18. 5 

7.7 

10.86 

4.50 

0.81 
0.87 

2.06 

2.2s 

2.15 

2.30 
2.20 

2.35 

2.25 

2.45 
2.34 

4    Xs'AXme 
Me 

18. 5 

7-7 

10.86 
4.50 

1. 01 
1.07 

1. 81 
1.73 

1. 91 
1. 81 

1.96 
1.86 

2.01 

1. 91 

2. II 
2.00 

4    X3    XI  Me 
H 

17. 1 
5.8 

10.06 
3.38 

0.83 
0.89 

1.88 
1.78 

It 

2.03 
1.92 

2.08 
1.96 

2.18 
2.06 

3HX3    X^Me 

IS. 3 
5.4 

9.24 
3.12 

0.85 
0.91 

1. 61 
1.52 

1. 71 
1. 61 

1.76 
1.65 

1. 81 
1.70 

1. 91 
1.80 

3y2X2}ixme 

12. 5 
4.9 

7.30 
2.88 

0.69 
0.74 

1.66 
1.58 

1.75 
1.67 

1.80 
1. 71 

1.86 
1.76 

1.96 
1.86 

3    X2>^XMe 

95 

4.5 

5.56 
2.64 

0.72 
0.75 

1.37 
1. 31 

1.46 
1.40 

I-Si 
1.45 

I.S6 
1.50 

1.66 
1.59 

3    X2    XH 

7-7 
4.1 

4-50 
2.38 

0.5s 
0.57 

1.42 
1.38 

1.52 
1.47 

1. 57 
1.52 

1.62 
1.57 

1.72 
1.67 

2HX2    X\i  ■ 
H 

6.8 
3.62 

4.00 
2.12 

0.56 
O.S9 

I. IS 
I. II 

I.2S 
1.20 

1.30 
I.2S 

1.35 
1.30 

1.46 
1.40 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 


Properties  of  Structural  Shapes,  etc. 


373 


Table  XVIII.    Properties  of  Double-Channel  Sections 

STAND^UlD  CHANNELS  PLACED  BACK  TO  BACl^ 


3 


^ 


^^ 


rrTTTy/        y7777n\ 


The  radii  of  gyration  given  correspond  to  directions  indicated  by  the  arrow-heads 


Radii  of  gyration,  r,  in  inches 

Depth, 

Thick- 
ness of 

Weight 

per  foot 

of  one 

channel, 

lb 

Area  of 
two 

Axis  2-2 

in 

web, 
in 

channels, 
sq  in 

A.xis  i-i 

Vx-\v\. 

%-in 

i-in 

apart 

apart 

apart 

0.40 

3300 

19.80 

5.62 

1.38 

1.48 

1.58 

0.43 

35.00 

20.58 

5.58 

1.38 

1.47 

1.57 

0.52 

40.00 

23.52 

5.43 

1.37 

1.46 

1.56 

15 

0.62 

45.00 

26.48 

5.32 

1.37 

1. 45 

1.56 

0.72 

50.00 

29.42 

•  5.23 

1.37 

1.46 

I  56 

0.82 

55-00 

32.36 

5.16 

1.38 

1.47 

I  58 

0.28 

20.50 

12.  o5 

4.61 

1.24 

1.34 

1.44 

0.39 

25.00 

14.70 

4.43 

1. 21 

1. 31 

1. 41 

12 

0.51 

30.00 

17.64 

4.28 

1.20 

1.30 

1.40 

0.64 

35.00 

20.58 

4.17 

1. 21 

1. 31 

1. 41 

1.76 

40.00 

23.52 

0.09 

1.23 

1.32 

1  =  43 

0.24 

15.00 

8.92 

3.87 

1. 14 

1,24 

1.34 

0.38 

20.00 

11.76 

3.66 

1. 10 

1.20 

1. 31 

10 

0.53 

25.00 

14.70 

3.52 

1. 10 

1.20 

1. 31 

0.68 

30.00 

17.64 

3.42 

1. 12 

1.22 

1.33 

0.82 

35.00 

20.58 

3. 35 

1. 16 

1.26 

1.37. 

0.23 

13.25 

7.78 

3.49 

1.09 

1. 19 

1.29 

9 

0.29 

15.00 

8.82 

3.40 

1.07 

1. 17 

I  28 

0.45 

20.00 

11.76 

3.21 

I. OS 

1. 15 

1.26 

0.62 

25.00 

14.70 

3.10 

1.07 

1. 17 

1.28 

374  Properties  of  Structural  Shapes,  etc.  Chap.  10 

Table  XVIII  (Continued).    Properties  of  Double-Channel  Sections 

STANDARD  CHANNELS  PLACED  BACK  TO  BACK 


^~1  1-4- 


<-— 4rs-> 


1 


The  radii  of  gyration  given  correspond  to  directions  indicated  by  the  arrow-heads 


Radii  of  gyration,  r,  in  inches 

Depth, 

Thick- 
ness of 

Weight 
per  foot 

of  one 

channel, 

lb 

Area  of 
two 

Axis  2-2 

in 

web, 
in 

channels, 
sq  in 

Axis  i-i 

YAn 

^^in 

i-in 

apart 

apart 

apart 

8 

0.22 

II. 25^ 

6.70 

3.11 

1.04 

1. 14 

1. 25 

8 

0.31 

13-75 

8.08 

2.98 

1.04 

1. 14 

1.25 

8 

0.40 

16.2s 

9-56 

2.89 

1.03 

1. 14 

1.24 

8 

0.49 

18.7s 

11.02 

2.82 

1.03 

■I.  14 

1.24 

8 

0.58 

21.25 

12.50 

2.77 

1.03 

1. 14 

1.24 

7 

0.21 

975 

5.70 

2.72 

0.99 

1.09 

1.20 

7 

0.32 

12.25 

7.20 

2.59 

0.99 

1.09 

1.20 

7 

0.42 

14.7s 

8.68 

2.50 

0.99 

1. 10 

1. 21 

7 

0.53 

17.25 

10.14 

2.44 

1. 00 

1. 10 

1. 21 

7 

0.63 

19.7s 

11.62 

2.39 

1. 00 

1. 10 

1.22 

6 

0.20 

8,00 

4.76 

2.34 

0.94 

1.05 

I. IS 

6 

0.32 

10.50 

6.18 

2.21 

0.94 

I.  OS 

1. 16 

6 

0.44 

1300 

7.64 

2.13 

0.9s 

1.06 

1. 16 

6 

0.56 

IS.  50 

9.12 

2.07 

0.9s 

1.06 

1. 17 

5 

0.19 

6.50 

3.90 

1.95 

0.89 

1. 00 

1. 10 

5 

0.33 

9.00 

5.30 

1.83 

0.90 

1. 00 

I. II 

S 

0.48 

II. SO 

6.76 

1.7s 

0.91 

1. 01 

1. 12 

4 

0.18 

5.25 

3-10 

1.56 

0.84 

0.9s 

1.06 

4 

0.25 

6.25 

3.68 

I. SI 

0.84 

0.95 

1.06 

4 

0.32 

7-25 

4.26 

1.46 

0.84 

0.9s 

1.06 

3 

0.17 

4.00 

2.38 

1. 17 

0.80 

0.91 

1.02 

3 

0.26 

5.00 

2.94 

1. 12 

0.81 

0.92 

1.03 

3 

0.36 

6.00 

352 

1.08 

0.83 

0.93 

I. OS 

Definitions,  Working  Stresses  and  Examples  375 


CHAPTER  XI 

RESISTANCE  TO  TENSION.    PROPERTIES  OF  IRON 
AND  STEEL 

By 
HERMAN  CLAUDE  BERRY 

PROFESSOR  OF  MATERIALS   OF  CONSTRUCTION,   UNIVERSITY  OF   PENNSYLVANIA 

1.   Definitions,  Working  Stresses  and  Examples 

The  Ultimate  Tensile  Strength  of  a  material  is  the  amount  of  internal 
stress  which  a  section  one  square  inch  in  area  is  capable  of  exerting  against  an 
external  axial  force.  It  is  the  unit  stress  or  intensity  of  stress,  expressed 
in  pounds  per  square  inch,  which  the  material  can  withstand.  It  is  often  called 
the  ultimate  strength  or  ultimate  stress  of  the  material.  Its  value  for 
any  material  depends  on  the  tenacity  of  the  fibers  or  the  cohesion  of  the  particles 
of  which  the  material  is  composed. 

An  Axial  Force  is  one  which  acts  uniformly  over  the  section  of  a  prismatic 
body  so  that  the  resultant  of  the  distributed  forces  coincides  with  the  axis  of 
the  body.  Hence  the  total  axial  force  which  any  cross-section  of  a  body  will 
resist  is  the  product  of  the  ultimate  strength  of  the  material  and  the  area  of 
the  cross-section,  in  square  inches. 

Safe  Working  Stress.  The  ultimate  strength  of  different  building  materials 
has  been  found  by  pulling  apart  bars  of  known  dimensions  and  dividing  the 
maximum  load  each  sustained  by  the  area  of  the  bar  before  testing.  This  ulti- 
mate strength,  however,  must  not  be  used  to  proportion  the  size  of  members 
of  structures,  because  of  variations  in  material,  hidden  defects  and  imperfect 
workmanship;  and,  especially,  because  of  indefiniteness  as  to  the  maximum  load 
that  may  be  imposed  on  the  structure.  To  provide  safety  against  the  rupture 
of  a  member  and  the  consequent  failure  of  the  structure  from  any  of  these 
causes,  the  proportions  of  the  members  must  be  based  on  safe  working  stresses 
which  are  usually  some  fractional  part  of  the  ultimate  strength  found  by 
experiment  to  provide  proper  security  against  failure. 

The  Factor  of  Safety  is  the  ratio  of  the  ultimate  strength  to  this  safe 
working  stress  for  that  material.  Its  value  ranges  generally  from  2  to  10, 
depending  upon  the  nature  of  the  material  and  the  service  to  which  it  is^applied. 

Safe  Working  Stress  in  Tension.  Table  I  gives  these  values  for  various 
building  materials.  The  total  safe  load  that  may  be  applied  to  a  piece  of 
material  of  uniform  section  is  found  by  multiplying  the  cross-section  of  the  piece, 
in  square  inches,  by  the  safe  working  stress  opposite  the  name  of  the  material 
of  which  the  piece  is  composed. 

Then  if  P  =  the  safe  load  in  lb, 

St  =  the  allowable  safe  working  stress  in  tension, 
b  =  the  width  of  a  rectangular  bar, 
h  =  the  depth  of  a  rectangular  bar, 
d  =  the  diameter  of  a  round  bar, 
there  results,  for  a  rectangular  bar, 

P=bhSt  ^      (i) 

and  for  a  round  bar, 

P  =  o.7S54  d^St  {2) 


376        Resistance  to  Tension.     Properties  of  Iron  and  Steel     Chap.  11 


The  area  of  cross-section  to  support  a  load  P  is,  for  a  rectangular  bar, 
P 


A  = 


St 


and  for  a  round  bar 


.=v^ 


0.7854  5« 
Table  I.    Safe  Working  Stress  in  Tension  for  Building  Materials  * 


(3) 


(4) 


Material 


Cast  iron 

Wrought  iron 

Steel,  medium 

Chestnut 

Douglas  fir 

Hemlock 

Pine,  long-leaf  yellow . 
Pine, short-leaf  yellow. 

Pine,  Norway 

Pine,  white 

Redwood 

Spruce. 

White  oak 


Safe  stress 

lb  per  sq  in  (St) 

3   000 

12  000 

16  000 

850 

800 

600 

I  200 

900 

800 

700 

700 

800 

I  200 

*  Note.  For  woods  these  values  may  be  increased  up  to  30%  for  selected,  perfectly 
protected,  commercially  dry  timber,  not  subject  to  impact,  that  is,  for  ideal  conditions. 
(See,  also,  pages  637  and  647.) 

Example  i.     What  size  of  medium-steel  angle  should  be  used  to  sustain  a 
tensile  force  of  64  000  lb? 
Answer.     By  formula  (3), 

64000 


the  net  sectional  area  = 


16000 


=  4.00  sq  m 


From  the  Table  of  the  Properties  of  Angles  (Chapter  X)  we  find  that  a  4  by 
4  by  ^-in  angle  has  an  area  of  4.61  sq  in,  which  is  to  be  reduced  by  a  H-in  hole 
for  a  H-'m  rivet,  leaving  4.61  —  {J4XH)  =  4.06  sq  in,  net  area.  This  is  slightly 
in  excess  of  the  required  amount. 

The  SAFE  LOAD  for  angles  commonly  used  in  roof-trusses  is  given  in  Table  X; 
and  the  reduction  in  sectional  area  caused  by  rivet-holes,  in  Tj^ble  XI, 
this  chapter,  and  in  Table  I,  Chapter  XX.  See  also,  Chapter  XII,  page  414, 
paragraph  on  Punching  Rivet-Holes. 

Example  2.  What  size  of  white-pine  tie-beam  should  be  used  to  sustain  a 
tensile  force  of  60  000  lb? 

Answer.     By  formula  (3), 

60000 
=  =  85.7  sq  m 


the  net  sectional  area  = 


If  the  depth  is  taken  at  1 2  in,  the  net  width  must  be 


85.7 


=  7.2  in.    Allowance 


must  be  made  for  the  increase  in  tension  on  the  lower  side  of  the  beam,  due  to 
its  own  weight,  and  also  for  any  cutting  that  may  be  necessary  in  making  the 
connections  or  holes  for  truss-rods.     If  there  is  a  2-in  hole  through  the  beam,  a 


Wrought  Iron  377 

lo  by  1 2 -in  timber  must  be  used.  This  makes  allowance  for  the  weight  of  the 
beam  itself.  If  the  unsupported  length  of  the  beam  is  great,  the  allowance  for 
the  weight  must  be  made  according  to  the  methods  explained  in  Chapter  XV, 
page  572,  for  the  calculation  of  tie-beams  subjected  to  transverse  loading. 

2.   Wrought  Iron 

Manufacture.  Wrought  iron  is  a  mixture  of  pure  iron  and  slag,  about 
96%  iron  and  3%  slag,  together  with  from  V2  to  %%  of  other  elements  including 
carbon,  phosphorus,  sulphur  and  manganese.  It  is  made  from  pig  iron  and 
iron  oxide,  or  mill-scale,  in  a  reverberatory  furnace  consisting  of  a  firebox,  a 
hearth  or  working-chamber,  and  the  necessary  dampers  and  flues.  The  impur- 
ities are  removed  from  the  iron  at  different  stages  in  the  process,  silicon  and 
manganese  during  the  melting-down  stage,  part  of  the  phosphorus  and  sulphur 
during  the  clearing-stage  and  the  carbon  and  remainder  of  the  phosphorus  and 
sulphur  during  the  boiling-stage.  The  iron  is  then  in  a  pasty  condition  ready 
for  a  thorough  stirring  by  the  workman,  who  collects  it  into  balls  of  about  80  lb 
weight  and  takes  it  to  a  squeezer  or  forge  where  the  greater  part  of  the  slag  is 
removed.  It  is  then  rolled  out  into  muck-bars.  These  bars  are  cut  into  pieces 
which  are  piled  into  bundles  suited  to  the  size  of  the  finished  bar.  The  piles 
are  heated  and  rolled  again.  The  rolling  reduces  the  amount  of  slag  and  makes 
the  material  denser.  The  process  of  reroUing  may  be  repeated  a  number  of 
times  to  produce  double  or  triple-refined  merchant-bar  iron. 

The  Appearance  of  Wrought  Iron  is  very  much  like  that  of  steel.  It  may 
be  distinguished  from  steel  by  nicking  one  side  of  the  bar  and  bending  it  away 
from  the  nick.  Iron  will  split  along  the  slag-laminations  and  show  the  coarsely 
fibrous  nature  of  the  material;  while  steel  will  bend  or  rupture  at  the  nick 
without  splitting,  any  fracture  being  finely  fibrous  or  crystalline.  When 
ruptured  in  a  tension-test  wrought  iron  shows  a  dark  fibrous  fracture.  If  the 
specimen  is  grooved  before  testing  or  broken  in  impact  the  fracture  will  be 
coarsely  crystalline. 

Welds,  Wrought  iron  is  more  easily  welded  than  steel  because  the  work 
may  be  accomplished  through  a  wider  range  of  temperature  than  with  steel. 
A  weld  may  develop  the  full  strength  of  the  bar,  but  tests  on  hand-forged  welds 
on  rough  tie-bars  reported  by  Kirkaldy  gave  average  values  of  about  60%  of 
the  strength  of  the  bar. 

Use.  Wrought  iron  is  no  longer  used  for  the  manufacture  of  structural 
shapes,  such  as  angles,  channels  and  beams,  its  use  for  structural  work  being 
practically  limited  to  bars,  rods  and  bolts.  It  can  be  worked  more  easily  than 
steel  in  threading-machines;  and  on  this  account,  unless  steel  is  specified,  some 
companies  will  furnish  truss-rods,  bolts,  etc.,  in  wrought  iron. 

Specifications  *  for  Wrought  Iron.  Wrought  iron  may  be  purchased  under 
the  Specifications  of  the  American  Society  for  Testing  Materials. 

Material  Covered,  i .  These  specifications  cover  two  classes  of  wrought-iron 
plates,  as  determined  by  the  kind  of  material  used  in  their  manufacture,  namely: 

Class  A,  as  defined  in  Section  2  (6); 
Class  B,  as  defined  in  Section  2  (c); 

♦These  Specifications  for  Wrought-Iron  Plates  are  issued  by  the  Society  under  the 
fixed  designation  A  42.  They  were  adopted  in  1913  and  revised  in  19 18.  There  are  also 
A.  S.  T.  M.  Standard  Specifications  for  Staybolt  Iton,  Refined  Wrought-Iron  Bars,  Iron 
and  Steel  Chain,  etc. 


37S       Resistance  to  Tension.    Properties  of  Iron  and  Steel     Chap.  11 


I.  Manufacture 
Process.     2.  (a)   All  plates  shall  be  rolled  from  piles  entirely  free  from  any 
admixture  of  steel. 

(b)  Piles  for  Class  A  plates  shall  be  made  from  puddle-bars  made  wholly  from 
pig  iron  and  such  scrap  as  emanates  from  rolling  the  plates. 

(c)  Piles  for  Class  B  plates  shall  be  made  from  puddle-bars  made  wholly  from 
pig  iron  or  frorrva  mixture  of  pig  iron  and  cast-iron  scrap,  together  with  wrought- 
iron  scrap. 

II.  Physical  Properties  and  Tests 
Tension-tests.     3.  (a)  The  plates  shall  conform  to  the  following  minimum 
reciuirements  as  to  tensile  properties: 


Properties  considered 

Class  A 

Class  B 

6  in  to  24  in 

incl, 

in  width 

Over  24  in 
to  90  in 

incl, 
in  width 

6  in  to  24  in 
incl, 

in  width 

Over  24  in 
to  90  in 

incl, 
in  width 

Tensile  strength,  lb  per  sq  in 

Yield-point,  lb  per  sq  in 

Elongation  in  8  in,  per  cent 

49  000 

26  000 

16  . 

48  000 

26  000 

12 

48  000 

26  000 

14 

47000 

26000 

10 

(h)  The  yield-point  shall  be  determined  by  the  drop  of  the  beam  of  the  testing- 
machine.  The  speed  of  the  cross-head  of  the  machine  shall  not  exceed  ^4  in  per 
minute. 

Modifications  in  Elongation.  4.  For  plates  under  V\&  in  in  thickness,  a 
deduction  of  1  from  the  percentages  of  elongation  specified  in  Section  3  shall  be 
made  for  each  decrease  of  Vm  in  in  thickness  below  He  in. 

Bend  Tests.  5.  (a)  Colu-Bend  Tests.  The  test-specimen  shall  bend 
cold  through  90°  without  fracture  on  the  outside  of  the  bent  portion,  as  follows: 
For  Class  A  plates,  around  a  pin  the  diameter  of  which  is  equal  to  il^i  times  the 
thickness  of  the  specimen;  and  for  Class  B  plates,  around  a  pin  the  diameter  of 
which  is  equal  to  three  times  the  thickness  of  the  specimen. 

(b)  Nick-Bend  Tests.  The  test-specimen,  when  nicked  on  one  side  and 
broken,  shall  show  for  Class  A  plates,  a  wholly  fibrous  fracture,  and  for  Class  B 
plates,  not  more  than  10%  of  the  fractured  surface  to  be  crystalHne. 

Test-specimens.  6.  Tension  and  bend-test  specimens  shall  be  taken  from 
the  finished  plates  and  shall  be  of  the  full  thickness  of  plates  as  rolled.  The 
longitudinal  axis  of  the  specimen  shall  be  parallel  to  the  direction  in  which  the 
plates  are  rolled. 

Number  of  Tests.  7.  (a)  One  tension,  one  cold-bend  and  one  nick-bend 
test  shall  be  made  for  each  variation  in  thickness  of  Ys  in  and  not  less  than  one 
test  for  every  ten  plates  as  rolled. 

(b)  If  any  test-specimen  fails  to  conform  to  the  requirements  specified  by 
reason  of  an  apparent  local  defect,  a  retest  shall  be  made.  If  the  retest  also  fails, 
the  plates  represented  by  such  test  will  be  rejected. 

III.  Finish 
Finish.     8.  The  plates  shall  be  straight,  smooth,  and  free  from  cinder-spots 
und  holes,  injurious  flaws,  buckles,  blisters,  seams,  and  laminations.  ^^ 


Cast  Iron  379 

IV.  Marking 
Marking.     9.  The  plates  shall  be  stamped  or  otherwise  marked  as  designated 
by  the  purchaser. 

V.  Inspection  and  Rejection 
Inspection.     10.  (a)  The  inspector  representing  the  purchaser  shall  have 
free  entry,  at  all  times  while  work  on  the  contract  of  the  purchaser  is  being  per- 
formed, to  all  parts  of  the  manufacturer's  works  which  concern  the  manufacture 
of  the  plates  ordered.     (See  complete  Specifications  for  Sections  10,  11  and  12.) 

3.   Cast  Iron 

Cast  Iron  has  been  defined  as  a  saturated  solution  of  carbon  in  iron,  the 
carbon-content  varying  from  i^/^  to  4%  according  to  the  other  impurities  con- 
tained. It  is  hard,  brittle,  non-malleable  and  very  fluid  when  melted,  so  that 
it  is  well  adapted  for  casting  into  complex  forms. 

Manufacture.  It  is  produced  in  the  blast-furnace,  which  is  essentially  a 
closed  refractory-lined  stack,  with  a  valve-charging  device  at  the  top,  tuyeres 
or  openings  in  the  lower  part  for  the  introduction  of  the  air-blast,  and  a  hearth 
at  the  bottom  with  a  tap-hole  for  the  periodic  withdrawal  of  the  iron  and  slag. 
The  FURNACE-IRON  is  cast  into  pigs  about  3  ft  long  and  weighing  about  icxd  lb 
each.  Foundry-castings  are  made  from  pig  iron  and  scrap  melted  in  a  cupola 
and  poured  into  green-sand  molds.  The  charge  is  made  up  of  different  quanti- 
ties of  the  different  grades  of  pig  so  as  to  control  the  physical  properties  of  the 
castings,  principally  through  control  of  the  silicon-content. 
.  Appearance.  Castings  have  a  gray  or  white  fracture  according  to  the  condi- 
tion of  the  contained  carbon,  the  gray  fracture  indicating  graphitic  or  separated 
carbon  and  the  white  the  combined  carbon.  Gray  iron  is  softer  and  tougher 
and  is  specified  for  ordinary  castings. 

Strength.     Cast  iron  does  not  have  a  definite  elastic  limit.     A  relatively 
small  stress  will  produce  some  permanent  deformation.     Its  ultimate  tensile 
strength  varies  from  15  000  to  20  000  lb  per  sq  in;  and  in  some  iron  is  as  high'' 
as  30  000  lb  per  sq  in.    Its  compressive  strength  varies  over  a  wide  range, 
80  000  lb  per  sq  in  being  a  fair  average  value. 

Defects.  Castings  are  liable  to  several  common  defects  the  chief  of  which 
are  blow-holes  due  to  the  formation  of  steam  from  the  damp  molds,  sand-holes 
due  to  misplaced  sand,  rough  surfaces,  cold  shuts  due  to  chilling  of  the  iron 
and  failure  to  fill  the  parts  of  the  mold,  shrinkage-cracks  due  to  uneven  cooling 
of  the  castings  in  parts  of  different  thickness.  In  cored  castings,  also,  the  walls 
are  frequently  of  variable  thickness  because  of  the  shifting  of  the  cores.  This  is 
especially  frequent  in  case  of  hollow  columns  cast  in  a  horizontal  position. 
Because  of  these  defects  and  on  account  of  the  low  ultimate  strength,  cast 
iron  should  never  be  used  where  it  is  subjected  to  any  great  tensile  stress. 

Specifications*  for  Cast  Iron.  The  specifications  of  the  American  Society 
for  Testing  Materials,  for  gray-iron  castings,  include  the  following  require- 
ments: 

1.  Unless  furnace -IRON  is  specified,  all  gray  castings  are  understood  to  be 
made  by  the  cupola-process. 

2.  The  sulphur-contents  are  to  be: 

For  light  castings,  not  over  o.io  per  cent. 
For  medium  castings,  not  over  o.io  per  cent. 
For  heavy  castings,  not  over  0.12  per  cent. 

*  These  specifications  are  issued  under  the  fixed  designation  A  48.  They  were  adopted 
in  1905  and  revised  in  1918.     The  complete  specification  can  be  obtained  from  the  Society. 


380      Resistance  to  Tension.     Properties  of  Iron  and  Steel      Chap.  11 

3.  In  dividing  castings  into  light,  medium  and  heavy  classes,  the  following 
standards  have  been  adopted: 

Castings  having  any  section  less  than  V2  in  thick  shall  be  known  as  light 

CASTINGS. 

Castings  in  which  no  section  is  less  than  2  inches  thick  shall  be  known  as 

HEAVY  CASTINGS. 

Medium  castings  are  those  not  included  in  the  above  classification. 

4.  Transverse  Test.  The  minimum  breaking  strength  of  the  arbi- 
tration-bar under  transverse  load  shall  be: 

For  light  castings,  not  under  2  500  lb. 

For  medium  castings,  not  under  2  900  lb. 

For  heavy  castings,  not  under  3  300  lb. 
In  no  case  shall  the  deflection  be  under  o.io  in. 
Tension-Test.    Where  specified  this  shall  be: 

For  light  castings,  not  less  than  18  000  lb  per  sq  in. 

For  medium  castings,  not  less  than  21  000  lb  per  sq  in. 

For  heavy  castings,  not  less  than  24  000  lb  per  sq  in. 

The  specifications  give  explicit  directions  for  casting  the  arbitration-bar, 
which  is  iV4  in  in  diameter  and  15  in  long.  Two  of  these  are  cast  for  each 
twenty  tons  of  castings.  One  of  each  pair  must  fulfill  the  requirements  to  per- 
mit acceptance  of  the  castings.  The  bar  is  loaded  at  the  middle  at  a  rate  that 
will  cause  a  o.io-in  deflection  in  from  twenty  to  forty  seconds.  The  tension- 
test  is  not  recommended. 

II.  Castings  shall  be  true  to  pattern,  free  from  cracks,  flaws  and  excessive 
shrinkage.  In  other  respects  they  shall  conform  to  whatever  points  shall  be 
specially  agreed  upon. 

4.   Steel 

Steel  is  a  mixture  of  compounds  of  iron  and  carbon  with  small  quantities  of 
other  elements,  including  manganese,  phosphorus,  sulphur,  silicon,  etc.  The 
carbon-content  controls  the  hardness  and  strength  of  the  steel.  Less  than 
0.10%  of  carbon  is  present  in  the  soft  steels,  which  have  most  of  the  charac- 
teristics of  wrought  iron;  while  steel  with  more  than  0.40%  carbon  is  capable 
of  being  tempered,  cannot  be  welded  and  is  very  much  stronger.  Manganese 
acts  as  a  cleanser  during  the  process  of  manufacture,  and  increases  the  forge- 
ab  lity  of  the  steel.  Phosphorus  and  sulphur  are  harmful  in  their  effects,  phos- 
phorus making  steel  brittle  under  sudden  loading  and  sulphur  making  it  hot -short 
or  brittle  when  heated. 

Manufacture.  Structural  steel  is  manufactured  by  the  Bessemer  and 
the  open-hearth  processes.  In  the  first,  molten  cast  iron  is  charged  into  a 
Bessemer  converter,  an  air-blast  is  driven  through  the  charge  from  i^erforations 
in  the  false  bottom  of  the  converter  and  the  silicon,  sulphur  and  carbon  burned 
out.  Carbon  in  the  form  of.fcrro-manganese  is  then  added  to  deoxidize  the 
charge  and  give  the  proper  content  of  carbon  in  the  finished  steel,  which  is 
quickly  drawn  off  and  poured  into  ingots.  Phosphorus  is  not  removed  ordi- 
narily by  the  Bessemer  process;  but  if  the  lining  of  the  converter  is  made  of 
basic  material,  such  as  dolomite  limestone,  and  if  lime  is  added  with  the  charge, 
the  phosphorus  will  unite  with  it  and  be  poured  off  with  the  slag. 

The  Open-Hearth  Process.  In  this  process  scrap-steel,  pig-iron  or  molten 
furnace-iron  and  limestone  flux  are  charged  on  the  hearth  of  a  Siemens  furnace, 
a  reducing  gas-flame  is  directed  onto  the  charge  and  the  carbon  and  other 
impurities  are  gradually  removed.    When  the  reduction  is  about  completed  sam- 


Steel  381 

pies  are  taken  and  carbon  determined  so  that  the  charge  may  be  withdrawn  at 
the  proper  time.  The  process  thus  permits  of  much  more  accurate  control  of 
the  product.  The  material  is  more  uniform  and  consequently  more  dependable 
in  service  than  Bessemer  steel.  Open-hearth  steel  is  used  for  most  struc- 
tural work. 

Phosphorus  may  be  removed  by  the  basic  process  as  in  case  of  Bessemer 
steel.  Ores  running  low  in  phosphorus  are  generally  used  in  America  so  that 
the  basic  process  is  httlc  employed  here. 

The  Effect  of  Carbon  and  Phosphorus  on  the  static  strength  of  steel 
for  the  limits  of  carbon  included  in  structural  steel  is  an  increase  in  strength  of 
about  I  ooo  lb  per  sq  in  for  each  o.oi%  increase  in  either  element.  Cunning- 
ham's formula 

St  =  40  000  +  100  000  (C  +  P) 

gives  the  approximate  relation  between  the  strength  and  the  chemical  composi- 
tion. C  and  P  are  respectively  the  amounts  of  carbon  and  phosphorus  ex- 
pressed in  percentage.  For  example,  the  ultimate  strength  of  a  steel  having 
0.15%  carbon  and  0.07%  phosphorus  is,  approximately, 

St  =  40  000  +  100  000  (0.15  +  0.07)  =  62  000  lb  per  sq  in 

The  Percentage  of  Elongation  decreases  as  the  carbon-content  and  ulti- 
mate strength  increase.     An  approximate  relation  being 

,    ,  .  I  400  000 

percentage  of  elongation  = • 

St 

Since  the  total  elongation  of  a  ruptured  specimen  is  due  to  the  local  stretch- 
ing at  the  point  of  rupture  and  the  uniform  elongation  over  the  whole  gauge- 
length,  it  is  necessary  to  report  the  gauge-length  when  reporting  this  result. 
Since  the  local  elongation  is  the  same  for  a  2  or  an  8-in  length,  the  percent- 
age OF  elongation  for  the  same  material,  tested  on  a  2-in  gauge-length,  is  greater 
than  if  measured  on  an  8-in  length. 

The  Elastic  Behavior  of  a  specimen  of  steel  loaded  to  rupture  is  best  shown 
by  a  stress-strain  diagram  on  which  the  stresses  are  plotted  as  vertical  ordi- 
nates  and  the  elongations  or  strains  as  abscissas,  as  in  Fig.  1.  Five  significant 
results  are  shown: 

(i)  The  Modulus  of  Elasticity  (E).  The  relation  between  the  stress  and  the 
strain  or  elongation  is  called  the  modulus  of  elasticity.  It  is  equal  to  the 
unit  stress  divided  by  the  unit  strain  or  deformation  and  is  represented  graph- 
ically by  the  tangent  of  the  angle  of  the  initial  line  with  the  horizontal.  Its 
value  for  steel  for  tension  is  about  30  000  000  lb  per  sq  in. 

(2)  The  Elastic  Limit  (E.L.)  is  that  unit  stress  beyond  which  the  ratio  of 
stress  to  strain  ceases  to  be  constant,  or  beyond  which  the  curve  ceases  to  be  a 
straight  line. 

(3)  The  Yield-Point  (F.P.),  slightly  above  or  beyond  the  elastic  limit, 
is  that  unit  stress  at  which  the  specimen  begins  to  stretch  without  increase  in 
the  load.  This  stress  may  be  determined  from  a  test  without  the  use  of  deli- 
cate measuring -apparatus  by  the  drop  of  the  beam  or  halt  in  the  gauge 
of  the  testing-machine. 

(4)  The  Ultimate  Strength  {U.S.)  is  the  greatest  unit  stress  the  specimen 
can  sustain. 

(5)  The  Rupture-Stress  (R)  is  the  unit  stress  at  the  time  of  failure.  This  is 
the  unit  stress  at  the  point  of  failure  after  the  area  of  the  cross-section  of  the 


382        Resistance  to  Tension.     Properties  of  Iron  and  Steel   Chap.  11 

specimen  has  been  reduced;  and  because  of  the  rapid  dropping  off  of  the  load 
it  is  difficult  to  determine.  It  is  not  regularly  observed  in  testing,  attention 
being  called  to  it  merely  to  emphasize  the  fact  that  the  ultimate  strength  of 
steel  is  not  the  stress  at  the  time  of  failure  of  the  specimen.  This  is  true,  alio, 
for  wrought  iron  and  ductile  materials  in  general. 

60000 


60000 


2    40000 


^_ 

U.S. 

\ 

-^ 

\ 

V.P. 

\ 

E.L 

^^ 

\ 

E  =  tan  a 
=  30000 

000 

0.0025  0.05  0.10  0.15  0.20  0.25  0. 

6  Unit  elongation 

The  horizontal  scale  for  the  distance  a  &  is  ten 
times  greater  than  for  the  remaining  distance 

Fig.  1.     Stress-strain  Diagram  of  Test  on  Steel  Specimens. 


0.35 


Effect  of  Punching  and  Shearing.  Structural  steel  is  hardened  by  the 
action  of  the  punch  and  shear  in  the  process  of  manufacture  in  the  shop.  On 
the  die-side  the  metal  is  forced  to  flow  from  the  tool  and  this  cold  working 
hardens  and  injures  it  as  may  be  shown  by  a  cold-bend  test.  The  effect  may 
be  removed  by  annealing;  but  in  the  best  work  it  is  usually  specified  that 
rivet-holes  shall  be  reamed  during  the  assembling  of  the  parts.  This  removes 
^e  injured  metal  and  brings  the  parts  into  better  alinement  for  the  insertion 
of  the  rivets.  The  injury  from  shearing  may  be  removed  by  milling  the  sheared 
edges. 

The  Coefficient  of  Expansion  of  steel  is  o.ooo  oo6  s  per  degree  Fahrenheit. 
The  ELONGATION  in  a  length  /,  due  to  a  change  in  temperature  of  /  degrees,  is 
then 

e  =  o.ooo  oo6  5  U 

in  which  /  is  expressed  in  inches  and  /  in  degrees  Fahrenheit. 

The  Weight  of  Steel  is  taken  at  489.6  lb  per  cu  ft.  The  sectional  area  of 
a  member  in  square  inches  multiplied  by  3.4  equals  the  weight  in  pounds  per 
linear  foot. 

The  Working  Stress  for  structural  steel  in  tension  in  buildings  and  bridges  is 


Standard  Specifications  for  Structural  Steel  for  Buildings      383 

i6  ooo  lb  per  sq  in  in  most  specifications  and  building  laws.  For  members 
subject  to  constant  load  some  designers  use  a  working  stress  of  20  000  lb 
per  sq  in. 

5.     Standard  Specifications  for  Structural  Steel  for  Buildings 

Specifications.  These  specifications  are  issued  by  the  American  Society  for 
Testing  Materials  under  the  fixed  designation  A  9.  They  were  adopted  in  1901 
and  revised  in  1909,  1913,  1914  and  1916.  Extracts  from  these  specifications 
follow: 

I.  Manufacture 

Process,  i.  (a)  Structural  steel,  except  as  noted  in  Paragraph  (6),  maybe 
made  by  the  Bessemer  or  the  open-hearth  process. 

(b)  Rivet  steel,  and  steel  for  plates  or  angles  over  %  in  in  thickness  which  are 
to  be  punched,  shall  be  made  by  the  open-hearth  process. 

II.  Chemical  Properties  and  Tests 
Chemical  Composition.     2.  The  steel  shall  conform  to  the  following  re* 

quirements  as  to  chemical  composition: 


Chemical  content 


Phosphorus 
Sulphur 


f  Bessemer. ... 
\  open-hearth. . 


Structural  steel 


not  over  o.  lo  per  cent 
not  over  o .  06  per  cent 


Rivet  steel 


not  over  0.06  per  cent 
not  over  0.045  per  cent 


Ladle  Analyses.  3.  An  analysis  of  each  melt  of  steel  shall  be  made  by  the 
manufacturer  to  determine  the  percentages  of  carbon,  manganese,  phosphorus 
and  sulphur.  This  analysis  shall  be  made  from  a  test-ingot  taken  during  the 
pouring  of  the  melt.  The  chemical  composition  thus  determined  shall  be  re- 
ported to  the  purchaser  or  his  representative,  and  shall  conform  to  the  require- 
ments specified  in  Section  2. 

Check  Analyses.  4.  Analyses  may  be  made  by  the  purchaser  from  finished 
material  representing  each  melt.  The  phosphorus  and  sulphur-content  thus 
determined  shall  not  exceed  that  specified  in  Section  2  by  more  than  25  per  cent. 


III.  Physical  Properties  and  Test 

s 

e  following  require- 

Tension-Tests.     5.  (a)  The  material  shallr conform  to  th 
ments  as  to  tensile  properties: 

Properties  considered 

Structural  steel 

Rivet  steel 

55  000-65  000 

0.5  tens,  strength 

I  400  000* 

Tens,  strength 

22 

46  000-56  000 

0 . 5  tens,  strength 

I  400000 

VielH-noint  min  lb  Der  so  in            

Elongation  in  8  in,  min,  per  cent 

Tens,  strength 

*  See  Section  6. 

(ft)  The  yield-point  shall  be  determined  by  the  drop  of  the  beam  of  the  testing- 
machine. 


384       Resistance  to  Tension.     Properties  of  Iron  and  Steel     Chap.  11 


Modifications  in  Elongation.  6.  (a)  For  structural  steel  over  %  in  in  thick- 
ness, a  deduction  of  i  from  the  percentage  of  elongation  in  8  in,  specified  in 
Section  5  (a),  shall  be  made  for  each  increase  of  }i  in  in  thickness  above  %  in, 
to  a  minimum  of  i8  per  cent. 

{h)  For  structural  steel  under  Mo  in  in  thickness,  a  deduction  of  2.5  from  the 
percentage  of  elongation  in  8  in,  specified  in  Section  5  (a),  shall  be  made  for  each 
decrease  of  He  in  in  thickness  below  Me  in. 

Bend  Tests.  7.  (a)  The  test-specimen  for  plates,  shapes  and  bars,  except  as 
specified  in  Paragraphs  {h)  and  (c),  shall  bend  cold  through  180°  without  cracking 
on  the  outside  of  the  bent  portion,  as  follows:  For  material  H  in  or  under  in 
thickness,  flat  on  itself;  for  material  over  %  in,  to  and  including  i  M  in  in  thick- 
ness, around  a  pin  the  diameter  of  which  is  equal  to  the  thickness  of  the  specimen; 
and  for  material  over  1 34  in  in  thickness,  around  a  pin  the  diameter  of  which  is 
equal  to  twice  the  thickness  of  the  specimen. 

{h)  The  test-specimen  for  pins,  rollers,  and  other  bars,  when  prepared  as 
specified  in  Section  8  {c),  shall  bend  cold  through  180°  around  a  i-in  pin  without 
cracking  on  the  outside  of  the  bent  portion. 

(c)  The  test-specimen  for  rivet  steel  shall  bend  cold  through  180°  flat  on  itself 
without  cracking  on  the  outside  of  the  bent  portion. 

Test-Specimens.     8.  (a)  Tension  and  bend-specimens  shall  be  taken  from 

rolled  steel  in  the  condition  in 


Parallel 
Section 
not  less 


Ci 


I 


which  it  comes  from  the  rolls, 
except  as  specified  in  Para- 
graph {h). 

{b)  Tension  and  bend-test 
specimens  for  pins  and  rollers 
shall  be  taken  from  the  fin- 
ished bars  after  annealing, 
when  anneaUng  is  specified. 

(c)  Tension   and   bend-test 

specimens   for   plates,  shapes 

r...       -n         re-        r     cx    i  x    ^  ^nd   bars,  except  as  specified 

Fig.  1a.    Form  of  Specimen  for  Steel-test  .      -^  1       /  j\     a  \  j 

in   Paragraphs    (a),    (e),   and 

CO.  shall  be   of   the  full  thickness   of   the   material  as  rolled;    and  may  be 

machined  to  the  form  and  dimensions  shown  in  Fig.  1a,  or  with  both  edges 

parallel. 

(d)  Tension  and  bend-test 

specimens  for  plates  over  i  ^ 


in  in  thickness  may  be  ma- 
chined to  a  tliickness  or  diam- 
eter of  at  least  %  in  for  a 
length  of  at  least  9  in. 

{e)  Tension-test    specimens 


\^e)    Jiension-iest    specimens  1"^  ; 

for  pins,  rollers   and  bars  over      ^ote>  ^e.GageI:engfh,,Earailel  Portions  and  jniTets 

shall  be  as  shown,  but  the  ends  may  be  of  any 
Form  -which  will  fil  the  Holders  of  "the  Testing 
Machine^ 

Fig.  2. 


Form  of  Specimen  for  Pins,  Rollers,  Bars, 
,  etc.,  Over  1}/^  Inches  Thick 


I H  in  in  thickness  or  diameter 
may  conform  to  the  dimen- 
sions shown  in  Fig.  2.  In  this 
case,  the  ends  shall  be  of  a 
form  to  fit  the  holders  of  the 
testing-machine  in  such  a  way  that  the  load  shall  be  the  axial.  Bend-test  speci- 
mens may  be  i  by  H  in  in  section.  The  axis  of  the  specimen  shall  be  located  at 
anj'  pcint  midway  between  the  center  and  surface  and  shall  be  parallel  to  the 
axis  of  the  bar. 


Tension-Members  385 

(/)  Tension  and  bend-test  specimens  for  rivet  steel  shall  be  of  the  full-size 
section  of  bars  as  rolled. 

Number  of  Tests.  9.  (a)  One  tension  and  one  bend-test  shall  be  made  from 
each  melt;  except  that  if  material  from  one  melt  differs  ^  in  or  more  in  thickness, 
one  tension  and  one  bend-test  shall  be  made  for  both  the  thickest  and  the 
thinnest  material  rolled. 

(6)  If  any  test-specimen  shows  defective  machining  or  develops  flaws,  it  may 
be  discarded  and  another  specimen  substituted. 

(c)  If  the  percentage  of  elongation  of  any  tension-test  specimen  is  less  than 
that  specified  in  Section  5  (a)  and  any  part  of  the  fracture  is  more  than  %  in 
from  the  center  of  the  gauge-length  of  a  2-in  specimen  or  is  outside  the  middle 
third  of  the  gauge-length  of  an  8-in  specimen,  as  indicated  by  scribe-scratches 
marked  on  the  specimen  before  testing,  a  retest  shall  be  allowed. 

IV.  Permissible  Variations  in  Weight  and  Thickness 
Permissible  Variations.   10.  The  cross-section  or  weight  of  each  piece  of  steel 
shall  not  vary  more  than  2.5  per  cent  from  that  specified;    except  in  case  of 
sheared  plates,  which  shall  be  covered  by  the  following  permissible  variations. 
One  cubic  inch  of  rolled  steel  is  assumed  to  weigh  0.2833  lb. 

(a)  When  Ordered  to  Weight  per  Square  Foot:  The  weight  of  each  lot  in 
each  shipment  shall  not  vary  from  the  weight  ordered  more  than  the  amount 
given  in  Table  I.* 

(b)  When  Ordered    to  Thickness:   The  thickness  of  each  plate  shall  not  . 
vary  more  than  o.oi  in  under  that  order. 

The  overweight  of  each  lot  in  each  shipment  shall  not  exceed  the  amount 
given  in  Table  II.* 

V.  Finish 

Finish,  i  t  .  The  finished  material  shall  be  free  from  injurious  defects  and  shall 
have  a  workmanlike  finish. 

VI.  Marking 
Marking.  12.  The  name  or  brand  of  the  manufacturer  and  the  melt-number 
shall  be  legibly  stamped  or  rolled  on  all  finished  material,  except  that  rivet  and 
lattice-bars  and  other  small  sections  shall,  when  loaded  for  shipment,  be  properly 
separated  and  marked  for  identification.  The  identification-marks  shall  be 
legibly  stamped  on  the  end  of  each  pin  and  roller.  The  melt-number  shall  be 
legibly  marked,  by  stamping  if  practical,  on  each  test-specimen. 

VII.  Inspection  and  Rejection  ''  ^'^  '^  \^/  "  ' 

Inspection.     13.  (See  complete  Specifications  for  Sections  13,  14  and  15.) 

6.  Tension-Members 
Angles.  The  best  section  for  tension-members  of  relatively  small  size  depends 
greatly  on  the  kind  of  end-connections  used.  Angles  or  channels  are  generally 
used  for  riveted  connections.  For  very  small  members  rectangular  bars,  such  as 
lacing-bars,  may  be  used.  The  strength  of  such  members  is  computed  on  the  net 
area  through  the  rivet-holes.  Angles  used  in  tension  should  have  lugs  riveted 
to  the  outstanding  legs  and  the  tie-plate  for  the  better  distribution  of  the  stress 
over  the  section.  Tests  on  angles  with  riveted  connections  reported  by  F. 
P.  McKibbenf  gave  from  77  to  86%  of  the  strength  of  the  material  as  shown  by 

*  Tables  I  and  II  are  omitted  here  for  lack  of  space.  The  complete  specifications  C3B 
be  obtained  from  the  Society. 

t  Proceedings  of  the  American  Society  for  Testing  Materials,  Vol.  VI,  1906.  , 


386        Resistance  to  Tension.     Properties  of  Iron  and  Steel     Chap.  11 

tension-tests  on  standard  specimens  cut  from  these  angles.  Lugs  increased  the 
strength  from  4.7  to  8.7%.  It  was  also  shown  that  a  connection  giving  the 
center  of  the  pull  on  the  center  of  gravity  of  the  section  gave  considerably  higher 
strengths  than  when  the  center  of  pull  was  in  line  with  the  gauge-line  of  the 
rivets.  In  computing  the  net  sectional  area  as  reduced  by  rivet  and  bolt- 
holes  Table  XI  will  be  found  very  convenient. 

Eye-Bars  are  used  for  the  main  tension-members  of  pin-connected  trusses. 
They  are  rectangular  in  section  with  a  forged  head  upset  in  dies  and  of  the  same 
thickness  as  the  bar.  The  eye  is  accurately  drilled  in  position  in  the  axis  of  the 
bar,  true  to  diameter  and  exact  central  distance.  Because  of  its  advantages 
for  forging,  soft  steel  is  used  in  making  eye-bars.  They  are  also  carefully  an- 
nealed before  drilling.  Table  VI  gives  the  dimensions  of  standard  eye -bars 
manufactured  by  the  mills  of  the  American  Bridge  Company.  These  bars 
are  of  practically  the  same  dimensions  as  the  standard  bars  of  other  com- 
panies. There  is  from  34  to  42%  excess  material  in  the  section  through  the  eye 
to  insure  in  the  forged  part  the  development  of  the  full  strength  of  the  body  of 
the  bar.  Standard  bars  should  be  used  in  design  to  avoid  the  expense  of  making 
special  dies  in  which  to  form  the  heads.  Bars  of  less  than  the  given  minimum 
thickness  are  liable  to  fail,  when  loaded,  by  buckling  in  the  head.  Thick  bars 
increase  the  bending-stresses  in  the  pins  and  thus,  indirectly,  the  necessary 
size  of  the  eye.  Except  for  very  large  structures  they  are  limited  to  about 
2  in. 

Tests  of  FuU-Size  Eye-Bars  are  generally  required  when  a  great  number  of 
them  are  to  be  used  in  a  structure,  one  in  every  fifty  bars  being  usually  tested. 
The  specifications  for  carbon-steel  bars  require  that  an  [ultimate  tensile 
strength  of  56  000  lb  per  sq  in  shall  be  developed,  that  the  elongation  in  the 
whole  length  shall  be  10%  and  that  failure  shall  occur  in  the  body  of  the  bar. 
Nickel  steel  has  been  used  for  tension-members  on  a  few  long-span  bridges.  The 
working  stress  on  the  eye-bars  was  increased  about  one-half  over  that  used  for 


O  J^Qnii  iHiQCr  O 


Fig.  3.     Eye-bar  with  Screw-ends  for  Sleeve-nut  or  Turn-buckle 

carbon  steel,  and  the  requirements  of  the  test-bars  made  correspondingly  severe. 
The  eye  is  made  Vso  in  greater  than  the  diameter  of  the  pin.  Bars  packed  on 
the  same  pins  are  drilled  at  the  same  setting  so  as  to  be  of  exactly  the  same 
length.  Bars  must  be  true  to  length  within  %2  in.  Small  eye-bars  are  some- 
times made  with  upset  screw-ends  and  sleeve-nuts  or  turnbuckles  in  the 
middle  for  adjustment,  as  shown  in  Fig.  3  and  Table  VI,  page  395. 


1^2  D-^. 
Loop-eyes  and  Sleeve-nuts 

Loop-Rods  (Fig.  4,  and  Table  VII)  of  round  or  square  section  with  welded 
loop-ends  are  used  for  counterties  and  bracing.  Because  of  the  weld  they 
are  not  so  dependable  as  other  types  of  tension-members,  but,  because  of  the 
adjustment,  are  well  adapted  for  this  service  as  secondary  members. 


Tension-Members 


387 


Fig.  5.     Forked  Loop 


A  Forked-Loop  Rod,  Fig.  5,  may  be  used  for  one  of  two  tension-rods  so  as 
to  avoid  eccentricity  where  two  rod^  balance  each  other  on  a  pin.  A  clevis 
at  each  end  of  one  of  the  rods 
accompUshes  the  same  object. 

Turnbuckles  and  Sleeve-Nuts. 
The  dimensions  of  these  for  adjust- 
ing the  lengths  and  initial  stress  in 
ties  are  given  in  Table  VIII,  page 
397.  The  open  turnbuckle  has  the 
advantage  of  being  easily  inspected 
to  note  that  the  thread  has  sufficient 
bearing  and  that  the  ends  of  the 
rods  do  not  butt  together. 

Upset  Screw-Ends  are  threaded  enlargements  on  the  ends  of  rods  or  bolts 
designed  to  give  to  the  threaded  portions  a  strength  as  great  as  that  of  the  body 
of  the  bar.  Because  of  effects  of  forging  it  is  necessary  to  make  the  area  of  the 
cross-section  of  the  upset  end  at  the  root  of  the  thread  a  little  larger  than  that 
of  the  rod  itself.  A  standard  upset  rod  will  fail  in  the  body  of  the  bar  with- 
out damaging  the  threaded  portion  enough  to  prevent  the  turning  of  the  nuts^ 
The  dimensions  given  are  nearly  the  same  with  all  manufacturers.  If  upset 
rods  can  not  be  obtained  the  section-area  at  the  root  of  the  thread  must  be 
used  in  computing  the  safe  load. 

Clevises.  Table  IX,  page  398,  gives  the  dimensions  and  other  details  fot 
clevises  according  to  the  latest  standards  of  the  American  Bridge  Company. 

Tables.  The  following  tables  will  be  found  useful  in  designing  tension* 
members,  or  for  drawing  turnbuckles,  sleeve-nuts,  clevises,  etc.  The  strength 
of  plain  rods  in  Table  II  is  based  on  the  area  at  the  root  of  tlie  thread.  For 
lengths  and  weights  of  tie-rods  and  anchors  for  steel  beams,  see  Table  XIX, 
Chapter  XV. 


Resistance  to  Tension.     Properties  of  Iron  and  Steel     Chap.  11 
Table  II.     Safe  Loads  in  Pounds  on  Round  Rods 


Plain  rods 

Upset  rods 

1 

Load  in  pounds  based  on  area 

Load  in 

pounds  based  on  full       | 

at  root  of  thread 

area  of  rod 

Diameter 

inches 

Stress  in  lb  per  sq  in 

Stress  in  lb  per  sq  in 

10  000 

12000 

16000 

10  000- 

12000 

16000 

^i 

270 

324 

432 

491 

590 

785 

^/ie 

450 

540 

720 

767 

920 

I  230 

% 

680 

816 

1088 

I  104 

I  320 

1770 

Vio 

930 

I  116 

1488 

1503 

I  800 

2  400 

% 

I  260 

I  513 

2  016 

1963 

2360 

3140 

«A6 

I  620 

1944 

2592 

2485 

2970 

3960 

% 

2020 

2424 

3232 

3068 

3680 

4910 

% 

3020 

3624 

4832 

4418 

5300 

7070 

% 

4  200 

5040 

6  720 

6013 

7  210 

9620 

I 

5500 

6600 

8800 

7854 

9420 

12570 

'     iVs 

6  940 

8328 

II  104 

9940 

II  930 

15900 

IH 

8930 

10  716 

14288 

12  270 

14720 

19630 

1% 

10570 

12680 

16  910 

14  840 

17  810 

23750 

IV2 

12950 

15  540 

20  720 

17670 

21  200 

28  270 

1% 

15  150 

18  180 

24240 

20730 

24  880 

33170 

18/4 

17440 

20030 

27900 

24  050 

28860 

38480 

iVs 

20  480 

24580 

32760 

27  610 

33  130 

44180 

2 

23020 

27620 

36830 

31  420 

37  700 

50270 

2V8 

26340 

31  610 

42150 

35  460 

42550 

56640 

2H 

30230 

36280 

48370 

39760 

47710 

63600 

2% 

33000 

39600 

52800 

44300 

53160 

70  880 

2y2 

37  ISO 

44630 

59440 

49  080 

58900 

78  530 

2% 

46190 

55430 

73900 

59390 

71  270 

95  020 

3 

54280 

65  140 

86  850 

70680 

84820 

113  090 

3V4 

65  100 

78  120 

lot  160 

82950 

99  540 

132  720 

31/2 

75480 

90570 

120  770 

96  210 

115  450 

153  840 

3% 

86410 

103  690 

138  250 

ITO  450 

132  540 

176690 

4 

99930 

119  920 

159  «*^9o 

125  660 

tso  790 

201  050 

4H 

113  290 

135900 

181  300 

141  800 

170  160 

226880 

4V2 

127  430 

152900 

203900 

159000 

190800 

254400 

4% 

142  200 

170  600 

227500 

177  200 

212  640 

283  520 

5 

157  630 

189  100 

252  200 

196300 

235  560 

314  080 

5V4 

175  720 

210  800 

'281  100 

216  400 

259  680 

346200 

5V2 

192  670 

231  200 

308300 

237500 

285000 

380000 

5% 

212  620 

255  100 

340  200 

259600 

311  000 

414700 

6 

230  980 

277200 

369600 

282  700 

339  200 

452  300 

Tension-Members 


389 


Table  III.     Safe  Loads  in  Pounds  for  Flat  Rolled  Bars 

Computed  for  a  stress  of  i6  coo  pounds  per  square  inch 


Thick- 
ness in 
inches 

Width  in  inches 

1 

I 

lU 

■ 

iy2 

1% 

2 

2V4 

2V2 

2«/4 

3 

3Vi 

Vifl 

1 000 

I  250 

2  000 

2  250 

2  500 

2750 

3  000 

3250 

I  500 

1750 

Vs 

2  000 

2500 

3000 

3500 

4  000 

4500 

5000 

5500 

6000 

6500 

yio 

3  000 

3750 

4500 

5250 

6  000 

6750 

7500 

8250 

9  000 

9750 

Vt 

4  000 

5  000 

6000 

7  000 

8000 

9  000 

10  000 

II  000 

12000 

13000 

•yi6 

5  000 

6  250 

7  500 

8750 

10  000 

II  250 

12500 

13  750 

15000 

16250 

% 

6  000 

7500 

9000 

10  500 

12  000 

13500 

15  000 

16500 

18  000 

19500 

Tifl 

7000 

8750 

10500 

12  250 

14000 

15  750 

17500 

19  250 

21  000 

22750 

V2 

8000 

10  000 

12  000 

14  000 

16  000 

18  000 

20  000 

22  000 

24  ooc 

26000 

rio 

9000 

II  250 

13500 

15750 

18  000 

20250 

22500 

24750 

27  000 

29250 

^^M 

ID  000 

12  500 

15  000 

17500 

20  000 

22  500 

25  000 

27500 

30  000 

32500 

Hio 

II  000 

13  750 

16  500 

19250 

22  000 

24750 

27500 

30250 

33000 

36750 

% 

12  000 

15  000 

18  000 

21  000 

24  000 

27  000 

30  000 

33000 

36  000 

39000 

i%o 

13000 

16  250 

19500 

22750 

26000 

29250 

32500 

35  750 

39000 

42250 

Vh 

14  000 

17500 

21  000 

24500 

28000 

31500 

35000 

38500 

42000 

'45500 

1^/la 

15000 

18750 

22  500 

26  250 

30000 

33750 

37500 

41  250 

45000 

48750 

I 

16  000 

20  000 

24  000 

28  000 

32  000 

36000 

46  000 

44000 

48000 

52000 

iVio 

17  000 

21  250 

25500 

29750 

34000 

38250 

42500 

46750 

SI  000 

55250 

iVs 

18  000 

22  500 

27  000 

31500 

36000 

40500 

45000 

49500 

54000 

58500 

rYio 

19  000 

23750 

28500 

33250 

38000 

42750 

47500 

52250 

57000 

61750 

iM 

20  000 

25000 

30  000 

35000 

40  000 

45000 

50000 

55000 

60000 

65000 

1% 

22  000 

27500 

33000 

3850c 

44000 

49500 

55  000 

60  500 

66000 

71500 

iy2 

24000 

30000 

36000 

42000 

48  000 

54  000 

60  000 

66  000 

72  000 

78  000 

i-ys  • 

26  000 

325CO 

39000 

45500 

52000 

58500 

65  000 

71500 

78  000 

84500 

1% 

28000 

35000 

42000 

49000 

56000 

63000 

70  000 

77000 

84  000 

91  000 

1% 

30000 

37500 

45  000 

53500 

60  000 

67500 

75000 

83500 

90  00c 

97500 

2 

32000 

40  000 

48  000 

56  000 

64000 

72000 

80000 

88000 

96000 

104  000 

' ,  '    ' _ _ - - .  -. 

390       Resistance  to  Tension.    Properties  of  Iron  and  Steel    Chap.  11 


Table  HI  (Continued).     Safe  Loads  in  Pounds  for  Flat  Rolled  Bars 

Computed  for  a  stress  of  i6  ooo  pounds  per  square  inch 


Thick- 

Width  in  inches 

ness  in 

inches 

3V2 

3% 

4 

4U 

4V2 

4«/4 

5 

5V2 

6 

6V2 

He 

3500 

3  750 

4  000 

4250 

450a 

4750 

5  000 

5500 

6  000 

6500 

Vs 

7  000 

7500 

8000 

8500 

9000 

9500 

10  000 

II  000 

12  coo 

13000 

8/16 

10500 

II  250 

12  000 

12750 

13500 

14250 

15  000 

16  500 

18  000 

19500 

H 

14  000 

15000 

16000 

17000 

18000 

19000 

20000 

22  000 

24000 

26000 

"/io 

17500 

18750 

20  000 

21  250 

22  500 

23750 

25  000 

27500 

30  000 

32500 

% 

21000 

22  500 

24000 

25500 

27000 

28  500 

30000 

33000 

360c 

XD 

39000 

'^/io 

24500 

26  250 

23  000 

29750 

31500 

33250 

35000 

38  500 

42  oc 

X) 

45500 

¥2 

28000 

30000 

32000 

34000 

36000 

38000 

40000 

44000 

480c 

50 

52  000 

»/l6 

31500 

33750 

36000 

38250 

40500 

42750 

45  000 

49  500 

54  o< 

)0 

58500 

% 

35  000 

37500 

40  000 

42500 

45000 

47  500 

50  000 

55  000 

60  oc 

XD 

65000 

Hie 

38  500 

41  250 

44  000 

46750 

49500 

52  250 

55000 

60  500 

66  a 

:o 

71500 

% 

42000 

45000 

48000 

51  000 

54000 

57000 

60000 

66  000 

720c 

)0 

78000 

13/iQ 

45  500 

48750 

52000 

55  250 

58500 

61750 

65  000 

71  500 

78  0< 

)0 

84500 

Vs 

49000 

52500 

56000 

59  500 

63000 

66  500 

70000 

77  000 

84  o< 

X) 

91  000 

"/!'« 

52  500 

56250 

60  000 

63750 

67  500 

71  250 

75000 

82  500 

900c 

)0 

97  500 

I 

56000 

60000 

64  000 

68000 

72000 

76000 

80  000 

88  000 

96  o< 

X) 

104  000 

iVia 

59  500 

63750 

68000 

72250 

76500 

80750 

85  000 

93500 

102  a 

50 

no  500 

i^^ 

63000 

67500 

72000 

76500 

8i  000 

85500 

90000 

99000 

108  0< 

X) 

117  000 

I%0 

66500 

71  250 

76000 

80750 

85500 

90250 

95000 

104  500 

114  o< 

X) 

123  500 

lU 

70000 

75  000 

80000 

85000 

90000 

95000 

100  000 

no  000 

120  0( 

X) 

130  000 

1% 

77000 

82  500 

88000 

93500 

99000 

104  500 

no  000 

121  000 

132  o< 

DO 

143  000 

1^2 

84000 

90  000 

96000 

102  000 

108000 

114  000 

120000 

132  000 

144  o< 

X) 

156000 

1% 

91  000 

97500 

104000 

no  500 

117  000 

123500 

130000 

143000 

156  0 

X) 

169  000 

1% 

98000 

105  000 

1X2  000 

119  000 

126000 

133000 

140  000 

154000 

168  a 

DO 

182  oco 

1% 

10$  000 

112  500 

120  000 

127500 

135  OQO 

142  500 

150  OQO 

165000 

i8qo( 

DO 

195000 

2 

112  000 

120  000 

128  000 

136000 

144000 

152000 

160000 

176000 

192  0( 

DO 

208000 

1 

Tension-Members 


Table  IV.     Safe  Loads  in  Pounds  for  Flat  Rolled  Bars 

Computed  for  a  stress  of  lo  coo  lb  per  square  inch* 


Thick- 
ness in 
inches 


iVi 


1V2 
1% 
1% 


Width  in  inches 


630 
I  250 
1880 
2500 

3  130 

3750 
4380 
Sooo 

5630 

6  250 
6880 

7  500 

8  130 
8  750 
9380 

10  poo 

10600 
n  300 
XI  900 

12  500 

13  800 
IS  000 
16300 
17500 

18800 
20  000 


iV*        1V2        i3/i 


780 
I  560 
2340 
3130 

3910 
4630 

5  470 
6250 

7030 
7810 
8590 
9380 

10  200 

10  900 

11  700 

12  500 

13300 

14  100 

14  800 

15  600 

17  200 
18800 

20  300 

21  900 

23400 
25  000 


940 
1880 
2810 
3750 

4  690 
5630 
6  560 

7500 

8  440 
9380 

10  300 

11  300 

12  200 

13  100 

14  100 

15  000 

15900 

16  900 

17  800 
18800 

20600 
22  500 
24  400 
26  300 

28  100 
30  000 


1  090 

2  190 
3280 
4380 

5470 
6560 
7660 
8750 

9840 
10  900 

12  000 

13  100 

14  200 
15300 

16  400 

17  soo 

18600 

19  700 
20800 
21  900 

24  100 
26  300 
28  400 
30  600 

32800 
35  000 


1  250 

2  500 
3750 
5  000 

6250 

7500 
8750 

10  000 

11  300 

12  500 

13  800 
15  000 

163PO 

17500 
18800 
20000 

21  300 

22  500 
23800 
2S  000 

27500 

30  000 

32  500 
35  000 

37500 
40  00c 


2l/4     2V3     2% 


1  410 

2  810 
4  220 
5630 

7030 
8440 
9840 

11  300 

12  700 

14  100 

15  500 

16  900 

18  300 

19  7»o 

21  100 

22  500 

23900 

25  300 

26  700 
28  100 

30900 
33800 
36  600 
39400 

49  200 
45000 


I  560 
3130 
4690 
6250 

7810 
9380 
10900 
12  500 

14  100 
15600 
17  200 
18800 

20300 
21  900 
23  400 
25  000 

26600 

28  100 

29  700 
31300 

34400 

37  500 

40600 
43800 

46900 
50  000 


I  720 
3440 
5  160 
6880 

8590 
10300 

12  000 

13800 

IS  500 

17  200 

18  900 
20600 

22300 

24  100 

25  800 
27  500 

39300 
30900 
32  700 
34400 

37800 
41300 

44700 
48  100 

51  600 
55  000 


I  880 
3750 
5630 
7500 

9380 
II  300 
13  100 
IS  000 

16900 
18800 
20  600 
22  500 

24  400 
26300 
28  100 
30000 

31900 
33800 
35600 
37500 

41300 
45000 
48800 
52500 

56300 
60000 


3V4 


2030 
4  060 
6  090 
8130 

JO  200 
12  200 
14200 
16300 

18300 
20300 
22300 
24  400 

126400 
28400 
30500 
32  SOO 

34  soo 
36600 
38600 
40600 

44700 
48800 

S2  800 
56900 

60900 
65000 


•  For  unit  stresses  of  12  000,  12  500,  and  15  000  lb  increase  by  ^o,  Vi,  and  V2  respec- 
tively. 

For  working  strength  of  wrought  iron  and  steel,  see  pages  376  and  382. 


392       Resistance  to  Tension.    Properties  of  Iron  and  Steel    Chap.  11 


Table  IV  (Continued).     Safe  Loads  in  Pounds  for  Flat  Rolled  Bars 

Computed  for  a  stress  of  lo  ooo  lb  p)er  square  inch 


Thick- 

Width in  inches 

ness  in 
inches 

3V2 

3% 

, 

4 

4V4 

* 

aV2 

4?i 

5 

5^/^ 

6 

6V2 

Vl6 

2  190 

2340 

2810 

2970 

3130 

3440 

3750 

4  060 

2500 

2660 

Vs 

4380 

4690 

5  000 

5310 

5630 

5  940 

6  250 

6880 

7500 

8  130 

%6 

6560 

7030 

7500 

7970 

8440 

8910 

9380 

10300 

II  300 

12  200 

■ .  i  ■ 

8750 

9380 

10  000 

10  600 

II  300 

II  900 

12  500 

13800 

15  000 

16300 

%e 

10  900 

II  700 

12  500 

13300 

14  100 

14800 

15600 

17  200 

18  800 

20  300 

-     % 

13  100 

14  100 

15  000 

15900 

16  900 

17800 

18800 

20  600 

22  500 

24400 

Vio 

IS  300 

16  400 

17500 

18600 

19700 

20  800 

21  900 

24  100 

26  300 

28  400 

V2 

17500 

18800 

20  000 

21  300 

22500 

23800 

25  000 

27500 

30000 

32500 

»/l6 

19700 

21  100 

22500 

23900 

25300 

26  700 

28  100 

30900 

33800 

36600 

% 

21  900 

23400 

25  000 

26  600 

28  100 

29700 

31  300 

34400 

37  SCO 

40  600 

Hio 

24  100 

25  800 

27500 

29  200 

30900 

32  700 

34400 

37800 

41  300 

44700 

8/4 

26300 

28  100 

30000 

31  900 

33800 

35600 

37500 

41  300 

45  000 

48800 

1«/16 

28  400 

30500 

32500 

34500 

36600 

38600 

40  600 

44700 

48800 

528C0 

% 

30600 

32800 

35000 

37200 

39400 

41  600 

43800 

48  100 

52  500 

56  900 

1-yio 

32800 

35  200 

37500 

39800 

42  200 

44500 

46  900 

SI  600 

56  300 

60900 

I 

35000 

37500 

40  000 

42500 

45000 

47500 

SO  coo 

55000 

60  000 

6s  000 

iVio 

37200 

39800 

42500 

45200 

47800 

SO  500 

53100 

58400 

63800 

69  100 

iVs 

39400 

42  200 

45000 

47800 

50600 

53400 

56300 

61  900 

67500 

73  TOO 

18A6 

41  600 

44500 

47500 

50500 

53400 

56400 

59400 

65300 

71  300 

77200 

IV4 

43800 

46  900 

SO  000 

53100 

56300 

59400 

62500 

68800 

75000 

81  300 

1% 

48  100 

SI  600 

55000 

58  400 

61  900 

65  300 

68800 

75  < 

XX) 

82500 

89400 

11/2 

52500 

56300 

60  000 

63800 

67500 

71300 

75000 

82. 

>oo 

90  000 

97S0O 

1% 

56900 

60  900 

6s  000 

69100 

73100 

77200 

81  300 

89. 

too 

97500 

105  600 

iVi 

61  300 

65  600 

70  000 

74400 

78800 

83  100 

87500 

96. 

JOO 

105  000 

113  800 

1% 

65  600 

70300 

75  000 

79700 

84  400 

89  100 

93800 

103 

00 

112500 

121  900 

2 

70000 

75000 

80  000 

8s  000 

90  000 

95000 

100  000 

no  c 

XX3 

120000 

130  000 

:.-.  r?  fO    ,,.>-;i 

1 

_ 

*  See  foot-note,  preceding  table. 

xx>  ?  I  nn;>  ,oc)?  c  i 


Tension-Members 


393 


Table  V. 


Standard  Proportions  of  Upset  Screw-Ends  for  Round  and 
Square  Bars 


Round  bars 

Square  bars 

Diam.  of 

round  or 

Excess 

Excess 

side  of 

Diam. 

Diam.  of 

Number 

of  effec- 

Diam. 

Diam.  of 

Number 

of  effec- 

square 

of  upset 

screw  at 

of 

tive  area 

of  upset 

screw  at 

of 

tive  area 

bar 

screw- 

root  of 

threads 

of  screw- 

screw- 

root  of 

threads 

of  screw- 

in 

end 

thread 

per 

end  over 

end 

thread 

per 

end  over 

in 

in 

inch 

bar 

% 

in 

in 

inch 

bar 

% 

V2 

8/4 

0.620 

10 

54 

% 

0.620 

10 

21 

«/l« 

3/4 

0.620 

10 

21 

Vh 

0.731 

9 

33 

% 

% 

0.731 

9 

37 

I 

0.8.37 

8 

41 

Hio 

I 

0.837 

8 

48 

I 

0.837 

8 

17 

% 

I 

0.837 

8 

25 

iVs 

0.940 

7 

23 

^u 

1% 

0.940 

7 

34 

iM 

1.065 

7 

35 

% 

iVi 

1.065 

7 

48 

1% 

1. 160 

6 

38 

i-yi« 

1V4 

1.065 

7 

29 

1% 

1. 160 

6 

20 

I 

1% 

1 .  160 

6 

35 

1V2 

1.284 

6 

29 

iVio 

1% 

1. 160 

6 

19 

1% 

1.389 

51/2 

34 

iVs 

1 1/2 

1.284 

6 

30 

1% 

1.389 

5V2 

20 

i-Tio 

11/2 

1.284 

6 

17 

1% 

1.490 

5 

24 

iM 

1% 

1.389 

sVi- 

23 

1% 

1. 615 

5 

31 

iV\ti 

1% 

1.490 

5 

29 

1% 

1. 615 

5 

•       19 

1% 

1% 

1.490 

5 

18 

2 

1. 712 

4V2 

•     22 

iVio 

1% 

1. 615 

5 

26 

21.^8 

1.837 

4^2 

28 

IV2 

2 

1. 712 

4V2 

30 

2V8 

1.837 

4V2 

18 

irio 

2 

1. 712 

4V2 

20 

2l/4 

1.962 

4V2 

24 

1% 

2V8 

1.8.37 

4V2 

28 

2% 

2.087 

4V2 

30 

1% 

2V8 
2U 

1.837 
1.962 

4V:i 
4VI. 

18 
26 

2% 

2.087 

4V2 

20 

2V2 

2.175 

4 

21 

i^'^/ui 

2U 

1 .  962 

4VI. 

17 

2% 

2.300 

4 

26 

iVs 

2% 

2.087 

4^2 

24 

2% 

2.300 

4 

18 

i^yio 

2I/2 

2.175 

4 

26 

2% 

2.425 

4 

23 

2 

2V2 

2.175 

4 

18 

2V8 

2.550 

4 

28 

2M« 

2% 

2.300 

4 

24 

2% 

2.550 

4 

20 

21/8 

2-''/8 

2.300 

4 

17 

3 

2.629 

31/2 

20 

23/lC 

2% 

2.425 

4 

23 

3V8 

2.754 

31/2 

24 

394       Resistance  to  Tension.    Properties  of  Iron  and  Steel     Chap.  11 

Table  V  (Continued).    Standard  Proportions  of  Upset  Screw-Ends  for 
Round  and  Square  Bars 


Round  bars 

Square  bars 

Diam.  of 

round  or 

Excess 

Excess 

side  of 

Diam. 

Diam.  of 

Number 

of  efTec- 

Diam. 

Diam.  of 

Number 

of  efifec- 

square 

of  upset 

screw  at 

of 

tive  area 

of  upset 

screw  at 

of 

tive  area 

bar 

screw- 

root  of 

threads 

of  screw- 

screw- 

root  of 

threads 

of  screw- 

in 

end 

thread 

per 

end  over 

end 

thread 

per 

end  over 

in 

in 

inch 

bar 

% 

in 

in 

inch 

bar 

% 

2V4. 

2V8 

2.S50 

4 

28 

3V8 

2.754 

3V2 

18 

2^/i6 

2^/8 

2.550 

4 

22 

3V4 

2.879 

3y2 

22 

23/^8 

3 

2.629 

3V2 

23 

3% 

3.004 

3^1- 

26 

aVie 

3V8 

2.754 

3V2 

28 

3% 

3  004 

3V2 

19 

2V2 

3V8 

2.754 

3V2 

21 

3V2 

3.100 

3V4 

21 

2»/l6 

3V* 

2.879 

3V2 

26 

3% 

3.225 

3y4 

24 

2% 

3H 

2.879 

3V2 

20 

3% 

3.225 

3H 

19 

2Hi6 

3% 

3.004 

3V2    . 

25 

3^/4 

3.317 

3 

20 

2% 

3% 

3.004 

zV^ 

19 

3% 

3.442 

3 

23    . 

2l8/i6 

3V2 

3- 100 

3V4 

22 

3'/8 

3-442 

3 

18 

2V8 

3% 

3.225 

3H 

26 

4 

3.567 

3 

21 

2i-ri6 

3% 

3.225 

3V4 

21 

4V8 

3.692 

3 

24 

3 

3^i 

3.317 

3 

22 

4V8 

3.692 

3 

19 

3V8 . 

3% 

3.442 

3 

21 

4% 

3.923 

2% 

24 

3V4 

4 

3.567 

3 

20 

4V2 

4.028 

2% 

21 

3^/^8 

4V8 

3.692 

3 

20 

4% 

4.153 

2% 

19 

3V2 

4U 

3.798 

2'V8 

18 

3% 

4V2 

4.028 

2% 

23 

3% 

4% 

4.IS3 

2% 

23 

3% 

4% 

4.255 

•2% 

21 

Remarks.  As  upsetting  reduces  the  strength  of  iron,  bars  having  the  same  diameter 
at  the  root  of  the  thread  as  that  of  the  bar  invariably  break  in  the  screw-end  when 
tested  to  destruction,  without  developing  the  full  strength  of  the  bar.  It  is  therefore 
necessary  to  make  up  for  this  loss  in  strength  by  an  excess  of  Tnetal  in  the  upset  screw- 
ends  over  that  in  the  bar. 

Table  V  is  the  result  of  numerous  tests  on  finished  bars  made  at  the  Keystone  Bridge 
Company's  Works  in  Pittsburgh,  Pa.,  and  gives  proportions  that  will  cause  the  bar  to 
break  in  the  body  rather  than  in  the  upset  end. 

The  screw-threads  in  the  above  table  are  the  Franklin  Institute  standards. 

To  make  one  upset  end  for  a  5-in  length  of  thread,  allow  6  in  in  length  of  rod,  addi- 
tional. 


Tension-Members 


395 


Table  VI 

.*     Steel  Eye-Bars 

(AMERICAN 

BRIDGE    COMPANY 

standard)  \ 

Ordinary  Eye-Bar 

5 

Adjustable  Eye-Bar 

Minimum  length  of  short  end  from 
center  of  pin  to  end  of  screw,  6  ft,  pref- 
erably 7  ft. 
Thread  on  short  end  to  be  left  hand 
Pitch  and  shape  of  thread  A.  B.  Co 
standard 

ii=::±g)--H 

j^ 
-t-> 

2 

3 

4 

5 
6 
7 
8 
9 

lO 
12 
14 

B 

Thicl 

ar 

Head 

cness 

Dia. 

Maximum 
pin 

Additional 

material, 

c,  ft  and 

in 

Max, 
in 

I 
I 

Min, 
in 

Bar 

Screw-end                  | 

Ex- 
cess 
head 
over 
bar, 

% 

37.5 
40.0 
41.7 

2 

2yi 

3 
4 

5 
6 

7 

8 

t  H 

^8 

Dia. 
in 

Ex- 
cess 
up- 
set 
over 
bar, 
% 

33.6 
36.6 
31.4 
41.2 
38.1 
36J 

34.3 
41.6 
23.9 

23.9 
32.0 
35.7 
44.6 
36.2 
24.1 
30.2 
34.2 
38.3 

L'th 
m, 
in 

Additional 

material, 

6,  ft  an(J 

in 

For 
or- 
der- 
ing 
bar 
I-  0 
I-  4 

I-   C) 

For 

figur- 
ing 

w't 

0-  7 

O-II 

1-  4 

in 

4K' 

t6H 

Dia. 

in 

2% 
3-M 

2K2 

33'-2 

4V2 

3H 
4H 
5H 

4'/2 

5K2 
6 1/2 

8H 

6K2 
ly 
7 
8 
9 

7 
8 

9 

7H 
9K2 

9 

loi.^ 

11^2 
10 

IIK2 
13 

12 
14 
15 

For 
or- 
der- 
ing 
bar 

For 
fig- 
ur- 
ing 
w't 

6 

7 

t  8 

7^/i 
8K2 

t   9V^2 

I-  3 

1-  7 

2-  0 

O-IO 

I-  2 

I-  7 

I-  I 
I-  5 

I-IO 

1-  6 

I-IO 

2-  2 
1-8 
2-  2 
2-9 

I-IO 
2-   I 
2-  8 
2-  2 
2-  6 
2-1 1 

2-  3 

2-  6 
2-1 1 
2-6 

3-  r 

i-M 
2 

4 

5 
5 
5 

I-  0 
I-  0 

O-IT 

8 

1-6 
i-ii 
2-  4 

t«/4 

'A 

I 

2% 
2H 
2% 

I-  0 
I-  0 
I-  0 
I-  0 
I-  I 
I-  I 
I-  I 

O-II 

I-  I 

I-  2 

I-  0 
O-II 

I-  0 

I-  I 

I-  2 
I-  0 
I-  0 

I-  I 

I-  2 

I-  0 

r-  I 
I-  2 
I-  2 
I-  0 
I-  I 
I-  I 
I-  2 
I-  3 

8 
8 

7H 
9H 
8H 

iH 

'A 

I 

10 
II 

tl2 

37.5 
35.0 

I-ll 
2-  3 
2-  8 

2-  I 

2-  8 

3-  3 

t  =)4 

I 

t  y^ 
I  , 

t  ^4 

I 

2\\ 
2\b. 
2\h 

2 

I 
I 

12 

I3K2 

ti5 

2H 
2% 

3 

3H 
274 
3 

zM 
z\^ 

3^/4 

5\^ 

6 

6J,^ 
6 
6 

7 

7 

7 

7 

iVi 

8 

7J'^ 

8H 

8K2 

8 

81/^ 

8K2 

9 

9V^ 

8i^^2 
^\^ 

8 

1 

8 

8^A 

9 

7'A 
8 

8H 
9H 

2 

2 

2 
2 
2 

I 
I 

— 
I 

1 5^^ 

l'/8 

14 

14M 

17K2 

fiSH 

375 

2-  4 

2-  6 

3-  2 
2-  7 
2-1 1 
3^ 

2-  8 

3-  0 
3-  4 
2-II 
3-  7 

3-  5 
3-9 

4-  I 
3-8 
4-  2 
4-8 

4-  3 
4-10 

5-  5 

35.7 

37.5 
38.9 
35.0 

ti 

i»/i 
i}4 

iH 

I3/^ 
1 1/2 

\iA 
i\i 
iH 
i\^ 
1% 

3J'^ 

3^4 

4 

4'/4 

4 

4H 

\Vi 

4^/4 

4K 

4^^ 

4^/4 

5 

5H 

25.8 
28.0 
33.2 
37.3 

I 

1 1/8 

18 
19 

t20_ 
20 
22 

26.9 
2(9.5 
32.4 
35.4 
25.9 
27.4 
29.3 
31.4 
35.2 

8 

SH 
9 

9H 
8 

8H 
81/i 
9 
10 

22I./2 

24 
t25 

26 1/2 

28 
t29H 

2-10 
3-  3 
3-  7 

2 

2 

lK4 

37.5 

3-3 
3-8 

4-  I 

3-  9 

4-  4: 
4-8 

31 

33 

t34 

35.7 

Bars  marked  f  should  be  used  onHy 
when  absolutely  unavoidable 

i6 

2 

36 

t37K2 

14 
16 

37.5 
34.4 

4-1 1 
5-  5 

4-5 
4-10 

Deduct    pin-hole    when    figuring 
weight 

*  From  Pocket  ComDanion.  Carneeie  Steel  Comoanv.  Pittsbureh.  Pa. 


396        Resistance  to  Tension.     Properties  of  Iron  and  Steel     Chap.  11 


Table  YH.*    Loop-Rods 

AMERICAN    BRIDGE    COMPANY    STANDARD 


„  [•  -Left  thread  ^T^nTTTLengthJ:., 
I  .fr  %|;~-'^g~P"'^  Min.lengthiV^  |  5"->;  For  Turnbnckle 
*-^  I  p-S-'sJ  For  sleeve-nut 

Pitch  and  shape  of  thread  A.  B.  Co  standard 
Additional  length  A,  in  feet  and  inches,  for  one  loop.     A=4.i7/>+5.8y 


Diam. 
of  pin, 


2^4 


•t3y4 


t4H 


t5^4 


t6K 
t6% 


Diameter  or  side  r  of  rod  in  inches 


4         ^^  I         i^       iW       I'M       1^12       i^i       1% 


o-  9^2 

O-IC 
O-II 


I-  3 

4 


-6 

I-  73'^ 
I-  8H 


•9^/i 


o-io 

o-ioH 

i-oH 

I-  ll'^ 

I-  3 

I-  4 
5 

I-  6 

I-  7 

1-  8 
1-9 

i-io 

i-ii 

2-  O 
2-   I 


O-II 
0-IlH 

-  I  Mi 

-  2H 

I-  3K2 

I-  4^'^ 
:-5H 

-  Wi 

■-  7K> 
I-  8H 

I-IO 


2-  4 
2-  5 
2-6 


0-113^^ 

I-  o 
I-  I 
I-  2 

I-  3 

I-  4H 

1-  6K2 

■  7K2 

•  8i^^2 
■9^i 

I-IOJ'^ 

2-  O^^ 
2-  1K2 

2M2 

2-  3K2 

2-  5 
2-6 
2-  7 


2-  9 

2-10 

2-1 1 


I-  9 


2-  oYl 

■  iH 
■23'2 

'  3H 


■  5I/2 

■6j.^2 

2-m 

-io3'^ 
3-  o 

3-  I 


I-  23/2 
I-  zVi 

I-  4^2 

I-SJ'^ 
I-  7 


1-  9 

-10 
I-II 

2-  o 


2—2 
2-  3 
2-  4 

2-  5 

2-  6 

2-.  73'^2 

2-  9H 

2  103-^ 
2-1 1 3'^ 

3-  o}'^ 

3-  l'/^ 


1-43^^ 


I-  63/2 
I-  7K2 


1-  93-^2 
i-ioH 

2-  03'^ 
2-  2 

2-  3 

2-  4 
2-  5 

2-  6 

2-   7 
2-  8 

2-  9 

2-10 

2-II 

3-  O 
3-  I 

3-23^ 


I-  5 
I-  6 

I-  7 

1-  9 

1-9J-I 

i-io3'^ 

1-113^^2 

2-  ©3^^ 
2-  VA 

'.-  2y2 

2-  3'/^2 
2-  4».^ 
2-  53^^ 


I-  6 


1-  8 
9 

I-IO 

I-II 

2-  O 
2-  I 

2-  2 

2-  3 

2-  ^^^ 
2-  S\^ 

2-  63.-a 


2-  63.^1 2-  73-^ 
2-  7'/^  2-  8'/ 


2-  9 

2-10  • 


3-  o 
3-  I 
3-  2 


3-  3 


2-  9H 

2-103^ 


3-  1K2 

3-33'i 

3-  3'/^ 


I-  75-^ 

1-8^^ 
I-  gVi 
i-i 


2-  I 
2-  2 
2-  3 

2-  4 

2-  s 
2-6 

2-  7 
2-  8 

2-  9 
2-10 
2-11  \i 

3-  o^^ 

3-  1K2 
3-23. 


-103^13 
-Il3'l2 

2-  03^^ 

■  l3'^2 

■  21/2 
3K2 

2-4^i 

■  6 

■  7 
-  8 

2-  9 


3-  AVi 


Pins  marked  f 
•  From  Pocket 


are  special.    Maximum  shipping  length  of  Z  =  35  ft. 
Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tension-Members 


397 


Table  VIII.*    Turnbuckles  and  Sleeve-Nuts 

AMERICAN    BRIDGE    COMPANY    STANDARD 


All 
s 

dimensions 

in  inch 

es 

T 

URNBUCKLE 

Sleeve- Nuts 

Or-^ 

c?-^ 

m 

±=^ 

^             "^ 

® 

\%m^ 

\  tut 

|-*^  '! • 

r  nl~ 

Tt 

319^ 

O-M 

1^^ 

^r-^ 

<^ 

r          1^ — ; 

^ — 

l-—-^ 

^  6  ->i 

K6-^ 

U— z!— >} 

a=e" 

;  a=g"  for  turnbuckles  marked  f 

Pitch  and  shape  of  thread,  A.  B.  Co 

Pitch 

and  shape  of  thread,  A.  B.  Co  standard 

standard 

Dia. 
of 

Standard  dimensions 

Dia. 

Standard  dimensions 

screw 

W't, 

of 

W't, 

u 

d 

/ 

c 

/ 

g 

6 

lb 

screw 
11 

d 

/ 

a 

b 

c 

t 

lb 

% 

Vie 

7K8 

91 6 

3/i6 

Vi 

iMe 

T 

Me 

21/^2 

vMe 

^8 

H 

H 

I3//8 

I 

H 

H 

iM 

5/i 

M 

H 

13/^8 

I 

Me 

2%o 
1^16 

7IH6 

7?^ 

1^6 

Me 

M 

I  Ma 

1 1/2 
IK2 

% 

1^6 

Me 

3/i 

iMe 

% 

iH 

8H 

iHe 

n^2 

>6 

2 

2 

Vs 

1V16 

8H 

IH 

H 

I 

2M 

3 

"% 

iK> 

7 

I'H 

1% 

1% 

H 

3 

I 

iH 

9 

iMg 

Vl6 

iM 

2Mc 

4 

I 

1M2 

7 

1^6 

m 

1% 

H 

3 

1% 

iiMe 

9% 

iMc 

Yi 

iH 

2^6 

S 

i.y% 

i-}4 

7M2 

2 

2M6 

1% 

Me 

4 

iM 

iH 

m 

iMc 

Vz 

1^2 

234 

6 

1% 

I'K 

7M2 

2 

2^6 

1% 

Me 

4 

i-ys 

2M6 

io\i 

iiMo 

Vi 

I^^ 

3M6 

7 

m 

2 

8 

23/i 

23/4 

iMs 

% 

5 

iH 

2^ 

10V2 

1% 

% 

l3/4 

3M6 

8 

iVz 

2 

8 

2% 

2% 

i^i 

% 

6 

1% 

2V16 

I078 

2 

% 

I^^ 

3^2 

10 

iMs 

2M 

m 

2% 

3-Ke 

m 

lie 

8 

ly^ 

2% 

II  Ki 

2>^ 

% 

2 

3% 

II 

1^4 

214 

m 

23/4 

3^6 

m 

Me 

9 

i~/k 

21^6 

11^4 

2^6 

iHo 

2^^ 

3^/^ 

12 

1% 

2H 

9 

3% 

3% 

2H 

K> 

10 

2 

3 

12 

2^/^ 

iHe 

2H 

4H 

14 

2 

2\^ 

9 

3\i 

3% 

2H 

'A 

II 

2\i 

3^6 

I23/i 

2).^ 

23/^,, 

2K2 

4^/^ 

17 

2\i 

2% 

9H 

3V2 

4He 

2% 

Me 

14 

2^-4 

?>% 

123/4 

2IM6 

1^6 

2M2 

4% 

20 

2% 

23/4 

9K2 

3^2 

4He 

2% 

Me 

15 

2^A 

iVi^ 

iM 

23/4 

1-Me 

2% 

43^6 

22 

2% 

3 

10 

3'A 

4K2 

2% 

% 

18 

21/2 

3% 

I3K2 

3H6 

2  ^^2 

3 

59^ 

25 

2H 

3 

10 

3% 

4K2 

2% 

% 

19 

2>4 

4H 

I4K4 

3H 

'Mc 

3H 

5% 

33 

2% 

3\i 

10M2 

A% 

4^  Me 

2li 

iMe 

23 

2% 

4M6 

I4H 

3M6 

I  ^^2 

3H 

6Hc 

36 

2li 

3V2 

II 

A% 

sH 

3% 

H 

27 

3 

\H 

IS 

3^^ 

^2 

3M2 

6% 

40 

3 

3y2 

II 

A% 

S% 

3% 

H 

28 

3H 

A% 

15% 

3^/i 

I  Me 

4 

6)4 

50 

3H 

3% 

II H 

5 

51  Me 

3% 

»Me 

35 

zYz 

5K1 

16K' 

4K 

I%2 

4 

7M 

65 

3H 

4 

12 

S% 

6M 

3% 

% 

40 

sH 

55^ 

17H 

4^6 

iMe 

S 

8M 

95 

3% 

4H 

12M2 

s% 

61  He 

3% 

iMe 

47 

4 

6 

18 

4-H 

iMe 

5 

8-M 

108 

4 

4M2 

13 

m 

7He 

AM 

I 

55 

t4K 

6H 

2m 

4«/^ 

1% 

5%2 

9H 

140 

4H 

A% 

13K' 

m 

7K2 

A% 

I  Me 

65 

U'A 

6% 

22^/^ 

5'/^ 

1% 

6H 

io->4 

19s 

4M2 

5 

14 

6% 

71  Me 

4% 

I  Me 

75 

UH 

7H 

23^/^ 

5'H 

2 

63^^ 

II M 

205 

ts 

7'/2 

24 

6 

2\i 

6K2 

11^^ 

250 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


398       Resistance  to  Tension.    Properties  of  Iron  and  Steel    Chap.  11 


Table  IX  *    Clevises 

AMERICAN    BRIDGE    COMPANY    STANDARD 


All  dimensions  in  inches 


Grip 


I    H  t^  *i    rClearance-lina 

■\<-n-^--\-- a — 


Grip=thickness  of  plate+H  in,  but  must  not  exceed  dimension/ 


Clevis- 
No. 


Head 


Max  Min 


Nut 


2H   4H 
3      S 


Max  Min 
u 


3Ha 
4H 

6^6 


Pork 


W't. 
lb 


CLEVIS-NUMBERS  FOR  VARIOUS  RODS  AND  PINS 


Rods 


Pins 


Round  Square  Upset 


I 


iH 

2 

2H 
2^ 


I 


iH 

m 

2 

2H 


I 

iH 

m 
m 

2 

2\i 

2H 
2% 

2\i 
2H 
2% 

2li 

3 


iH    iH     1% 


2H       2H       2% 


3H     3H 


Clevises  above  and  to  right  of  zigzag  line  may  be  used  with  forks  straight,  tho^ 
below  and  to  left  of  this  line  should  have  forks  closed  so  as  not  to  overstress  the  pin. 

L  ?  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tehsion-Members  399 

Table  X.     Safe  Loads  in  Tension  for  Common  Sizes  of  Angles  with  On^s 
%-Inch  Rivet-Hole  for  a  %-Incli  Rivet 
Load  in  pounds  for  a  stress  of  i6  coo  lb  per  sq  in 


Size  of  angle 

Load 

Size  of  angle 

Load 

6X4X% 

100  SCO 

3V2X2HX% 

45000 

% 

85  000 

Vw 

41  100 

Va 

68900 

V2 
% 

37  000 
28500 

5X3^2  X% 

82  500 

M 

19500 

% 

70  100 

V2 

57000 

3X3X% 

V2 

45000 
37000 

5X3X% 

76500 

% 

28500 

% 

64900 

% 

19500 

V2 

53000 

% 

40  500 

3X2V2XV2 

% 

33000 
25  600 

4X-lX«4 

76500 

f/i« 

21  800 

% 

40  500 

V4 

17  600 

4X3V3X% 

60000 

% 

37600 

3X2X7x0* 

25900 
25600 

4X3X% 

53  000 

«/io* 

21  8oo 

Va 

45  000 

H* 

17  600 

% 

34600 

272X2^15X710 

25900 

3V2X3V2XH 

64500 

% 

22600 

% 

55  000 

^Aq 

19200 

V2 

45  000 

Vi 

15500 

% 

34600 

2^X2X'^Aq 

22400 

3V2X3X% 

SO  100 

% 

19500 

V2 

41  000 

S/io 

16600 

% 

31  500 

Vi 

12800 

•  These  are  special  angles, 
risk  of  delay  in  delivery. 


It  is  better  not  to  use  them  in  ordinary  work  because  of 


The  End-Connections  often  determine  the  strength  of  angle  tension- 
members.  Some  specifications  for  structural  work  require  angles  subject  to 
direct  tension  to  be  connected  by  both  legs  if  the  section  of  both  legs  is  con- 
sidered; and  if  connected  by  one  leg,  the  section  of  one  leg  only  is  considered 
effective.  Reliable  tests  (page  385)  show  this  requirement  to  be  needlessly 
severe.  For  single  angles  connected  by  one  leg,  the  Specifications  for  the 
Structural  Steelwork  of  Buildings,  Chapter  XXX,  allow  the  net  area  of  the 
connected  leg  and  one-half  that  of  the  outstanding  leg  to  be  considered  effective. 
(See  Waterbury,  Stresses  in  Structural  Steel  Angles,  John  Wiley  &  Sons,  Inc., 
New  York,  1917.) 


400        Resistance  to  Tension.     Properties  of  Iron  and  Steel     Chap.  11 

Table  XI.     Sectional  Area  to  be  Deducted  from  Plates  and  Angles  for 
One  Round  Hole 

Note.     Bolt-holes  should  be  Via  in  larger  than  the  diameter  of  the  bolt;   rivet-holes 
are  usually  Vs  in  larger  than  the  diameter  of  the  rivet.* 


II 

Diameter  of  hole  in  fractions  of  an  inch  and  inches                             i 

H 

Ho 

% 

Ho 

V2 

»/l6 

% 

Hie 

% 

1%G 

Vs 

i-Tio 

I 

iHc 

l3/l6 

ivic 

I»/i6 

%6 

V4 

0.05 

0.06 

0.07 

0.08 

0.09 

O.II 

C.12 

0.13 

O.I-i 

0.15 

0.16 

0.18 

0.19 

0.20 

0.23 

0.27 

0.30 

0.06 

0.08 

0.09 

O.II 

0.13 

0,14 

0.16 

0.17 

0.19 

0.20 

0.22 

0.23 

0.25 

0.27 

0.30 

0.36 

0.39 

•ri6 

0.08 

O.IO 

0.12 

0.14 

0.16 

0.18 

0.20 

0.21 

0.23 

0.25 

0.27 

0.29 

0.31 

0.33 

0.37 

0.45 

0.49 

% 

0.09 

0.12 

0.14 

0.16 

0,19 

0.21 

0.23 

0:26 

0.28 

0.30 

0.33 

0.35 

0.38 

0.40 

0.45 

0.54 

0-59 

Via 

Q.II 

0.14 

0.16 

0.19 

0.22 

0.25 

0.27 

0.30 

0.33 

0.36 

0.38 

0.41 

0.44 

0.46 

0.52 

0.63 

0.69 

1/2 

0.13 

0.1() 

0.19 

0.22 

0.25 

0.28 

0.31 

0.34 

0.38 

0.41 

0.44 

0.47 

0.50 

0.53 

0.59 

0.72 

0.78 

ric 

0.14 

0.18 

0.21 

0.25 

0.28 

0.32 

0.3.5 

0.39 

0.42 

0.46 

0.49 

0.53 

0.56 

0.60 

0.67 

0.81 

0.88 

% 

0.16 

0.20 

0.23 

0.27 

0.31 

0.35 

0.39 

0.43 

0.47 

0.51 

0.55 

0.59 

0.63 

0.66 

0.74 

0.90 

0.98 

Hie 

0.17 

0.21 

0.26 

0.30 

0.34 

0.39 

0.43 

0.47 

0.52 

0.56 

0.60 

0.6/. 

0.69  0.73 

0.82 

0.99 

1.08 

3/4 

0.19 

0.23 

0.28 

0.33 

0..S8 

0.42 

0.47 

0.52 

0.56 

0.61 

0.66 

0.70 

0.75 

0.80 

0.89 

1.08 

1. 17 

i%c 

0.20 

0.25 

0.30 

0.36 

0.41 

0.46 

0.51 

0.56 

0.61 

0.66 

0.71 

0.76 

0.81 

0.86 

0.97 

1. 17 

1.27 

% 

0.22 

0.27 

0.33 

0.38 

C.44 

0.49 

0.55 

0.60 

0.66 

0.71 

G.77 

0.82 

0.88 

0.93 

1.04 

1.26 

1.37 

1%6 

0.23 

0.29 

0.35 

0.41 

0.47 

0.53 

0.59 

0.64 

0.70 

0.76 

0.82 

0.88 

0.94 

1. 00 

I. II 

1.35 

1.47 

I 

0.25 

0.31 

0.38 

0,44 

0.5c 

0.56 

0.63 

0.69  0.75 

0.81 

0.88 

0.94 

1. 00 

*■" 

I -19 

1.44 

1.56 

*  See  also  Table  I,  Chapter  XX  and  paragraph,  Punching  Rivet-Holes,  page  414. 


7.    Wire 

Manufacture.  Iron  and  steel  wires  are  made  from  billets  a])out  4  in  square. 
These  are  rolled  into  long  rods  which  are  dipped  in  acid  to  remove  the  scale 
And  furnish  lubrication  for  the  drawing  process.  This  consists  in  pulling  the 
rods  while  cold  through  steel  dies  haying  a  series  of  holes  of  gradually  decreasing 
diameters.  The  cold  working  of  the  metal  hardens  it  and  makes  it  brittle  so 
that  it  is  necessary  to  anneal  it  at  intervals  during  the  process.  The  drawing 
increases  the  strength  of  the  material,  so  that  wires  of  different  sizes,  although 
made  of  the  same  material,  differ  greatly  in  ultimate  strength. 

Finish.  The  common  grades  of  iron  and  steel  wire  are  furnished  in  several 
different  finishes:  plain  black,  bright  tinned,  copper-coated,  japanned  and  with 
single  and  double  coats  of  zinc  galvanizing.  The  last  is  applied  by  passing  the 
wire  through  the  melted  zinc  which  is  deposited  as  a  coating  and  forms  one  of 
the  best-known  protections  against  corrosion. 

Wire-Gauges.  Table  XIII  gives,  according  to  several  gauges,  the  diameters 
of  the  different  numbers  of  wire  that  have  come  into  use  for  different  purposes 
and  have  been  brought  out  by  different  manufacturers.  In  ordering  wire  by 
number  it  is  best  to  specify  which  gauge  is  meant. 

Strength.  Table  XIV  gives  the  sizes  according  to  the  J.  A.  Roebling's  Sons 
Company  gauge,  with  the  weight  and  length  and  the  strength  on  an  assumed 
basis  of  100  000  lb  per  sci  in.  The  different  kinds  of  wire  vary  so  widely  in  ulti- 
mate strength,  on  account  of  both  the  difference  in  quality  of  the  material  and 
the  effect  of  the  drawing,  that  in  order  to  obtain  the  approximate  strength  of  ^ 


Wire 


401 


wire,  reference  must  be  made  to  Table  XII  in  connection  with  the  foot-note  to 
Table  XIV.  The  following  table  is  arranged  from  values  which  were  published 
in  the  Catalogue  of  the  J.  A.  Roebling's  Sons  Company: 


Table  XII.     Approximate  Ultimate  Strength  of  Different  Sizes  of  Iron 
and  Steel  Wire 


Kind  of  wire 


Soft  iron 

Telegraph  and  telephone  (steel) 

Special  aviator 

Piano  wire 

Plough  steel  wire 

Hard-drawn  copper  trolley  wire 

Hard-drawn  telegraph  and  telephone  copper 


Ultimate  strength 


Large  size 

Small  size 

lb  per  sq  in 

lb  per  sq  in 

45  000 

60  000 

60  000 

80  000 

247000 

28s  000 

307  000 

340000 

200  000 

345  000 

50  000 

not  used 

56  000 

66  oco 

The  Uses  of  Wire  are  so  many  and  varied  that  a  bulky  treatise  would 
be  required  to  adequately  cover  the  subject.  The  catalogues  of  the  American 
Steel  and  Wire  Company  mention  electrical  wires  and  cables  of  many  kinds, 
telephone  and  telegraph  wires,  ignition-wires  and  cables  for  automobiles,  motor- 
boats  and  aeroplanes,  wire  rope,  wire  tacks,  wire  fences,  piano-wire,  barbed 
wire,  flat  wire  and  so  on,  through  a  long  list.  The  magnitude  of  the  wire-output 
in  the  United  States  is  seen  from  the  fact  that  of  the  total  production  of  32  000  000 
tons  of  all  kinds  of  finished  rolled  iron  and  steel  for  the  year  19 16,  3  500  000  tons 
were  wire  rods.  For  electrical  purposes  copper  wire  is  mostly  used.  See 
Electric  Work  for  Buildings,  Part  III,  for  information  regarding  wires  and  wire- 
calculations. 

The  Brown  &  Sharpe  Gauge  is  followed  in  the  United  States  as  the 
standard  for  copper  wire>  though  there  is  a  growing  tendency  to  distinguish 
different  electrical  wires  by  their  diameters,  expressed  in  mils.  (One  mil  = 
o.ooi  in.     A  circular  mil  is  the  area  of  a  circle  o.ooi  in  in  diameter.) 

The  American  Steel  and  Wire  Company's  Gauge  is  almost  universally 
followed  throughout  the  United  States  for  steel  wire.  The  Birmingham  gauge, 
an  English  gauge,  is  the  only  wire-gauge  recognized  in  successive  Acts  of 
Congress  establishing  tariffs,  and  for  many  years  has  been  used  as  the  basis 
for  duties  assessed  on  imported  wire.  Aside  from  these  purposes  its  use  is  not 
extensive.  The  American  Steel  and  Wire  Company's  Music-Wire-Gauge, 
now  known  as  the  Music- Wire-Gauge,  upon  recommendation  of  the  United 
States  Bureau  of  Standards,  has  been  adopted  as  the  standard  for  piano-wire. 

*  See,  also,  pages  402,  403,  1469,  1473,  1509,  1510,  1512,  and  1600. 


402       Resistance  to  Tension.     Properties  of  Iron  and  Steel     Chap. 


Table  XIII.     Comparison 

of  Standard  Gauges  for  Wire  and  Sheet  Metal  * 

Diameter  or  thickness  in  decimals  of  an  inch 

Washburn 

Birm- 
ingham 
or  Stubs 

iron- 

United 

&  Moen, 

Ameri- 

British 

Number 
of 

American 
or  Brown 

States 
standard 

Roebling, 
American 

Stubs 
steel - 

can 

Screw 

Imperial 
or  English 

gauge 

&  Sharpe 

gauge  for 

Steel  & 

Co. 

legal 

wire- 
gauge 

wire- 
gauge 

sheet  and 
plate  iron 
and  steel 

Wire  Co., 

stccl- 
wire-gauge 

wlre- 
gauge 

wire- 
gauge 

standard 
wire- 
gauge 

ooooooo 



0.5 

0 . 4900 

0.500 

oooooo 

0.580000 

0.4687s 

0.461S 

0.464 

ooooo 

0.500 

0.516500 

0.4375 

0.4305 

0.432 

oooo 

0.454 

0 . a6dooo 

0.4062s 

0.3938 

0.400 

ooo 

0.42s 

0.409642 

0.37s 

0.362s 

0.0315 

0.372 

CX) 

0.380 

0.364796 

0.34375 

0.3310 

0.0447 

0.348 

o 

0  340 

0.324861 

0.312s 

0.3065 

0.0578 

0.324 

I 

0.300 

0.289297 

0.28125 

0.2830 

0.227 

0.0710 

0.300 

2 

0.284 

0.257627 

0.265625 

0.2625 

0.219 

0.0842 

0.276 

3 

0.259 

0.229423 

0.2s 

0.2437 

0.212 

0.0973 

0.252 

4 

0.238 

0.204307 

0.23437s 

0.22S3 

0.  207 

0.1105 

0.232 

5 

0.220 

0.181940 

0.21875 

0.2070 

0.204 

0.1236 

0.212 

6 

0 .  203 

0.162023 

0.20312s 

0.1920 

0.201 

0.1368 

0.192 

7 

0.180 

0  114285 

0.1875 

0.1770 

0.199 

0.1500 

0.176 

8 

0  165 

0. 128490 

0  17187s 

0.1620 

0.197 

0.1631 

0.160 

9 

0.148 

0.114423 

0.15625 

0.1843 

0.194 

0.1763 

0.144 

lO 

0.134 

0.101897 

0.140625 

0.1350 

0.191 

0.1894 

0.128 

ir 

0.120 

0.090742 

0.125 

0.1205 

0.188 

0.2026 

0.116 

12 

0.109 

0.080808 

0.10937s 

0.1055 

0.185 

0.2158 

0.104 

13 

0.095 

0.071962 

0.09375 

0.0915 

0.182 

0.2289 

0.092 

14 

0.083 

0.064084 

0.078125 

0 . 0800 

0.180 

0.2421 

0.080 

15 

0.072 

0.057068 

0.070312s 

0.0720 

0.178 

0.2552 

0.072 

i6 

0.065 

0.050821 

0.0625 

0.0625 

0.175 

0.2684 

0.064 

17 

0.058 

0.045257 

0.05625 

0.0540 

0.172 

0.2816 

0.056 

i8 

0.049 

0.040303 

0.05 

0.047s 

0.168 

0.2947 

0.048 

19 

0.042 

0.035890 

0.04375 

0.0410 

0.164 

0.3079 

0.040 

20 

0.035 

0.031961 

0.037s 

0.0348 

0.161 

0.3210 

0.036 

21 

0.032 

0.028462 

0.03437s 

0.0317 

0.157 

0.3342 

0.032 

22 

0.028 

0.025346 

0.03125 

0.0286 

0.155 

0.3474 

0.028 

23 

0.025 

0.022572 

0.028125 

0.0258 

O.IS3 

0.3605 

0.024 

24 

0.022 

0.020101 

0.025 

0.0230 

0.151 

0.3737 

0.022 

25 

.0.020 

0.017900 

0.021875 

0.0204 

0.148 

0.3868 

0.020 

26 

0.018 

0.015941 

0.01875 

0.0181 

0.146 

0.4C00 

0.018 

27 

0.016 

0.014195 

0.0171875 

0.0173 

0.143 

0.4132 

0.0164 

28 

0.014 

0.012641 

0.015625 

0.0162 

0.139 

0.4263 

0.0148 

29 

0.013 

0  011257 

0.0140625 

0.0150 

0.134 

0.4395 

0.0136 

30 

0.012 

0.010025 

0.0125 

0.0140 

0.127 

0.4526 

0.0124 

31 

O.OIO 

0.008928 

0.0109375 

0.0132 

0. 120 

0.4658 

0.0116 

32 

0.009 

0.007950 

0.01015625 

0.0128 

6.115 

0.4790 

0.0108 

'  33 

0.008 

0.007080 

0.009375 

0.0118 

0.112 

0.4921 

0.0100 

34 

0.007 

0 . 006305 

0.0085937s 

0.0104 

O.IIO 

0.5053 

0.0092 

35 

0.005 

0.005615 

0.0078125 

0.009s 

0.108 

0.5184 

0.0084 

36 

0.004 

0.005000 

0.00703125 

0 . 0090 

0.106 

0.5316 

0.0076 

37 

0.004453 

0.006640625 

0.0085 

0.103 

0.5448 

0.0068 

38 

0.003965 

0.00625 

0.0080 

0.  lor 

0.5579 

0.0060 

39 
40 

0.003531 
0  003144 

0.0075 

0.0070 

0.099      0.5711   1 
0.097      0.1:842   1 

0.0052 
0.0048 

The  United  States  Standard  Gauge  was  legalized  by  Act  of  Congress,  March  3, 
as  a  standard  gauge  for  sheet  and  plate  iron  and  steel,  and  is  used  by  the  Custom  I 
Department  and  by  sheet-plate  and  tin-plate  manufacturers. 

•  See  also,  pages  401,  403,  1469,  1473,  1509,  1510,  1512,  and  1600. 


Wire 


403 


Table  XIV.     Weight,  Length  and  Strength  of  Steel  Wire  * 
Gauge  of  J.  A.  Roebling's  Sons  Company  j 


Breaking- 

Number 
of 

Diameter 

Area 

load  in 
pounds  at 

Weight  in  pounds 

Number 
of  feet  in 

gauge 

in 

sq  in 

rate  of 
100  000  lb 

Per  I  000 
ft 

Per  mile 

2  000  pounds 

persq  in 

oooooo 

0.460 

0.166191 

16  619 

558.4 

29-18 

3582 

ooooo 

0.430 

0.145221 

14  522 

487.9 

2576 

4099 

0000 

0.394 

0.121304 

12  130 

407.6 

2  152 

4907 

000 

0.362 

0.102922 

10  292 

345.8 

1826 

5783 

oo 

0.331 

0 . 0S6049 

8605 

289.1 

I  527 

6917 

0 

0.307 

0.074023 

7402 

248.7 

I  313 

8041 

I 

0.283 

0.062902 

6  290 

211. 4 

I  116 

9463 

2 

0.263 

0.054325 

5  433 

182.5 

964 

10  957 

3 

0.244 

0 . 046760 

4676 

157. 1 

830 

12  730 

4 

0.225 

0.039761 

3976 

133.6 

705 

14970 

s 

0.207 

0.033654 

3365 

113. 1 

597 

17687 

6 

0.192 

0.028953 

2895 

97.3 

514 

20  559 

7 

0.177 

0 . 024606 

2  461 

82.7 

437 

24  191 

8 

0.162 

0.020612 

2061 

69.3 

366 

28878 

9 

0.148 

0.017203 

I  720 

57.8 

305 

34600 

lo 

0.135 

0.014314 

I  431 

48.1 

254 

41584 

II 

0.120 

0.0113T0 

I  131 

38.0 

201 

52  631 

12 

0.105 

0.008659 

866 

29.1 

154 

68  752 

13 

0.092 

0 . 006648 

665 

22.3 

118 

89525 

14 

0.080 

0.005027 

503 

16.9 

89.2 

118  413 

15 

0.072 

0.004071 

407 

13.7 

72.2 

146  198 

i6 

0.063 

0.0031 17 

312 

10. 5 

55.3 

191  022 

17 

0.054 

0.002290 

229 

7.70 

40.6 

259  909 

i8 

0.047 

0.001735 

174 

5. 83 

30.8 

343  112 

19 

0.041 

0.001320 

132 

4.44 

23.4 

450  856 

20 

0.035 

0 . 000962 

96 

3.23 

17. 1 

6x8  620 

This  table  was  calculated  on  a  basis  of  483.84  lb  per  cu  ft  for  steel  wire.  Iron  wire  is 
a  trifle  lighter. 

The  breaking  strengths  were  calculated  for  100  000  lb  per  sq  in  throughout,  simply 
for  convenience,  so  that  the  breaking  strengths  per  square  inch  of  wires  of  any  strength 
may  be  quickly  determined  by  multiplying  the  values  given  in  the  table  by  the  ratio 
between  the  strength  per  square  inch  and  100  000.  Thus,  a  No.  15  wire,  with  a  strength 
per  square  inch  of  150  000  pounds,  has  a  breaking  strength  of 

150000       -         „ 

407  X =  610.5  lb. 

100  000 

It  must  not  be  inferred  from  this  table  that  steel  wire  invariably  has  a  strength  of 
100  000  lb  per  sq  in.  As  a  matter  of  fact  its  strength  ranges  from  45  000  lb  per  sq  in  for 
soft,  annealed  wire  to  over  400  000  lb  per  sq  in  for  hard  wire. 

*  See,  also,  pages  401,  402, 1469,  1473,  1509,  iSio,  1S12,  and  i6oa 
t  Also  American  Steel  &  Wire  Company,  etc. 


404       Resistance  to  Tension.     Properties  of  Iron  and  Steel    Chap.  11 

8.   Wire  Rope 

Kinds  of  Wire  Rope.  There  are  several  kinds  of  wire  rope  in  common 
use.  In  each  there  are  three  or  more  qualities  depending  on  the  kind  of  wire 
used  and  the  kind  of  core  about  which  the  strands  are  laid.  The  Trenton  Iron 
Company  Hsts  the  following: 

(i)  Hatilage  or  Transmission-Rope,  composed  of  six  strands  of  seven  wires 
each,  laid  about  a  hemp  core.  It  is  used  for  haulage,  transmission  of  power,  in 
places  where  surface-wear  is  of  chief  consideration  and  where  sheaves  of  suflScient 
diameter  may  be  used. 

(2)  Hoisting-Rope,  composed  of  six  strands  of  nineteen  wires  each.  It  is 
used  for  elevator  service,  shafts  and  derricks,  and  in  places  where  it  is  not  sub- 
ject to  abrasion  and  where  flexibility  is  of  chief  consideration. 

(3)  Scale  Rope,  composed  of  six  strands  of  nineteen  wires  each,  the  inner 
coils  of  the  strands  being  of  fmer  wire.  It  is  intermediate  in  flexibihty  between 
the  first  and  second  kinds  of  rope. 

(4)  Non-Spinning  Hoisting-Rope,  having  eighteen  strands  of  seven  wires  each. 
Twelve  of  the  strands  are  laid  in  reverse  direction  to  the  inner  six,  making 
it  well  adapted  for  hoisting  in  free  suspension  without  untwisting  and  turning 
the  load. 

(5)  Extra-Flexible  Hoisting-Rope,  having  eight  strands  of  nineteen  wires  each. 

(6)  Special  Flexible  Hoisting-Rope,  having  six  strands  of  thirty-seven  wires 
each. 

(7)  Hawser-Rope  and  Flexible  Running-Rope,  having  six  strands  of  twelve 
galvanized  wires  each,  laid  about  a  hemp  core. 

(8)  Tiller-Rope,  composed  of  six  small  seven-strand  ropes  laid  about  a  hemp 
core.  It  is  the  most  flexible  of  wire  ropes  and  is  used  to  operate  tillers  and  for 
hand-ropes  in  elevators. 

The  Lay  of  Wire  Rope  is  the  twist  of  the  wires  in  the  strands  relatively  to 
the  strands  in  the  rope.  In  the  ordinary  lay  the  twist  of  the  strands  is  the 
reverse  of  that  of  the  wires,  while  in  the  Lang  lay  the  strands  are  laid  in  the 
same  direction  as  the  twist  of  the  wires.  This  latter  gives  a  greater  distribution 
of  the  wearing-surface  and  a  somewhat  greater  flexibility;  but  it  has  the  dis- 
advantage of  a  tendency  to  untwist  and  for  this  reason  should  not  be  used  for 
hoisting  weights  in  free  suspension.  Wire  rope  is  also  made  up  in  flat  or  rib- 
bon FORM.  For  large  sizes  it  is  more  flexible  than  standard  rope  and  may  be 
run  over  smaller  drums. 

Materials  for  Rope.  Nearly  all  of  the  above  kinds  of  rope  are  made  up  in 
the  following  materials: 

(i)  Best  Grade  of  Wrought  Iron.  This  is  used  in  high-speed  passenger- 
elevator  SERVICE  as  it  seems  to  suffer  less  from  the  .effects  of  the  stresses  due 
to  the  starting  and  stopping  of  the  cars. 

(2)  Cast-Steel  Wire,  with  an  ultimate  strength  of  from  160  000  to  210  000  lb 
per  5q  in,  according  to  the  size  used. 

(3)  Extra-Strong  Cast-Steel  Wire,  with  an  ultimate  strength  of  from  190  000 
to  230  000  lb  per  sq  in. 

(4)  Plow-Steel  Wire  with  an  ultimate  strength  of  from  200  000  to  230  000  lb 
per  sq  in. 

Ordinary  galvanized-wire  rope  should  not  be  used  for  other  than  standing 
rope.    A  short  service  running  through  sheaves  will  break  the  coating  and  permit 


Wire  Rope 


405 


Table  XV.     Strength  of  Wire  Rope 

Arranged  from  the  191 2  list  of  John  A.  Roebling's  Sons  Company 


Approximate  breaking- 

Minimum  diameter  of 

Weight 

load  in  pounds 

drum  or  sheave 

Trade 

Diameter 

per  foot, 

in  feet                  j 

number 

inches 

hemp 

core 

Iron 

Cast  steel 

Iron 

Cast  steel 

IIOISTING-ROPE 

Six  str 

xnds  of  nint 

iteen  wires  each,  about  a  hemp  core 

I 

2\i 

8.00 

144  000 

266  000 

14 

9 

2 

2 

C.30 

110  000 

212  000 

12 

8 

21/1. 

1% 

5.55 

100  000 

192  000 

12 

8 

3 

1% 

4.85 

88000 

170  000 

11 

7 

4 

1% 

4.15 

76000 

144000 

10 

6.5 

5 

iVi' 

3.55 

66  000 

128  000 

9 

6 

5¥2 

r'/8 

3 

56000 

112  000 

8.5 

5.5 

6 

•iVi 

2.45 

45  600 

94000 

7.5 

5 

7 

1% 

2 

37200 

76  000 

7 

4.5 

8 
9 

I 

1.58 

29  000 

60  000 

6 

4 

Vh 

] 

.20 

23600 

46  000 

5-5 

3.5 

ID 

% 

C 

.89 

17000 

35000 

4.5 

3 

10^/4 

% 

c 

.62 

12  000 

25  000 

4 

2.5 

lO^/l' 

^1(5 

c 

.50 

9400 

20  000 

3-5 

2.25 

io=)4 

1/ij 

c 

•39 

7800 

16800 

3 

2 

loa 

VlO 

0.30 

5800 

13  000 

2  75 

1.75 

lob 

% 

0.22 

4800 

9600 

2.25 

1.5 

STANDING   ROPE 

Six  str 

ands  of  seven  wires  each 

II 

IV2 

3  55 

64  000 

126  000 

16 

II 

12 

1% 

3 

56000 

106  000 

15 

10 

13 

lu 

2.45 

46  000 

92  000 

13 

9 

14 

iVs 

2 

38000 

74000 

12 

8 

15 

I 

I  58 

30  000 
24  000 

62  000 

48  000 

10.5 
9 

7 
6 

16 

Vs 

1.20 

17 

% 

0.89 

17  600 

37200 

7.5 

5 

18 

11/10 

0.75 

14  600 

30800 

7-25 

4.75 

19 

f>:s 

0  62 

12000 

26  000 

7      . 

4.50 

20 

»/i« 

0.50 

9600 

20  000 

6 

4 

21 

1/2 

0.39 

7400 

15  400 

5.5 

3.5 

22 

VlO 

0.30 

5  200 

II  000 

4  5 

3 

23 

% 

0.22 

4400 

9  200 

4 

2.75 

'         24 

^/i« 

0.15 

3400 

7  000 

3  5 

2.25 

25 

9/1j2 

0.125 

2  400 

5000 

3 

1.75 

The  working  load  is  to  be  taken  at  one-fifth  the  breaking-load.    This  is  assumed  i 
calculating  the  diameter  of  the  sheaves. 


406       Resistance  to  Tension.    Properties  of  Iron  and  Steel    Chap.  11 

rapid  corrosion  of  the  rope.  Because  of  the  many  kinds  and  qualities  of  rope 
it  is  well  to  consult  the  manufacturers  as  to  which  kind  will  best  suit  the  condi- 
tions for  any  particular  service.  The  John  A.  Roebling's  Sons  Company,  Tren- 
ton, N.  J.,  the  Trenton  Iron  Company,  Trenton,  N.  J.,  and  A.  Leschen  &  Sons 
Rope  Company,  St.  Louis,  Mo.,  are  among  the  largest  manufacturers  of  full 
lines  of  ropes. 

I  Coils.  Wire  rope  should  not  be  coiled  like  hemp  rope,  and  in  order  to  avoid 
kinking,  should  be  taken  from  the  reels  without  twisting.  If  it  is  not  shipped  on 
a  reel,  to  avoid  injury  it  must  be  rolled  over  the  ground  like  a  wheel.  ^ 

Lubrication.  It  is  very  important  that  running  ropes  be  properly  lubri- 
cated, since,  if  proper  care  is  not  taken,  the  wear  on  the  interior  parts,  between 
the  wires,  may  be  almost  as  great  as  the  outside  abrasion.  The  oil  should  pene- 
trate to  the  core  of  the  rope  and  yet  not  drip  ofif  a  few  days  after  application. 
Information  as  to  the  care  of  rope  may  be  obtained  of  the  Wire  Rope  Lubrica- 
ting Company,  Newark,  N.  J. 

Sheaves.  The  size  of  sheaves  recommended  in  the  tables  are  calculated  for 
a  working-load  of  one-fifth  the  given  breaking-load.  If  smaller  sheaves  are  used 
the  life  of  the  rope  will  be  greatly  shortened,  because  of  the  excessive  bending 
of  the  outer  wires. 


Table  XVI.     Galvanized,  Steel- Wire  Strands 

For  guys,  signal-cords,  trolley-line  span  wire,  etc.     Taken  from  the 
American  Steel  &  Iron  Company's  list 


Diameter  in 

inches 

List  price  per 
100  feet* 

Weight  per  loo 
feet 

Approximate 

breaking-load 

in  pounds 

% 

$7.25 

80 

14000 

%o 

5.75 

65 

II  000 

V2 

4.50 

S2 

8500 

Via 

3.7s 

41 

6  soo 

% 

2.75 

30 

5000 

%6 

2.2s 

22 

3800 

V4 

1.75 

13 

2300 

?32 

I. SO 

9^/2 

I  800 

«/!• 

1. 25 

7V2 

I  400 

%2 

I. IS 

5V2 

900 

Vs 

1. 00 

3V4 

600 

%2 

.80 

2 

400 

9.    Cotton,  Hemp  and  Manila  Rope 

Rope  is  made  of  cotton,  hemp,  and  Manila  fiber.  Cotton  is  used  for  small 
iJizes,  only,  and  for  such  purposes  as  sash-cord,  etc. 

Manufacture.  In  the  manufacture  of  rope  the  fiber  is  first  spun  into  yarn. 
J'rom  twenty  to  eighty  threads  are  twisted  together  into  strands  and  the 
Strands,  three  or  four,  are  laid  together,  opposite  in  direction  to  the  twist  in 
\he  strands,  but  in  the  same  direction  as  the  threads.  This  causes  the  fibers 
»;o  be  twisted  as  the  rope  untwists  and  produces  a  balancing  of  forces  that  tends 
to  keep  the  rope  in  shape. 

Cables  and  Hawsers,  are  made  up  of  strands  of  rope. 

*  These  pre-war  prices  must  be  increased  as  per  current  price-lists. 


Cotton,  Hemp  and  Manila  Rope 


407 


Rope  used  forHoisting  wears  rapidly  from  the  action  of  the  pulleys  and 
also  from  the  bending  which  causes  a  slight  internal  motion  between  the  fibers 
and  a  chafing  and  grinding  away  of  the  interior. 

Stevedore-Rope,  of  the  C.  W.  Hunt  Company,  is  filled  with  a  tallow  and 
plumbago  lubricant  which  decreases  the  internal  friction,  lubricates  the  outside 
of  the  rope  and  thus  greatly  prolongs  its  life. 

Strength.  The  values  of  the  strength  of  new  rope,  given  in  Table  XVII,  are 
taken  from  the  Specifications  of  the  United  States  Navy  Department,  issued 
in  June,  1910,  at  the  Boston  Navy- Yard.  Manufactu .'ers  generally  adopt  these 
sizes  and  weights  and  claim  a  strength  equal  to  or  a  little  greater  than  the  values 
given.  The  unit  strength  for  the  different  sizes  varies,  being  about  14  000  lb 
per  sq  in  for  the  smaller  and  about  10  000  for  the  largest  size.  The  approx- 
imate formula,  offered  by  C.  W.  Hunt,  of  720  times  the  square  of  the  circum- 
ference in  inches,  is  equivalent  to  about  9  000  lb  per  sq  in.  American  hemp, 
tarred,  has  about  5%  greater  strength  than  Manila  rope  of  the  same  size.  The 
navy  specifications  give  for  two-strand  American-hemp  rope,  85%  of  the  strength 
of  the  three-strand  rope  of  the  same  material. 

Table  XVII.     Strength  and  Weight  of  Rope 

Specifications  of  the  United  States  Navy,  June,  1910 


Circum- 
ferences 
in 

Diameters 
in 

Manila  hemp,  plain-laid 

American  hemp,  tarred, 
plain-laid,  three  strands 

Weights 
lb  per  ft 

Breaking- 
loads 
lb 

Weights 
lb  per  ft 

Breaking- 
loads 
lb 

I 

iH 

1V2 

l8/4 

2 

2Vi 
2«/4 

3 

3V4 
3V2 

3% 

4 

4V2 
5 

5V2 
6 

7 
8 
9 
10 

0.24 
0.32 

0.40 
0.48 
0.56 
0,64 

0.72 
0.80 
0.87 
0.95 

1.03 
1. 16 
1. 19 
1.27 

1.43 
1. 59 
1. 75 
1.90 

2.22 
2.54 
2.87 
3.14 

0.02 
0.033 

0.05 
0.083 

O.IO 

0.14 

0.17 
0.21 
0.26 
0.30s 

0.36 
0.42 
0.47 
0.54 

0.67 
0.83 
1. 00 
1. 21 

1.63 
2.17 
2.70 
3.33 

700 
I  000 

I  800 
2500 

3  000 

4  000 

5  000 
5500 
6600 
7800 

9  200 
IC500 
12  200 
13700 

17400 
21  800 
27700 
31  000 

36  200 
47300 
60  000 
74200 

0.051 
0.06 

0.067 
0.083 
0.105 
o.i6 

0.21 
0.26 
0.32 
0.37 

0.44 
o.Si 
0.59 
0.67 

750 
I  060 

1  670 
2340 
3325 
3  955 

4720 
5770 
7  000 
8400 

9800 
II  200 
13000 
14550 

1 

Manila-hemp  rope  is  made  in  three  strands  and  in  sizes  up  to  3  in  in  circumference; 
four  strands  are  used  for  s'zes  larger  than  3  in  in  circumference. 


408        Resistance  to  Tension.    Properties  of  Iron  and  Steel    Chap.  11 

Working  Load.  The  working  load  for  slow-speed  derrick  and  hoisting- 
service  is  usually  taken  at  one-seventh  the  breaking-load.  This  makes  some 
allowance  for  the  loss  of  strength  at  splices  and  connections.  The  deterioration 
of  rope  exposed  to  the  weather  is  very  rapid.  For  Manila  rope  from  i  to  i%  in 
in  diameter,  running  over  sheaves  of  the  diameters  given,  C.  W.  Hunt  in  Trans. 
Am.  Soc.  M.  E.,  Vol.  XXIII,  gives  a  table  embodying  approximately  the  fol- 
lowing results  of  experience: 

Table  XVIII.     Working  Loads  for  Manila  Rope 

Working  load  =  C  X  breaking-load  of  new  rope 

D  =  minimum  diameter  of  sheave  in  inches 


Speed 

Feef  per 
minute 

Kind  of  work 

Value  of 
C 

D  for  rope  of 
diameter  of 

I  in 

1%  in 

Slow 

Medium . . . 
Rapid 

so  to  100 
150  to  300 
400  to  800 

Derrick,  crane,  quarry,  etc. 
Wharf,  cargo,  etc. 

0.014 
0.056 
0.028 

8 
12 

40 

14 
18 

70 

The  wear  in  such  service  is  very  rapid,  a  ii/^-in  rope  wearing  out  in  lifting  from 
7000  to  10  000  tons  of  coal.  On  the  other  hand,  a  i^/^-in  transmission-rope 
running  at  5  000  ft  per  min  and  carrying  i  000  horse-power  over  sheaves  5  ft 
and  17  ft  in  diameter,  lasts  for  years,  the  difference  being  due  to  the  smaller 
stress  and  larger  sheaves. 


10.    Chains 

Manufacture.  Large  chains  are  made  by  hand- welding  from  best  wrought- 
iron  bar,  and  small  chains  up  to  H  in  are  best  made  of  mild  open-hearth  steel, 
electric-welded.  The  bending  and  welding  reduce  the  strength  so  that  the 
chain  is  not  twice  but  only  from  1.55  to  1.70  times  as  strong  as  the  original  bar 
from  which  it  was  made.  Stud  chain  having  a  bar  welded  across  each  link 
to  stiffen  it  and  prevent  fouling  in  handling,  is  not  as  strong  as  open-link 
CHAIN,  but  has  a  higher  elastic  limit  and  working  strength.  G.  A.  Goodenough, 
in  a  Bulletin  from  the  IlHnois  Engineering  Experiment-Station,  finds  the  maxi- 
mum stresses  at  the  elastic  hmit  of  the  material  to  be  as  follows:  If  F  is  the 
load,  d  the  diameter  of  the  bar,  and  S  the  stress,  the  formulas  are: 

P  =  0.5  d^S  for  stud-link,  and 
P  =  0.4  d^S  for  open  link. 

Proof-Tests.  A  proof-test  is  applied  to  chains  by  the  manufacturers.  The 
load  applied  is  one-half  the  average  breaking-loaix  It  serves  to  detect  bad 
welds  and  gives  a  chain  a  slight  permanent  sot,  so  that  for  working  loads  there- 
after there  will  be  Uttle  stretching  of  the  chain. 

Care  of  Chains.  Chains  in  constant  use  require  lubrication  and  frequent 
annealing.  They  harden  in  service  and  are  liable  to  unexpected  failure  if  not 
annealed.  It  is  recommended  that  hoisting  chains  and  sUng  chains  be  annealed 
at  least  once  a  year. 


Chains 


409 


Table  XIX.     Sizes,  Weights,  Proof-Tests  and  Average  Breaking-Loads  for 
Chains 

Bradlee  and  Company,  Philadelphia 


D.B.G.  special  crane 

Crane 

Size  of 

Approxi- 
mate 

chains 

weight 
per  foot 

Average 

Average 

in 

Proof-test 

breaking- 

Proof-test 

breaking- 

lb 

load 

lb 

load 

lb 

lb 

Vt 

% 

I  932 

3864 

1680 

3360 

% 

1% 

4186 

8372 

3640 

7280. 

V2 

2.5 

7728 

15456 

6  720 

13  440 

% 

4.1 

II  914 

23828 

10360 

20720 

«/4 

6.2 

17388 

34  776 

15  120 

30  240 

Vs 

8.4 

22  484 

44968 

20440 

40880 

I 

10.5 

29  S68 

59  136 

26880 

53  760 

iVs 

13.6 

37576 

75  152 

34  160 

68  320         ' 

lU 

16 

46  200 

92400 

42  000 

84  000 

1% 

19.2 

55  748 

III  496 

50680 

loi  360 

IV2 

23 

66528 

133  056 

60480 

120  960 

1% 

28 

74  382 

148  764 

1% 

31 

82  320 

164  640 

1%' 

35 

94360 

188  720 

2 

40 

107  520 

215  040 

2% 

46. 5 

121  240 

242  480 

The  speciQcatious  of  the  United  States  Navy  Department  require  the  same  proof-test 
as  is  given  above  for  crane-chain  and  a  breaking-strength  .10%  greater  than  that  given 
for  special  crane-chain. 

Table  XX.     Proof-Tests  and  Average  Breaking-Loads  for  Studded  Chain- 
Cables 

Specifications  of  the  United  States  Navy  Department 


Size  of 

cable 

in 

Proof-test 
lb 

Average 
breaking- 
load 
lb 

Size  of 

cable 

in 

Proof-test 
lb 

Average 
breaking- 
load 
lb 

I 

iVh 

iH 

i-yio 

1% 

iVio 

iVl> 

iri6 

1% 
1% 

1% 

34  607 
43812 
54  194 
59784 

65  574 
71  672 
78041 
84678 

91588 
106  222 
121  937 

67  526 
82  686 
100  630 
109  771 

119  355 
129  38s 
139  861 
150  783 

162  152 
186  228 
212  188 

2 
2V10 

21/8 

2H 
2V2 
2% 
2% 

2% 

3 

3Vs 

130  202 
138  739 
147  544 
156  622 

175  591 
216  779 
238  995 
262  302 

286  692 

312  i6s 

•     339  102 

225  687 
239  732 
254  223 
269  160 

300373 
368  153 
404  719 
443  069 

483  203 
52s  121 
567  823 

410        Resistance  to  Tension.     Properties  of  Iron  and  Steel     Chap.  11 

Factors  of  Safety.  For  dead  loads  the  factor  of  safety  may  be  as  low 
as  four  provided  the  breaking  of  the  chain  would  not  imperil  life.  This  is  the 
factor  generally  quoted  in  catalogues,  but  is  too  low  for  most  purposes  as  the 
MAXIMUM  fiber-stress  is  then  well  above  the  elastic  limit  of  chain-iron. 
Where  loads  are  to  be  raised  repeatedly  with  machinery  which  can  be  operated 
without  jerks  or  sudden  change  of  speed,  the  use  of  a  factor  of  six  is  good" 
practice.  If  a  chain  must  be  used  where  shocks  occur,  the  instantaneous 
LOAD  should  be  calculated,  and  a  high  factor  of  safety  employed. 

Grades  of  Chain.  Chains  up  to  i}4  in  are  usually  made  in  three  grades, 
called  PROOF,  bb,  and  bbb.  The  proof  is  the  cheapest  grade,  and  is  made  in 
longer  links  than  the  others.  This  is  not  ordinarily  proof-tested,  bb  is  the 
next  grade,  somewhat  shorter  linked,  and  is  proof-tested,  bbb  is  of  still 
shorter  link  and  more  carefully  made. 

Crane  Chair  is  finished  in  such  a  way  as  to  be  without  twist  when  hanging 
with  one  end  free,  so  that  hooks  and  fittings  are  always  facing  their  proper 
direction. 

Dredge  Chain  is  straightened  as  is  Crane  Chain,  and  made  with  uniform 
links  to  run  over  a  wheel. 

Steel  Loading  Chain  is  made  mostly  in  small  sizes  for  use  where  the  weight 
compared  to  the  strength  is  to  be  a  maximum.  It  is  the  highest-grade 
hand-made  chain. 

Block  Chain  is  fitted  to  the  pocket-wheel  in  which  it  is  to  run.  In  small 
sizes  it  is  usually  electric-welded. 

Electric- Welded  Chain  is  made  in  small  sizes  and  is  rapidly  replacing  the 
hand-made  below  H  in.     It  is  stronger  and  more  uniform. 

Sizes  of  Chain.  Chain  is  ordinarily  made  of  wire  or  rod,  H2  in  larger  than 
the  NOMINAL  diameter,  by  which  it  is  called.  If  chain  is  desired  made  of  wire  of 
the  size  by  which  it  is  called,  it  must  be  specified  as  exact  size.  Steel  Loading 
Chain,  Block  Chain,  and  frequently  Dredge  Chain,  are  made  exact.  Stud- 
Link  Anchor  Chain  is  made  of  wirC;  Vti^  in  above  its  nominal  diameter. 


Shear 


411 


CHAPTER  XII 

RESISTANCE  TO   SHEAR.    RIVETED  JOINTS. 
PINS  AND  BOLTS 

By 
HERMAN  CLAUDE  BERRY 

PROFESSOR  OF  MATERIALS   OF  CONSTRUCTION,   UNIVERSITY  OF  PENNSYLVANIA 

1.   Shear 

Shear  is  the  internal  stress  in  a  body  which  resists  the  tendency  of  two  adja- 
cent parts  to  sUde  on  each  other,  due  to  the  action  of  two  equal  and  parallel 
external  forces,  called  shearing- 
FORCES,  acting  on  opposite  sides 
of  the  plane  of  shear. 

If  the  piece  abed  of  Fig.  1  repre- 
sents a  short  simple  beam  of 
brittle  material  on  which  a  suffi- 
cient load  is  applied,  it  will  fail  in 
VERTICAL  shear  at  /  and  g,  as 
shown,  by  a  sliding  on  the  sections 
of  the  beam  at  these  points,  be- 
cause the  upward  force  of  the 
reaction  at  5  and  the  downward 
force  of  the  load  adjacent  to  S, 
against  which  it  acts  across  the 
section  at  5,  is  greater  than  the  total  shearing  resistance  of  the  section. 
Shear  is  present  over  the  entire  length  of  the  beam,  and  at  any  section  is  equal 
to  the  reaction  at  S  minus  the  weight  of  the  load  between  the  reaction  and  the 
section  in  question.  In  general,  the  vertical  shear  at  any  section  of  a  beam 
subjected  to  vertical  loads  is  equal  to  the  algebraic  sum  of  all  the  vertical  forces 

acting  on  the  beam  on  either  side  of 
the  section. 

Single  and  Double  Shear.  A 
rivet  connecting  two  bars  under 
tension  (Fig.  2)  is  subjected  to  a 
shearing-stress.     If  one  section  of 


Shearing-failure  of  Beam 


Fig.  2.    Example  of  Single  Shear 


the  rivet  transmits  the  force  the  rivet  is  said  to  be  in  single  shear;  if  two 
sections,  it  is  in  double  shear. 

Distribution  of  Shear.    Shear  is  considered  to  be  uniformly  distributed 
over  the  section  except  in  cases  of  torsion  and  of  complex  stresses. 
For  the  ordinary  cases  of  shear  in  rivets,  etc.,  if 

5s  ==  the  allowable  unit  stress  in  shear, 
A  =  the  area  under  stress, 
and  P  =  the  safe  shearing-load; 

then  P  =  ASs  (i) 

The  Ultimate  Strength  in  Shear  has  been  determined  for  building  materials 
by  testing  suitably  prepared  specimens  and  dividing  the  maximum  load  ob- 


412    Resistance  to  Shear.     Riveted  Joints.     Pins  and  Bolts    Chap.  12 

served  by  the  area  tinder  stress.  For  material  like  wood,  in  which  there  are 
planes  of  weakness,  tests  must  be  made  which  take  these  into  account.  The 
direction  of  the  force  with  respect  to  these  planes  must  be  considered  in  choos- 
ing the  SAFE  WORKING  STRESS  from  the  tables. 

Safe  Working  Stresses  in  Shear.    Table  I  gives  safe  working  stresses. 
in  SHEAR  for  those  building  materials  usually  subjected  to  such  stresses. 


Table  I.     Safe  Working  Stress  in  Shear  for  Building  Materials* 


Material 


Safe  stress  in  lb  per 

sq 

in 

3000 

7SOO 

10  coo  (average) 

With  the 

Across  the 

grain 

gram 

200 

I  000 

lOO 

-     500 

ISO 

I  250 

130 

I  000 

100 

900 

ICX> 

600 

100 

750 

Cast  iron  (New  York). 

Wrought  iron 

Steel,  bolts,  rivets 


White  oak 

White  pine 

Long-leaf  yellow  pine. . 
Short-leaf  yellow  pine. 

Douglas  fir 

Hemlock 

Spruce 


*  Note.  For  woods,  these  values  may  he  increased  up  to  30%  for  selected,  perfectly 
protected,  commercially  dry  timber,  not  subject  to  impact,  that  is,  for  ideal  conditions. 
(See,  also,  pages  637  and  647.) 

Shear  in  Wooden  Tie-Beams.  There  are  a  few  cases  in  architectural  con- 
struction in  which  the  weakness  of  wood  in  shear  must  be  provided  for.     The 

one  most  frequently  arising  is  the 
framing  of  the  end  of  the  tie- 
'  beams  in  wooden  trusses. 
i)  oi  \nvi  Y'lg.  3  was  made  from  a 
photograph  of  a  shearing- 
failure  of  a  tie-beam  from  the 
thrust  of  the  rafter. 

Horizontal    Shear    in 

Wooden  Beams.     Failure  Hke 

that    shown    in    Fig.    1    rarely 

occurs  in  wood;    but  rectangular 

Fig.  3.     Shearing-failure  m  Wood  wooden   beams,    the    length    of 

which    is    less  than   about   twenty    times   the  depth,   are  liable   to    fail  by 

HORIZONTAL  SHEAR  along  the  middle,  under  about  the  same  loads  that  cause 

the  allowable  working  stresses  in  bending. 

Shear  at  the  End  of  a  Tie-Beam.  In  the  case  of  the  truss- joint  (Fig.  4), 
the  thrust  S  of  the  rafter  tends  to  shear  off  the  part  A  BCD  along  the  pkmc  of 
which  CD  is  the  trace.  This  area  under  stress  must  offer  a  shearing  resist- 
ance equal  to  the  horizontal  component  H  of  the  thrust  S.  The  width  of  the 
beam  b,  being  fixed,  formula  (i)  gives 
^,,  n={CDx  b)  Ss     or    CD  =  n/hs., 

The  shear  being  in  the  same  direction  as  the  grain  of  the  wood,  the  lower  value 

r„    'T'„U1„   T 4.   U«   ,-.^ — 1  


Riveted  Joints 


413 


Example  i  (Fig.  4).  The  horizontal  component  of  the  thrust  of  a  rafter  is 
20  GOO  lb.  The  long-leaf  yellow  pine  tie-beam  is  10  in  wide.  How  far 
should  the  beam  extend  beyond  the 
point  D? 

Solution.     In  this  case  H  =  20  000 

lb.     From  Tabfe  I,  Ss=  150  lb  per 

20  000 
sq  m.     Then  CD  =       ^         =  13.3 


10  X  150 
in   and   should   be   made    at 


least 


Truss-joint 


As  actually  constructed  a  large 
part  of  the  thrust  is  generally  taken 
up  by  a  bolt  or  strap  at  the  foot  of 
the  rafter  to  hold  it  in  place.  As 
the  bolt  and  shoulder  seldom  act  together,  either  the  length  CD  on  the  tie-beam 
should  be  made  long  enough  to  resist  the  entire  thrust,  or  the  bolt  or  strap 
designed  to  do  so  without  relying  on  the  shearing  resistance  in  the  plane  of  CD. 
The  design  of  such  joints  is  more  fully  considered  under  Subdivision  4,  pages 
429  to  439  of  this  chapter. 

2.   Riveted  Joints 

Use  of  Rivets.  Rivets  almost  exclusively  are  used  in  connecting  the  plates 
and  shapes  which  make  up  the  members  of  framed  steel  construction.  ' 

Rivet-Definitions.  A  rivet  is  a  piece  of  cylindrical  rod  with  a  head  forged 
on  one  end  and  usually  with  a  slight  taper  at  the  other  end  of  the  shank.  The 
grip  (Table  IV)  of  the  rivet  is  the  length  betweeen  the  under  sides  of  the  heads 
after  driving,  or  the  thickness  of  the  parts  joined.  The  length  (Table  IV)  of 
the  rivet  is  equal  to  the  grip  plus  enough  of  the  stock  to  form  a  head,  and  is 
measured  from  the  end  of  the  shank  to  the  under  surface  of  the  head.  The 
DIAMETER  OF  THE  SHANK  of  a  rivct  is  made  equal  to  its  nominal  diameter, 

but  rivets  are  driven  into  holes 

/^'"^ y^  Vh  in  larger  in  diameter  and 

upset  by  the  driving  so  as  to 
completely  fill  the  holes.  The 
shearing  values  and  bearing 
values  are  based  upon  the 
nominal  area  and  not  upon 
the  area  of  the  hole. 

Riveting  consists  in  heating 
the  rivet  to  a  welding-heat, 
passing  it  through  holes  in  the 
parts  to  be  joined  and  forging 
another  head  out  of  the  pro- 
jecting shank.  This  may  be 
done  by  hand-hammering;  but 


\^7 


1 — ^ 

/ 

/ 

- 

\ 

*- 

Fig.  5.     Forms  of  Rivet-heads 


shops  use  compressed-air-operated  hand-hammers  or  large  riveting-machines 
which  form  the  head  and  cause  the  shank  to  completely  fill  the  hole  by  heavy 
pressure  on  a  die. 

Material  of  Rivets.  Rivets  are  made  of  soft  steel  and  of  wrought  iron. 
Rivet-steel  is  generally  used.  The  head  may  have  any  of  the  forms  shown  in 
Fig.  5,  although  the  first,  called  the  rutton-head,  is  the  standard  for  structural 
work.  The  fourth  or  countersunk  head  is  used  where  it  is  necessary  to  have 
a  flat  surface,  as  over  a  bearing-plate. 


1^4    Resistance  to  Shear,     Riveted  Joints.    Pins  and  Bolts    Chap.  12 

The  Sizes  of  Rivet-Heads  differ  slightly  at  different  mills,  The  Standards 
of  the  American  Bridge  Company  give  for  the  diameter  of  the  head,  one  and 
one-half  times  the  diameter  of  the  shank  plus  Vs  in,  and  for  the  height  of  the 
head,  0.425  times  the  diameter  of  the  head.  Countersunk  heads  have  a  SLOPE 
of  30°  and  a  depth  equal  to  one-half  the  diameter  of  the  shank. 

The  Pitch  of  Rivets.  By  this  is  meant  the  center-to-center  distance 
between  them  in  a  line  of  riveting.  The  distance  between  lines  of  rivets,  or 
from  the  back  of  an  angle  or  channel  to  a  rivet-line. is  called  the  gauge-dis- 
tance. By  staggered  pitch  is  meant  the  arrangement  of  rivets  midway 
between  others  on  successive  rivet-lines  in  order  to  decrease  the  section  less 
than  when  they  are  arranged  in  rectangular  rows,  and  at  the  same  time  to  place 
a  greater  number  of  rivets  in  a  definite  area.  The  pitch  should  not  be  made 
less  than  three  diameters  of  the  rivet  and  the  distance  from  the  edge  of  the 
plate  not  less  than  one  and  one-half  diameters,  although  it  may  be  necessary 
to  make  the  distance  less  when  small  angles  are  used.  The  pitch  of  counter- 
sunk rivets  must  be  greater  than  that  of  button-head  rivets  because  of  the 
greater  amount  of  material  removed. 

Punching  Rivet-Holes.  Rivet-holes  are  made  with  power-punches.  The 
spacing  is  marked  on  the  different  parts  to  be  fastened  together  by  means  of 
wooden  templates  with  holes  drilled  to  locate  the  position  of  the  rivets.  When 
the  different  parts  are  assembled,  the  holes  are  laid  out  by  the  same  template- 
register,  so  that  the  rivets  may  be  inserted  without  difficulty.  Punching 
makes  a  ragged  hole.  The  flow  of  the  metal  under  the  great  pressure  hardens 
it  and  causes  a  loss  in  strength  of  from  11  to  33%  as  reported  by  W.  C.  Unwia 
for  soft  steel.  The  injury  may  be  removed  by  annealing  or  by  reaming  away 
the  injured  part  of  the  metal.  Enlarging  a  %-in.  hole  by  reaming  to  iVs  in 
has  been  found  to  remove  all  the  injurious  effects  of  punching.  One  method 
practiced  in  the  best  work  is  to  punch  the  holes  Via  in  less  in  diameter  than  the 
diameter  of  the  rivets,  and  to  ream  them  to  a  diameter  Via  in  greater,  after  the 
parts  are  assembled  and  bolted  together.  This  removes  the  greater  part  of 
the  injury  from  punching  and  corrects  the  alinement  of  the  holes.  (See 
Table  XI,  page  400,  and  Table  I,  page  702.) 

Drift-Pins.  When  the  alinement  of  a  hole  is  such  as  to  prevent  the  insertion 
of  the  rivet,  it  is  the  practice  in  some  shops  to  drive  in  a  tapered  drift-pin  and 
distort  the  holes  in  some  of  the  plates  sufficiently  to  set  the  rivet.  This  causes 
local  stresses  and  injury  to  the  plates  and  should  not  be  permitted. 

Shop-Riveting  is  done  with  powerful  air  or  hydraulic  riveting-machines 
which  may  exert  a  pressure  of  from  30  to  50  tons,  sufficient  to  upset  a  perfect 
head  on  the  projecting  end  of  the  shank  and  to  completely  fill  the  hole  even 
though  the  alinement  is  imperfect.  Contraction  on  cooling  causes  great  pres- 
sure between  the  parts,  so  that  it  is  probable  that  in  good  work  the  rivet  is  under 
little  or  no  shearing-stress,  the  force  being  transmitted  through  the  frictional 
resistance  of  the  plates. 

Clearance.  It  is  important  that  the  designer  place  the  rivets  so  they  may 
be  inserted  from  one  side  and  pounded  on  the  other  for  hand-work,  or  so  that 
the  machine  may  reach  them  for  machine-riveted  work.  For  example,  the 
minimum  distance  from  the  inside  face  of  the  leg  of  one  angle  to  a  line  of  rivets 
in  the  other  leg  must  not  be  less  than  i^s  in  for  %-in  rivets,  i  in  for  %-in  rivets, 
etc.  In  general,  a  distance  %  in  greater  than  the  diameter  of  the  head  should 
be  allowed  for  clearance. 

Inspection.  The  common  imperfections  in  riveting  are  loose  rivets  and 
ECCENTRIC  HEADS.     Loose  rivets  may  be  detected  by  holding  the  hand  against 


Riveted  Joints 


415 


one  side  of  the  rivet-head  and  tapping  the  other  side  with  a  light  hammer. 
If  loose,  a  slight  slip  may  be  felt.  The  loose  rivets  should  be  marked  to  be  cut 
out  and  replaced.  The  inspector  should  also  carefully  check  open  holes  left 
for  field-connections,  and  see  that  flattened  and  countersunk  rivets  are  as  called 
for,  because  such  work  may  be  done  at  less  expense  in  the  shop  than  in  the 
field,  where  it  may  cause  delay. 

The  Failure  of  Riveted  Joints  may  occur 

(i)  In  TENSION,  by  the  tearing  of  the  plate  through  the  line  of  rivets  (Fig.  8). 

(2)  In  SHEAR,  by  the  cutting  of  the  rivets  (Fig.  7). 

(3)  In  BEARING,  by  the  crushing  of  the  plate  in  front  of  the  rivets,  the  split- 
ting of  the  plate,  or,  in  some  cases,  by  the  shearing  out  of  the  sections  in  front 
of  the  rivets.  In  a  careful  design  of  a  joint  the  strength  against  failure  by  eaph^ 
of  these  methods  must  be  investigated  (Fig.  6  and  Fig.  9).  ', 


Fig.  6  Fig.  7   .  Fig.  8 

Figs.  6  to  9.     Methods  of  Failure  in  Riveted  Joints 


"X 


Fig.  9 


The  Steps  in  the  Design  of  any  type  of  riveted  joint  are,  (i)  the  selec- 
tion of  the  size  of  the  rivet  to  be  used,  (2)  the  determination  of  its  shearing 
and  bearing  strength  and  the  use  of  the  smaller  value  of  the  two  to  divide  into 
the  total  load  to  be  transmitted  and  thus  determine  the  number  of  rivets, 
(3)  the  arrangement  of  the  rivets  in  the  plate  and  the  investigation  of  its  strength 
in  tension  at  the  dangerous  section. 

The  Size  of  Rivets  is  determined  in  part  by  shop-practice.  Holes  can- 
not be  punched  in  plates  which  are  thicker  than  the  diameter  of  the  punch. 
The  following  table  gives  the  size  of  rivets  used  with  plates  of  different  thickness. 
Some  specifications  for  structural  work  require  all  rivets  to  be  %  in,  except 
where  thick  plates  require  larger  ones. 


tiickness  of  plates 

Size  of  rivets 

V4to7/iy    in 

%  in 

^2  to  %      in 

%in 

iVi6toi8/i6in 

%  in 

%  to  I       in 

I  in 

Tables  II  and  III  give  the  shearing  and  bearing  values  for  different  sizes 
of  rivets  in  plates  of  different  thickness  for  two  values  of  working  stresses  each; 
shear  at  7  500  and  10  000  lb  per  sq  in  and  bearing  at  15  000  and  18  000  lb  per 
sq  in.  Values  for  higher  stresses  can  be  figured  by  proportion  from  these  tables. 
The  lower  stresses  should  be  used  with  wrought  iron  or  in  parts  subjected  to 
live  loads;  the  higher  stresses  where  only  constant  or  dead  loads  are  present. 


416     Resistance  to  Shear.     Riveted  Joints.     Pins  and  Bolts    Chap.  12 


The  SHEARING  VALUE  is  cqual  to  the  area  of  the  rivet  multiplied  by  the  working 
stress;  the  bearing  value  is  equal  to  the  area  of  the  projected  surface  under 
pressure  multiplied  by  the  working  stress  in  bearing,  or,  if 

/=  the  thickness  of  the  plate; 

d  =  the  diameter  of  the  rivet ; 
and  Sb  =  the  working  stress  in  bearing; 

then  the  bearing  value    P  =  dtSb  (2) 

The  Shearing  and  Bearing  Values  may  be  taken  directly  from  the  tables, 
and  if  a  rivet  is  in  double  shear,  twice  the  quantity  in  the  table  is  to  be  used  for 
its  shearing  value.  Quantities  above  the  heavy  broken  lines  are  bearing 
VALUES  greater  than  the  values  in  single  shear,  so  that  for  these  conditions,  the 
number  of  rivets  necessary  in  a  joint  required  to  transmit  a  certain  load  is 
determined  by  dividing  the  load  by  the  value  in  single  shear.  If  rivets  are  in, 
double  shear,  the  number  of  rivets  required  is  found  by  dividing  the  load  by  the 

BEARING  VALUE. 

Rivet-Proportions.*  The  following  diagrams  show  various  rivet-proportions, 
including  the  dimensions  of  shanks  and  of  finished  and  countersunk  heads: 


COUNTERSUNK  HEADS 


FINISHED   HEADS 

Diam  head  =  V/2  diani  of 
3baQk+  J^'dept^  of  head 
=  ^^u)«diamof.head 

-'  These  proportions  vary  slightly  at  different  mills  and  in  different  handbooks. 


Depth  of  head  =  V2  diara  of 
shank.  Bevel  of  head  =  60° 


Riveted  Joints  417 

Conventional   Signs  for  Riveting.     The  following  diagrams  show  some 
conventional  signs  for  riveting: 

Shop  Field 


Two  Full  Heads 


Countersunk  Inside  (Farside)  and  Chipped 


Countersunk  Outside  (Nearside)  and  Chipped 


Countersunk  both  Sides  and  Chipped 


o 


iNsroE         Outside 
(Farside)    (Nearside) 


Both  Smfea 


Flattened  to  y^  in  high  or  Counter- 
sunk and  not  Chipped 


Flattened  to  vi  in  high 


Flattened  3/^  in  high 


This  system,  designed  by  F.  C.  Osborn,  has  for  its  foundation  a  diagonal  cross 
to  represent  a  countersink,  a  blackened  circle  for  a  field-rivet  and  a  diagonal 
stroke  for  a  flattened  head.  The  position  of  the  cross  with  respect  to  the  circle, 
inside,  outside,  or  on  both  sides,  indicates  the  location  of  the  countersink;  and 
similarly,  the  number  and  position  of  the  diagonal  strokes  indicate  the  height 
and  position  of  the  flattened  heads.  Any  combination  of  field,  countersunk 
and  flattened-head  rivets  liable  to  be  used  may  be  readily  indicated  by  the 
proper  combination  of  the  above  signs. 


Resistance  to  Shear.     Riveted  Joints.     Pins  and  Bolts     Chap.  12 


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Resistance  to  Shear.     Riveted  Joints.     Pins  and  Bolts     Chap.  12 


Length  of  Rivet-Shank 


ible  IV.      Length  of  Field-Rivets  for  Various  Grips, 
to  Form  Head 

American  Bridge  Company  Standard.     Dimensions  in  Inches    . 
^Grip,a^  |<-Grip,Ct — >]  \< — Grip,5-?i  [<— Grip,  6- 


J< ^Length- 

-^: 

k 

Length- 

— >i 

!<— 

Length- 

— > 

^ — 

Length- 

>i 

Diameter 

Diameter 

Grip     _ 

Grip 
6 

a 

V2  ^ 

% 

% 

Vs 

I 

y2 

% 

3/4 

78 

I 

V2 

l\^ 

I«/4 

iVs 

2 

2y8 

V2 

iVs 

iy4 

iTt 

1% 

1% 

% 

1% 

iVs 

2 

2y8 

2y4 

% 

iy4 

1% 

l3/^8 

l72 

IVI' 

% 

1% 

2 

2y8 

2y4 

2% 

3/4 

l3/^8 

11^2 

iy2 

1% 

1% 

Vs 

iVs 

2y8. 

2y4 

2% 

2y2 

Vs 

iy2 

1% 

1% 

l3/4 

l3/4 

I 

2 

2H 

2% 

2y2 

26/8 

I 

1% 

l3/4 

l3/4 

l78 

l78 

Vs 

2y8 

2% 

2V2 

2% 

2% 

Vs    ■ 

l3/4 

I78 

l78 

2 

2 

u 

2H 

2V2 

2% 

23/4 

278 

y4 

iVs 

2 

2 

278 

278 

% 

2% 

2% 

2% 

278 

3 

3/8 

2 

278 

278 

274 

2y4 

% 

2y8 

2% 

3 

3ys 

3y4 

y2 

2y8 

2y4 

23/^8 

2% 

2y2 

% 

2% 

3 

3y8 

3U 

3% 

% 

2y4 

23/^8 

2y2 

2y2 

2% 

% 

3 

3V4 

3% 

3y2 

3% 

3/4 

2l/l>. 

25/^8 

23/4 

2^4 

278 

% 

3Vs 

3% 

3y2 

3% 

33/4 

% 

2% 

23/4 

278 

278 

3 

2 

3V4 

3V2 

3% 

3% 

sVs 

2 

23/4 

278 

3 

3 

378 

Vh 

3% 

3% 

3% 

3y8 

4  , 

ys 

278 

3 

378 

37s 

3y4 

3V. 

3'r4 

3V8 

4 

4^8 
4V4 

y4 
% 

k 

3V8 

3y4 

3y4 
33/8 

374 

3% 

33/8 
3y^: 

3% 

3V8 

4 

4y8 

V2 

3V4 

4 

4ys 

4y4 

43/8 

y2 

3V4 

33/^8 

3y2 

372 

3%  - 

% 

3% 

4ys 

4y4 

4% 

4y2 

^/^S 

3% 

3y2 

3% 

3% 

3% 

.  §4 

4 

4y4 

4% 

4^2 

4% 

3/4 

3y2 

3% 

33/4 

3% 

378- 

-i.'5& 

4V8 

4% 

4y2 

4% 

43/4 

Vs 

3% 

3% 

378 

378 

4     -'. 

3 

4% 

4% 

4«/4 

4% 

5 

3 

378 

4 

4 

4% 

4Vi' 

Vs 

4^1' 

4% 

4y8 

5 

sVs 

.  Vs 

■    4 

4y8 

478 

4y4 

4%'r 

Vi 

4% 

4y8 

5 

sVs 

sU 

y4 

478 

4y4 

4V4 

43/8 

472^ 

% 

4% 

5^, 

'Yf 

5y4 

5% 

8/^8 

4y4 

43/8 

43/^8 

4y2 

4%^: 

V2 

4Vs 

5^^ 

sVf 

5% 

sVs 

y2 

43/^8 

4y2 

472 

4%. 

4%- 

% 

5 

5V4 

5% 

5y2 

5% 

% 

4y2 

4^5/^8 

4^8 

43/4 

4%^ 

% 

sVs 

5% 

5}^ 

5% 

53/4 

3/4 

4% 

43/4 

,43/4 

478 

5-    ■^. 

Vs 

5V4 

sV. 

5% 

5^4 

sVs 

% 

43/4 

478 

478 

5 

sVs- 

4 

5% 

5% 

5% 

5% 

6 

4 

478 

S 

5 

5V8 

SV4 

Vs 

5% 

sVs 

6 

eVs 

6y4 

ys 

sVs 

sH 

sV^ 

5% 

sy2 

Vi 

5% 

6 

eVs 

6y4 

6% 

y4 

.5% 

5% 

53/8 

572 

5^8 

% 

6 

6y4 

6% 

6% 

6% 

% 

5V2 

5% 

5% 

5% 

53/4 

V2 

6V8 

6% 

eVs 

6% 

63/4 

H' 

5% 

5% 

53/4 

5% 

578 

% 

6V4 

6\^ 

6% 

63/4 

6% 

% 

5^4 

578 

578 

578 

6 

3/1 

6% 

6% 

6% 

eVs 

7 

3/4 

578 

6 

6 

6 

678 

% 

6V2 

6% 

eVs 

7 

7y8 

Vs 

6 

678 

678 

678 

674 

5 

6-'>8 

eVs 

7 

7ys 

7yi 

5 

6y8 

6y4 

674 

674 

6% 

Vs 

TVs 

7y4 

7% 

ys 

6% 

6% 

672 

V4 

7V4 

73/8 

7y2 

y4 

672 

672 

6% 

% 

7% 

7y2 

7% 

3/^8 

6% 

6% 

63/4 

Va 

7% 

734 

778 

V2 

678 

678 

7 

% 

.  7% 

7% 

8 

% 

7 

7 

7y8 

% 

7ys 

8 

SVs 

..   3/4 

778 

778 

7y4 

Vs 

8 

sys 

8V4 

•       ^8 

7y4 

774 

7% 

For  weight  of  rivets,  see  page  1443. 


Riveted  Joints 


421 


Use  of  Riveted  Joints.  Riveted  joints  are  used  in  building-construction 
(i)  in  tie-bar  splices,  (2)  in  floor-beam  connections,  (3)  in  the  joints  of  trusses, 
(4)  in  riveted  girders,  and  (5)  in  column-connections. 


r^ 


TIT- 

Fig.  10.     Lap-joint 


Fig.  11.     Butt-joint  with  Single  Cover-plate 


o  o 


splicing  of  Tie-Bars.     Tie-bars  may  be  spliced  by  a  lap-joint  (Fig.  10); 
by  a  BUTT-JOINT  with  a  single   cover-plate    (Fig.   11);   or  by  a  butt-joint 
with     two     cover-plates     (Fig. 
12). 

The  Butt-joint  is  symmet- 
rical and  more  efficient  than 
the  others  because  of  the  absence 
of  any  tendency  to  bend  when 
under  a  load.  The  net  area  of 
the  cover-plates  at  the  section 
through  the  rivets  at  the  end  of 
the  main  plate  must  be  equal  to 


Fig.  12.    Butt-joint  with  Two  Cover-plates 


O       010       O 
O         O       I       O         O 
O         O  OjO  o 

0000 

O         OiO         o 
Joint  I 


the  net  area  of  the  main  plate  through  the  rivets  at  the  end  of  the  cover-plate. 
Fig.  14  shows  a  better  arrangement  of  rivets  than  that  in  Fig.  13,  because  less 
area  is  removed  at  the  critical  section  of  the  cover-plates.     In  some  cases  it 

may  be  necessary  to  make  the 
aggregate  thickness  of  the  cover- 
plates  greater  than  the  thickness 
of  the  main  plates. 

A  joint  with  one  line  of  rivets 
is  said  to  be  single-riveted, 
one    with    two    lines    double- 

Fig.13.   Cover-plate.   Six  Rivets  at  Critical  Section    riveted,    and    one    with    more 

than  two  unes,  chain-riveted. 

Example  2.  It  is  required  to  determine  the  number  of  rivets  in  the  splice 
of  a  12  by  V2-in  tie-bar  which  is  subject  to  a  tensile  force  of  65  000  lb. 

Solution.  Assuming  that  the  load  is  constant,  the  stresses  in  Table  III  may 
be  used.  Assuming,  also,  a  lap-joint  like  that  in  Fig.  15,  and  %-in  rivets,  the 
value  in  shear  of  one  rivet  is  found  to  . 

be   4  420  lb   and    the    bearing   value     V  ^^  o   o  O   0^\.  1 

against  a  V2-in  plate,  6  740  lb.  The 
number  of  rivets  is  determined  by  the 
shear  to  be  equal  to  65  000  divided  by 
4  420,  or  fifteen.  Since  sixteen  rivets 
are  required  to  complete  a  figure 
smaller  but  similar  in  arrangement  to 
that  shown  in  Fig.  15,  this  number  is 
used.  There  is  some  latitude  possible  in  the  spacing  of  the  rivets,  but  with  a 
width  of  12  in,  the  horizontal  gauge-lines  are  placed  1^2  in  apart  for  symmetry. 
If  the  pitch  P,  as  shown  in  Fig.  15,  is  required  to  be  three  times  the  diameter 
of  the  rivet,  this  diagonal  pitch  across  the  rivet-spacing  n^ust  be  2.23  in,  qr 


o  o     I      o 
o  o!  o  o 

00  00       o  I 

O  CO  o 

00  00 


Joint  I 
Fig.  14.    Cover-plate.    Four  Rivets  at  Criti- 
cal Section 


422    Resistance  to  Shear.    Riveted  Joints.    Pins  and  Bolts    Chap.  12 

greater.    The  length  of  the  horizontal  or  third  side  of  the  right-angled  triangle, 
having  an  hypotenuse  of  2.25  in  and  a  vertical  altitude  of  1.5  in,  is  1.68  in, 

which  requires  that  this  distance 
ED,  etc.,  be  1.75  in,  if  measured 
in  multiples  of  ^  in. 

Floor-Beam  Connections. 
The  two  following  examples  il- 
lustrate common  types  of  floor- 
beam  connections. 

Example  3.     It  is  required  to 
determine  the  number  of  %-in 
rivets  to  connect  a  lo-in  25-lb 
Fig.  15.    Rivet-spacing  in  Cover-plate  '  beam  supporting  24  000  lb  to 

a  15-in  42-lb  I  beam,  using  a 
shearing-stress  of  10  000  lb  per  sq  in  and  a  bearing-stress  of  18  000  lb 
per  sq  in. 

Solution.  From  the  table  of  properties  of  standard  I  beams,  pages  354-5.  the 
thickness  of  the  web  of  the  lo-in  25-lb  beam  is  found  to  be  0.31  in,  say  ^lo  in, 
and  of  the  15-in  42-lb  beam,  0.41  in,  say  Vie  in.  Referring  to  Table  III,  page 
419,  the  bearing  values  for  a  %-in  rivet  for  these  tliicknesses  of  webs  are  re- 
spectively 4  210  lb  and  5  890  lb.  The  shearing  value  of  the  rivet  is  4  420  lb. 
The  rivets  in  the  lo-in  beam  are  in  double  shear;  hence  the  bearing  value  gov- 
erns. The  number  of  rivets,  then,  is  12  000,  the  end-reaction,  divided  by  4  210, 
or  3.  For  the  15-in  beam  the  shearing  value  is  less,  and  the  number  of  rivets 
required  is  12  000  divided  by  4  420,  or  3.  Hence  two  standard  connection- 
anglesi  6  by  4  by  %  in  and  5  in  long,  may  be  used.  Each  has  three  holes  in  one 
leg  and  two  in  the  other.  The  leg  with  three  holes  is  placed  on  the  lo-in  beam 
with  the  rivets  in  double  shear,  and  the  leg  with  two  holes  is  connected  to  the 
15-in  beam;  thus,  in  the  latter  case  there  are  four  rivets  where  only  three  are 
required  for  strength.  They  are  driven  in  the  field  during  the  erection  of  the 
structure  and  the  working  stress  is  accordingly  made  less  in  most  specifications 
because  of  the  better  work  possible  with  the  heavy  machines  used  in  shop-work, 
than  with  the  tools  available  in  the  field. 

Example  4.  It  is  required  to  determine  the  number  of  %-in  rivets  in  a 
4  by  4  by  H-in  angle-bracket  attached  to  an  i8-in  5  5 -lb  beam  and  support- 
ing a  10  by  i2-in  wooden  beam  on  which  there  is  a  load  of  18  000  lb. 

Solution.  The  rivets  are  in  single  shear  with  a  shearing-resistance  of  4  420  lb, 
taken  from  Table  III. '  The  thickness  Of  the  web  of  the  I  beam  is  Vio  in,  giving 
a  bearing  value  of  5  890  lb.  Dividing  9  000  lb,  the  end-reaction,  by  4  420  lb, 
the  controlling  value,  we  find  that  two  rivets  are  insufficient.  The  bracket  may 
be  fastened  with  three  'li-in  rivets  with  a  spacing  of  4  in.  Two  Vs-in  rivets 
are  sufficient  to  hold  the  bracket. 

Rivets  in  Plate  Girders.  The  methods  of  determining  the  rivets  in  plate 
and  box  girders  are  given  in  Chapter  XX. 

Bending  Stress  in  Rivets.  While  the  bending  strength  of  rtNS  at  the 
joints  of  articulated  trusses  is  always  investigated,  this  is  never  done  in  the 
case  of  RIVETS.  A  hot  rivet  properly  driven  is,  when  cold,  under  a  tensile 
stress  which  is  nearly  equal  to  the  elastic  limit  of  the  material.  This  causes 
great  pressure  between  the  plates  and  a  consequent  frictional  resistance  to 
movement,  which,  under  the  usual  conditions,  equals  the  allowed  shearing-force 
on  the  rivet;  and  so,  until  an  initial  slip  occurs,  there  can  be  no  bending 
STRESSES  in  the  rivet.    In  the  case  of  very  long  rivets  driven  in  holes  where 


Strength  of  Fins  in  Trusses 


423 


there  is  an  imperfect  alinement  of  the  plates  and  a  consequent  difficulty  in 
making  the  rivets  fill  the  holes  completely,  it  is  not  probable  that  any  large 
bending  stresses  can  occur  in  the  rivets  of  a  structure.  This  has  been  avoided 
in  a  few  structures  for  which  long  taper  rivets  were  specified  to  be  used  in 
holes  REAMED  with  TAPERED  REAMERS,  thus  insuring  a  perfect  filling  of  the  holes. 
Working  Stresses.  Tables  II  and  III  are  based  on  stresses  which  approx- 
imate those  used  in  the  best  practice.  Table  II  is  used  for  the  few  structures 
made  of  wrought  iron  and  for  those  places  in  steel  structures  that  are  subject 
to  severe  conditions  of  service,  as  in  the  floor-systems  of  bridges.  Table  III 
is  used  for  ordinary  structural  work  made  under  the  conditions  governing  in 
modern  shop-practice.  For  comparison,  the  following  stresses  taken  from  the 
specifications  of  Theodore  Cooper  for  Steel  Railroad  Bridges  and  Steel  Highway 
Bridges  are  given: 


Specification  for 


Steel  railroad  bridges 
Steel  highway  bridges 


Allowable  stresses  on  rivets,  lb  per  sq  in 


Bearing 


IS  000  (i2  ooo  on  floors) 
22  500  for  laterals 
18  000  (14  400  on  floor- 
beams) 
27  000  for  laterals 


Shear 


9  000  (7  200  on  floors) 

13  500  for  laterals 

10  000  (8  000  on  floor- 
beams) 

14  000  for  laterals 


Rivets  driven  in  the  field  are  allowed  two-thirds  the  value  of  shop-driven  rivets. 


3.    Strength  of  Pins  in  Trusses* 

Truss-Pins.  In  the  design  of  the  pins  at  the  joints  of  trusses  the  stresses  in 
SHEAR,  BEARING  FLEXURE  or  BENDING  must  be  investigated. 

The  Shearing-Force  at  any  section  of  the  pin  is  the  algebraic  sum  of  all 
the  forces  acting  on  the  pin  on  either  side  of  the  section.  The  stress  is  considered 
to  be  uniformly  distributed  over  the  cross-section  of  the  pin.  When  the  forces 
do  not  act  in  the  same  plane  they  must  be  resolved  into  vertical  and  horizontal 
components  and  the  resultant  of  these  components  taken  as  the  shear  at  any 
desired  section.  This  may  be  done  by  the  principles  of  graphic  statics,  or 
by  TRIGONOMETRICAL  and  ALGEBRAICAL  METHODS,  the  graphic  method  being, 
for  some,  the  more  rapid. 

The  Bearing  Area  on  the  pin  is  taken  as  the  projection  of  the  area  of 
CONTACT,  the  area  of  this  projection  being  equal  to  the  diameter  of  the  pin 
multiplied  by  the  thickness  of  the  plate.  The  bearing  is  assumed  to  be  uni- 
formly distributed;  hence  for  any  load  the  intensity  of  the  pressure  may  be 
decreased  by  increasing  the  thickness  of  the  plate  or  the  diameter  of  the  pin. 

The  Bending  Moments  on  the  pin  may  be  found  by  the  principle  of 
MOMENTS  or  by  methods  involving  the  principles  of  graphic  statics  explained 
in  Chapter  IX  in  finding  the  bending  moments  of  beams.  The  forces  are  con- 
sidered to  be  concentrated  at  the  middle  of  the  bearing-plates.  If  they  do  not 
lie  in  a  plane  with  the  pin  they  must  be  resolved  into  their  vertical  and  hori- 

*  Since  the  introduction  of  rolled-steel  shapes  and  riveted  joints,  pin-joints  for  trusses 
of  moderate  span  in  buildings  have  fallen  into  disuse.  The  general  principles  of  theijt 
design,  however,  are  given  here. 


424    Resistance  to  Shear.     Riveted.  Joints.     Pins  and  Bolts     Chap.  12 

zontal  components  and  these  component  forces  in  the  two  planes  treated  sepa- 
rately. The  resultants  in  both  planes  at  any  section  may  be  combined  and  a 
single  resultant  force  acting  on  the  section  obtained,  and  also  the  consequent 
stresses  due  to  it. 


Table  V.     Shearing  and  Bearing  Values  of  Pins  for  One-Inch  Thickness 

of  Plate 

,  in  Pounds  per   Square  Inch 

Diam- 
eter of 
pin, 
in 

Area  of 
pin, 
sq  in 

Bearing 
value  at 
12  000  lb 
per  sq  in, 
lb 

Single 

shear  7  Soo 

lb  per  sq  in, 

lb 

Diam- 
eter of 
pin, 
in 

Area  of 
pin, 
sq  in 

Bearing 
value  at 
12  000  lb 
per  sq  in, 
lb 

Single 

shear  7  500 

lb  per  sq  in, 

tons 

I 

0.78s 

12  000 

5  890 

'     4 

4V8 

12.57 
13.36 

48000 
49500 

47.0 
50.1 

iVs 

0.994 

13  500 

7  455 

1V4 

1.227 

IS  000 

9  202 

a\\ 

14.19 

51  000 

53.2 

1% 

1. 48s 

16500 

II  132 

4% 

15.03 

52500 

56.3 

1V2 

1.767 

18  000 

13252 

4y2 

IS.  90 

54000 

59- 6" 

1% 

2.074 

19500 

15555 

4% 

16.80 

55  500 

63.0 

1% 

2.405 

21  000 

18037 

4% 

17.72 

57000 

66.3 

1% 

2.760 

22500 

20707 

4% 

18.67 

58500 

70.0 

2 

3.142 

24  000 

23565 

5 

19  64 

60  000 

73.6 

2V8 

3.547 

25500 

26  Goo 

sVs 

20.63 

61  500 

.77.3 

2V4 

3.976 

27  000 

29820 

sU 

21.65 

63000 

81.2    » 

2% 

4.430 

28  500 

33225 

5% 

22.69 

64500 

85.1 

2V2 

4.909 

30000 

36817 

5^1' 

23.76 

66  000 

89.1 

2% 

5.412 

31  500 

40590 

5% 

24.8s 

67500 

93.2 

2% 

5.940 

33000 

44550 

5% 

25.97 

69  000 

97.3 

2% 

6.492 

34500 

48690 
tons 

5% 

27.11 

70500 

lOI.I 

3 

7.069 

36000 

26. 5 

6 

28.27 

72  000 

106 

3V8 

7.670 

37500 

28.7 

6% 

29.46 

73500 

no 

3V4 

8.296 

39000 

31.0 

GM 

30.63 

75000 

115 

3% 

8.946 

40500 

33.5 

63/8 

31.92 

76  500 

119 

3y2 

9.621 

42000 

36.0 

6V2 

33.18 

78  000 

124 

3% 

10.32 

43500 

38.7 

6% 

34.47 

79  500 

129 

3% 

II.  OS 

45  000 

41.4 

6% 

35.79 

81  000 

134 

3% 

11.79 

46500 

44.2 

6% 

37.12 

82  500 

139 

^ 


L 


I      ^wwwva'^     Dg~ 


1  X  4-40,000 


I? 


In  the  Method  of  Moments  a  section  is  taken  at  each  force  in  succession 
and  the  moment  of  the  forces  about  a  point  in  the  section  found,  due  consider- 
ation being  given  to  the  direc- 
tion of  turning.  This  is  done 
at  each  force  on  one  side  of  the 
pin,  if  the  bars  are  arranged 
symmetrically,  and  in  both  the 
vertical  and  horizontal  planes. 
Inspection  of  the  results  will 
usually  indicate  which  section 
the   horizontal    and   vertical 


E 


IT 


Fig.  16.    Pin- joint 

has  the  greatest  resultant   moment   when 

components,  H  and  F,  are  combined.    This  is  done  by   using  the  formula 

B?^  W-\-  7*  since;  graphically,  the  resultant  R  is  the  diagonal  of  the  rectangle 


Strength  of  Pins  in  Trusses 


425 


Table  VI.     Maximum  Bending  Moments  in  Inch-Poimds  to  be  Allowed 

on  Pins  for  Maximum  Fiber-Stresses  of  is  ooo,  20  000  and  22  500 

Pounds  per  Square  Inch 


Diam- 

Moment 

Moment 

Moment 

Diam- 

Moment 

Moment 

Moment 

eter  of 

for  S  = 

for  5  - 

for  5  = 

eter  of 

for  S  = 

for  5  = 

for  5  = 

pin, 

IS  000 

20  000 

22  500 

pin, 

IS  000 

20  000 

22  500 

in 

in-lb 

in-lb 

in-lb 

in 

in-lb 

in-lb 

in-lb 

I 

1470 

i960 

2  210 

4 

94200 

125700 

141  400 

iVs 

2  100 

2800 

3140 

4V8 

103  400 

137800 

155  000 

M 

2880 

3830 

4310 

aM 

113  000 

150700 

169  600 

1% 

3830 

5  100 

5740 

4% 

123300 

164  400 

185000 

iVs 

4970 

6630 

7460 

4V2- 

134200 

178  900 

201  300 

1% 

6  320 

8430 

9480 

4% 

145  700 

194300 

218500 

1% 

7890 

10500 

II  800 

4% 

157800- 

210  400 

236  700 

iVh 

9710 

12  900 

14  600 

4% 

170  600 

227  500 

255900 

2 

II  800 

15700 

17700 

5 

184  100 

245400 

276  100 

2V8 

14  100 

18800 

21  200 

5V8 

198200 

264300 

297300 

2Va 

16800 

22  400 

25  200 

sM 

213  100 

284  100 

319600 

xYs 

19700 

26300 

29  600 

5% 

228  700 

304900 

343000 

2V2 

23000 

30700 

34500 

SV2 

24s  000 

326700 

367500 

2% 

26  600 

35  500 

40  000 

5% 

262  100 

349500 

393  100 

2% 

30600 

40800 

45900 

5«/4 

280  000 

373300 

419  900 

2% 

35000 

46  700 

52500 

5% 

298  600 

398200 

447900 

3 

39800 

53000 

59600 

6 

318  100 

424  100 

477100 

3V8 

44900 

59900 

67  400 

61/s 

338  400 

451  200 

507600 

3H 

50600 

67400 

75800 

6Vi 

359500 

479400 

539  300 

3% 

56600 

75500 

84  900 

6^^8 

381500 

508  700 

572300 

3^/1' 

63  100 

84  200 

94700 

6y, 

404400 

539200 

606600 

f/n 

70  100 

93500 

105  200 

6% 

428  200 

570900 

642300 

3% 

77700 

103  500 

116  500 

6% 

452900 

603900 

679400 

3% 

85700 

114  200 

128500 

6% 

478  500 

638  000 

717800 

Remarks.  The  following  is  the  formula  for  flexure,  If =5"/ /c,  with  the  reductions 
made  to  adapt  it  to  a  beam  of  circular  section: 

M  =  S7rd^/2,2  =  SAd/?, 

M  =  the  moment  of  forces  for  any  section  through  the  pin;  :  .;fj'{; 

S  =  the  stress  per  sq  in  in  extreme  fibers  of  pin  at  that  section; 
A  =  the  area  of  the  section; 
d  =  the  diameter; 
TT  =  3-14159. 

The  forces  are  assumed  to  act  in  a  plane  passing  through  the  axis  of  the  pin. 

The  above  table  gives  the  values  of  M  for  different  diameters  of  pin,  and  for  three 
values  of  S. 

If  the  maximum  value  of  M  is  known,  an  inspection  of  the  table  will  show  what  the 
diameter  of  the  pin  must  be  so  that  S  will  hot  exceed  15  000,  20  000,  or  22  500  lb,  as 
the  requirements  of  the  case  may  be.  i    i 


on  //  and  V.  Example  6  illustrates  the  method  for  the  condition  of  inclined 
FORCES  acting  on  the  pin.  In  Example  5  the  same  method  is  employed  to  deter- 
mine the  size  of  the  pin  in  a  simple  joint. 


426    Resistance  to  Shear.     Riveted  Joints.     Pins  and  Bolts     Chap.  12 

Example  5.  It  is  required  to  determine  the  size  of  the  pin  for  the  joint  shown 
in  Fig.  16  in  the  lower  chord  of  a  steel  truss.  The  middle  bar  is  a  vertical  sus- 
pension-rod to  hold  the  chord  in  place. 

Solution.  Beginning  at  the  section  between  the  outer  bars,  the  algebraic 
sum  of  the  forces  on  either  side  of  the  section  is  40000  lb,  hence  this  is  the 
shear.  At  the  section  next  to  the  suspender  the  sum  is  zero;  therefore  there 
is  no  shear  at  the  middle  of  the  pin.  The  bearing  pressure  is  40  000  lb.  Its 
intensity  depends  on  the  diameter  of  the  pin  and  the  thickness  of  the  bars.  To 
find  the  bending  moment  on  the  pin  the  forces  are  considered  concentrated  at 
the  middle  of  the  bars  and  moments  taken  about  sections  through  the  forces. 
The  moment  at  the  section  through  the  second  bar  is  40  000  lb  X  i  in,  equal 
to  40  000  in-lb.  If  moments  are  taken  about  a  point  between  the  inner  forces 
the  same  result  is  obtained.  From  Table  VI  it  is  found  that  a  2%-in  pin  at 
20  000  lb  per  sq  in  is  sufficient.  From  Table  V  the  bearing  value  of  a  2%-in 
pin'  is  found  to  be  only  33  000  lb  at  a  stress  of  1 2  000  lb  per  sq  in,  which  makes 
it  necessary  to  increase  the  size  of  the  pin  to  3%  in.  The  shearing  value  of 
this  pin  is  67  000  lb.  In  this  case  the  diameter  of  the  pin  is  determined  by 
the  bearing-stress,  but  it  is  necessary  to  investigate  the  oth6r  stresses  to  be 
sure  of  the  correct  size,  especially  in  case  of  heavy  bearing-plates. 

Bending  Moments  on  Pins.  The  finding  of  the  bending  moment  due  to 
the  forces  acting  on  a  pin  is  usually  the  most  difficult  part  of  the  work  of  deter- 
mining its  proper  size.  In  the  case  of  a  simple  pin,  properly  packed  and  lying 
in  the  plane  of  the  forces  acting  on  it,  the  greatest  moment  is  usually  the  prod- 
uct obtained  by  multiplying  the  outer  force  by  the  central  distance  between 
the  outer  bars;  but  when  the  forces  act  in  several  planes  the  work  is  more 
complicated.  The  graphical  method  illustrated  in  the  solution  of  the  two 
following  examples  has  some  advantages;  but  the  method  of  moments  applied 
at  the  end  of  the  solution  of  the  first  example  is  equally  rapid  in  practiced 
hands  and  capable  of  greater  refinement  in  the  results. 

Example  6.  It  is  required  to  find  the  bending  moment  on  tne  pin  of  the 
joint,  one-half  of  which  is  shown  in  Fig.  17.  The  bars  are  each  i  in  thick, 
the  channel  of  the  vertical  member  V^  in  thick  and  the  center  of  the  hanger 
is  %  in  from  the  center  of-  the  channel. 

Solution.  Since  the  joint  is  symmetrical  it  is  necessary  to  construct  but  one- 
half  of  the  force-diagram  and  equilibrium-polygon  which  really  apply  to 
the  joint.  From  the  conditions  of  equiUbrium  of  forces,  the  vertical  com- 
ponent of  the  inclined  force  is  upward,  and  equal  to  the  sum  of  the  downward 
forces,  34  000  lb;  and  its  horizontal  component  acts  with  the  60  000-lb  force, 
to  the  amount  of  17000  lb,  a  sufficient  amount  to  close  the  force-diagram. 
The  following  construction  is  special,  in  that  but  one-half  of  the  entire  graphical 
diagram  is  shown.  This  is  made  possible  because  of  the  symmetry  of  the  joint, 
the  bending  moment  being  constant  over  the  middle  of  the  pin. 

In  the  diagram  (Fig.  18)  ^1J5  is  drawn  at  an  angle  of  45°  with  the  horizontal, 
and  commencing  at  c,  the  distances  are  laid  off  to  scale  between  the  bars,  and 
the  lines  1-2,  2-3,  etc.,  drawn  parallel  to  the  forces  they  represent  at  the  joint. 
The  oblique  force  is  resolved  into  its  components  1-4  and  1-5. 

The  stress-diagram  (Fig.  19)  is  drawn  as  follows:  On  a  horizontal  fine  the 
forces  are  laid  off  to  scale  in  the  order  they  occur  on  the  pin,  1-2,  2-3,  3-4  and 
4-1,  the  closing  of  the  diagram  being  a  check  on  the  correctness  of  the  value  of 
the  forces.  Beginning  at  i,  1-5,  5-6  and  6-1  are  laid  off  to  scale,  parallel  to 
the  forces  in  the  vertical  plane.  From  i  the  line  r-o  is  drawn  at  an  angle  of 
45**,  for  convenience  in  making  good  intersections,  and  equal  to  a  convenient 
number,  say  20  000  lb,  in  the  same  sgale  to  which  the  loads  are  drawn.    The 


StrengUi  of  Pins  in  Trusses 


427 


point  O  is  the  pole  of  the  stress-diagram,  the  pole-distance  being  20  000  lb. 
From  the  principles  of  graphics  the  bending  moment  at  any  point  on  the  pin 
is  equal  to  the  intercept  between  the  proper  ray  of  the  equilibrium-polygon 
and  the  closing  Une,  multipUed  by  the  pole-distance.  To  complete  the  figures, 
a-2,  0-3  and  0-4  are  drawn  from  O,  and  from  c  cd  is  drawn  parallel  to  0-2,  c^ 
parallel  to  0-3,  ef  parallel  to  0-4  and  fk  parallel  to  o-i.  In  the  same  way 
rs  is  drawn  parallel  to  0-5,  st  to  0-6  and  tv  to  o-i.  Then  according  to  the 
above  principles,  the  moment  at  any  section  due  to  the  forces  in  the  horizontal 
plane  is  proportional  to  the  ordinate  at  that  section  drawn  from  the  line  AB 
to  the  line  cdefk  bounding  the  equilibrium-polygon;  and  the  moments  due  to 
the  vertical  forces  are  proportional  to  the  ordinates  drawn  to  the  line  rstv,  the 
numerical  value  being  the  length  of  the  ordinate  times  20  000,  the  pole-distance. 


Fig.  19 


Fig.  20 


Figs.  17  to  20.     Pin-joint  and  Moment-diagrams 


Where  both  moments  are  present,  the  resultant  or  true  rrioment  is  proportional 
to  the  hypotenuse  of  the  right-angled  triangle  having  for  its  sides  the  ordinates 
in  the  two  planes  at  the  point  in  question.  At  X  this  is  shown  by  the  line  mn. 
This  measures  2,42  in,  and  being  the  longest  diagonal  or  hypotenuse  that  can 
be  drawn  in  the  figure,  it  follows  that  the  maximum  bending  moment. on  the 
pin  is  2.42  X  20  000  =  48  400  in-lb. 

To  find  the  effect  of  changing  the  arrangement  of  the  members  on  the  pin, 
it  may  be  assumed  that  the  inclined  bar  is  placed  outside  the  inner  chord-bar. 
The  horizontal  stress-diagram  then  becomes  1-2,  2-3,  3-4',  4-1.  The  equilib- 
rium-polygons become  cdefk'  and  r's't'w,  as  shown  in  Fig.  20.  In  these  polygons 
the  longest  diagonal  measures  3%  in,  which  gives  a  bending  moment  of  3% 
in  X  20  000  lb  =  75  000  in-lb,  showing  that  the  arrangement  of  the  eye-bars  in 
Fig.  17  is  better.    As  a  rule  the  bending  moment  is  less  when  those  forces  that 


428    Resistance  to  Shear.     Riveted  Joints.     Pins  and  Bolts     Chap.  12 

oppose  each  other  are  placed  together.     It  may  be  further  reduced  by  making 
the  outside  bar  one-half  the  thickness  of  the  main  horizontal  bars. 

To  check  by  the  method  of  moments  the  value  of  the  maximum  bending 
moment  obtained  by  the  graphic  method  for  the  first  arrangement,  the  mo- 
ments of  the  forces  in  the  horizontal  plane  are  taken  about  r.    This  gives 

Mh  =  38  500  lb  X  3.0  in  +  38  500  lb  X  I. o  in  —  60  000  lb  X  2.0  in 
=  34  000  in-lb, 

which  is  the  value  of  the  moment  in  the  horizontal  plane  across  the  middle  of 
the  pin. 

In  the  vertical  plane  moments  are  taken  about  a  point  /,  giving 

Mv  =  34  000  lb  X  1.5  in  —  22  000  lb  X  0.75  in 
=  34  500  in-lb 

From  these  component  moments  the  resultant  maximum  bending  moment  is 

M  =  V  34  ooo2  +  34  5002  =  48  400  in-lb 

Example  7.  Another  illustration  of  the  graphical  method  of  finding  the 
bending  moment  on  a  pin  is  given  for  the  joint  A  of  the  truss-diagram  shown  in 


Fig.  23 


Fig.  24 


Figs.  21  to  24.     Force-polygons  and  Equilibrium-polygons  for  Bending  Moments 

a  Pin 


4 


Fig.  21.-^  Fig.  22  shows  the  arrangement  and  size  of  the  members.  The  stresses 
given  in  Fig.  21  are  for  one-half  the  number  of  members  at  the  joint.  As  in 
Example  6,  the  symmetrical  arrangement  makes  it  unnecessary  to  draw  more 


Strength  of  Bolts  in  Wooden  Trusses  and  Girders  429 

than  one-half  of  the  force-polygon  and  equilibrium-polygon.    The  web  of  the 
,  channel  is  reinforced  to  make  it  %  in  thick. 

Solution.  The  line  AB  (Fig.  24)  is  drawn  at  an  angle  of  45°  and  ah,  etc.,  are 
laid  off  to  scale,  equal  to  the  distances  between  the  members.  At  each  point 
of  application  of  a  force  a  line  is  drawn  parallel  and  to  scale,  to  represent  that 
force.  The  inclined  forces  are  then  resolved  into  their  horizontal  and  vertical 
components.  The  force-diagram  (Fig.  23)  is  then  drawn,  the  horizontal  forces 
being  laid  off  to  scale  in  the  order  in  which  they  occur,  1-2,  2-3,  3-4  and  4-1. 
The  pole-distance  is  then  laid  off  at  an  angle  of  45°  and  equal  to  20  000  lb  to 
the  same  scale  of  forces.  The  pole  o  is  then  joined  with  2,  3,  4  and  i.  Then 
in  Fig.  24,  ab  is  drawn  parallel  to  0-2,  be  to  0-3,  cd  to  0-4  and  de  to  o-i.  In 
the  same  way  the  line  hjkB  is  drawn.  From  inspection  it  is  seen  that  hb  is'the 
longest  intercept,  even  longer  than  any  diagonal  that  may  be  drawn  from  the 
extremities  of  the  horizontal  and  vertical  intercepts  at  any  point  along  AB. 
To  the  same  scale  that  makes  o-i  represent  20  000  lb,  hb  represents  31  800  in- lb; 
therefore  the  bending  moment  on  the  pin  is  31  800  in-lb.  In  Table  VI  a  pin 
2%  in  in  diameter,  at  a  fiber-stress  of  20  000  lb  per  sq  in,  has  an  allowable 
moment  of  35  500  in-lb,  and  in  Table  V  a  bearing  value  on  i  in  of  31  500  lb. 
A  force  of  31  800  lb  on  %  in  is  equal  to  42  400  for  a  i-in  bar;  so  it  is  necessary 
to  use  a  larger  pin  to  accommodate  the  bearing  requirement.  From  Table  V 
a  pin  3V2  in  in  diameter  is  found  to  be  necessary.  The  shearing  value  of  this 
pin  is  72  000  lb  more  than  twice  the  load,  so,  again,  it  is  the  bearing  that  con- 
trols the  size  of  the  pin.  If  the  thickness  of  the  bars  is  increased  the  diameter 
of  the  pin  may  be  reduced  to  3  in. 

4.   Strength  of  Bolts  in  Wooden  Trusses  and  Girders 

The  Working  Stresses  for  Bolts  on  which  Table  VII  and  Table  VIII  are 
computed  are  based  on  a  factor  of  safety  of  five  applied  to  the  average  of 
many  tests  on  dry  timber.  In  some  specifications  it  is  permitted  to  increase  the 
BEARING  PRESSURE  between  timber  and  bolts  as  much  as  50%  above  that  per- 
mitted for  short  struts.  The  values  in  the  tables  are  somewhat  less  than  the 
tests  on  large  trusses  made  at  the  Massachusetts  Institute  of  Technology,  in 
1897,  would  indicate  as  safe  values.  These  were  reported  in  the  Engineering 
Record,  November  17,  1900.  Table  IX  gives  the  allowable  maximum  tension, 
shear  and  bending  moments  for  wrought-iron  and  steel  bolts. 

Kinds  of  Stress  in  Bolts.  Bolts  in  wooden  trusses  are  subject  to  the 
same  kinds  of  stress  as  the  rivets  and  pins  in  steel  structures.  When  the 
pieces  joined  are  less  than  2  in  thick  and  the  bolts  are  tightly  drawn  up  so  as 
to  develop  considerable  frictional  resistance  between  the  pieces,  the  bolts  are 
proportioned  to  resist  the  total  force  in  shear  and  in  bearing.  When  the 
pieces  are  more  than  2  in  thick  the  bending  is  taken  into  account  and  the  bolts 
must  be  investigated  for  stresses  in  shear,  in  bearing  and  in  bending.  The 
SHEAR  is  assumed  to  be  uniformly  distributed  over  the  cross-section  of  the  bolt, 
and  the  bearing  area  is  the  area  of  the  projection  of  the  bolt  on  the  timber, 
which  area  is  equal  to  the  diameter  of  the  bolt  multiplied  by  the  length  in  con- 
tact. The  BEARING  STRENGTH  is  given  as  a  property  of  the  bolt  although  its 
value  depends  upon  the  crushing  strength  of  the  tim,b.er.  The  bending  mo- 
ment on  the  bolt  is  found  in  the  same  manner  as  for  pins  in  steel  trusses, 
although  the  cases  are  usually  less  complicated. 

Illustrations  of  the  Use  of  Bolts.  The  principles  involved  in  the  use  of 
bolts  in  wooden  trusses  and  girders  and  in  the  use  of  the  tables  may  be  best 
illustrated  by  the  solution  of  examples  in  each  of  the  following  cases: 


430    Resistance  to  Shear.     Riveted  Joints.    Pins  and  Bolts    Chap.  12 

(i)  Bolts  in  tie-beams,  thin  pieces. 

(2)  Bolts  in  girders  to  support  brackets. 

(3)  Bolts  as  pins  in  the  joints  of  trusses. 

(4)  Bolt-and-strap  joints  in  trusses. 

(5)  Bolts  under  tension  to  hold  the  foot  of  a  rafter. 

(See,  also,  "  Joints  in  Wooden  Trusses,"  Chapter  XXVIII,  pages  1149  to  11 60. 

Case  I.  Bolts  in  Tie-Beams,  Thin  Pieces.  Tie-beams  of  wooden  trusses, 
when  longer  than  30  ft,  are  usually  made  up  of  a  number  of  pieces.  This  con- 
struction is  cheaper  than  the  use  of  a  single  stick.  Two-inch  planks  bolted 
together  are  generally  used.  The  location  of  the  joints  in  the  courses  of  planks 
and  the  number  and  size  of  the  bolts  are  the  special  considerations  in  the  design 
of  such  a  joint.  In  general,  the  joints  in  adjacent  courses  are  placed  as  far 
apart  as  possible  and  not  more  than  two  joints  are  placed  opposite  each  other 
in  the  same  section.  The  simplest  case  is  that  of  a  plain  fish-plate  joint  like 
a  common  butt-joint  with  two  cover-plates  as  shown  in  Fig.  12.  The  number 
of  BOLTS  for  such  a  joint  is  found  in  the  same  way  as  the  number  of  rivets  in 
steel  tie-bars.  The  bolts  must  be  spaced  as  required  in  the  second  column  under 
each  timber  in  Table  VII,  to  provide  against  shearing  in  front  of  the  bolt. 


Table  VU.*     Safe  Bearing  Value  of  Bolts  per  Inch  of  Length  Parallel  to 

the  Grain  in  Timber  and  Distance  from  Center  to  Center  of  Bolts 

or  to  End  of  Timber 


Diam- 
eter of 
bolt, 

Long-leaf 
yellow  pine 

White  pine 

and  short-leaf 

yellow  pine 

Doug 

as  fir 

White  oak 

Bearing 

Bearing 

Bearing 

Bearing 

1 

in 

at  I  400 

Dis- 

at I  100 

Dis- 

at I  200 

Dis- 

at I  400 

Dis- 

lb per 

tance, 

lb  per 

tance, 

lb  per 

tance, 

lb  per 

tance, 

sq  in, 

in 

sq  in, 

in 

sqin, 

in 

sqin, 

in 

lb 

lb 

lb 

lb 

% 

I  050 

4V2 

82s 

5V4 

900 

4V4 

I  050 

3y2 

Vs 

1225 

5 

960 

s«/4 

I  050 

5 

1225 

4 

I 

I  400 

5% 

I  100 

6V2 

I  200    . 

5V2 

I  400 

4H 

iVs 

I  575 

6V2 

1237 

7^1' 

1350 

6y4 

1575 

5 

IV4 

I7SO 

1 

1375 

8 

I  500 

7 

1 750 

5y2 

1% 

1925 

7% 

I  512 

9  , 

I  650 

78/4 

1925 

6^i 

1V2 

2  100 

8V2 

I  650 

9% 

1800 

8y2 

2  100 

6% 

1^4 

2450 

10 

1925 

iiy2 

1950 

9V4 

2450 

7% 

2 

2800 

11V2 

2200 

13 

2400 

11V4 

2800 

9 

2V4 

3150 

12% 

2475 

14% 

2  700 

i2y2 

3  150 

10 

2V2 

3  500 

14V4 

2750 

i6Vt 

3000 

14 

3500 

iiy4 

2% 

3850 

15V4 

302s 

18 

3300 

i5y2 

3850 

i2y4 

3 

4  200 

17 

3300 

19 

3600 

17 

4  200 

i3y2 

The  distance  from  the  end  is  equal  to  the  diameter  of  the  bolt  plus  the  length  on  which 
twice  the  shear  is  equal  to  the  bearing  value  of  the  bolt  against  the  end-fibers.  See 
Notes  with  Table  XVI,  Chapter  XVI,  for  increase  in  allowed  stresses. 

•  When  the  effect  of  the  inclined  surfaces  upon  the  unit  stresses  is  taken  into  account, 
the  formula  for  the  normal  intensity  of  stress  for  cylindrical  pins  or  bolts,  given  in  Chapter 
XXVIII,  page  11^8,  may  be  used.  This  formula  will  give  lawef  Values  than  those  of 
Table  VII. 


Strength  of  Bolts  in  Wooden  Trusses  and  Girders 


431 


Table  VIII.*     Safe  Bearing  Value  of  Bolts  per  Inch  of  Length  Across  the 
Grain  in  Timber 


Long-leaf 

yellow  pine, 

lb 


Short-leaf 

yellow,  pine 

and  Douglas 

fir,  lb 


White  pine, 
lb 


White  oak, 
lb 


262 
306 
3SO 
394 
437 
482 
52s 
612 
700 


187 
218 
250 
281 
312 
343 
375 
437 
500 


150 
175 
200 
225 
250 
275 
300 
350 
400 


375 
437 
500 
562 
625 
687 
750 
875 
1000 


Table  IX.     Maximum  Allowable  Tension,  Shear  and  Bending  Moment  for 
Wrought-Iron  and  Steel  Bolts 


Diam- 
eter of 
bolt, 
in 

Net 
area, 
sq  in 

Wrought  iron 

Steel 

Tension 

at  12  000 

lb  per 

Shear 
at  7500 
lb  per 

Bending 

moment 

at  15000 

lb  per 

Tension 

at  16  000 

lb  per 

Shear 

at  10  000 
lb  per 

Bending 

moment 

at  20000 

lb  per 

sq  in, 

in-lb 

sq  m, 

sq  in, 
lb 

sq  m, 

sq  m. 

lb 

in-lb 

lb 

lb 

% 

0.302 

3620 

3310 

620 

4830 

4420 

830 

% 

0.420 

5040 

4510 

980 

6  720 

6  010 

I  3i(i 

I 

iVs 

0.550 
0.694 

6600 
8328 

5  890 

I  470 

8800 

7  850 

I  960 

7460 

2  100 

II  100 

9940 

2800 

iM 

0.893 

10  716 

9200 

2880 

14290 

12  270 

3830 

1% 

1.057 

12680 

II  140 

3830 

16  910 

14850 

5  100 

1V2 

1.295 

15  540 

13250 

4970 

20  720 

17670 

6630 

i«/4 

1 .  746 

20  930 

18  040 

7890 

27910 

24050 

10500 

2 

2.302 

27  620 

23560 

II  800 

36830 

31420 

15700 

2V4 

3.023 

36280 

29820 

16800 

48370 

39760 

22  400 

2V2 

3.719 

44  630 

36820 

23000 

59510 

49090 

30700 

2% 

4.620 

55430 

44550 

30  600 

73910 

59400 

40800 

3 

5.428 

65  140 

53010 

39800 

86850 

70690 

53000 

3V1 

6.510 

78  120 

62  220 

SO  600 

104  160 

82960 

67400 

Example  8.  A  typical  tie-beam  used  as  a  lower  chord  of  a  Howe  truss  is 
shown  in  Fig.  25.  It  is  50  ft  long,  of  Douglas  fir  and  subject  to  the  tension  in 
the  different  panels  shown  in  the  figure. 

Solution.  The  thickness  of  the  plank  Is  drawn  out  of  scale  in  the  figure  to 
show  the  joints  more  clearly.  The  black  circles  show  the  vertical  tension-rods, 
which  so  nearly  cut  the  middle  plank  in  two  that  it  is  not  considered  a  part  of 
the  tensile  member.  The  arrangement  of  the  planks  and  the  lengths  to  be 
used  must  be  determined  for  each  case.  In  the  one  shown  there  is  but  one 
splice  in  the  middle  panels  where  there  is  the  greatest  tension.    The  distance 


432    Resistance  to  Shear.     Riveted  Joints.     Pins  and  Bolts    Chap.  12 


XY  is  12  ft,  which  is  about  as  small  as  will  serve  for  the  transfer  of  the  tension 
from  A'  X.Q  B.  In  this  beam  the  two  outer  planks,  A  and  A',  must  be  large 
enough  to  resist  the  whole  tensile  stress  in  the  middle  panels  because  of  the 
joints  in  B  and  C.  At  the  inner  end  of  the  second  panel  there  is  58  000  lb 
tension  which  must  be  carried  to  the  end  of  the  first  panel.     Because  of  the 


-50  0- 


6-^  bolts 


-11-1  bolts Y^*^—' *-^  -H  Y' 


-^-^ 


I   !   I 


■  36000  Ibs.T— >|<-58000  Ibs.T  >i<     66000  lbs.Tj>|< 8  0^^ >^ 8'0- 

Fig.  25.    Plan  of  Built-up  Tie-beam 

joints  in  A  and  A'  this  must  be  transmitted  to  B  and  C  in  order  to  pass  the 
point  X. 

.  Assuming  that  29  000  lb,  one-half  the  tension,  is  carried  on  plank  A  to  be 
transmitted  to  C  by  the  shear  and  bearing  on  the  bolts,  and  dividing  this  by 
7  850  lb,  the  allowable  shear  on  a  i-in  bolt,  four  bolts  are  found  to  be  necessary. 
But  the  bearing  value  of  a  i-in  bolt  in  Douglas  fir  2  in  thick,  is  only  2  400  lb, 
which  makes  twelve  bolts  necessary.  These  are  required  in  the  distance  XV, 
12  ft. 

From  the  distances  in  Table  VII,  it  is  found  that  the  end-bolts  must  be  5^^^  in 
from  the  ends  of  the  planks,  say  6  in;  this  leaves  ii  ft,  in  which  distance  eight 
bolts  are  to  be  arranged.    If  four  bolts  are  placed  in  pairs,  two  at  each  end,  as 


-c->h- 


^14?^''- 


-14%"- 


Fig.  26.    Elevation  of  Beam  Opposite  X  of  Fig.  25 

shown  in  Fig.  26,  the  intermediate  spaces  are  14?^  in.  The  bolts  bind  the  beam 
together  better  if  they  are  staggered,  as  indicated  in  Fig.  26,  and  not  placed  on 
the  middle  line. 

The  number  of  bolts  mentioned  is  sufficient  to  make  the  splice,  but  there 
should  be  bolts  in  the  distance  YV,  and  between  the  ends  and  X  and  X\  to 
bind  the  planks  together.  These  need  not  be  as  large  or  as  close  together  as 
the  others;  %-m  bolts  spaced  2  ft  are  sufficient.  There  should  be  two  bolts 
at  the  end  of  the  beam.  Each  bolt  should  be  driven  through  a  hole  of  the  same 
size  as  the  bolt  and  the  nuts  should  be  screwed  up  tight. 

Case  II.  Bolts  in  Girders  to  Support  Brackets.  The  construction  shown 
in  Figs.  27  and  28  is  commonly  used  in  cases  in  which  the  requirements  do  not 
allow  the  girder  to  project  its  full  depth  below  the  joists.  The  bolts  shown  in 
Fig.  27  must  be  investigated  for  bearing  and  shear,  and  those  shown  in  Fig.  28 
for  BEARING,  SHEAR  and  BENDING.  In  either  case  the  shearing  value  of  the  bol^ 
in  single  shear  must  equal  or  be  greater  than  the  greater  of  the  forces  S  or  S', 

The  BEARING  per  inch  on  the  wood  of  the  girder,  when  B  is  in  inches,  is 


Strength  of  Bolts  in  Wooden  Trusses  and  Girders 


433 


This  must  be  kept  within  the  values  given  in  Table  VII  for  the  timber  used. 
For  the  case  shown  in  Fig.  28  the  bending  moment  in  pound-inches  is 

M^SLh   or  u^s'Lh  i;;: 

yd. I 
whichever  is  the  larger.    B  and  L  are  measured  in  inches  and  S  in  pounds.  ■•  >  ■■•■> 


Fig.  28 
J^igs.  27  and  28.     Bolts  Supporting  Brackets  on  Girders 

Example  9.  For  the  construction  shown  in  Fig.  27  it  is  required  to  determine 
the  number  and  size  of  bolts,  the  Douglas  fir  girder  being  8  by  14  in,  with  a 
span  of  14  ft,  and  the  Douglas  fir  joists  3  by  12  in,  with  a  span  of  20  ft,  center  to 
center  of  girders.  The  floor-load,  including  the  floor,  is  60  lb  per  sq  ft.  The 
angles  are  4  by  3^2  by  %\\x.  * 

Solution.  The  floor-area  supported  by  the  girder  is  14  by  20  ft.  At  60  lb 
per  sq  ft,  the  load  is  14  X  20  X  60  =  16  800  lb.  The  load  5,  on  one  side,  is 
8  400  lb.  • 

A  34-in  bolt  has  a  shearing-value  of  4  420  lb.  Hence  two  bolts  are  necessary 
to  satisfy  the  shearing  condition.  The  bearing  value  of  the  bolt  in  the  wood, 
across  the  grain,  is,  from  Table  VIII,  1S7  lb  per  inch  of  length,  or  i  496  lb  for 
the  width  of  the  girder.  The  number  of  bolts  required,  then,  is  16  800  divided 
by  I  496  or  approximately  ii,  which  gives  a  spacing  of  about  15  in. 

Example  10.  In  the  construction  shown  in  Fig.  28,  the  girder  is  6  by  14  in,  of 
Douglas  fir  and  has  a  span  of  12  ft.  The  joists  are  2  by  12  in  and  have  an  i8-ft 
span,  center  to  center  of  girders.  The  floor-load  is  65  lb  per  sq  ft.  There  are 
3  by  4-in  strips  on  the  sides  of  the  girder.  The  distance  L  is  3  in.  It  is  ji;Qqjaifj?4 
to  find  the  number  and  size  of  bolts  to  be  used.  *  -,  ^j  •\'i\\i\-\ 

Solution.    The  total  load  on  the  girder  is  ■'        '    ■"■' 

12  X  18  X  65  =  14  040  lb 
5=7  020  lb 

The  bearing  load  per  inch  of  thickness  of  the  girder  is 


14  040 


=  2  340  lb 


The  bending  moment  on  one  side  of  the  girder  is 

7020X3  .    ,, 
•  =  10  530  m-lb 


.XX5  o^  10  jrri'jn<«{ 

-  n. 


since  the  force  S  acts  at  the  center  of  pressure  on  the  bracket-strip,  iVi  in  from 
the  edge  of  the  girder. 

The  shear  is  7  020  lb,  which  requires  two  %-m  steel  bolts  at  4  420  lb  for  oii^ 
as  given  in  Table  IX.  '^''  ^ 

The  bearing  (Table  VIII)  on  a  ^i-in  bolt  is  187  lb  per  inch  of  length;  thei'efore 
it  requires  thirteen  bolts  for  bearing. 


434    Resistance  to  Shear.     Riveted  Joints.     Pins  and  Bolts     Chap.  12 

The  allowable  bending  moment  on  a  %-in  steel  bolt  is  830  in-lb,  from  Table  IX. 
To  take  care  of  the  lo  530  in-lb  requires  thirteen  bolts.  A  Vs-in  steel  bolt  has 
an  allowable  bending  moment  of  i  3 10  Ib-in,  making  eight  of  them  sufficient. 
The  3  by  4-in  pieces  may  be  held  in  place  by  thirteen  •ji-'m  bolts  spaced  11  in 
on  centers,  if  two  of  them  are  placed  6  in  from  the  ends. 

Case  III.    Bolts    as   Pins   in    the    Joints    of    Trusses.     For    ties   or 

STRUTS  joined  by  bolts  in  the 
manner  indicated  in  Figs.  29, 
30  and  31  and  having  the 
thickness  B  exceeding  2  in, 
the  diameter  of  the  bolt  or 
the  number  of  bolts  must  be 
computed  for  shearing,  bear- 
ing and  FLEXURE. 

For  any  of  these  joints  the 
forces  are  as  follows: 

The  single  shear  =  S/2 

On  the  sections  between  B 
and  B'  (Fig.  30) 

The  bearing  on  the  pin  per 
inch  of  length  =  S/B  or  S'/B' 

The  greater  is  to  be  used. 

The  bending  moment  =  SL/iz 

on  the  assumption  of  a  contin- 
uous BEAM,  uniformly  loaded. 
If  there  are  more  bolts  than 
one,   the   quantities    obtained 


ELEVATION 


B' 


_a^ 


B' 


V2S- 


1/2  S- 


PLAN 
Fig.  29.     Bolt  through  Rafter  and  Tie-beam 


a 


-Vo  S  - 


3 


by  the  above  formulas  are  to  be  divided  by  the  number  of  bolts  to  find  the  part 
to  be  taken  care  of  by  one  bolt. 

In  Fig.  29,  S  is  the  horizontal  component  of  the  thrust  T, 

Example  11.  It  is  required  to  determine  the  diameter  of  a  bolt  for  a  joint 
like  that  shown  in  Fig.  29.  The 
rafter  is  6  by  10  in,  of  Douglas 
fir,  the  tie-beams  3  by  10  in,  of 
the  same  material,  the  thrust  in 
the  rafter  30  000  lb,  and  its  inch- 
nation  30°. 

Solution.  The  horizontal  com- 
ponent of  30  000  lb  at  30°  is  prac- 
tically 26  000  lb.  Then  5=2$  000 
lb  and  the  shear  =13  000  lb. 
.B  =  6  in  and  L  =  9  in. 

Bearing  per  inch  of  length  on  the  bolt  =  26  000/6 
Bending  moment  =  26  000  X  9/12  =  1.9  500  in-lb 

In  Table  IX,  a  i%-in  steel  bolt  is  found  to  be  necessary  to  resist  a  shear  of 
13  000  lb,  and  a  2M-in  bolt  for  a  bending  moment  of  19  500  in-lb.  To  resist 
4  333  lb  end-bearing  pressure  on  i  in  a  larger  bolt  is  required  than  is  given  in 
Table  VII.  Dividing  4  333  by  i  200,  the  allowable  bearing  on  Douglas  fir,  a 
3%-in  bolt  is  found  to  be  necessary.  This  is  larger  than  it  is  desirable  to  use, 
so  the  joint  must  be  redesigned  with  a  view  to  reduce  the  bearing  pressure  on 


Fig.  30.     Bolt  in  Wooden  Tie-beam  . 


■  4  333  lb 


-f-l 


I 


%SM==^B', 


'    I  I  B    iL! !       S- 


I 


Strength  of  Bolts  in  Wooden  Trusses  and  Girders  435 

the  bolt.     If  an  8  by  8-in  strut  and  4  by  8-in  tie-beams  are  used,  B  becomes 
8  in  and  L  12  in.    This  gives 

•    Bearing  pressure  =  26  000/8  =  3  250  lb  per  inch  of  length  of  the  bolt 
(:  Bending  moment  =  26  000  X  12/12  =  26  000  in-lb 
The  total  shear  at  the  section  on  one  side  of  the  strut  is  the  same  as  before. 

From  Table  VII  it  is  found  that  a  2%-in  bolt  is  large  enough  to  provide  for 
the  bearing  and  that  a  2Mj-in  bolt  is  sufficient  for  the  bending  as  given  in  Table 
IX.  Hence  if  an  8  by  8-in  strut  is  used,  there  must  be  a  2%-in  bolt  and 
the  distance  D  must  be  15H'  in  (Table  n 

VII).  2^  s^- B-T7^  J^     I 

Example  12.  For  the  same  construc- 
tion as  in  Fig.  29  and  the  same  con- 
ditions as  in  the  first  part  of  Example 
II,  it  is  required  to  determine  the  size  ,  , . 

of  the  bolts  when  it  is  necessary  to       '5/s<-| 1   B'i  |   "  -A 

use  three.  j    *  "^    /^ 

Solution.     The  shear,  beanng,  and  ' 

bending  moment  are  the  same  as  in         Fig.  31.     Bolts  in  Wooden  Tie-beam 
Example   11,   but  because  there  are  •      j  u 

three  bolts  each  quantity  is  divided  by  3  to  determine  the  force  resisted  by 
each. 

Shear  =  13  000/3  =  4  333  lb  and  requires  a  %-m  steel  bolt  (Table  IX) 
Bearing  =  4  333/3  =  i  444  lb  and  requires  a  iV+in  bolt  (Table  VII) 
Bending  moment  =  19  500/3  =  6  500  in-lb,   and  requires  a  iMi-in  steel  bolt 
(Table  IX). 

In  this  case  the  bending  moment  determines  the  size  of  the  bolts,  which  may 
be  arranged  as  shown  by  the  dotted  circles  in  Fig.  29. 

Example  13.     It  is  required  to  determine  the  diameter  of  the  bolt  for  the 
construction  shown  in  Fig.  30,  in  which  the  inner  beam  is  of  Douglas  fir  and 
6  by  8  in  in  section,  and  the  outer  beams  3  by  8  in,  the  tension  being  24  000  lb. 
Soludon.  S=  24  000;     B=6m;    X  =  9  in. 

Single  shear  on  the  bolt  =  24  000/2  =  12  000  lb  r 

Bearing-pressure  per  inch  of  length  of  bolt  =24  000/6  =  4  000  lb 
Bending  moment  =24000X9/12=18000  in-lb 
From  Table  IX  a  lU-in  steel  bolt  is  found  sufficient  to  resist  the  shear,  and 
a  2V4-in  bolt  large  enough  to  resist  the  bending.  In  Table  VII  the  largest  bolt 
considered,  3  in,  is  too  small  in  bearing  value.  Dividing  the  load  to  be  resisted 
by  I  200  gives  sVs  in,  as  the  diameter  necessary  to  resist  the  bearing.  The 
distance  D  must  be  4  000/(2  X  130)  +  3^  in  or  i834  in. 

Example  14.  If  two  bolts  are  used,  one  behind  the  other,  it  is  required  to 
determine  the  diameter  of  the  bolt  that  should  be  used,  the  conditions  and 
loading  being  the  same  as  in  Example  13. 

Solution.    Dividing  the  quantities  obtained  in  Example  13  by  2, 
Single  shear  =  6  000  lb  and  requires  a  %-in  steel  bolt 
Bearing  =  2  000  lb  and  requires  a  2-in  bolt 
Bending  moment  =  9  000  in-lb  and  requires  a  i%=-in  steel  bolt 
The  allowable  bearing  on  a  i^/i-in  bolt  is  (2y2  %)  less  than  the  required  amount, 
so  that  in  general,  since  the  other  requirements  are  more  than  satisfied,  the 
smaller  bolt  would  be  used.     For  the  18/4-in  bolt,  the  distance  D  is  9H  in.    The 
space  between  the  bolts  may  be  increased  somewhat  beyond  the  value  given  m 


436    Resistance  to  Shear.     Riveted  Joints.     Pins  and  Bolts     Chap.  12 


Fig.  32.     Strap  and  Bolt  at  Foot  of  Rafter 


Table  VII,  and  they  may  be  located  out  of  the  same  line  as  a  further  precau- 
tion against  splitting. 

Case  IV.  Bolt-and-Strap  Joints  in  Trusses.  The  construction  shown  in 
Fig.  32  is  sometimes  used  to  connect  the  foot  of  the  rafter  of  a  wooden  truss 
to  the  tie-beam.  When  the  distance  D  is  sufficient  to  resist  the  shear  due  to 
the  thrust  of  the  rafter,  the  strap  is  of  value  only  in  holding  the  rafter  in  place, 
and  there  are  no  greater  pressures  brought  upon  the  bolt.  When  it  is  impos- 
sible to  make  D  the  necessary  length,  the  bolt  and  strap  must  be  designed 
to  resist  the  full  force  in  the  direction  of  the  strap. 

As  the  STRAP  is  usually  not  more  than  from  V-^  to  %  in  thick,  its  width 
is   such   that    the   bearing    between   it   and    the    rafter    is   small    compared 

^  with  that  between  the  bolt  and 
rafter.  The  forces  acting  on  the  bolt 
are  the  only  ones  that  need  con- 
sideration. These  are:  /u 
Single  shear  =  5/2  =  the  ten-* 
sion  in  the  strap  on  one  side 

Bearing  pressure  per  inch  of 
length  =  S/B,  where  B  is  the  width 
of  the  tie-beam  in  inches 

Bearing  pressure  per  inch  of 
length  between  strap  and  bolt  =  S/2  t 


To  fmd  the  value  of  5,  the  force- 
polygon  is  drawn  as  shown  at  the  right 
in  Fig.  32.  T  is  drawn  parallel  to  the 
rafter  and  with  a  length,  to  a  con- 
venient scale,  equal  to  the  thrust.  From  the  end  a  an  indefinite  line  is  drawn 
parallel  to  the  axis  of  the  strap,  and  from  b  another  line  perpendicular  to  the 
seat  of  the  rafter.  These  intersect  at  c,  so  that  ac,  measured  by  the  same 
scale  used  in  laying  off  T,  is  the  magnitude  of  the  force  S  in  the  strap.  If  the 
rafter  rests  on  top  of  the  beam,  be  is  vertical,  but  if  the  tie-beam  is  dapped,  as 
shown  by  the  dotted  line,  the  line  from  b  is  drawn  perpendicular  to  the  bottom 
of  the  notch,  making  the  intersection  at  c'.  It  is  seen  that  notching  the  tie- 
beam  in  this  way  increases  the  stress  in  the  strap. 

Example  15.  It  is  required  to  determine  the  size  of  a  strap  and  pin-bolt 
to  hold  the  rafter  without  notching  into  the  tie-beam  of  a  long-leaf  yellow-pine 
king-post  truss.  •  The  rafter  is  6  by  6  in,  is  inclined  at  an  angle  of  45°  and  is 
under  a  compressive  stress  of  18  000  lb.     The  tie-beam  is  6  by  8  in  in  section. 

Solution.  Since  the  inclination  is  45°,  a  consideration  of  the  force-polygon 
in  Fig.  32  shows  ab  equal  to  ac,  so  that 

The  force  5  =  the  thrust  T  =  18  000  lb 
Single  shear  on  bolt  =18  000/2  =  9  000  lb 
Tension  in  strap  on  one  side  =  9  000  lb 

Bearing  pressure  per  inch  of  bolt  against  wood  =18  000/6  =  3  000  lb 
Bearing  pressure  in  pounds  per  inch  between  strap  and  bolt  =  9  000// 
in  which  /  equals  the  thickness  of  the  strap. 

The  allowable  pressure  between  the  strap  and  the  top  of  the  rafter  is  350  lb 
per  sq  in  (Table  VII),  which,  on  the  6-in  rafter,  gives 

Allowable  load  per  inch  of  width  of  strap  =  6  X  350  =  2  100  lb 

The  strap  then  must  be  18  000/2  100  or  8.6  in  wide.  At  10  000  per  sq  in 
in  tension  the  necessary  section  of  the  strap  is  0.9  sq  in,  requiring  a  thickness  of 


Strength  of  Bolts  in  Wooden  Trusses  and  Girders 


437 


about  O.I  in,  a  sufficient  thickness  if  the  strap  were  strong  enough  to  develop  a 
uniform  pressure  over  the  rafter.  It  is  not  good  practice,  however,  to  use  such 
thin  material,  because  of  the  danger  of  loss  of  strength  due  to  corrosion.  No 
metal  less  than  %  in  thick  should  be  used  in  such  places. 

The  bearing-pressure  per  inch,  between  the  strap  and  the  bolt,  for  a  %-in 
strap  =  9  ooo/%  =  24  000  lb 

The  bolt,  then,  must  take  a  single  shear  of  9  000  lb,  a  bearing  pressure  of 
3  000  lb  against  the  wood  for  each  inch  of  length,  and  a  bearing  of  24  000  lb 
per  inch  of  length  against  the  strap.  From  Table  IX  a  i^^-in  steel  bolt  is 
sufficient  to  resist  the  shear,  from  Table  V  a  2-in  bolt  is  large  enough  to  resist 
the  bearing  from  the  strap,  and  from  Table  VII  a  2^4 -in  bolt  is  found  necessary 
to  resist  the  3  000-lb  bearing  from  the  wood  per  inch  of  length  of  bolt.  This 
makes  the  2^4-in  bolt  satisfactory  for  the  joint. 

The  pressure  from  the  bolt  to  the  wood,  however,  is  not  parallel  with  the 
grain  but  inclined  at  45°.  The  allowable  pressure  against  wood  across  the 
grain  is  about  one-fourth  of  that  with  the  grain.  According  to  the  formula 
given  in  Chapter  XXVIII,  page  1138,  the  allowable  pressure  per  square  inch  for 
this  case  is  612  lb  instead  of  the  1  400  per  sq  in  allowed  for  direct  compression 
with  the  grain.  The  reduced  allowable  pressure  makes  it  necessary  to  use  a 
4.9-in  bolt,  say  a  5-in  bolt,  which  would  be  impracticable,  for  it  would  almost  cut 
the  tie-beam  in  two.  It  thus  appears  that  this  form  of  joint  is  not  good  design 
for  a  truss  of  this  span.  For  shorter 
spans  the  joint  may  be  made  in 
accordance  with  the  requirements 
given.  It  has  the  advantage  of  not 
presenting  any  projections  below  the 
tie-beam. 

Case   V.    Bolts    in    Tension  to 
Hold  the  Foot  of  a  Rafter.    In  the 

joint    shown  in  Fig.  33    the   bolt  is 

subject      to      DIRECT      TENSION      Only. 

The  amount  of  the  tension  5  is  found 

by    the    construction     explained     in 

Case  IV.     The  rafter  may  be  let  into 

the  tie-beam  or  rest  on  top  of  it,  the 

tensioa  in    the    bolt    being    less    in 

the  latter  case;  but  it  is  easier  to  erect  the  truss  if  the  rafter  is  notched  into 

THE  BEAM  from  iM  to  1V2  in  for  ordinary  spans  and  loads,  to  hold  it  while  the 
pieces  are  fitted.  After  this  is  done,  the  holes  may 
be  bored  exactly  where  required. 

Whenever  S  exceeds  about  10  000  lb  for  trusses 
made  of  timber  for  which  the  highest  bearing  stresses 
are  allowed,  a  cast  plate,  as  shown  in  Fig.  34  and 
made  to  fit  the  inclination  of  the  bolt,  should  be  let 

Fig.  34.  Special  Washer  into  the  tie-beam  at  the  head  of  the  bolt  to  distribute 
the  pressure.     The  diameter  of  the  hole  for  the  bolt 

should  be  Vs  in  larger  than  the  diameter  of  the  bolt.     The  distance  D  must  be 

made  sufficient  to  provide  for  the  horizontal  component  of  S,  at  the  allowed 

working  stress  of  the  material  for  shear  with  the  grain. 

The  horizontal  component  is  found  by  drawing  a  vertical  line  from  c  and  a 

horizontal  line  from  a  and  measuring  ad  to  the  scale  of  the  diagram.     For 

safety,  this  force  must  be  less  than  the  product  of  the  distance  D,  the  width  of 

the  beam  and  the  allowed  shearing-stress  given  in  Table  I,  page  41?;.^  ^^^^^^^    ,, 


Fig.  33.    Bolt  in  Tension  at  Foot  of  Rafter 


438    Resistance  to  Shear.    Riveted  Joints.     Pins  and  Bolts    Chap.  12 

Example  i6.  For  the  same  conditions  as  in  Example  15,  for  the  size  of  the 
members  and  the  thrust  in  the  rafter,  it  is  required  to  determine  the  diameter 
of  the  bolt  and  the  distance  D  for  a  joint  of  the  type  shown  in  Fig.  33. 

Solution.  To  find  S,  draw  T  equal  to  i8  000  lb,  at  a  convenient  scale,  and 
parallel  to  the  rafter.  At  a,  draw  an  indefinite  line  perpendicular  to  the  rafters 
and  at  6  a  fine  perpendicular  to  the  seat  of  the  rafter.  This  makes  .S"  greater 
than  in  Example  15,  as  ac  now  scales  27  000  lb.  From  Table  IX,  a  i%-in  steel 
bolt  is  sufficient  to  take  this  in  direct  tension.  The  horizontal  component 
found  as  directed  above,  scales  19  000  lb.  The  width  of  the  tie-beam  is  6  in, 
which  at  the  allowed  shearing-stress,  150  lb  per  sq  in,  gives  900  lb  as  the  stress 
that  must  be  cared  for  by  each  inch  oi  D.  19  000  lb  divided  by  900  gives  21  in, 
the  required  distance  D.  (See,  also,  Chapter  XXVIII,  Joints  in  Wooden 
Trusses.) 

The  compression  against  the  grain  on  the  end  of  the  cast-iron  washer  must 
also  be  investigated.  19  000  lb  divided  by  the  width,  6  in,  gives  3  166  lb  that 
must  be  resisted  per  inch  of  width  of  beam.  At  i  400  lb  per  sq  in,  as  an  allow- 
able working  stress,  this  makes  it  necessary  to  set  the  casting  2V4  in  into  the 
lower  side  of  the  beam,  which  exceeds  the  depth  usual  in  ordinary  practice. 
Some  tests  made  at  the  Massachusetts  Institute  of  Technology  on  large  trusses, 
and  reported  in  1897,  indicated  that  for  a  test  carried  to  rupture  the  stresses 
prescribed  for  usual  designs  might  safely  be  more  than  doubled.  Tests  on 
timber  under  long-continued  loading  indicate  that  rupture  finally  occurs 
for  stresses  approximating  one-half  of  those  developed  in  tests  carried  to 
immediate  failure.  This,  and  the  fact  that  decay  may  affect  the  strength  of 
the  members,  emphasizes  the  wisdom  of  using  conservative  working-stresses 
in  this  material. 


8x8' 
Cast  Washers 


Fig.  35.    Joint  with  Two  Bolts  in  Direct  Tension 


Example  17.  It  is  required  to  determine  the  size  of  bolts  for  the  joint  shown 
in  Fig.  35,  the  thrust  being  65  500  lb  and  the  truss-members  being  made  of 
long-leaf  yellow  pine. 

Solution.  The  tension  in  the  bolts  is  found  first  by  drawing  the  force-polygon 
as  shown  at  the  right  in  the  figure.  To  the  same  scale  that  ab  represents  65  500, 
ac  represents  96  500  lb.  If  the  load  is  equally  divided  between  the  bolts,  each 
has  a  tension  of  48  250  lb.  From  Table  IX  this  force  requires  a  2\i-\n  steel 
bolt. 

The  horizontal  component  ad  is  68  350  lb,  which  must  be  resisted  by  the  shear- 
ing strength  of  the  wood  between  the  end  of  the  cast-iron  washer  on  the  under 


Strength  of  Bolts  in  Wooden  Trusses  and  Girders  i39 

side  of  the  tie-beam  and  the  end  of  the  beam  resting  on  the  wall.  At  150  lb 
per  sq  in,  this  requires  68  350/150,  or  455  sq  in.  If  the  beam  is  8  in  wide,  this 
requires  a  length  of  57  in  along  the  beam  from  the  washer  to  the  end. 

The  bearing  of  the  cast-iron  washer  against  the  end-fibers  of  the  tie-beam  is 
also  68  250  lb.  At  an  allowable  pressure  of  i  400  lb  per  sq  in  the  depth  of 
the  washer  should  be  68  350/(8  X  i  400)  =  6.1  in.  This  would  almost  cut  the 
beam  in  two.  The  ultimate  strength  of  the  wood  in  compression  is  about  five 
times  the  working  stress,  and  since  a  considerable  part  of  the  horizontal  force 
may  be  resisted  by  the  body  of  the  bolt  as  well  as  by  the  friction  of  the  washer, 
it  is  probable  that  with  washers  %  in  thick  there  would  be  little  sign  of  weak- 
ness at  the  joint  even  when  the  truss  is  fully  loaded. 

Theoretically  the  washers  on  the  top  surface  of  the  rafter  should  be  deter- 
mined by  the  allowable  working  stress  in  compression  across  the  fi.bers.  This 
for  long-leaf  pine  is  taken  at  350  lb  per  sq  in  (Table  VI,  page  454).  The  area, 
then,  is  48  250/350,  or  138  sq  in.  This  requires  a  washer  11%  in  square. 
The  8  by  8-in  washer  used,  assumes  a  pressure  of  755  lb  per  sq  in,  but  as  the  tests 
of  the  Forest  Service  of  the  United  States  Department  of  Agriculture  give  3  480 
lb  per  sq  in  as  the  elastic  limit  for  long-leaf  yellow  pine,  it  is  very  likely  that 
there  would  be  no  signs  of  injury  at  this  point,  other  than  a  slight  indenta- 
tion, when  the  truss  is  fully  loaded.  ! 


440 


Bearing-Plates  and  Bases  for  Columns,  etc.       Chap.  13 


CHAPTER  XIII 

BEARING-PLATES  AND   BASES  FOR  COLUMNS,   BEAMS 

AND   GIRDERS.    BRACKETS  ON   CAST-IRON 

COLUMNS* 


By 
HERMAN   CLAUDE  BERRY 

PROFESSOR  OF  MATERIALS   OF  CONSTRUCTION,   UNIVERSITY  OF  PENNSYLVANIA 

1.   Bearing-Plates  and  Bases 

The  Purpose  of  Bearing-Plates  or  Bases.  When  a  heavily  loaded  col- 
umn, beam  or  girder  is  supported  on  a  masonry  wall  or  pier,  a  bearing-plate  or 
BASE  of  suitable  dimensions  must  be  used  to  distribute  the  load  so  that  the 
pressure  will  not  exceed  the  safe  bearing  strength  of  the  masonry  (Table  I). 


< 

UJ 
CQ 

<— p— > 

SECTION 


Fig.  1. 


Simple  Bearing- 
plate 


K n 


^ 


\ 

V 

/J 

xx      • 

•        // 

/ 

-~ 

i      ( ( 

'                  1 

/ 

n 

s, 

J. 

f 

\ 

^ 

Fig.    2.     Beveled    Cast- 
iron  Plate  with  Pin 


Fig.  3. 


PLAN 
Ribbed  Cast-iron  Plate 


The  bearing-plate  is  designed  to  be  stiff  enough  to  distribute  the  pressure 
under  it  uniformly,  and  its  area  is  determined  by  dividing  the  load  on  it  by 
the  allowable  pressure  per  unit  of  area  (Table  II). 

Simple  Bearing-Plates.  Fig.  1  shows  a  simple  bearing-plate  under  a 
beam.  It  may  be  a  steel  or  cast-iron  rectangular  plate  of  sufficient  thickness 
to  prevent  its  bending  at  the  edge  of  the  beam  from  the  pressure  of   the 

*  See,  also,  Chapter  XIV,  Subdivisions  8  to  ii. 


Bearing-Plates  and  Bases 


441 


masonry  below.  For  anchors  for  steel  beams  on  bearing-plates,  see  Chapter 
XV,  page  619. 

Cast-iron  Plates  with  Pin.  Fig.  2  is  a  cast-iron  plate  wixg  a  dowel-pin 
to  fit  inside  the  shell  of  a  cast-iron  column,  or  into  a  recess  cut  in  the  bottom 
of  a  wooden  one.    The  pin  holds  the  base-plate  in  position. 

Cast-iron  Ribbed  Bases.  Fig.  3  is  a  cast-iron  ribbed  base  for  a  large 
cylindrical  cast-iron  column,  capable  of  supporting  a  load  heavy  enough  toj 
break  a  plate  similar  to  the  one  shown  in  Fig.  2,  at  the  edges  of  the  columnj 
unless  the  plate  were  made  unduly  thick.  ' 


Table  I.    Allowable  Bearing  Pressure  on  Different  Kinds  cf^Masonry 


Kind  of  masonry 


Allowable  pressures 


Lb  per  sq 


Tons  per 
sq  ft 


From  the  building  laws  of  New  York,  19 17 


Brick,  in  lime  mortar , 

in  lime-and-cement  mortar 

in  Portland-cement  mortar 

Rubble  masonry,  in  Portland-cement  mortar. . 

Concrete,  Portland  cement,  1:2:4 


no 
160 
250 
140 

500 


11^ 
18 
10 
36 


From  the  building  laws  of  Chicago,  191 6 


Rubble,  in  lime  mortar 

in  Portland-cement  mortar 

Coursed  rubble,  in  lime  mortar 

in  Portland-cement  mortar 

Ashlar,  limestone,  in  Portland-cement  mortar 

granite,  in  Portland-cement  mortar. 

Concrete,  Portland-cement,  1:2:4,  hand-mixed . . . . 

machine-mixed . 


60 
100 
120 
200 
400 
600 
350 
400 


4-32 
7-2 
8.6 
14.4 
28.8 
43.2 
25-4 
28.8 


The  Bases  of  the  Steel  Cores  of  Composite  Columns  used  in  reinforced- 
concrete  construction  have  areas  sufficient  to  distribute  the  loads  of  the  columns 
over  the  concrete  in  the  foofings  at  the  allowable  working  stress  of  the  concrete. 
(See,  also,  page  474,  Figs.  14  and  15.) 

Example  i.  The  basement-columns  of  a  warehouse  are  designed  for  a  load 
of  212  000  lb  each.  It  is  required  to  determine  the  size  of  the  base-plates  to 
rest  on  the  concrete  foundations.     (Table  II  used.) 

Solution.  At  an  allowable  pressure  of  208  lb  per  sq  in,  the  required  area  is 
212  006/208  or  I  020  sq  in,  or  about  32^2  in  square.  The  plan  and  section  of 
the  base-plate  is  shown  in  Fig.  3. 

Forms  of  Base-Plates.  For  small  columns  and  wooden  posts  with  light 
loads,  plain  flat  plates  of  cast  iron  or  steel  are  generally  used.  The  cast-iron 
plates  may  have  a  raised  ring  or  cross  to  fit  inside  a  hollow  metal  column,  or 
a  dowel,  from  i>2  to  2  in  in  height  for  a  wooden  one.  If  the  plate  is  very  thick 
the  outer  edges  may  be  beveled  to  save  weight,  as  shown  in  Fig.  2,  but  no  part 
of  it  should  be  less  than  about  %  in  thick.  \ 


442  Bearing- Plates  and  Bases  for  Columns,  etc.       Chap.  13 

Table  n.     Allowable  Loads  on  Standard,  Steel  Bearing-Plates  on  Walls 


Bearing  on 
wall, 
in 

Safe  bearing  value  of  plate  in  pounds 

Size  of  plate, 
in 

Bricks  laid  in  mortar  of 

Lime,  112* 
lb  per  sq  in 

Lime  and 
cement,  162* 
lb  per  sq  in 

Cement,  208* 
lb  per  sq  in 

6 

6X  6 
6X  8 

4070 
5400 

5  800 

7800 

7500 
10  000 

8 

6Xio 
8X  8 

6  700 

7  200 
9  000 

10700   • 

II  200 

9700 

10200 
I?,  vx> 
15500 

16  200 

12500 

13300 
16  600 
20000 

20  800 

10 

8XIO 
8X12 

loXio 

12 

14 

I0XI2 

10X14 

13450 
15700 

19500 
22  700 

25  200 
27900 

I2XI2 

12X14 
12X16 
12x18 

14X14 

16  150 
18800 
22  000 
24  200 

22  TOO 

f-.,  25  000 
28  200 

23300 
27  400 
31  200 
34500 

31  800 
36300 
40  800 

30000 
35000 
40  100 

45  000 

40800 

46  600 
52  400 

i6 

14X16 
14X18  ' 

14X20 

16x16 
16x18 
16x20 
16x22 

31  400 
28  700 

32300 
35800 
39500 

45400 

41500 
46  600 

SI  900 
57000 

58  200 

53200 
59800 
66  700 
73200 

♦  These  valu 

es  are  slightly 

difi 

erent  from  those 

Df  the  New  York 

Code  (1916). 

Ribbed  Bases.  If  the  calculated  size  of  a  bearing-plate  is  so  large  that  its 
projection  beyond  the  edge  of  the  column  would  be  more  than  about  6  in,  a 
RIBBED  BASE  similar  to  that  shown  (Fig.  3)  for  a  cylindrical  column  is  used. 
For  such  bases  it  is  unnecessary  to  consider  the  transverse  stresses.  When 
these  bases  are  bolted  to  the  columns  they  add  greatly  to  the  general  stability 
of  the  supporting  members  because  of  the  greater  width  of  such  bases. 

Proportions  of  Ribbed  Bases.  The  height  H  of  this  type  of  base  should 
be  approximately  equal  to  the  projection  P,  and  the  diameter  D  equal  to 
the  diameter  of  the  column.  The  projection  C  should  be  at  least  3  in  to  permit 
the  bolting  of  the  column  to  the  base.  The  thickness  of  all  parts  of  the  casting 
should  be  the  same  and  approximately  equal  to  the  thickness  of  the  column- 
shell.  There  must  be  no  thin  webs  as  they  result  in  breakage  from  shrinkage- 
stresses. 

Base-Plates  for  Steel  Columns  are  usually  made  of  steel  plates  and  shapes 
as  shown  on  the  channel-columns  in  Chapter  XIV,  Figs.  17,  18  and  19.  Cast- 
iron  bases  are  sometimes  used  for  very  heavy  columns.  If  conditions  are 
favorable  to  the  action  of  corrosion  the  cast  iron  is  to  be  preferred.     ' 


Bearing-Plates  and  Bases 


448 


The  Area  of  Bearing-Plates  under  Beams  and  Girders  is  found  in  the 
same  manner  as  the  area  of  plates  under  columns.  If  the  load  on  the  beam  is 
uniformly  distributed  over  the  beam  or  concentrated  at  its  middle,  the  required 
area  of  the  plate  is  one-half  the  total  load  on  the  beam  divided  by  the  allowable 
bearing  per  unit  of  area  on  the  masonry;  but  if  the  load  is  a  moving  load,  the 
greatest  possible  end-reaction  must  be  divided  by  the  allowable  bearing.  For 
example,  a  heavily  loaded  truck  standing  near  the  end  of  the  beam  causes  a 
pressure  on  the  bearing-plate  much  greater  than  one-half  its  weight.  The 
true  reaction  for  the  actual  conditions  must  be  found  by  the  methods  explained 
in  Chapter  IX. 

The  Thickness  of  the  Bearing-Plate  is  found  by  the  formula  used  to 
determine  the  flexure  of  beams.  It  must  be  determined  in  each  case.  For  a 
typical  case  the  forces  acting  are  shown  in  Fig.  5,  which  represents  a  transverse 


rt 


M 


t< — b — >|        \< 1 H 

[  Fig.  4.     Simple  Bearing-plate  under  I'Beara 


ciifffflmT 


Fig.    5.     Forces    Acting 
on  Half  of  Bearing-plate 


vertical  section  through  one-half  the  plate.  The  vertical  section  at  C,  and 
through  and  parallel  with  the  web  of  the  I  beam,  is  taken  through  the  center  of 
the  plate,  which  is  the  dangerous  section,  or  section  of  maximum  bending  mo- 
ment. 

In  Figs.  4  and  5,  b'  is  the  bearing  depth  on  the  wall; 

/  is  the  length  of  the  plate,  parallel  with  the  wall; 

b  is  the  width  of  the  flange  of  the  beam; 

R  is  the  load  on  the  bearing-plate. 

Replacing  the  uniform-  loads  by  the  equivalent  forces  at  the  center  of  gravity 
of  each,  these  forces  are  represented  by  the  longer  arrows.  The  bending  mo- 
ment at  the  section  at  c  is  the  same  as  the  moment  of  the  concentrated  forces, 
giving, 

M={R/2Xl/4)-{R/2Xb/4) 
or  M=R/2X{l-b)U 

This  is  equal  to  the  resisting  moment  at  the  same  section  c,  or,  at  stress  5", 
Sl/c,  in  which  l/c  is  the  section-factor.  (See  Chapter  XV.)  This  reduces  to 
Sf^b  /6.     Equating  the  bending  moment  and  the  resisting  moment  there  results 

St''b'/6  =  Ril-b)/S 


and  t=  O.S66  Vr  {I -b)/Sb' 

For  5=3  GOO  for  cast  iron,  tliis  reduces  to 


t  =  o.oiBSVR{l-b)/b' 
For  5  =  i6  GOO  for  steel  plates,  it  becomes 

t  =  b.oo68s  Vr  (/  -  b)/b' 


(i) 


(a) 


444  Bearing-Plates  and  Bases  for  Columns,  etc.       Chap.  13 

Example  2.  It  is  required  to  determine  the  length  and  thickness  of  a  cast- 
iron  bearing-plate  linder  a  wooden  beam  which  is  10  in  wide  and  supports  a 
load  of  24  ocK>  lb.  The  plate  is  8  in  wide  and  bears  that  width  on  a  brick  wall 
laid  up  in  lime  mortar. 

Solution.  The  load  on  the  plate  is  24  000/2  =12  000  lb.  From  Table  II, 
the  area  of  the  plate  is  12  000/112  =  108  sq  in.  Hence,  if  the  width  of  the 
plate  is  8  in,  its  length  must  be  13 V2  in.    Then,  from  Formula  (i) 

/  =  0.0158  V  12  000  (13%  —  io)/8  =  1. 15  in 
A  plate  iVi  in  thick  would  be  used. 

Example  3.  It  is  required  to  determine  the  length  and  thickness  of  a  steel 
bearing-plate  under  the  end  of  a  24-in  8o-lb  I  beam  supported  on  a  12-in  brick 
wall  laid  up  in  lime-and-cement  mortar  and  carrying  a  load  of  60  000  lb.  The 
width  of  the  flange  of  the  beam  is  7  in.     (See  Table  I.) 

Solution.     The  load  on  the  plate  is  60  000/2  =  30  000  lb 

The  area  of  the  plate  =  30  000/160  =  iSjH  sq  in 
The  length  of  the  plate  is  187. 5/1 2  =  15.6  in 

Then,  from  Formula  (2) 

/  =  0.00685  "^30  000  (15,5  —  7)/i2  =  I  in 

Standard  Sizes  of  Steel,  Wall  Bearing-Plates.    These  are  given  in  Table 

II,  and  are  based  upon  ALLOWABLE  pressures  of  112,  162  and  208  lb  per  sq  in. 

These  unit  pressures  are  based  upon  the  allowable  pressures  of  the  New 
York  and  Philadelphia  building  laws  which  are  ex- 
pressed in  tons  per  square  foot.  Because  of  the 
complicated  formula  on  which  the  thickness  depends 
it  is  best  to  compute  the  thickness  for  each  case. 

Bearing-Plates  under  Columns.  The  general 
rules  already  given  j^for  the  proportions  of  ribbed 
bases  similar  to  that  shown  in  Fig.  3  are  a  sufficient 
guide  for  detailing  such  bases;  but  in  case  simple 
FLAT  PLATES  are  used  under  columns,  their  thickness 
must  be  computed  according  to  the  principles  govern- 
ing bending.     The  stress  in  a  flat  plate  supported 

Fig.  6.     Flat  Bearing-plate    at  the  middle  and  subjected  to  a  uniform  load  cannot 

for  Column  be  determined  by  the  ordinary  methods  of  mechanics. 

The   approximate   solution   here  given  is  generally 

used  in  the   design  of  base-plates  and  column-footings.     It  gives  values 

found  to  be  safe  in  practice. 

In  Fig.  6,  let  B  =  the  length  of  the  side  of  the  plate  as  determined  by  tht 
allowable  pressure  on  the  supporting  masonry; 
D  =  the  side  or  diameter  of  the  column; 
P  =  {B  —  D)l 2  =  the  projection  of  the  plate; 
/  =  the  thickness  of  the  plate; 
A'  =  the  area  of  the  plate  outside  the  column; 
w  =  the  allowable  bearing  pressure  on  the  masonry  due  to  the 
load  on  the  column. 

Then  in  Fig.  6,  the  pressure  on  one-fourth  of  A',  shown  enclosed  by  the  dotted 
lines  in  the  figure,  causes  shearing  and  bending  stresses  in  the  section  of  the 
plate  along  the  line  ab.  Considering  the  part  enclosed  and  taking  moments 
|^|x)Ut  the  section  ab,  the  following  equation  is  obtained  from  the  usual  bend- 


g/ilbn^  0 

7 

/ 

a 
b 

\ 

Bearing-Brackets  on  Cast-iron  Columns  445 

ing-moment  formula.     (See  Chapter  XV,  page  557.)     That  is,   the  resisting 
moment  equals  the  bending  moment,  or 

t  Sl/c^MA'Pw 

For  the  rectangular  section  at  ah,  this  may  be  written 

StW/^^VWPw 
whence  /  =  V^ATw/VsD 

which  becomes  for  5  =  3  000 

t  =  0.022^  V A' Pw/D 
and  for  5  =  16  000 

/  =  0.0097  VA'Piv/D 

Example  4,  It  is  required  to  determine  the  size  and  thickness  of  a  cast-iron 
bearing-plate  to  be  used  under  a  wooden  post  12  in  square  in  cross-section  and 
designed  for  a  load  of  115  200  lb.  The  plate  is  to  be  set  on  brickwork  laid  in 
cement  mortar  in  New  York.     (See  Table  I.) 

Solution.     The  required  area  of  the  base  is  115  200/250  =  461  sq  in.     V^46i 
=  21.47  and  a  22-in.  square  plate  would  be  used. 
Then  A'  =  461  —  144  =  317  sq  in 

P  =  (22  —  i2)/2  =  5  in 
D  =  12  in 
w  =  250  lb  per  sq  in  j^ 

Hence  /  =  0.0224  V317  X  5  X  250/12  =^  4  iii     ' 

This  thickness  may  be  beveled  to  i  K  in  at  the  edge.  The  computed  thickness 
is  greater  than  is  usual  for  such  plates,  some  formulas  having  more  practical 
constants  which  really  assume  a  stress  of  about  10  000  lb  per  sq  in  in  cast  iron 
in  bending. 

If  the  plate  is  made  of  steel 


/  =  o.oo97\/3i7  X  5  X  250/12  =  i^  in 

2.   Bearing-Brackets  on  Cast-iron  Columns 

The  Usual  Column-Connections  for  fastening  beams  and  girders  to  cast- 
iron  columns  are  shown  in  Fig.  7.*  The  end  of  the  beam  or  girder  is  set  on 
a  SHELF  P,  under  which  is  a  bracket-support  C,  cast  on  the  side  of  the  column. 
For  a  single  beam,  one  bracket  is  sufficient;  for  wide  beams  or  girders  there 
should  be  two  ribs.  The  ends  of  the  beams  are  fastened  to  the  column  by 
bolting  to  LUGS  L,  cast  on  the  column  above  the  bracket.  Sometimes  a  column 
is  fastened  by  bolts  passing  through  the  bottom  flange^of  the  beam  and  through 
the  shelf-plate.  This  connection  greatly  decreases  the  lateral  stabihty  of  a 
building  and  should  not  be  used. 

The  Shelf  and  Brackets,  when  loaded,  are  subject  to  shearing  and  bend- 
ING-STRESSES.  The  SHEAR  at  thc  outer  surface  of  the  column-shell  is  equal 
to  the  end-reaction  of  the  beam  it  supports.  The  bending-stress  is  due  to  the 
application  of  the  load  on  the  shelf-plate  at  some  distance  from  the  surface  of 
the  column.  It  causes  a  tension  at  the  top  of  the  bracket  which  tends  to  tear 
out  the  shell  of  the  column,  and  causes,  also,  a  compression  at  the  foot  of  the 
rib.  The  thickness  of  the  rib  must  be  great  enough  to  withstand  the  com- 
pression from  the  load  above;    and  since  the  stress  is  variable  along  a  section^ 

*  See  also,  Figs.  5  and  7,  pages  457  and  458.  --^^ 


446 


Bearing-Plates  and  Bases  for  Columns,  etc.       Chap.  13 


as  along  the  line  X,  a  rough  approximation  may  be  made  by  assuming  the 
stress  at  the  extreme  edge  to  be  twice  the  average  stress,  and  by  further  assum- 
ing that  the  section  in  the  rib  takes  care  of  all  the  compression.  This  maj^es  it 
unnecessary  to  find  the  center  of  gravity  and  the  moment  of  inertia  of  the 
section  at  X,  both  of  which  must  be  known  if  the  flexure-formula  is  used. 
This  procedure,  also,  makes  unnecessary  any  assumption  as  to  the  true  position 
of  the  center  of  pressure  on  the  top  surface  of  the  bracket.  With  the  thick- 
ness of  rib  given  in  the  tables  there  is  an  ample  factor  of  safety  for  any  load 


Fig.  7.  •  Cast-iron  Columns  with  Bearing-brackets 

that  may  be  applied  through  a  beam.  The  double  ribs  are  required  when  wide 
beams  are  used,  not  for  strength,  but  to  prevent  the  failure  of  the  shelf  from 
eccentric  loading. 

Tests  of  Cast-iron  Brackets.  Brackets  of  cast-iron  columns  tested  by  the 
New  York  Building  Department  gave  a  shearing  strength  of  4  200  lb  per 
sq  in  on  the  section  at  the  column  when  the  load  was  applied  at  the  end  of  the 
bracket,  and  an  average  of  8  000  lb  per  sq  in  when  the  load  was  distributed  over 
the  bracket-shelf.  The  range  of  stress  in  the  first  case  was  from  2  450  to 
5  600  and  in  the  second  from  4  100  to  10  906  lb  per  sq  in.  In  seventeen  out  of 
twenty-two  tests  the  manner  of  failure  was  the  tearing  out  of  a  hole  in  the 
body  of  the  column.  It  appears  that  when  the  thickness  of  the  rib  and  shelf 
is  the  same  as  that  of  the  shell  of  the  column,  there  is  generally  ample  strength 
for  the  support  of  beams  and  girders;  but  that  in  the  case  of  very  heavily 
loaded  beams,  the  shearing  and  crushing  strength  should  be  investigated. 
From  the  results  of  the  tests  mentioned,  a  low  working  stress  for  shear 
must  be  assumed. 

The  Bevel  of  Brackets.  If  the  shelf  P  (Fig.  7),  on  which  the  beam  rests, 
16  cast  square  with  the  column,  when  the  beam  deflects,  the  load  is  brought  on. 
the  extreme  end  of  the  bracket,  causing  an  increased  bending-stress  in  the 


Beadng-Brackets  on  Cast-Iron  Columns 


447 


bracket  and  connections  and  tending  to  tear  a  hole  In  the  column-shell.  To 
avoid  this  the  bracket-shelf  should  be  sloped  downward,  away  from  the  column, 
and  should  have  a  bevel  of  Vh  in  to  the  foot. 

Standard  Connections  for  Cast-iron  Columns.  Table  III,  published 
originally  in  the  Bassiac  Rolling  Mill  Handbook,  and  widely  used  by  other 
manufacturers,  will  be  found  useful  when  detailing  cast-iron  columns. 


Table  IH.     Standard  Connections  for  Cast-iron  Columns 

All  dimensions  are  in  inches 


Depth 

Thick- 

of 

A 

B 

C 

D 

E 

F 

G 

// 

K 

ness  of 

beam 

2 

1 1/2 

2 

lugs 
I 

20 

5 

5 

6 

10^/^ 

1V2 

lV2 

18 

4 

■; 

6 

loi/i. 

1V2 

1^2 

2 

1V2 

2 

I 

IS 

4 

.V/2 

.SV2 

qVa 

1V2 

iVi 

2 

1V2 

1% 

I 

12 

3 

3 

4y2 

7% 

■  1V4 

IM 

2 

iVa 

1V2 

I 

Holes 

cored 

for 

%-in 
bolts 


\h'd  9dT 
!  fM:df  r»-jt> 


Depth 

Thick- 

of 

A 

B 

C 

D 

E 

F 

^ 

H 

K 

ness  of ' 

beam 

lugs 

10 

3V4 

^V2 

4 

7 

1V4. 

I 

2 

1I/2 

1V2 

I 

9 

3 

3 

4 

7 

I 

I 

2 

1V2 

1V2 

I 

8 

2y2 

3 

4 

7 

I 

I 

2 

1V2 

1V2 

% 

7 

2V4 

2H' 

4 

7 

I 

I 

2 

i^l> 

iH 

8/4 

■ 

Holes 
cored 
for 
%-in 
bolts 


448  Strength  of  Columns,  Posts  and  Struts  Chap.  14 

CHAPTER  XIV 
STRENGTH  OF  COLUMNS,  POSTS  AND  STRUTS 

By 
CHARLES  P.  WARREN 

LATE   ASSISTANT  PROFESSOR  OF  ARCHITECTURE,   COLUMBIA   UNIVERSITY 

1.   General  Principles  and  Definitions 

Slenderness-Ratio.  The  manner  in  which  a  material  fails  under  compression* 
or  pressure  depends  not  only  upon  its  nature,  but  also  upon  its  dimensions  and 
form,  that  is,  upon  the  ratio  of  its  length  to  its  cross-section  or  diameter.  This 
ratio  is  denoted  by  Ijr  and  is  known  as  the  slenderness-ratio. 
I  Three  Classes  of  Columns.  The  actual  compressive  strength  of  a  material 
tnust  be  determined  on  very  short  specimens  in  which  there  is  no  tendency  to 
bend  or  to  buckle.  The  load  required  to  break  the  specimen  does  not  change 
much  until  the  length  is  increased  to  about  ten  times  the  diameter  or 
LEAST  LATERAL  DIMENSION.  When  that  ratio  is  exceeded,  the  specimen  tends 
to  fail  by  bending  or  by  buckling  instead  of  by  direct  compression.  According 
to  their  manner  of  failure,  therefore,  columns  in  general  may  be  divided  into 
three  classes: 

'■  (i)  Short  Columns,  in  which  the  slenderness-ratio  does  not  exceed  lo 
iand  which  fail  by  direct  compression. 

I  (2)  Columns  in  which  the  slenderness-ratio  varies  from  10  to  30  for  timber 
and  cast  iron  and  from  10  to  90  for  steel.  The  failure  of  columns  of  this  class 
is  due  partly  to  direct  compression  and  partly  to  bending. 

(3)  Long  Columns,  in  which  the  slenderness-ratio  exceeds  30  for  timber  and 
cast  iron  and  90  for  steel.  These  columns  fail  wholly  by  bending  or  buckling, 
which  causes  flexural  stresses  of  compression  and  tension  on  the  concave  and 
convex  sides  respectively.   . 

2.   Strength  of  Short  Wooden  Columns 

The  Safe  Load  for  a  Short  Wooden  Column,  the  length  of  which  is  not 
more  than  10  times  the  least  dimension,  may  be  computed  by  the  formula 

_  ,    ,      ,      area  of  cross-section  X  5  ,  . 

Safe  load  = '—, — (i) 

factor  of  safety 

;in  which  5  denotes  the  crushing  strength  of  the  given  material  as  stated  in 

!  Table  I. 

;  I    The  Factor  of  Safety  to  be  selected  depends  upon  the  place  where  the  col- 

!  umn  is  used,  the  load  which  comes  upon  it,  the  quality  of  the  material  and,  in  a 
large  measure,  upon  the  value  given  to  S.  For  lumber  of  ordinary  quality,  con- 
taining no  very  bad  knots,  a  factor  of  safety  of  five  may  be  used;  or,  in  other 
words,  the  safe  stress  per  square  inch  of  section-area  may  be  taken  as  one-fifth 
of  the  values  given  in  Table  I.  If  the  column  is  badly  season-checked,  cross- 
grained,  or  contains  bad  knots,  a  larger  factor,  say  six  or  seven,  should  be  used. 
The  character  of  the  load,  also,  should  be  taken  into  consideration  in  determining 
the  factor  of  safety.  Thus  for  a  wooden  post  supporting  a  brick  wall  a  larger 
factor  should  be  used  than  for  one  supporting  a  floor,  as  in  the  former  case  the 
full  lo?d  is  at  all  times  on  the  post,  and  the  least  reduction  of  its  section-area  in 


Strength  of  Wooden  Columns  or  Struts 


449 


case  of  fire  might  cause  it  to  give  way.  Wooden  posts  supporting  machinery,  or 
wooden  struts  in  railway  bridges,  should  have  a  factor  of  safety  of  from  six  to 
eight,  if  the  values  of  S  given  in  Table  I  are  used. 


Table  I.* 


Average  Crushing-Loads  in  Pounds  per  Square  Inch,  for  Build- 
ing Materials 


Materials 


For  stone,  brick,  concrete 
and  masonry,  see  Chap- 
ter V 

Metals 

Cast  iron 

Wrought  iron 

Steel,  rolled  shapes 


Woods,  with  the  grainf 

Cedar 

Chestnut 


Crushing- 
loads, 
lb  per  sq 


80  000 
55  000 
60  000 


3500 

4  000 


Materials 


Woods  (continued) 

Cypress 

Hemlock 

Oak,  white 

Pine,  long-leaf  yellow. . . 
Pine,  short-leaf  yellow, . 

Douglas  fir 

Pine,  Norway 

Pine,  white 

Redwood,  California. . . 

Spruce 

Whitewood 


Crushing- 
loads, 
lb  per  sq 


3500 
4  000 
Sooo 
Sooo 
4000 
4500 
3500 
4  000 
4  000 
4500 
3000 


.b 


*  See,  also.  Table  XVI,  pap;e  647,  and  Table  I,  page  1138. 

t  These  are  values  for  wooden  columns  under  15  diameters  in  height  and  are,  of 
course,  average  values.  For  the  safe  loads,  per  sq  in,  on  timbers,  perpendicular  to 
the  grain,  see  Table  VI. 

Example  i.  What  is  the  safe  load  for  a  long-leaf  yellow-pine  column,  10  by  icv- 
in  in  cross-section  and  12  ft  long,  using  a  factor  of  safety  of  5? 

Solution.     Area  of  cross-section  =  100  sq  in;  safe  load  per  sq  in  =5  000/5 
I  000  X  100  =  100  000  lb.  p 

Example  2.  It  is  required  to  support  a  brick  wall  weighing  80000  lb  by  a 
Douglas-fir  column  1 1  f t  long.     What  should  be  the  cross-section  of  the  column? 

Solution.  As  previously  stated,  for  these  conditions  it  would  be  wise  to  use  a 
factor  of  safety  of  6.  Then  the  safe  resistance  per  square  inch  of  section-area  = 
4  500/6  =  750;  80000/750  =106  sq  in  required,  about  equivalent  to  a  10  by 
lo-in  cross-section. 


3.    Strength  of  Wooden  Columns  or  Struts  Over  Ten  Diameters     j 
in  Length.     Formulas 

Formulas  for  Wooden  Columns.  When  the  length  of  a  column  exceeds 
about  ten  times  its  least  cross-dimension  it  is  liable  to  bend  under  the  load,  and 
hence  to  break  under  a  less  load  than  would  break  it  if  it  were  shorter  and  of 
the  same  cross-section.  To  deduce  a  formula  which  will  make  the  proper  allow- 
ance for  the  length  of  a  column  has  been  the  aim  of  many  engineers,  but  their 
formulas  have  not  always  been  exactly  verified  by  actual  results. 

Until  recently  the  formulas  of  Lewis  Gordon  and  C.  Shaler  Smith  have  been 
used  generally  by  engineers,  but  the  extensive  series  of  tests  made  by  the  Govern- 
ment testing-machine  at  Watertown,  Mass.,  on  full-sized  columns,  showed  that 
these  formulas  did  not  agree  with  the  results  there  obtained.  James  H.  Stan- 
wood  in  the  year  1891  plotted  the  values  of  all  the  tests  made  at  the  Watertown 
Arsenal  up  to  that  time  on  full-size  columns.     From  the  results  thus  obtained 


450  Strength  of  Columns,  Posts  and  Struts  Chap.  14 

he  deduced  the  following  straight-line  formula  for  long-leaf  yellow-pine  and 

white-oak  columns: 

^  ,    ,      ,  .     ,  length  in  inches  ,  ^ 

Safe  load  per  square  inch  =  i  coo  —  lo  X  ,— — rT~' — • — ^ —  (2) 

breadth  in  inches 

The  author  has  carefully  compared  this  formula  with  the  results  of  actual 
tests,  and  with  other  formulas,*  and  believes  that  for  timber  without  serious 
defects  and  with  not  more  than  10  or  12%  of  moisture,  it  meets  the  actual  con- 
ditions as  nearly  as  any  other  formula.  He  has  therefore  prepared  Tables  II 
HI,  IV  and  V  for  the  strength  of  round  and  square  columns  of  the  sizes  generally 
iised  in  practice.  Of  course  other  formulas  must  be  used  when  required  by  cer- 
tain city  building  laws.  For  other  sizes  the  loads  can  easily  be  computed  by 
the  formulas.  For  columns  having  bad  knots  or  other  defects,  or  more  than 
io  or  12%  of  moisture,  or  which  are  to  be  exposed  to  the  weather  or  known  to 
be  eccentrically  loaded,  a  deduction  of  from  10  to  25%  should  be  made  from  the 
values  given  in  the  tables. 

The  loads  for  columns  of  other  species  of  wood  were  computed  by  the  following 

formulas  of  the  same  form  as  that  of  Formula  (2) : 

For  Douglas  fir  and  spruce, 

^  -   ,      ,  .     ,       „  „  length  in  inches  ,  . 

Safe  load  per  square  inch  =  850  —  8.5  X  , r-z—. — : — - — •  (3) 

breadth  in  inches 

For  chestnut,  hemlock,  short-leaf  yellow  pine  and  white  pine, 

^  .    .      .  .     .  length  in  inches  ,  . 

Safe  load  per  square  inch  =  75°  —  7-5  X  , rT~' — ; — \ —  (4) 

breadth  in  inches 

For  cedar,  cypress,  redwood,  Norway  pine  and  whitewood, 

„  ,   .      .  .     ,       ^  ^       length  in  inches  ,  . 

Safe  load  per  square  inch  =  625  —  6  X  : 1,^-. — : — ; — •  (5) 

breadth  in  inches 

In  these  formulas  the  breadth  is  the  least  side  of  a  rectangular  column,  or  the 
diameter  of  a  round  column.  The  round  columns  were  computed  for  the  half- 
inch,  to  allow  for  being  turned  out  of  a  square  column,  of  the  next  size  larger. 
The  formulas  were  used  only  for  columns  with  a  diameter  or  least  side  exceed- 
ing 12  diameters  for  yellow  pine  and  white  oak,  and  exceeding  10  diameters 
for  other  woods. 

4.   Tables  of  Safe  Loads  for  Wooden  Columns 
Tables  II,  III,  IV  and  V  give  the  safe  loads  in  pounds  for  round  and  square 
wooden  columns  of  different  cross-sections  and  lengths  and  of  different  kinds  of 
wood.     They  were  computed  from  formulas  as  explained  above  and  are  for 
favorable  conditions  of  material,  seasoning  and  position  in  buildings. 

*  There  are  many  formulas  for  the  safe  loads  per  square  inch  of  cross-section  of  wooden 
columns.     Among  those  frequently  used  are  the  following: 
American  Railway  Engineering  and  Maintenance  of  Way  Association, 

F/A  ^S{i-l/6od) 
Department  of  Agriculture, 

P/A  =  5  (700  -f  15  l/d)/{7oo  +  IS  l/d  +  lydn 
Winslow  Formula  (Chicago  Law), 

P/A  =5(i-//8od) 
In  these  formulas,  P  is  the  safe  load  in  pounds,  A  the  area  of  the  cross-section  in  square 
inches,  P/A  the  safe  load  in  pounds  per  square  inch,  S  the  safe  end-bearing  compression 
per  square  inch,  /  the  length  in  inches  and  d  the  least  side  or  diameter  in  inches.  These 
formulas  give  smaller  safe  loads  than  those  of  Tables  II,  III,  IV  and  V;  but  as  the  loads 
of  these  tables  are  to  be  decreased  for  unfavorable  conditions  and  the  loads  determined 
from  the  three  formulas  mentioned  increased  for  favorable  conditions,  the  results  are 
about  the  same. 


Tables  of  Safe  Loads  for  Wooden  Columns 


451 


Table  II.     Safe  Loads  in  Pounds  for  Long-Leaf  Yellow-Pine  and  White- 
Oak  Columns,  Round  and  Square 


Size  of  column 
in  inches 


4X6 

sVi  round. 

6X6 

6X8 

6XiO 

yH  round . 

8X3 

8X10 

8Xl2 

93^^  round , 

loXlo 

I0Xl2 

ioXl4 

iij-i  round 

I2XI2 

12X14 

12X16 

14X14 

16X16 

18X18 

20X20 


Length  of  column  in  feet 


18  200 
19590 
30  200 
40300 
50400 
38  540 
64  000 
80  000 
96  000 
7090© 
100  000 
120  000 
140  000 
103900 
144  000 
168  000 
192  000 
196  000 
256  000 
324  000 
400  000 


16  80Q 
18760 
28800 
38  400 
48  000 
37  130 
54  400 
68  000 
8 1  600 
61  970 
100  000 
120  000 
140  000 
103  900 
144  000 
168  000 
192  000 
196  000 
256  000 
324  000 
400  000 


15  360 
17550 
27  400 
36  500 
45  600 
35  710 
52  500 
65  600 
78  700 
60  190 
85  600 
102  700 
119  800 
90  912 
144  000 
168  000 
192  000 j 
196  000  j 
256  000 
324  000; 
400  000 1 


16  500 
25  900 
34600 
43200 
34300 
50  600 

63  200 
76  800 
58350 
83  200 

99  800 
116  500 

88730 
123  800 
144500 
[I65  100 
j  196  000 
256  000 
324  000 
400  000 


I 


25  200 
33600 
42  000 
33590 
49  600 
62  000 
74400 
57429 
82  000 
98  400 
114  800 
87  690 
122  400 
142  800 
163  200 
170  900 
229  100 
324  000 
400  000 


16 


24  500 

32  600 

40  800 

32890 

48  600 

60  800 

73000 

56580 

80800 

97  000 
113  100 

86550 
121  000 
141  iooii37 
161  300: 157 
169  100 1 165 
225  300J221 
289  400  285 
400  000  356 


109440  , 
127  680 
145  920  . 


115  5 

1344 

153  t         ._  , 

162  400  155  800 

217  f 

2808 

352  c 


J  600 
)8oo 
2  000 


209900 
272  i6o 
342400 


Table  HI.     Safe  Loads  in  Pounds  for  Douglas-Fir  and  Spruce  Columns, 
Round  and  Square 


Size  of  column 
in  inches 


4X6 

SVz  round. . 

6X6 

6X8 

6X10 

7>^  round , . 

8X8 

8X10 

8X12 

gVi  round.  . 

10X10 

10X12 

10X14 

II H  round. 

12X12 

12X14 

i2Xi6 

14X14 

i4Xi6 

16X16 


Length  of  column  in  feet 


15500 
16  650 
25704 
34272 
42  840 
32740 
47870 
59840 
71808 
54150 
85  000 
102  000 
119  000 
88290 
122  400 
142  800 
163  200 
166  600 
190400 
217  600 


14  280 

15790 
24  480 
32  640 
40  800 
31540 
46  240 
57800 
69360 
52650 
74800 
89  760 
104  700 
79  100 
no  160 
128  520 
146  880 
166  600 
190  400 
217  600 


13050 
14  900 
23  256 
31  008 
37760 
30340 
44  600 
55  760 
66  910 
51  150 
72  760 
87300 
loi  860 
77  250 
107  700 
125  660 
143  600 
149  450 
170  800 
217  600 


14030 
22  032 
29376 
36  720 
29  140 
42970 
53720 
64  460 
49580 
70  720 
84860 
99  000 
75400 
105  260 
122  800 
140  350 
146  600 
167  500 
194700 


21  420 
28560 
35700 
28540 
42  160 
52  700 

63  240 
48820 

69  700 
83  640 
97580 
74470 

104  040  j 

121  38O1 

138  7;?o, 
145  i8o| 
165  900; 
193  000 


20808 
27744 
34'68o 
27940 
41  340 
51680 
62  000 
48  070 
68680 
82  400 
96  150 
73  550 
102  800 
119  950 
137  080 
143  760 
164300 
191  400 


26  740 
39710 
49  640 
59560 
46570 
66  640 
80  000 
93300 
71  700 
loo  360 
117  100 
133800 
140900 
161  000 
188200 


64  600 
77500 
90  400 
69850 
97  920 
114  240 
130  560 
138  ( 
157  800 
184900 


66  160  , 

93  000 ; 

108  S20 

124030  i 
132  400 

IS  I  3Q0 

178  400 


452 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


Table  IV.     Safe  Loads  in  Pounds  for  Chestnut,  Hemlock,  Short-Leaf 
Yellow-Pine  and  White-Pine  Columns,  Round  and  Square 


Size  of  column 
in  inches 


4X6 

5'/^  round 

6X6 

6X8 

6Xio 

jH  round 

8X8 

8Xio 

8Xi2 

9^^  round 

loXio 

10X12  

10X14 

II H  round. . . 

12X12 

12X14 

12X16 

14X14 

16X16 

18X18 

20X20 


Length  of  column  in  feet 


12  600 
13900 
21  600 
28800 
36  000 
27850 
40  768 
50960 
61  152 
46  440 
66  000 
79  200 
92  400 
69  820 
108  000 
000!  126  000 
000  144  000 

000  147  003 
000 ' 192  ODD 
000  j  243  000 
0001300  000 


II  520 
13  160 

20  520 
27360 

34  200 
26780 
39360 
49  200 
59  040 
45  160 
64  200 
77040 
89880 
68  160 
95040 
no  8oo 
126  700 
147  000 
192  000 
243  000 
300  000 


12370 
19440 
25  920 
32  400 
25  720 
37880 
47  360 
56830 
43740 
62  400 
74880 
87  360 
66  490 
92880 
loS  300 
123  800 
129  300 

192  000] 

243  000 
[300  000 


16 


18  900 
25  200 
31  500 
25  190 
37  120; 
46  400 
55  68o| 
43  100 
61  500- 
73  800' 

86  100; 

65  770: 
91  700' 
107  000 
122  300 
128  100 
170  500 
243  000 
300  000 


18360 
24  480 
30  600 
24  660 
36480 
44  600 
54720 
42  400 
60  600 
72720 
84840 
64  833 
90  700 
105  840 
120  900 
127  000 
168  900 
217  000 
300  000 


35  000 
43  760 
52500 
41  120 
58800 
70  560 
82  320 
63  170 
88  560 
103  300 
118  000 
124  400 
166  100 
213  800 
267  6001 


57  000 

68  400 

79  800 

61  600 

86  400 

100  802 

115  200 

121  900 

163  000 

210  600 

264  000 


82080 
95  760 
109  400 
116  800 
157400 
204  100 
256  000 


Table  V. 


Safe  Loads  in  Pounds  for  Cedar,  Cypress,  Redwood,  Norway- 
Pine  and  Whitewood  Columns,  Round  and  Square 


Size  of  column 
in  inches 


4X6 

SH  round/. , . 

6X6 

6X8 

6X10 

7'/^  round 

8X8 

8X10 

8X12 

gH  round 

10X10 

10X12 

10X14 

II H  round. . . 

12X12 

12X14 

12X16 

14X14 

16X16 

18X18 

20X20 


Length  of  column  in  feet 


II  520 
12350 
19  080 
25440 
31  800 
24  220 
35  450 
44320 
53180 
40  000 
62  500 
75000 
87500 
64  930 
90  000 
105  000 
120  oco 

122  500 
160  000 
202  500 
250  000 


10550 
II  730 
18  216 
24  290 
30360 
23380 
34300 
42  480 
51  450 
39000 

55  400 
66480 
77560 
58390 
90  000 
105  000 
120  000 
122  500 
160  000 
202  500 
250  000 


9  800 
II  180 
17352 
23140 
28  920 
22540 
33  150 
41  440 
49730 
37860 
53  960 
64  800 
75600 
57  140 
79780 
93  170 
106  300 
no  350 
160  000 
202  500 
250  000 


8  700 
10  490 
16  490 
21  980 
27  480 
21  660 
32  000 
40  000 
48  000 
36  800 
52  520 
63  000 
73500 
55800 
78  000 
91  050 
104  000 
108  350 
143  870 
202  500 
250000 


16050  15 
21  400 
26  760  26 
21  260 1  20 
31  420J  30 
39280J  38 
47  1401  46 
36  230  35 
51  800;  51 
62  i6oj  61 
72520  71 
55  170'  54 
77  180;  76 
90  050'  89 
102  900  lor 
107  400  106 
142  590  141 
183  060  181 
250  ooo'25o 


620 
830  .. 
040  . . 
820  . . 
850  29 
560  37 
270  44 
730  34 
080  49 
300  59 
510  69 
550'  53 
320  74 
000  87 
700  99 
400  104 
570  139 
760  179 
000  224 
i 


48  200 
57840 
67  480 
51  950 
72  860 
85  000 
97  150 
102  300 
136  960 
176  580 
221  200 


69  400 
80  900 
92500 
98  400 
132  360 
171  400 
215  200  . 


Eccentric  Loading  of  Wooden  Columns 


453 


5.   Eccentric  Loading  of  Wooden  Columns 

General  Principles.  When  the  load  on  a  short  column  or  post  is  not  axial, 
that  is,  when  the  column  supports  a  girder  on  one  side  only,  or*when  the  weight 
from  one  girder  is  much  more  than  that  from  the  others,  the  load  is  said  to  be 
ECCENTRIC,  and  the  distance  from  the  point  of  application  of  the  load  to  the  axis 
of  the  column,  denoted  by  p,  is  called  the  eccentricity  of  the  load.  It  is  evi- 
dent that  the  stress  in  the  column  will  increase  with  p,  and  that  the  total  unit 
stress  S,  on  the  side  of  the  column  in  which  the 
compression  is  the  greatest,  will  be  greater  than  for 
an  equal  axial  load. 

Formula  for  Eccentric  Load.  Suppose  the 
eccentric  load  to  be  applied  as  shown  in  Fig.  1, 
then  the  sectional  area  of  the  required  square  or 
rectangular  column  may  be  computed  by  the  fol- 
lowing formula  (See,  also,  page  486) : 

The  sectional  area  of  the  column  in  square 
inches  is 

A  =  {P-VPx)/S^^PiP/Sd  (C) 

in  which  A  =  sectional  area  in  square  inches 

P  =  concentric  load  on  column  in  pounds 
Pi  =  eccentric  load  in  pounds 
S  =  safe  stress  in  pounds  per  square  inch 
p  =  distance  from  axis  of  column  to  cen- 
ter of  bearing  in  inches 
d  =  side  of  column  parallel  with  girder,  in 
inches 


ELEVATION 


Gfirder  A 


Fig. 


PLAN 


1.    Eccentric  Load   on 
Wooden  Column  , 


In  assuming  the  value  of  S,  the  probable  ratio  of 
the  side  to  the  length  of  the  column  should  be  taken 
into  account.  Thus  if  it  is  probable  that  the  length 
will  not  exceed  12  times  the  side,  both  being 
measured  in  inches,  for  oak,  long-leaf  yellow-pine  or 
Douglas-fir  columns,  or  10  times  the  side  for  other 
woods,  then  the  value  of  S  for  short  columns  may 
be  taken.  If  the  ratio  will  probably  be  greater 
than  this,  then  the  probable  ratio  should  be  roughly 
calculated  and  S  computed  for  that  ratio  by  the 

formula  given  for  columns  more  than  10  or  12  diameters  in  length,  as  noted  in 
preceding  paragraphs. 

Example  3.  The  lower  post  in  Fig.  1  supports  a  total  load  on  its  cap-plate 
of  60  000  lb,  including  the  reaction  of  1 2  000  lb  from  girder  A .  What  should  be 
the  size  of  the  column  if  made  of  Douglas  fir  and  if  12  ft  in  height? 

Solution.  As  it  is  probable  that  the  column  will  have  to  be  10  in  square  S  may 
be  taken  from  Table  I.  With  a  factor  of  safety  of  5,  this  is  equal  to  4  500/5  =» 
900  lb  per  sq  in.  Pi=  12  000  \h,  d  =  10  in  and  p,  the  distance  from  the  axis  of 
the  column  to  the  center  of  bearing  of  the  girder  =  7  in.  Then  from  Formula  (6), 
the  sectional  area  of  the  column  is 


A  = 


60  000       6X12  000  X  7 


=  66.6  +  56  =  122.6  sq  in. 


900  900  X  10 

about  equivalent  to  a  12  by  12-in  square  column.    From  Table  III,  it  may  be 
seen  that  an  8  by  lo-in  column  concentrically  loaded  will  carry  almost  60  000  lb. 


454 


Strength  of  Columns,  Posts  and  Struts  Chap.  14 


Hence,  the  eccentric  load  from  the  girder  increases  the  dimensions  of  <he  cross- 
section  of  the  column  from  8  by  lo  to  12  by  12  in. 

For  wooden  columns  having  a  length  of  over  12  diameters  for  Douglas  fir  and 
spruce  and  over  10  diameters  for  other  woods  the  safe  load  per  square  inch 
should  be  found  by  using  Formulas  (3),  (4)  or  (5). 

Example  4.  What  size  will  be  required  for  a  white-oak  column,  14  ft  in  length 
to  carry  a  total  load  of  56  000  lb,  16  000  lb  of  which  act  as  an  eccentric  load  from 
a  girder,  the  distance  from  the  center  of  bearing  of  the  girder  to  the  column  being 
2  in. 

Solution.  From  Table  II,  it  is  probable  that  at  least  a  10  by  lo-in  column 
will  be  required,  so  that  5  must  be  calculated  by  Formula  (2). 


■■  I  000—  10  X 


Substituting, 


length  in  in 
breadth  in  in 
168 


S  =  1  000  —  10  X  —  =  832  lb  per  sq  in 


Substituting  in  Formula  (6), 


56000  6X16000X7  ^„  „  o  . 

A  =  V—  +  — ^777Tm~^  =  68  +  80  =  148  sq  in 


832  832X10 

equivalent  to  a  12  by  12 -in  column. 


6.   Metal  Caps  and  Bolsters  for  Wooden  Columns 

Use  of  Metal  Post-Caps.  Whenever  wooden  posts  are  used  in  tiers,  one 
above  another,  each  post  except  the  top  one  should  have  an  iron  cap-plate, 
jand  the  upper  post  should  be  set  on  the  cap  of  the  post  below  and  not  on  the 
girder.  Where  a  wooden  post  supports  a  girder,  only,  a  wooden  bolster  may  be 
used  in  place  of  the  cap  but  modern  approved  metal  post-caps  are  always  pref- 
erable to  wooden  bolsters.  Details  of  post-caps  and  bolsters  are  shown  in 
Chapter  XXII. 

7.   Crushing  of  Wood  Perpendicular  to  the  Grain 

Safe  lyni^  Stresses.  The  bearing  of  wooden  girders,  the  ends  of  columns 
resting  on  girders,  and  washers  on  truss-rods,  should  be  proportioned  so  that 
the  quotient  obtained  by  dividing  the  load  by  the  bearing  area  will  not  exceed 
the  safe  unit  stresses  given  in  Table  VI. 


Table  VI.    Safe  Loads  for  "Wood  Perpendicular  to  the  Grain 


Kind  of  wood 

Safe 

loads, 

lb  per  sq  in 

Kind  of  wood 

Safe 

loads, 

lb  per  sq  in 

White  oak 

Soo 
350 
200 
200 
200 

250 

Cedar 

200 

200 
150 
200 
150 

250 

Long-leaf  yellow  pine 

Douglas  fir 

Spruce 

Hemlock 

Norway  pine 

Cypress 

White  pine 

Redwood 

1  Short-leaf  yellow  pine 

Chestnut 

Cast-iron  Columns  455 

8.   Cast-Ifon  Columns* 

,  Cast-iron  Versus  Steel  Columns.  Although  steel  is  being  used  more  and 
more  every  year  for  columns  in  buildings,  it  will  probably  never  entirely  supplant 
cast  iron  for  buildings  of  moderate  height.  For  skeleton  construction,  however, 
when  the  height  of  the  building  exceeds  twice  its  width,  riveted  steel  columns, 
with  riveted  connections  with  the  beams  and  girders,  are  unquestionably  better; 
but  for  the  larger  proportion  of  buildings  of  moderate  height,  cast  iron  will 
probably  have  the  preference  for  some  time  to  come  because  it  is  more  economi- 
cal. 

Advantages  of  Cast-iron  Columns.  The  commercial  advantages  which 
favor  the  use  of  cast-iron  columns  are  these: 

(i)  Cheapness.  As  far  as  the  cost  of  production  is  concerned,  cast  iron  is 
cheaper  than  steel.  This  consideration  alone  often  decides  in  favor  of  its  em- 
ployment. The  raw  material  is  easily  transported  as  pig  iron  is  sometimes 
brought  over  as  ballast;  so  that  competition  with  foreign  countries  keeps  down 
the  price. 

(2)  Availability.  Cast  iron  is  the  most  available  form  of  iron.  An  iron- 
foundry  requires  no  very  elaborate  plant,  scarcely  more  than  a  few  furnaces 
and  sand  molds,  and  moreover,  no  very  extensive  capital  is  required  to  operate 
it;  consequently,  the  product  may  be  obtained  in  almost  any  locality.  In 
rolling-mills,  on  the  contrary,  the  machinery  must  be  very  heavy  in  order  that 
it  may  overcome  the  enormous  pressure  due  to  the  resistance  of  the  steel  in 
rolling,  and  to  operate  it  requires  a  great  amount  of  power. 

(3)  Readiness  with  Which  it  May  be  Obtained.  Columns  and  other  struc** 
tural  members  if  made  of  cast  iron  may  be  obtained  much  more  quickly  than  if 
made  of  steel.  After  the  pattern  has  once  been  prepared,  a  dozen  castings  may 
be  made  alm9st  as  quickly  as  one,  and  with  but  very  Httle  extra  cost,  except 
that  of  the  additional  raw  material  and  the  expense  of  remelting  it.  On  the 
other  hand,  columns  and  girders  built  up  of  rolled  sections  take  considerably 
longer  to  make.  Sections  can  be  punched  only  one  at  a  time,  and  if  they  do 
not  happen  to  be  of  some  standard  length,  they  must  be  cut  and  fitted  separately 
before  all  can  be  finally  riveted  together. 

(4)  Physical  Advantages.  Cast  iron  is  one  of  the  best  materials  to  resist 
compression,  its  ultimate  compressive  strength  being  as  high  as  80  000  lb  per 
sq  in  and  even  higher.  Moreover,  it  can  be  molded  into  almost  any  desired 
form,  and  lugs,  brackets  and  flanges  may  be  cast  upon  a  column  all  in  one  piece 
thus  greatly  simplifying  the  cost  of  erection.  In  fact,  the  ease  with  which  th6 
beam  and  girder-connections  can  be  made  is  one  of  the  chief  reasons  for  thd 
popularity  of  cast  iron.  Finally,  it  resists  fire  better  than  steel  and  it  corrodes 
less  easily.  Because  of  this,  its  use  is  advocated  by  many  for  the  wall  columns 
of  skeleton  structures,  as  these  columns  are  particularly  liable  to  corrode.  In 
the  Mutual  and  Manhattan  Life  Insurance  Company's  Buildings  in  New  York 
City,  for  example,  the  wall  columns  are  of  cast  iron,  whereas  the  interior  onds 
are  of  steel.  1 

Disadvantages  of  Cast-iron  Columns.  The  disadvantages  of  cast  iron  folf 
columns  are  as  follows: 

(i)  Physical  Disadvantages.  Cast  iron  is  hard  and  brittle  and  cannot  be 
punched  or  riveted,  as  the  blows  required  in  driving  the  rivets  would  very  likely 
fracture  the  castings;  consequently,  all  connections  have  to  be  made  with  bolt3i 
A  bolted  connection  even  under  the  most  favorable  conditions  is  not  very  rigidj 

*  See,  also,  Chapter  XIII,  pages  445  to  447. 


456  Strength  of  Columns,  Posts  and  Struts  Chap.  14 

as  it  allows  more  or- less  lateral  movement,  which,  in  the  case  of  a  tall,  narrow 
building,  is  a  serious  matter.  Owing  to  the  low  tensile  and  shearing  strengths  of 
cast  iron,  the  brackets  supporting  beams  and  girders  are  unreliable  and  require 
great  skill  in  designing.     (See  pages  445  to  447.) 

(2)  Defects  in  the  Castings  and  the  Difficulties  of  Thorough  Inspection.    The 

castings  themselves  are  subject  to  a  number  of  serious  defects.  In  the  first  place, 
owing  to  the  shifting  or  floating  of  the  cores,  variations  in  the  thickness  of  hollow 
castings  are  not  infrequent;  in  fact,  it  is  very  difficult  to  avoid  them  even  with 
the  best  care  and  workmanship.  Moreover,  there  are  apt  to  be  concealed 
cavities,  blow-holes  or  honeycomb,  and  foreign  substances,  such  as  cinders  and 
sand,  any  of  which  may  be  on  the  inside  of  a  casting,  where  a  careful  examina- 
tion often  fails  to  reveal  them.  The  most  critical  condition,  however,  is  that 
due  to  the  uneven  contraction  of  the  metal  during  the  process  of  cooling,  the 
thin  parts  of  the  casting  cooling  and  contracting  more  quickly  than  the  thick 
ones,  thereby  giving  rise  to  initial  stresses,  at  times  of  sufficient  intensity 
to  fracture  the  casting  before  any  external  loads  whatever  have  been  placed 
upon  it.  In  many  cases  this  trouble  is  due  to  faulty  designing  or  to  carelessness 
in  handling  the  molds;  yet,  even  under  the  most  favorable  conditions,  it  is  so 
difficult  to  secure  equal  radiation  from  the  molds  in  all  directions  that  castings 
entirely  free  from  inherent  shrinkage-stresses  are  probably  seldom  produced. 

9.    Design  of  Cast-iron  Columns 

Common  Forms  of  Cast-iron  Columns.  Figs.  2,  3  and  4  show  some 
common  forms  of  cross-sections  of  cast-iron  columns.  Columns  of  circular  or 
rectangular  cross-sections  are  always  made  hollow  and  the  diameter  should  be 
made  as  large  as  possible,  within  reason  of  course;   because  of  two  columns 


^^^ 


^^ 


^/////////.//^ 


-^^—dr^ 


Fig.  2  Fig.  3  Fig.  4 

Figs.  2,  3  and  4.     Cross-sections  of  Cast-iron  Columns 

having  the  same  area  of  cross-section,  the  one  which,  within  certain  limits,  has 
the  greater  diameter,  and  consequently  the  thinner  shell,  is  the  stronger.  The 
maximum  thickness  of  shell  is  1%  or  2  in,  because  of  the  difficulty  of  keeping 
the  core  from  shifting  in  columns  of  greater  thickness;  and  the  minimum  thick- 
ness is  %  in.  The  latter  is  a  requirement  of  most  municipal  building  codes. 
As  the  maximum  Hmit  of  diameter,  16  in  may  be  taken;  beyond  this,  built-up 
steel  columns  can  be  used  to  better  advantage  and  are  less  expensive.  The 
minimum  diameter  permitted  by  most  building  codes  is  5  in,  and  the  unsupported 
length  of  the  column  is  Umifed  to  20  times  the  least  diameter. 

Hollow,  Cylindrical  Cast-Iron  Columns.  The  most  economical  form  of 
cross-section,  as  far  as  structural  requirements  are  concerned,  is  the  hollow 
CIRCLE  (Fig.  2).  This  form  is  generally  used  for  interior  columns;  but  for  ex- 
terior columns  it  is  not  so  desirable,  because  such  columns  cannot  be  bonded  into 
walls  so  readily,  and  do  not  present  the  same  facilities  for  the  design  of  the  beam 
and  girder-connections  as  columns  having  the  other  forms  of  cross-sections. 


Design  of  Cast-iron  Columns 


457 


li^ 


CAST-mO?r  COLUMNS 

"Cast-iron  columns  shall  be  true  and 
straight,  of  full  and  uniform  tbickncBS 
for  the  entire  length,  oast  with  top  and 
b(>ttom  flanges,  (extending  around  all 
sides  of  the  coluoin,    unless  otherwiso 
detailed,)  lugs,  seats,  brackets  and 
separators,  reinforced  bj  lilleta  and 
webs,  all  as  detailed. 
Brackets  shall  be  beveled  on  seats  and 
be  provided  with  ample  fillets  and  webs. 
CONNECTIONS 

"All  columns  shall  be  bolted  together 
throuph  their  flanges  and  top  plaice 
with  not  less  than  four,  and  to  the 
bases  with  not  less  than  eight,  ^4,"  bolts. ' 
"Beams,  channels  and  beam-girders  shall 
be  bolted  to  the  lugs,  or  web-separators, 
of  cast-iron  columns  by  two  bolts  for 
beams  12"or  less  in  depth  and  by  three 
bolts  for  all  others.  In  all  cases  the 
webs  are  to  be  in  close  contact  with  the 
lugs  and  separators.  Built-up  girders 
shall  be  bolted  to  the  columns  through 
web  angle-Btiffeners-" 
TESTS 

"All  hollow  castings  shall  have' two,  or, 
more,  ^"  holes  drilled  in  the  shell  as 
directed,  to  exhibit  the  thickness  of  the 
metal,  and  those  showing  a  variation  of 
more  than 3^' will  be  rejected.'* 


\J 


All  holts  to  be  %"m  diameter  unless 

lave  a  projection  of  S'except  where  other-w 

eled  on  seatt  and  ample  flUeta  proy Wed  whi 

'flanges  to  be  drilled  to  a  template  ^g 


saop  piREC 

.  Column  flanges 
Brackeisto  bt.  bev 
Open  h  )les  In  00 
diameter  of  bolt 
Open  I  oles  in  bea!m•^agB  t^  be  ooted  ^^'larger  than,  dhtmetei 


3ni[; 


4? 


/ 


oftherwiee  marked^ 

shown. 

practicable* 
1  irger  than 


CH 


ofjjolK 


-ir- 


^ 

¥ 


^ 


Fig.  5.    Connections  for  Cylindrical  Cast-iron  Columns 

Typical  Connections  for  a  Cylindrical  Cast-iron  Column.  Fig.  5  shows 
the  details  of  a  cylindrical  cast-iron  column  with  typical  beam  and  girder-con- 
nections, dimensions  and  specification-notes.  (See,  also,  details  of  connections, 
brackets,  base-plates,  etc.,  for  cyUndrical  columns  in  Chapter  XIII,  Figs.  2,  3 
and  7  and  Table  III  of  same  chapter.) 


45S 


Strength  of  Columns,  Posts  and  Struts  'Chap.  14 


G^st-Iroi  Columns  M'ith  Hollow-Square  Cross-Section.     The  columns 

•  I  '  )  next  in  point  of  economy  of  cross-section  are    those 

with  the  HOLLOW-SQUARE  cross-section  (Fig.  3). 
They  are  generally  used  for  wall  columns  because 
it  is  easier  to  bond  them  into  the  masonry  than  if 
they  had  a  circular  section.  Columns  of  hollow 
rectangular  cross-section  of  unequal  sides  are  some- 
times found  to  be  more  available  than  those  of  square 
section. 
The  H-Shape  Column  (Fig.  4)  ranks  third  in 

regard  to  economy  of  material.     It  is  particularly  well  adapted  for  wall  columns 

in  skeleton  construction  for  the  following  reasons: 


Fig.'  6.     H-shaped    Cross- 
section  of  Cast-iron  Column 


*  *  "VjThBlsa  l)olte  go  ihrough  Ijevelea^aEnge^,/" 

"beveled  waehexe to  "match  shall  Ije  used,  ^o  thatrthe 
lieatkantltiufcof  the  bolt'^ill  be  parallel.  V- 

TaPPLA33:H. 

"Steel  top  plates,  not  leas  than  }i  fhicTc,  of  the  size 
Teqiiined  l)y  tlie  dimensions  of  tho  joint,  and.  to  afford 
.f  ulLbeaTings  for  the  angle-bracketSj  shall  be  placed  be- 
tween Qie  ends  of  all  columns  cast  with  one  side  or  \eith 
one  bacJCopen,  and  whenever,  a  column  of  less  diameter 
is  placed  upon  top  of  anotjier.  TJiey  shall  also-bcruBed — 
to  make  up  any  shortage  in  length  of  casWron  xsohinms. 
l?lates  for  double  columns  ehaTLbe  cast  •vdth.  top  and  \>ot-   .1 
torn  flanges. .A^terthe  plates  have  been  f1rin<='(l  -aifl.  tho       j 


- J 


proper  lioles  for  connections,  they  shall  be  truljr  fiekti 
and  of  uniform  thickness.*' 

Note  J  These  y  columns  ace  particularly  welt  adapted 
ton  itall. columns  in  skeleton  constr.uction.  Only  the  edges 
come  near  the  face  of  the  vail  and  there  are  no  project- 
ing .rime  or  flang^ee  to  be  in.  the  yrsey. 


Fig.  7.     Connections  for  H-shaped  Cast-iron  Column 


(i)  Being  entirely  open,  with  both  the  interior  and  exterior  surfaces  exposed, 
any  inequalities  in  thickness  can  be  readily  discovered  and  the  thickness  itself 


Strength  of  Cast-iron  Columns.     Formulas 


459 


easily  measured,  thus  obviating  any  necessity  for  drilling,  and  rendering  the 
inspection  of  the  columns  much  easier. 

(2)  The  entire  surface  of  the  column  may  be  protected  by  paint. 

(3)  When  built  in  brick  walls  the  masonry  fills  all  voids,  so  that  no  open  space 
is  left;  and  if  the  column  is  placed  as  shown  in  Fig.  6,  only  its  edges  come  near 
the  face  of  the  wall. 

(4)  Lugs  and  brackets  can  be  cast  on  such  columns  more  readily  and  effectively 
than  on  cylindrical  columns,  especially  for  wide  and  heavy  girders,  and  the. 
connections  do  not  require  projecting  flanges,  which  are  often  in  the  way  on 
cylindrical  columns. 

(5)  An  eccentric  load  may  be  applied  to  the  web  where  its  effect  is  less  and 
where  it  is  more  evenly  distributed  than  when  it  is  applied  to  the  outer  rim  or 
shell. 

Details  of  connections  and  brackets  for  H -shaped  cast-iron  columns  are  shown 
in  Fig.  7. 

Details  of  Connections  of  Cast-iron  Columns.  The  bearings  of  a  cast- 
iron  column  should  always 
be  faced  true  to  the  axis  of 
the  column,  and  the  columns 
should  be  bolted  together  by 
four  ^4-in  bolts  for  columns 
10  in  in  diameter  or  less,  and 
by  six  bolts  for  12-in  and 
larger  columns.  Faced 
plates,  as  shown  in  Fig.  5, 
are  inserted  between  the 
flanges  of  columns  to  make 
up  for  any  shortage  in  length 
and  also  when  a  column  of 
smaller  diameter  is  placed" 
over  one  of  greater  diameter. 
For  convenience  in  erecting 
columns,  the  joint  is  gen- 
erally placed  just  above  the 
beams  or  girders  supported 
by  the  columns. 

Projecting  Caps  and 
Bases.  A  column  with  or- 
namental cap  and  base  should 

that  is,  if  it  is  to  support 


Fig.  9.  Cast-iron 
Column  with  Cap 
and  Base.  Slight 
Projections 


Fig.   8.     Cast-iron   Column  with 
Cap  and  Base.     Wrong  Method 

never  be  cast  as  shown  in  Fig. 

a  load.     In  every  bearing  column,  the  core  should  extend 

in  a  straight  line  from  end  to  end.     Plain  molded  caps  and  bases  may  be  cast 

solid  as  in  Fig.  9;  but  if  more  ornamental  caps  are  desired,  or  heavy  projecting 

bases,  they  should  be  cast  separately  and  attached  to  the  straight  columns  by 

screws. 


W,   Strength  of  Cast-iron  Columns.     Formulas 

Formulas  for  Cast-iron  Columns.  The  ultimate  resistance  of  cast  iron 
to  crushing  is  generally  taken  at  80  000  lb  per  sq  in,  and  for  posts,  pintels,  etc., 
where  the  length  is  not  more  than  six  times  the  diameter  or  breadth,  it  will 
usually  be  safe  to  assume  a  working  strength  of  six  tons  per  square  inch  of 
metal.    For  longer  posts  or  columns,  the  strength  is  affected  by  the  ratio  of 


460 


Strength  of  Cclumns,  Posts  and  Struts 


Chap.  14 


length  to  diameter,  but  to  just  what  extent  is  not  known  with  absolute  certainty; 
hence  all  formulas  for  columns  must  be  more  or  less  theoretical.  The  conse- 
quence is  that  while  a  great  many  formulas  have  been  published,  there  is  none 
that  is  universally  accepted.  The  two  following  Formulas  *  (7)  and  (8),  were 
for  many  years  more  commonly  adopted  than  any  others,  as  they  appeared  to 
agree  as  well  as  any  with  actual  tests. 

Formula  for  Hollow,  Cylindrical,  Cast-iron  Columns  with  Square  Ends 
Ultimate  strength,  in  pounds.  * 

sq  of  length  in  in 


=  metal-area  X 


[80000^(1+- 


800  X  sq  of  diam  in  in 


)] 


(7) 


Ultimate  strength,  in  pounds  = 


80000  A 


in  which  A  is  the  area  of  the  cross-section  in  square  inches. 

*  The  tables  in  the  handbook  of  the  Cambria  Steel  Company  (1913)  are  based  on 
Formulas  (7)  and  (8),  and  they  were  adopted  in  some  building  laws.  They  are  based  upon 
the  form  of  Gordon's  formula,  which,  in  turn,  is  Rankine's  formula  with  d,  the  diameter 
or  least  lateral  dimension,  substituted  for  r,  the  least  radius  of  gyration  of  the  cross-sec- 
tion. Rankine's  formula  is  sometimes  referred  to  as  Gordon's  formula.  The  values 
obtained  by  these  formulas  will  be  slightly  in  excess  of  those  given  in  the  old  Chicago 
building  law  (see  tabulation  in  this  foot-note),  and  considerably  less  than  those  permitted 
by  the  former  building  law  of  New  York  City,  S  =  11  300  —  30  l/r.  (Present  code, 
5  =  9000  -  40 l/r.  "■     '■'^■'  '''^■.  i 

In  1898  Professor  W.  H.  Burr  made  an  analysis  of  the  results  of  a  number  of  experi- 
ments on  full-size,  hollow,  cylindrical  cast-iron  columns  made  at  the  Watertown  Arsenal, 
Mass.,  and  at  PhcenLxville,  Pa.,  and  by  plotting  the  results  found  that  a  straight-line 
formula  having  the  equation  5  =  30500—  160  l/d,  in  which  S  is  the  ultimate  strength 
of  the  metal  per  square  inch  of  column-area,  represented  the  average  of  the  plotted 
results.  With  a  factor  of  safety  of  4  this  would  become  5=7  625  —  40 l/d  and  with  a 
factor  of  safety  of  5,  5  =  6  100  —  32  l/d. 

According  to  Professor  Burr's  analysis  the  values  for  S  given  in  the  fourth  column  of 
Table  VII  represent  a  factor  of  safety  of  a  little  over  4  for  l/d  =  20,  and  of  nearly  7  for 
l/d  =  36. 

Formulas  for  finding  the  value  of  S  according  to  the  former  codes  of  Chicago  and  Boston. 


Cylindrical  columns 

Rectangular  columns 

Old  Chicago  Code 

Old  Boston  Code 

Old  Chicago  Code 

Old  Boston  Code 

TO  000 

10  000 

10  000 

10  000 

^  '^eoo'd^ 

800T2 

/2 

^       800  d^ 

I    1       ^' 

1066  (/2 

The  former  New  York  City  Building  Code  Formula  was 
S  =  11  300  — 30 //r 
Compared  with  the  results  of  tests  that  have  been  made  on  full-size  cast-iron  columns  it 
has  been  shown  that  while  in  Chicago  a  factor  of  safety  of  8  was  allowed,  the  actual  factor 
of  safety  was  a  little  over  4,  that  in  Boston  it  was  slightly  under  4,  while  in  New  York  it 
was  a  trifle  over  6.  The  formula  in  the  new  (1916)  Chicago  code  is  5  =  10  000  —  60  l/r, 
while  the  new  (1915)  Boston  code  gives  the  values  of  S  for  l/r  from  10  to  70. 

A  series  of  tests  on  full-size  cast-iron  columns  and  brackets  was  made  under  the  direc- 
tion of  Stevenson  Constable,  in  December,  1897,  a  report  of  which,  with  illustrations, 
may  be  found  in  the  Engineering  Record  for  January  8  and  22,  1898. 


Tables  of  Safe  Loads  for  Cast-iron  Columns.     Examples      461 

Formula  for  Hollow,  Rectangular,  Cast-iron  Columns  with  Square  Ends 

Ultimate  strength,  in  pounds 


=  metal-area  X  fso  ooo  ^  (  i  +  ^Q  °f 'ength  in  in \  "j 

L  \        I  067  X  sq  of  least  side  in  in  /  J 

Ultimate  strength,  in  pounds 


(8) 

aiiac  in  111  y  _j 

80  000  A 
i  +  /Vio67^2 
in  which  A  is  the  area  of  the  cross-section  in  square  inches 

Formula  for  Solid,  Cylindrical,  Cast-Iron  Columns 
Ultimate  strength,  in  pounds 

=  metal-area  X  fso  ooo  -  .  +  -  L^^fJ^SS^i^il^^^"]  ,. 

L  266  X  sq  of  diam  in  in  J 

or 

Ultimate  strength,  in  pounds  = 

I  +  /V266^2 

in  which  A  is  the  area  of  the  cross-section  in  square  inches. 

For  H -shaped  cokimns  use  formula  (7),  taking  d  as  the  feast  side. 

The  safe  load  is  generally  taken  at  one-eighth  of  the  ultimate  strength  or 
breaking-load. 

Eccentric  Loading.  Cast-iron  columns  should  not  be  loaded  with  a  heavy, 
ECCENTRIC  LOAD,  that  is,  a  load  applied  on  one  side  of  the  column  without  a 
corresponding  load  on  the  other  side,  as  cast  iron  is  unable  to  resist  very  great 
bending  stresses.  (See,  also,  eccentric  loading  of  wooden  and  steel  columns, 
pages  453  and  485.) 

11.    Tables  of  Safe  Loads  for  Cast-iron  Columns.     Examples 

Explanation  of  Tables.  As  the  allowable  pressure  per  square  inch  op 
METAL  depends  upon  the  ratio  of  length  to  diameter,  without  regard  to  actual 
dimensions  (that  is,  it  would  be  the  same  for  a  column  6  in  in  diameter  and  1 2  ft 
long,  as  for  one  8  in  in  diameter  and  16  ft  long),  it  is  practicable  to  prepare  a 
table  which  will  give  the  value  of  the  terms  of  Formulas  (7)  and  (8)  inclosed  in 
brackets  for  all  ratios  of  diameter  to  length,  and  thus  simplify  very  much  the 
computation  for  any  particular  column.  Table  VII  has  been  computed  by 
means  of  Formulas  (7)  and  (8)  for  ratios  of  length  to  diameter  varying  from  8 
to  36,  and  the  same  result  will  be  obtained  by  using  the  values  given  in  this 
table  as  by  using  the  corresponding  formula.  To  use  this  table  it  is  only  neces- 
sary to  divide  the  length  of  the  column  by  the  least  thickness  or  diameter,  both 
in  inches,  and  opposite  the  number  in  the  first  column  of  the  table  coming  nearest 
to  the  quotient,  find  the  safe  strength  per  square  inch  for  the  column. 
This  load  is  multiplied  by  the  metal-area  in  the  cross-section  of  the  column 
and  the  result  is  the  safe  load  for  the  column.  Examples  (5)  and  (6)  will  illus- 
trate the  use  of  Tables  VII  to  X. 

Example  5.  What  is  the  safe  load  for  a  lo-in  hollow,  cylindrical  cast-iron 
column,  15  ft  long,  the  shell  being  i  in  thick? 

Solution.  In  this  case  the  ratio  l/d,  which  is  the  length  of  the  column  divided 
by  the  diameter,  both  in  inches,  is  18,  and  opposite  18  in  Table  VII  the  safe 
load  per  square  inch  for  a  cyhndrical  column  is  found  to  be  7  1 17  lb.  The  metal- 
area  of  the  column,  from  the  table  of  areas  on  pages  42  and  463,  is  equal  to  the 
area  of  a  lo-in  circle  minus  the  area  of  an  8-in  circle,  or,  78.53  —  50.26  =  28.27 
sq  in.  Multiplying  these  two  together,  for  the  safe  load  of  the  column  the  result 
is  28.27  sq  in  X  7  n?  lb  per  sq  in  =  201  917  lb,  or  about  100.5  tons. 


462 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


Tables  VIII,  IX  and  X.  To  still  further  facilitate  computations,  Tables 
VIII,  IX  and  X,  have  been  prepared,  which  give  at  a  glance  the  safe  loads, 
based  on  a  factor  of  safety  of  8,  for  columns  of  the  more  common  sizes  and 
lengths.  For  lengths  between  those  given  in  the  tables  sufficiently  accurate 
results  may  be  obtained  by  interpolation.  For  any  other  factor  of  safety, 
multiply  the  safe  load  given  in  the  table  by  8,  and  divide  by  the  new  factor 
of  safety. 

Example  6.  What  is  the  safe  load  for  a  Q-in  hollow,  cast-iron  column  of 
square  cross-section  1 2  ft  long,  the  shell  being  i  in  thick? 
•  Solution.  From  Table  IX,  the  safe  load  is  129  tons.  The  same  result  may 
be  obtained  by  using  Table  VII.  The  ratio  Ifd  in  this  case  is  144/9  =16  and 
the  corresponding  safe  load  in  pounds  per  square  inch  is  8  064.  The  area  of 
the  column  is  32  sq  in.  Hence,  the  safe  load  is  32  sq  in  X  8  064  lb  per  sq  in  = 
258  048  lb,  'or  129  tons,  which  agrees  with  the  safe  load  given  in  Table  IX  for 
the  same  column. 


Table  VII.     Breaking-Loads  and  Safe  Loads  in  Pounds  per  Square  Inch 
for  Hollow,  Cylindrical  and  Hollow,  Rectangular,  Cast-Iron  Columns 

Calculated  by  Formulas  (7)  and  (8) 


Length  in 

Breaking-weight  in  pounds 

Safe  loads  in  pounds  per 

inches  divided 

per  square  inch 

square  inch.    Safety- 

by  external 

factor  8 

breadth  or 

diameter 

Cylindrical 

Rectangular 

Cylindrical 

Rectangular 

8 

V4  074 

75470 

9259 

■9433 

9 

72661 

74350 

9082 

9293 

10 

71  no 

73126 

8  888 

9140 

11 

6950s 

71870 

8  688 

8983 

12 

67800 

70487 

8  475 

8  811 

13 

66060 

69084 

8257 

8  635 

i:              14 

64257 

67567 

8032 

8446 

IS 

62450 

66060 

7806 

8257 

16 

60606 

64516 

7576 

8064 

17 

58780 

62942 

7  347 

7867 

18 

56  940 

61  360 

7  117 

7670 

19 

SS  134 

59  745 

6892 

7468 

20 

53  333 

S8180 

6  666 

7272 

21 

SI  S8o 

56  610 

6447 

7  076 

22 

49  843 

55  020 

6  230 

6877 

23 

48163 

53470 

6  020 

6684 

24 

46512 

51  950 

5814 

6494 

25 

44918 

50440 

5614 

630S 

26 

43360 

48960 

5420 

6  120 

27 

41  862 

47530 

5  233 

5940 

28 

40404 

46  no 

5  050 

5764 

29 

39000 

44742 

4  875 

5  592 

30 

37647 

43390 

4706 

5  424 

31 

36347 

42  080  • 

4  543 

5260 

32 

35090 

40816 

4386 

5  102 

33 

33  m 

39  580 

4  235 

4  947 

34 

32  720 

38380 

4090 

4  797 

35 

31608 

37  244 

3  951 

465s 

36 

30  534 

36  120 

3817 

4515 

Tables  of  Safe  Loads  for  Cast-iron  Columns. 


Table  VIII.     Safe  Loads  in  Tons  of  2  000  pounds  for  Hollow,  Cylindrical, 
Cast-iron  Columns  with  Square  Ends 

Based  on  Formula  (7).     Safety-factor  8 


Diam-  T 
eter,    1 
in 

hick- 
aess, 
in 

Length  of  column  in  feet 

Area  of 
metal, 
sq  in 

Weight, 
linft 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

5 

34 

38 

29 
32 

24 
27 

10.0 
11.3 

11.2 
12.7 

12.4 
14. 1 
15  7 

14.7 
16.8 
18.8 

31.3 
35.3 

35.0 
39-7 

38.7 

44.0 
490 

46.0 
52. 6 
58.9 

53.4 
61.2 
68.7 

H 
li 

39 

45 

5'A 

I 

46 
52 

40 
16 

■10 

30 
34 

26 
29 

3! 
36 
39 

43 
49 
54 

6 

52 
60 

47 
53 
59 

41 
47 
52 

36 
41 

45 

48 
55 
61 

27 
31 
34 

24 
27 
30 

34 
38 
43 

.... 

7 

% 

I 

65 
74 
8^ 

60 
68 

76 

54 
62 
6S 

38 
43 
18 

8 

H 

I 

78 
89 
100 

72 
83 
93 

67 
76 
86 

61 

70 
79 

71 

50 
57 
64 

45 
51 
58 

40 
46 
52 

36 

41 
47 

33 
37 
42 

17. 1 
19.6 
22.0 

9 

I 

103 
117 
129 

98 
no 
122 

91 
103 
114 

85 
95 
105 

80 
90 
99 

71 
80 
89 

6S 
73 
81 

67 

74 

54 
61 
67 

49 
55 
61 

22.3 

25.1 

27.8 

69.8 
78. 5 
87.0 

10 

I 

118 
133 

147 
161 

112 
127 
141 
154 

106 

120 
133 
146 

100 

1X2 

12.=; 
136 

93 

105 
116 
127 

86 
97 
107 
118 

79 
89 
99 
109 

73 
82 
91 
100 

67 
76 
84 
92 

62 
69 

77 
84 

25.1 
28.3 
31  4 
34.4 

78  4 
88.4 
98.0 
107.4 

II 

I 
i^ 

1% 

149 
165 
182 
197 

143 
159 
175 
190 

137 
152 
167 
181 

129 
144 
158 
171 

122 
135 
148 
161 

114 
126 
139 
151 

106 
118 
129 
140 

98 
109 
120 
130 

91 

lOI 

III 
121 

85 
94 
103 
112 

31  4 

34.9 
38.3 
41.6 

98.2 
109. 1 
119. 7 
129.9 

12 

1K2 

184 
202 
220 
237 

178 
195 
212 
229 

171 
188 
204 
220 

163 
179 
194 
210 

154 
170 
184 
199 

146 
160 
174 
187 

137 
150 

128 
141 
153 
165 

120 
132 

143 
154 

112 
123 
133 
144 

3«.4 
42.2 
45.9 
49-5 

120. 1 
131. 9 
143.4 
154.6 

13 

202 
222 
242 
261 

196 
216 
235 
254 

190 
209 

227 
245 

182 
200 
218 
235 

174 
191 
208 
224 

165 
181 
197 
213 

156 
172 
187 
201 

147 
162 
176 
190 

138 
152 
166 
179 

130 
143 
156 
168 

42.0 
46.1 
50.2 
54.2 

131 .2 
144.2 
156.9 
169.4 

14 

iH 
1% 

242 
264 
285 
306 

236 
258 
278 
298 

229 
250 
270 
289 

221 

241 
260 
279 

212 
231 

250 
268 

203 
221 
238 
256 

193 
210 
227 
243 

183 
199 
215 
231 

173 
189 
204 
219 

164 
178 
193 
207 

50.1 
54.5 
58.9 
63.2 

156.5 
170.4 
184.1 
197.4 

rS 

i^^ 

1% 
1% 

268 
309 
332 

354 

280 
303 
325 
346 

272 
295 
316 

337 

264 
285 
306 
327 

254 
275 
295 
315 

244 
264 
283 
302 

234 
252 
271 

288 

223 

241 
259 
276 

212 

229 
246 
263 

203 
219 
235 
251 

68.3 
72.8 

183  9 

203.4 
213-4 
227.6 

16 

iH 

333 
358 
382 

455 

327 
351 
375 
446 

3T9 
343 
366 

435 

310 
333 
356 
423 

300 
322 
344 
410 

290 
3tl 
332 
395 

278 
299 
319 
380 

267 
286 
306 
364 

255 
273 
292 
347 

243 
261 
279 
332 

68.3 
73.4 
78.3 
93.2 

213. 5 
229.3 
244.8 
291.3 

■      J 

464 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


Table  IX.     Safe  Loads  in  Tons  of  2  000  Pounds  for  Hollow,  Square  and 
Rectangular,  Cast-iron  Columns,  with  Square  Ends 

Based  on  Formula  (8).    Safety-factor  8 


Size, 


4X  6 
4X  8 
4X  9 
4X10 
4X12 

5X  8 

5X  9 

5X10 

5X12 

6X  6 
6X  8 
6X  9 

6X10 
6X12 
6X15 

7X  7 
7X  9 
7X12 

8X  8 

8X10 

8X12 


Thick- 
ness, 


Length  of  column  in  feet 


28 
35 
39 

42 
49 

48 
61 
52 
67 
57 
73 
65 
84 

51 
65 
60 
78 
65 
84 

70 
91 
80 

104 
95 

123 

67 
85 
77 

100 
93 

121 

83 
107 
129 

95 
122 
148 


106 

138      127 

167      154 


16        18 


Area  of 
metal, 
sq  in 


12.75 
15.75 
17.25 
18.75 
21.75 

17.25 
22.00 
18.75 
24.00 
20.25 
26.00 
23.25 
30.00 

15.75 
20.00 
18.75 
24.00 
20.25 
26.00 

21.75 
28.00 
24.75 
32.00 
29.25 
38.00 

18.75 
24.00 
21.75 
28.00 
26.2s 
34.00 

21.75 
28.00 
33-75 
24.75 
32.00 
38.75 

27.7s 
36.00 
43.7s 


Tables  of  Safe  Loads  for  Cast-iron  Columns. 


465 


Table  IX   (Continued).     Safe  Loads  in  Tons  of  2  000  Pounds  for  Hollow, 
Square  and  Rectangular,  Cast-iron  Columns,  with  Square  Ends 

Based  on  Formula  (8).     Safety-factor  8 


] 

Lengt 

in  feet 

1  of  column 

Size, 

Thick- 
ness, 

Area  of 
metal, 

Weight, 
linft 

in 

8 

10 

12 

14 

20 

24 

sq  in 

16 

18 

8X16 

I 

193 

181 

168 

155 

142 

130 

119 

99 

44.00 

137.5 

iVi 

236 

221 

206 

190 

174 

159 

145 

121 

53  75 

168.0 

9X  9 

¥i 

III 

106 

99 

93 

86 

80 

74 

63 

24.75 

77.3 

t 

144 

137 

129 

120 

112 

103 

96 

85 

32.00 

100. 0 

9X12 

I 

171 

162 

153 

143 

133 

123 

114 

97 

38.00 

118. 8 

iH 

209 

198 

186 

174 

162 

149 

138 

118 

46.25 

144.5 

9X16 

I 

207 

196 

185 

173 

161 

149 

138 

117 

46.00 

143.8 

iH 

254 

240 

226 

212 

197 

182 

168 

143 

56.25 

175.8 

10X10 

I 

165 

158 

150 

142 

133 

125 

117 

lOI 

36.00 

112. 5 

iH 

201 

193 

183 

172 

162 

152 

142 

123 

43.75 

136.7 

10X12 

I 

184 

176 

167 

158 

148 

139 

129 

112 

40.00 

125.0 

iKi 

224 

214 

204 

192 

181 

169 

158 

137 

48.75- 

152.3 

10X15 

I 

211 

202 

192 

181 

170 

160 

149 

129 

46.00 

143.8 

iH 

258 

247 

235 

222 

209 

19s 

182 

158 

56.25 

175-8 

10X16 

I 

220 

211 

200 

189 

178 

167 

155 

135 

48.00 

150.0 

iH 

270 

258 

245 

232 

218 

204 

190 

165 

58.75 

183.6 

10X18 

I 

239 

228 

217 

205 

193 

181 

168 

146 

52.00 

162.5 

iH 

293 

280 

266 

251 

236 

221 

207 

179 

63 -75 

199  2 

10X20 

I 

257 

246 

234 

221 

208 

194 

181 

157 

56.00 

175.0 

iH 

316 

302 

287 

271 

255 

239 

223 

193 

68  75 

214-9 

10X24 

I 

294 

281 

267 

252 

237 

222 

207 

180 

64.00 

200.0 

iH 

362 

346 

329 

311 

292 

274 

255 

221 

78.75 

246.1 

12X12 

li 

183 

177 

171 

164 

156 

149 

141 

126 

38.90 

121. 7 

I 

207 

201 

193 

185 

177 

168 

159 

142 

44.00 

137.5 

iH 

253 

245 

236 

223 

•216 

206 

195 

174 

53.75 

168.0 

\Vi 

296 

288 

277 

26s 

253 

241 

228 

204 

63.00 

196.9 

12X1S 

I 

235 

228 

220 

211 

201 

191 

181 

162 

50.00 

156.3 

iH 

288 

280 

269. 

258 

246 

234 

222 

198 

61.25 

191-4 

12X16 

I 

245 

237 

228 

219 

209 

199 

188 

168 

52.00 

162.5 

12X18 

I 

263 

256 

246 

236 

225 

214 

203 

181 

56.00 

175.0 

12X20 

I 

282 

274 

264 

253 

241 

229 

217 

194 

60.00 

187-5 

12X24 

I 

320 

310 

299 

287 

274 

260 

246 

220 

68.00 

212.5 

14X16 

I 

268 

261 

254 

246 

238 

229 

219 

200 

56.00 

175.0 

14X20 

I 

307 

298 

290 

281 

272 

261 

250 

228 

64.00 

200.0 

14X24 

I 

345 

336 

326 

316 

306 

294 

280 

257 

72.00 

225.0 

16X16 

I 

300 

284 

278 

271 

264 

256 

247 

229 

60.00 

187.5 

16X24 

I 

380 

360 

352 

344 

334 

324 

313 

291 

76.00 

237.5 

18X18 

I 

340 

340 

320 

314 

307 

299 

291 

274 

68.00 

212.5 

20X20 

I 

380 

380 

361 

356 

349 

342 

334 

317 

76.00 

237.5 

20X24 

I 

420 

420 

399 

393 

386 

378 

369 

351 

84.00 

262.5 

.._ 

,     |, ,           , 

466 


Strength  of  Columns,  Posts  and  Struts 


Table  X.     Safe  Loads  in  Tons  of  2  000  Pounds  for  H-Shaped,  Cast-iron 
Columns 


Based  on  Formula  (7).     Safety-factor  8 


Size, 
in 

Area  of 

Length  of  column 

in  feet 

i 

X . 

1 

metal, 

?! 

\^ 

s-^ 

^xx  ^^^^^J^;X\-^ 

a       b       t 

in 

10 

12 

13 

14 

: 

1 

- 

f 

i 

6X  6X  % 

I 

123/^ 
16 

41 
53 

36 
46 

33 
43 

31 

40 

h                  u' 

0        '  ■■    *i 

1% 

19^^ 

64 

56 

52 

48 

15 

16 

■   18 

20 

6X  8X  M 

I 

18 

46 
60 

40 
52 

37 
48 

34 
45 

iH 

21  ^i 

73 

63 

59 

54 

7X  7X1 

19 

69 

62 

58 

55 

52 

49 

43 

38 

iM 

23]^ 

84 

75 

71 

67 

63 

59 

53 

46 

7X  9X1 

21 

76 

68 

64 

61 

57 

54 

48 

42 

iH 

25H 

93 

83 

79 

74 

70 

66 

59 

51 

8X  8X  M 

16% 

66 

60 

57 

54 

51 

49 

44 

39 

I 

22 

86 

78 

74 

70 

67 

64 

57 

51 

iH 

26^i 

105 

95 

91 

86 

82 

78 

70 

63 

8X10X1 

24 

93 

85 

81 

77 

73 

69 

62 

56 

iM 

293/i 

114 

104 

99 

94 

90 

85 

76 

69 

1K2 

34K2 

134 

122 

117 

III 

105 

100 

89 

81 

9X  9X1 

25 

102 

94 

91 

87 

83 

79 

72 

66 

iM 

30H 

125 

116 

III 

106 

102 

97 

89 

81 

1K2 

36 

147 

136 

130 

125 

120 

114 

104 

95 

9X10X1 

26 

106 

98 

94 

90 

86 

83 

75 

69 

1% 

31^6 

130 

120 

IIS 

III 

106 

lOI 

92 

84 

i\^ 

37^^ 

153 

142 

136 

130 

125 

119 

108 

99 

loXioXi 

28 

118 

III 

107 

103 

99 

95 

88. 

81 

iH 

34^/^ 

145 

136 

131 

127 

122 

127 

108 

100 

1 1/2 

40H 

171 

160 

155 

149 

144 

138 

128 

117 

1% 

46% 

196 

184 

177 

171 

165 

158 

146 

134 

10X12X1 

30 

127 

119 

IIS 

III 

106 

102 

94 

87 

iM 

36^:^ 

156 

146 

141 

136 

131 

126 

116 

107 

1^2 

43H 

184 

172 

166 

160 

154 

148 

137 

126 

m 

49^^ 

211 

198 

191 

184 

177 

170 

157 

144 

2 

56 

236 

222 

214 

207 

199 

191 

.176 

162 

12X12X1 

34 

151 

144 

140 

136 

132 

128 

121 

113 

iw 

4l7/^ 

186 

177 

172 

167 

163 

158 

149 

139 

ii/^ 

49H 

220 

209 

203 

198 

193 

187 

177 

165 

1% 

56^ 

252 

241 

234 

227 

221 

216 

202 

i89 

2 

64 

284 

271 

263 

256 

249 

242 

227 

213 

12X14X1H 

44% 

197 

188 

183 

177 

173 

168 

158 

148 

i\^ 

52}^^ 

233 

222 

216 

210 

204 

199 

186 

174 

m 

60H 

268 

255 

248 

241 

235 

228 

214 

201 

2 

68 

302 

288 

280 

272 

265 

257 

241 

226 

2H 

75^/^ 

335 

319 

310 

301 

292 

285 

268 

251 

Types,  Forms  and  Connections  of  Steel  Columns 


467 


12.   Types,  Forms  and  Connections  of  Steel  Columns 

Use  of  Steel  Columns,  Struts,  Trusses,  etc.  Owing  to  the  many  ad- 
vantages of  built-up  steel  columns  over  cast-iron  columns,  especially  for  all 
buildings,  and  to  the  great  reduction  that  has  taken  place  in  the  cost  of  steel 
construction,  built-up  columns  are  now  very  extensively  used  in  buildings  of 
even  moderate  height;  and  for  skeleton  construction,  or  for  buildings  exceeding 
six  stories  in  height,  they  are  certainly  much  to  be  preferred  to  cast-iron  columns. 
Steel  trusses,  also,  are  no\y  much  more  commonly  used  in  buildings  than  in 
former  years,  so  that  the  architect  must  have  at  hand  data  for  designing  them 
and  for  computing  their  strength.  In  the  following  pages  the  author  has  en- 
deavored to  cover  the  subject  of  columns  and  struts  quite  completely,  to  furnish 
such  data  as  will  enable  the  designer  to  decide  upon  the  shape  of  column  or 
strut  it  is  best  to  use,  and  also  to  determine  the  sizes  and  sections  of  such  col- 
umns with  the  least  labor. 

Types  and  Forms  of  Steel  Columns.  The  following  are  cross-sections 
of  the  majority  of  steel  columns  in  general  use,  arranged  in  the  order  of  their  sim- 
plicity of  construction,  that  is,  the  number  of  rows  of  rivets  they  require: 


Bethlehem  H  col 


No  rivets 


Lally     steel-con- 
crete column 
No  rivets 


Plate-and-angle  j 

column 
Two  rows  of 
rivets 


Channel-column 
with    plates     or 
lattice-bars 
Four   rows   of 
rivets 


Plate-and-angle 
column  with 
side  plates 
Six  rows  of  rivets 


Box  column 
Eight  rows  of 
rivets 


Considerations  Governing  the  Selection  of  Steel  Columns.  There  are 
considerations  other  than  simplicity  of  construction  which  sometimes  govern 
the  selection  of  a  column.  Some  of  the  most  important  of  these  are  explained 
in  the  following  paragraphs: 

(i)  Cost  and  Availability  of  Material.  I  beams,  channels,  plates  and  angles 
are  the  most  common  commercial  sections.  They  are  easily  rolled  and  are 
manufactured  by  all  of  the  large  mills.  They  are  reasonable  in  price  and  may 
be  obtained  promptly  in  large  numbers  in  any  locality  where  a  steel  building  ia 
likely  to  be  erected.  Patented  sections,  or  the  product  of  one  mill,  do  not,  as 
a  rule,  fulfill  these  conditions. 


468  Strength  of  Columns,  Posts  and  Struts  Chap.  14 

(2)  Amount  of  Labor  Required  and  Facility  With  Which  it  can  be  Performed  in 
Shop  and  Field.  In  the  shop  the  complexity  of  the  column-section  and  the 
number  of  pieces  of  which  it  is  composed  greatly  affect  the  cost  of  labor.  If 
there  are  numerous  small  pieces  such  as  lattice-bars,  splice-plates,  etc.,  each 
of  which  requires  cutting  and  fitting  together,  with  frequent  handling,  the  cost 
is  proportionately  great.  The  cost  of  a  column  depends,  also,  largely  upon  the 
number  of  rivets  required  and  whether  they  can  all  be  driven  by  machine  so 
as  to  avoid  the  slower  and  more  expensive  hand-riveting.  The  same  general 
remarks  apply  to  labor  in  the  field;  the  connections  should  be  as  simple  as 
possible,  the  rivets  easy  of  access  and  as  few  in  number  as  is  consistent  with 
strength. 

(3)  Simplicity  of  Connections  Between  Column  and  Supported  Members. 
This  is  quite  an  important  consideration  in  the  design  of  a  large  building  and 
sometimes  governs  the  choice  of  the  section  to  be  used.  Where  there  are  four 
beams  to  a  column,  on  opposite  sides,  and  all  of  the  same  height,  a  satisfactory 
connection  can  be  made  with  almost  any  section;  but  where  the  beams  are 
spaced  irregularly,  both  in  regard  to  position  in  plan  and  to  height,  and  where 
eccentric  loads  must  be  provided  for,  it  is  very  important  that  the  section  of 
the  column  itself  affords  as  great  an  opportunity  as  possible  for  the  connections 
of  the  beams.  In  this  respect,  possibly,  closed  sections  are  inferior  to  open 
sections  having  a  central  web. 

(4)  Adaptability  to  Connections  Which  Transfer  Compressive  Stresses 
Directly  to  Axis  of  Column,  In  this  respect,  also,  sections  of  an  open  construc- 
tion, in  which  the  girders  transmit  their  loads  almost  directly  to  the  central 
axis  of  the  column,  thus  avoiding  the  disadvantage  of  eccentric  loading,  are 
superior  to  those  of  a  closed  construction. 

(5)  Adaptability  to  Changes  in  Thickness  of  Metal  in  Members  of  Columns, 
to  Suit  Different  Loads  in  Different  Stories.  It  is  not  desirable  to  make  the 
columns  carrying  the  upper  floors  of  a  building  very  small,  since  the  beams  and 
girders  supporting  the  upper  floors  are  usually  of  the  same  dimensions  as  those 
of  the  lower  floors  and  consequently  require  just  as  heavy  and  secure  connec- 
tions. It  is  almost  impossible  to  make  such  connections  with  small  columns, 
and  consequently,  in  order  to  reduce  the  area  of  a  column  in  proportion  to  a 
lighter  load  to  be  carried,  it  is  better  to  reduce  the  thickness  of  the  material 
used  and  to  keep  the  general  dimensions  of  the  section  the  same. 

(6)  Adaptability  to  Fire-Proof  Covering.  Closed  sections  in  general  can  be 
more  compactly  fireproofed  than  open  sections. 

General  Considerations  Affecting  the  Choice  of  Steel  Columns.    It  is 

almost  impossible  to  say  that  any  one  of  the  foregoing  types  of  steel  columns 
is  superior  to  the  others.  Each  has  its  own  good  points,  and  the  column  whose 
section  has  theoretically  the  best  distribution  of  material  may  not  always  be 
the  best  one  to  use,  because  of  the  eccentric  loads  to  be  carried,  or  because  of 
other  conditions.  The  choice  in  most  cases  will  depend  upon  the  personal  views 
of  the  designer,  as  well  as  upon  the  local  conditions  as  to  cost  and  manufacture, 
promptness  of  delivery  and  the  details  of  the  problem.  Further  descriptions 
of  the  different  columns,  and  also  the  special  advantages  claimed  for  them,  are 
given  in  the  following  pages. 

Steel-Column  Connections.  When  steel  columns  were  first  designed  it  was 
customary  to  use  cap-plates  to  connect  the  story-lengths,  and  the  beams  or 
girders  often  rested  upon  these  plates.  In  modern  practice,  however,  the  col- 
umn-joint is  generally  placed  just  above  the  beams  and  girders  for  convenience 
in  erection  and  the  plates  are  often  omitted     The  columns  are  closely  fitted 


Types,  Forms  and  Connections  of  Steel  Columns  469 

together  with  milled  ends,  and  spHce-plates  are  riveted  to  the  sides  or  flanges 
as  shown  in  the  illustrations  of  typical  steel-column  details,  Figs.  17  and  18. 
As  it  is  impossible  in  these  pages  to  include  the  subject  of  column-connections 
in  anything  but  a  general  way,  the  only  attempt  that  has  been  made  in  this 
direction  is  to  illustrate  common  forms  of  connections  that  have  been  used  with 
different  kinds  of  columns.  These  will  be  found  in  the  description  of  columns 
in  the  following  pages. 

Number  of  Rivets  Required.  No  general  rule  can  be  given  for  the  number 
of  rivets  and  size  of  the  brackets  required  for  column-connections,  as  the  loads 
to  be  supported  vary  in  different  buildings  and  in  different  parts  of  the  same 
building.  The  number  of  rivets  required  in  each  connection  must  therefore 
be  determined  by  the  rules  given  in  Chapter  XII  for  designing  riveted  joints. 
Connections  for  single  beams,  however,  will  generally  require  the  same  number 
of  rivets  as  are  given  for  beam-connections  (Chapter  XV,  page  617).  The 
allowable  stress  for  rivets  in  column-connections  is  generally  taken  at  10  000  lb 
per  sq  in  for  single  shear  and  18  000  or  20  000  lb  per  sq  in  for  bearing.  (See 
Tables  II  and  III,  pages  418  and  419,  Chapter  XII.) 

Spacing  of  Rivets.  Steel  columns  fail  either  by  deflecting  bodily  out  of  a 
straight  line  or  by  the  buckling  of  the  metal  between  rivets  or  other  points  of 
support.  Both  actions  may  take  place  at  the  same  time,  but  if  the  latter  occurs 
alone,  it  may  be  an  indication  that  the  rivet-spacing  or  the  thickness  of  the  metal 
is  insufificient.  The  rule  has  been  deduced  from  actual  experiments  upon  riveted 
columns  that  the  distance  between  centers  of  rivets  should  not  exceed,  in  the 
line  of  stress,  sixteen  times  the  thickness  of  metal  of  the  parts  joined,  with  a 
maximum  spacing  of  6  in,  and  that  the  distance  between  rivets  or  other  points 
of  support,  at  right-angles  to  the  line  of  stress,  should  not  exceed  thirty-two 
times  the  thickness  of  the  metal.  The  usual  practice  in  designing  columns  is 
to  space  the  rivets  the  minimum  distance  on  centers  at  both  ends,  for  a  length 
equal  to  twice  the  least  dimension  of  the  column,  with  the  maximum  spacing  of 
6  in  between. 

Steel-Pipe  Columns.*  Steel-pipe  columns  are  used  for  interior  construction 
to  carry  beams  and  girders  supporting  floors,  walls  and  chimneys  in  all  classes  of 
buildings,  such  as  tenements  and  apartment-houses,  factories,  garages,  churches, 
warehouses,  etc.  A  particular  demand  for  steel-pipe  columns  is  at  the  angles 
of  show-windows  in  mercantile  buildings.  In  buildings  of  moderate  height 
the  floor-joists  are  usually  supported  by  the  side  walls  and  the  columns  have  to 
support  only  a  relatively  light  wall  above.  For  such  places  wrought-steel  pipes 
may  be  advantageously  used  for  the  columns.  They  may  be  used,  also,  for  the 
columns  supporting  the  roof  of  one-story  buildings.  In  the  Borough  of  Brook- 
lyn, New  York  City,  pipe-columns  were  formerly  calculated  by  the  formula 
S  =  14  000—  8o//r,  in  which  S,  I  and  r  have  values  as  explained  below  for  New 
York  and  Chicago  formula.  If  the  columns  are  filled  with  concrete,  the  area  of 
the  cross-section  of  the  concrete  is  multiplied  by  500  and  the  product  added  to 
the  load  supported  by  the  pipe.  (See,  also,  page  477  and  the  Tables  on  page 
516).  This  formula  gave  a  factor  of  safety  of  four.  New  York  and  Chicago 
Codes  now  use  the  formula,  S=  16000— 7o//r  in  which  S  is  the  permissible 
unit  fiber-stress,  /  the  length  in  inches  and  r  the  radius  of  gyration  of  the  cross- 
section  of  the  pipe.  This  gives  a  carrying  capacity  greater  than  the  former 
formulas     gave.       In     Philadelphia,    pipe-columns     are     allowed    to    carry 

*  Much  valuable  data  relating  to  steel-pipe  columns  was  furnished  the  editor-in-chief 
by  P.  C.  Patterson  and  J.  A.  McCullough  of  the  National  Tube  Company,  Pittsburgh, 
Pa. 


470 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


ahout  6%  more  than  is  allowed  in  New  York.  Where  pipe-columns  are  fdlcd 
with  concrete  the  cast  cap  and  base  are  secured  to  the  pipe  in  each  case  by  con- 
crete which  is  reinforced  internally  by  a  pipe  of  smaller  diameter.     Where 


Fig.  10.    Coanections,  Caps  and  Bases  for  Steel -pipe  Columns 


these  steel-pipe  columns  filled  with  concrete  are  used,  care  should  be  taken 
that  the  pipes  are  entirely  filled,  and  that  there  are  no  air-spaces  in  the  concrete. 
These  concrete-filled  columns,  sometimes  reinforced  with  smaller  pipes,  have 


Types,  Forms  and  Connections  of  Steel  Columns 


471 


a  large  carrying  capacity.  Pipe-columns  may  have  their  supporting  power 
about  doubled  in  many  cases  by  concrete  filling.  (See,  also,  paragraph  on  Lally 
Columns,  page  477).     One  type  of  steel  post-cap  used  in  connection  with  pipe. 


Fig.  11.     Connections,  Caps  and  Bases  for  Steel-pipe  Columns 


columns  to  carry  wooden  girders  is  shown  in  Figs.  62  and  63  of  Chapter  XXII. 
There  are  many  other  forms  of  cast  and  wrought  caps  for  pipe-columns.  The 
design  of  proper  caps  and  bases  is  the  most  difficult  part  of  adapting  tubular 
columns  to  practical  problems  in  building-construction.     Figs.  10  and  11  show 


472  Strength  of  Columns,  Posts  and  Struts  Chap.  14 

various  forms  of  steel-pipe  column-connections,  caps  and  bases  sufficiently  sug- 
gestive to  enable  a  designer  to  properly  develop  their  details. 

Advantages  of  Steel-Pipe  Columns.  A  wrought-steel  pipe  when  used 
as  a  column  generally  has  the  following  advantages: 

(i)  It  will  support  a  greater  load  per  square  inch  of  cross-section  than  any 
other  shapes  and  styles  of  mild-steel  columns  of  the  same  slendeeness-ratio, 
II r,  for  most  of  the  columns  of  different  slenderness-ratios  recently  tested  (1908 
and  1909)  at  the  Watertown  Arsenal. 

(2)  Its  section  has  the  greatest  possible  least  radius  of  gyration,  r,  for 
the  same  outside  diameter  and  section-area.  This  makes  pipe-columns  espe- 
cially advisable  when  it  is  desired  to  obstruct  the  view  as  little  as  possible,  as  in 
the  corners  of  show-windows,  in  balcony-supports,  etc. 

(3)  It  may  be  used  with  greater  slendcrness-ratio,  //r,  than  any  other  section 
without  reducing  the  load  per  square  inch  in  order  to  conform  to  permissible 
loading-rules,  such  as  those  of  the  New  York  City  and  the  Chicago  building 
codes. 

(4)  Its  curved  walls  permit  the  use  of  relatively  thinner  material  than  may 
be  used  with  columns  with  flat  surfaces;  that  is,  its  thickness,  /,  divided  by  the 
outside  diameter,  d,  may  be  iji  =  ^^0  with  as  great  security  from  wrinkling, 
called  also  buckling,  bulging  or  local  failure,  as  the  box  column,  which 
good  practice  of  competent  engineers  limits  to  Ho  of  the  unsupported  width 
of  flat  surfaces.  The  ratio  ild=\^v>  =^/^"/2o"  is  about  the  limit  of  practicable 
working  of  the  ordinary  lap-weld  process,  and  all  commercial  pipes  have  a  smaller 
ratio. 

(5)  Manufacturers  are  now  regularly  making  pipes  for  sizes  up  to  and  includ- 
ing 16  in  outside  diameter,  in  lengths  up  to  40  ft. 

Notes  on  the  Use  of  Steel-Pipe  Columns.  The  following  general  notes 
and  suggestions  should  be  observed  in  the  use  of  steel  pipe  for  columns: 

(i)  As  in  the  case  of  columns  of  any  construction,  it  is  obvious  that  com- 
petent designing  and  detailing  as  well  as  proper  fabrication  of  the  end-connec- 
tions for  pipe-columns  be  insisted  upon.  Otherwise  the  advantages  of  the 
circular  section  may  be  nullified. 

(2)  When  the  loading  must  be  eccentric  care  must  be  exercised  in  the  proper 
selection  and  size  of  pipe  to  be  used.  The  relative  economy  in  the  use  of  the 
circular  section,  however,  increases  with  the  length  and  slenderness  of  the  column. 

(3)  A  capital  or  base  should  never  be  screwed  to  a  pipe,  because  cutting 
the  thread  reduces  the  section.  Where  screw-threads  must  be  used,  only  the 
area  below  the  root  of  the  threads  should  be  considered  as  available  for  the  sup- 
porting power. 

(4)  The  ends  of  a  pipe  to  be  used  for  a  column  should  always  be  faced  off 
in  a  lathe,  the  facing  being  normal  to  the  general  axis.  A  pipe  should  not  be 
turned  nor  bored  in  fitting  capitals  or  bases  but,  if  possible,  the  capital  or  base 
should  always  be  forced  or  shrunk  to  an  even  bearing  on  the  faced  end  of  the 
pipe.  Where  the  capital  or  base  must  be  inserted,  it  is  hable  to  start  a  wrinkle 
or  buckle  and  the  load  should  be  adjusted  to  the  probable  lessening  of  supporting 
power.  The  bearing  surfaces  in  capitals  and  bases  should  be,  of  course,  always 
lathe-faced.  It  may  be  found  that  with  careful  foundry-work  it  is  not  neces- 
sary to  bore  the  castings;  but  it  may,  in  some  cases,  be  cheaper  to  use  relatively 
poor  foundry-work  and  bore  the  castings,  as  well  as  face  the  seats. 

(5)  Pin-ends  or  ball-and-sockrt  ends  are  generally  preferable  to  flat 
or  fixed  ends  for  a  slenderness-ratio  l/r,  of  100  or  less,  because  tests  show  that 
columns  so  fitted  usually  carry  heavier  loads  before  failure.    This  is  increasingly 


Types,  Forms  and  Connections  of  Steel  Columns 


473 


evident  as  llr  decreases.     Any  form  of  end-connection  of  column  that  may 
cause  a  flexure  from  a  falling  floor  may  endanger  the  whole  structure. 


Fig.  12.     Connections  for  Bethlehem  H  Columns 

(6)  "All  columns  should  have  sufficient  stiffness  to  safely  withstand  the 
chance  deflecting  forces  to  which  they  may  be  exposed.  This  usually  involves 
considerations  of  eccentricity  as  wefl  as  of  flexure  due  to  transverse  load. 

(7)  "It  is  desirable  to  adhere  always  to  the  trade  sizes  of  pipe  Icnown  as 
M^flCHANT,  STANDARD,  EXTRA  STRONG,  DOUBLE-EXTR4  STRONG,  CASING,  BOILER* 


474 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


TUBES,  etc.,  and  avoid  special  production  which  usually  entails  delays  and  special 
prices, 

(8)  Tables  XII  and  XIII  give  the  safe  loads  which  standard  and  extra- 
si  rong  steel-pipe  columns  are  permitted  to  carry  under  the  New  York  and 
Chicago  codes.  Philadelphia  laws  permit  slightly  greater 
loads.  Supplementary  tables  of  safe  loads  for  double- 
extra  STRONG  steel-pipe  columns  are  furnished  by  the 
manufacturer  and  may  be  useful  in  cases  where  a  mini- 
mum diameter  is  required;  but  it  should  be  remembered 
that  such  pipe  always  costs  more  per  pound,  owing  to  its 
greater  cost  of  manufacture. 

H-Beam  and  I-Beam  Struts  and  Columns.  For 
struts  and  columns  carrying  light  loads,  H  beams  and 
I  BEAMS  are  probably  the  most  economical,*  as  they 
require  very  little  riveting  except  for  the  splices  and 
connections.  Owing,  however,  to  the  narrow  flanges  of 
even  the  deepest  I  beams  it  is  not  practicable  to  rivet  very  heavy  girders  to  them; 
nor  can  they  ordinarily  be  riveted  to  the  web,  because  the  latter  is  generally  so 


1 


Fig.  13.  Section  gf 
Bethlehem  H  Column 
Showing  Variation  in 
Area 


I_ 


^ 


z 


w 


Fig.  14.     Concrete-filled  Lally  Steel  Column 


Fig.  15.     Lally  Column.     Typical 
Connections 


thin  that  too  many  rivets  will  be  required  for  the  connection.  Tables  XVII  is 
a  table  of  safe  loads  for  the  Carnegie  steel  H  beams  or  I  beams  used  as 
columns. 


Types,  Forms  and  Connections  of  Steel  Columns 


475 


Bethlehem  Columns.  As  far  as  shop-work  is  concerned  the  Bethlehem 
COLUMNS  are  just  as  economical  as  the  ordinary  H-beam  or 
I  beam  columns  as  they,  also,  are  rolled  and  not  built  up 
or  assembled.  The  only  fabrication  required  is  that  for  the 
si)lic:e-plates  and  connections.  Typical  connections  are 
shown  in  Fig.  12  from  which  the  simpHcity  of  detail  and 
small  amount  of  fabrication  required  are  apparent.  They 
are,  moreover,  superior  to  the  I-beam  columns  because  they 
afford  a  wider  flange  for  attaching  the  beams   and    girders,   besides  being 


tL   J 

Fig.  16.  Section 
of  Steel  ,Plate- 
and-angle  Column 


TYPICAL  ANGLE-COLUMN 
Bearing  on  masonry 


TYPICAL  ANGLE-COLUMN 
Bearing  on  steel 


Fig.  17.*    Connections  for  Steel  Plate-and-angle  Columns 
*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


476 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


more  economical  of  cross-section.  Bethlehem  columns  are  rolled  in  four 
sizes,  8,  lo,  12  and  14  in  in  width,  but  by  spreading  the  rolls,  as  shown 
in  Fig.  13,  the  section-area  of  each  width  can  be  increased  considerably.     The 


TYPICAL  splice; 

4:ngle-coJluma  to  Channel-col.iamB| 


TYPICAL  SPLICE 
Angl^-colnmnSj  differjeut  sizes 


TYPICAL  CHANNEL-COLUMN  TYPICAL  SPLICE 

Bearing  on  steel  Channel-columns,  different  sizes 

Fig.  18.*     Connections  for  Steel  Plate-and-channel  Columns 

section-areas  of  columns  of  the  largest  size  may  also  be  increased  by  riveting  side 
plates  to  the  flanges.  Tables  of  dimensions  and  properties  of  Bethlehem 
rolled  steel  columns  and  of  the  safe  loads  they  will  carry  are  given  in  Tables 
XVIII  to  XXI.     Although  these  columns  have  been  rolled  in  Germany  since 

*  Fronn  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 


Types,  Forms  and  Connections  of  Steel  Columns 


477 


1902,  it  was  not  until  the  establishment  in  1908  of  the  larger  improved  mills 
at  Bethlehem,  Pa.,  that  these  sections  became  available  for  use  in  this  country. 
They  are  gradually  superseding  plate-and-angle  and  box  columns,  particularly 
those  of  the  smaller  sizes. 

Lally  Columns.  Lally  columns  (see,  also,  pages  469  to  474  and  Tables  on 
page  516)  are  patented  columns  made  with  a  circular  steel  shell,  as  shown  in- 
Fig.  14,  and  filled  with  a  concrete  composed  of  sand, 
cement  and  blue  trap-rock,  and  thoroughly  com- 
pressad.  The  larger  columns  have,  in  addition,  a 
steel  reinforcement,  which  makes  a  light,  but  strong 
support.  They  are  in  many  buildings  replacing 
masonry  piers  for  supporting  girders  because  of  the 
saving  in  space,  and  are  extensively  used  in  mill- 
construction.  Typical  connections  are  shown  in 
Fig.  15.  The  Lally  formula  for  the  safe  loads  in 
tons  is  given  with  Tables  XXII  and  XXIII,  page 
516. 

Plate-and-Angle  Columns.     Four  angles  and  a 

plate    riveted    together    as    shown    in  Fig.    16  are 

now  being  extensively  used  in  building-construction; 
particularly  for  columns  having 
an  unsupported  length  of  less 
than  90  radii;  also  for  the  outer 
columns  in  steel-mill  buildings, 
and  for  light  columns  support- 
ing the  roofs  of  railway  stations, 
etc.  Columns  with  this  form  of 
cross-section  are  especially  con- 
venient for  making  beam  and 
girder-connections  and  for  splic- 
ing, and  are  also  well  adapted 
to  resist  eccentric  loads.  The 
width  of  the  plate  is  generally 
such  that  the  least  radius  of 
GYRATION  is  in  the  direction  ^2, 

and  this  radiuc  may  be  obtained  directly  from  Tables  XVI 
and  XVII,  pages  370  and  372. 


Fig.  19.     Steel   Channel- 
column  with  Lattice-bars 


Fig.  20.  Spacing 
of  Lattice-bars  in 
Channel-columns 


Pocket  Companion, 


Channel-Columns.  Typical  column-details  for  plate- 
and-angle  and  channel-columns,  taken  from  the  Carnegie 
19 1 5  edition,  are  shown  in  Figs.  17  and  18  and  represent 


current  practice  in  office-building  construction. 

Lattice-Columns.  Two  channels,  set  back  to  back,  at  such  a  distance 
that  the  radii  of  gyration  will  be  equal  about  both  axes,  and  connected  by  lattice- 
bars,  as  shown  in  Fig.  19,  make  a  very  desirable  column  for  moderate  loads,  as 
in  the  upper  stories,  or  in  buildings  of  three  or  four  stories  in  height.  For 
greater  loads,  short  cover-plates  may  be  riveted  to  the  flanges  in  place  of  the 
lattice-liars.  Such  columns  are  very  satisfactory,  especially  for  making  con- 
nections. 

Rule  for  Latticing  of  Channels  and  Angles.  When  channels  are  con- 
nected by  lattice-work,  as  in  Fig.  20,  in  order  that  there  may  not  be  a  tendency 


478 


Strength  of  Columns,  Posts  and  Struts  Chap.  14 


in  the  channels  to  bend  between  the  points  of  bracing,  the  distance  /  should  be 
made  equal  to  the  total  length  of  the  strut  multiplied  by  the  least  radius  of  gyra- 
tion of  a  single  channel,  and  the  product  divided  by  the  least  radius  of  gyration 
for  the  whole  section;   or, 

in  which  I  -  length  between  points  of  bracing; 

h  =  total  length  of  strut; 
r  =  least  radius  of  gyration  for  a  single  channel; 
n  =«  least  radius  of  gyration  for  the  whole  section. 

This  same  rule  will  also  apply  to  angles,  although  with  them  the  lattice-work 
is  generally  doubled,  as  in  Fig.  21. 


L .^ J 

Total  length=i^  ( 

Fig.  21.     Double  Lattice-bars  on  Angle-columns 


It  is  generally  found  desirable  to  make  the  distance  I  less  than  that  obtained 
by  the  above  formula.  The  inchnation  of  the  lattice-bars  with  the  axis  of  the 
column  or  strut  is  usually  about  6o°  for  single  and  45°  for  double  bars. 

The  proper  distance  for  d  or  D,  Fig.  20,  for  a  pair  of  channels,  so  that  the  radius 
of  gyration  will  be  the  same  in  both  directions,  is  given  in  Table  VIII, 
page  359. 

The  following  tabulations  are  taken  from  the  Handbook  of  the  Cambria 
Steel  Company,  1915  edition. 


Sizes  of  Lattice-Bars  to  be  Used  with  Latticed  Channel-Columns 


Dimensions  of 

Center  of 

hole  to  end 

of  bar, 

Distance  center  to 

Depth 

of 

channels 

lattice-bars 

Weight  of 

lattice-bars 

per  foot 

center  of  rivets,  d 

w 

Thickness 

a 

Maximum 

Minimum 

in 

in 

in 

lb 

in 

ft      in 

in 

6 

iH 

H 

1.28 

i'/^ 

0      iii/^ 

6^ 

7 

m 

H 

■1.49 

iH 

I        i\^ 

1% 

8 

2 

Me 

2.12 

iH 

I        3 

81  He 

9 

2 

M6 

2.12 

iM 

1         4H 

9H 

10 

2 

% 

2.55 

iH 

I         ^M 

iQiHe 

12 

2H 

H 

2.87 

m 

I       \o\^ 

13 

IS 

2H 

% 

3.19 

TYi 

2           2\(l 

15M6 

Types,  Forms  and  Connections  of  Steel  Columns  47^ 

Sizes  of  Stay-Plates  to  be  Used  with  Latticed  Channel-Columns 


Minimum  size  of  stay-plates  at 

ends  of  columns 

Weight  of 
minimum 
stay-plates 

Diameter 

of 

rivets 

oil 

pi!   . 

|0 

19 

6 

Thickness 

I 

Oj 
01 

u 

16 

|0 

in 

lb 

-< 

M 

8H 

H 

1H 

4.38 

H 

9H 

'A 

10 

6.5S 

H 

f^. 

c 

lOj.^ 

Me 

9 

8.37 

H 

itH 

Ma 

13 

II. 95 

H 

ub 

12H 

H 

13 

15.62 

H 

-*4 

t§ 

uVa 

H 

IS 

22.73 

H 

i6H 

^4 

IS 

25.90 

H 

Plate-and-Angle  and  Box  Columns.  Plate-and-angle  columns,  as  showri 
in  Fig.  16,  requiring  but  two  rows  of  rivets  are  very  economical  columns  for 
buildings  of  moderate  height,  as  they  afford  excellent  opportunities  for  connect- 
ing the  beams  and  girders.  Tables  of  safe  loads  are  given  in  Table  XXIV 
of  this  chapter.  When  a  more  compact  section  is  required  than  that  afforded 
by  the  larger  sizes,  the  section-area  may  be  increased  by  riveting  plates  to  the 
angles  as  shown  in  Fig.  22  which  is  a  section  of  one  of  the  columns  in  the  Munic- 


Fig.  22.  Heavy  Plate- 
and-angle  One-web 
Column 


Fig.  23.  Heavy  Plate- 
and-angle  Two-web 
Column 


Fig.   24.    Heavy   Plate-and-angle 
Three-web  Column 


ipal  Building,  New  York  City.  This,  however,  greatly  increases  the  expense 
of  the  shop-work,  and  it  is  therefore  usually  more  economical  to  substitute 
Bethlehem  H  columns,  or  channel  or  box  columns.  For  high  buildings  or  heavy 
loads,  where  the  required  section^  areas  of  columns  are  greater  than  can  be 
obtained  by  using  channel-columns  or  Bethlehem  columns  without  flange-plates, 
BOX  COLUMNS  made  of  plates  and  angles,  as  shown  in  Fig.  23,  which  is  one  of  the 
columns  in  the  Bankers'  Trust  Company  Building,  New  York  City,  will  prob- 
ably be  found  to  be  more  satisfactory.  The  thickness  and  number  of  web-plates  . 
and  flange-plates  can  be  varied  with  the  load  to  be  supported.  Ordinary  con- 
nections for  BOX  COLUMNS  are  the  same  as  those  for  channel-columns,  shown 
in  Fig.  18.  For  the  tallest  buildings  and  heaviest  loads  box  columns  with 
TRIPLE  WEBS  as  showu  in  Fig.  24  are  the  best.  They  are  used  in  the  highest 
buildings  erected,  such  as  the  Masonic  Temple  in  Chicago,  and  the  Bankers* 


480  Strength  of  Columns,  Posts  and  Struts  Chap.  l4 

Trust  Building,  the  Municipal  Building,  the  Wool  worth  Building  and  the  Met- 
ropoUtan  Tower  in  New  York  City.  Fig.  24  is  a  cross-section  of  one  of  the 
columns  in  the  last-mentioned  building.  Details  of  a  similar  column  used  in 
the  Bankers'  Trust  Company  Building  are  shown  in  Fig.  7  on  page  342.  It 
is  of  course  impracticable  to  give  tables  of  safe  loads  for  plate-and-angle 
COLUMNS  with  flange-plates  and  for  box  columns,  owing  to  the  great  variety  of 
combinations  that  can  be  used,  but  Example  10  of  this  chapter  shows  how  the 
columns  are  designed  and  their  strength  determined.     (See  page  485.) 

Steel  Struts  in  Trusses.  These  are  generally  made*  of  a  pair  of  latticed 
channels,  or  of  channels  aiid  plates  for  heavy  trusses  with  pin-connections,  and 
of  either  a  pair  of  light  channels  or  a  pair  of  angles  with  uneven  legs  for  light 
trusses.  For  roof-trusses  having  a  span  not  exceeding  80  ft,  a  pair  of  4  by  6  by 
^4-in  angles  is  generally  sufficient  for  any  of  the  compression-members  unless 
they  are  subjected  to  transverse  stress;  and  the  minor  struts  are  very  often 
made  of  a  pair  of  3 H  by  2 J' 2  by  H-in  angles.  The  angles  arc  placed  from  ^  to 
%  in  apart  to  permit  the  filler-plates  used  at  the  joints  to  go  between  them. 
For  compression-members  subject  to  transverse  stress  a  pair  of  channels  gen- 
erally offers  the  best  section.  If  necessary  the  channels  can  be  reinforced  by 
plates  at  the  top  and  bottom.  A  pair  of  angles,  with  a  deep  web -plate  riveted 
between,  is  often  used  for  the  principles  of  Fink  trusses  where  they  are  subject 
to  a  slight  transverse  stress.  (See,  also,  Fig.  6,  page  1146.)  For  very  light 
compressive  stresses  and  for  short  members  a  single  angle  is  sometimes  used;  but 
this  is  not  considered  good  practice,  as  it  causes  eccentric  loading  on  the  gusset- 
plates  at  the  truss-joints.  A  pair  of  small  angles,  or  some  other  combination 
with  a  symmetrical  cross-section  should  always  be  used  for  truss-members. 

Where  angles  are  used  in  pairs  they  should  be  connected  by  a  rivet  and  small 
filler-plate  or  separator  every  two  feet  in  length,  to  prevent  them  from  spring- 
ing apart.  In  regard  to  the  maximum  length  of  steel  struts  in  trusses  it  is 
not  considered  good  practice  to  use  a  strut  whose  unsupported  length  exceeds 
ISO  times  its  least  radius  of  gyration,  or  50  times  its  least  width, 

13.   Strength  of  Steel  Columns.     Formulas 

Principles  Governing  the  Resistance  of  Built-up  Steel  Columns.  Pro- 
fessor William  H.  Burr  states  *  that  "the  general  principles  which  govern  the 
resistance  of  built-up  columns  may  be  summed  up  as  follows:  the  material 
should  be  disposed  as  far  as  possible  from  the  neutral  axis  of  the  cross-section, 
thereby  increasing  the  radius  of  gyration,  r;  there  should  be  no  initial  internal 
stress;  the  individual  portions  of  the  column  should  be  so  firmly  secured  to  each 
other  that  no  relative  motion  can  take  place,  in  order  that  the  column  may  fail 
as  a  whole,  thus  maintaining  the  original  value  of  f."  The  experiments  made 
by  Professor  Burr  indicate  that  a  closed  column  is  stronger  than  an  open  one. 
It  should  also  be  remembered  that  any  column  such  as  an  I  beam,  channel,  or 
angle,  the  cross-section  of  which  has  a  maximum  and  a  minimum  radius  of 
gyration,  is  not  economical  for  use  under  a  single  concentric  load,  as  the  mini- 
mum radius  of  gyration  must  be  used  in  the  calculation,  and  part  of  the  mate- 
rial is  to  a  certain  extent  wasted  when  the  ideal  efficiency  of  the  column  is 
considered. 

Formulas  for  Steel  Columns.  A  great  many  formulas  are  used  for  cal- 
culating the  strength  of  steel  columns  and  struts,  of  the  lengths  usually  em- 
ployed in  practice,  but  scarcely  any  two  authorities  agree  upon  the  same  one. 
These  formulas  may  all  be  grouped  into  two  general  classes,  those  founded 

*  Elasticity  and  Resistance  of  the  Materi'ds  of  Engineering,  by  William  H.  Burr. 


Strength  of  Steel  Columns.     Formulas  481 

on  Rankine's  formula  *  (ii)  and  those  founded  on  the  straight-line  formula 
(12).  (See  the  following  paragraphs.)  In  the  dilTerent  formulas  different  values 
arc  assigned  to  the  arbitrary  constants.  Previous  to  1888  Rankine's  or 
Gordon's  formulas  were  almost  universally  used  for  all  columns,  although  with 
more  or  less  variation  in  the  constants  employed.  About  1885  Professor  Burr, 
after  having  conducted  a  series  of  tests  upon  full-size  column-sections  deduced 
what  is  now  known  as  the  straight- line  formula.  As  this  is  easier  of  applica- 
tion than  Rankine's  formula,  it  has  gradually  found  favor  with  engineers,  espe- 
cially as  the  results  differ  but  little  from  those  obtained  by  the  older  formula. 

Formulas  Compared.  Which  one,  of  all  the  formulas  in  use,  should  be 
employed  in  calculating  the  safe  load  for  columns  is  an  open  question,  but  the 
author,  after  careful  deliberation,  has  decided  to  recommend  Rankine's  for- 
mula for  the  following  reasons.  In  the  first  place  it  is  safe  and  conservative 
and  if  it  errs  at  all,  it  is  on  the  side  of  safety;  and  in  the  second  place  it  has  a 
wider  application,  as  the  values  assigned  to  the  arbitrary  constants  have  been 
more  generally  agreed  upon,  whereas  there  is  a  greater  variety  in  the  values  of 
the  constants  employed  in  the  straight-line  formula.  Of  course  one  is  not 
free  to  choose  when  city  laws  compel  the  use  of  certain  formulas.  No  tables  of 
safe  loads  for  columns,  satisfying  the  requirements  of  all  cities,  could  be  com- 
piled. The  author  has  accordingly  thought  it  best  to  insert  the  various  tables 
of  SAFE  LOADS  for  different  forms  of  columns  as  computed  in  the  very  latest 
handbooks  although  not  necessarily  based  upon  Rankine's  formula,  and  to 
insert  Table  XI,  specially  computed  and  giving  the  comparative  safe  loads  in 
POUNDS  PER  square  INCH  OF  METAL-AREA  for  columns,  as  determined  by  seven 
different  formulas.     (See  pages  493  to  495.) 

Formulas  Used  in  Building  Codes.  Rankine's  formula  (called  Gordon's 
FORMULA  in  many  codes)  is  specified  in  the  building  codes  of  the  following  cities: 
Philadelphia,  Boston,  Baltimore,  and  Milwaukee;  and  in  the  Cambria  hand- 
book. The  straight-line  formula  is  specified  in  the  building  codes  of  New 
York  City,  Chicago,  St.  Louis,  Minneapolis,  Washington  and  many  other  cities, 
and  is  used  in  the  Carnegie  and  Bethlehem  handbooks. 

Formulas  Used  in  Practice.  The  following  formulas,  in  the  opinion  of  the 
author,  represent  the  best  current  practice.  They  are  formulas  for  safe 
loads,  S,  in  pounds  per  square  inch  of  cross-section,  on  steel  columns  and  struts. 
In  these  formulas  /  is  the  length  of  the  column  in  inches  and  r  the  least  radius 
OF  GYRATION  of  the  cross-section.     (See,  also,  Chapter  X,  pages  333,  34^,  etc.) 

The  SAFE  LOAD,  P,  for  any  column  is  equal  to  S,  obtained  by  one  of  the  follow- 
ing formulas,  multiplied  by  the  section-area  of  the  calumn  in  square  inches; 
or  P=AS  (10) 

Rankine's  formula,  used  in  the  Cambria  handbook,  is 


12  500 


(11) 


i  +  /V36ooor2 
The  formula  recommended  by  Professor  Burr  is 

S  =  10  000  —  40  l/r  (12) 

The  formula  used  by  the  American  Bridge  Company  and  Carnegie's  Pocket 
Companion  is 

5  =  19  000  —  100  l/r  (13) 

with  a  maximum  of  13  000  lb  per  sq  in. 

*  Rankine's  formula  is  sometimes  referred  to  as  Gordon's  formula,  but  Gordon  used 
the  least  lateral  dimension  or  the  diameter  of  the  column  instead  of  the  least  radius  o| 
gyration  of  the  cross-section. 


482  Strength  of  Columns,  Posts  and  Struts  Chap.  14 

The  formula  used  by  the  American  Raihvay  Engineering  Association  and 
the  New  York  and  Chicago  building  codes  is 

5  =  i6  ooo  —  7o//r  (14) 

with  a  maximum  of  16  000  lb  per  sq  in  for  New  York  and  14  000  for  the  others. 
The  formula  used  in  the  New  York  City  building  code  previous  to  19 16  was 

5=  IS  200- 58 //r  (is) 

The  formulas  used  in  the  Catalogue  of  the  Bethlehem  Steel  Company  are 

5  =  16  000  -  SS  ^h,  for  //f  over  S5  (^6) 

and  5  =  13  000  lb  per  sq  in,  for  Ijr  under  55 

Fowler's  shghtly  modified  formula  for  steel  struts  in  trusses  is 

5  =  12  500  —  so  ^h  (17) 

The  value   so  in  Fowler's  formula  is  41%  when  /  is  in  inches,  and  soo  when  / 
is  in  feet. 

For  a  comparison  of  most  of  these  formulas,  see  Table  XI,  pages  493  to  495 
and  the  comparative  diagram  of  formulas,  page  496. 

14.   Design  of  Steel  Columns.     Examples 

Practical  Use  of  Column-Formulas.  UnUke  the  beam-formula  the  column- 
formulas  in  general  use  do  not  give  a  direct  method  of  calculating  the  dimensions 
of  a  column  that  will  support  a  given  load,  owing  to  the  presence  in  the  column- 
formula  of  two  unknown  quantities,  A  and  r,  which  are  dependent  upon  one 
another.  Hence  in  designing  columns,  the  section  must  be  first  assumed  and 
then  tested  for  the  safe  load  P,  or  for  the  maximum  unit  fiber-stress  S.  This  is 
an  apparently  roundabout  method  of  designing  columns,  but  unfortunately 
there  seems  to  be  no  more  direct  way.  When  a  column,  is  to  be  selected  or 
designed,  its  axial  load  P  is  given  and  also  its  length  and  the  condition  of  its 
ends.  A  proper  allowable  unit  stress,  5,  is  assumed,  suitable  for  the  given 
material  and  for  the  conditions  under  which  it  is  to  be  used,  or  in  accordance 
with  the  requirements  of  the  local  building  code;  or  the  value  of  S  is  given  in 
the  specification  according  to  which  the  column  is  to  be  designed.  A  cross- 
section  is  then  selected  in  accordance  with  the  principles  explained  on  pages  467 
to  469.  For  this  assumed  cross-section  A  and  r  are  determined  and  then  sub- 
stituted in  the  formula,  which  is  solved  for  P.  If  the  assumed  dimensions  give 
a  value  for  P  that  agrees  with  the  actual  load,  they  are  correct.  If,  however, 
the  resulting  value  of  P  is  smaller  than  the  actual  load,  the  assumed  size  is  too 
small,  and  it  will  be  necessary  to  choose  a  larger  size  and  solve  again.  If  on 
the  contrary,  the  actual  load  is  less  than  the  safe  calculated  load,  a  column  with 
a  smaller  element  of  cross-section  is  assumed  and  a  new  value  of  P  obtained. 
After  a  few  trials  a  size  that  gives  a  satisfactory  result  for  the  required  conditions 
will  be  found. 

Examples  Illustrating  the  Use  of  Column-Formulas  and  Tables.  Since 
the  column-tables  in  the  last  half  of  this  chapter  give  the  safe  loads  of  the  major- 
ity of  column-sections  of  current  practice,  having  determined  which  section  it 
is  most  advisable  to  use  under  any  given  conditions,  it  is  merely  necessary  to 
consult  the  tables  and  select  the  column  of  the  required  size  to  support  the  actual 
load. 

Example  7.  The  following  is  an  example  showing  the  method  of  selecting 
pETULKHEM  ROLLED  H  COLUMNS  for  buildings. 


Design  of  Steel  Columns.     Examples 


483 


Example  Showing  the  Method  of  Selecting  Bethlehem  Rolled  H  Columns 
for  Buildings 

For  illustration,  the  interior  columns  of  an  actual  sixteen-story  building  are  taken  as 
an  example.  The  story-heights  and  the  loads  on  the  columns  are  given  in  the  following 
tabulation: 


Stories 

Heights 
of 

stories , 
ft 

Loads 
on 

col- 
umns, 

tons 

Safe 
loads , 
tons 

H  column-section  required 

Dimensions 

Weights 
of  sec- 
tions, 
lb  per 
linft 

Section- 
numbers 

D, 

in 

in 

B, 

in  . 

i6th 

15th 
14th 

13th 
I2th 

nth 
loth 

9th 
8th 

7th 
6th 

5th 
4th 

3d 

2d 

ISt 

Basement 

12 

13 

14 

13 
13 

13 
13 

13 
13 

13 
13 

13 
13 

13 
15 

17 
12 

27 

53 
79 

104 
128 

151 
174 

197 
219 

241 
261 

281 
301 

321 
341 

363 
395 

55.0 
81.5 
132.2 
174.8 
219. 1 
263.8 
310- 1 
341.3 
403.5 

1% 

m 

io-% 

12H 

uM 

14')^ 
15 

15H 
1S% 

Me 
iHe 

I'Me 
iMe 
i^He 

8.00 
8.12 

10.12 

12.08 

14.08 

14.19 

14.31 

14.39 

14.54 

31.5 
48.0 

71.0- 

91. 5 

II4-5 

138.0 

162.0 

178.5 

211. 0 

H8 
H8 

Hio 

H12 

H14 

H14 

H14 

H14 

H14 

D  is  the  depth  of  the  column,  T  the  thickness  of  the  flanges  and  B  the  breadth  of  the 
flanges. 

Columns  for  buildings  are  usually  selected  in  lengths  of  two  stories.  By  inspection  of  the 
tables  of  safe  loads  for  H  columns,  it  is  found  that  no  columns  smaller  than  14-in  H  sec- 
tions have  sufficient  capacity  for  the  lower  stories.  Where  there  is  no  Umitation  as  to 
the  size  of  the  column,  the  column  with  the  largest  dimensions  and  having  the  required 
capacity  will  be  the  most  economical.  The  unsupported  length  of  a  column  should  not 
exceed  150  radii  of  gyration,  which  is  the  Hmit  of  length  for  which  safe  loads  are  given 
in  the  tables.  In  the  best  practice  the  unsupported  length  of  a  column  is  frequently 
required  not  to  exceed  120  or  125  times  the  least  radius  of  gyration;  various  Umits  for 
l/r  are  indicated  in  the  tables  by  zigzag  lines.  The  safe  loads  given  in  the  tables  are  for 
concentric  or  symmetric  loading.  When  the  loads  are  not  centrally  or  symmetrically 
applied,  the  size  of  the  column  should  be  calculated  by  Formula  (18),  page  486. 

Example  8.  Suppose  that  in  a  20-story  office-building  to  be  erected  in  Chicago, 
the  load  on  each  of  the  first-story  columns,  which  are  16  feet  in  length,  is  700 
tons.     What  columns  should  be  used? 

Turning  to  Table  XXI,  page  515,  giving  the  safe  loads  for  Bethlehem  14-in 
H  columns  it  is  seen  that  a  14-in  287,5-lb  column,  the  heaviest  rolled,  will 
support  only  549.3  tons;  this  type  of  column,  therefore,  cannot  be  used.     More- 


484  Strength  of  Columns,  Posts  and  Struts  Chap.  l4 

over  a  casual  inspection  of  the  tables  of  safe  loads  for  plate-and-angle  and 
channel-columns  shows  that  they  are  not  suitable  because  of  the  thick  flanges 
and  web-plates  required.  Consequently  the  columns  in  the  lower  stories  will 
probably  have  to  be  of  the  box  type,  with  double  or  triple  webs,  as  shown  in 
Figs.  23  and  24.  The  upper  columns,  however,  may  be  of  the  plate-and-angle 
or  channel-type,  whichever  will  be  the  more  economical.  The  heaviest  plate- 
and-angle  column,  without  flange-plates  (Table  XXIV,  page  522),  composed  of 
four  6  by  4  by  %-in  angles  and  one  12  by  y^-in  web,  will  support,  for  a  length 
of  14  feet,  the  height  of  most  of  the  upper  stories,  469  000  lb;  and  a  channel-col- 
umn (Table  XXVI,  page  541)  composed  of  two  12-in  30-lb  channels  and  two 
14  by  yi-'m  plates  will  support  502  000  lb.  The  former  weighs  125  and  the  latter 
13 1. 4  lb  per  hn  ft,  so  there  is  not  much  choice  as  far  as  economy  of  material  is 
concerned.  The  channel-column,  however,  requires  four  rows  of  rivets  while 
the  plate-and-angle  column  requires  only  two  rows,  so  this  added  expense  of 
fabrication  would  have  to  be  considered.  Assuming,  however,  that  the  plate- 
and-angle  type  is  more  desirable,  the  next  step  is  to  design  the  individual 
columns. 

The  load  upon  each  of  the  uppermost  columns,  which  are  20  ft  in  length,  is 
70000  lb.  Turning  to  Table  XXIV,  page  518,  it  will  be  seen  that  a  column 
composed  of  four  4  by  3  by  ^-in  angles  and  one  8  by  ^-in  web  will  support, 
for  a  length  of  20  ft,  77  000  lb;  but  this  load  is  below  the  lower  zigzag  line  and 
hence  the  slenderness-ratio  of  the  column  exceeds  120.  Assuming,  for  the  pur- 
pose of  illustration,  that  the  limit  of  l/r  is  120,  a  heavier  section  must  be 
selected.  On  page  519  of  Table  XXIV,  continued,  it  is  seen  that  the  lightest 
20-ft  column,  for  which  l/r  does  not  exceed  the  required  ratio,  is  one  composed 
of  four  5  by  3).^  by  %-'m  angles  and  one  10  by  %-'m  web,  and  that  for  a  length 
'  of  20  ft  it  will  support  121  000  lb,  or  51  000  lb  more  than  will  come  upon  it. 

Continuing  the  design  of  the  columns,  suppose  that  one  in  the  14th  story, 
14  ft  in  length,  supports  175  tons,  or  350  000  lb.  From  Table  XXIV,  page  522, 
it  is  found  that  a  column  composed  of  four  6  by  4  by  %-'m  angles  and  one  12  by 
J-i-in  web-plate,  for  a  length  of  14  ft,  will  carry  373  000  lb.  In  the  table,  the 
safe  load  is  calculated  by  Formula  (13),  whereas  the  Chicago  Building  Code 
specifies  Formula  (14).  Hence,  as  this  building  is  to  be  erected  in  Chicago,  the 
chosen  column  must  be  tested  by  the  latter  formula.  Its  A  is  29.44  sq  in  and 
its  least  r,  2.65  in.  To  test  it  by  the  formula,  /  =  14  ft  X  12  =  168  in,  and  l/r  = 
168  in/2.65  in  =  63.  Substituting  in  Formula  (14),  S  =  16000  —  (70  X  63)  = 
16  000— 4  410  =11  590  lb  per  sq  in.  From  Formula  (10),  the  safe  load  for  the 
column,  P  =  AS  =  29.44  sq  inX  11  590  lb  per  sq  in  =  341  209  lb,  which  is  less 
than  the  actual  load.  Therefore,  the  next  heavier  column,  with  angles  ^He  in 
thick,  should  be  selected. 

Example  9.  In  an  ofiice-building  to  be  erected  in  Philadelphia,  the  use  of  the 
Bethlehem  rolled-steel  H  columns  has  been  decided  upon.  One  of  these  col- 
umns, 15  ft  in  length,  supports  170  000  lb,  or  85  tons.  What  should  be  the  size 
of  this  column? 

According  to  Table  XIX,  page  508,  giving  the  safe  loads  for  Bethlehem  col- 
umns, a  lo-in  49-lb  column,  15  ft  in  length,  will  carry  86.3  tons,  an  apparently 
safe  load.  Bethlehem-column  loads,  however,  are  calculated  by  the  straight-line 
formula,  whereas  in  Philadelphia,  Rankine's  (called  Gordon's)  formula  is  the 
standard.     This  formula  with  the  arbitrary  constants  inserted  is 

S  =       ■  ^    ^^^ (See  Table  XI,  page  493-) 


I  +  • {l/rp 


Eccentric  Loading  of  Steel  Columns  485 

From  Table  XIX,  A  =  14.37  sq  in  and  the  least  r  =  2.49  in;  /  is  15  ft  or  180  it? 

l/r=  180  in/2.49  in=  72.3. 

Substituting  in  the  formula, 

16  250  16  250  16  250 

I  1  +  5  227/11  000       16  227/11  000 

iH (72.3r 

II  000 

16  250X11  000       178750000 
— = .  ==  jj  015  lb  per  sq  m 

16  227  16  227 

and  from  Formula  (10),  page  481, 

P  =  AS  =  14.37  sq  in  X  II  015  lb  per  sq  in  =  158  285  lb  or  79.1  tons, 

which  is  less  than  the  tabular  load.     Hence  the  next  heavier  column,  weighing 
54  lb  per  sq  ft,  would  have  to  be  used. 

Example  10.  Figure  7,  page  342,  shows  the  cross-section  of  one  of  the 
basement-columns  in  the  Bankers'  Trust  Company'sBuilding,  New  York  City. 
It  is  20  ft  in  length  and  supports  2  230  tons.     Is  the  column  safe? 

The  first  step  is  to  find  its  least  radius  of  gyration  which  is  equal  to  V//.4. 
The  least  moment  of  inertia  of  this  section  was  found  to  be  17  030.  (See  page 
343.)     The  area  is  made  up  as  follows: 

Flanges.  The  flanges  are  composed  of  six  27  by  %-in  plates 
and  two  27  by  iMe-in  plates.  The  area  of  the  cross-section  of 
each  27  by  %-m  plate  is  20.25  sq  in  and  of  the  six  plates,  121.50  sq 
in.  The  area  of  the  section  of  each  27  by  iHe-in  plate  is  18.56 
sq  in  and  of  the  two  plates,  37.12  sq  in.  Hence  the  total  sectional 
flange-area  is  121.50+ 37.12  =  158.62  sq  in 

Flange-angles.  Each  flange-angle  is  6  by  6  by  ^Vie  in.  Its 
section-area  is  10.38  sq  in.     Hence  for  the  four,  A  =  10.38  X  4  =         41.52  sq  in 

Outer  Web.  The  outer  web-plates  are  each  18  by  iMs  in. 
The  area  of  each  one  is  12.375  sq  in  and  of  the  eight  99.00  sq  in 

Web.  Each  web-angle  is  6  by  3!/^  by  i^e  in  with  a  section- 
area  of  8.03  sq  in;  and  for  four  angles  the  section-area  is  32,12  sq  in 

Web.  The  web  is  composed  of  two  18  by  ^le-in  plates,  each 
with  a  section-area  of  10.125  sq  in.     For  two  the  area  is  20.25  sq  in 

The  area  of  the  entire  section,  therefore,  is  35151  sq  in 

^2  =  7/^  =  17030/351.5  =  48.5    and    r=V48.5  =  7in 
/  =  20  ft  =  240  in  and  l/r  =  240  hi/7  in  =  34.3 
Substituting  in  the  former  New  York  City  building  code  Formula  (15),  page  482, 

S  --=  1$  200-  58  X  34-3  =  15  200—  1989  =  13  211  lb  per  sq  in 
From  Formula  (10) 

P  =  AS  =  351.5  sq  inX  13  211  lb  per  sq  in  =  4643  666  lb,  or  2  321  tons. 
Hence  the  column  is  perfectly  safe. 

15.   Eccentric  Loading  of  Steel  Columns 

General  Principles.  Where  columns  are  used  in  tiers,  one  above  another, 
the  beams  and  girders  which  they  support  must  necessarily  rest  upDii  brackets 
projecting  or  extending  varying  distances  beyond  the  shell  or  section-areas  or 
axes  of  the  columns.  Such  connections  cause  BEisrorNG  moments  in  the  columns. 
When  equal  loads  are  applied  at  equal  distances  on  opposite  sides  of  a  column. 


486 


Strength  of  Columns,  Posts  and  Struts  Chap.  14 


the  bending  moments  caused  by  them  in  the  column  balance  each  other,  and 
the  CENTER  OF  STRESS  may  be  considered  as  coinciding  with  the  axis  of  the 
column.  When,  however,  a  load  is  applied  on  one  side  (Fig.  25)  without  a 
corresponding  load  on  the  opposite  side,  it  is  called  an  eccentric  load  and  the 
area  of  the  cross-section  of  the  column  should  be  increased  correspondingly. 
There  is  unfortunately  no  direct  method  by  which  this  additional  area  can  be 
determined.  The  usual  method  of  procedure  is  to  assume  a  section  in  excess 
of  that  required  to  support  the  total  load  and  then  compute  the  fiber-stress  due 
to  the  combined  balanced  and  eccentric  loads.  If  this  works  out  too  large 
or  too  small  another  trial  is  made. 

Formula  for  Eccentric  Loads  on  Steel  Columns.    The  following  formula 
(compare  with  Fig.  25)  is  used  to  determine 
the  combined  fiber-stresses  due  to  the  concen- 
trie  and  eccentric  loads  (See,  also,  page  453): 
Let     P  =^  the  concentric  or  balanced  load  in 
pounds. 
Pi  =  the  eccentric  load  in  pounds, 
M  =  the   bending   moment    due    to   the 
eccentric  load  in  inch-pounds  =  Pix, 
X  =  the  eccentricity  of   the  load  Fi  in 

inches.     (See  note  below.) 

I  =  the  moment  of  inertia  of  the  area 

of  the  cross-section  of  the  column 

about  an  axis  at  right-angles  to  the 

direction  of  the  bending, 

c  =  the  distance  of  the  outermost  fiber  in 

the  cross-section  from  the  same  axis, 

A  =  the  area  of  column-section  in  square 

inches  and 
S  =  the  actual  fiber-stress  in  pounds  per 
square  inch 


Fig.    25.     Channel-column    with 
Eccentric  Load.     Elevation 


Then 


S={P-{-PO/A-hMc/I 


(18) 


Note.  In  measuring  the  eccentricity,  the  distance,  x,  is  generally  measured 
from  the  axis  of  the  column  to  the  center  line  or  half-breadth  line  of  the  bracket 
or  bearing. 

Examples  of  Eccentric  Loading  of  Steel  Columns.     The  following  ex- 
amples illustrate  the   use  of   the  formula  and 
tables  in  determining  the  safe  eccentric  loads  } 

for  steel  columns. 

Example  11.  The  total  load  on  the  top  of  a 
column  32  ft  in  length  is  194  000  lb,  of  which 
30  000  lb  come  from  the  end  of  a  girder.  There 
is  no  corresponding  load  on  the  opposite  side. 
(See  Fig.  26.)  It  is  proposed  to  use  a  channel- 
column.  What  is  the  size  of  the  required 
column? 

By  referring  to  Table  XXVI,  page  539,  it  is 
seen  that  a  column  composed  of  two  12-in 
20.5-lb  channels  and  two  14  by  ^i-in  plates  will  support,  for  a  length  of  32 
ft,  227  000  lb,  a  somewhat  greater  load  than  will  come  on  the  column.  For 
the  sectioii  of  this  column,  /»-2=  41S,  A  =  22.56  sq  in,  r  =  4.29  in  and  l/r  ** 


Fig, 


26.     Channel -column    with 
Eccentric  Load.     Section 


Eccentric  Loading  of  Steel  Columns  487 

384/4.29  =  89.     Substituting  in  Formula  (ii),  page  481,  to  find  the  safe  unit 
fiber-stress 

12500  12500  12500  12500 


I    ///  ^9   I +(89)^36  000    I -1-7  921/36  000  ~*  43  921/36  000 

36000 

12500X36000      450000000  „ 

=s •  =  =  10  245  lb  per  sq  in 

43921  43921 

The  actual  stress  in  pounds  per  square  inch  of  the  column-section  is  found 
by  Formula  (18),  5  =  (P  +  Px)lA  +  Mcjl.  P  =  164  000  lb,  Pi  =  30  000  lb, 
A  =  22.56  sq  in  and  M  =  Pio;  in-lb.  x=  the  distance  in  inches  from  the  axis 
2-2  of  the  column  to  the  outside  of  the  web,  plus  the  distance  from  the  outside 
of  the  web  to  the  center  of  the  bracket.  The  former  distance  can  be  found  from 
Table  XXVI.  It  is  4  in.  Let  the  distance  from  the  outsldq  of  the  web  of  the 
channel  to  the  center  of  the  bracket  riveted  to  the  web  of  the  channel  be  2  in, 
the  projection  of  the  bracket  being  4  in;  then  x,  the  lever-arm  of  the  moment  of 
the  load  Pi,  or  the  eccentricity,  is  4  in  4-  2  in  =  6  in.  M,  therefore,  is  Pix  or 
30000  lb  X  6  in.  c  is  7  in,  since  the  plates  are  14  in  wide.  I2-2  =  415.  Sub- 
stituting in  Formula  (i8) 

■  164000+30000        30000X6X7        oc        I  c  c   ciu  .       ' 

5  = 1 =  8  5qq  ^  2  036  =  II  636  lb  per  sq  m  , 

22.56  415  >.  7t)u 

As  this  exceeds  the  safe  unit  fiber-stress  of  10  245  lb  per  sq  in,  the  column- 
section  is  too  small. 

For  a  second  trial,  consider  a  12-in,  20.5-lb  channel-column  with  14  by  ^^-in 
plates.  For  this  section,  /2— 2  =  473,  A  =  26.06  sq  in,  rz— 2 «  4.26  in  and  l/r  ^ 
384/4.26  =  90. 

„ 12  500         "  12  500  1250Q 

I +(90)2/36  000      1  +  8100/36000      44100/36000 

12500X36000  ,, 

= .  —  JO  204  lb  per  sq  in. 

44 100  ■ 

The  actual  stress  from  Formula  (18),  as  before,  is 

164OOO+3OOOQ         30000X6X  7  ,        ^^  '      OIU 

o  =  — ■  i ■  =  7  444  +  2  664  =  10  108  lb  per  sq  in 

26.06  473  - 

As  this  is  less  than  the  safe  stress  of  10  204  lb,  the  second  selection  is  safe. 

Example  12.  A  Bethlehem  H  column  14  ft  long  carries  90.56  tons,  of  which 
15.52  tons  are  eccentric,  being  apphed  to  the  flange  of  the  column  as  shown 
in  Fig.  27,  the  distance  from  the  outside  of  the  flange  to  the  center  of  the 
bearing  being  2  in.     What  is  the  size  of  the  column  required? 

Try  a  12-in,  84.5-lb  column,  which,  for  a  length  of  14  ft,  or  168  in,  will  carry 
161.4  tons  (Table  XX).  For  this  column,  A  =  24.92,  ^2— 2  =  3.03,  /i— 1  =  676.1, 
72-2  =  228.5  and  /  is  14  ft,  or  168  in;  hence  l/r  =  168/3.03  =  55.  Substituting 
in  Formula  (15),  assuming  that  that  formula  is  specified,  5  =  15  200  —  58  X55  == 
12  010  lb  per  sq  in.  Since  the  eccentric  load  causes  bending  in  a  direction  at 
right-angles  to  the  axis  i-i.  Fig.  27,  the  bending  moment  due  to  the  eccentric 
load  is  Pi,  or  15.52  tons  or  31  040  lb,  multiplied  by  its  lever  arm  x,  which  is  the 
distance  from  the  axis  i-i  to  the  outside  of  the  flange  plus  the  distance  from 
this  surface  to  the  center  of  bearing.  The  former  dimension,  taken  from  the! 
Bethlehem  Catalogue,  is  6H6  in  and  the  latter  is  2  in;  hence  x  =  8H6  in  dr  fdr 
convenience,  8  in.     The  distance,  c<  also,  of  the  outermost  fiber  Irom  ih^  ^pps 


488  f 


Strength  of  Columns,  Posts  and  Struts  Chap.  14 


i-i  is  6M«  in,  which  for  convenience  will  be  considered  6  in.    /i— i  about  the 
axis  i-i  is  676.1.     Substituting  in  Formula  (i8-),  5  =(150  080+  31  040)724.92  + 

(31  040  X  8  X  6)/676.i  =  7  268  +  2  204  =  9  472 
lb  per  sq  in.  As  this  is  far  below  the  safe 
stress  of  12  010  lb,  the  column  selected  is 
too  large,  and  a  smaller  one,  probably  a  12-in 
64.5-lb  column  would  prove  sufficient. 

Suppose,  on  the  other  hand,  the  eccentric 
load  were  applied  to  the  web  and  the  balanced 
loads  to  the  flanges.  The  safe  unit  fiber- 
stress,  as  before,  is  12  010  lb  per  sq  in,  for 
no  matter  how  the  loads  are  applied,  the  safe 
unit  stress  determined  by  reference  to  the 
least  radius  of  gyration,  ri—i,  should  not  be 
exceeded.  Under  the  second  condition  of 
loading  the  eccentric  load,  also,  will  cause 
bending  about  this  same  axis  2-2;  hence  in 
Formula   (^)  the  1  for  this  axis,  which  is 


Fig.  27. 


Bethlehem  H  Column  with 
Eccentric  Load 


228.5,  must  be  used,  a;  =  2  in +0.25  in  = 
2.25  in,  0.25  in  being  one-half  the  thickness 
of  the  web.  (See  the  Bethlehem  Catalogue.)  Hence,  from  Formula  (18),  the 
actual  unit  fiber-stress  is  6*  =  (150080 +31 040)724.92+  (31  040X6X2.25)7228.5 
=  7  268+  I  835  =  9  103  lb  per  sq  in. 


16.   Tables  of  Safe  Loads  for  Steel  Columns 

Safe  Loads  per  Square  Inch  of  Metal-Area  for  Steel  Columns  and 
Struts.  To  lessen  the  labor  of  calculating  the  strength  of  steel  columns  and 
struts,  of  whatever  shap3,  the  author  has  computed  Table  XI,  which  gives  safe 
VALUES  of  S  for  ratios  of  llr  varying  from  30  to  120.  For  ratios  of  Ijr  which  are 
not  whole  numbers,  the  values  can  be  readily  interpolated.  The  values  in  this 
table  should  correspond  exactly  with  the  results  obtained  by  using  the  corre- 
sponding formulas. 

Safe  Loads  for  Steel-Pipe  Columns.  Tables  XII  and  XIII  give  the  safe 
LOADS  for  STEEL-PIPE  COLUMNS.  These  loads  are  based  upon  the  formula  recom- 
mended by  the  New  York  and  Chicago  Codes,  5  =  16  000—70  llr.  (See  Steel- 
Pipe  Columns,  pages  469  to  474.) 

Safe  Loads  for  Channel  and  Angle-Struts.  Tables  XIV,  XV  and  XVI 
give  the  safe  loads  for  standard  CHAt^fNELS  and  angles  used  as  struts.  Only 
those  sizes  that  are  most  commonly  used  are  given.  In  Table  XIV  the  safe 
LOADS  for  both  the  minimum  and  the  maximum  radius  of  gyration  are  given. 
If  the  strut  is  used  also  as  a  beam,  or  is  stayed  so  that  it  cannot  bend  sidewise, 
the  larger  value  may  be  taken;  but  if  free  to  bend  in  either  direction,  then  the 
smaller  value  should  be  taken.  If  the  struts  are  subjected  to  a  transverse 
stress  they  should  be  computed  as  explained  under  the  heading  Strut-Beams, 
pages  571  and  572. 

Safe  Loads  for  Steel-Beam  Columns,  Bethlehem  Columns,  Lally  Col- 
umns, Plate-and-Angle  and  Channel  Columns.  Tables  XVII  to  XXVII, 
givinsj  the  safic  loads  for  these  columns,  were  not  computed  by  the  author, 
but  by  the  different  manufacturers;  they  are,  however,  believed  to  be  perfectly 
safe,  provided  that  an  increase  in  area  is  made  for  eccentric  loads. 

Use  of  Table  XI  for  Determining  Safe  Loads  for  Steel  Columns. 
This  table  will  be  found  of  great  assistance  in  calculating  the  strength  of  col- 


Tables  of  Safe  Loads  for  Steel  Columns  4SS 

limns  and  of  struts  and  also  in  making  calculations  for  eccentric  loads.  To  use 
it  to  find  the  strength  of  a  column,  it  is  merely  necessary  to  multiply  the  value 
corresponding  to  the  slenderness-ratio  of  the  column,  by  the  section-area, 
the  result  being  the  safe  load  the  column  can  support.  As  an  illustration  of 
this,  the  column  considered  in  Example  8  has  a  slenderness-ratio  of  63  and  a 
section-area  of  29.44  sq  in.  Its  strength  is  to  be  calculated  by  the  Chicago 
Building  Code  formula,  the  results  of  which  are  tabulated  in  the  sixth  column 
of  Table  XL  From  this  the  value  of  a  slenderness-ratio  of  63  is  11  590  lb 
per  sq  in.  Therefore,  by  the  rule  stated  above,  the  safe  load  is  11  590  lb  per 
sq  in  X  29.44  sq  in  =  341  209  lb.  In  Example  10,  the  column  in  the  Bankers* 
Trust  Company  Building  has  a  slenderness-ratio  of  34.3,  and  an  area  of 
351.5  sq  in.  The  value  corresponding  to  34,  from  column  5  of  Table  XI, 
is  13  228  and  for  35  it  is  13  170  lb  per  sq  in;  hence  for  34.3  it  would  be  about 
13  2 1 1  lb  per  sq  in.  Accordingly,  the  safe  load  is  13  2 1 1  lb  per  sq  in  X35 1 .5  sq  in 
=  4  643  666  lb.     Column  5  of  Table  XI  gives  values  for  old  New  York  code. 

Example  13.  What  is  the  safe  resistance  of  a  strut  composed  of  two  s-in 
9-lb  channels,  separated  %  in  aij^  free  to  bend  in  either  direction,  the  length  of 
the  strut  being  7  ft  6  in? 

Solution.  From  Table  XVIII,  page  374,  the  least  radius  of  gyration  for  this 
section  is  i,  hence  l/r=  90/1  =  90.  From  the  eighth  column  of  Table  XI,  the 
value  of  S  opposite  90  is  8  000  lb  per  sq  in;  the  safe  load,  then,  is  equal  to  8  000  lb 
per  sq  in,  multiplied  by  the  area  of  the  two  channels,  5.3  sq  in,  or  42  400  lb. 

Example  14.  What  is  the  safe  stress  for  a  7-in  15-lb  I  beam  when  used  as 
a  strut?     It  is  90  in  in  length  and  free  to  bend  in  either  direction. 

Solution.  From  Table  IV,  page  355,  the  least  radius  of  gyration  of  this  sec- 
tion is  0.78,  and  the  area  is  4.42  sq  in.  l/r  =  90/0.78  =  115.4.  From  the  eighth 
column  of  Table  XI,  the  value  opposite  115  is  6  750  and  opposite  116  it  is  6  700 
lb  per  sq  in;  so  for  115.4  it  would  be  about  6  730  lb  per  sq  in.  The  safe  lead, 
therefore,  is  6  730  lb  per  sq  in  X  4.42  sq  in  =  29  746  lb. 

By  means  of  the  tables  and  rules  given  in  Chapter  X  the  section-area  and 
LEAST  radius  OF  GYRATION  of  any  Standard  section  or  any  combination  of  sec- 
tions may  be  found;  and  once  these  arc  determined  the  strength  of  a  strut  or 
column  may  be  readily  computed,  as  in  the  above  examples.  

Use  of  Table  XI  for  Eccentric  Loads  for  Steel  Struts.  A?  an  illustra- 
tion of  its  application  to  determine  eccentric  loads,  refer  again  to  Example  11. 
The  value  of  l/r  for  this  column  is  89.  The  safe  unit  fiber-stre^  was  found  to  be, 
by  Formula  (11),  10245  lb  per  sq  in.  The  practically  identical  result  can  be 
obtained  by  looking  for  the  value  opposite  89  in  column  2  of  Table  XI.  It  is 
found  to  be  10  250  lb. 

Proportion  of  Floor-Loads  Borne  by  Columns.  (See,  also,  pages  148 
to  152.)  In  tall  buildings  it  is  customary  to  reduce  the  column-loads  some- 
what fro.n  the  loads  used  in  calculating  the  floor-beami.  This  is  done  on  the 
theory  that  it  is  quite  impossible  for  the  entire  floor-area  of  every  story  to  be 
loaded  to  the  maximum  limit  at  the  same  time.  For  all  buildings  except  ware- 
houses it  would  seem,  in  general,  to  be  good  practice  to  design  the  columns  to 
carry  all  the  dead  load  and  75%  of  the  assumed  live  load.  Of  course  city 
laws  vary  in  these  requirements.  Thus,  if  in  an  office-building,  the  dead  load, 
or  weight  of  the  floor-construction,  is  80,  and  the  live  load  80  lb  per  sq  ft,  the  load 
on  the  columns  would  be  8o-|-  60=  140  lb  per  sq  ft  times  the  floor-area  sup- 
ported by  the  column.  In  some  cases  the  reduction  might  be  even  greater, 
depending  upon  the  live  load  assumed  and  the  position  of  the  column  in  the 
building,  the  reductions  being  greater  in  the  lower  than  in  the  upper  stories. 


490 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


The  Building  Code  of  New  York  City  specifies  that  for  buildings  exceeding 
five  stories  in  height  the  column-loads  shall  be  made  up  as  follows:  For  the 
roof  and  top  floor  the  full  Uve  loads  shall  be  used;  for  each  succeeding  lower 
floor  it  shall  be  permissible  to  reduce  the  live  load  by  s%  until  50%  of  the  live 
load  is  reached,  when  such  reduced  loads  shall  be  used  for  all  remaining  floors. 
(For  assumed  loads  for  ofiice-buildings,  required  by  the  building  codes  of  sev- 
eral cities,  see  page  151). 

Column-Sheets.  In  a  high  building  the  column-loads  vary  to  such  an 
extent  and  are  made  up  of  so  many  elements,  that  to  avoid  omissions  and  errors 
it  is  necessary  to  make  a  tabulated  list  of  all  the  loads  transferred  through 
the  columns  to  the  footings.  In  a  building  of  skeleton  construction  the  column- 
loads  include  floor  and  roof-loads,  wind-loads,  spandrel  and  pier-loads,  the 
weight  of  the  columns  themselves  and  their  fire-proof  covering,  and  in  some  cases 
special  loads,  such  as  tanks,  vaults,  safes  and  elevator-loads.  In  tabulating 
the  floor-loads  it  is  advisable  to  separate  the  dead  and  live  loads  for  con- 
venience in  proportioning  the  footings.  (See,  also,  pages  148  to  160.)  Formulas 
for  computing  the  wind-loads  on  columns  are  given  in  Chapter  XXIX;  these 
loads,  also,  are  considered  as  Hve  loads.  Eccentric  loads  should  always  be 
tabulated  separately  from  the  balanced  column-loads.  On  page  491  is  shown 
a  form  of  column-sheet  which  combines  all  ordinary  requirements.  The 
total  load  for  each  story  is  the  sum  of  all  of  the  loads  above.  The  schedule 
on  page  492  shows  a  very  convenient  form  for  column-lengths  and  column-parts. 

Important  Notes  Regarding  Safe  Loads  on  Columns.  (See  pages  504  and 
505,  and  517  to  554.)  "For  ratios  of  Ih  up  to  120  and  for  greater  ratios  up  to 
200,  use  the  values  given  in  the  following  table  for  the  allowable  stress  in 
pounds  per  square  inch.     For  intermediate  ratios,  use  proportional  amounts."* 


Ratio 

Amount 

Ratio 

Amount 

60 

13000 

130 

6  500 

70 

12  000 

140 

6oo<} 

80 

II  000 

ISO 

5  500 

90 

10  000 

160 

Sooo 

100 

9  000 

170 

4500 

no 

8000 

180 

4000 

120 

7  000 

190 

3SOO 

"(s).  For  bracing  and  combined  stresses  due  to  wind  and  other  loading, 
the  permissible  working  stresses  may  be  increased  25  per  cent,  provided  the 
section  thus  found  is  not  less  than  that  required  by  the  dead  and  live  loads 
alone.* 

"(6).  General.  The  effective  or  unsupported  length  of  main  compression 
members  shall  not  exceed  120  times,  and  for  secondary  members  200  times,  the 
least  radius  of  gyration."* 

The  values  for  ratios  of  Mr  above  120  are  computed  from  the  formula 

5=  13  000— 50 //r, 

but  the  important  condition  should  be  observed,  that  for  //r  above  120,  com- 
pression-members should  never  be  used  for  main  members  but  only  as  secondary 
members  subject  to  wind-stresses,  etc.  (See,  also,  page  495  for  minimum  ratio 
of  II r  for  main  members  and  for  secondary  members,  such  as  bracing  struts,  etc.) 

*  From  the  Construction  Specifications  of  the  American  Bridge  Company. 


Column-Sheets 
Form  of  Column-Sheet 


491 


Story 

Character  of  loading 

Column  No.  i 

Column  2 

Load  on 

column, 

concentric 

Load  on 
column, 
eccentric 

1     i8th 
top 

Roof  and  ceiling,  dead  load 

Roof  and  ceiling,  live  load 

Masonry  piers 

Spandrels,  cornice,  etc 

Elevators 

Tanks 

Column  and  casing 

Wind-load 

Total 

Sectional  area  required 

sq  in 

sq  in 

;    17th 

From  column  above.* 
Floor,  dead  load 

Floor,  live  load 

Masonry  piers 

Spandrels 

Safes,  vaults,  etc 

Column  and  casing 

Wind-load 

Total 

Sectional  area  required 

sqin 

sqin 

1    Base- 
;    ment 

i 

From  column  above.* 
Floor,  dead  load 

Floor,  live  load 

Masonry  piers 

Spandrels 

Sidewalk' 

Column  and  casing 

Wind-load 

Total 

Footings 

Sectional  area  required 

sq  in 

sqin 

Deduct  m)  live  load , 

Total  footing-load 

Area  of  footing  required 

•      sqft 

*  In  bringing  down  the  load  from  the  column  above,  the  eccentric  loads  may  be  added 
to  the  concentric  loads  and  their  sum  placed  in  the  first  column. 


492 


Strength  of  Columns,  Posts  and  Struts 
Schedule  of  Column-Lengths  and  Parts 


Chap.   14 


Column  No.  i 

Column  No.  2 

Roof -line 

• 

Top  of  columns 

t 
i 

7th  story 
7th  Floor-line 

23' 

x^ 

Xox 

4"             >X 

• 

6th  Story 
6th  Floor-line 

0   ^ 
^0 

i      >< 

Sth  Story 
1       5th  Floor-line 

13' 
- 

\^X 

0  c 

t 

4H" 

i 

ist  Floor-line 

r     T 
I 

Basement 
Top  of  stool 

11' 

xx 

Grade  15.0 

T             Si" 
8H-         .    £S 

Tables  of  Safe  Loads  for  Steel  Columns 


493 


Table    XT.     Safe   Loads    in   Pounds   per    Square   Inch  of  Metal   Area  for  Steel 

Columns  and  Struts 

/  =  length  in  inches  r  =  least  radius  of  gyration  in  inches 


Mr 

Rankine' s 
(Gor- 
don's) 
and 
Cambria 

Phila- 
delphia 

Boston 
Code 

Wash- 
ington, 
D.  C* 

Chi- 
cago t 

and 
N.  Y. 

n\ 

§  .^  >^ 

Am. 

Bridge 

Co.  and 

Carnegie 

Fowler's 

formula 

for 

struts 

l/r 

8 

- 

0 

CO 

h 

0 

•0 

- 

- 

<o 

0 

00 

7 

8 

0  CO 

"o 

1 

8 

■    H 

x: 

M 

M 

I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

30 

12 195 

15020 

15  310 

13460 

13900 

13000 

II  000 

30 

31 

12  170 

14945 

1526s 

13402 

13830 

13000 

10950 

31 

32 

12  155 

14865 

15220 

13344 

13760 

13000 

10  900 

32 

33 

12  135 

14785 

15 175 

13286 

13  690 

13000 

10850 

33 

34 

12  no 

14705 

15 125 

13228 

13620 

13000 

10  800 

34 

35 

12090 

14  620 

15075 

13 170 

13550 

13000 

10750 

35 

36 

12065 

14535 

15025 

13 112 

13480 

13000 

10700 

36 

37 

12045 

14450 

14975 

13054 

13  410 

13000 

10650 

37 

38 

12  020 

14365 

14925 

12996 

13340 

13000 

10600 

38 

39 

II  995 

14275 

14  870 

12938 

13270 

13  000 

10550 

39 

40 

II  970 

14  185 

14  815 

12880 

13200 

13000 

10  500 

40 

41 

II  945 

14095 

14760 

12822 

13 130 

13000 

10450 

41 

42 

II  920 

14005 

14705 

12764 

13060 

13000 

10  400 

42 

43 

II  890 

13  915 

14650 

12  706 

12990 

13000 

10350 

43 

44 

II  860 

13  820 

14590 
14530 

12648 

12  920 

13  000 

10  300 

44 

45 

II  835 

13725 

12590 

12  850 

13000 

10250 

45 

46 

II  805 

13630 

14470 

12532 

12780 

13000 

10  200 

46 

47 

II  780 

13535 

14  410 

12474 

12  710 

13000 

10  150 

47 

48 

II  750 

13440 

14350 

12  416 

12640 

13000 

10  100 

48 

49 

II  720 

13340 

14285 

12358 

12570 

13000 

10  050 

49 

SO 

II  690 

13240 

14220 

12  300 

12500 

13000 

10  000 

50 

51 

II  660 

13  145 

14  160 

12  242 

12430 

13000 

9950 

51 

52 

II  620 

13045 

14095 

12 184 

12  360 

13000 

9900 

52 

S3 

II  595 

12945 

14030 

12 126 

12  290 

13000 

9850 

53 

54 

II  565 

12845 

13965 

12068 

12  220 

13000 

9800 

54 

55 

II  530 

12745 

13900 

12  010 

12 150 

13000 

9750 

55 

S6 

II  500 

12645 

13835 

II 952 

12  080 

13000 

9700 

56 

57 

II  465 

12545 

13770 

II 894 

12  010 

13  000 

9650 

57 

58 

II  430 

12445 

13700 

II 836 

II 940 

13000. 

9600 

58 

59 

II  400 

12345 

13630 

II 778 

II 870 

13  000 

9550 

59 

60 

II  365 

12  240 

13560 

II 720 

II 800 

13000 

9500 

60 

61 

II  330 

12  140 

13490 

II 662 

II 730 

12900 

9450 

61 

62 

II  295 

12  040 

13420 

II 604 

II 660 

12  800 

9400 

62 

63 

II  260 

II  940 

13350 

11546 

II 590 

12700 

9350 

63 

64 

II  225 

II  840 

13280 

II 488 

II 520 

12  600 

9300 

64 

65 

II  185 

II  740 

13  210 

II 430 

II 450 

12  500 

9250 

65 

66 

II  150 

II  640 

13  140 

II 372 

II 380 

12  400 

9  200 

66 

67 

II  115 

II  540 

13070 

II 314 

II 310 

12300 

9150 

67 

68 

II  080 

II  440 

13  000 

II 256 

II 240 

12  200 

9100 

68 

69 

II  040 

II  340 

12925 

II 198 

II 170 

12  100 

9050 

69 

*  Also  Atlanta,  Ga.,  Jersey  City,  N.  J.,  Newark,  N.  J.,  Paterson,  N.  J.,  Worcester, 
Mass.,  and  old  New  York  Code. 

t  Am.  R'y  Engrg.  Ass'n  the  same  up  to  Ifr,  100,  for  main  members.     Maximum,  14  000. 


Strength  of  Columns,  Posts  and  Struts 


Table  XI  (Continued). 


/  =  length  in  inches 


Safe  Loads  In  Pounds  per  Square  Inch  of  Metal-Area 
for  Steel  Columns  and  Struts 

f  =  least  radius  of  gyration  in  inches 


Rankine's 
(Gor- 
don's) 
and 

Cambria 

Phila- 

Boston 

Wash- 
ington, 
D.  C* 

Chi- 
cago! 

Am. 
Bridge 

Fowler's 
formula 

delphia 

Code 

and 

Co.  and 

for 

l/r 

N.  Y. 

Carnegie 

struts 

l/r 

•. 

>» 

K 

K 
\ 

0  0  0 

1         0     KO 

8| 

^ 

8 

^ 

§ 

0 

0 

-.    0 

-  8 

8 
0 

^ 

0 

CO 
1 

0 
1 

M 

+ 

KO 

+ 

VO 

+ 

8 

2"     "^ 

8  fo 

8 

1      ►"• 

M 

Is^ 

M 

M 

I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

70 

II    000 

II  240 

12850 

II 140 

II 100 

12  000 

9000 

70 

71 

10965 

II  140 

12780 

II 082 

II 030 

II  900 

8950 

71 

72 

10930 

II  040 

12  710 

II  024 

10960 

II  800 

8900 

72 

73 

10890 

10940 

12640 

10966 

10890 

II  700 

8850 

73 

74 

10  850 

10845 

12565 

10-903 

10  820 

11  600 

8800 

74 

75 

10  810 

10750 

12  490 

10850 

10750 

11  500 

8750 

75 

76 

10770 

10655 

12  420 

10792 

106S0 

II  400 

8700 

76 

77 

10735 

10560 

12345 

10734 

10  610 

II  300 

8650 

77 

78 

10695 

1046s 

13270 

10676 

10540 

II  200 

8600 

78 

79 

10655 

10  370 

13  19s 

10  618 

10470 

II  100 

8550 

79 

8o 

I06IS 

10  275 

13  120 

10  560 

10  400 

II  000 

8500 

80 

8i 

10  575 

10  180 

13  045 

10502 

10330 

10900 

8450 

81 

82 

10535 

10085 

II  970 

10444 

10260 

10800 

8400 

82 

83 

1049s 

9990 

II  895 

10386 

10  190 

10700 

8350 

83 

84 

10450 

9800 

1182s 

10328 

10  120 

10  600 

8300 

84 

85 

10  410 

9810 

II  755 

10270 

10050 

10500 

8  250 

85 

86 

10370 

9720 

II  680 

10  212 

9930 

10  400 

8  200 

86 

87 

10330 

9630 

II  605 

10  154 

9910 

10300 

8  150 

87 

88 

10290 

9  540 

IIS30 

10096 

9840 

10200 

8  100 

88 

89 

10  250 

9450 

II  460 

10  038 

9770 

10  100 

8050 

89 

90 

10205 

9360 

II  390 

9980 

9700 

10  000 

8000 

90 

91 

10  165 

9370 

II  315 

9922 

9630 

9900 

8950 

91 

92 

10  125 

9285 

II  240 

9864 

9560 

9800 

8900 

92 

93 

10085 

9200 

II  165 

9806 

9490 

9700 

8850 

93 

94 

10040 

9  115 

II  095 

9748 

9420 

9  600 

8800 

94 

95 

9  995 

8930 

II  025 

9690 

9350 

9500 

7750 

95 

96 

9  955 

8845 

10950 

9632 

9280 

9400 

7700 

96^ 

97 

9915 

8760 

10880 

9  574 

9  210 

9300 

7650. 

97 

98 

9875 

8675 

10  810 

9516 

9  140 

9200 

7600 

98 

99 

9830 

8590 

10740 

9458 

9070 

9  100 

7  550 

99 

lOO 

9785 

8510 

10  670 

9400 

9000 

9000 

7500 

100 

lOI 

9740 

8430 

10595 

9  342 

8930 

8900 

7450 

lOI 

102 

9695 

8350 

1052s 

9234 

8860 

8800 

7  400 

102 

103 

9650 

8270 

10455 

9  226 

8790 

8  700 

7350 

103 

104 

9610 

8190 

1038s 

916S 

8720 

8600 

7300 

104 

105 

9570 

8  115 

10  315 

9  no 

8650 

8500 

7250 

los 

io6 

9525 

8  040 

10245 

•     9052 

8580 

8400 

7  200 

106 

107 

9480 

7965 

10  175 

8994 

8510 

8300 

7  150 

107 

io8 

9  435 

7890 

10  105 

8936 

8440 

8200 

7  100 

108 

109 

9  395 

7815 

1003s 

8878 

8370 

8100 

7050 

109 

*  Also  Atlanta,  Ga.,  Jersey  City,  N.  J.,  Newark,  N.  J.,  Paterson,  N.  J..  Worcester, 
Mass.,  and  old  New  York  Code, 
^     I  Am.  R'y  Eqgrg.  Ass'n  th©  sarfte  upto//r,  100,  i(or  ^s^kniiftembers.^  Maximum,  I4.000. 


Tables  of  Safe  Loads  for  Steel  Columns 


Table  XI  (Continued) .     Safe  Loads  in  Pounds  per  Square  Inch  of  Metal- 
Area  for  Steel  Columns  and  Struts 


/  =  length  in  inches  • 


r  =  least  radius  of  gyration  in  inches 


l/r 


no 
III 

112 

113 
114 
IIS 
116 
117 
118 
119 
120 


Rankine's 
(Gor- 
don's) 
and 
Cambria 


II 

9  355 
9310 
9265 
9  220 
9  180 
9  140 
9095 
9050 
9  010 
8970 
8930 


Phila- 
delphia 


III 

7740 
766s 
7590 
7  520 
7450 
7380 
7310 
7240 
7  170 
7  100 
7035 


Boston 
Code 


IV 

9970 
9  900 
9830 
9  760 
9695 
9630 
9560 
9  495 
9430 
9365 
9300 


Wash- 
ington, 
D.  C* 


8820 
8762 
8704 
8646 
8588 
8530 
8472 
8414 
8356 
8293 
8  240 


Chi- 
cago t 

and 
N.  Y. 


^E  S 


VI 
8300 
8230 
8  160 

8090 
8  020 
7950 
7880 
7810 
7740 
7  670 
7  600 


Am. 

Bridge 

Co.  and 

Carnegie 


VII 
8  000 
7900 
7  800 
7700 
7  600 
7  500 
7400 
7300 
7  200 
7  100 
7  000 


Fowler's 

formula 

for 

struts 


VIII 
7000 
6950 
6  900 
6850 
6800 
6750 
6  700 
6650 
6  600 
6550 
6500 


l/r 


IX 
no 
III 
112 
113 
114 
IIS 
116 
117 
118 
119 
120 


In  the  Comparative  Diagram  (page  496)  of  Compression  Formulas  the 
names  of  the  formulas  and  the  maximum  ratio  of  l/r  for  main  members  and 
secondary  members  are  as  follows: 


Compression-formulas 

Maximum  ratio  of  l/r 

Main 

members 

Secondary 
members 

American  Bridge  Company 

American  Railway  En:,Mneering  Association .... 

v_  hicago  Building  Laws 

Ranltine's  (Gordon's)  formula 

New  York  Building  Laws                  

120 
100 
120 

X20 

1 20 

140 

120 

200 
120 
150 

120 
140 
120 

Boston  Building  Laws 

*t  See  foot-notes  on  pages  493  and  494. 


496  Strengths  of  Columns,  Posts  and  Struts  Chap.  14 

Comparative  Diagram  of  Compression-Formulas 


§ 


Allowable  Untt  Stresses  in  Pounds  per  Square  Inch 


g 


§ 


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A'         r      -h 

Tables  of  Safe  Loads  for  Steel  Columns 


Table  XII.- 

Safe  Loads  in  Tons  of  2  000  Pounds 

for  Standard  Stc 

el-Pipe 

Columns.    See  National  Tube  Company's  Handbook  for  Values  of  r  Used 

Loads  in 

tons  of  2  000  pounds.     Table  based  on  New  York  and  Chicago  laws.     For- 

mula  used, 

6"=  16  000—  70  l/r,  in  which 

S  =  allowable  compressive  stress  for  steel  in  pounds  per  square  inch, 

/=  length  of  column  in  ir.ches. 

r=  least  radius  of  gyration  in  inches. 

Loads  above  or  to  the  left  of  the  zigzag  lines  correspond  to  values  of  l/r  greater  than  1 20.  1 

Lengths 

2       1 

Nominal  sizes  of  pipe.     Inside  diameters  in  inches 

2M     1       3       1     3M     1       4       1     4H     1       5       1       6       1       7 

ft 

Thickness  in  decimal  parts  of  an  inch                                     1 

c 

3-154   1 

0.203   1 

0.216 

0.226 

0.237 

0.247 

0.258 

0.280 

0.301 

40 
36 

15.00 

33 

10.20 

18.37 

30 
24 

13.33 
16.46 

19.60 

21-73 
25.10 

5 

7 

9 

11 

96 
73 
50 
26 

7.41 

92.5 
11.09 

12.94 

8.43 

11.32 

13.24 
15.16 

28.47 

21.68 

30.71 
32.96 
35.20 
37.45 
39-69 
.-10.81 

20 
18 
16 
14 
13 

12 
II 

4.96 
6.57 
7-37 

4.60 
6.28 
7.97 
9.65 

23.77 
25.86 
27.9s 
30.04 
31.08 

17.09 
19.01 
20.93 
21.90 

14.78 
16.62 
17.54 

3.06 
3.81 

13 

03 

10.49 

T^ 

PT 

4.57 

8.18 

11.33 
12.18 

14 

15 

79 
68 

18.46 
19.38 

22.86 
23,82 

32.12 
33.17 

41.94 
43.06 

2 

29 

5.32 

8.q8 

ID 
9 

2 
3 

86 

44 

6.08 

9.78 
10.59 

13.02 
13.86 

lb 
17 

5b 
44 

20.30 
21.22 

24.78 
25.74 

34.21 
35-26 

44.18 
45.30 

6.83 

8 

4 

01 

7-59 
8.34 

11.39 
12.20 

14.70 
15 -.54 

18 

19 

33 
21 

22.14 
23.06 

26.71 
27.67 

36.30 
37.34 

46-43 
47-55 

7 

4 

S8 

6 

S 

16 

9.10 

13.00 

16.38 

20 

09 

23.98 

28.63 

38.39 

48.48 

5 

5 

73 

9  86      13-81   '   17.23 

20 

98       24.90 

29 -59      39 -07 

48.48 

Nominal  sizes  of  pipe.     Inside  diameters  in  inches. 

8       1        9        1       10       1       II       1       12       1       13       1       14              15 

Lengths 

ft 

Thickness  in  decimals  parts  of  an  inch 

0.322 

0.342 

0.365 

0.375 

0.375 

0.375 

0.375 

0.37s 

40 
36 

19.16 
23.96 

28.77 
33.87 

40.81 

51.26 
56.85 

60.68 
66.27 

72.45 
78.05 

81,88 
87.47 

91.30 
96.89 

46   26 

33 
30 

27.57 
31.17 

37-70 

50.34 
54.43 
58.51 

61.05 
65.24 
69.44 

70  .•47 
74.67 
78.86 

82.25 

91.67 

101.09 
105 . 29 
109.49 

41.53 
45.35 

86.44 
90.64 

95.87 

27 

34.77 

I 

00.06 

24 

38.37 

40.18 

62.59 

73. 6i 

83.06 

94.84 

104.26 

113.68 

22 

40.78 

51.73 

65.32 

76.43 

85.86 

97.64 

107.06 

116.48 

20 

43.18 

54-28 

68.04 

79.23 

88.65 

100.43 

109 . 86 

119.28 

18 

45.58 

56.83 

70.76 

82.03 

91.45 

103.23 

112.65 

122.08 

16 

47.98 

59-38 

73.48 

84-83 

94.25 

106.03 

115.45 

124.88 

14 

50.38 

61.93 

76.21 

87.62 

97.05 

108.83 

118.25 

127.67 

13 

51-58 

63.21 

77.57 

89.02 

98.4s 

110.23 

119.65 

128.85 

12 

52.78 

64.49 

78.93 

90.42 

99.8s 

111.62 

120.61 

12S.85 

II 

53-99 

65.76 

80.29 

91.82 

101,24 

112,36 

120.61 

128.85 

10 

55-19 

67.04 

81.65 

93-22 

102.05 

112.36 

120.61 

128.85 

9 

56.39 

68.31 

83.01 

93.81 

102.05 

112.36 

120.61 

128.85 

8 

57.59 

69.59 

83.36 

93.81 

102.05 

112.36 

120.61 

128.85 

7 

58.79 

69.82 

83.36 

93.81 

102.05 

112.36 

120.61 

128.85 

6 

58.79 

69.82 

83.36 

93.81 

102.05 

112.36 

120.61 

128.85 

1         5 

58.79 

69.82 

83.36 

93.81      102.05  1  112.36  1  120.61  1 

128.85 

*  Furnished  by  the  National  Tube  Company,  Pittsburgh,  Pa. 


498 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


Table  XIII.*    Safe  Loads  in  Tons  of  2  000  Pounds  for  Extra-Strong  Steel- 
Pipe  Columns.     See  National  Tube  Company's  Handbook  for  Values  of  r  Used 


Loads 

in  tons  of  2  000  pounds.     Table  based  on  New  York  and  Chicago  laws.     For-  1 

mula  used  5  =  16  000  -  ^ol/r,  in  which 

S=  allowable  compressive  stress  for  steel  in  pounds  per  square  inch. 

/=  length  of  column  in  inches, 

r=  le  1st  radius  of  gyration  in  inches. 

Loads  above  or  to  the  left  of  the  zigzag  lines  correspond  to  values  of  l/r  greater  than  120.  | 

Lengths, 
ft 

Nominal  sizes  of  pipe.     Inside  diameters  in  inches 

2             2H     1       3       1     3M            4            4K     1       5              6       1       7 

Thickness  in  decimal  parts  of  an  inch 

0.218   1 

0.276 

0.300 

0.318 

0.337 

0.355 

0.375 

5-432 

0.500 

36 



22.52 

33 



14.16 

28.11 

30 
27 

24 
22 

18.99 
23.81 

28.64 

33.69 
39.28 

9.74 
12.38 

11.21 
15.39 
18.19 

44.86 
48.58 

7.68 

31.86 

20 
18 
16 
14 
13 

5.78 

8.14 

10.51 

10.19 
12.69 

1=^.20 

15.02 
17.66 

20.  q8 

35.07 
38.29 
41.51 
44.72 
46.33 

52.31 
56.03 

59-75 
63.48 
65-34 

23 -77 
26 .  56 
29.3s 
30.75 

6.29 

20.31 
22.95 
24.27 

3.69 
4-71 

8.52 

12.87 

17.71 

9.64 

14.06 

18.96 

12 
II 

2 

91 

5-74 
6.76 

10  75 

15.24 
16.42 

20.22 
21.47 

25-59 
26.91 

32.15 
33.54 

47-94 
49-55 

67.20 
69.06 

11.87 

10 

3 
4 

72 

7.79 

12.98 
14. 09 

17.60 

18.79 

22.72 
23-98 

28.23 

34.94 
36.33 

51.16 
52.76 

70.92 
72.78 

S3 

8.81 

7 

5 

34 

9.83 
10.86 

15-21 

16.32 

19.97 

21.15 

25  -  23 
26.48 

30.88 
32.20 

37.73 
39.12 

54.37 
55.98 

74-64 
76.51 

6 

15 

6 

b 

96 

11.88 

17.44 

22.33 

27-74 

33.32 

40.52 

57.79 

78.34 

S 

7 

77 

12.91   '   18.55   '   23.52 

28.99 

34.84    '    4192 

58.83 

78.. 34 

Nominal  sizes  of  pipe.     Inside  diameters  in  inches 

8               9        1       10       1       II       1       12       1       13       1       14       1       15 

ft 

Thiekness  in  decimal  parts  of  an  inch 

0.500 

0 .  500 

0.500 

0.500       0.500 

0.500 

0.500 

0.500 

40 
36 

27.60 

40.14 

47  -  .59 

54.25 

66.80 

74-26 

79-36 

95.06 
102.52 

107.62 
11508 

120. i8 
127.64 

61.71 
67.30 
72.89 
78.48 
84.07 

86.82 

33 
30 
27 

40.64 

S3. 18 

79-85 
85.45 
91.04 
96.63 

92.41 
98.00 
103.60 
109.19 

108. II 
113-70 
119.30 
124.89 

120.67 
126.27 
131.86 

138.83 
144-42 

46 .  23 

58.77 
64.36 
69.95 

5i-8i 

22 

61.13 

73.68 

87.80 

100.36 

112 .92 

128.62 

141.18 

153.75 

20 

64.85 

77.40 

91.53 

104.09 

116.65 

132.35 

144.91 

157.48 

18 

68.58 

81.13 

95.26 

107.82 

120.38 

136.08 

148.64 

161. 21 

16 

72  30 

84.86 

98.98 

111.54 

124.11 

139-81 

152.37 

164.94 

14 

76.03 

88.58 

102.71 

115.27 

127.84 

143 ■ 54 

156.10 

168.67 

13 

77-89 

90.45 

104.58 

117.14 

129-70 

145.40 

157.97 

170  43 

12 

79-75 

92.31 

106.44 

119.00 

131.56 

147.27 

159.44 

170-43 

II 

81.61 

-   94.17 

108.30 

120.87 

133.43 

148.44 

159.44 

170.43 

10 

83.48 

96.04 

no. 17 

122.73 

134.70 

148.44 

159.44 

170.43 

9 

85-34 

97-90 

112.03 

123-70 

134.70 

148.44 

159.44 

170.43 

8 

87.20 

99.76 

112.70 

123-70 

134.70 

148.44 

15944 

170.43 

7 

89.06 

100.33 

112.70 

123-70 

134.70 

148.44 

1.59-44 

170.43 

6 

89.34 

100.33 

112.70 

123.70 

134.70 

148.44 

159-44 

170.43 

•■? 

89.34  '   TOO. 33      112.70  '   123.70  1   134.70  1   148.44   '   159-44   '   170.43   1 

*  Furnished  by  the  National  Tube  Company,  Pittsburgh,  Pa, 


Tables  of  Safe  Loads  for  Steel  Columns 


499 


Table  XIV.     Safe  Loads  in  Tons  of  2  000  Pounds  for  Struts  Formed  of  a 
Pair  of  Steel  Channels 


Distance  between  webs,  ^  in 
If  strut  is  free  to  bend  in  either  direction,  use  smaller  load  given 
Stresses  in  pounds  per  square  inch: 

12  000  for  lengths  of  30  radii  and  under; 

13  500  —  50  l/r  for  lengths  over  30  radii 


<i^--i 


Depth, 


Weight 

per  lin 

foot, 

lb* 


Thick- 
ness 
of  web 


Area 
of  two 
chan- 
nels, 
sq  in 


Length  in  feet 


33 
35 

40 
45 
50 
55 


0.40 
0.43 
0.52 
0.62 
0.72 
0.82 


25    * 

30 

35 

40 


0.23 

0.39 
0.51 
0.G4 
0.76 


15 
20 
25 
30 
35 


0.24 
0.38 
0.53 
0.68 
0.82 


I3H 
15 


0.23 
0.29 
0.45 
0.62 


19.80 j 
20.58  { 
23.52} 
26.43! 
o>n  /I -7  ) 


32.36] 


5.62 
1.47 
5.53 
1.46 
5.43 
1.45 
5.32 
1.46 
5.23 
1.47 
5.16 


101.57 
118.80 
105.32 
123.48 
T20.I3 
141. 12 
134.91 
158.88 
150.36 
176.52 
165.60 


194.16  194.16 


17.64 
20.58- 


23.52 


8.92  j 

11.76 j 
14.70 j 
17.64 j 
20.58 j 


7.78; 

8.82  j 
11.76] 
14.70] 


1.34 
4.61 
I  31 
4.43 
1.30 
4.23 
1. 31 
4.17 
1.32 
4.09 


59.81 
72.36 
72.32 

83.20 
86.52 
105.84 
101.25 
123.48 
116. 01 
141. 12 


1.24 
3.87 
1.20 
3.66 
1.20 
352 
1.22 
3.42 
1.26 
3.35 


42.94 
53.52 
55  "" 
70.56 
69.82 
88.20 
84.40 

105.84 
99.76 

123.48 


1. 19 
3.49 
1. 17 
3.40 
1. 15 
3.21 
1. 17 
3.10 


36.83 
46.68 
41.45 
52.92 
54.85 
70.56 
69.09 
87.83 


57.  ic 
72  / 
63.95 
83.20 
82.46 

105.84 
96.52 

123 

110.66 

141. 12 


40.78 
53.52 
52.92 
70.56 
66.15 
87.94 
80.04 

105.13 
94.' 

122.34 


34.87 
46.48 
39.18 
52.52 
51.77 
69  50 
65.31 
86.43 


54  85 
80  118 
73  88 
48' 123 
66.100 
12] 141 
50  113 
88,158 
17  126 
52,176 
78  139 
16  194 


54.40 
72.36 
65 .  60 
83.20 
78.36 
105.84 
91.78 
123.43 
105.31 
141. 12 


SI.  70 
72.36 
62.21 
88.20 
74.30I 

105.48, 
87. TO: 

122.65 
99.96 

139.82 


38.64 
53.29 
49.93 
69 -73 
62.47 
86.69 
75.71 

103.63 
89.93 

120.49 


36.48 
52.62 
47.04 
68.79 
58.80 
«5.44 
71.35 

102.04 
85.04 

118.64 


32.91 
45.82 
36.93 
51.81 
48.71 
68.38 
61.55 
85.00 


30.94 
45.16 
34.66 
50.98 
45.65 
67.39 
57.77 
83.56 


49.02 
71.99 
58.83 
87.28 
70.25 

104 . 25 
82.37 

121. 16 
94.66 

138.06 


44.50 
32.41 
50.10 
42.57 

66.23 

54.00 
82.17 


77.44 
IT8.80 

80.09 
123.00 

91  14 
140.41 

102. oS 

1.57.82 

114.00 
174-75 
126.10 
192.00 


43.62 
70.43 
52.03 
85 .  26 
62.09 

101.78 
72.90 

118.33 
83.96 

134.65 


30.01 
50.43 
38.22 
65.85 
47.77 
81.69 
58.34 
97.41 
70.33 
IJ3.I3 


25.07 

43.15 

27.8 

48.64 

36.42 

64.00 

46.48 

79-30 


*  0{  single  channel 


Strength  of  Columns,  Posts  and  Struts 


Table  XIV  (Continued).     Safe  Loads  in  Tons  of  2000  Pounds  for  Struts 
Formed  of  a  Pair  of  Steel  Channels 


? 

A 

Distance  between  webs,  li  in 

^^te 

If  strut  is  free  to  bend  in 

either  direction 

use  smaller  load  given 

i 

Stresses  in  pounds  per  square 

inch: 

♦i— 

1 

-^-i 

II  000  for  lengths  of  50  radii  and  under; 

1 

13  500  -  50 

l/r  for  lengths  over  50  radii 

^^ 

Depth, 
in 

Weight 
per  lin 
foot. 

Thick- 
ness 
of  web. 

Area 
of  two 
chan- 
nels, 

^2-2 

ri-u 
in 

Length  in  feet 

lb* 

in 

sq  in 

6 

7 

8 

9 

10 

II 

II.  25 

0.22 

6.70  { 

1.04 

33.63 

31.70 

29.76 

27.83 

25.91 

23.96 

3. II 

36.85 

36.85 

36.85 

36.85 

36.85 

36.85 

13.75 

0.31 

8.o8| 

1.04 
2. 98 

40.56 
44-44 

38.23 
44.44 

35.89 
44-44 

33.57 

44-44 

31.24 
44-44 

28.90 
44.44 

8 

16.25 

0.40 

9.56{ 

1.03 
2.89 

47-82 
52.58 

45.05 
52.58 

42.25 
52.58 

39-48 
52-58 

36.68 
52.58 

33-91 
52.58 

18.75 

0.49 

11.02 j 

1.03 

55-12 

51.93 

48.70 

45-51 

42.29 

3909 

2.82 

60.61 

60.61 

60.61 

60.61 

60.61 

6S.6i 

0.58 

12.50  { 

1.03 

62.53 

58.90 

55-25 

51.62 

47-96 

44-34 

21 .25 

2.77 

68.75 

68.75 

68.75 

68.75 

68.75 

68.75 

9-75 

0.21 

5.7o{ 

0.99 
2.72 

28.11 
31.35 

26.39 
31.35 

24.66 
31.35 

22.94 
31.35 

21.20 
31-35 

19-47 
31.35 

7.20 1 

0.99 

35.  SI 

33.33 

31-15 

28.98 

26.78 

24-60 

12.25 

0.32 

2.59 

39.60 

39.60 

39-60 

39-60 

39-60 

39  42 

7 

14.75 

0.42 

8.68  { 

0.99 
2.50 

42.71 
47.74 

40.18 
47.74 

37.56 
47.74 

34-93 
47'- 74 

32.28 
47.74 

29-66 
47.13 

17.25 

0.53 

10.14  { 

1. 00 
2.44 

50.19 
55.77 

47.15 
55.77 

44.10 
55.77 

41.06 
55-77 

38.02 
55.77 

34.98 
54.73 

0.63 

11.62I 

1. 00 

57.52 

54.03 

50.54 

47-06 

43.57 

40.08 

19 -75 

2.39 

63-91 

63.91 

63.91 

63.91 
18.46 

63.91 

62.39 

8.00 

4.76  { 

0.94 

23.02 

21.50 

19.98 

16.94 

15.42 

0.20 

2.34 

26.18 

26.18 

26.18 

26.18 

26.02 

25.41 

6 

10.50 

0.32 

6.i8{ 

0.94 
2.21 

29.89 
33.99 

27.91 
33.99 

25.94 
33.99 

23-97 
33.99 

22.00 
33.32 

20.02 
32.48 

13.00 

0.44 

7.64 1 

0.95 

37.11 

34.68 

32-27 

29.87 

27.44 

25.04 

2.13 

42.02 

42.02 

42.02 

41.88 

40.81 

39-72 

0.56 

9.12I 

0.95 

44.30 

41.40 

38.53 

35.66 

32.78 

29.89 

15.50 

2.07 

50.16 

50.16 

50.16 

49.68 

48.33 

47-03 

6.50 

0.19 

3.90  { 

0.89 

18.43 

17.13 

15.81 

14.49 

13.18 

11.86 

1-95 

21.45 

21.45 

21.45 

20.92 

20.32 

19-72 

t;   ■2ni 

0.90 

25.17 

23.41 

21.65 

19.87 

18. II 

16.35 

5 

9.00 

0.33 

5 .301 

1.83 

29-15 

29.15 

28.83 

27.97 

27.10 

26.22 

0.48 

6.76J 

0.91 

32.26 

30.03 

27.81 

25.58 

23.35 

21.12 

11.50 

1. 75 

37.18 

37.18 

36.36 

35.20 

34.03 

32.88 

0.18 

0.84 

14.28 

13.17 

12.07 

10.96 

9.8s 

5.25 

3.iO| 

I.S6 

17.05 

16.75 

16.15 

15.55 

14.96 

14-36 

6.25 

3.68  { 

0.84 

16.95 

15.64 

14.33 

13.02 

11.70 

4 

0.25 

1. 51 

20.24 

19.72 

18.99 

18.26 

17.53 

ieiso 

4.26 

0.84 

19.62 

18.10 

16.59 

15.07 

13.54 

7.25 

0.32 

1.46 

23.43 

22.63 

21.75 

20.87 

19.98 

19.12 

*  Of  single  channel, 


Tables  of  Safe  Loads  for  Steel  Columns 


501 


Table  XV.     Safe  Loads  in  Tons  of  2  000  Pounds  for  Single-Steel-Angle 

Struts  1^ 


Angles  with  Unequal  Legs 

Stresses  in  pounds  per  square  inch:  . 
II  000  for  lengths  of  50  radii  and  under;" 
13  500  —  SO  llr  for  lengths  over  50  radii 

Size, 
in 

Thick- 
ness, 
in 

r 

axis 

3-3,* 

in 

Area, 
sq  in 

Length  in  feet 

4 

5 

6 

7 

8 

9 

10 

6    X4 

0.88 
0.86 

3.61 
7.99 

42.78 

40.00 

37 

21 

34.44 

31.64 

28.86 

26.07 

5    XaVi 

0.76 

0.7s 

3-05 
5.81 

5     X3 

Me 

0.66 
0.64 

2.40 
5.44 

4HX3 

Mo 

0.66 
0.64 

2.25 
5.06 

24^66 

22.29 

19 

92 

17.55 

15.18 

4     X3K2 

Mo 
•>4 

0.73 
0.72 

2.25 
5. 06 

11.49 
25.73 

10.57 
23.62 

9 
21 

65 
51 

8.72 
19.40 

7.79 
17.29 

6.86 
15.18 

4     X3 

Me 
•>4 

0.6s 
0.64 

2.09 
4. 09 

10.25 
22.86 

9.28 
20.67 

8 
18 

32 

47 

7.36 

16.27 

6.39 

14.07 

3K2X3 

Me 

Ms 

0.63 
0.62 
0.62 

1.93 
2.30 
3-67 

9-35 
11.07 
17.67 

8.43 
9.9(3 
15.90 

7 
8 
14 

51 

84 
12 

6.59 
7.74 
12.35 

3I/2X2I/2 

Ki 
H 
I/I2 

0.54 
0.54 
0.53 

1.44 
2. II 
2.75 

6.52 
9-55 
12.34 

5.72 
8.38 
10.78 

4 
7 
9 

92 
21 
22 

3      X2l.^2 

Ms 
K2 

0.53 
0.52 
0.52 

1. 31 

1.92 
2.50 

5.88 
•8.52 
II. 10 

5.13 
7.42 
9.66 

4 
6 
8 

39 
31 
22 

3     X2 

K2 

0.43 
0.43 
0.43 

1. 19 
1.73 
2.25 

4.71 
6.85 
8.91 

3.88 
5.64 
7.34 

2K'X2 

% 

0.42 
0.42 
0.42 

1.06 
1.55 
2.00 

4.13 
6.03 

7.79 

3.37 
4.93 
6.36 

*  This  is  the  least  radius  of  gyration  with  reference  to  the  diagonal  axis  3-3.     (See 
Table  XI,  pages  362  to  365.) 


Strength  of  Columns,  Posts  and  Struts 


Table  XV  (Continued).     Safe  Loads  in  Tons  of  2  000  Pounds  for  Single- 
Steel-Angle  Struts 


Angles  with  Equal  Legs 

Stresses  in  pounds  per  square  inch: 

II  000  for  lengths  of  50  radii  and  under; 

13  SCO  —  so  l/r  for  lengths  over  50  radii 

Size, 
in 

Thick- 
ness, 
in 

r 
axis 
3-3.* 

in 

Area, 
sqin 

Length  in 

feet  . 

4 

S 

6 

7 

8 

9 

10 

6    X6 

3/i 

1.19 
1. 18 
1.17 

4.36 
7. It 
9.74 

33.98 
39.10 
53.57 

33.93 
38.96 
53.37 

33.83 
37.14 
50.77 

31.74 
35.35 
48.28 

30.64 
33.54 
45.77 

19.54 
31.72 
43.36 

18.44 
29.93 
40.78 

5    X5 

H 

0.99 
0.97 
0.96 

3.61 
5.86 
7.99 

19.85 
32.23 
43.94 

18.89 
30.50 
41.44 

17.80 
28.68 
38.95 

16.71 
26.86 
36.45 

15.64 
25.06 
33 .95 

14.53 
23.24 
31.46 

13.42 
21.43 
28.96 

4     X4 

0.79 
0.78 
0.77 
0.77 

2.86 
3.75 
4.61 
5.44 

14.96 
19-54 
23 -93 
28.24 

13.88 
18.10 
22.13 
26.12 

12.79 
16.65 
20.33 
23.99 

II. 71 

15-22 
18.55 
21.89 

10.61 
13-78 
16.75 
19.77 

9.53 
12.33 
14.95 
17.65 

3V2X3H 

Me 

K2 
% 

0.69 
0.68 
0.67 
0.67 

2.09 
3.25 
3.98 
4.69 

10.47 
16.20 
19-74 
13.26 

9.56 
14-77 
17-95 
21.16 

8.65 
13.34 
16.17 
19.06 

7-74 
11.90 
14.39 
16.96 

6.83 
10.47 
12.61 
14-86 

3     X3 

0.59 
0.58 
0.58 
0.57 

1.44 
2. II 
2.75 
3.36 

6.79 
9.88 
12.87 
15.60 

6.06 
8.73 
11-45 
13.84 

5-32 
7-69 
10.03 
12.07 

4-59 
6.60 
8.60 
10.30 

2^X2'/^ 

0.49 
0.49 
0.48 
0.47 

0.90 
1. 19 
1.73 
2.2s 

3.87 
5.10 
7-35 
9-44 

3.32 
4.39 
6.27 
8.01 

2.76 
3-66 
5.19 
6.57 

2HX2H 

Mc 
M 
% 
Me 

0.44 
0.44 
0.43 
0.43 

0.81 
1.06 
1. 55 
1.78 

3.26 
4.26 
6.13 
7.14 

2.70 
3.54 
5.05 
5.80 

2.80 
3-95 
4.53 

2      X2 

Me 
H 

0.40 
0.39 

0.72 
0.94 

2.70 
3.45 

2.16 
2.72 

2.00 

*  This  i 

i  the  least  radius  of  gyratic 

n,  with  reference  to  the  dia 

gonal  i 

ixis  3-: 

.     (See 

Table  XII 

pages  36 

6  and  36 

7-) 

Tables  of  Safe  Loads  for  Steel  Coiuiriri^ 


Table  XVI.    Safe  Loads  in  Tons  of  2  000  Pounds  for  Double-Steel-Angle 

Struts 

Long  Legs  Parallel 

AND  One-Halt  Inch  Apart 

? 

Stresses 

in  pounds  per  square  inch: 

1-^J 

IM. 

-L 

) 

II  00c 

for  lengths  of  50  radii  and  under; 

r  ' 

13  50c 

—  so  IJr  for  lengths  over  50  radii 

'^ 

Si2e, 
in 

Thick- 
ness, 
in 

Least 
in 

Area. 

two 
angles. 

Length  in  feet 

• 

sqin 

S 

6 

7 

8 

10 

II 

12 

8    X6 

H 

2.49 

13.  S3 

74.36 

74.36 

74.36 

74.36 

74.36 

73.34 

71.72 

1 

2,65 

26.82 

147-51 

147.51 

147.51 

147.51 

147.51 

147.51 

144.62 

6    X4 

% 

1.67 

7.22 

39.71 

39.71 

39.65 

38.35 

35.77 

34.47 

33.14 

1^6 

1.74 

14.94 

82.17 

82.17 

82.17 

80.26 

75.07 

72.50 

69.91 

6    X3H 

34 

1.43 
1.46 

6.84 

3' 

r.62 

>.50 

37.57 
49.50 

36.13 
47.81 

34 

45 

.69 

31.82 

30.38 
40.41 

29.00  ■ 
38.56 

9.00 

45 

•97 

42.27 

% 

1.49 

II.  10 

61.05 

61.05 

59  27 

57.05 

52.51 

50.29 

48.07  ' 

^Me 

1-52 

14.12 

77.66 

77.66 

75.82 

73.03 

67.42 

64.65 

61.88 

5    X4 

3/^ 

1-59 

6.46 

3« 

.53 

35.53 

35.07 

33.86 

31.41 

30.20 

28.99 

M 

1.54 

12.38 

68.09 

68.09 

66.69 

64.28 

59-45 

57  04 

54.62 

5     X3V2 

H 

1. 51 

6.10 

33.55 

33.55 

32.70 

31.49 

29.05 

27.84 

26.64 

H 

1. 55 

11.62 

63.91 

63.91 

62.69 

6c 

.45 

55.95 

53.71 

51.44 

H 

1.27 

5-72 

31 

.46 

30.50 

29.15 

27 

.80 

25.09 

23.75 

22.39 

5     X3 

H 

1.30 

7.50 

41.25 

40.23 

38.51 

36 

.78 

33.32 

31.59 

29.85 

H 

1.33 

9.22 

5C 

).7i 

49.76 

47.69 

45 

.59 

41.40 

39.30 

37.29 

% 

1.36 

10.88 

.5c 

.84 

58.94 

56.63 

54 

.23 

49.42 

47.05 

44.66 

4    XaH 

% 

1.25 

5.34 

2C 

>.37 

28.35 

27.07 

25.79 

23.23 

21.94 

20.66 

% 

1.20 

10.12 

5= 

.66 

53.13 

50.60 

48.07 

43.01 

40.48 

39.95 

4     X3 

% 

1.26 

4.96 

2' 

.28 

26.28 

25.12 

24.00 

21.64 

20.49 

19.30 

M 

1.22 

9.38 

51.59 

49.47 

47.18 

44.85 

40.24 

37.94 

3564 

H 

1. 12 

2.88 

I, 

.58 

14.81 

14.03 

13.26 

11.72 

10.95 

10.18 

3K2X3J'i 

% 

1. 10 

4.22 

22 

.73 

21.59 

20.42 

19.28 

16.97 

15.82 

14.67 

Vz 

1.09 

5.50 

2S 

.56 

28.05 

26.53 

25.02 

21.98 

20.47 

18.96  • 

3     X2 

1.06 
0.93 

7.30 
2.38 

3? 

.92 

36.86 
11.45 

34.78 
10.69 

32.74 

28.58 
8.39 

26.51 
7.62 

24.43 

12.22 

9 

.92 

H 

0.92 

4.50 

23.04 

21.58 

20.10 

J8 

.64 

15.70 

14.23 

2K2X2 

3/l6 

0.79 

1.62 

7.86 

7.24 

6.63 

6 

.01 

2      X2 

K2 

Me 

0.75 
0.62 

4.00 

ic 

.00 
.22 

17.40 
5.54 

15.80 
4.82 

14 

.20 

1.44 

t 

4.13 

2      X2 

H 

0.61 

1.88 

8.08 

7.14 

6.20 

5.26 

Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


Table  XVII.*     Safe  Loads  in  Units  of  i  ooo  Pounds  for  Steel-Beam 
Columns 


Allowable  fiber-stress  in    pounds  per    square  inch: 
.13  000  for  lengths  of  60  radii  or  under 
Reduced   for  lengths   between   60  and    120  radii,   by 
Formula  (13), 

5  =  19  000  —  ioo//r 
Weights  do  not  include  details 
For  values  for  l/r  above  120,  see  notes  on  page  490 


Effective 

length, 

ft 


13 
14 
15 
16 
17 
18 


23 
24 
25 

26 
27 
28 
29 
30 

31 


8-in 
34-lb 


130.0 
130.0 
130.0 
130.0 
130.0 
130.0 
130.0 
130.0 


125.8 

119-4 
1130 

106.6 
100.2 
93.8 

87.3 
80.9 
74.5 


69.0 
65.8 

62.6 
59-4 
56.2 
53.0 
49.8 

46.6 
43.4 
40.2 
370 
33-7 

30.5 


Depth  and  weight  of  sections 


H  beams 


6-in 
23.8-lb 


91.0 
91.0 
91.0 
91.0 
91.0 
91.0 


86.7 
80.9 
75.1 

693 
63.5 

57.7 
51-9 


47-6 

44-7 
41.8 
38.9 
36.0 
33-1 
30.2 
27.3 
24.4 
21.5 


5-in 
18.7-lb 


71.5 
71.5 
71.5 
71.5 
71-5 


66.0 
60.5 
55.0 
49-5 

44.0 
38.5 


35.8 
33.0 

30.3 

27.5 
24.8 
22.0 

19-3 
16.5 


4-1  n 
13.6-lb 


I  beams 


15-in 
42-lb 


162.2 
162.2 
162.2 
162.2 


153-9 
140. 1 
126.2 
112. 3 

98.5 


86.0 
79.0 
72.1 
65.2 
58.2 

51.3 
44.4 
37.4 


i2-in 
3i3'^-lb 


120 
120. 
120 


lo-in 
25-lb 


95.8 
95.8 
95.8 


94.4 

85.3 
76.2 
67.1 
58.0 


50.2 

45.7 
41. 1 

36.5 
32.0 

27.4 

22.9 


Area,  sq  in 


10.00 


7.00 


5.50 


12.48 


7.37 


/,  i.in*., 
r\  I,  in.., 
/2  2.  in*  . 
^2  2,  in.. 


115-4 
3.40 
35.1 
1.87 


45.1 
2.54 
14.7 
1.45 


23.8 
2.08 
7.9 
1.20 


10.7 

1.63 

3.6 

95 


441.8 
5-95 
14.6 


215.8 

83 

9.5 


Weight, 
lb  per  lin  ft 


34 


23.8 


18.7 


13.6 


42 


31H 


122.1 

4.07 
6.9 
0.97 


Safe  load- values  above  the  upper  heavy  line  are  for  ratios  of  llr  not  over  60; 
between  the  heavy  lines  for  ratios  up  to  120  llr\  and  those  below  the  lower 
line  are  for  ratios  not  over  200  llr 


25 
those 
heavy 


•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


Table  XVII  *  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  Steel- 
Beam  Columns 


i' 

Allowable 

fiber-stress  in  pounc 

s  per  square  inch: 

^f 

l 

3  000  for  lengtns  ot  bo  raan  or  under 
deduced  for  lengths  between   60  and   120    radii,   by 
Formula  (13), 

5  =  19  000  —  lool/r 
Veierhts  do  not  include  details 

J 

>             ^ 

1 

For  values  for  l/r  above 

120,  see  notes  on  page  490 

Eflfective 

length, 

ft 

Depth  and  weight  of  sections 

I  beams 

9-in 
2i-lb 

8-in 
i8-lb 

7-in 
15-lb 

6-in 
i2H-lb 

S-in 
9%-lb 

4-in 
7K2-lb 

2 

3 

4 
5 
6 
7 
8 
9 

10 

II 

12 

13 
14 
IS 
i6 
17 
i8 

19 

20 

21 
22 
23 
24 
25 

26 
27 
28 
29 

3P 

82.0 
82.0 
82.0 

69.3 
69.3 
69.3 

57-5 

57.5 

46.9 
46.9 

37.3 
37.3 

28.7 

28.5 
24.0 
19  S 

56.8 
50.0 
43.2 
36.4 

44-5 

38. S 
32. s 

26.5 

33.3 

28.0 

22.7 

77.8 

69.4 
61.0 
52.6 

44.2 

63.2 

55.6 
48.0 

40.4 

IS. 2 
13.0 
10.8 
8.S 

18.8 
16. 1 
13. 5 
10.8 

30.3 
26.9 
23.5 
20.1 

22.9 

19-9 
16.8 

13.8 

35.0 

40.0 

35.8 
31.5 
27-3 
23.1 
18.9 

31.2 
27.4 

2^.6 

16.7 
13.3 

10.8 

19.8 
16.0 



31 

Area,  sq  in 

6.31 

5. 33 

4.42 

3.61 

2.87 

2.21 

/i-i.  in^ 

ri-i,  in 

h  2.  in* 

ra  2,  in.,... 

84.9 

3.67 

5.2 

0.90 

56.9 
3.27 
3.8 
0.84 

36.2 
2.86 
2.7 
0.78 

21.8 

2.46 

1-9 

0.72 

12. 1 

2.0s 

1.2 

0.6s 

6.0 
1.64 
0.77 
0.S9 

Weight. 
lb  per  lin  ft 

21 

18 

IS 

12H 

9% 

7H 

Safe  load- values  above 
between  the  heavy  lines 
line  are  for  ratios  not  ove 

:he  upper  heavy  line  are  for  ratios  of  l/r  not  over  60;  those 
for  ratios  Up  to  120  l/r;  and  those  below  the  lower  heavy 

r  200  l/r 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa,, 


606 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


Table  XVIH. 


Safe  Loads  in  Tons  of  2  000  Pounds  for  Bethlehem  Rolled- 
Steel  8-Inch  H  Columns  with  Square  Ends 


Unsupported 

length, 

ft 


Allowable  stress  in  pounds  per  square  inch: 
13  000  for  lengths  under  55  radii; 
16  000  —  55  IJr  for  lengths  over  55  radii 


14 
IS 
16 

17 
18 
20 


24 
26 


Area,  sq  in 


/i-i,  in*, 
J-i  1,  in. 
72-2.  in*, 
Ti-i,  in. 


Weight 
of  section, 
lb  per  lin  ft 


59-7 
59.7 
58. 1 

56. 5 
55.0 
S3. 5 

52.0 
50.4 
48.9 

47.4 
4S.9 
42.8 


66.1 
66.1 
64.7 

63.0 
61.3 
59-7 

58.0 
56.3 
54.6 

S3.0 
SI. 3 
48.0 


39.7 
36.7 


44.6 

41.3 
38.0 


9.17 


105.7 
3.40 
35. 8 
1.98 


121. 5 
3.46 
41. 1 
2.01 


34.5 


74.8 

74-8 
73.3 

71.4 
69.6 
67.7 

65.8 
64.0 
62.1 

60.2 
58.4 
54.6 

83.4 
83.4 
81.9 

79.8 
77.7 
75.7 

92.2 
92.2 
90.6 

88.3 
86.1 
83.8 

lOI.O 
lOI.O 

99-5 
97.0 

94.  S 

92.1 

73.6 
71.5 
69.4 

81.5 
79-2 
76.9 

89.6 
87.1 
84.6 

82.2 

67.4 
65.3 
61. 1 

74.6 

72.4 
67.8 

79.7 
74.7 

50.9 
47.1 
43.4 


139-5 
3.48 
47.2 
2.03 


39.0 


12.83 


158.3 
3-51 
53.4 
2,04 


14.  x8 


177.7 
3. 54 
59-8 
2.05 


48.0 


197  8 
3.57 
66.3 

2.07 


53.0 


109.9 
109.9 
108.4 

105.7 
103.0 
100.3 

97.7 
95.0 
92.3 

89.6 
86.9 
81.6 


57.0 

63.2 

69.8 

76.2 

52.8 

58.7 

64.8 

70.9 

48.7 

54.1 

59.9 

65.5 

16.90 


218  6 
3  60 
731 
2.08 


57-5 


Loads  below  the  heavy  line  are  for  lengths  greater  than  125  radii 


Tables  of  Safe  Loads  for  Steel  Columns 


507 


Table  XVIII  (Continued).     Safe  Loads  in  Tons  of  2000  Pounds  for  Beth- 
lehem Rolled-Steel  8-Inch  H  Columns  with  Square  Ends 


Unsupported 

length, 

ft 


Allowable  stress  in  pounds  per  square  inch: 
13  000  for  lengths  under  55  radii; 
16  000  —  55  llr  for  lengths  over  55  radii 


14 
15 
16 

17 
18 


24 
26 


Area,  sq  in 


/i  1,  in* 
ri-i,  in. 
/2-2,  in* 
y%~i,  in. 


Weight 
of  section, 
lb  per  lin  ft 


118. 8 
118. 8 
117. 3 

114-4 
iii.S 
108  7 


102.9 
100.  o 

97.1 
94.2 
88.5 


82.7 

76.9 
71.2 


18.27 


240.2 
3.63 
80.0 
2.09 


62.0 


127.8 
127.8 
126.5 

123-5 
120.4 
117.3 

II4-2 
III. 2 
108. 1 

105 -o 
101.9 
95.8 


136.8 
136.8 
135-6 

132.4 

129. 1 
125.8 

122.  5 

119. 2 

116. 0 

112. 7 
109.4 
102.9 

9<3.3 


146.0 
146.0 
144-9 

141 -4 
137-9 
134.4 

131.  o 
127-5 
124.0 

120.5 
117. o 
no. I 


83.5 
77.3 


19.66 


262.5 
3.65 
87.1 


67.0 


83-2 


96.2 


154-6 
154.6 
153-6 

149-9 
146.2 
142.6 

138.9 
135.2 
131.6 

127.9 
124.2 
116. 9 

109.6 


163.8 
163.8 
163. 1 

159.3 
155.4 
151. 6 

147.7 
143.9 
140.0 

136. 1 
132.3 
124.6 

116. 9 


102.2 
94.9 


109.2 
101.5 


21.05 


285.6 
3.68 
94.4 
2.12 


22.46 


309.5 
3.71 

101.9 
2.13 


76.5 


23.78 


333.  S 

3.75 
109.2 
2.14 


81.0 


25.20 


359.0 
3.77 

117. 2 
2.16 


85.5 


173.2 
173.2 
172.6 

168.6 
164.5 
160.5 

156.4 
152.4 
148.3 

144.3 
140.2 
132. 1 

124.0 


115.9 
107.8 


26.64 


385.3 
3.80 

125.1 
2.17 


90.5 


Loads  below  the  heavy  line  are  for  lengths  greater  than  125  radii 


508 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


Table  XIX.     Safe  Loads  in  Tons  of  2  000  Pounds  for  Bethlehem  Rolled- 
Steel  lo-Inch  H  Columns  with  Square  Ends 


Unsupported 

length, 

ft 

2 

'   1 

1 

r. 

Allowable  stress  in  pounds 
13000  for  lengths  under  55 

per  square  inch: 
radii* 

r_.  „r 

16  000  -  55  llr  for  lengths  over  55  radii 

1 

10 
II 
12 

13 
14 
IS 

16 
18 

20 

22 
24 
26 

28 

93.5 

93.5 
92.1 

90.2 
88.3 
86.3 

84. 5 
80.7 
76.9 

73.1 
69.3 
65.4 

103.4 
103.4 
102.2 

lOO.I 

98.0 

95.9 

93.8 
89.6 
85.4 

81.3 
77.1 
72.9 

114. 2 
114. 2 
113. 1 

110.8 
IC8.S 
106.2 

103.9 
99-3 
94.7 

90.1 
85.6 
81.0 

125.0 
125.0 
123.9 

121. 4 
118. 9 
116. 4 

113. 9 
108.9 
103.9 

989 
93.9 
88.9 

135.9 
135.9 
134-9 

132.2 
129.5 
126.9 

124.2 
118. 8 
113. 4 

108.0 
102.6 
97.2 

146.8 
146.8. 
145.9 

143.0 
140. 1 
137.2 

134.3 
128.5 
122.7 

116. 9 
III. I 
105.3 

157.9 
157.9 
157.0 

153.9 
150.8 
147.7 

144.6 
138.4 
132.2 

126.0 
119. 8 
113.5 

61.6 

68.7 

76.4 

83.9 

91.8 
86.4 
80.1 

99.5 
93.7 
87.9 

107.3 

lOI.I 

94.9 

30 
32 

57.8 
54. 0 

64. 5 
60.3 

71.8 
67.2 

78.9 
73.9 

Area,  sq  in 

14.37 

15.91 

17.57 

19.23 

20.91 

22.59 

24.29 

/i-i.in* 

^i-i.  in 

/2-2.in< 

^-2  2.  in 

263. 5 
4.28 
89.1 
2.49 

296.8 
4.32 

100.4 
2.51 

331.9 
4-35 

112. 2 
2.53 

368.0 
4.37 

124.2 
2.54 

405.2 
4.40 

136.5 
2.56 

443.6 
4.43 

149. 1 
2  57 

483.0 
4.46 

162.0 
2.58 

Weight 
of  section, 
lb  per  lin  ft 

49.0 

54.0 

59.5 

65.5 

71.0 

77.0 

82.5 

Loads  below  the  heavy  line  are  for  lengths  greater  than  125  radii 

Tables  of  Safe  Loads  for  Steel  dolumnS 


too 


Tiblie  XIX  (Continued) .     Safe  Loads  in  Tons  of  2  000  Pounds  for  Bethle- 
hem Rolled-Steel  lo-Inch  H  Columns  with  Square  Ends 


Unsupported 

length, 

ft 

2 

1 

Allowab 
i^  000 

r. 

le  stress  in  pounds  per  square  inch: 

l_         u 

16  000  —  55  l/r  for  lengths 

over  55  radii 

1 

10 
II 
12 

13 
14 
IS 

16 
18 

20 

22 
24 

168.9 
168.9 
168.3 

165.0 

161. 7 
158.4 

155. 1 
148.5 
142.0 

135.4 
128.8 

180. 1 
180. 1 

179-6 

176. 1 
172.6 
169.1 

165.6 
158.6 
151.6 

144.6 
137.6 

190-6 
190.6 
190.2 

186.6 
182.9 
179-2 

175.5 
168. 1 
160.7 

153.3 
145.9 

201.9 
201  9 
201.9 

198.0 
194. 1 
190.3 

186.4 
178.6 
170.8 

163. 1 
155.3 

213.2 
213.2 
213.2 

209.3 
205.2 
201.2 

197.0 
188.9 
180.7 

172. 5 
164.4 

224.6 
224.6 
224.6 

220.7 
216.4 
212. 1 

207.8 
199-2 
190.7 

182. 1 
173-5 

236.1 
236.1 
236.1 

232.2 
227.7 
223.2 

218.7 
209.8 
200.8 

191-8 
182.8 
173.8 

26 

28 
30 
32 

122,2 

1,^0.6 

138.5 

147-5 

156.2 

165  0 

115. 6 
109.0 
102.4 

123.6 
116. 6 
109.6 

131.2 
123.8 
116. 4 

139  8 
132.0 
124.2 

148.0 
139-9 
131. 7 

1.56.4 
147-8 
139.2 

164.9 
155.9 
146.9 

Area,  sq  in 

25.99 

27.71 

29.32 

3^.06 

32.80 

34-55 

36.32 

/i-i.  in* 

^11.  in 

^2-2.  in* 

^2-  2.  in 

523.5 

4.49 
175.1 
2.60 

565  2 
4.52 

188.6 
2.61 

607.0 

.    4.55 

201.7 

2.62 

651.0 
4.58 

215.6 
2.64 

696.2 
4.61 

229.9 
2.65 

742.7 
4.64 

244.4 
2.66 

790.4 
4.67 

259  3 
2.67 

Weight  of 

section, 

lb  per  lin  ft 

88.5 

94.0 

99.5 

105. 5 

in. 5 

117. 5 

123.5 

Loads  below  the  heavy  line  are  for  lengths  greater  than  125  radii 

510 


Strength  of  Columns,  Posts  and  Struts  Chap.  14 


Table  XX.     Safe  Loads  in  Tons  of  2  000  Pounds  for  Bethlehem  Rolled- 
Steel  z  2-Inch  H  Columns  with  Square  Ends 


Unsupported 
length, 

r   ft 


2 
1 


Allowable  stress  in  pounds  per  square  inch: 
13  000  for  lengths  under  55  radii; 
16  000  —  55  //r  for  lengths  over  55  radii 


16 
18 


24 
26 

28 
30 
32 

34 
36 


123.5 
123.5 

122. 5 

136.2 
136.2 
135.4 

149-1 
149-1 
148.3 

162.0 
162.0 
161. 4 

118. 3 
114. 1 

109.9 

130.8 
126.2 
121. 6 

143-3 
138.3 
133.2 

155.9 
150.5 
145. 1 

105.7 

101. 5 
97.3 

117. 0 
112.4 

107.8 

128.2 
123.2 
118. 1 

139.7 
134-2 
128.8 

93.1 
88.9 

103. 1 
98.5 

113-1 

T08  I 

123  4 
117  9 

175.  o 
175.0 
174.5 

168.6 
162.8 
156.9 

151. 1 
145  2 
139  4 

133.5 

127.7 


84.7 


80.5 
76.3 


89.3 
84.7 


98.0 
93.0 


107. 1 
101.7 


121. 9 

116  o 
110.2 
104  3 


188.0 
188.0 
187.7 

181.5 
175.2 
169.0 

162.8 
156.5 
i50.3 

144.0 
137  8 


201. 1 
201.1 
201.0 

194  3 
187-7 
181. 0 

174-4 
167.7 
161.1 

154-4 
147  8 


131 -6 

i2.S.3 
119  I 
112. 8 


134.4 
127.8 

121.1 


214.2 
214.2 
214.2 

207.2 
200.1 
193.1 

186.0 
178.9 
171.9 

164.8 
157.7 
150  7 


143.6 
136.6 
129.5 


Area,  sq  in 


/i-i,in*. 
ri-i,in.. 
/2-2,in*. 
rj-2.  in. . 


Weight 
of  section, 
lb  per  Hn  ft 


19.00 


499.0 
5.13 
168.6 


64.5 


20.96 


556.6 
5. IS 

188.2 
3.00 


22.94 


615.6 
5.18 

208.1 
3.01 


78.0 


676.1 
5.21- 

228.5 
303 


84.5 


26.92 


738.1 
5. 24 

249.2 
304 


28.92 


801.7 
5.27 

270.1 
306 


98.5 


30  94 


866.8 
5.30 

291.7 
3  07 


32.96 


933.4 
5.33 

313.6 
3.08 


Loads  below  the  heavy  line  are  for  lengths  greater  than  125  radii 


Tables  of  Safe  Loads  for  Steel  Columns 


511 


Table  XX  (Continued).     Safe  Loads  in  Tons  of  2000  Pounds  for  Bethl«^ 
hem  Rolled-Steel  la-Inch  H  Columns  with  Square  Ends 


Unsupported 

length, 

ft 

2 

Allowab 

"^ 

le  stress  in  pounds  per  square  inch: 

jL-i' 

16  000  —  55  l/r 

or  lengths 

over  55  radii 

1 

10 
12 
14 

16 
18 
20 

22 
24 
26 

28 
30 
32 

34 

236.7 
226.7 
226.7 

219.6 
212. 1 
204.7 

197.3 
189.9 
182.5 

175.0 
167.6 
160.2 

239.9 
239 -9 
239.9 

232.6 

224.8 
217.0 

209.1 
201.3 
193.5 

185.6 
177.8 
170.0 

253.3 
253.3 
253.3 

246.0 
237.8 
229.6 

221.4 

213.2 

204.9 

196.7 

188. 5 
180.3 

266.7 
266.7 
266.7 

259.3 
250.6 
242.0 

233.4 
224.8 
216. 1 

207.5 
198.9 
190.3 

28 
28 
28 

25 

24 
23 

22 

21 

2C 
2C 

0.3 
0.2 
o.a 

2.6 
3.S 
4.S 

5.5 
6.4 
7.4 

8.4 
•0.3 

293.7 
293.7 
293.7 

286.0 
276.6 
267.1 

257.7 
248.3 
238.8 

229.4 
219.9 
210.5 

307.3 
307.3 
307.3 

299.7 
289.9 
280.1 

270.3 
260.5 
250.7 

240.9 
231.0 

221.2 

152.8 

162. 1 

172. 1 

181. 6 

191. 3 

201. 1 

211. 4 
201.6 
191. 8 

36 
38 

145.3 
137.9 

154.3 
146.5 

163.9 
155.6 

173.0 
164.4 

182.3 
173.2 

191. 6 
182.2 

Area,  sq  in 

34.87 

36.91 

38.97 

41.03 

43.10 

45.19 

47.28 

A-i.  in* 

''i-i.  in 

h^2,  in* 

r-i-i,\n 

I  000.0 

5.36 

335.0 

3.10 

I  069.8 
5.38 
357.7 
3. II 

1141.3 
5.41 

380.7 
3.13 

I  214.5 
5-44 
404.1 
3.14 

1289.4 

5.47 
428.0 
3.15 

X  366.0 
5.50 
452.2 
3.16 

1444.3 
5.63 
477.0 
3.18    . 

Weight 
of  section, 
lb  per  lin  ft 

118. 5 

125.5 

132.5 

139.5 

146.  s 

153.5 

161. 0 

Loads  below  the  heavy  line  are  for  lengths  greater  than  125  radii 

512 


Strength  of  Columns,  Posts  and  Struts 


Chap,   li 


Table  XXI.     Safe  Loads  in  Tons  of  2  000  Pounds  for  Bethlehem  Rolled- 
Steel  14-Inch  H  Columns  with  Square  Ends 


Unsupported 

length, 

ft 


Allowable  stress  in  pounds  per  square  inch: 
13  000  for  lengths  under  55  radii; 
16  000  —  55  IJY  for  lengths  over  55  radii 


16 
18 


24 
26 

28 
30 
32 

36 

40 
44 


159  o 
159  o 
159  o 

158.5 
153.8 
149.2 

144  5 
139-9 
135.2 

130. 5 
125.9 

121. 2 

111.9 


102.6 


Area,  sq  in 


24.46 


/i-i.  inf 
ri_i,  in. 
li^i,  in< 
r2-2.  in. 


884.9 
6.01 

294. 5 
3.47 


Weight 
of  section, 
lb  per  lin  ft 


83.5 


173.9 
173-9 
173.9 

173.9 
168.5 
163.4 

158.4 
153.3 
148.2 

143.2 
138. 1 
133. 1 

122.9 


188.9 

204.0 

219. 1 

234-3 

188.9 

204.0 

219. 1 

234.3 

188.9 

204.0 

219. 1 

234.3 

188.6 

204.0 

219. 1 

234.3 

183.2 

198. 1 

212.9 

228.0 

177.7 

192.2 

206.6 

221.3 

172.2 

186.3 

200.3 

214.6 

166.7 

180.4 

194.0 

207.9 

161. 2 

174.6 

187-7 

201.2 

155.8 

168.7 

181. 4 

194.5 

150.3 

162.8 

175. 1 

187.8 

144.8 

156.9 

168.8 

181. 1 

133.8 

145. 1 

156.2 

167.7 

112. 8 


26.76 


976.8 
6.04 

325.4 
3.49 


91.0 


122.9 
III. 9 


29.06 


1070.6 
6.07 
356.9 
3.50 


99.0 


133.4 
121. 6 


143-6 
131.0 


31.38 


1166.6 
6.10 
387.8 
3.52 


106.5 


33.70 


I  264. 5 
6.13 
420.3 
3.53 


114.5 


154.3 

140.9 


36.04 


1364.6 
6.16 

453.4 
3.55 


122.5 


249-5 
249-5 
249-5 

249.5 
243-0 
235-9 

228.8 
221.7 
214.5 

207.4 
200.3 
193-2 

1790 


164.7 
150. 5 


38.38 


1466.7 
6.18 
486.9 
3.56 


Loads  below  the  heavy  line  are  for  lengths  greater  than  125  radii 


Tables  of  Safe  Loads  for  Steel  Columns 


513 


Table  XXI  (Continued).     Safe  Loads  in  Tons  of  2  000  Pounds  for  Beth- 
lehem Rolled-Steel  14-Inch  H  Columns  with  Square  Ends 


2 

Allowable 
13  000  foi 
16000  — 

Unsupported 

length, 

ft 

"^ 

Y 

5tress  in  pounds  per  squ. 
lengths  under  55  radii; 
55  l/r  for  lengths  over  5 

ire  inch: 

.\\—=i 

5  radii 

,.      1 

10 
12 
14 

16 
18 

20 

22 
24 
26 

28 
30 
32 

36 

263.8 
263.8 
263.8 

263.8 
257.4 
249  9 

242.4 
234.9 

227.4 

220.0 
212.5 
205.0 

190.0 

279.2 
279.2 
279.2 

279.2 
27*5 
264.6 

256.7 
248.9 
241.0 

233   I 

225.2 
217.3 

201.5 

294.7 
294.7 
294.7 

294.7 
288.1 
279.8 

271.5 
263 . 2 
254-9 

246.6 
238.3 
230.0 

213.5 

310. 1 
310. 1 
310. 1 

310.1 
303.4 
294.7 

286.0 
277.3 
268.6 

259-9 
251.2 
242.5 

225.1 

325.7 
325.7 
325.7 

325.7 

319  0 

309.9 

300.8 
291.7 
282.6 

273-5 
264.4 
255.3 

237.1 

341.3 
341.3 
341.3 

341.3 
334-6 
325.1 

315-6 
306.1 
2966 

287.1 
277.6 
268.1 

249-1 

40 
44 

175. 1 
160. 1 

185.7 
170.0 

196.9 
180.3 

207.7 
190.3 

218.9 
200.7 

230.1 
211. 1 

Area,  sq  in 

40.59 

42.9s 

45.33 

47.71 

50.11 

52.51 

^1-1.  in* 

ri_i,  in 

/^2.in* 

I  568.4 
6.21 
519-7 
3.58 

I  674.7 

6.24 

554.4 

3.59 

I  783.3 
6.27 
589. 5 
3.6i 

1894.0 
6.30 
626.1 
3.^2 

2007.0 

6.33 
662.3 
3.64 

2122.3 
6.36 
699.0 
3.65 

Weight 
of  section, 
lb  per  lin  ft 

138.0 

146.0 

154.0 

162.0 

170.5 

178.5 

Loads  below  the  heavy  line  are  for  lengths  greater  than  125  radii 

Strength  of  Columns,  Posts  and  Struts  Chap.  14 


Table  XXI  (Continued).     Safe  Loads  in  Tons  of  2  000  Pounds  for  Beth- 
lehem Rolled-Steel  x  4-Inch  H  Columns  with  Square  Ends 


Unsupported 

length, 

ft 

2 

1 

1 

r. 

Allowable 
13000  f 
16000  - 

stress  in  pounds 
3r  lengths  under  55 
-  55  l/r  for  lengths 

per  square  inch: 
radii; 

r._  7 

I 

over  55  radii 

i 

10 
12 
14 

16 
18 

20 

22 
24 
26 

28 
30 
32 

36 
40 
44 

357.0 

357-0 
357.0 

357.0 
350.3 
340.4 

330. 5 
320.6 
3I0.7 

300.8 
290.9 
281.0 

261.2 

372.8 
372.8 
372.8 

372.8 
366.1 

355.8 

345.5 
335.2 
324.9 

314.6 
304.3 
294.0 

273.4 

388.6 
388.6 
388.6 

388.6 
381.9. 
371.2 

360.5 
349.8 
339.1 

328  4 
317-7 
307.0 

285.6 

403.5 
403.5 
403.5 

403.5 
396  •» 
385.8 

.374.8 
363.7 
352.6 

341 -6 
330-5 
319.4 

297.3 

419-4 
419-4 
419  4 

419-4 
412.9 
410.5 

390.0 
378.5 
367.1 

355.6 
344.1 
332.6 

309.7 

435.4 
435  4 
435.4 

435.4 
429.0 
417.2 

405.3 
393-4 
381.6 

369.7 
357.8 
345. 9 

322 . 2 

451.4 
451.4 
451.4 

451.4 
445-2 
433-0 

420.7 
408.4 

396 -2 

383.9 
371.6 
350.4 

334  8 

241.4 
221.6 

252.8 
232.2 

264.2 
242.8 

275.1 
253.0 

286.8 
263-8 

298.5 
274.8 

310.3 
285.8 

Area,  sq  in 

54  92 

57.35 

59.78 

62.07 

64-52 

66.98 

69.45 

/i-i.in* 

ruuin 

lutAn* 

^2-8.  in 

2239.8 
6.39 
736.3 
3.66 

2359.7 

6.41 

744.2 

*3.67 

2481.9 
6.44 
812.6 
3.69 

2603.3 
6.48 
849.8 
3.70 

2730.2 
$.51 
889.3 
3.71 

2859.6 

6:53 

9294 

3.73 

2 991. 5 

6.56 

970.0 

3.74 

Weight 
of  section, 
lb  per  lin  ft 

186. 5 

19s -0 

203.5 

211. 0 

219. S 

227.5 

236.0 

Loads  below  the  heavy  line  are  for  lengths  greater  than  125  radii 

Tables  of  Safe  Loads  for  Steel  Columns 


515 


Table  XXI  (Continued).     Safe  Loads  in  Tons  of  2  000  Pounds  for  Bethle- 
hem Rolled-Steel  14-Inch  H  Columns  with  Square  Ends 


Unsupported 

length, 

ft 


1 -1 


Allowable  stress  in  pounds  per  square  inch:      ' 
13  000  for  lengths  under  55  radii; 
16  000  —  55  llr  for  lengths  over  55  radii 


10 

467.6 

12 

467.6 

14 

467.6 

16 

467.6 

18 

461.5 

20 

448.9 

24 
26 

28 
30 
32 

36 

40 

44 


436.2 
423.6 
410.9 

398.2 
385.6 
372.9 

347.6 


483.8 
483.8 
483.8 

483.8 
477-9 
464.8 

451.8 
438.7 
425.7 

412.6 
399-6 
386.5 

360.4 


322.2 
296.9 


334.3 
308.1 


500.0 
500.0 
500.0 

500.0 
494.4 
480.9 

467.4 
454.0 
440.5 

427.1 
413.6' 

400.2 

373.3 


516.4 
516.4 
516.4 

516.4 
510.9 
497.0 

483.2 
469.3 
455.5 

441.6 
427.8 
413.9 

386.3 


532.8 
532.8 
532.8 

532.8 
527.6 
513.3 

499-1 
484.8 
470.6 

456.3 
442.1 
427.8 

.399-4 


346.4 
319.5 


358.6 
330.9 


370.9 
342.4 


549. 3 
549.3 
549-3 

549-3 
544-3 
529.6 

515.0 
500.4 
485-7 

•471  - 1 
4.56.4 
441.8 

412.5 


383 -3 
354.0 


Area,  sq  in 


-^1-1.  in" 
n^i,  in. 
^2-2.  in* 


Weight 
of  section, 
lb  per  lin  ft 


71.94 


3125.8 
6.59 

I  011.3 
3.75 


244. 5 


74.43 


3262.7 
6.62 

1053.2 
3.76 


76.93 


79-44 


3402.1 

6.65 

1095.6 

3  77 


3544.1 
6.68 

1 138.7- 
3.79 


261.5 


81.97 


3688.8 
6.71 

1 182.4 
3.80 


273.5 


84.50 


3836.1 
6.74 

I  226.7 
3.81 


287. 5 


Loads  below  the  heavy  line  are  for  lengths  greater  than  125  radii 


516 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


Table  XXII.     Safe  Loads  in  Tons  of  2  000  Pounds  for  Light- Weight  Lally 
Columns,* 


Factor  of  safety  between  4,5  and  5 
Calculated  by  theiormula,  P  =  ^^(13  500  —  140 //J)  -\- 

AAi 

000  4- 

II  //J) 

in  which  yl  5  and  ^c'^''^' t^ie  areas  of  steel  pipe  and  concrete,  in  square  inches,  /the 
length  ill  inches,  and  d  the  outside  diameter  of  pipe,  in  inclies 

Outside 
diam- 

Weight 

per 
Hnear 

Length  of  co 

lumn  in  feet 

13 

14 

15 

16 

eter, 
in 

foot, 
in 

6 

7 

8 

9 

10 

II 

12 

3 

3^ 

4 

5 
6 

9.64 
13.09 
17.02 
21.05 
25  90 
36.82 

6 
9 
13 
14 
20 
28 

6 
9 
13 
14 

20 
28 

5 
8 
12 
13 

19 
27 

'8" 

12 

13 

19 

27 

7 
n 
12 
18 
26 

10 
II    • 

18 
26 

10 
17   . 
25 

17 

24 

23 

22 

16 
23 

Table  XXin. 

Safe  Loads  in  Tons  of  2  000 

Pounds  for  Heavy-Weight 

Lally  Columns* 

Factor  of  safety  between  4.5  and  5 

These  loads  can  be  greatly  increased  by  reinforcing  the  concrete 

Calculated  by 
in  which  A^  am 

the  formula,  P  =  Agiis  500  —  140  l/d) 
Ar  are  the  areas  of  steel  pipe  and  concret 

+  Ac{i  000 +  11  l/d) 

e,  in  square  inches,  /  the 

length  in  inches,  and  d  the  outside  diameter  of  pipe,  in  inches 

Weight 

1 
Length  of  columns  in  feet 

Outside 
diameter, 

per 
linear 

in 

foot, 
lb 

6 

8 

10 

12 

14 

16 

18 

20 

3H 
4 

IS 

20 

12 
16 

II 
15 

10 

9 
12 

14 

II 

4K2 

24 

20 

18 

17 

16 

15 

5 

29 

27 

26 
31 

24 
29 

22 
28 

21 
26 

19 

5K 

36 

32 

24 

22 

6^ 

49 

45 

43 

41 

40 

38 

35 

34 

32 

7% 

64 

58 

56 

54 

52 

51 

49 

46 

44 

m 

81 

74 

72 

69 

67 

•65 

62 

60 

57 

9% 

100 

93 

89 

87 

85 

82 

79 

77 

75 

10^ 

123 

III 

109 

107 

104 

lOI 

99 

96 

93 

X1V4, 

146 

131 

128 

124 

122 

119 

117 

113 

III 

I2M 

169 

150 

146 

144 

141 

139 

135           133 

■  130 

*For  areas  of  cross-sections  of  metal  and  concrete,  and  for  other  data  used  in  compu- 
tations for  determining  safe  loads  by  formula,  see  Handbook  of  the  United  States  Coluj 
Company,  Cambridge,  Mass.     (See,  also,  pages  469  to  474,  and  page  477.) 


1 


Tables  of  Safe  Loads  for  Steel  Columns 


517 


Table  XXIV.* 


Safe  Loads  in  Units  of  i  ooo  Pounds  for  Plate-and-Angle 
Columns 


Vn 

3 

Allowable  fiber-stress  in 

pounds  per  square  inch. 

^K     I 

1 

13  000  for  lengths  of  60  radii  or  under 
Reduced   for  lengths  between   60   and    120  radii,   by 
Formula  (13), 

5  =  19  000  —  100  l/r 
Weights  do  not  include  rivet-heads  or  other  details 
For  values  for  l/r  above  120,  see  notes  on  page  490 

13 

Web-plate  6"  XK"            | 

Web-plate  8''XH'' 

Effective 

length, 

ft 

SX 

^1 
5x 

JX 
^X 

>5 

Jx 

^X 

\x. 

'bo'^ 

'bCNf< 

6 

7 
8 

69  ' 

63 

56 

81 

88 

94 
86 
79 
72 
65 

57 

no 

lOI 
lOI 

119 
119 

78 
72 

82 

76 

69 
63 

56 

50 

103 

95 
87 
78 

70 
62 

96 

?9 
83 

76 
70 
63 

57 

115    \ 
107    ' 

100 

92 

85 
78 
70 

9 

10 

II 

12 

13 
14 
15 

i6 
17 
i8 
19 

20 

21 
22 
23 
24 
25 

26 
27 
28 
29 

30 

49 
43 

66 
60 

54 
49 

38 
35 
32 

28 

25 

22 
18 

50 

47 
43 
39 

36 
32 
28 
25 

43 

40 

37 

34- 
32 

11 

23 

20 

45 
42 

39 

35 
32 

26 
22 

56 
52 
48 

44 
40 
36 
32 
28 

52 

49 
46 
43 
39 
36 

33 
30 
27 
23 

63 

60 
56 
52 
49 
45 

41 
38 
34 
30 

Area,  sq  in 

5.74 

6.26 

6.74 

7.24 

8.48 

7.76 

9.12 

/i-i.in* 

n-i,  m 

^2,  in* 

^2-2.  in. ... . 

34.3 
2.45 
6.2 
1.04 

39-1 

-2.50 

10.3 
1.28 

42.6 
2.51 
10.3 
1.24 

81.2 
3.35 
10.3 
1. 19 

96.9 
3.38 
12.9 
1.23 

90.1 
3.41 
16.0 
1.44 

107 
3.43 
20.2 
1.49 

Weight, 
lb  per  lin  ft . . 

1Q.6 

21. 5 

23.1 

24.8 

29.2 

26.4 

31.2 

The  safe  load-values  above  the  upper  heavy  line  are  for  ratios  oil/r  not  over  6o; 
those  beTweenthrheavy  lines  are  for  ratios  up  to  120  l/r;  and  those  below  the  lower 
heavy  line  are  for  ratios  not  over  200  l/r 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


TaWe  XXIV 

*  (Continued).     Safe  Loads  in  Units  of  i  000  Pounds  for  Plate^ 
and-Angle  Columns 

n>,    . 

2 

_        Allowable  fiber-stress  in  oounds 

oer  sauare  inch: 

^ 

V 

13  000  for  lengths  of  60  ra 
Reduced  for  lengths  betw 
Formula  (13), 

5  =  19  oo( 

Weights  do  not  include  rive 

)    For  values  for  l/r  above  1 2 

dii  or  under 

een   60   and    120   radii,   by 

D  —  TOO  l/r 

t-heads  or  other  details 

0,  see  notes  on  page  490 

12 

Effective 
length, 

Web-plate  S^XMe" 

Web-plate  8"XW 

it 

El 

It 

>0 

1? 

IS; 

g^5 

•wX 
•*X 

If 

if 

5 

^X 

6 
7 
8 
9 

10 

II 

12 
13 

IS 
i6 
17 
i8 
19 

20 

21 
22 

23 

24 
25 

26 

27 

28 

29 

30 

] 
1 

25 

142 

141 
141 
141 

161 
161 
161 

168 
168 
168 

188 
188 
188 

208 
208 
208 

25 

142 

112 
104 

96 

138 

130 

121 

ri2 

136 
128 

121 

158 
149 

140 
131 
123 
114 
105 

97 
88 

163 

154 

145 
136 

127 
1x8 

109 

100 
90 

185 

175 

165 
155 
14s 
135 
124 

114 
104 

206 
196 

185 
174 
163 
152 

141 

130 
120 

89 

J04 

113 

105 
97 
89 

81 

31 
73 

ii 

77 

66 

62 

58 

54 
50 

47 

43 
39 
35 
31 

73 

68 

64 
60 
55 

SI 

47 
42 
38 
34 

75 

71 
67 
63 

59 
55 
51 

48 

44 

40 
36 

83 
79 
74 

70 
66 
61 
57 
53 

48 
44 
39 

86 
81 

77 

11 
63 
59 
54 

49 
45 
40 

a 
I 

5 
5 
4 

18 
3 
»8 

3 
8 
3 

3 

8 
3 
8 

no 
105 
100 

94 
89 
83 
78 
72 

67 
62 
56 
51 

Area,  sc^  in 

9.62 

IQ.94 

10.86 

12.42 

12.92 

.14.48 

16. 00 

/i-i.  in* 

''i-i.  in 

/2-2,  in*,.... 
«rj-5,  in 

no 
3.38 

29.7 
1.47 

127 

I    51 

122 
3. 35 
303 
1.67 

I4J 
3.36 
36.3 
I  71 

143 
3.33 
37.2 
1.70 

161 
3.34 
43.5 
1.73 

178 
3  33 

50.2 
i  77 

•  Weight, 
Ibperlinft.. 

32.9 

37.3 

37.3 

42. s 

44.2 

49.4 

54)5 

The  safe  load-values  above  the  upper  heavy  line  are  for  ratios  of  l/r  not  over  6o: 
those  between  the  heavy  lines  are  for  ratios  up  to  i2ol/r;  apd  tho$,e  below  the  lower 
heavy  line  are  for  ratios  not  over  200  l/r 

?  From  P.Qpket  Copipanipp,  Carpegfje  Steel  Copip^ny,  J?k|:sl^ur^h,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


§1? 


Table  XXIV*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  Plate- 
and-Angle  Columns 


.. 

'5 

\           Allowable  fiber-stress  in  pounds  per  square  inch: 

A  \ — ,r 

^> 

+ 

-^- 

13  000  for  lengths  of  60  radii  or  under 

1.- 

Reduced   for  lengths  between   60   and    120   radii,   by 

Formula  (13), 

^ 

t^ 

S  =  19  000  —  100  l/r 
Weights  do  not  include  rivet-heads  or  other  details 

For  values  for  l/r  above  120,  see  notes  on  page  490 

1 

\2 

Web-plate  io"XH" 

Web-plate  lO^XMe" 

Web-plate  io"X?i" 

,^ 

^ 

Effective 

length, 

ft 

jx 

gX 

to 

^x 

sx 

^i 

4^ 

-# 

i 

,x 

C-x 

^X 

Cx 

«5? 

^X 

*ro 

"^ 

"po 

't 

%!• 

^ 

V> 

6 

99 
91 

82 

74 

107 

125 
125 

133 
133 

149 
149 
149 

170 
170 
170 

178 
178 
178 

198 
198 
198 

207 
207 
207 
207 

7 
8 
9 

107 

100 

93 

119 
III 

125 

117 

142 

164 

170 

192 

10 

II 

12 

66 
58 

86 

79 
71 

103 

95 

87 

108 

99 
91 

133 

125 
116 

154 

145 
135 

160 

150 

140 

181 

170 
160 

207 

203 
194 

52 

13 
14 
15 

48 
44 
40 

64 

79 
71 

82 
73 

108 
99 
91 

126 

107 

^,39 
121 
III 

149 
138 
127 

18S 
175 
166 

57 
54 

65 

68  ■ 

i6 
17 

36 
32 

50 

47 

61 

57 

64 
60 

82 

98 

lOI 

116 

157 
148 

77 

90 

93 

106 

i8 

28 

43 

53 

55 

73 

85 

88 

lOI 

139 

19 

24 

40 

49 

51 

69 

Si 

u 

95 

130 

20 

36 

45 

47 

64 

76 

90 

121 

21 
22 

33 

29 

41 
37 

42 
38 

60 
56 

71 
.67 

73 

84 
79 

112 

107 

23 

25 

34 

34 

SI 

62 

'^} 

74 

103 

24 

30 

47 

57 

58 

68 

98 

25 
26 

43 
39 

5? 

53 

48 

63 

57 

93 
89 
84     , 

48 

34 

43 

43 

52 

28 

47 

80     1 

29 

75 

30 





71 

Area,  sq  in 

7.74 

8.26 

9.62 

10.25 

If -49 

13-05 

13., ^7 

15.23 

15.9s 

/i-i.  in* 

134 

148 

176 

181 

201 

232 

237 

267 

279 

^1-1.  in 

4.16 

4.23 

4.28 

4.20 

4.18 

4  22 

4.17 

4.19 

4.18 

/2-2.in* 

10.3 

16.0 

20.2 

20.7 

30.3 

36.3 

37.2 

43.5 

70.6 

r2_o,  m 

1. 15 

1-39 

1.45 

1.42 

1.62 

1.67 

.1.65 

1.69 

2.10 

Weight, 

Iboerlinft  .. 

26.5 

28.1 

32.9 

35  0 

39-4 

44.15 

46.8 

52.0 

54.4 

The  safe  load-valu 

es  above  the  upper  heavy  line  are  for  ratios  of  l/r  not  over  60; 

those  between  the  hej 

ivy  lines  are  for  ratios  up  to  120  l/r;  and  those  below  the  lower 

heavy  line  are  for  rat 

los  not  over  200  l/r 

•From  ?oc]k^t  Cpmpa^ipii,  Carnegie  5teel  Compaqj^,  Pittsburgh,  Pa. 


520 


Strength  of  Columns,  Posts  and  Struts 


Chap.. 


Table  XXIV*  (Continued)* 


Safe  Loads  in  Units  of  i  ooo  Pounds  for  Plate- 
and-Angle  Columns 


\^ 

^^^_ 

e  inch; 
dii.   by 

ails 
490 

+ 

1 

i 

1 

r 

I          Allowable    fiber-stress  in  pounds    per   squar 
13  000  for  lengths  of  60  radii  or  under 
Reduced   for  lengths  between   60   and    120   ra 
Formula  (13), 

5  =  19  000  —  100  l/r 
Weights  do  not  include  rivet-heads  or  other  det 

2 

For  values  for  l/r  above  120,  see  notes 

on  page 

Effective 

length, 

ft 

Web-plate  io"X^^" 

Web- 

plate  io"XF2" 

Web-pl. 
10"  X  H" 

JX 
^X 

"0 

-ax 

^x 

0 

1 

IF 

s;x 

:x 

6 
7 
8 
9 

lO 

II 

13 
13 

232 
232 
232 
232 
232 

236 
236 
236 
236 

236 

236 
236 

266 
266 
266 
266 
266 

266 
266 
266 

296 
296 
296 
296 
296 

296 
296 
296 

312 

341 

370 
370 
370 
370 
370 

370 

370 
370 

386 
386 
386 
386 
386 

386 
386 
386 

312 
312 
312 
312 

312 
312 
312 

341 
341 
341 

341 

341 
341 

341 

230 
220 
210 
.   200 
190 
180 

235 
226 
218 

200 

257 

248 

238 

229 

220 
210 
201 

191 
182 
172 
163 

IS4 
144 

288 

302 
291 
280 

269 
258 
247 
236 

225 
214 
203 
192 
181 

170 

333 
321 

309 
297 
28S 
274 
262 

250 
238 
226 
214 
203 

191 

363 
350 

337 
325 
312 
299 
287 

274 
261 
249 
236 
223 

210 

378 
36s 

351 
338 
32s 
312 
298 

285 
272 
258 
245 
232 

218 

15 
i6 

278 
267 

2S7 
247 
237 
226 

216 
206 
19s 
18S 
175 

164 

17 
i8 
19 

20 
21 

170 
160 
150 
140 

130 

201 
192 
184 

167 
158 

ISO 
141 
132 

22 
23 
24 
25 

26 

27 
28 
29 

30 

123 
118 
113 
108 

103 
98 
93 
88 
83 

126 
121 
117 
113 
109 

139 
134 
130 
125 

IS7 

146 
141 

164 
158 

IS3 

147 

181 
164 

198 
192 
186 
179 

207 
200 
193 
187 

Area,  sq  in 

17.87 

18.19 

20.47 

22.75 

24.00 

26.24 

28.44 

29.69 

500 
4.10 

213 
2.68 

/i-i.in* 

ri-i,  in 

-^2-2.  in* 

»'2-2.  in 

31S 
4.20 
82.3 
2. IS 

319 
4.19 

^2 

361 
4.20 

2.61 

401 
4.20 

160 
2.6s 

412 
4.14 

i6S 
2.62 

451 
4.15 

186 
2.66 

489 
4. IS 

206 
2.69 

Weight, 
Ibperlinft.. 

60.8 

62.0 

70.0 

77.6 

81.8 

89.4 

97.0 

101.3 

The  safe  load-values  above  the  upper  heavy  line  are  for  ratios  of  l/r  not 
those  between  the  heavy  lines  are  for  ratios  up  to  I2Q  l/r;  and  those  below  t 

over  60; 
he  lower 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 


Tables  of  Safe  Loads  for  Steel  Columns 


521 


I'able  XXIV  *  (Continued) .     Safe  Loads  in  Units  of  i  ooo  Pounds  for  Plate- 
and-Angle  Columns 


2 

All 

,^„-oK1„ 

pound 

„,..„,„...    1 

^^"^ 

J 

f) 

13  000  for  lengths  of  60  rad 

ii  or  ui 

der 

:^!      X 

/, 

Reduced   for   lengths   between    60 

and    120   radii,   by 

-f|      L.. 

_  1 

Formula  (13), 

>- 

^   =  19  GOG  —  100 
Weights  do  not  include  rivet-heads 

l/r 

or  other  details 

^— . 

For  values  for  l/r  above  120 

,  see  no 

tes  on  page  490 

b 

J 

Effective 

Web-plate 

Web-plate 

X2"X^l6" 

Web-plate  I2''X^^" 

k 

:; 

^ 

^ 

"v, 

jx 

^^ 

Nf> 

length, 
ft 

-SbX 

^X 

|x 

# 

Sx 

c!";^ 

cX 

c:: 

C5 

P!^/^ 

a%^ 

a^^ 

CsJM 

a"*!;' 

ci^ 

c3  (^ 

rt  ro 

rt  ro 

^0 

aO 

"5  To 

^x 

ri-.N 

rtT^ 

-.-• 

^X 

^X 

^X 

rfX 

-.^ 

-<? 

^X 

"ro 

'^ 

■* 

-* 

%t 

V. 

:: 

^o 

6 

7 
8 
9 

114 

132 
132 

148 
148 

148 

157 

1^7 

178 
178 
178 

187 
187 

187 

217 
217 
217 
217 

242 
242 

242 
242 

266 
266 

266 
266 

112 
104 
96 

123 
115 

157 
147 

140 

169 

177 

lO 

II 

89 
81 

106 
98 

131 
123 

138 
129 

159 
149 

167 
156 

217 

242 

266 

210 

237 

264 

12 

73 

89 

114 

120 

139 

145 

201 

226 

252 

13 
14 
15 
i6 
17 

65 

80 
72 

106 
97 
89 

80 

III 

lOI 

92 

129 
119 

109 

99. 

134 
124 
113 

102 

191 

181 
171 
162 
152 

215 

205 
194 

184 
173 

241 
229 
218 

206 
19s 

59 
55 

52 

48 

67 

63 

58 

84 
79 

76 

92 

96 

i8 

44 

54 

71 

75 

87 

91 

142 

162 

184 

19 

40 

50 

67 

70 

82 

85 

132 

152 

172 

20 

21 
22 

36 

32 

28 

45 

41 

37 

03 

59 
55 

C5 
6i 
56 

77 
72 
67 

80 

75 
69 

123 

141 
130 

161 
149 

115 

no 

125 

141 

23 

33 

50 

52 

62 

64 

105 

120 

135 

24 

46 

47 

57 

58 

100 

114 

129 

25 
26 

42 
38 

42 
38 

52 

53 

95 
91 

109 
104 

123 
118 

47 

48 

27 

42 

86 

98 

112 

28 

81 

93 

106 

29 

76 

88 

lOI 

30 



71 

82 

95 

Area,  sq  in 

8.76 

10.12 

11.36 

14.42 

12. 11 

13.  G7 

16.70 

18.62 

20.50 

/i-i,  in4  .... 

222 

264 

295 

304 

350 

35<j 

421 

476 

526 

ri-i,in 

5.04 

5.  II 

5.09 

5.01 

5.06 

4.99 

5.02 

5- OS 

5.07 

h-2f  ml 

16.0 

20.2 

29.6 

30.3 

30.3 

37.3 

70.6 

82.3 

94.6 

^2-2.  in 

1.35 

1. 41 

i.6i 

1.58 

1.63 

1. 61 

2.06 

2.10 

2.15 

Weight, 

lb  per  lin  ft. . 

29.8 

34.6 

390      41.6     1 

46.8 

49-3 

56.9 

63.3 

69.7 

The  safe  Ic 

)ad-valu 

ss  above  the  upper  heavy  line  a 

re  for  ra 

tios  of  l/r  not  over  60; 

those  between  the  I 

leavy  lines  are  for  ratios  up  to 

120  l/r; 

and  those  below  the 

lower  heavy  line  are 

for  ratios  not  over  200  l/r 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Strength  of  Columns,  Posts  and  Struts  Chap.  14 


Table  XXIV*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  Plate- 
and-Angle  Columns 


2 

re  inch: 

» ' — i 

T  r ' 

Allowable  nber-stress  in  pounds  per  squa 

^ 

-4 

p-              13  000  for  lengths  of  6o  radii  or  under 

L.. 

•^  -j^            Reduced   for  lengths   between   6o   and    120  i 
Formula  (13), 

aoii,   by 

o 

A 

\                                            6"  =  19  000  —  100  l/r 

^ 

-r^ 

^~             Weights  do  not  include  rivet-heads  or  other  details             | 

2 

VdlUC 

a  lui  *•/'    dL'^-'vc  i^u,  &CC  liULCb  uii  pcigu  4y>J                 | 

Effective 

Web-plate 
12'' x%" 

Wph-nlatp  jy  Vl<i" 

Web-plate          | 

>VcU-pi<itc  1^     ?\./2 

I2"XH" 

I2''xr4" 

^ 

^ 

^ 

^ 

*'.o 

^ 

^ 

length, 

|x 

'tix 

If 

'Hex 

|x 

ll 

|| 

^X 

fx 

-tX 

e;^ 

^X 

Tx 

? 

5x 

^ 

^ 

^ 

to 

0 

vb 

^ 

.    0 

UD 

6 

276 

30s 

325 

354 

383 

411 

439 

458 

478 

7 
8 

276 
276 

305 

325 
32s 

354 
354 

383 

411 

439 

458 
458 

478 
478 

30s 

383 

411 

439 

9 

276 
276 

305 
305 

325 
325 

354 
354 

383 
-383 

411 
411 

439 

458 
458 

478 
478 

lO 

439 

II 

276 

305 

325 

354 

383 

411 

439 

458 

478 

12 

13 

14 

276 

305 
305 

325 

354 
354 

383 
383 

411 

/ITT 

439 
439 

458 
4S8 

478 
478 

274 
264 

323 
312 

295 

342        373 

403 

433 

451 

469 

15 

254 

284 

300 

330        359 

389 

418 

435 

452 

i6 

244 

274 

288 

317 

346 

375 

403 

419 

436 

17 

234 

26Z 

277 

305 

333 

361 

388 

404 

420 

i8 

224 

252 

265 

292 

319 

347 

373 

388 

403 

19 

214 

241 

253 

280 

306 

333 

358 

372 

387 

20 

204 

230 

242 

267 

293 

318 

344 

357 

370 

21 

194 

220 

230 

255 

279 

304 

329 

341 

354 

22 

184 

209 

218 

242 

266 

290 

314 

325 

338 

23 

174 

198 

207 

230 

253 

276 

299 

310 

321 

24 

164 

187 

195 

217 

239 

262 

284 

294 

305 

25 
26 
27 
28 

ISS 

176 
166 

183 

204 
192 

226 
213 

248 
234 

269 

254 
239 

278 
262 

247 

288 
272 

147 
142 
137 

173 
167 
162 

160 
154 

185 
179 

203 
196 

220 
213 

256 
248 

230 

239 

29 

132 

149 

IS6 

173 

189 

205 

223 

231 

240 

30 

127 

143 

150 

166 

183 

199 

215 

223 

232 

Area,  sq  in 

21.22 

23.50 

25.00 

27.24 

29.44 

31.60 

33.76 

35.26 

36.76 

A-i.  in* 

544 

605 

623 

683 

741 

794 

849 

867 

885 

ri_i,  in 

5.06 

5.07 

4.99 

5.01 

5.02 

5-01 

5.01 

4.96 

4.91 

/2_2,  in*.... 

139 

160 

165 

186 

206 

228 

249 

257 

266 

»'2-2,  in 

2.56 

2.61 

2.57 

2.61 

2.65 

2.69 

2.72 

2.70 

2.69 

Weight. 

.Ibperlinft.. 

72. 5 

80.1       85.2 

92.8    100.4 

107.6 

114. 8 

119. 9 

125.0 

The  safe  lo 

ad-values  above  the  upper  heavy  line  are  for  ratios  of  l/r  no 

t  over  60; 

those  betwee 

n  the  heavy  lines  are  for  ratios  up  to  120  l/r\  and  those  below 

the  lower 

.  heavy  line  ai 

e  for  ratios  not  over  200  l/r 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh.  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


523 


TaWe  XXIV  *  (Continued).     Safe  Loads  in  Units  of  i  600  Pbuiidfe  for  Plate- 
and-Angle  Columns 


A      12     ! 

Allowable  fiber-stress  in  pounds  per  square  inch: 
13  000  for  lengths  of  60  radii  or  under 
Reduced   for  lengths  between   60  and    120   radii,   by 
Formula  (13), 

5  =  19  000  —  100  l/r 
Weights  do  not  include  rivet-heads  or  other  details 
For  values  for  l/r  above  120,  see  notes  on  page  490 

'  ^  I2  t ' 

Web-plate  I2''X>^" 

Web-plate  i2"X3'^" 

Effective 
length, 
ft 

0 

rf^  IN    ^ 

^b 

0 

'g^^X 

«5 

II 
12 
13 
14 
15 

16 

383 
333 
3S3 
383 
383 

428 
428 
423 
428 
428 

428 

458 
458 
458 
45s 
458 

458 

487 
487 
487 
487 
487 

487 

507 
507 
507 
507 
507 

553 
553 
553 
553 
553 

553 

379 

506 

491 
476 
461 
447 

432 
417 
•       403 
338 
373 

358 
344 
329 
314 
299 

285 

17 
18 
19 
20 

21 
22 
23 
24 
25 

26 

27 
28 
29 
30 

31 
32 
33 

34 
3.'^ 

368 
357 
346 
334 

323 

312 
301 
289 
278 

267 
256 
244 
233 
222 

211 

419 
407 

395 
383 

370 

346 
334 
322 

310 
297 
28S 
273 
261 

249 
237 

447 
434 
421 
407 

394 
381 
368 
355 
342 

329 
316 
303 
290 

277 

264 
250 

475 
461 
447 
433 

419 
405 
391 
377 
363 

349 
335 
321 
307 
293 

279 
26s 

542 
526 
510 
495 

479 
463 
448 
432 
416 

401 
385 
369 
354 
338 

323 

307 

203 
197 
191 
186 

272 

228 
221 
215 

242 

235 

229 

257 
250 
243 

264 
257 
249 

294 
287 
279 

Area,  sq  in 

29-44 

32.94 

35.22 

37.50 

39^00 

42.50 

7i-i.ini 

''1-1,  in 

V2.  in* 

''2-2.  m 

916 
5. 58 

291 
3.14 

1073 
5.71 
348 
3.2s 

1 136 

5.68 

368 

3.23 

I  197 

5.65 

388 

3.22 

I  215 

S.58 

394 

3.18 

1377 

5.69 

451 

3.26 

Weight, 
lb  per  lin  ft.. 

100.2 

112. 1 

120. 1 

127.7 

132.8 

144.7 

The  safe  load- values  a 
those  between  the  heav^ 
heavy  line  are  for  ratios 

bove  the  upper  heavy  line  are  for  ratios  of  l/r  not  over  60; 
i  lines  are  for  ratios  up  to  120  l/r]  and  those  below  the  lower 
not  over  200 //>          j    , 

"From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


524 


Strength  of  Columns,  Posts  and  Struts 


Table  XXIV*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  Plate- 
and-Angle  Columns 


y 


^ 


.j^\- 


•        |2      • 


w 


Allowable  fiber-stress  in  pounds  per  square  inch: 
13  000  for  lengths  of  6o  radii  or  under 
Reduced  for  lengths  between   6o   and    120   radii,   by 
Formula  (13), 

5  =  19  000  —  100  l/r 
Weights  do  not  include  rivet-heads  or  other  details 
For  values  for  l/r  above  120,  see  notes  on  page  490 


Effective 

length, 

ft 


Web-plate  i2"X3'i" 


13 
14 
15 


17 
18 
19 


23 
24 
25 

26 
27 
28 
29 
30 

31 
32 
33 

34 
35 


Area,  sq  in 

h-u  in* 

ri-i,  in 

72-2,  in*. .  .  . 
^2-2'  ill 


Weight, 
lb  per  lin  ft. 


582 
582 
582 
S82 

582 


610 
610 
610 
610 
610 

610 


Web-plate  i2"X^A'' 


K4^ 


630 
630 
630 
630 
630 

630 


675 
675 
675 
675 
675 

675 


1.^|x 


721 
721 
721 
721 

721 


569 
553 
536 

520 

503 
487 
470  < 

454 
437 

421 
404 
388 
371 
354 

338 
321 


596 
579 
562 
544 

527 
509 
492 
475 
457 

440 
422 
405 


353 

336 


613 

663 

594 

644 

576 

625 

558 

606 

540 

587 

522 

568 

504 

548 

486 

529 

468 

510 

450 

491 

431 

472 

413 

453 

395 

434 

377 

415 

359 

396 

341 

377 

309 

323 

30T 
293 

315 
306 

331 
322 
313 


44.74 


1437 

5.67 

472 

3  25 


152.3 


46.94 


1495 

5.64 

492 

3.24 


159-9 


48.44 


I  513 

5.59 

499 

3.21 


165.0 


361 

351 
342 


51.94 


1682 
5.69 


176.9 


714 
694 
674 
654 

634 
614 
594 
574 
554 

534 
514 
494 
474 
454 

434 
414 
394 


381 
371 


55.44 


1856 

5.79 

613 

3.33 


188.8 


766 
766 
766 
766 
766 

766 


763 
742 
721 
700 

679 
658 
637 
616 

595 

574 
553 
532 
511 
490 

469 
448 
427 


409 
399 


58.94 


2037 

5.88 

671 

3.37 


200.7 


The  safe  load- values  above  the  upper  heavy  line  are  for  ratios  of  l/r  not  over  60; 
those  between  the  heavy  lines  are  for  ratios  up  to  120  l/r',  and  those  below  the  lower 
heavy  line  are  for  ratios  not  over  200  l/r 


*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


525 


Table  XXIV 

^=  (Continued).     Safe  Loads  in  Units  of  i  000  Pounds  for  PUte- 
and-Angle  Columns 

^A_ 

f  ^ 

Allowable  fiber-stress  in  pout] 
13  000  for  lengths  of  60  radii  or 
Reduced   for  lengths   between   6 
Formula  (13), 

5  =  19  000  —  10 
Weights  do  not  include  rivet-head 

•4^ 

ds  per  square  inch: 

under 

D  and   120  radii,   by 

ol/r 

s  or  other  details 

Y 

t^ 

For  values 

for  l/r  above  120,  see  notes  on  page  490 

1 

Effective 
length. 

Web-plate  i2"X^i" 

to 

to 

|x|S 

^X  {^%t 

to 

II 
12 
13 
14 
15 

812 
812 
812 
812 
812 

857 
857 
857 
857 
857 

903 
903 
903 
903 
903 

948 
948 
948 
948 
948 

948 
948 

994 
994 
994 
994 
994 

994 
994 

1039 
1039 
1039 
I  039 
1039 

1039 
1039 

16 
17 
18 

19 
20 

21 

22     * 
23 
24 
25 

26 
27 
28 
29 
30 

31 

812 
812 

857 

857 

903 
903 

791 
769 

747 

725 
703 
681 
659 
637 

615 
593 
571 
549 
527 

505 

840 

817 
794 

771 
748 
725 

702 
679 

657 
634 
611 
588 
565 

542 

888 

864 

840 

817 
793 
769 
745 
721 

697 
673 
649 
62s 
601 

577 

937 
912 
887 

862 

837      . 
812 

787 
762 

738 
713 
688 
663 
638 

613 
588 
563 
538 

513 

986 
960 
934 

908 
882 
856 
830 
805 

779 
753 
727 
701 
675 

649 
623 
•  597 
571 
545 

1034 
I  007 

980 

953 
926 
899 
872 
845 

818 
791 
764 
737 
710 

684 

657 
630 
603 

576 

32 

33 
34 
35 

483 
461 
439 

519 

496 
473 

553 

•529 
505 

427 

456 

484 

Area,  sq  in 

62.44 

65.94 

69.44 

72.94 

76.44 

79.94 

Ji-i,  in* 

ri-i,  in 

/2-2.  in* 

r2-2f  in 

2224 

5.97 

728 

341 

2418 

6.06 

785 

3.45 

2618 
6.14 
842 
3.48 

282s 
6.22 
899 
3.51 

3038 

6.30 

956 

3.54 

3259 
6.38 
1014 
3.56 

Weight, 
lb  per  lin  ft.. 

212.6 

224. 5 

236.4 

248.3 

260.2 

272.1 

The  safe  lo 
those  betweer 
heavy  line  art 

ad-values  i 
1  the  heav3 
i  for  ratios 

ibove  the  upper  heavy  line  are  for  ratios  o(l/r  not  over  60; 
/  lines  are  for  ratios  up  to  120  l/r;  and  those  below  the  lower 
not  over  200  l/r 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Strength  of  Columns,  Posts  and  Struts 


Chap. 


Table  XXIV  =<"  (eontinued). 


Safe  Loads  in  Units  of    i  ooo  Pounds  for  Plater 
and-Angle  Columns 


1 

^^ 

Allpwable  fiber-stress  in  pounds  per  square  inch: 
13  000  for  lengths  of  60  radii  or  under 
Reduced   for  lengths  between    60  and   120   radii,   by 
Formula  (13), 

5=19  000  —  100  l/r 
Weights  do  not  include  rivet-heads  or  other  details 
For  values  for  l/r  above  120,  see  notes  on  page  490 

1  u  1 

1 

T 

2    Y 

Effective 

length, 

ft 

Web-plate  I2^'XH^' 

Web-plate  14"  X^^'^ 

to 

0 

Ixl'^. 

cv^j3X 
ttXn  ^ 
to 

III 

-fX^^^. 

0 

n.X«V 

II 

12 

13 
14 

15 

i6 
17 

I  085 
I  08s 
I  085 
I  085 
1 08s 

I  08s 
1 08s 

I   130 
I    130 
I    130 
I    130 
I    130 

I   130 
I   130 

39? 
392 
392 
392 
392 

422 
422 

422 
422 
422 

452 

452 
452 
452 
452 

4.74 
474 
474 
474 
474 

497 
497 
497 
497 
497 

387 
375 

415 
403 

444 
431 

470 
456 

497 
482 

468 

453 
439 

425 
410 
396 
381 
367 

353 
338 

324 
309 
295 

281 

i8 
19 

20 

21 
22 
23 
24 
25 

26 
27 
28 
29 

30 

31 
32 
33 
34 
35 

1082 

1054 
I  026 

998 

970 
942 

IS 

858 

830 

802 

774 
746 

718 
690 
662 
634 
606 

I   130 

363 
352 
340 

328 
317 
305 

270 
?58 
246 
235 
223 

311 

390 
377 
365 

352 
340 
327 
314 
302 

264 

251 

239 

417 
404 
390 

377 
363 
350 
336 
323 

309 
296 
282 
269 
255 

442 
428 
415 

401 
387 
373 
359 
345 

331 
317 
3P3 
289 
275 

261 

I  lOI 

1072 

1043 
J  014 

985 

9S6 
927 

898 
^69 
840 
811 
782 

753 

S^ 

667 
638 

227 

220 
214 
208 

243 
236 
229 
222 

205 

200- 
194 

251 
244 
237 
230 

267 
260 
253 
245 

188 

201 

216 

Area,  sq  in 

83.44 

86.94 

30.19 

32.47 

34.75 

36.50 

38.25 

/i-i,  in4 

ri-i,  in 

/?-2.in4 

ri-2,in 

3486 
6.46 
107 1 
3.58 

3  721 
6.54 
1128 
3.60 

I  261 

6.46 

291 

3.10 

I  351 

6.45 

311 

3.09 

1436 

6.43 

331 

3.09 

1539 
6.49 
360 
3.14 

1643 

6.55 

388 

3.T9 

Weight, 
lb  per  lin  ft.. 

284.0 

295.9 

102.8 

II0.8 

118. 4 

124.3 

130.3 

The  safe  lo 
those  betwee 
heavy  line  ai 

ad- values  £ 
n  heavy  li 
e  for  ratios 

ibove  the  upper  heavy  line  are 
nes  are  for  ratios  up  to  120  l/r 
not  over  200  l/r. 

for  ratios  of  l/r  not  over  60; 
and  those  below  the  lower 

*  From  Pocicet  Corapanion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


527 


Table  XXIV*  (Continued).     Safe  Loads  in  Units  of  i  opo  Pounds  for  Plate- 
and-Angle  Columns 


■      ,   A      12    A    . 

1 

.      .        1 

f        '    i            Allowable  fiber-stress  in  pounds  per  square  inch: 
1  h-  1            13  000  for  lengths  of  60  radii  or  under 

1            Reduced   for  lengths  between   60   and    120  j-adii,   by 

Formula  (13), 

\X    .                                          S  =  19  000  —  100  l/r 
VA\          Weights  do  not  include  rivet-heads  or  other  details 

Y     '2  "^ 

Effective 
length, 

Web-plate  ia^'XYs" 

Web-plate  I4"XK2'' 

0       "" 

0 

to 

0 

G-   SX         f 

II 
12 
13 

14 
IS 

16 

17 

520 
520 
520 
520 
520 

520 

543 
543 

543 
543 
543 

543 

566 
566 
566 
566 
566 

5^6 

595 
595 
595 
595 
595 

623 

623 

623 
623 
623 

595 

623 

507 

533 

517 
502 
487 

472 
456 
441 
426 
410 

395 
380 
364 
349 
334 

318 
303 

S5r 

535 
518 
502 

486 
470 
454 
437 
421 

405 
389 
373 
356 
340 

324 
308 

■   578 
561 
544 
527 

510 
493 
476 
459 
442 

424 
407 
390 
373 
356 

339 
322 

605 
587 
569 

551 

533 
51S 

497 

tl? 

443 
425 
407 
390 
^72 

^54 
336 

18 
19 
20 

21 
22 
23 

24 
25 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

493 
478 
463 

448 
433 
418 
403 
388 

374 
359 
344 
329 
314 

299 
284 

275 

267 
260 

290 
282 
275 

298 
290 
282 

312 

304 
295 

327 
318 
309 

Area,  sq  in 

40.00 

41-75 

43.50 

45.74 

47-94 

ii-i.in* 

^1-1.  m 

/2-2.  in* 

^2-2,  in 

417 
3.23 

I8S7 

6.67 

446 

3.27 

I  885 

6.58 

451 

3.22 

1970 
6.56 
472 
3.21 

2053 
6.54 
.492 
3.20 

Weight, 
lb  per  lin  ft.. 

136.2 

142.2 

14S.1 

155.7 

163.3 

The  safe  load-values  above  the  upper  heavy  line  are  for  ratios  of  l/r  not  over  60; 
those  between  the  heavy  lines  are  for  ratias  up  to  120  l/r;  and  those  below  the 
lower  heavy  line  are  for  ratios  not  over  200  l/r 

,..,  „. • 1 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  l>ittsburgb»  Pa. 


528 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


Table  XXIV*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  Plate- 
and-Angle  Columns 


,  ^    '-^  ^ 

i   inch: 
dii,   by 

ails 
490 

A 

? 
M 

Allowable  fiber-stress  m  pounds   per   square 
13  000  for  lengths  of  60  radii  or  under 
Reduced   for  lengths   between   60   and    120  ra 
Formula  (13), 

5  =  19  000  —  100  l/r 
Weights  do  not  include  rivet-heads  or  other  det 
For  values  for  l/r  above  120,  see  notes  on  page 

'  Y    I2  V  ■ 

Effective 

length, 

ft 

Web-plate  u"XH" 

0 

0 

^r^x 

0 

rj-XN%t 
0 

|x|| 

rtX(N%t 

II 

12 

13 
14 
IS 

i6 

737 
737 
737 
737 
737 

737 

782 
782 
782 
782 
782 

782 

828 
828 
828 
828 
828 

828 

873 
873 
873 
873 
873 

873 
873 

919 
919 
919 
919 
919 

919 
919 

646 
646 
646 
646 

691 
691 
691 

691 

691 
691 

643 

17 
i8 
19 

20 

21 
22 
23 
24 
25 

26 
27 
28 
29 

30 

31 
32 

624 
606 
587 
568 

549 
530 
511 
493 

474 

455 
436 
417 
399 
380 

361 

6^- 
055 

635 

615 

596 
576 
556 
536 
517 

497 
477 
457 
438 
418 

398 
378 

726 

705 
684 
664 

643 
622 
602 
581 
560 

540 
519 
498 
477 
457 

436 
415 

776 

754 
733 
711 

689 
668 
646 
62s 
603 

S81 
560 

516 
495 

473 

452 

'  430 

826 

803 
780 
758 

735 
713 

66? 
645 

622 
600 
577 
554 
532 

509 
487 
464 

852 
829 
805 

782 
758 

734 
711 
687 

664 
640 
617 
593 
569 

546 

522 

499 

[      475 

901 
876 
851 

827 
802 

778 

753 
728 

704 
679 
655 
630 
60s 

581 
556 
532 

507 

345 

33 
34 
35 

336 
326 
317 

365 
356 
346 

396 
385 
375 

415 
404 

444 
432 

461 

489 

Area 

sq  in 

49.69 

53.19 

56.69 

60.19 

63.69 

67.19 

70.69 

/i-i. 

^2-2. 

in^ 

n 

in* 

n 

2081 

6.47 

499 

3.17 

2302 

6.58 

556 

3.23 

2529 

6.68 

613 

3.29 

2"764 

6.78 

671 

3.34 

3006 

6.87 

728 

3.38 

3255 

6.96 

785 

3.42 

3512 

7.05 

842 

3.45 

Weight, 
lb  per  lin  ft.. 

169.3 

181. 2 

193.1 

205.0 

216.9 

228.8 

240.7 

The  safe  load-values 
those  between  the  hea 
lower  heavy  line  are  fo 

above  the  upper  heavy  line  are  for  ratios  of  l/r  not 
vy  lines  are  for  ratios  up  to  120  l/r;  and  those  b 
r  ratios  not  over  200  l/r 

over  60; 
slow  the 

•Fft 

m  Pocket  ( 

^mpanion 

Carnegie 

Steel  Com 

pany,  Pitt 

sburgh,  Pa 

I, 

Tables  of  Safe  Loads  iot  Steel  Columns 


529 


Table  XXIV*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  Plate- 
and-Angle  Columns 


^       1^     ^ 


^^ifT" 


M 


[tk 


Y       '2    ^ 


Allowable  fiber-stress  in  pounds  per  square  inch: 
13  000  for  lengths  of  6o  radii  or  under 
Reduced   for  lengths  between   6o  and    120   radii,   by 
Formula  (13), 

5  =  19  000  —  100  l/r 
Weights  do  not  include  rivet-heads  or  other  details 
For  values  for  l/r  above  120,  see  notes  on  page  490 


Effective 

length, 

ft 


13 
14 
15 

16 
17 
18 
19 


23 
24 
25 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 


Web-plate  u"XW 


4J  w  (U^X 


964 
964 
964 
964 
964 

964 
964 


949 
924 


872 
847 
821 
796 
770 

744 
719 
693 
668 
642 

617 
591 
565 
540 


1  010 

I  010 

I  010 
I  010 
I  010 

I  dio 
I  010 


§v<x 

,+  A  c^%x. 


1055 
I  055 
I  055 

I  055 
I  055 

I  055 
1055 


I  lOI 
I  lOI 
I  lOI 
I  lOI 
I  lOI 

I  lOI 
I  lOI 


998 

971 
945 

918 
892 
865 
839 
812 

786 
759 
732 
706 
679 

653 
626 
600 
573 
546 


I  046 
1018 

991 

963 
935 
908 
880 
853 

825 
797 
770 
742 
715 

687 
659 
632 
604 


I  095 
I  067 
1038 


953 
924 
895 

867 
838 
810 
781 
753 

724 
696 
667 
639 
610 


I  146 
I  146 
I  146 
I  146 
I  146 

1-146 
I  146 


I  144 
I  114 
I  084 

1055 

I  025 

996 

966 

937 

907 
877 
848 
8i8 
789 

759 
730 
700 
671 

641 


T  A  cs  vo 


I  198 
I  198 
I  198 


I  174 

I  146 

I  119 

I  091 

I  064 

I  036 

I  009 

981 

954 
926 

899 
871 
843 
816 


Area,  sq  in 


77.69 


81.19 


84.69 


7i_i,  in* 

3776 

ri-i,  in 

7-13 

/.,_2,  in* 

899 

ro-2,  in 

3.48 

4048 

7.22 

956 
3.51 


4327 

7-30 
I  014 
3.53 


4615 
7.38 
I  071 
3. 56 


Weight, 
lb  per  lin  ft. 


252.6 


264.5 


276.4 


88.19 


3C0.2 


92.19 


4910 

5  120 

7.46 

7-45 

1 128 

1493 

3.58 

4.02 

313.8 


The  safe  load- values  above  the  upper  heavy  line  are  for  ratios  of  l/r  not  over  60; 
those  between  the  heavy  lines  are  for  ratios  up  to  120  l/r;  and  those  below  the 
lower  heavy  line  are  for  ratios  not  over  200  l/r 


*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh.  Pa. 


Strength  of  Columns,  Posts  and  Struts 


Chap. 


Table  XXIV*  (Continued). 


Safe  Loads  in  Units  of  i  ooo  Pounds  for  Plate- 
and- Angle  Columns 


ff 


^     !2   ^ 


Allowable  fiber-stress  in  pounds  per  square  inch: 
13  000  for  lengths  of  60  radii  or  under 
Reduced  for  lengths  between   60  and   120  radii,  by 
Formula  (13), 

1^1        J^~^"!  P~J>,         Weights  do  not  include  rivet-heads  or  other  details 
^..,f    ,        M^i.     For  values  f( 


1 


Y    "i  '^ 


For  values  for  l/r  above  120,  see  notes  on  page  490 


Effective 

length, 

ft 


13 
14 
15 

16 

17 

'  18 

19 


23 
24 
25 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 


Web-plate  u"XH" 


o 


I  250 
I  250 
I  250 
I  250 
I  250 

I  250 
1250 

I  250 
I  250 
I  250 


I  229 
I  201 
I  172 
I  144 
I  115 

1087 
1058 
I  030 
I  001 

973 

944 
916 
887 
859 
830 


I  315 
I  315 
I  315 
I  315 
I  135 

I  315 
I  315 
I  315 
I  315 


4J  V  (u;?; 


1367 
1367 
I  367 
I  367 
1367 

1367 
1367 
I  367 
I  367 


1 308 
1277 

I  246 
I  216 

1 185 

ri54 

I  12^ 
10^ 
I  062 
I  031 
I  000 

970 
939 
908 
877 
847 


1364 

I  333 
I  301 
I  269 
I  237 
I  206 

I  174 
I  142 
I  III 

1079 
1047 

I  015 
984 
952 
920 


I  419 

I  419 

I  419 

I  419 

I  419 

1419 

I  419 

I  419 

I  419 

I  419 


1388 
1356 
1323 

I  290 
I  258 

I  225 
I  192 
I  160 
I  127 
1094 

I  062 

1  029 

996 

964 

931 


I  471 
I  471 
I  471 
I  471 
I  471 

I  471 

I  471 
1471 
I  471 
I  471 


1443 
I  409 
1375 
I  342 
1308 

1274 
I  241 
I  207 
I  173 
I  139 

I  106 
I  072 
I  038 
I  C05 
971 


^?5x 


I  523 
I  523 
I  523 
I  523 
I  523 

I  523 
I  523 
I  523 
I  523 
1523 


I  497 
I  463 
I  428 
I  393 
I  359 

I  324 
1289 
I  254 
I  220 
I  185 

I  150 
I  115 
I  081 
I  046 
I  on 


Area ,  sq  in 


/i-i,  in*. 


ri_i,  in.. 
7^2.  in*. 
r^-h  in. 


Weight, 
lb  per  lin  ft. , 


96.19 


5  457 
7.53 
1579 
4-05 


327.4 


101.19 


105.19 


109.19 


5484 
7.36 
I  581 
3.95 


5830 
7-44 
1666 
3.98 


6187 
7-53 
1752 
4.01 


344.2 


357.8 


371.4 


113.19 


6552 
7.61 
1837 
4.03 


385.0 


117. 19 


6928 
7.69 
I  922 
4-05 


398.6 


The  safe  load- values  above  the  heavy  line  are  for  ratios  of  l/r  not  over  60;  and 
those  below  the  heavy  line  are  for  ratios  not  over  120  l/r 


*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


531 


Table  XXIV*  (Continued).     Safe  Loads  in  Units  of   i  ooo  Pounds  for  Plate- 
and-Angle  Columns 


A        |2     A 

1 

^1          — 
o 

-  Jf  -  _1 , k 

Allowable  fiber-stress  in  pounds  per  square  inch: 
13  000  for  lengths  of  60  radii  or  under 
Reduced   for  lengths  between   60   and    120  radii,   by 
Formula  (13), 

S  =  ig  000  —  100  l/r 
Weights  do  not  include  rivet-heads  or  other  details 
For  values  for  l/r  above  120,  see  notes  on  page  490 

^ 

Ir-T" 

':     ElTcctive 
length, 
ft 

Two  web-plates  I4''X3'2-" 

'Scroti  <^ 

rtX  M^b 

|x|| 

00 

^X<N^ 
00 

1'^:§x 

00 

00 

Jxl^ 

00 

II 

12 
13 
14 
15 

i6 
17 
IS 
19 

20 

21 
23 
23 

24 
25 

26 
27 
28 
29 

i            30 
31 

i                 32 

33 
34 
35 

1592 
1592 
1592 
1592 
1592 

1592 
I  592 
1592 
I  592 

1657 
1657 

I  6j7 
10:7 
1657 

I  657 
1637 

I  0:7 
16.7 
I  657 

1728 
I  72S 
1723 
1  728 
I  728 

I  728 
1723 

1723 
1723 
1728 

I  728 
1723 
I  728 

I7S7 
I7S7 
I    737 

I  7^7 
1787 

I  787 
I  737 
1737 
I  737 
1737 

I  787 
1787 
1737 

1845 
1845 
1845 
1845 
1845 

1845 
1845 
1845 
1845 
1845 

1845 
1845 
1845 

I  904 
1904 
I  904 
1904 
I  904 

1904 
I  904 
X  904 

1904 
I  904 

I  904 
I  904 
1904 

I  590 

I  553 
I  516 
1479 
1443 
I  406 

1369 
1332 
1295 
I  258 
I  222 

I  185 
I  148 
I  III 

I  074 
1038 

I  6:,3 

iGiG 
I  580 

I  543 

1507 

I  470 
1434 
1397 
1  360 
1324 

1287 
I  251 
I  214 
I  177 
I  141 

i6x=: 
I  661 

1626 
1592 
1 557 

1522 

1488 

1453 
I  419 
1384 

I  349 
131S 

I  75G 
I  721 

1C85 
I  650 
I  614 
I  578 
I  543 

1507 
I  471 
1436 
I  400 
1365 

I   818 
I    781 

I  744 
I  708 
I  671 
1635 
1598 

I  561 
1525 
1488 
I  451 
I  415 

1879 
1842 

I  804 
1766 
I  729 
I  691 
1653 

I  616 
1578 
I  541 
1503 
1465 

Area,  sq  in 

122.44 

127.44 

132.94 

137.44 

141.94 

146.44 

7i_i,  in*. .... 

n-i,  in 

72-2,  i  a* 

^2-2,  in . 

7014 
7.57 
1946 
3.99 

7254 
7.54 
2229 
4.18 

7  559 
7.54 

•2831 
4.61 

7981 
7.62 
2953 
4.63 

8415 
7.70 
3074 
4.65 

8  859 
7.78 

Weight, 
lb  per  lin  ft.. 

416.4 

433.6 

452.3 

467.6 

482.9 

49s. 2 

Safe  load- values  abo\ 
below  heavy  line  are  for 

'•e  the  heavy  line  are  for  ratios  of  l/rnot  over  60;  thope 
ratios  not  over  120  l/r 

*  fXQiti  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 


534 


Strengtii  of  Columns,  Posts  and  Struts 


Table  XXV*  (Gontinued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  lo-Inch 
Channel-Columns 


1 

,  t-'T'-l 

1                   All          .-1_1 

6J^- 

_L-/-          /iLiiowauie  iiuer-stress  in  pounas  per  square  men: 
J         13  000  for  lengths  of  60  radii  or  under 

^       Reduced  for  lengths  between   60  and   120  radii,   by 
— i            Formula  (13), 

5  =  19  000  —  100  l/r 
i^       Weights  do  not  include  rivet-heads  or  other  details 

1  S^         ,,2         ^  ' 
.-—12-- ^ 

Two  lo-in  channels,. two  12-in  plates 

Effective 
length, 

a'S 

'0   0) 

is 

•s.s 

J2 

11 

J- 

a'S 

4-s 

If 

1^ 

II 

12 

13 

14 
IS 

i6 
17 

328 
328 
328 
328 
328 

328 
328 

348 
343 
348 
348 
348 

348 
348 

367 

307 
367 
367 
367 

367 
367 

386 
386 
386 
386 
386 

386 
386 

405 
405 
405 
40s 
405 

405 

424 
424 
424 
424 
424 

424 

443 
443 
443 
443 
443 

443 

463 
463 
463 
463 
463 

463 

403 
392 
381 
370 

337 
326 
314 

303 
292 
281 
270 
259 

248 
237 
226 

423 
411 

437 
424 

457 

444 

431 
418 

405 
392 
379 
366 
354 

341 
328 
315 
302 
289 

276 
263 

250 

l8 
19 

20 

21 

22 
23 

24 

25 

26 
27 
28 
29 

30 
31 

32 

33 
34 
35 

324 
315 

307 

298 
289 
281 
272 
263 

255 
246 
237 
229 
220 

211 
203 
194 
185 
177 

343 
334 
32s 

316 

307 
297 
288 
279 

270 
261 
252 
242 
233 

224 
215 
206 

196 

187 

359 
349 
339 

329 
319 
310 
300 
290 

230 

270 
260 
251 
241 

231 
221 

211 
201 

378 
367 
357 

347 
336 
326 
316 
305 

295 
285 
274 
264 
253 

243 
233 
222 

212 

388 

376 
364 
353 
341 
330 

318 
306 
295 
283 
271 

260 
248 
237 

400 

387 
375 
362 
350 
338 

325 
313 
301 
288 
276 

263 
251 
239 

216 

227 
221 

232    1       243 
226    1      237 

194              205      1         211 

Area,  sq  in 

25.26 

26.76 

28.20 

29.70 

31.14 

32.64 

34.08 

35.58 

A-i,  in* 

»-i-i,  in 

^!^-2.  m* 

^a-2.  in 

534 
4.60 
310 
3.50 

581 
4.66 
328 
3.50 

559 
4.45 
333 

3.44 

606 
4.52 
351 

3.44 

583 
4.33 

354 
3.37 

630 
4.39 
372 
3.37 

608 
4.22 

372 
3.30 

655 
4.29 

390 
3.31 

Weight. 
lb  per  lin  ft.. 

85.9 

91.0 

95.9 

lOI.O 

105.9 

III.O 

115. 9 

121. 0 

Safe  load-values  above  the  upper  heavy  line  are  for  ratios  of  l/r  not  over  6o; 
those  between  the  heavy  lines  are  for  ratios  up  to  120  l/r;  and  those  below  the 
lower  heavy  line  are  for  ratios  not  over  200  l/r 

• 

Froi 

nPo 

cket 

Compan 

on.  Cam 

egie  Steel 

Compan 

y.  Pittsbi 

irsh.  Pa, 

1 
1 

tables  of  Safe  Loads  for  Steel  Cbluiiiii^ 


m 


Table  XXV*  (Continued). 


Safe  Loads  in  Units  of   i  ooo  Pounds^  for  lo-Inch 
Channel-Columns 


Jl^fcl 

A  11.^'r^r.l^ln        AV.^..      ^4--^r^ 

:_^t-. 

T^ 

i 

r 

Allowaole    nDer-Strebb    m    yuunuis    pei    ij^uaie    iiicii; 
13  000  for  lengths  of  60  radii  or  under                                 | 

1 

■m'(—' 

_i 

Reduced  for  lengths 

between   60   and 

120  radii,   by 

s  - 

Formula  (13), 

) 

i 

5  =  I 

9  000  -  100  l/r 

IM 

1 

-^ 

Weights  do  not  include 

rivet-heads  or  0 

ther  details 

— \ — 

,     For  values  for  l/r  above  120,  se 

e  notes  on  page  490           | 

T^      „l2        ^ 

\<---u- >; 

1 

Effective 
length, 

Two 

[o-in  channels,  latticed 

Two  lo-in  channels,  two  14-in 
plates 

J2  a> 

^"0 

OJ   0 

il 

4^ 

n 

1' 

•38 

ft 

1 » 

11 

a^' 

a^ 

^.a 

a^ 

^J 

a  2 

47. 

xi  i 

lO  w 

6-w 

10  w 

cS'w 

i 

ir)f-"^ 

ly^'^^ 

^^ 

cs 

ro 

•^ 

M 

N 

II 

ii6 

153 

191 

229 

252 

275 

298 

312 

12 

ii6 

IS3 

191 

229 

252 

275 

298 

312 

13 

ii6 

153 

191 

229 

252 

275 

298 

312 

14 

ii6 

153 

191 

229 

252 

275 

298 

312 

15 

ii6 

153 

191 

229 

252 

275 

298 

312 

i6 

ii6 

153 

191 

229 

252 

275 

298 

312 

17 
i8 
19 

20 

ii6 
ii6 
ii6 

153 

153 

191 

229 

252 
252 
252 

252 

275 
275 
275 
275 

298 
298 
298 
298 

312 
312 
312 
312 

189 
184 
179 

224 
2l3 
211 

150 
146 

114 

21 
22 

III 
109 

142 
139 

174 
169 

205 
199 

252 

275 

298 

312 

251 

273 

295 

308 

23 

io6 

135 

164 

193 

246 

267 

289 

302 

24 

103 

131 

159 

187 

241 

261 

282 

295 

25 

100 

127 

154 

iSo 

235 

256 

276 

288 

26 

98 

123 

149 

174 

230 

250 

270 

282 

27 

95 

119 

144 

168 

235 

244 

263 

275 

28 

92 

IIS 

139 

162 

219 

238 

257 

268 

29 

89 

112 

134 

156 

214 

232 

250 

261 

30 

87 

108 

129 

149 

209 

226 

244 

255 

31 

84 

104 

124 

143 

203 

220 

238 

248 

32 

8i 

100 

119 

137 

198 

214 

231 

241 

33 

78 

96 

114 

131 

193 

209 

225 

235 

34 

75 

92 

109 

125 

187 

203 

219 

228 

35 

73 

88 

104 

121 

182 

197 

2212 

221 

Area,  sq  in 

8.92 

11.76 

14.70 

17.64 

19.42    1      21.17 

22.92 

24.01 

h-i,  in4 

134 

158 

182 

207 

416 

468 

520 

491 

^i-i.in 

3.87 

3.66 

3.52 

3.42 

4.63 

4.70 

4.76 

4-52 

h-2.in* 

197 

241 

284 

323 

369 

398 

426 

442 

^2-2.  in 

4.70 

4.53 

4.39 

4.23 

4.36 

4.33 

4.31 

4.29 

Weight, 

lb  per  lin  ft.. 

39.3 

49-4 

.59.4 

69.4 

65.7 

71.7 

77.6 

81.7 

Safe  load-values  a1 

oove  the  upper  heavy  line 

are  for  ratios  of 

l/r  not  over  60; 

those  between  the  h 

javy  lines  are  for  ratios  u 

p  to  120  l/r\  and 

those  below  the 

lower  heavy  line  are 

or  ratios  not  over  200  l/r 

Strength  of  Columns,  Posts  and  Struts 


Chap.   14 


Table  XXIV*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  Plate- 
and-Angle  Columns 


^  A       |2    A  J 

Allowable  fiber-stress  in  pounds  per  square  inch: 
13  000  for  lengths  of  60  radii  or  under 
Reduced   for  lengths  between   60   and    120  radii,   by 
Formula  (13), 

5  =  19  000  —  100  l/r 
Weights  do  not  include  rivet-heads  and  other  details 
For  values  for  l/r  above  120,  see  notes  on  page  490 

1^: 

'  Y 

2  ^ 

Effective 
length, 

Two  web-plates  u"XW 

00 

(L(  ON   W^fO 
00 

00 

00 

lx?^8 

.    00 

^X..o 

00 

II 

12 
13 
14 
15 

I6 

17 
i8 
19 

20 

21 
22 
23 

1949 
1949 
I  949 
1949 
1949 

1949 
I  949 
1949 
I  949 
1949 

1949 
1949 
1949 

2  027 
2027 
2  027 
2027 
2  027 

2  027 
2027 
2  027 
2  027 
2027 

2027 
2  027 
2  027 

2  092 
2092 
2  092 
2092 
2  092 

2  092 
2092 
2  092 
2  092 
2092 

2092 
2  092 
2  092 

2157 

2  157 
2  157 
2  157 
2  157 

2  157 
2  157 
2  157 
2  157 
2157 

2  157 
2  157 
2157 
2  157 
2157 

2  222 
2  222 
2  222 
2  222 
2  222 

2  222 
2  222 
2  222 
2  222 
2  222 

2  222 
2  222 
2  222 
2222 
2  222 

2287 

2  287 

2287 

2  287 
2287 

2  287 
2  287 
2287 
2287 
2287 

2  287 
2287 
2  287 
2  287 
2  287 

24 
25 

26 
27 
28 
29 

30 

31 
32 
33 
34 
35 

I  918 
1879 

I  841 
I  802 
I  763 
1724 
1686 

1647 
I  608 
1569 
I  530 
1492 

2027 
2  027 

2  092 
2  092 

2  009 
I  972 

I  935 
I  8Q9 
1862 

182s 
1789 
I  752 
I  715 
1679 

2077 
2039 
2  002 
1964 
I  926 

1889 
I  851 
I  813 

I  775 
1738 

2  146 
2  107 
2068 
2029 
I  991 

1952 
I  013 
1874 
1836 

I  797 

2  214 
2  175 
2  135 
2095 
2055 

2  016 
1976 
I  936 
1896 
1857 

2283 
2242 
2  202 
2  161 
2  120 

2079 
2039 
1998 
1957 
I  916 

Area,  sq  in 

149.94 

155.94 

160.94 

165.94 

170.94 

175.94 

/i-i.in* 

ri-i,  in 

/^2.in4 

r2-2.  in 

8  916 
7.71 

3  222 
4.64 

9248 
7.70 

4049 
5. 10 

9741 
7.78 

421I6 
5.12 

10248 
7.86 
4383 
5.14 

10767 
7.94 
4  549 
5.16 

II  298 

8.01 
4716 
5.18 

Weight, 
lb  per  lin  ft.. 

510. 1 

S30\S 

547.5 

564.5 

581.5 

598.5 

Safe  load-values  abo 
below  the  heavy  line  ai 

ve  the  heavy  line  are  for  ratios  of  l/r  not  ovc 
•e  for  ratios  not  over  120  l/r 

r  60;  those 

*  From  Pocket  Companion,  Carnegie  Steel  Company.  Pittsburgh,  Pa, 


I 

Tables  of  Safe  Loads  for  Steel  Col 

umns 

533 

Table  XXV.*     Safe  Loads  in  Units  of  i  ooo  Pounds  for  lo-Inch  Channel- 

Columns 

t-^y-t 

T-^ 

\ 

— T-r         Allowable  nbcr-strcr.s  in  pounds  per  square 
X         13  000  for  lengths  of  60  radii  or  under 

inch: 

oyJi--- 

?  - 

-       Reduced   for  lengths   between   60   and    120   radii,   by    | 

—            Formula  (13), 

1 

5=19  000  —  100  l/r 

l^ 

1 

j^       Weights  do  not  include  rivet-heads  or  other  details           1 

^^         T7^, 

values  for  l/r  above  120,  see  notes  on  page  490 

:  4^    ,.b    ^ 

1----12--- ->^ 

Two  lo-in  channels 
latticed 

Two  lo-in  channels,  two  12-in  plates 

. 

^ 

, 

^ 

Effective 
length, 

,i2  oj 

d)  0 

J2  0 

Is 

|l 

11 
art 

a.5 

ll 

Cj2 

ft 

3^ 

.  f^  J2 

^J-^ 

CS   Q< 

rt'ft 

ri-Q, 

rt  Qh 

-^o 

'0  <" 

•Si; 

-s.s 

la 

^.B 

-Sa 

^.a 

la 

il 

fl 

=2.1 

10^ 

1- 

'"' 

0» 

cs 

*-* 

M 

<N 

II 

116 

153 

191 

213 

233 

252 

272 

289 

309 

12 

116 

153 

191 

213 

233 

252 

272 

289 

309 

13 

116 

153 

191 

213 

233 

252 

272 

289 

309 

14 

116 

153 

191 

213 

233 

252      1      272 

289 

309 

15 

116 

153 

191 

213 

233 

252 

272 

289 

309 

i6 

116 

153 

191 

213 

233 

252 

272 

289 

309 

17 
i8 
19 

116 
116 

153 

191 

213 

233 

252 

272 

289 

309 

152 
148 

186 
181 

2X3    1 

233 

•227 

252 

245 

271 
264 

286 
278 

305 
297 

115 

208 

20 

112 

144 

176 

203 

221 

239 

257 

271 

289 

21 

109 

140 

171 

197 

215 

232 

250 

263 

280 

22 

106 

136 

165 

192 

209 

226 

243 

256 

272 

23 

103 

132 

160 

186 

203 

219 

236 

248 

264 

24 

100 

128 

155 

181 

197 

213 

229 

240 

256 

25 

98 

124 

150 

175 

191 

206 

222 

233 

248 

26 

95 

120 

145 

170 

185 

200 

215 

22s 

240 

27 

92 

116 

140 

164 

179 

193 

208 

217 

231 

28 

89 

112 

134 

159 

173 

187 

201 

210 

223 

29 

86 

loS 

129 

153 

167 

180 

194 

202 

215 

30 

83 

104 

124 

148 

161 

174 

187 

195 

207 

31 

80 

100 

119 

142 

15s 

167 

i3o 

187 

199 

32 

77 

96 

114 

137 

149 

161 

173 

179 

191 

33 

75 

92 

109 

131 

143 

154 

1G6 

172 

183 

34 

35 

72 
69 

88 
84 

103 

126 

120 

137 
131 

148 
141 

159 
152 

164 
157 

174 
166 

lOI 

Area,  sq  in 
Ii-u  in* 

8.92 

11.76 

14.70 
182 

16.42 

17.92 

19.42 

20.92 

22.26 

23.76 

134 

158 

333 

376 

420 

■    465 

444 

489 

n-i.  in 

3.87 

3.66 

3.52 

4.50 

4.58 

4.6s 

4.71 

4.46 

4.53 

/2-2.  in* 

123 

148 

171 

213 

231 

249 

267 

274 

292 

^2-2.  in 

Weight. 

3.72 

3.55 

3.41 

3.60 

3.5Q 

3.58 

3.58 

3.51 

3.  SO 

lb  per  lin  ft.. 

37.8 

47.8 

57.8 

55.5 

60.6 

•    65.7 

70.8       75.7 

80.8 

Safe  load-values  above  the  upper  heavy  line  are  for  ratios  of  l/r  not  oa 

^er  60; 

those  between  the  heavy  lines  are  for  ratios  up  to  120  l/r;  and  those  belc 

)w  the 

lower  heavy  line  are  for  ratios  not  over  200  l/r 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


536 


Strength  of  Columns,  Posts  and  Struts  Chap.  14 


Table  XXV*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  lo-Inch 
Channel-Columns 


X^'-rX 

Allowable  fiber-stress  in  pounds  per  square  inch: 
13  000  for  lengths  of  60  radii  or  under 

yV| 

': 

r 

1 

syi(-< 

Reduced   for  lengths  between   60   and    120  radii,   by 

s  — 

1 

Formula  (13), 

\J 

i 

5  =  19  000  —  100  l/r 

1 

A. 

Weights  do  not  include  rivet-heads  or  other  details 

— 1 — 

For  values  for  l/r  above  120 

,  see  notes  on  page  490 

Tv       I2      ^' 

:<---l4'--- — >: 

Two  lo-in  channels,  two  14-in  plates 

. 

w 

w 

OT 

w 

4S 

w 

Effective 
length. 

c  c2 

c3 

Is 

ft 

^■3. 

^^ 

•^? 

c3  0, 

M^ 

•§•? 

i-s 

0  c 

CJ.5 

0  c 

0.5 

0  2 

^  c 

^'0 

6«N 

0  ^  ■' 

:2  2 

4:k 
10 

f? 

<N 

M 

(N 

w 

N 

N 

11 

335 

358 

380 

396 

419 

441 

464 

12 

335 

358 

380 

396 

419 

441 

464 

13 

335 

358 

380 

396 

419 

441 

464 

14 

335 

358 

380 

396 

419 

441 

464 

IS 

335 

358 

380 

396 

419 

441 

464 

16 

335 

358 

380 

396 

419 

441 

464 

17 

335 

358 

380 

396 

419 

441 

464 

18 
19 

20 

21 

335 

335 
335 

335 

358 
358 
358 

358 

380 
380 

380 

380 

396 

419 

441 
441 

464 
464 
464 

396 
396 

396 

419 

419 
419 

441 
441 

464 

453 

22 

330 

352 

374 

388 

410 

432 

23 

323 

344 

365 

379 

401 

422 

443 

24 

316 

337 

357 

371 

392 

412 

433 

25 

308 

329 

349 

362 

382 

403 

423 

26 

301 

321 

341 

353 

373 

393 

412 

27 

294 

313 

332 

345 

364 

383 

402 

28 

287 

306 

324 

336 

355 

373 

392 

29 

279 

298 

316 

327 

346 

364 

382 

30 

272 

290 

308 

319 

336 

354 

372 

31 

265 

282 

299 

310 

327 

344 

361 

32 

258 

275 

291 

301 

318 

335 

351 

33 

251 

267 

283 

293 

309 

325 

341 

34 

243 

259 

274 

284 

300 

315 

331 

35 

236 

251 

266 

275 

291 

306 

320 

Area,  sq  in 

25.76 

27.51 

29.26 

30.45 

32.20 

33.95 

35.70 

Ii-i,  in* 

544 

597 

652 

622 

676 

732 

790 

n-i,  in 

4.59 

4.66 

4.72 

4.52 

4.58 

4.64 

4.70 

■^2-2.  in* 

470 

499 

527 

541 

570 

598 

627 

»'2-2,  m 

4.27 

4.26 

4.24 

4.22 

4.21 

4.20 

4.19 

Weight, 

lb  per  Hn  ft.. 

87.6 

93.6 

99-5 

103.6 

109.5 

115. 5 

121. 4 

Safe  load- values  abov 

e  the  heavy  line  are  for  ratios  of  l/r  not  over  60;  and  those  | 

below  the  heavy  line  ar 

e  for  ratios  not  over  120  l/r                                                             1 

"  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


537 


Table  XXV*  (Continued). 


Safe  Loads  in  Units  of  i  ooo  Pounds  for  lo-Inch 
Channel-Columns 


r^ P 4^           

1      ^ 

HT-           /viiowauie   iiijer-siress  111   puunus  per  square   incn: 
1          13  000  for  lengths  of  60  radii  or  under 

a,/' 

1 

i 

^        Reduced   for  lengths  between   60  and    120  radii,   by 
—               Fonnula  (13), 

S  =  19  000  —  100  l/r 

_t       ,  A" 

1 

M.        Weights  do  not  include  rivet-heads  or  other  details 

1 

^^ 

For  values  for  l/r  above  120,  see  notes  on  page  490 

lY    ,Jji       v[ 

:^---l4 ^; 

Two  lo-in  channels,  two  14-in  plates 

- 

trt 

W    t/3 

w 

W    M 

to 

Effective 

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502 

525 

548 

571 

593 

12 

480 

502 

525 

548 

571 

593 

13 

480 

502 

525 

548 

571 

593 

14 

480 

■502 

525 

548 

571 

593 

15 

480 

502 

525 

548 

571 

593 

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480 

502 

525 

548 

571 

593 

17 

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502 

525 

548 

571 

593 

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480 

502 

525 

548 

571 

593 

19 

480 

502 

525 

548 

571 

593 

20 

480 

502 

525 

548 

571 

593 

21 

477 

500 

522 

544 

567 

589 

22 

467 

488 

510 

532 

554 

575 

23 

456 

477 

499 

520 

541 

562 

24 

446 

466 

487 

508 

529 

549 

25 

435 

455 

475 

495 

516 

536 

26 

424 

444 

464 

483 

503 

522 

27 

414 

432 

452 

471 

490 

509 

28 

403 

421 

440 

459 

478 

496 

29 

392 

410 

429 

446 

465 

483 

30 

382 

399 

417 

434 

452    . 

469 

31 

371 

388 

405 

422 

440 

456 

32 

360 

377 

394 

410 

427     - 

443 

33 

350 

36s 

382 

398 

414 

430 

34 

339 

354 

370 

385 

401 

416 

35 

328 

343 

359 

373 

389 

403 

Area,  sq  in 

36.89 

38.64 

40.39 

42.14 

43.89 

45.64 

^1-1.  in* 

757    ■ 

814 

873 

932 

994 

I  056         1 

^i-i,  in 

4.53 

4.59 

4.65 

4.70 

4.76 

4.81          1 

72-2.  in* 

637 

666 

695 

723 

752 

780          I 

»'2-2.  in 

4.16 

4.15 

4.15 

4.14 

4.14 

4.13        ; 

Weight. 

( 

lb  per  lin  ft.. 

125.5 

131. 4 

137.4 

143.3 

149.3 

155.2          ; 

Safe  load- values  above  the  heavy  line  are  for  ratios  of  l/r  not  over  6o;  those  be-     ' 

low  the  heavy  line  are  for  ratios  not  over  120  l/r 

*  prom  Pocket  Companion,  Carnegie  Steel  Company,  J*ittsburgh,  Pa, 


638 


StreBLgth  of  Columns,  Posts  and  Struts 


Chap. 


Table  XXV*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  lo-Inch 
Channel-Columns 


„ 

-H 

i 

);-"' 

]2" 

.     L.                  '               1  "^ 

Allowable  fiber-stress  in  pounds  per  square  inch: 

1  ^ 

r 

0.)' 

13  000  for  lengths  of  60  radii  or  under 

i  ^ 

8>^— ; 

-L  " 

Reduced   for  lengths  between   60   and    120  radii,  by 

Formula  (13), 

1 

i 

5  =  19  000  —  100  l/r 

t    ^ 

1 

u 

Weights  do  not  include  rivet-heads  or  other  details 

_  1 

For  values  for  l/r  above  120,  see  notes  on  page  490 

1           ;   f 

V  .  J2      V 

.•^---u- ->|_ 

Effective 

Two  lo-in  channels,  two  14-in  plates 

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4s 

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610 

632 

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697 

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596 

617 

639 

660 

681 

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561 

582 

603 

624 

644 

665 

25 

547 

568 

588 

608 

628 

648 

26 

533 

553 

573 

593 

612 

632 

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520 

539 

559 

578 

596 

616 

28 

506 

525 

544 

563 

581 

599 

29 

492 

511 

529 

547 

565 

583 

30 

479 

496 

514 

532 

549 

567 

31 

465 

482 

500 

517 

533 

550 

32 

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468 

485 

502 

517 

534 

33 

437 

454 

470 

487 

502 

S18 

34 

424      . 

440 

455 

471 

486 

502 

35 

410 

42s 

441 

456 

470 

485 

Area,  sq  in 

46.83 

48.58 

50.33 

52.08 

53.83 

55.58 

/i-|.in^ 

I  018 

1080 

I  144 

1 209 

.       1275 

I  343 

ri-i,  in 

4.66 

4.72 

4.77 

4.82 

4.87 

4.92 

/2-2.  in^ 

.   788 

816 

845 

874 

902 

931 

^2-2.  in 

4.10 

4.10 

4.10 

4.10 

4.09 

4.09 

Weight, 

lb  per  Un  ft. 

159-3 

165.2 

171. 2 

177. 1 

183. 1 

189.0 

Safe  load- values  abo^ 

re  the  heavy  line  are  for  ratios  of  l/r  not  over  60;  those  be- 

low  the  heavy  line  are 

or  ratios  not  over  120  l/r 

♦  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


530 


Table  XXVI.*     Safe  Loads  in  Units  of  i  ooo  Pounds  for  12-Inch  Channel- 
Columns 


;: 

-11 

"|2  " 

'-i. 

Allowable  fiber-stress  in 

!in 

cT 

pounds  per  square  inch:      1 

M 

13  000  for  lengths  of  60  radii  or  under 

=^^  L 

J. 

Reduced  for  lengths  between   60  and    120  radii,   by 

Formula  (13), 

J 

1 

5  =  19  000  -  100  l/r 

l^ 

1 

k 

Weights  do  not  include  rivet-heads  or  other  details 

i 

For  values  for  l/r  above  120,  see  notes  on  page  490 

'S^ — ;;:t2 — ^ 

Two  i2-in  channels,  latticed 

Two  i2-in  channels,  two 

Effective 

length, 

ft 

14-in  plates 

-3  g 

^3 

1j  0 
OS  «3 

6-3 

J2  a; 

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157 

191 

229 

268 

293 

316 

339 

12 

157 

191 

229 

268 

293 

316 

339 

13 

157 

191 

229 

268 

293 

316 

339 

14 

157 

191 

229 

268 

293 

316 

339 

IS 

157 

191 

229 

268 

293 

316 

339 

16 

157 

191         • 

229 

268 

293 

316 

339 

17 

157 

191 

229 

268 

293 

316 

339 

18 

157 

191 

229 

268 

293 

316 

339 

19 

157 

191 

229 

268 

293 

316 

339 

20 

157 

191 

229 

268 

293 
293 

316 
316 

339 
339 

21 
22 
23 

157 
157 

191 

229 

2^5 
259 
253 

190 
186 

225 

220 

290 
283 

312 

305 

334 
326 

155 

24 

152 

182 

215 

248 

277 

298 

319 

25 

149 

178 

210 

242 

271 

291 

312 

26 

146 

174 

205 

236 

265 

284 

304 

27 

142 

^Z^ 

200 

230 

258 

277 

297 

28 

139 

166 

19s 

224 

252 

271 

290 

29 

136 

162 

190 

218 

246 

264 

282 

30 

133 

158 

185 

212 

239 

257 

275 

31 

129 

154 

180 

206 

233 

250 

268 

32 

126 

^50 

175 

200 

227 

243 

260 

33 

123 

146 

170 

194 

220 

2I0 

253 

34 

120 

142 

165 

188 

214 

246 

35 

117 

138 

160 

182 

208 

223 

238 

Area,  sq  in 

12.06 

14.70 

17.64 

20.58 

22.56 

24.31 

26.06 

^1-1.  in4 

256 

288 

323 

359 

658 

730 

803 

''1-1.  m 

4.61 

4.43 

4.28 

4.17 

5.40 

5.48 

5.55 

V2.  in* 

244 

279 

316 

351 

415 

444 

473 

^2-2.  m 

4.50 

4.36 

4.23 

4.13 

4.29 

4.27 

4.26 

Weight. 

lb  per  Un  ft.. 

50.4 

59.4 

694 

79-4 

76.7 

82.7 

88.6 

Safe  load-values  abc 

/e  the  heavy  line  are  for  ratios  of  l/r  not  over  60;  those 

below  the  heavy  line  ar 

e  for  ratios  not  over  120  l/r 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


540 


Strength  of  Columns,  Posts  and  Struts 


Chap. 


Table  XXVI*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  12-Inch 
Channel-Columns 


^--"',v-i 

L                                       ■ 

Allowable  fiber-stress  in  pounds  i 
13  000  for  lengths  of  60  radii  or  unde 

^pr    Qnii;^r 

a    Jnr^Vr 

t^ 

J"  -J 

1 

r 

1          ' 

-4-1 

_J, 

Reduced   for  lengths  between   60  and    120  radii,   by    | 

Formula  (13). 

i 

S  =  19  000  —  100  1/ 

r 

[^ 

1 

^ 

Weights  do  not  include  rivet-heads  or 

other  details 

i — 

\ 

For  values  for  l/r  above  120,  see  notes 

on  page  490 

hn? 1^ C71 

Effective 

Two  i2-in  channels,  two  14-in  plates 

'3  w 

Is 

4^ 

1  ^ 

II 

II 

length, 

J!  P. 

S3 

C  03 

^  a 

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362 

384 

396 

419 

441 

464 

487 

12 

362 

384 

396 

419 

441 

464 

487 

13 

362 

384 

396 

419 

441 

464 

487 

14 

362 

384 

396 

419 

441 

464 

487 

15 

362 

384 

396 

419 

441 

464 

487 

16 

362 

384 

396 

419 

441 

464 

487 

17 

362 

384 

396 

419 

441 

464 

487 

18 

362 

384 

396 

419 

441 

464 

487 

19 

362 

384 

396 

419 

441 

464 

487 

20 

21 
22 
23 

362 
362 

384 
384 

396 
396 

419 

441 

464 

487 

418 

409 

400 

440 
431 

463 
453 

485 

474 
464 

3 
3 

55 
47 

377 
369 

387 
378 

421 

443 

24 

3 

39 

360 

370 

390 

411 

432 

453 

25 

3 

32 

352 

361 

381 

401 

422 

442 

26 

3 

24 

344 

352 

372 

392 

412 

431 

27 

T 

16 

335 

344 

363 

382 

402 

421 

28 

3 

08 

327 

335 

354 

372 

391 

410 

29 

3 

00 

318 

326 

344 

362 

381 

399 

30 

2 

92 

310 

318 

335 

353 

371 

388 

31 

2 

84 

302 

309 

326 

343 

361 

377 

32 

1 

77 

293 

300 

317 

333 

350 

367 

33 

2 

69 

285 

291 

307 

323 

340 

356 

34 

2 

61 

277 

283 

298 

314 

330 

345 

35 

2 

53 

268 

274 

289 

304 

320 

334 

Area,  sq  in 

27.81 

29.56 

30.45 

32.20 

33.9s 

35.70 

37.45 

I\-u^n* 

878 

954 

910 

986 

I  063 

I  142 

I  223 

ri-i,  in 

5.62 

5.68 

5-47 

5-53 

5.60 

5.66 

5.71 

-^2-2,  in< 

501 

530 

537 

565 

594 

622 

651 

r2-2.  in. 

4.24 

4.23 

4.20 

4.19 

4.18 

4.18 

4.17 

Weight, 

lb  per  lin  ft.. 

94.6 

TOO. 5 

103.6 

109.5 

115. 5 

121. 4 

127.4 

Safe  load-values  abo 

ve  the  heavy  line  are  for  ratios  of  l/r 

not  over 

60;  those 

below  the  heavy  line  a 

re  for  ratios  not  ovqr  120  l/r 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  .Columns 


541 


Table  XXVI*  (Continued). 


Safe    Loads  in  Units  of  i  ooo  Pounds  for  12-Inch 
Channel-Columns 


X-"'wt 

>-» 

J^ 

—rr        Allowable  hber-stress  in  pounds  per  square  inch: 

J' 

"u/ 

13  000  for  lengths  of  60  radii  or  under 

i  -^- 

— 8j  — 

^ 

Reduced  for  lengths  between   60  and 

120  radii,   by 

j — 

Formula  (13), 
,                                5=19  000  —  100  l/r 

1-J. 

1 

As 

Weights  do  not  include  rivet-heads  or  other  details           1 

[— 

—X    For  \ 

^alues  for  l/r  above  120,  s< 

je  notes 

Dn  page  490 

W   ,2    t 

1 

^-—ii'-- — &i 

— 7     ■■ 

Two  12- in  channels,  two  14-in  plates 

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527 

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580 

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514 

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545 

566 

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469 

489 

508 

518 

537 

557 

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420 

439 

457 

476 

495 

504 

523 

542 

29 

409 

427 

445 

463 

482 

490 

509 

527 

30 

397 

415 

432 

450 

468 

477 

494 

512 

31 

386 

404 

420 

438 

455 

463 

480 

497 

32 

375 

392 

408 

425 

442 

449 

466 

483 

33 

364 

380 

396 

412 

428 

435 

452 

468 

34 

352 

368 

383 

399 

415 

421 

437 

453 

35 

341 

357 

371 

386 

402 

408 

423 

438 

Area,  sq  in 

38.64 

40.39 

42.14 

43.89 

45.64 

46.83 

48.58 

50.33 

h-u  in* 

I  174 

1258 

I  340 

I  424 

I  509 

1459 

1544 

1630 

n-i,  in 

5.52 

5.58 

5.64 

5.70 

5.75 

5.58 

5.64 

5.69 

I2-2.  in* 

659 

688 

717 

745 

774 

779 

808 

837 

''2-2,  in 

4.13 

4.13 

4.12 

4.12 

4.12 

4.08 

f.o8 

4.08 

Weight, 

lb  per  lin  ft.. 

131. 4 

137.4 

143.3 

149.3 

155.2 

159.3 

165.2 

171. 2 

Safe  load- values  al 

30ve  the  heavy  line  are  for  ratios  of  l/r  no 

t  over  60;  those 

below  the  heavy  line 

are  for  ratios  not  over  120  l/r 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


542 


"Strength,  of  Columns,  Posts  and  Struts  Chap.  14 


Table  XXVI*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  12-Inch 
Channel-Columns 


L 

^^ 

7 

1 

e  inch: 

Xi 

^2"' 

Allowable  fiber-stress  in  pounds  per  squai 

T% 

r^ 

.-i-. 

13  000  for  lengths  of  60  radii  or  under 

i-'- 

J, 

Reduced   for  lengths  between   60   and    120  radii,   by    | 

T 

Formula  (13), 

1 

5  =  19  000  —  100  l/r 

1-^ 

' 

k 

Weights  do  not  include  rivet-  heads  or  other  details 

— — 

For  values  for  l/r  above  120,  sec  notes  on  page  490 

Tv  ,,2    V 

h"— 14 H 

Effective 

Two  i2-in  channels,  two  14-in  plates 

"o   QJ 

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668 

689 

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757 

779 

802 

22 

653 

674 

695 

717 

739 

761 

783 

23 

637 

658 

679 

700 

722 

743 

765 

24 

622 

642 

663 

684 

704 

725 

746 

25 

607 

626 

646 

667 

687 

707 

728 

26 

591 

610 

630 

650 

670 

689 

709 

27 

576 

594 

614 

633 

652 

672 

691 

28 

561 

578 

597 

616 

635 

654 

672 

29 

545 

S63 

581 

599 

617 

636 

654 

30 

530 

547 

564 

582 

600 

618 

635 

31 

515 

531 

548 

565 

583 

600 

617 

32 

515 

532 

548 

565 

582 

599 

33 

484 

499 

515 

531 

548 

564 

580 

34 

469 

483 

499 

515 

530 

546 

562 

35 

453 

467 

482 

498 

513 

528 

543 

Area,  sq  in 

52.08 

53.83 

SS.58 

57.33 

5908 

60.83 

62.58 

/i-i,  in* 

I  719 

1808 

1899 

1992 

2087 

2183 

2280 

n-i,  in 

5. 74 

5.80 

5.85 

5.89 

5.94 

5.99 

6.04 

/j-o,  in* 

865 

894 

922 

951 

980 

I  008 

1037 

rj_2,  in : 

4.08 

4.07 

4.07 

4.07 

4.07 

4.07 

4.07 

Weight, 

lb  per  liii  ft.. 

177. 1 

183. 1 

189.0 

195.0 

200.9          206.9 

212.8 

Safe  load-values  abo 

ve  the  heavy  line  are  for  ratios  of  l/r  not  over  t 

K);  those 

below  the  heavy  line  a 

re  for  ratios  not  over  120  l/r 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


54d 


Table  XXVI'* 

(Continued). 

Safe  Loads 

m  Units  of  i 

000  Pounds 

for  12-Inch 

Channel-Columns 

,.S"'"r 

i 

Ulowable  fiber-stress 

in  pounds 

nch: 

per   square   1 

■  Vi 

1 

'      13 

1        ^ 

1 

.lof-^ 

000  for  lengths  of  60  radii 

or  under 

r^ 

_l         Reduced   for  lengths  between 
Formula  (13), 

60  and    120  radii 

.by 

1 

U,       We 

S  =  19 

000  - 

100// 

r 

1      r^ 

i 

ights  do  not  include  rivet-heads  or  other  details 
values  for  l/r  above  120,  see  notes  on  page  490 

r    ,k 

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686 

711 

736 

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9         623 

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756 

781 

805 

27 

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7         611 

635 

659 

683 

707 

718 

741 

766 

789 

28 

57 

5         599 

622 

646 

669 

693 

703 

726 

750 

773 

29 

56 

3         586 

609 

633 

655 

678 

688 

711 

734 

757 

30 

55 

2         574 

596 

619 

642 

664 

674 

696 

719 

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31 

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0         562 

583 

606 

628 

649 

659 

681 

703 

724 

32 

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8          549 

571 

593 

614 

635 

644 

665 

687 

708 

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621 

630 

650 

672 

692 

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545 

566 

586 

606 

615 

635 

656 

676   : 

35 

49 

3         512 

532 

553 

572 

592 

600 

620 

640 

660 

Area,  sq  in 

47- 

64     49  64 

51.64 

53.64 

55.64 

57.64 

58.58 

60.58 

62.58 

64.58 

/i-i.  in^ 

~T1 

81       I  678 

I  777 

1878 

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2084 

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2  IIQ 

2225 

2333 

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5.87 

5.92 

5.97 

6.01 

5.87 

5.91 

5.96 

6.01 

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I  I 

21       I  164 

1206 

1249 

I  292 

1334 

1349 

1392 

1434 

1477 

^2-2.  in 

4. 

85       4.84 

4.83 

4.83 

4.82 

4.81 

4.80 

4.79 

4.79 

4.78 

Weight, 

lb  per  lin  ft.. 

162 

.0      168.8 

175.6 

182.4 

189.2 

196.0 

199-2 

206.0 

212.8 

219.6 

Safe  load- value 

s  above  the 

heavy  line  are  for  ra 

tios  of 

llr  not 

over  i 

)o;  tho 

se  be- 

low  the  heavy  lir 

le  are  for  rt 

itios  not  over  120  l/r 



•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


644 


Strength  of  Columns,  Posts  and  Struts 


Table  XXVI  "*■  (Continued).     Safe  Loads  in  Units  of  i  ooo  Potmds  for  Z2-Inch 
Channel-Columns 


"             1 

•v-^ 

'^J-'t 

D               .„            ,  ,       /-.            . 

i-r           /\iiowaDie  noer-stress 

in  pounas 

per  square  men:      1 

lOj'  -^ 

T 
_1 

13  000  for  lengths  of  60  radii  or  under 
Reduced   for  lengths  between   60  and    120 

radii, 

by 

-— 1 

Formula  (13), 

i 

1 

S  =  19  000  — 

100  1/ 

i   A^ 

j 

^ 

Weights  do  not  include  rivet-heads  or 

other  details 

1 

ij      For  values  for  l/r  above 

120,  see  notes  on  page  490 

!  V  ,J2    S^ 

^---IQ >; 

Two  i2-in  channels,  two  i6-in  pk 

Effective 

ites 

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ll 

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903 

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I  002 

27 

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862 

885 

909 

934 

957 

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1006 

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28 

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820 

844 

867 

891 

914 

937 

961 

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I  007 

29 

780 

803 

826 

848 

872 

895 

917 

941 

964 

986 

30 

764 

785 

808 

830 

853 

876 

897 

920 

943 

965 

31 

747 

768 

791 

812 

834 

857 

878 

900 

922 

943 

32 

730 

751 

773 

794 

81S 

837 

858 

880 

901 

922 

33 

713 

734 

755 

775 

797 

818 

838 

859 

881 

900 

34 

697 

716 

737 

757 

778 

799 

818 

839 

860 

879 

35 

680 

699 

720 

739 

759 

779 

798 

819 

839 

858 

Area,  sq  in 

66.58 

68.58 

70.58 

72.58 

74.58 

76.58 

78.58 

80.58 

82.58 

84.58 

h-i.in* 

2443 

2555 

2668 

2783 

2901 

3  020 

3  141 

3264 

T389 

3516 

ri-u  in 

6.06 

6.10 

6.15 

6.19 

6.24 

6.28 

6.32 

6.36 

6.41 

6.45 

/2-2,  in* 

I  520 

1 562 

I  60s 

1648 

1690 

I  733 

1776 

I  818 

I  861 

I  904 

r2-5.  in 

4.78 

4.77 

4.77 

4.76 

4.76 

4.76 

4.75 

4.75 

4.75 

•4.74 

Weight, 
lb  per  lin  ft.. 

226.4 

233.2 

240.0 

246.8 

'253.6 

260.4 

267.2 

274.0 

280.8 

287.9 

Safe  load- values  a 

bove  the  heavy  line  are  for 

ratios 

of  l/r 

not  ov 

er  60; 

those 

below  the  heavy  lin 

e  are  for  ratios  not  over  120  / 

/r 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


545 


Table  XXVII.*     Safe  Loads  in  Units  of   i  ooo  Pounds  for  15-Inch  Channel- 
Columns 


Li                                                  »                   »  n              ,   <         /-i 

pounds  per  square  inch: 

1  "h 

TT-           /iiiowanie   iioer-stress   in 
T          13  000  for  lengths  of  60  rad 

'X- 

ii  or  under 

=i  - 

-         Reduced   for  lengths  between   60   and    120  radii,   by 

-^              Formula  (13), 

; 

i 

.S  =  19  000 

—  100  l/r 

i  /^ 

1 

1 

.A        Weights  do  not  include  rivet-heads  or  other  details 

.          1           '  ■ 

For  values  for  l/r  above  120              '^""        — 

,  bcc  lUJi-eb  uii  page 

4y" 

1  y    ,k    ^ 

r '--16 > 

Two  i^in  channels,  latticed 

Two  15-in  channels,  two 
i6-in  plates 

Effective 

(U  0 

(U  0 

i^ 

<u  a 

-SS 

length, 

«1 

gl 

ci3 

ft 

0  <u 

0  <u 

0  fl 

0  CI 

II 

at 

6  w 

a'4. 

II 

257 

268 

306 

344 

413 

439 

465 

12 

257 

268 

306 

344 

413 

439 

465 

13 

257 

268 

306 

344 

413 

439 

46s 

14 

257 

268 

306 

344 

413 

439 

465 

IS 

257 

268 

306 

344 

413 

439 

465 

16 

257 

268 

306 

344 

413 

439 

465 

17 

257 

268 

306 

344 

413 

439 

465 

18 

257 

268 

306 

344 

413 

439 

46s 

19 

257 

268 

306 

344 

413 

439 

465 

20 

257 

268 

306 

344 

413 

439 

465 

21 

257 

268 

306 

344 

413 

439 

465 

22 

257 

268 

306 

344 

413 

439 

465 

2Z 

257 

268 

306 

344 

413 
413 

439 
439 

46s 
46s 

24 
25 

257 

268 

306 

343 
336 

257 

266 

301 

407 

432 

457 

26 

252 

261 

295 

329 

400 

424 

448 

27 

247 

256 

289 

322 

392 

415 

440 

28 

243 

251 

284 

316 

384 

407 

431 

29 

238 

246 

278 

309 

376 

399 

422 

30 

233 

241 

272 

302 

368 

390 

413 

31 

228 

236 

266 

296 

360 

382 

404 

32 

224 

231 

260 

289 

352 

373 

395 

33 

219 

226 

254 

282 

345 

365 

386 

34 

214 

221 

249 

276 

337 

357 

377 

35 

209 

216 

243 

269 

329 

348 

368 

Area,  sq  in 

19.80 

20.58 

23.52 

26.48 

31.80 

33.80 

35.80 

A-i.  in* 

625 

640 

695 

750 

I  334 

I  459 

1586 

ri-i,  in 

5.62 

5. 58 

5. 43 

5.32 

6.48 

6.57 

6.66 

/2-2.  in< 

491 

504 

552 

597 

747 

789 

832 

^2-2.  in 

4.98 

4.9s 

4.84 

4.75 

4.85 

4.83 

4.82 

Weight, 

lb  per  lin  ft. . 

80.2 

84.2 

92.1 

102.2 

106.8 

113. 6 

120.4 

Safe  load-values  above  the  heavy  line  are  for  rati 

OS  of  l/r  not  over  60;  those 

below  the  heavy  line  are  for  ratios  not  over  120  l/r 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


646 


Strength  of  Columns,  Posts  and  Struts 


Chap. 


Table  XXVII*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  15-Inch 
Channel-Columns 


^'^i--^ 

Allowable  fiber-stress  in  pounds  per  square  inch: 

''^% 

t- 

T         13  000  for  lengths  of  60  radii  or  under 

1        '    - 

Reduced   for  lengths  between   60  and    120   radii,   by 
—              Formula  (13). 

1 

i 

S  =  19  000  —  100  l/r 

i  aj 

1 

i.         Weights  do  not  include  rivet-heads  or  other  details 

'^ 

For  values  for  l/r  above  120,  see  notes  on  page  490 

\    \ 

1  Y   ,  J2       ^1 

r^-- 16- >i 

^iii 

j'  '  ^j J ^                     Two  15-in  channels ,  two  i6-in  plates 

^ 

Effective 

»2  w 

0)    OJ 

'%  S 

P 

^  S 

•SI 

length, 

g« 

C  ct3. 

B^ 

C  d 

gj3 

H 

ft 

03  a. 

<^7^ 

f^-o. 

rt  ^ 

rt  V! 

a  ^ 

ci-^ 

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fO 

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491 

517 

528 

554 

580 

606 

632 

12 

491 

517 

528 

554 

580 

606 

632 

13 

491 

517 

528 

554 

580 

606 

632 

14 

491 

S17 

528 

554 

580 

606 

632 

IS 

491 

517 

528 

554 

580 

606 

632 

16 

491 

517 

528 

554 

580 

606 

632 

17 

491 

517 

528 

554 

580 

606 

632 

18 

491 

517 

528 

554 

580 

606 

632 

19 

491 

517 . 

528 

554 

580 

606 

632 

20 

491 

517 

528 

554 

580 

606 

632 

21 

491 

517 

528 

554 

580 

606 

632 

22 

491 

517 

528 

5.54 

580 

606 

632 

23 
24 

491 
491 

517 
517 

528 

554 

580 

606 

632 

527 

552 

578 

604 

629 
617 

:77.2sT  *  ■ 

,    482 

507 

517 

542 

567 

592 

26 

473 

498 

507 

531 

555 

580 

605 

27 

464 

488 

497 

520 

544 

.569 

592 

28 

454 

478 

486 

510 

533 

557 

580 

29 

445 

468 

476 

499 

522 

545 

568 

30 

435 

458 

466 

488 

SIX 

533 

556 

31 

426 

448 

456 

478 

499 

522 

543 

32 

416 

438 

446 

467 

488 

510 

531 

33 

407 

428 

436 

456 

477 

498 

519 

34 

398 

418 

42s 

446 

466 

487 

507 

35 

388 

408 

415 

435 

454 

475 

494 

Area,  sq  in 

37.80 

39-80 

40.58 

42.58 

44.58 

46.58 

48.58 

/i-i,  in*..... 

1 715 

1847 

I  861 

1994 

2  129 

2  267 

2406 

n-i.in 

6.74 

6.81 

6.77 

6.84 

6.91 

6  98 

7.04 

/i-2.  in* 

875 

917 

930 

973 

I  016 

I  058 

I  lOI 

ra-j.in 

•  4.81 

4.80 

4.79 

4.78 

4.77 

4.77 

4.76 

Weight. 

lb  per  Un  ft.. 

127.2 

134.  c 

138.0 

144.8 

151. 6 

158.4 

165  2 

Safe  load- values  above  the  heavy  line  are  for  ratios  of  l/r  not  over  60;  those 

below  the  heavy  line  are  for  ratios  not  over  120  l/r 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


547 


Table  XXVII*  (Continued). 


Safe  Loads  in  Units  of  i  ooo  Pounds  for  15-Inch 
Channel-Columns 


r^Q — -^ a^ 

Allowable  fiber-stress  in  pounds  per  square  inch: 

\    ^ 

r 

:i: 

13  000  for  lengths  of  60  radii  or  under 

I 

Reduced  for  lengths  between   60  and    120  radii,   by 

Formula  (13), 

1 

5  =  19  000  —  100  l/r 

M\ 

Weights  do  not  include  rivet-heads  or  other  details 

1 

For  values  for  l/r  above  120,  see  notes  on  page  490 

y      ,h      y\ 

1<---16--- ^. 

Effective 

Two  15-in  channels,  two  r6-in  plates 

•SS 

<^  !^, 

is 

0  w 

-^1 

-SS 

4m 

length, 
ft 

it 

H 

C5 

§1 

g5 

§5 

Crt 
g- 

-^  vi 

XI  ^ 

'^  B 

x:  p< 

XJ  c 

-s.^ 

X5  c! 

u.n 

<^  c 

^  a 

*-*■?' 

CJ.w 

SI  !o 

•^"i 

X)  2 

^•r 

^  =0 

U2NCfl 

j3   « 

i? 

1'-- 

1>T 

6^ 

'si 

6- 

"^r^ 

"* 

^ 

"^ 

'f 

'* 

■<t 

"*    ^ 

II 

644 

670 

696 

722 

748 

774 

786 

12 

644 

670 

C96 

722: 

748 

774 

786 

13 

644 

670 

696 

722 

748 

774 

786 

14 

644 

670 

696 

722 

748 

774 

786 

IS 

644 

670 

(>9^ 

722 

748 

774 

786 

16 

644 

670 

6q6 

722 

748 

774 

786 

17 

644 

670 

696 

722 

748 

774 

786 

18 

644 

670 

696 

722 

748 

774 

786 

19 

644 

670 

696 

722 

748  , 

774 

.786 

20 

644 

670 

696 

722 

748 

774 

786 

21 

644 

670 

696 

722 

748 

774 

786 

22 

644 

670 

696 

722 

748 

774 

786 

23- 

24 

644 

670 

696 

722 

748 

774 

786 

639 

665 

690 

715 

741 

767 

777 

25 

627 

651 

677 

701 

727 

752 

761 

26 

614 

638 

663 

687 

712 

737 

746 

27 

602 

625 

649 

673 

697 

721 

730 

28 

589 

612 

636 

6S9 

683 

706 

715 

29 

577 

599 

622 

645 

668 

691 

699 

30 

564 

586 

609 

631 

653 

676 

684 

31 

551 

573 

595 

616 

639 

661 

668 

32 

539 

560 

581 

602 

624 

646 

653 

33 

526 

517 

568. 

588 

609 

630 

637 

34 

514 

534 

554 

574. 

595 

615 

622 

35 

501 

520 

541 

560 

580 

600 

606 

Area,  sq  in 

49-52 

51.52 

53-52 

55.52 

57.52 

59-52 

60.48 

/i-i,in« 

2  322 

2  461 

2  602 

2  746 

2891 

3039 

2946 

''i-i.  m 

6.85 

6.91 

6.97 

7.03 

7.09 

7.15 

6.98 

/2-2.in* 

I  106 

I  149 

I  192 

I  234 

I  277 

I  320 

1322 

r2-2,  m 

4.73 

4.72 

4.72 

4.71 

4.71 

4.71 

4.68 

Weight, 

lb  per  lin  ft.. 

168.4 

175.2 

182.0 

188.8 

195-6 

202.4 

205.6  ' 

Safe  load-values  abo 

ve  the  heavy  line  are  for  ratios  of  l/r  not  over  60;  those 

below  the  heavy  line  ar 

e  for  ratios  not  over  120  l/r 

*From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


648 


Strength  of  Columns,  Posts  and  Struts  Chap.  14 


Table  XXVII*  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  1 5-Inch 
Channel-Columns 


Allowable  fiber-stress  in  pounds  per  square  inch: 

T>] 

r 

^'T^ 

13  000  for  lengths  of  60  radii  or  under 

i  -- 

1 

Reduced   for  lengths   between    60   and    120   radii,   by 

Formula  (13), 

,i 

5  =  19  000  —  100  l/r 

♦       r^ 

^ 

Weights  do  not  include  rivet-heads  or  other  details 

i 

For  values  for  l/r  above  120,  see  notes  on  page  490 

!V     J2      v! 

W      'IQ- -5- 

Effective 

Two  iS-in  channels,  two  i6-in  plates 

4  s 

4  s 

Oi    <D 

-^1 

•^S 

4s 

4^ 

length. 

gs 

§1 

^1 

§3 

H 

§5 

ft 

rt  P< 

03  ^ 

rt  0. 

rt  ^ 

a  0, 

05  ^ 

a  p. 

•g.E 

-g.s 

-g.s 

-s.a  • 

-g.a 

-5.5 

5'^' 

:2  N- 

£:^ 

£•- 

£^ 

£x2 

£4, 

J^'J^ 

%t: 

10 '-' 

»o'm 

10  >-* 

^•;ii' 

"^M 

■* 

Tj- 

^ 

■^ 

II 

812 

838 

864 

890 

916 

942 

968 

12 

812 

838 

864 

890 

916 

942 

968 

13 

812 

838 

864 

890 

916 

942 

968 

14 

8X2 

838 

864 

890 

916 

942 

968 

15 

812 

838 

864 

890 

916 

942 

968 

16 

812 

838 

864 

890 

916 

942 

968 

17 

812 

838 

864 

890 

916 

942 

968 

18 

812 

838 

864 

890 

916 

942 

968 

19 

812 

838 

864 

890 

916 

942 

968 

20 

812 

838 

864 

890 

916 

942 

968 

21 

812 

838 

864 

890 

916 

942 

968 

22 

812 

838 

864 

890 

916 

942 

968 

23 
24 

812 

838 

864 

890 

916 

942 

968 

802 

827 

853 

879 

904 

930 

956 

25 

786 

811 

836 

861 

886 

912 

937 

26 

770 

794 

819 

844 

868 

893 

918 

27 

754 

778 

802 

826 

850 

874 

898 

28 

738 

761 

785 

808 

832 

856 

879 

29 

722 

745 

768 

791 

814 

837 

860 

30 

705 

728 

751 

773 

796 

818 

841 

31 

689 

711 

734 

756 

778 

800 

822 

32 

673 

695 

716 

738 

760 

781 

803 

33 

657 

678 

699 

720 

741 

763 

784 

34 

641 

662 

682 

703 

723 

744         764 

35 

625 

645 

665 

685 

705 

725         745 

Area,  sq  in 

62.48 

64.48 

66.48 

68.48 

70.48 

72.48 

74.48 

A-i.  in* 

3094 

3244 

3396 

3550 

3707 

3865 

4026 

^i-j.in 

7.04 

7.09 

7.15 

7.20 

7.2s 

7.30 

7.35 

I2-2,  in* 

1365 

1 408 

I  450 

1493 

1536 

1578 

I  621 

^2-2.  in 

4.67 

4.67 

4.67 

4.67 

4.67 

4.67 

4.67 

Weight, 
lb  per  lin  ft.. 

212.4 

219.2 

226.0 

232.8 

239-6 

246.4 

253.2 

Safe  load-values  abo 

ve  the  heavy  line  are  for  ratios  of  l/r  not  over  60;  those 

below  the  heavy  line  a 

re  for  ratios  not  over  120  l/r 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


549 


Table  XXVII*  (Continued).    Safe  Loads  in  Units  of  i  ooo  Pounds  for  xs-Inch 
Channel-Columns 


T^T-i 

r^ 

1 

(^ 

Allowable  fiber-stress  in  pounds  per  square  inch      j 

:-iii'--^ 

13  000  for  lengths  of  60  radii  or  under 

'^  - 

.J_.. 

1 

Reduced  for  lengths  between   60  and 

120  radii,  by 

— =• 

Formula  (13), 

1 

i 

5  =  19  000  —  100  l/r 

lA 

1 

— 1 — 

■^ 

Weights  do  not  include  rivet-heads  or  other  detai  Is 
For  values  for  l/r  above  120,  see  notes  on  page  490 

IV       J2        V 

[<— -18- ->i 

Two  i5-in  channels,  two  i8-in  plates 

- 

^  « 

w" 

> 

w 

w 

w 

w 

Effective 
length, 

II 

11 

s| 

Is 

C  05 

Is 

^1 

Is 

ft 

cj  r:; 

ci  0< 

'^'^ 

a  Oi 

f^":^ 

rt';3 

rt  O4 

d'Ti 

^   ^ 

■Ss 

^  ^ 

-s.s 

M  ^ 

^  ^ 

-^  d 

^  ^ 

o  ti 

"  a 

^  rt 

^  ti 

0.5 

0  c 

^"t 

^  L 

^•v 

^  i 

XI  "t 

rO"? 

Xi   <o 

XI  "t* 

i^"^ 

'e 

%'- 

r 

r 

If^ 

II 

433 

462 

491 

521 

550 

560 

589 

619 

12 

433 

462 

491 

521 

550 

560 

589 

619 

13 

433 

462 

491 

521 

550 

560 

589 

619 

14 

433 

462 

491 

521 

550 

560 

589 

619 

15 

433 

462 

491 

521 

550 

560 

589 

619 

i6 

433 

462 

491 

521 

550 

560 

589 

619 

17 

433 

462 

491 

521 

550 

560 

589 

619 

i8 

433 

462 

491 

521 

550 

560 

589 

619 

19 

433 

462 

491 

521 

550 

560 

589 

619 

20 

433 

462 

491 

521 

550 

560 

589 

619 

21 

433 

462 

491 

521 

550 

560 

589 

619 

22 

433 

462 

491 

521 

550 

560 

589 

619 

23 

433 

462 

491 

521 

550 

560 

589 

619 

24 

433 

462 

491 

521 

550 

560 

589 

619 

25 

433 

462 

491 

521 

550 

560 

589 

619 

26 

433 

462 

491 

521 

550 

560 

589 

619 

27 

433 

462 

462 

491 

49t 

521 

5SO 

560 

589 

619 

28- 
29 

433 

520 
512 

549 
539 

558 
549 

586 

577 

615 

60s 

428 

456 

484 

30 

421 

449 

476 

503 

530 

540 

567 

594 

31 

414 

441 

468 

494 

521 

530 

557 

584 

32 

407 

433 

459 

486 

512 

521 

547 

574 

33 

400 

426 

451 

477 

503 

512 

537 

563 

34 

393 

418 

443 

469 

494 

502 

527 

553 

35 

386 

411 

435 

460 

485 

493 

518 

543 

Area,  sq  in 

33.30 

35.55 

37.80 

40.0s 

42.30 

43.08 

45.33 

47.58 

/i-i.in* 

I  423 

1564 

I  707 

I  852 

1999 

2  014 

2  164 

2316 

n-i.  in 

6.54 

6.63 

6.72 

6.80. 

6.87 

6.84 

6.91 

6.98 

/2-2,  in'* 

I  069 

I  130 

I  190 

I  251 

I  312 

1332 

1393 

1453 

^2-2.  in 

5.67 

5.64 

5.61 

5.59 

5.57 

5.56 

5.54 

5.53 

Weight, 

lb  per  lin  ft.. 

III. 9 

119. 6 

127.2 

1.34.9 

142.5 

146.5 

154.2 

161. 8 

Safe  load- values  ah 

)Ove  the  heavy  line  are  for  ratios  of  l/r  no 

t  over  60;  those  . 

below  the  heavy  line 

are  for  ratios  not  over  120  l/r 

•■  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


550 


Strength  of  Columns,  Posts  and  Struts 


Chap.  14 


Table  XXVII 'I'  (Continued).     Safe  Loads  in  Units  of  i  ooo  Pounda  for  x 5-Inch 
Channel-Columns 


T^T'-i 

;  inch: 

T"f\ 

1 

7^ 

Allowable  fiber-stress  in  pounds  per  squan 

-Ht  —  ^ 

13  000  for  lengths  of  60  radii  or  under 

%    L 

-^- 

;|^       Reduced   for  lengths  between   60  and    120  radii,   by    | 

'             Formula  (13), 

1 

5  ==  19  000  —  100  l/r 

1^ 

1 

— 1 — 

.A        Weights  do  not  include  rivet-heads  or  other  details 
''»     For  values  for  l/r  above  120.  see  notes  on  oaee  ziQO 

V      J2       V 

|<— -18- >1 

Effective 
length, 

Two  15-in  channels,  two  i8-in  plates 

II 

S4 

4b 

^1 

4'^ 

a  0, 

|l 

u 

xi  a 

J  ^ 

-g.s 

^  ^ 

-^  a 

X  0, 

X!  c! 

-^  a 

O'Y 

0  a 

^  fl 

o.n 

^•? 

O-Y 

0.5 

" 

-^xS 

^•r 

J3^2 

JD-V 

JD    i> 

-OS. 

Xi-fo 

^  -4« 

65 

%T 

^-^ 

It 

6-^ 

4? 

6"" 

6'^ 

fO 

ro 

rr 

■^ 

^ 

Tt 

■«* 

II 

648 

677 

686 

715 

745 

774 

803 

832 

12 

648 

677 

686 

715 

745 

774 

803 

832 

13 

648 

677 

686 

715 

745 

774 

803 

832. 

14 

648 

677 

686 

715 

745 

774 

803 

832 

15 

648 

677 

686 

715 

745 

774 

803 

832 

i6 

648 

677 

686 

715 

745 

774 

803 

832 

17 

648 

677 

686 

715 

745 

774 

803 

832 

i8 

648 

677 

686 

715 

745 

774 

803 

832 

19 

648 

677 

686 

715 

745 

774 

803 

832 

20 

648 

677 

686 

715 

745 

774 

803 

832 

21 

648 

677 

686 

715 

745 

774 

803 

832 

22 

648 

677 

686 

715 

745 

774 

803 

832 

23 

648 

677 

686 

715 

745 

774 

803 

832 

24 

648 

677 

686 

715 

745 

774 

803 

832 

25 

648 

677 

686  . 

715 

745 

774 

803 

832 

26 

648 

677 

686 

715 

745 

774 

803 

832 

27 
28 
29 

648 

677 

686 

715 

745 

774 

803 

832 

643 
632 

671 
660 

680 
668 

708 

736 

764 

793 

821 
807 

696 

723 

751 

779 

30 

621 

649 

657 

684 

711 

738 

766 

793 

31 

610 

637 

645 

672 

698 

725 

752 

779 

32 

599 

626 

634 

660 

685 

712 

738 

764 

33 

589 

615 

622 

648 

673 

698 

725 

750 

34 

578 

603 

610 

636 

660 

685 

711 

736 

35 

S67 

592 

599 

624 

648 

672 

698 

722 

Area,  sq  in 

49  83 

52.08 

52.77 

55.02 

57.27 

59-52 

61.77 

64.02 

Ii-i.in* 

2470 

2627 

2525 

2682 

2841 

3002 

3166 

3332 

ri_i,  in 

7.04 

7.10 

6.92 

6.98 

7.04 

7.10 

7.16 

7.21 

-^M.  in* 

IS14 

1575 

1589 

I  649 

I  710 

I  771 

1832 

1892 

r2-8.  in 

Weight. 

5. 51 

5.50 

5.49 

5.48 

5.46 

5.45 

5.45 

5.44 

lb  per  lin  ft.. 

169.5 

177. 1 

179-5 

187. 1 

194.8 

202.4 

210. 1 

217.7 

Safe  load- values  above  the  heavy  line  are  for  ratios  of  l/r  not  over  6o 

;  those 

below  the  heavy  line  are  for  ratios  not  over  120  l/r 

^1 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


Table  XXVII*  (Continued).    Safe  Loads  in  Units  of  x  ooo  Pounds  for  X5-Ineh 
Channel-Columns 


J:-"Kr--i 

r-  cr^       '        ^^ 

Allowable  ftber-stress  in  pounds   per   square   inch: 
13  000  for  lengths  of  60  radii  or  under 

1  ^ 

r 

1 

-'Xi 

Reduced  for  lengths  between   60   and    120   radii,   by- 

■  5!     1 

M5      ■ — 

4 

Formula  (13), 

tH 

1 

5=19  000  —  100  l/r 

i,^ 

1 

^. 

Weights  do  not  include  rivet-heads  or  othei*  details 

— 1 — 

For  values  for  l/r  above  120 

,  see  notes  on  page  490 

•;^..i8.k...x' 

Effective 

Two  15-in  channels,  two  i8-in  plates 

is 

i'& 

i^ 

•s'l 

-%  s 

•ss 

length, 

§1 

g^ 

§:§ 

§1 

gs 

«l 

ft 

d  ^ 

rt  ft 

w  ^ 

rt  P* 

rt  ^ 

rt^ 

CO    ^ 

^  a 

-S.a 

^  C! 

•s.s 

^  rt 

•S.s 

^  a 

o-Y 

0-^ 

o-S 

o.« 

^   <o 

s^^ 

£\2 

jD\4< 

^  to 

J3s*o 

^  « 

•t:s: 

^-t: 

-?:§: 

•-J*  c<N 

-r^ 

\r>  *-• 

10 'm' 

in  ^ 

>0  M 

10  "^ 

>0  M 

■^ 

Tf 

"* 

-"T 

II 

841 

871 

900 

929 

958 

988 

I  017 

12 

841 

871 

900 

929 

958 

988 

I  017 

13 

841 

871 

900 

929 

958 

988 

I  017 

14 

841 

871 

900 

929 

958 

938 

I  017 

15 

841 

871 

900 

929 

958 

988 

I  017 

16 

841  • 

871 

900 

929 

958 

988 

I  017 

17 

841 

871 

900 

929 

958 

988 

I  017 

18 

841 

871 

900 

929 

958 

988 

I  017 

19 

841 

871 

900 

929 

958 

988 

I  017 

20 

841 

871 

900 

929 

958 

988 

I  017 

21 

841 

871 

900 

929 

958 

988 

I  017 

22 

841 

871 

900 

929 

958 

988 

I  017 

23 

841 

871 

900 

929 

958 

988 

1  017 

24 

841 

871 

900 

929 

958 

988 

I  017 

25 

841 

871 

900 

929 

958 

988 

I  017 

26 

841 

871 

900 

■929 

958 

988 

I  017 

27 
28 

841 

871 

900 

929 

958 

987 
970 

I  015 

^29 

857 

885 

913 

942 

29 

814 

843 

870 

897 

926 

953 

980 

30 

800 

828 

855 

882 

909 

936 

963 

31 

786 

813 

839 

866 

893 

919 

945 

32 

771 

798     • 

824 

850 

877 

902 

928 

33 

757 

783 

809 

834 

860 

885 

911 

34 

743 

768 

793 

818 

844 

868 

893 

35 

728 

754 

778 

802 

827 

852 

876 

Area,  sq  in 

64.73 

66.98 

69.23 

71.48 

73.73 

75.98 

78.23 

/i-i.in* 

3  221 

3387 

3556 

3727 

3900 

4076 

4  255 

ri-i,  in 

7.05 

7. II 

7.17 

7.22 

7.27 

7.32 

7.37 

^5^2.  in* 

1903 

1964 

2  025 

2086 

2  146 

2  207 

2268 

^8-2.  in 

5.42 

5.42 

5. 41 

5.40 

5.40 

5.39 

5.38 

:      Weight. 
Hb'per  lin  ft.. 

220.1 

227.7 

235.4 

243.0 

250.0 

258.3 

266.0 

Safe  load-values  abo 

ve  the  heavy  line  are  for  ratios  of  l/r  not  over  60;  those 

below  the  heavy  line  ai 

e  for  ratios  not  over  120  l/r 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Strength  of  Columns,  Posts  and  Struts  Chap.  14 


Table  XXVU*  (Continued). 


Safe  Loads  in  Units  of  i  ooo  Pounds  for  x  5-Inch 
Channel-Columns 


X 


uW-, 


1 


1^ 

..L. 

J. 

J 

! 

\ 

18'i-?.., 

-tl 

Allowable  fiber-stress  in  pounds  per  square  inch' 
13  000  for  lengths  of  60  radii  or  under 
Reduced  for  lengths  between   60  and   120  radii,  by 
Formula  (13), 

5  =  19  000  —  100  l/r 
Weights  do  not  include  rivet-heads  or  other  details 
For  values  for  l/r  above  120,  see  notes  on  page  490 


Effective 

length, 

ft 


Two  is-in  channels,  two  i8-in  plates 


is 

4S 

0  1 

J^M 

'^'m 

I  105 

I  134 

I  105 

I  134 

I  105 

I  134 

I  IDS 

1  134 

1 105 

I  134 

1 105 

I  134 

I  105 

I  134 

I  105 

I  134 

I  105 

1  134 

I  105 

I  134 

I  105 

I  134 

I  105 

I  134 

I  105 

I  134 

I  105 

I  134 

I  105 

I  134 

I  105 

I  134 

§1 


Gi3 


0/   to 


13 
14 
IS 

16 
17 
18 
19 


VI    24 

25 


26 

27 


H«.i  28 

0-29 

i.'  30 

uc  31 

i^-.V  32 

??;33 

3^1 

35 

I  046 
I  046 
I  046 
I  046 
I  046 

I  046 
I  046 
I  046 
1  046 
I  046 

I  046 
I  046 
I  046 
I  046 
I  046 

I  046 


1075 
1075 
1075 
I  075 
1075 

1075 
1075 
1075 
I  075 
1075 

1075 

1075 
I  075 
1075 
1075 

1075 


I  163 
I  163 
I  163 
I  163 
I  163 

I  163 
I  163 
I  163 
I  163 
I  163 

I  163 
I  1^13 
I  163 
I  163 
I  163 

I  163 


I  222 
I  222 
I  222 
I  222 
I  222 

I  222 

I  222 
I  222 
1  222 
I  222 

I  222 
I  222 
I  222 
I  222 
I  222 

I  222 


1044 

I  026 

I  009 

991 

973 
955 
937 
919 
901 


1073 

I  102 

I 

054 

I  083 

1 

036 

I  064 

I 

017 

I  045 

999 

I  026 

980 

I  007 

962 

988 

943 

969 

925 

950 

1 131 

I  112 

I  092 
I  073 

I  053 
I  034 
I  014 

995 
975 


I  159 

I  139 
I  119 
1099 

1079 
1059 
1039 
I  019 
999 


I  195 
I  174 
I  153 

I  132 
I  III 
I  090 
I  069 


I  280 
I  280 
I  280 
I  280 
I  280 

I  280 
I  280 
I  280 
I  280 
I  280 

I  280 

I  280 
I  280 
I  280 
I  280 

I  280 


I  253 
I  231 
I  208 

I  186 
I  164 
I  142 
I  120 


Weight, 


80.48 


4436 
7.42 

2329 
5. 38 


273.6 


82.73 


4619 
7-47 

2389 
5.37 


281.3 


84.98 


4805 
7.52 
2450 
5-37 


288.9 


87.23 


89.48 


4  994 
7.57 

2511 
5.37 


5185 
7.61 

2572 
5.36 


296.6 


304.2 


93.98 


5  575 
7.70 

2693 
5.35 


319. 5 


98. 4S 


5  976 
7.79 

281S 
5.35 


334.8  - 


Safe  load-values  above  the  heavy  line  are  for  ratios  of  l/r  not  over  60;  those 
below  the  heavy  line  are  for  ratios  not  over  120  l/r 


*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Columns 


553 


Table  XXVII*  (Continued).     Safe  Loads  in  Units  of  i  coo  Pounds  for  15-Inch 
Channel-Columns 


^   f  ^ 

Allowable  filler-stress  in 
13  000  for  lengths  of  60  rad 
Reduced   for  lengths  betwe 
Formula  (13), 

S  =  19  000 
Weights  do  not  include  rivet 
For  values  for  l/r  above  120 

e  inch: 
idii,  by 

ails 
490 

>- 

< 

F 

..L 

ii  or  under 

en   60   and    120  k 

—  100  l/r 

-heads  or  other  det 
see  notes  on  page 

> 

'. 

' .       .            ' 

^       I2     ^ 

Effective 
length, 

Two  15-in  channels 

Two  15-in,  45-lb  channels 

35  lb 

45  lb 

i  1= 

Ceo  SJ%. 

1    s. 

03  M  fe  ^ 

m 

n5   f^    fe   M 

II 
12 
13 
14 
15 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

26 

27 
28 
29 

I  340 
I  340 
I  340 
I  340 

I  340 

1340 
1340 
1340 
1340 
1340 

I  340 
I  340 
1340 
1340 
1340 

I  340 

I   408 
1408 
I   408 
I   408 
1408 

1408 
I   408 
I   408 
I   408 
1408 

I   408 
I   408 
1408 
I  408 
1408 

I   408 

I  485 
1485 
1485 
1485 
1485 

1485 
1485 
1 485 
1 485 
1485 

1485 
1485 
1485 
1485 
1485 

1485 

1547 

I  547 
I  547 
I  547 
I  547 

1547 
I  547 
1547 
I  547 
1547 

1547 
I  547 

I  547 
I  547 
I  547 

I  547 
1547 
1547 
1547 

I  612 
I  612 
I  612 
I  6X2 

1 612 

I  612 
I  612 
I  612 
I  612 

I  612 

1 612 

I  612 
I  612 
I  612 
I  612 

I  612 
I  612 
I  612 
I  612 

I  677 
1677 
1677 
I  677 
1677 

1677 
1677 
1677 
I  677 
1677 

1677 
I  677 
1677 
1677 
1677 

1677 
1677 
I  677 
1677 

I  742 
I  742 
I  742 
1  742 
1742 

1.742 
1742 
1742 
1742 
1742 

I  742 
I  742 
I  742 
I  742 
I  742 

1742 
1742 
1742 
I  742 

I  331 

1307 
I  284 

.        1394 
1369 
1344 

1 465 

I  439 
I  413 

30 

31 
32 
33 
34 
35 

I  261 

I  238 
I  214 
I   191 
I   168 
I   145 

I  320 

I   295 
I   270 
1246 

I  221 
I  197 

1387 

I  361 
1335 
I  309 
I  283 
I  257 

1543 

I  519 

1495 
I  471 
I  447 
1424 

I  607 

1582 
1557 
1532 

I  507 
I  482 

I  670 

1644 
I  618 

I  592 
1566 
I  540 

1735 

1708 
I  681 
1654 
I  627 
I  600 

Area,  sq  in 

103.08 

108.33 

114.23 

118.98 

123.98 

128.98 

133.98 

/i-i.in* 

Ti  1,  in 

6037 
7.65 

2919 
5.32 

6  123 
7.52 

3  021 

5.28 

6233 
7.39 

3148 
5.25 

6397 
7.33 

4  240 
5.97 

404.5 

6843 

7.43 
4407 
5.96 

7300 
7.52 

4  573 
5-95 

7769 
7.61 

4  740 
5.9s 

/2-2,  in* 

;'2  2t  in 

Weight, 
lb  per  lin  ft.. 

350. 5 

368.4 

388.4 

421. 5 

438.5 

4SS.5 

Safe  load-values  above  the  heavy  line  are  for  rati 
below  the  heavy  line  are  for  ratios  not  over  120  l/r 

Ds  of  l/r  not  over  6 

0;  those 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


554 


Strength  of  Columns,  Posts  and  Struts  Chap.  14 


Table  XXVU*  (Concluded).     Safe  Loads  in  Units  of  i  ooo  Pounds  for  is-Inch 
Channel-Columns 


1           |3 

are  inch: 
radii,   by 

letails 
e  490 

Allowable  nber-stress  m  pounds  per  squ 
13  000  for  lengths  of  60  radii  or  under 
Reduced   for  lengths  between    60   and    120 
Formula  (13). 

S  =  19  000  -  iQo//r 
Weights  do  not  include  rivet-heads  or  other  c 
For  values  for  l/r  above  120,  see  notes  on  pag 

>- 
> 

j 

F 
k. 

< 

'       r      I2     ^ 

Two  15-in,  45-lb  channels 

Effective 
length, 

Is. 

txfy 

mi 

nS    P    ^    M 

1      S 

II 

v.-    14 
i         15 

s^r,..i6i     ., 

'.:      20 
'^'.\   ^I 

>24 

25 

26 

27 
28 
29 

I  807 

r      I  807 

r,     I  807 
I  807 
I  807 

1807 
p     I  807 
l\     I  807 
:■■      I  807 

1807 

1807 

0      I  807 

\i  ,  I  807 

I  807 

I  807 

I  807 
I  807 
I  807 
I  807 

1872 
I    872 
1872 
I    872 
1872 

1872 
I   872 
1872 
I   872 
1872 

1872 
1872 
1872 
I   872 
1872 

I   872 
I   872 
I   872 
I   872 

1937 

I  937 
I  937 
I  937 
I  937 

1937 
I  937 
I  937 
I  937 
I  937 

I  937 
I  937 
I  937 
I  937 
1937 

1937 
1937 
I  937 
I  937 

2002 
2  002 
2  002 
2  002 
2  002 

2002 
2  002 
2002 
2  002 
2  002 

2002 
'2  002 
2  002 
2  002 
2  002 

2002 
2  002 
2  002 
2  002 

2067 
2  067 
2067 
2067 
2  067 

2  067 
2  067 
2  067 
2067 
2  067 

2  067 
2067 
2  067 
2067 
2  067 

2  067 
2067 
2  067 
2067 

2  132 
2  132 
2  132 
2132 
2132 

2  132 
2132 
2  132 
2132 
2  132 

2  132 
2  132 
2  132 
2132 
2  132 

2  132 
2  132 
2  132 
2132 

30 

.    31 
32 
33 
34 
35 

1798 

I  770 
I  742 
I  714 
.     1686 
I  658 

1863 

1834 
1805 
I    776 

I  747 
I  718 

I  926 

1896 
1866 
1836 
1806 
1775 

1 991 

1 960 
1929 
1897 
1866 
1 835 

2054 

2  022 
1989 
1957 
1925 
1893 

2  118 

2085 
2  052 
2  019 
1985 
1952 

Area,  sq  in 

138.98 

143.98 

148.98 

153.98 

158.98 

163.98 

10846 

8.13 

5740 
5.92 

A-i,  in* 

ri_i,  in 

J^2-2,  in* 

^2-2.  in 

8251 

7.70 
4907 
5.94 

8744 
7.79 

5073 
5.94 

9251 
7.88 

5  240 
5.93 

506.5 

9770 
7.97 
5  407 
5.93 

10  301 
8.05 
5  573 
5.92 

Weight, 
lb  per  lin  ft.. 

472.5 

489. 5 

523.5 

540.5 

557.5 

Safe  load- values  abo\ 
below  the  heavy  line  ar 

-^e  the  heavy  line  are  for  ratios  of  l/r  not  ovei 
e  for  ratios  not  over  120  l/r 

"  60:  those 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


General  Principles  of  the  Flexure  of  Beams  555 


CHAPTER  XV  .,,  ,;,  ji,. 

STRENGTH    OF    BEAMS  AND   BEAM    GIRDERS.    FRAM- 
ING AND   CONNECTING   STEEL  BEAMS 

By 
CHARLES  P.   WARREN 

LATE   ASSISTANT   PROFESSOR   OF   ARCHITECTURE,    COLUMBIA   UNIVERSITY 

1.    General  Principles  of  the  Flexure  of  Beams 

Definitions.  A  structural  member  placed  in  a  generally  horizontal  position 
upon  two  or  more  supports  or  projecting  from  some  other  construction  is  called 
a  BEAM.  A  GIRDER  is  a  beam  carrying  smaller  or  secondary  beams.  A  canti- 
lever BEAM  is  a  beam  supported  at  the  middle,  or  having  one  end  fixed,  as  in  a 
wall,  and  the  other  end  free;  or  it  is  the  part  of  a  beam  which  overhangs,  or 
projects,  beyond  a  support.  A  simple  beam  is  one  which  rests  upon  two  sup- 
ports, one  at  each  end.  A  continuous  beam  rests  upon  more  than  two  supports. 
The  distance  between  the  supports  of  a  simple  beam,  or,  when  so  specially  desig- 
nated from  center  to  center  of  the  bearings,  is  the  span.  It  is  usually  designated 
by  l.  The  loads  on  beams  are  either  uniformly  distributed  or  concen- 
trated. A  uniformly  distributed  or  uniform  load  includes  the  weight  of  the 
beam  itself  and  any  load  spread  evenly  over  it,  such  as  the  weight  of  a  wall. 
Uniform  loads  are  estimated  by  their  intensity  per  unit  of  length  of  the  beam, 
in  pounds  per  linear  foot.  A  uniform  load  per  linear  foot  is  represented  by  w, 
and  the  total  uniform  load  by  wl  or  W.  A  concentrated  load  is  a  single  applied 
weight,  such  as  a  column  and  its  load,  or  the  load  from  another  hJeam,  and  iS 
designated  hy  P. 

Stresses  and  Deformations.  A  load  on  a  simple  beam  causes  the  fibers  to 
bend  or  deflect,  and  eventually  to  break  across,  or  in  other  words,  a  load  induces 
transverse  or  flexural  stresses  in  the  fibers.  Since  it  is  impossible  to  bend 
or  deflect  a  simple  beam  without  causing  a  shortening  of  the  fibers  on  the  upper 
or  concave  side  and  an  elongation  of  the  fibers  on  the  lower  or  convex  side,  a 
load  on  a  beam  causes  compression  in  the  upper  fibers  and  tension  in  the 
lower  fibers,  while  between  the  two  there  is  a  neutral  layer  or  surface  of  fibers 
which  is  unchanged  in  length  and  which  is  called  the  neutral  surface  of  the 
beam.  In  a  cantilever  beam  the  reverse  is  the  case,  the  upper  fibers  being 
in  tension  and  the  lower  ones  in  compression. 

Laws  Determined  by  Experiment.  From  experiments  it  has  been  found 
that  the  amount  of  elongation  or  shortening  of  any  fiber  is  directly  propor- 
tional to  its  distance  from  the  neutral  surface  of  a  beam;  hence,  if  the  elastic 
limit  is  not  exceeded,  the  stresses,  also,  are  proportional  to  their  distances  from 
this  neutral  surface.  The  trace  of  the  neutral  surface  on  a  cross-section  of  a 
beam  is  called  the  neutral  axis  of  the  cross-section.  Within  the  elastic 
limit  of  a  material  the  neutral  surface  passes  through  the  centers  of  gravity 
of  the  cross-sections  of  a  beam  for  all  materials. 

Bending  Moments  and  Resisting  Moments.*  To  determine  the  strength 
of  any  beam  to  resist  the  effects  of  any  load  or  series  of  loads,  two  things  must 

*  See,  also,  Chapter  IX,  pages  324  and  325.  .jjiO  oi  ^td 


556  Strength  of  Beams  and  Beam  Girders  Chap.  15 

be  determined:  first,  the  moment  or  moments  of  the  external  destructive  force 
or  forces  tending  to  bend  and  break  the  beam,  which  is  called  the  maximum 
BENDING  moment;  and,  secondly,  the  moments  of  the  combined  resistances  of 
all  the  libers  in  the  dangerous  section  of  the  beam  to  being  broken,  which, 
in  their  summation,  are  called  the  moment  of  resistance  or  the  resisting 
moment.  ' 

The  Methods  of  Finding  the  Bending  Moments  for  any  load  or  series 
of  loads  are  explained  in  Chapter  IX.  The  moment  of  resistance  is  equal  to 
the  SECTION-MODULUS  or  section-factor,  denoted  by  Ijc,  multiplied  by  the 
unit  stress  on  the  outermost  fiber  of  the  material,  denoted  by  5",  and  it  equals 
the  bending  moment. 
Hence  M  =  Sljc  (i) 

This  is  known  as  the  flexure-formula  and  it  is  the  fundamental  formula  for 
designing  beams.  Formulas  for  finding  the  section-moduli  of  common  shapes 
are  given  in  Chapter  X,  and  the  values  of  Ijc  or  the  section-moduli  of  the 
standard  rolled  shapes,  are  given  in  the  tables  in  the  same  chapter. 

The  Coefficient  of  Strength,*  sometimes  given  in  tables  of  steel  beams,  is 
the  maximum  distributed  load  that  a  beam  of  one  foot  span  would  support 
without  producing  a  fiber-stress  exceeding  the  safe  limit,  generally  i6  ooo  lb 
per  sq  in.  As  the  strength  of  a  beam  varies  inversely  as  its  span,  the  safe  load 
for  any  span  may  be  obtained  by  dividing  this  coefiicient  by  the  span  in  feet. 
I  ,  Factors  of  Safety.  In  order  that  a  beam  shall  just  be  able  to  carry  a  load 
and  not  break,  that  condition  of  equilibrium  must  exist,  in  which  the  maxi- 
mum bending  moment  in  the  beam  is  equal  to  the  section-modulus  multiplied 
by  the  ultimate  strength  of  the  material.  In  order  that  a  beam  may  be 
abundantly  safe  to  carry  a  given  load,  the  product  of  the  section-modulus  by 
the  ultimate  strength  of  the  material  must  be  several  times  greater  than  the 
maximum  bending  moment;  and  the  ratio  which  this  product  bears  to  the 
maximum  bending  moment,  or  which  the  breaking-load  bears  to  the  safe 
LOAD,  is  known  as  the  factor  of  safety,  that  is, 

ultimate  strength 

Factor  of  safety  =  • — 

working  stress 

Ultimate  Strengths  and  Safe  Fiber-Stresses.  By  the  strength  of  the 
MATERIAL  is  meant  a  certain  constant  quantity  which  is  determined  by  experi- 
ment, and  which  is  known  as  the  ultimate  breaking  strength.  This 
value  is  of  course  different  for  each  material.  Table  I  gives  the  values  of  this 
constant  divided  by  the  factor  of  safety,  or  in  other  words,  the  working  stress, 
for  most  of  the  materials  used  in  building-construction.  The  section-moduli 
multiplied  by  these  values  will  give  the  safe  resisting  moments  for  the  beams. 
The  values  of  S  in  Table  I  for  steel  are  about  one-fourth  those  of  the  breaking- 
loads;  for  cast  iron,  about  one-sixth;  for  average  specimens  of  wood,  one-sixth; 
and  for  stone  and  concrete,  one-tenth.  The  safe  compressive  strength  of  cast 
iron  for  the  compression-side  of  beams  is  i6  ooo  lb  per  sq  in,  in  the  New  York 
Building  Code.  This  is  considered  too  high  by  some  engineers  and  the  author 
recommends  lo  ooo  lb  per  sq  in.  This  value  has  been  used  in  calculating  the 
safe  loads  for  cast-iron  columns.  (See  Chapter  XIV,  page  461.)  The  safe 
loads  for  the  steel  shapes  given  in  the  tables  in  this  chapter  are  all  computed 

♦  The  values  for  coeflficients  of  strength  have  been  omitted  from  most  of  the  tables, 
following  the  policy  of  some  of  the  latest  handbooks,  as  the  safe  loads  for  beams,  for 
example,  can  be  as  readily  determined  from  the  data  of  the  tables  directly,  as  by  the 
process  of  dividing  such  coefficients  by  the  spans.  See,  however,  pages  586  to  591  and 
623  to  628. 


General  Principles  of  the  Flexure  of  Beams 


657 


)n  the  value  of  i6  ooo  lb  per  sq  in  for  S,  but  these  full  loads  should  be  used 
vith  caution,  and  reduced  when  necessary  to  satisfy  any  unusual  conditions. 
For  riveted  steel  girders  14  000  lb  per  sq  in  was  the  value  formerly  given  to  5, 
mi  the  usual  value  now  is  16  000  lb  per  sq  in. 

Table  I.     Safe  Unit  Fiber-Stresses,  S,  for  Flexure  of  Beams  * 

ft  is  to  be  noted  that  these  are  average  values,  especially  those  for  wood.     For  allowable 

higher  stresses  for  timber,  see  also,  notes  on  pages  628,  637  and  647- 


Materials 
Wood  unseasoned  f 


Cast  iron,  tension-side. . 
Cast  iron,  compression-side 
Wrought       iron       (rolled 

beams) 

Steel  (rolled  beams) 

Steel  (riveted  girders)  both 

flanges    

Steel     (pins,    rivets    and 

bolts) 

Cedar 

Chestnut 

Cypress 

Douglas  fir 

Elm 

Hemlock 

Locust 

Long-leaf  yellow  pine 

Norway  pine 


Values  of 

S, 
lb  per  sq  in 


3000 
16  000 

12  000 
16  000 

16  000 

24  000 

700 

800 

800 

I  000 

900 

600 

I  200 

I  200 

800 


Materials 
Wood  unseasoned  f 


Values  of 
lb  per  sq  in 


Redwood,  California 

Short-leaf  yellow  pine 

Spruce 

White  oak 

White  pine 

Bluestone  flagging  (North 

River) 

Brick  (common) 

Brickwork  (in  cement)... 

Granite  (average) 

Limestone  (average) 

Marble  (average) 

Sandstone  (average) 

Slate  (average) 

Concrete  (Portland)  1:2:4 
Concrete  (Portland)  1:2:5 
Concrete  (natural)  1:2:4- 
Concrete  (natural)  1:2:5. 


750 
I  000 

700 
I  200 

700 

305 
50 
30 
180 
145 
125 
no 
400 
30 


*  For  a  comparison  of  values  given  in  different  building  laws  see  Table  XVII,  page  648, 
Chanter  XVI.  Compare,  also,  with  Table  XVI,  page  647,  Chapter  XVI.  For  ultimate 
stresses  for  woods,  see  Tables  XVIII  and  XIX,  pages  650  and  651,  Chapter  XVI.  For 
safe  loads  for  unit  beams,  see  Tables  II  and  III,  page  628,  Chapter  XVI. 

t  Add  from  30  to  40%  for  seasoned,  protected  timber,  used  without  impact. 

Beams  Unsymmetrically  Loaded  or  of  Irregular  Cross-Section.  There 
are  certain  loadings  and  cross-sections  of  beams  that  occur  most  frequently  in 
building-construction,  and  for  which  tables  have  been  worked  out  that  give  the 
safe  loads  directly;  but  for  a  beam  unsymmetrically  loaded,  or  for  a  beam  of 
irregular  cross-section,  it  is  impossible  to  compute  tables  for  strength,  as  in  each 
case  the  values  must  be  computed  by  determining  either  the  section-modulus, 
I/c  required  to  resist  the  maximum  bending  moment,  or  the  maximum  bend- 
ing'moment  that  may  be  allowed  for  a  given  value  of  the  section-modulus. 

General  Formulas  for  the  Flexure  of  Beams.*  The  general  formula  for 
any  beam  in  a  state  of  flexure  under  any  system  of  loading  is 

Maximum  bending  moment  in  inch-pounds  =  section-modulus  X  S 
or 

Also  .    .    It 

maximum  bending  moment  m  in-lb 
Section-modulus  = ^ 

I/c    =  Mm^/S 


or 


(2) 
(2)' 

(3) 
(3)' 


•  See,  also,  Chapters  IX.  X  and  XVI. 


558 


Strength  of  Beams  and  Beam  Girders  Chap.  15 


If  the  bending  moment  is  computed  in  foot-pounds,  these  formulas  become 

section-modulus  X  S 


or 
and 


Maximum  bending  moment  = 


Section-modulus 


Mmax=  SI / 12  C 

1 2  X  maximum  bending  moment 


(4) 
(4)' 
(5) 


l/c=  12  i/max/5 


(5)' 


By  substituting  for  the  bending  moments  their  values  in  terms  of  the  loads 
and  the  spans,  the  following  formulas  which  apply  to  beams  of  any  cross-section 
are  readily  deduced. 

2.   Formulas  for  Safe  Loads  for  Beams  for  Dififerent  Conditions 
of  Loading  and  Support 

I/c  =•  the  section-modulus; 
S  =  the  safe  unit  fiber-stress  in  pounds  per  square  inch; 
W  =  the  total  uniform  load  in  pounds; 
P  =  the  concentrated  load  in  pounds; 
/  =  the  span  in  feet. 

Values  of  l/c  for  the  various  shapes  and  sizes  of  structural-steel  shapes  are 
given  in  the  tables  of  Chapter  X. 

Case  I 
Beam  Fixed  at  One  End  and  Loaded  with  a  Concentrated  Load  P,  Near  the  Free 
End  (Fig.  1). 

From  Formula  (4)', 

MraAX  =  SI/ 12  C 

From  Case  I,  Chapter  IX, 

^/max  =  PI 

Hence 

PI  =  SI/12 c 

and  the  safe  load  in  pounds  is 

P  =  SI/12  cl 
Load    and  the  section-modulus  is 

I/c  =  12  Pl/S 

Example  i.  A  steel  T  bar  is  fixed  at  one  end  in  a  brick  wall,  and  loaded  at 
the  other  end  with  600  lb,  the  distance  /  being  4  ft.  What  is  the  size  of  the  bar 
required  to  support  the  load  with  safety?  (In  all  examples  the  weights  of  the 
beams  are  neglected,  unless  particularly  mentioned.) 

Solution.  Allowing  16  000  lb  per  sq  in  for  the  value  of  S,  Formula  (6)'  gives 
l/c  =  (12  X  600  X  4)/i6  000  =  1.8 

The  next  step  is  to  ascertain  what  T  bar  has  a  section-modulus  equal  to  1.8. 
In  Table  XIV,  page  369,  the  nearest  section-modulus  to  this  is  i  .9,  correspond- 
ing to  a  3  by  4  by  H-in  T  bar. 

^For  an  I  beam,  by  Table  IV,  page  355,  l/c  =  1.8,  the  same  as  for  the  T  bar, 
and  calls  for  a  3-in  6.5-lb  I  beam. 


Fig.  1. 


Cantilever  Beam, 
near  Free  End 


(6) 


(6)' 


Formulas  for  Safe  Loads  for  Beams,  etc. 
Case  II 


650 


Beam  Fixed  at  One  End  and  Loaded  with  a  Uniformly  Distributed  Load  W 
(Fig.  2). 

From  Formula  (4)' 

Mmi.x==  SI/12C 
From  Case  II,  Chapter  IX, 

Mu,ax=lf//2 

Hence 

Wl/ 2==  SI /12  c 
and  the  safe  load  in  pounds  is 

W=^Sl/^cl  (7) 

and 

l/c  =  6  Wl/S  (7)'    Fig.    2.     Cantilever    Beam.     Dis- 

tributed Load  over  Entire  Span 
Example  2.     What   is   the    size  of  a  can- 
tilever steel  I  beam  required  to  carry  a  uniformly  distributed  load  of  150  lb  per 
ft  over  a  length  of  6  ft? 

Solution.     W  =  150  X  6=  900  lb.     Substituting  in  formula  (7)', 

^  .       6  X  900  X  6 

I  c  =  — =  2.02s 

16  000 

In  Table  IV,  page  355,  the  nearest  section-modulus  to  this  is  1.9,  which  is 
that  of  a  3-in  7.5-lb  beam,  the  heaviest  of  that  depth.  However,  as  the 
lightest  4-in  beam,  also,  weighs  7.5  lb  per  ft  it  probably  would  be  selected  be- 
cause of  its  greater  stillness,  although  its  section-modulus  is  3,  still  greater 
than  required. 

Case  III 

Beam  Supported  at  Both  Ends  and  Loaded  with  a  Concentrated  Load  at  the 
Middle  (Fig.  3). 

From  Formula  (4)' 

Afm»x=  SI /12  c 

From  Case  IV,  Chapter  IX, 

l/max  =  PI/ 4 

Hence 

P//4  =  57/12  c 

and  the  safe  load  in  pounds  is 
P  =  Sl/3cl        (8) 
and 

l/c  =  3Pl/S        (8)' 


P 


Fig.  3.     Simple  Beam.    Load  at  Middle  of  Span 


Example  3.    What  steel  I  beam  will  safely  support  a  concentrated  load  of 
7  tons  applied  at  the  middle  of  a  15-ft  span? 

Solution.     P=  7  tons=  14000  lb.     Substituting  in  formula  (8)', 
3X  14000X  15 


/A  = 


16000 


39-3 


Referring  again  to  Table  IV,  page  355,  it  is  seen  that  a  12-in  35-lb  beam  has 


560 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


a  section-modulus  of  38,  while  a  12-in  40-lb  beam,  the  next  larger  size,  has  a 
section-modulus  of  44.8.  The  35-lb  beam,  however,  would  undoubtedly  be 
safe. 

Case  IV 

Beam  Supported  at  Both  Ends  and  Loaded  with  a  Uniformly  Distributed  Load 
(Fig.  4). 


Mm&x=  SI /12  c 
i/max  =  Wl/S 
Wl/S  =  Sl/l2C 

W  =  2  SI/ 3  cl 


(9) 


Fig.  4.     Simple  Beam.     Distributed  Load  over  Entire  Span 
From  Formula  (4)' 

From  Case  V,  Chapter  IX, 

Hence 

and  the  safe  load  in  pounds  is 

ancf 

l/c  =  3Wl/2S  (9)' 

example  4.     What  steel  I  beam  will  safely  carry  a  uniformly  distributed  load 
of  I  000  lb  per  ft  over  a  span  of  25  ft? 

Solution.     W  =  wl==  I  000  X  25  =  25  000  lb.     Substituting  in  Formula  (9)', 

.       3X25000X25 
^A  = Tr~r- =  58.6 

2  X  16000 

From  Table  IV,  page  354,  the  nearest  section-modulus  is  58.9,  which  is  that  of 
a  15-in  42-lb  beam. 

Case  V 

Beam  Supported  at  Both  Ends  and  Loaded  with  a  Distributed  Load  Over  a  Part 
of  the  Span  (Fig.  5). 


Fig.  6.     Simple  Beam.     Distributed  Load  over  Part  of  Span 

In  this  case  the  load  is  generally  given,  and  the  problem  is  to  determine  the 
Bize  of  the  required  beam.    This  can  be  done  accurately  only  by  computing 


Formulas  for  Safe  Loads  for  Beams,  etc. 


561 


the  maximum  bending  moment  as  explained  for  Case  VIII,  Chapter  IX,  and 
substituting  the  value  thus  found  in  Formulas  (3)'  or  (5)'. 

Example  5.  What  steel  I  beam  will  safely  carry  a  uniformly  distributed  load 
of  I  200  lb  per  ft, over  part  of  the  span,  beginning  at  a  point  5  ft  from  the  left 
reaction  and  extending  over  a  distance  of  G  ft,  the  span  of  the  beam  being  18  ft? 

Solution.  The  first  step  is  to  find  the  point  of  maximum  bending  moment, 
which  is  the  point  ol  no  shear.  Obviously  the  maximum  shear  is  just  at  the 
right  of  the  reaction  nearest  the  load,  which  in  this  case  is  the  left  reaction. 
To  find  the  left  reaction  (see  Chapter  IX,  page  324)  the  center  of  moments 
is  taken  at  the  right  reaction  and  the  equation  of  moments  is  RiXiS  it  — 
(i  200  lb  X  6  ft)  X  10  ft  =  o.  18  i?i  =  72  000  and  Ki  =  4  000  lb.  The  shear  just 
at  the  right  of  Ri  is  therefore  +4  000  lb  which,  if  the  weight  of  the  beam  itself 
is  not  considered,  remains  unchanged  for  every  section  of  the  beam  between  the 
left  reaction  and  the  uniformly  distributed  load  of  i  200  lb  per  ft.  From  there 
on  in  passing  to  the  right,  the  shear  is  diminished  at  the  rate  of  i  200  lb  per  ft; 
and  it  becomes  zero,  therefore,  at  a  point  4000  Ib/i  200  lb  per  f t  =  ss  ft  to 
the  right  of  the  5-ft  point.  Hence  the  point  of  no  shear  and  consequently  the 
point  of  maximum  bending  moment  is  at  5  ft  +  3-3  ft,  or  8.3  ft,  from  the  left  end. 
The  equation  for  the  maximum  bending  moment  at  this  point  is,  therefore, 

Mraax  =  4  000  lb  X  8.3  ft  -  (i  200  lb  X3-3  ft)  X  3.3/2  ft 

=  33  200  ft-lb  —  6  534  ft-lb  =  26  666  ft-lb,  or  319  992  in-lb 

From  Formula  (3),  I/c  =  319  992  in-lb/i6  000  lb  per  sq  in  =  20.  From  Table 
IV,  page  355,  the  nearest  section-modulus  corresponding  to  this  is  20.4,  that 
of  a  9-in  25-lb  beam.  A  lo-in  25-lb  beam,  however,  being  stronger  and  stiller, 
would  probably  be  used.  The  lo-in  2 2. 2 5 -lb  beam  is  what  is  termed  a  sup- 
plementary BEAM.     (See  Case  VIII,  Chapter  IX,  and  pages  352  and  353.) 


Case  VI 

Beam  Supported  at  Both  Ends  and  Loaded  with  a  Concentrated  Load,  not  at 
the  Middle  (Fig.  6). 

iniiflrh'iV  rti -s  ' 


Fig.  6.     Simple  Beam.     Concentrated  Load  at  any  Point 
From  Formula  (4)', 


From  Case  VI,  Chapter  IX, 

Hence 

and  the  safe  load  in  pounds  is 

and 

m,  n  and  /  being  in  feet. 


Mm^x=  SI /12  c 

iWinax  =  Pmn/l 
Pmn/l  =  SI/12  c 

P  =  SIl/ 12  cmn 
I/c  =  12  Pmn/lS 


(10) 
(10)' 


562 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


Example  6.  A  steel  I  beam  20  ft  in  span  is  to  support  a  concentrated  load  of 
24  000  lb  at  a  distance  of  6  ft  from  the  left  support.  What  must  be  the  size 
and  weight  of  the  beam? 

Solution.  In  this  case  P  =  24  000  lb,  /  =  20  ft,  w  =  6  ft,  n  =  14  ft  and  S  = 
16  000  lb  per  sq  in. 

Then  Formula  (10)'  gives 

12  X  24  000  X  6X  14 


I/c 


20  X  16  000 


=  75-6 


Table  IV,  page  354,  the  nearest  value  for  the  section-modulus  l/c  for  axis 
i-i  is  above  75.6,  or  81.2  for  a  15-in  60-lb  beam.  An  i8-in  55-lb  beam  having 
a  section-modulus  of  88.4  would  be  used,  unless  conditions  fix  the  head  room, 
as  it  weighs  5  lb  per  ft  less,  and  being  deeper  is  consequently  stiffer. 


Case  VII 

Beam  Supported  at  Both  Ends  and  Loaded  Symmetrically  with  Two  Equal 
Concentrated  Loads  (Fig.  7). 


Fig.  7.     Simple  Beam.     Equal  Concentrated  Loads  Symmetrically  Placed 

From  Formula  (4)'  and  Case  VII,  Chapter  IX,  each  of  the  safe  loads  in  pounds 
is  P  =  SI/ 12,  cm  {iV) 

and 


I/c=  12  Pm/S  (11) 

Example  7.  A  12-in  steel  channel,  12  ft  in  span,  supports  half  the  loads  of 
two  ro-in  beams  4  ft  from  each  end.  Each  beam  is  designed  to  carry  16  000  lb. 
What  is  the  size  and  the  weight  of  the  channel  required? 

Solution.    The  channel  supports  only  one-half  the  load  on  each  beam;  hence, 
jP  =  8  000  \h;m  =  4  ft,  5  =  16  000  lb  per  sq  in,  and  by  Formula  (11)', 
12  X  8000X4 


I/c 


16  000 


■  24, 


which   is   the   section-modulus  of   a    12-in   25-lb  channel.     (See  Table  VIII, 
page  359-) 

Weights  of  Beams  in  Flexure-Formulas.  It  will  be  noticed  that  in  for- 
mulas (11)  and  (11)'  the  span  of  the  beam  is  not  taken  into  account,  and  if  the 
beam  itself  had  no  weight  there  would  be  no  difference  in  the  fiber-stresses 
no  matter  how  far  apart  the  loads  P  were  placed.  In  reality,  however,  steel 
beams  have  considerable  weight,  and  to  be  absolutely  correct  an  example  such 
as  the  one  above  should  include  the  weight  of  the  beam,  which  would,  of  course, 
be  a  uniformly  distributed  load.  The  maximum  bending  moment  of  the  beam 
can  be  found  graphically  as  explained  on  page  329,  and  the  value  of  I/c  com- 
puted by  Formulas  (3)'  or  (5)'.  Where,  however,  the  loads  are  spaced  so  as 
to  divide  the  beam  into  three  equal  parts,  as  in  the  last  example,  one-third  of 
the  weight  of  the  beam  may  be  added  to  P  with  sufficient  accuracy.    Thus,  the 


Formulas  for  Safe  Loads  for  Beams,  etc.  663 

weight  of  the  channel  in  the  above  example  between  the  supports  would  be 
25  IbX  12,  or  300  lb,  and  F  would  be  8  100  lb,  which  would  give  a  value  for 
l/c  of  24.1.  The  factor  of  safety  in  the  loads  allowed  is  generally  large  enough 
to  offset  the  slight  effect  produced  by  the  weight  of  the  beam;  but  if  the  full 
load  assumed  is  likely  to  be  imposed  on  the  beam,  then  allowance  must  be  made 
for  the  weight  of  the  beam  itself. 

Case  VIII 

Beam  Supported  at  Both  Ends  and  Loaded  Symmetrically  with  Several  Con- 
centrated Loads  (Fig.  8). 

In  this  case  it  is  necessary  to  compute  the  maximum  bending  moment  in  the 
beam  and  proportion  the  beam  by  Formulas  (3)'  or  (5)'. 

Example  8.     A  steel-beam  girder  is  to  be  designed  to  support  a  brick  wall, 
16  in  thick  and  weighing  138  000  lb,  over  an  opening  22  ft  wide.     The  girder 
must  also  support  the  ends 
of    four    lo-in    floor-beams  j<  -23  ■  ^      .-»> 

beam    carrying    16  000    lb.      — =j  TK,  Tji^  TT^^  rfg^^       p- 

What  is  the  size  and  weight  1  |j  { |  |||  1 1  j 

of  the  girder  required?  k-3J^-'-4^ — 5^--^ — 5^-4k- — b^-^-^^ 

Solution.  The  first  step  pjg  §.  Simple  Beam.  Several  Concentrated  Loads 
is  to  make  an  allowance  for  Symmetrically  Placed 

the   weight   of    the    girder. 

The  total  load  on  the  girder  (neglecting  the  weight  of  the  girder  itself)  =  138  000 
lb+4X  8000  lb  (one-half  the  load  on  each  beam)  =  170000  lb,  or  85  tons. 
As  this  is  much  more  than  the  heaviest  single  rolled  beam  will  carry,  it  will  be 
necessary  to  use  a  pair  of  beams  and  the  load  on  each  beam,  therefore,  will  be 
42.5  tons.  Considering  for  the  present  the  entire  load  as  uniformly  distributed, 
Table  IV,  page  577,  shows  that  to  support  42.5  tons,  or  85  000  lb,  over  a  span 
of  22  ft  requires  a  24-in  85-lb  beam.  The  girder  then  will  weigh  between  sup- 
ports 2X85X22=3  740  lb,  or  about  4  000  lb."  This  added  to  the  weight  of 
the  wall  makes,  for  the  total  distributed  load,  142  000  lb.  The  next  step  is  to 
determine  the  maximum  bending  moment. 

By  the  formulas  given  in  Chapter  IX  the  maximum  bending  moments  for 
the  various  loads  may  be  found  as  follows: 
For  the  wall  and  girder  (Case  V,  page  326), 

22  X  142  000  ,   „ 

ITmax  =  ■ =  390  500  ft-lb 

For  the  beam  Bi  (Case  VI,  page  327), 

8oooX3HXt81/4  .   ,, 

il/imax  = ■ =  23  545  ft-lb 

22 

For  the  beam  B2  (Case  VI,  page  327), 

8  000X81/^X13^2  ... 

M2m«  = =  41  727  ft-lb 

22 

The  beams  being  spaced  symmetrically  from  the  middle  of  the  span,  the  bend- 
ing moments  for  ^3  and  Ba  will  be  equal  to  those  of  B2  and  Bi  respectively. 
Plotting  the  bending  moments  to  a  scale,  in  the  manner  explained  for  Figs.  17 
and  18,  page  330,  the  diagram  shown  in  Fig.  9  is  obtained.  The  greatest  bend- 
ing moment  is  the  ordinate  Mx,  which  scales  486  500  ft-lb,  or  5  838  000  in-lb. 


504 


Strength  of  Beams  and  Beam  Girders 


Chap.   15 


Note.  Since  the  loads  arc  symmetrically  placed,  this  ordinate  is  over  the 
middle  point  of  the  girder,  but  it  is  drawn  to  one  side  in  the  figure  in  order  not 
to  confuse  it  with  the  ordinate  M,  the  maximum  bending  moment  for  the  uni- 
formly distributed  load.     Substituting  this  value  of  Mx  in  formula  (3)', 


l/c 


5  838000  in-lb 
16  000  lb  per  scj  in 


--3^5 


the  section-modulus  for  both  beams,  or  182.5  for  one  beam.     From  Table  IV, 
page  354,  it  is  found  that  a  24-in  90-lb  beam  has  a  section-modulus  of  186.5, 

and  two  90-lb  beams  will  just  answer. 
The  assumption  of  a  uniform  distribution 
of  such  a  loading  over  every  foot  of  a 
girder  usually  results  in  the  selection  of 
lighter  beams  than  are  indicated  by  the 
second  solution,  in  which  each  concen- 
trated load  is  considered  as  really  con- 
centrated at  a  point.  The  two  beams 
should  be  securely  bolted  together  with 
separators  near  each  connection  of  beams 
jBi,  B2,  Bs,  B\,  and  at  each  end  of  the 
girder. 

A  DOUBLE-BEAM  GIRDER,  however,  is 
not  considered  the  best  kind  of  girder  to 
use  under  this  condition  of  loading,  as  it  is 

r/ ^ Vl        ^^^  good  construction  nor  economical  of 

!li4^te^M-r — d^  I  J ■M-t::3^/A  material.  As  a  general  rule  beam  gir- 
ders should  be  used  only  when  the  loads 
can  be  applied  to  the  upper  flanges  of 
both  beams.  Transferring  a  load  directly 
to  the  web  of  one  beam,  even  though  it 
is  connected  with  the  other  beam  by 
means  of  separators,  does  not  insure  as 
equal  distribution  of  the  loading.  The  author,  therefore,  recommends  in  this 
case  a  riveted  beam  girder  or  a  riveted  plate  girder.  The  method  above 
indicated  applies  to  any  method  of  loading,  the  only  difference  in  the  cal- 
culation being  in  the  determination  of  the  maximum  bending  moments. 

Inclined  Beams.  The  strength  of  beams  inclined  to  the  horizontal  may  be 
computed,  with  sufficient  accuracy  for  most  purposes,  by  using  the  formulas 
given  for  horizontal  beams,  and  taking  the  horizontal  projeciions  of  the  beams 
as  the  spans. 

3.   Steel  Beams  and  Girders* 

Materials  Used  for  Beams.  Practically  the  only  materials  used  in  struc- 
tural work  for  beams,  at  the  present  day,  are  wood,  steel  and  reinforced  concrete. 
As  wooden  beams  are  always  rectangular  in  cross-section,  the  general  formulas 
used  in  this  chapter  can  be  much  simplified  by  substituting  for  l/c  its  value  in 
terms  of  the  breadth  and  depth  of  the  beam.  Formulas  for  wooden  beams  will 
therefore  be  found  in  Chapter  XVI.  Cast  iron,  also,  is  occasionally  used  for 
beams  or  lintels,  but  as  this  material  is  much  stronger  in  resisting  compression 
than  tension,  the  beam  must  be  of  a  special  shape  in  order  to  use  the  material 
to  advantage.     The  strength  of  cast-irou  beams  is  therefore  considered  under 

♦  For  the  deflection  of  steel  bearns,  see  Chapter  XVIII. 


Bending-moment  Diagram  for 
Beam  Shown  in  Fig.  8. 


Steel  Beams  and  Girders  565 

a  special  heading  in  Chapter  XVI.     Formulas  for  reinforced-concrete  beams  are 
given  in  Chapter  XXIV,  pages  924  to  939;  and  Chapter  XXV,  page  992. 

Forms  of  Steel  Beams.  Since  1893,  steel  beams  have  superseded  wrought- 
iron  beams,  and  the  latter  are  now  never  used.  Any  shape  of  rolled  steel  may 
be  used  as  a  beam,  but  the  I  shape  is  the  most  economical,  as  it  possesses  the 
greatest  resistance  for  a  given  weight  of  metal.  Next  to  the  I  beam,  in  economy, 
is  the  channel,  then  the  deck  beam;  angles  and  tees  are  the  least  economical 
of  all  shapes.  The  following  values  show  the  safe  loads  per  pound  of  steel,  for 
the  various  shapes,  for  a  lo-ft  span;   the  same  ratio  would  hold  for  other  spans. 


lo-in  I  beam 

lo-in  channel 

lo-in  deck-beam 

4  by  6-in  angle 

4  by  5 -in  tee 

104 

94.6 

83.0 

28.7 

21.6 

The  Deepest  Beams,  the  Strongest,  Stiffest  and  Most  Economical. 

The  STRENGTH  of  a  wooden  or  steel  beam  of  rectangular  cross-section  varies  as 
the  SQUARE  OF  THE  DEPTH,  directly  as  the  breadth  and  inversely  as  the  length, 
and  the  stiffness  varies  directly  as  the  cube  of  the  depth,  directly  as  the 
breadth  and  inversely  as  the  cube  of  its  length;  hence  the  deeper  beam  will 
have  the  greater  strength  and  stiffness  in  proportion  to  its  sectional  area.  With 
I  beams  these  relations  do  not  hold  strictly,  because  of  the  variation  in  the 
forms  of  the  cross-sections,  but  they  are  approximately  true.  It  therefore 
follows  that,  for  any  given  span,  it  is  more  economical  in  floors,  where  other 
conditions  will  permit,  to  use  deep  beams  spaced  farther  apart  or  to  use  one  deep 
beam  in  place  of  two  shallower  beams.  Thus  if  a  distributed  load  of  39  tons 
is  to  be  supported  over  a  span  of  16  ft,  one  20-in  65 -lb  beam,  two  15-in  42-lb 
beams,  or  three  12-in  40-lb  beams,  could  be  used;  but  the  20-in  beam  would 
weigh  only  i  105  lb,  allowing  for  6-in  bearings,  as  compared  with  i  428  lb  for 
the  15-in  beams  and  2  040  lb  for  the  12-in  beams,  and  the  bolts  and  separators 
would  be  saved. 

Light  and  Heavy  Steel  Beams.  Light  beams  are  more  economical  than 
heavy  beams  of  the  same  diopth,  except  when  the  span  is  so  short  that  the 
safe  load  is  governed  by  the  resistance  of  the  web  to  buckling,  in  which  case  the 
heavy  beams  are  the  more  economical. 

Maximum  Safe  Loads  for  Steel  Beams.  All  loaded  beams  are,  in  general. 
Subject  to  three  kinds  of  stresses.  The  most  destructive  are  generally  those 
due  to  the  bending  moments,  and  have  already  been  considered.  The  second 
kinds  are  those  which  tend  to  shear  a  beam,  or  to  make  one  part  slide  on 
the  other  vertically.  (See  paragraph  on  Shearing-Stresses  in  Steel  Beams  and 
Girders,  page  567.)  These  stresses,  however,  seldom  need  to  be  considered 
except  in  the  case  of  riveted  girders  and  short  beams  with  very  thick  webs. 
The  third  kind  of  stress  is  that  which  tends  to  cause  the  web  of  a  beam  to 
buckle;  and  in  a  steel  beam  over  a  span  very  short  in  proportion  to  the 
depth  of  the  beam,  the  resistance  of  the  web  to  buckling  generally  determines 
the  maximum  load  that  the  beam,  without  stiffeners  on  the  web,  will  support. 
(See,  also,  pages  182,  183  and  567.) 

Safe  Loads  for  Steel  Beams.*  To  save  time  in  calculating,  tables  of  safe 
loads  for  structural  and  supplementary  beams  and  channels  used  as  beams 
under  conditions  of  transverse  loading,  have  been  prepared,  which  give  the  uni- 
formly distributed  safe  loads  in  thousands  of  pounds  for  spans  customary 

*  Part  of  the  matter  of  the  following  paragraphs  relating  to  steel  I  beams  has  been 
adapted  by  permission,  from  the  Pocket  Companion,  Carnegie  Steel  Company,  Pitts- 
burgh, Pa. 


566  Strength  of  Beams  and  Beam  Girders  Chap.  15 

in  building-construction.     They  are  based  upon  an  extreme  fiber-stress  of 
1 6  GOO  lb  i^er  sq  in  on  the  fibers  farthest  from  the  neutral  surface  of  the  beam. 

The  Tables  of  Safe  Loads  for  Angles  and  Tees,  pages  586  to  591,  give 
the  values  at  the  same  fiber-stress  on  spans  of  one  foot,  from  which  the  safe  load 
for  any  span-length  may  be  obtained  by  direct  division,  and  also  the  values  for 
those  spans  at  which  the  allowed  safe  load  will  produce  a  deflection  of  Heo  of 
the  span-length.  The  loads  in  all  cases  include  the  weight  of  the  beam,  which 
should  be  deducted  in  order  to  arrive  at  the  net  load  which  the  beam  will  support. 
For  several  concentrated  loads  or  for  a  combination  of  distributed  and  concen- 
trated loads  it  will  be  necessary  to  use  the  methods  previously  explained  under 
Case  VIII,  page  563. 

Use  of  Tables  for  Concentrated  Loads.  To  use  any  of  the  following 
tables  for  concentrated  loads,  find  the  equivalent  distributed  load  by  multi- 
plying the  concentrated  load  by  the  factor  given  in  Table  IV,  page  632,  and 
then  use  the  beam  having  a  safe  load  equal  to  the  load  thus  found. 

In  addition  to  the  conversion-factors  in  that  table  the  following,  also,  will  be 
found  convenient: 

For  two  equal  loads  applied  at  one-third  the  span  from  each  end,  multiply  one 
load  by  2%. 

For  two  equal  loads  applied  at  one-fourth  the  span  from  each  end  multiply 
one  load  by  2. 

For  a  beam  fixed  at  one  end,  and  loaded  at  the  other,  multiply  by  8. 

Fqr  a  beam  fixed  at  one  end,  and  uniformly  loaded  over  the  entire  length, 
multiply  by  4. 

Unusual  Conditions  of  Loading  of  Beams.*  It  is  assumed  in  all  cases 
that  the  loads  are  applied  normal  to  the  axis  i-i  as  shown  in  the  tables  of  the 
properties  of  sections  in  Chapter  X,  and  that  the  beam  deflects  vertically  in  the 
plane  of  bending  only.  If  the  conditions  of  loading  involve  the  introduc- 
tion of  forces  outside  this  plane  of  loading,  the  allowable  safe  loads  must  be 
determined  from  the  general  theory  of  flexure  in  accordance  with  the  mode  of 
application  of  the  load  and  its  character.  This  applies  particularly  to  unsym- 
metrical  sections,  such  as  angles,  which  should  be  used  under  those  condi- 
tions of  loading  where  the  section  can  deflect  vertically  only,  being  rigidly  se- 
cured against  lateral  deflection  or  twisting  throughout  the  entire  span. 
In  all  such  cases  of  eccentric  loading,  the  actual  safe  loads  would  be  considerably 
lower  than  the  tabulated  safe  loads,  which  have  been  based  upon  the  most 
favorable  conditions  of  loading. 

Vertical  Deflection  of  Steel  Beams.*  In  the  case  of  beams  intended  to 
carry  plastered  ceilings,  experience  indicates  that  the  vertical  deflection, 
to  avoid  cracking  the  plaster,  should  be  limited  to  not  more  than  Heo  of  the 
span-length.  This  span-limit  for  steel  beams  is  approximately,  in  feet,  twice 
the  depth  in  inches  and  is  indicated  in  the  tables  by  the  lower,  broken,  hori- 
zontal lines.  Beams  intended  for  such  purposes  should  not  be  used  for  greater 
spans  unless  the  allowable  tabular  safe  load  exceeds  the  actual  load  to  be  sup- 
ported. As  the  dead  load  of  a  floor  is  supported  by  the  floor-beams  before  the 
plaster  is  applied,  only  the  deflection  due  to  the  live  load  really  needs  to  be 
considered.     The  vertical  deflection  of  beams  is  explained  in  Chapter  XVIII. 

Lateral  Deflection  of  Steel  Beams.*  The  tabular  safe  loads  are  based 
upon  the  assumption  that  the  compression-flanges  of  the  various  sections  are 

*  Part  of  the  matter  of  this  paragraph  has  been  adapted,  by  permission,  from  the  Pocket 
Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


J 


Steel  Beams  and  Girders  567 

secured  at  proper  intervals,  against  lateral  deflection,  by  the  use  of  tie-rods 
or  by  other  means.  The  lateral  unbraced  length  of  steel  beams  and 
girders  should  not  exceed  forty  times  the  width  of  the  compression-flanges. 
When  the  unbraced  length  exceeds  ten  times  the  width,  the  tabular  safe  loads 
should  be  reduced.  An  explanation  of  the  method  of  reducing  the  tabular  loads 
when  the  unsupported  length  exceeds  ten  times  the  flange-width  is  given  in 
Chapter  XVIII,  page  670.     (See  Bethlehem  Handbook  for  sidewise  deflection.) 

Shearing-Stresses  in  Steel  Beams  and  Girders.*  The  safe-load  tables  for 
beams  and  channels  arc  computed  solely  with  reference  to  safe  unit  stresses 
DUE  to  flexure,  and  the  safe  loads  uniformly  distril^uted  on  the  spans  given 
will  not  cause  average  shearing-stresses  in  the  web  greater  than  the  10  000 
lb  per  sq  in,  the  average  safe  working  strength  of  steel  in  shear.  When, 
however,  beams  are  loaded  with  heavy  loads  concentrated  near  the  supports, 
or  when  beams  of  short  span  are  loaded  with  uniformly  distributed  loads  to  their 
full  carrying  capacity  as  regards  flexure,  the  bending  moments  may  be  small 
in  comparison  with  the  reactions  at  the  supports,  and  the  beams  may  fail  along 
the  neutral  surface  as  a  result  of  longitudinal  shearing-stresses,  or  they  may 
BUCKLE  as  a  result  of  the  combined  longitudinal  and  vertical  web-stresses. 
On  such  spans  the  safe  shearing  or  buckling  strength  of  the  web  rather  than 
the  resistance  of  the  flanges  to  bending-stresses  may  limit  the  carrying  capacity 
of  the  beam. 

Buckling  Values  of  Beam- Webs.*  The  vertical  shearing-stresses  or 
the  vertical  compressive  components  of  the  web-strcsscs  may  under  some  con- 
ditions exceed  the  safe  resistance  of  the  beam  to  buckling,  and  there  remains 
the  possibility  that  a  web  or  web-plate,  which  is  amply  secure  against  the  safe 
allowed  shear  of  10  000  lb  per  sq  in,  will  not  be  of  sufficient  strength  when  con- 
sidered as  a  column.  In  such  cases  provision  must  be  made  for  security  against 
buckling  either  by  stiffeners  or  by  an  increased  thickness  of  the  web  or  web- 
plate.  (For  the  determining  conditions  for  web-buckling  of  steel  beams  in  gril- 
lages, based  on  direct  compression,  see  page  183.) 

Conditions  of  Web-Buckling  of  Steel  Beams.  There  are  two  conditions 
of  WEB -buckling  (scc,  also,  foot-note  for  paragraphs  relating  to  Tables  II  and 
III). 

(i)  The  part  of  the  beam  bearing  on  the  support  is  subject  to  direct  com- 
pression, and  the  web  over  this  part  must  be  capable  of  resisting  it.  If  this 
area  is  too  small  the  end  of  the  beam  will  fail,  as  a  column,  causing  the  web  to 
buckle.  It  is  therefore  necessary  to  calculate  the  required  length  of  the  bear- 
ing. 

(2)  The  beam  throughout  its  length  between  the  supports,  or  in  case  of  a 
cantilever  beam,  from  its  end  to  the  support,  is  subject  to  shear.  It  is  gen- 
erally supposed  that  the  shear  develops  stresses  of  tension  and  compression 
in  the  web;  that  these  stresses  act  at  right-angles  to  each  other  in  the  plane  of 
the  web  and  at  an  angle  of  45"  with  the  neutral  surface  of  the  beam;  and  that 
these  DIAGONAL  STRESSES  are  equal  in  magnitude  or  intensity  to  the  vertical 
shear  at  any  point.  It  is  the  compressive  stress  that  tends  to  buckle  the 
web. 

Formulas  for  Safe  Buckling  Resistance  of  Steel  Beams.*  In  regard  to 
the  first  condition  of  buckling  a  series  of  experiments  has  been  made  on  beams 
of  various  depths  and  web-thicknesses  to  arrive  at  a  basis  for  a  simpler  method 
of  computation  to  use  in  the  investigation  of  the  safe  buckling  resistance  of 

*  Part  of  the  matter  of  this  paragraph  has  been  adapted,  by  permission,  from  the 
Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


568  Strength  of  Beams  and  Beam  Girders  Chap.  15 

beams  with  unsupported  webs,  and  from  these  experiments  the  following  for- 
mulas *  have  been  deduced: 


ilUlinTli    .  Safe  end-reaction  R=   SbXi 


Safe  interior  load  F  =  2SbXt 


(-;) 
(•■n) 


In  these  formulas,  R  is  the  end-reaction,  P  the  concentrated  load,  /  the  web- 
thickness,  d  the  depth  of  the  beam,  ai  half  the  distance  over  which  the  concen- 
trated load  is  applied  and  a  the  whole  distance  over  which  the  end-reaction  is 
applied;  while  Sb  is  the  safe  resistance  of  the  web  to  buckling,  in  fxjunds 
per  square  inch,  by  the  straight-line  formula 

Sb  =  19  000  —  100  d/2  r 

d/2  =  I  in  the  column-formula  f-  The  first  formula  is  general  and  applies  to 
any  condition  of  loading.  The  second  formula  covers  the  case  of  a  single  load 
concentrated  at  the  middle  of  a  span;  it  can  be  extended  to  cover  a  system  of 
concentrated  loads  provided  the  sum  of  the  distances  ai  is  not  less  than  a. 

Tables  II  t  and  III  J  give  for  beams  and  channels  with  unsupported 
webs: 

*  These  formulas,  in  order  to  satisfy  the  first  condition,  are  used  in  the  Pocket  Com- 
panion, 1915  Edition,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 

t  This  is  the  column-formula  used  by  the  American  Bridge  Company  and  in  Carnegie's 
Pocket  Companion,  S  being  the  allowable  compressive  unit  stress  in  pounds  per 
square  inch  within  the  usual  hmits  of  l/r.     See  Formula  (13),  page  481. 

t  In  regard  to  the  shearing  of  steel  beams,  allowable  web-shears,  etc.,  the  value,  for 
example  (see  Example  15,  this  chapter,  and  on  pages  182  and  183  of  Chapter  II),  of 
42  000  lb  per  sq  in  for  a  12-iu,  3iy2-lb  I  beam,  given  in  Table  II,  page  575,  taken  from 
Carnegie's  Pocket  Companion,  is  based  on  the  allowed  direct  shear  without  including  the 
condition  of  web-crippling.  That  is,  the  42  000  lb  is  determined  by  taking  the  area  of 
the  web,  0.35  X  12=  4.2  sq  in  and  multiplying  it  by  10  000  lb  per  sq  in,  which  is  the 
value  there  used  for  the  safe  unit  shearing -stress. 

The  beam  is  therefore  calculated  as  being  good  for  42  000  lb  shear,  but  it  is  necessary 
to  make  a  further  investigation  to  ascertain  whether  the  stresses  due  to  shear  will  cause 
the  web  of  the  beam  to  buckle.  As  stated  in  the  paragraph  on  page  567,  on  the  Buckling 
Values  of  Beam- Webs  there  are  two  conditions  of  web-buckling  or  web-crippling. 

In  the  case  of  a  plate  girder  the  end-stiffeners  provide  for  the  first  condition,  and  the 
intermediate  stiffeners  for  the  second  condition.  The  web  itself  may  then  be  counted  on 
for  its  full  shearing  value.  In  the  case  of  beams,  however,  it  is  not  generally  economical 
to  use  stifiFeners,  so  that  the  web  alone  must  meet  every  condition. 

The  Carnegie  Pocket  Companion  gives  a  formula,  reproduced  in  the  preceding  para- 
graph, and  gives  the  derived  lengths  of  bearings  in  Tables  II  and  III,  to  satisfy  the  first 
condition.  Some  of  the  formulas  used  in  the  manufacturers'  handbooks,  for  maximum 
safe  shear  based  on  web-buckling  for  the  second  condition,  are  as  follows: 

Passaic  Steel  Company,        V  = 


.+  " 


3000/2 

1 2  000  di 
Cambria  Steel  Company,      V  =  .j 

I  500 /2 

Bethlehem  Steel  Company,  V=  ' 

3  000/2 


Steel  Beams  and  Girders  569 

V '  (i)  "  The  allowed  wkb  -resistance  Sb,  in  pounds  per  square  inch,  computed 
from  this  compression-formula.     (See,  also,  page  183.) 

(2)  *'  The  distance  a,  or  the  distance  over  which  the  end-reaction  must  be  dis- 
tributed when  the  shearing-stress  V  in  the  web  is  the  maximum  allowal^le 
stress  of  10  000  lb  per  sq  in. 

(3)  "  The  allowable  end-reaction  R,  when  a  is  taken  at  sli  in,  which  is  the 
usual  length  of  beam  actually  resting  on  the  4-in  angles  ordinarily  used  in  build- 
ing-construction for  beam-seats. 

(4)  *'  The  allowable  shear  V,  on  the  gross  area  of  the  cross-section  of  the  beam 
or  channel-webs,  at  10  000  lb  per  sq  in." 

In  regard  to  the  second  condition  of  web-buckling,  the  maximum  allow- 
able SHEAR  may  be  calculated  by  the  formula, 

12  000  di 


in  which  V  =  the  maximum  safe  web-shear  in  pounds;  d  =  the  depth  of  the 
beam;  /  =  the  thickness  of  the  web;  and  h  =  the  height  between  the  flange- 
fillets.     (See  Example  15,  this  chapter  and  also  example  on  pages  182  and  183.) 

"  In  addition  to  these  data  which  have  to  do  with  the  maximum  loads  on  beams 
and  channels  as  computed  from  the  web-resistance,  Tables  II  and  III  give, 
also,  the  maximum  bending  moments  in  foot-pounds,  obtained  by  the  multi- 
plication of  the  section-modulus  of  each  section  by  the  allowed  fiber-stress 
of  16  000  lb  per  sq  in  and  the  division  of  the  product  by  12  in  order  to  reduce 
to  a  foot-pound  basis.  These  maximum  bending  moments  may  be  used  on 
inspection  instead  of  the  table  of  properties  to  ascertain  the  proper  size  of  a 
section  to  be  used  in  any  particular  instance." 

in  all  of  which  V  =  the  maximum  safe  web-shear  in  pounds;  d  =  the  depth  of  the  beam; 
i  =  the  thickness  of  web:  and  A  =  the  distance  between  the  flange-fillets. 

It  is  to  be  noted  that  the  length  of  the  element  in  compression  on  the  45°  line  is  h  V2, 
and  that  the  square  of  this  length  is  2  h"^.  It  is  this  value,  2  h-,  that  is  substituted  for  /2 
in  the  column-formula  used  by  the  Cambria  Steel  Company  in  deducing  its  formula  for 
shear  based  on  web-buckling.  The  tensile  stress,  however,  tends  to  keep  the  compressive 
stress  from  buckling  the  web,  and  for  this  reason  the  Passaic  and  Bethlehem  engineers 
take  the  more  liberal  value  of  3  000  P  instead  of  i  500  P.  The  Passaic  Steel  Company, 
however,  used  the  more  conservative  unit  value  of  10  000  lb,  reduced,  instead  of  the 
12  000  lb  used  by  the  others.  The  Passaic  and  Cambria  formulas  give  about  the  same 
results,  a  12-in,  3i3'^-lb  I  beam  by  the  former  having  a  safe  shear  of  33  352  lb  and  by  the 
latter,  33  188  lb. 

The  Passaic  Steel  Company  is  no  longer  in  existence  and  their  handbook  is  out  of  print. 
The  Bethlehem  Steel  Company's  handbook  has  tables  for  Bethlehem  shapes  only.  If, 
in  any  case,  no  table  of  maximum  shears  of  beams,  based  on  web-crippling,  is  at  hand,  it 
is  suggested  that  the  values  may  be  determined  from  the  formula, 

^.        12  000  dt 


1  + 


I  SCO  P 


in  which,  as  before,  V  =  the  maximum  safe  web-shear  in  pounds;  d  =  the  depth  of  the 
beam;  /  =  the  thickness  of  the  web;  and  h  =  the  distance  between  the  flange-fillets. 
For  the  beam  mentioned  and  used  in  Example  15,  page  571,  in  this  chapter  and  in  the 
example  on  pages  182  and  183,  d  =  12  in,  /  =  0.35  in.  It  =  9.762  in,  /2  =  0.1225, 
/{2  =  95.296644  and  V  =  33  i88  lb.  This  formula  is  recommended  as  being  the  most 
conservative,  although  there  is  not  a  great  difference  in  the  results,  and  the  formula  of 
the  former  Passaic  Steel  Company  is  i^tained  elsewhere  in  Kidder's  Pocket-Book.  See, 
for  example,  page  686  and  Table  III  of  Chapter  XX.     Editor-in-chief. 


670  Strength  of  Beams  and  Beam  Girders  Chap.  15 

Table  VII  is  a  table  computed  by  Mr.  Kidder,  giving  the  strength  of 
small  rectangular  steel  channels  or  grooved  steel.  These  are  often  used  for 
supporting  metal  lath  in  suspended  ceilings,  and  the  table  will  be  found  useful 
in  determining  the  size  to  use  for  any  given  span  and  spacing. 

4.   Tables  of  Safe  Loads  for  Steel  Beams  and  Girders.     Examples 

Example  9.  Direct  Bending  from  a  Uniformly  Distributed  Load.  As  an 
illustration  of  the  use  of  these  tables  let  it  be  required  to  determine  the  proper 
size  and  weight  of  an  I  beam  to  carry  safely  a  uniformly  distributed  load  of 
34  000  lb  over  a  span  of  20  ft,  the  weight  of  the  beam  not  being  included. 

Solution.  From  Table  IV,  page  579,  a  15-in  50-lb  beam  will  carry  34400  lb. 
The  weight  of  this  beam  is  50  lb  X  20  ft  =  i  000  lb,  making  a  total  load  to  be 
supported  of  35  000  lb.  This  is  so  little  in  excess  of  the  safe  load  that  the  excess 
need  not  be  considered.  Had  the  dilTerence  been  more,  however,  the  next 
heavier  beam  should  be  used. 

Example  10.  Direct  Bending  from  a  Concentrated  Load.  To  illustrate  the 
use  of  the  tables  to  determine  the  size  and  weight  of  beams  required  to  carry 
concentrated  loads,  Examples  10  and  11  are  given.  What  I  beam,  15  ft  in  span, 
will  safely  support  8  000  lb,  concentrated  at  a  point  5  ft  from  the  left  support? 

Solution.  The  distance  5  ft  is  one-third  of  the  span,  and  the  conversion- 
factor  for  this  (Table  IV,  page  632)  is  1.78.  The  equivalent  uniformly  dis- 
tributed load,  therefore,  is  8000X  1.78=  14  240  lb,  and  from  Table  IV,  page 
581,  a  9-in  25-lb  I  beam  will  carry  14  500  lb  for  a  span  of  15  ft,  and  will  just 
answer  the  purpose. 

Example  11.  Direct  Bending  from  Two  Equal  Concentrated  Loads.  What 
I  beam,  15  ft  in  span  will  safely  support  two  equal  concentrated  loads  of  6  000 
lb  each,  appUed  5  ft  from  each  end? 

Solution.  The  distance  5  ft  is  one-third  the  span,  but  the  multiplier  in  this 
case  is  2^  (page  566)-  Hence,  the  equivalent  uniformly  distributed  load  is 
6  oooX  2%  =  16  000  lb  and  the  beam  required  (Table  IV,  page  580)  is  a  lo-in 
25-lb,  I  beam  which  will  carry  17  400  lb.  The  same  result  is  obtained  by 
using  Formula  (11)',  page  562.  This  formula  is,  I/c  =  12  P?n/S.  Substituting, 
l/c  =12X6  000  X  5/16  000  =  22.5.  The  nearest  section-modulus  to  this  is  24.4, 
that  of  a  lo-in  25-lb  I  beam. 

Example  12.  Maximum  Bending  Moment  from  a  Distributed  Load  Over  Part 
of  the  Span.  The  beam  in  Example  5,  Case  V,  page  561,  has  a  maximum  bend- 
ing moment  of  26  626  ft-lb.     What  beam  is  required? 

Solution.  The  nearest  bending  moment  to  this  in  the  first  column  of  Table 
II,  page  575,  is  27  240  ft-lb,  which  corresponds  to  a  9-in  25-lb  I  beam. 

Example  13.  Allowable  Web-Shear.*  The  maximum  shear  in  the  beam  of 
Example  12  is  just  at  the  right  of  the  left  reaction  or  bearing,  and  equals  4  000 
lb.     Is  the  beam  safe  for  shear? 

Solution.  From  Table  II,  page  575,  in  the  column  for  V,  the  allowable  web- 
shear  for  a  9-in  25-lb  beam  is  36  540  lb.  Hence,  the  beam  is  safe  if  web-buckling 
is  not  taken  into  account. 

Example  14.  Shear.*  It  is  required  to  determine  the  maximum  load  which 
a  9-in  25-lb  I  beam  can  support  without  exceeding  the  safe  web-resistancy  ' 
the  section. 

*  See  paragraphs  and  foot-note  relating  to  buckling  of  beam-webs,  pages  567  to  561 


ice^j 

I 


Tables  of  Safe  Loads  for  Steel  Beams  and  Girders.    Examples      671 

Solution.  From  Table  IV,  page  581,  the  maximum  load  for  this  beam,  given 
in  small  figures  above  the  heavy,  horizontal  lines,  is  73  100  lb. 

Example  15.  Safe  Buckling  Resistance.  See,  also,  paragraphs  and  foot-note 
relating  to  buckling  of  beam-webs  on  pages  567  to  569  and  also  example  oq 
pages  182  and  183.  According  to  Table  II,  page  575,  the  allowable  web-shear 
for  a  i2-in,  31.5-lb  I  beam  is  42  000  lb.  Will  this  shear  cause  the  web  of  the 
beam  to  buckle? 

Solution.  The  web-shear  is  determined  by  multiplying  the  area  of  the  web, 
that  is,  0.35  in  X  12  in  =  4.2  sq  in,  by  10  000  lb  per  sq  in,  the  safe  unit  shearing- 
stress.  The  maximum  shear  which  will  not  cause  the  web  to  fail  by  buckling 
may  be  found  by  the  formula  given  on  page  569  for  the  second  condition  of  web- 
buckhng. 

12  000  dt 

i  +  - 


I  500  /2 

From  the  dimensions  of  structural  beams  (see  Carnegie's  Pocket  Companion, 
I  Beams,  Profiles,  Weights,  etc.)  the  thickness  t  of  the  web  of  a  12-in,  3i-5-lb 
I  beam  is  0.35  in,  the  depth  of  the  beam  isd=  12  in  and  h,  the  distance  between 
flange-fillets,  is  9.762  in.     Substituting  these  values  in  the  formula, 

12  000  X  12X0.35 50400 50  400        ^      50  400 

9-7'32^  "  95.296644  95.296644      279.046644    . 

1500X0.352  1 500X0.1225  183.7s  183.75 

50400X183.75  9  261  OCO  00  u       ^  iu 

=  ^-^ — = — —  =  ss  188,  or  about  33  190  lb 

279.040644  .       279.046644 

As  this  is  less  than  the  allowable  web-shear  of  42  000  lb  given  in  the  tables, 
if  account  is  to  be  taken  of  the  web-buckling  from  the  second  condition  men- 
tioned in  the  preceding  pages,  a  larger  or  heavier  beam  should  be  used  or  the 
loads  reduced,  so  that  the  maximum  shear  will  not  exceed  ss  190  lb.  (For  de- 
termining conditions  for  web-buckling  of  steel  beams  in  grillages,  based  on 
direct  compression,  see  page  183.) 

Example  16.  Safe  End-Reactions  for  Web-Buckling.  In  Example  8,  page 
563,  the  two  24-in  9o-lb  I  beams  carry  170000  Ib-H  (4  000  lb,  the  weight  of  the* 
beams)  =  174000,  lb  or  87  000  lb  for  each  beam.  Assuming  that  they  rest' 
upon  4-in  brackets  riveted  to  columns  at  each  end  of  the  span,  are  the  end- 
reactions  excessive? 

Solution.  Since  the  loading  is  symmetrical,  each  reaction  for  each  beam  is 
one-half  the  total  load  on  each  beam,  or  43  500  lb.  From  the  last  column  in> 
Table  II,  page  574,  the  maximum  end-reaction  R,  for  a  24-in  90-lb  beam,  is' 
74  410  lb.  Hence,  the  beam  is  safe  as  far  as  the  compression  from  the  end- 
reactions  is  concerned. 

Strut-Beams.  It  is  not  considered  good  construction  to  subject  a  strut  to  a 
transverse  loading,  causing  a  certain  amount  of  flexure  in  it  and  thus  adding  to  the 
compressive  stress.  Conditions  often  exist,  however,  where  practical  consider- 
ations make  it  desirable  to  use  a  strut  as  a  beam,  also,  as  in  the  top  chord  or  in 
the  principals  of  a  truss.  To  determine  the  size  of  a  member  in  a  case  of  this 
kind  the  following  method  should  be  used: 

(i)  Find  the  section-modulus  l/c,  for  the  member  for  the  transverse  load  by 
Formulas  (2)'  to  (11)',  using  12  000  lb  per  sq  in  as  the  value  of  S,  and  find  the 
area  of  the  cross-section  of  a  steel  shape  corresponding  to  the  value  of  l/c  thus 
found.    See  note  at  end  of  Example  17.  f 


572  Strength  of  Beams  and  Beam  Girders  Chap.  15 

(2)  Find  the  section-area  required  to  resist  the  compressive  stress,  by  dividing 
that  stress  by  the  vakie  opposite  //r  in  column  VIII  of  Table  XI,  page  493. 

(3)  Add  together  the  two  areas  and  use  for  the  required  member  a  piece  or 
pieces  of  material  having  a  section-area  next  larger  than  the  total  area  found. 

Example  17.  Strut-Beam.  Combined  Bending  and  Compression.  The 
principal  rafter  in  a  truss,  8  ft  6  in  long  between  joints,  supports  the  end  of  a 
purlin  at  the  middle  of  the  span.  The  weight  from  the  purlin  is  2  800  lb  and  the 
compressive  stress  in  the  rafter  30  000  lb.  It  is  proposed  to  use  a  pair  of  angles 
for  the  rafter,  set  with  the  long  legs  vertical  and  K2  in  apart.  What  are  the 
dimensions  of  the  angles,  the  strut  being  braced  laterally  ? 

Solution,  (i)  By  Formula  (8)',  //c  =;  3X2  800  X  8.5/12  000=  5.95  for  the 
pair  of  angles,  or  2.98  for  each  angle.  (See  note  at  end  of  this  example.)  From 
Table  XI,  page  363,  the  nearest  vakie  to  this  with  reference  to  the  axis  i-i  is 
3.0,  the  section-modulus  for  a  5  by  3V2  by  ^i-in  angle.  The  section-area  of  one 
angle  is  4  sq  in  and  of  two  angles,  8  sq  in. 

(i)  From  Table  XVI,  page  371,  the  least  r  for  a  pair  of  5  by  3H  by  \h-m 
angles,  which  would  be  about  the  axis  i-i,  since  the  strut  is  braced  laterally, 
is  about  1.58  (between  1.55  and  1.61).  Then  the  slenderness-ratio  //r  =  8  ft 
6  in/1.58  in=  102  in/1.58  in=  64.5.  From  column  VIII,  Table  XI,  page 
493>  -S*  =  9  250  lb  per  sq  in.  Hence,  30  000  lb/9  250  lb  per  sq  in  =  3.24  sq  in, 
approximately. 

(3)  The  section-area  required,  therefore,  is  8 -j-  3.24  =  11.24  sq  in,  which,  from 
Table  XI,  page  363,  is  about  equivalent  to  that  of  two  5  by  4  by  iHe-in 
angles.  As  the  section-area  in  both  calculations  exceeds  that  actually  required, 
no  allowance  for  the  weight  of  the  angles  need  be  made. 

Note.  Because  of  the  increase  in  the  tendency  of  the  strut  to  deflect,  caused 
by  the  combined  stresses  of  flexure  and  compression,  lower  values  of  S  are  used 
than  in  the  cases  of  simple  flexure,  or  of  simple  compression. 

Tie-Beams.  Steel  beams  subject  to  combined  tensile  and  transverse  stresses 
should  be  calculated  in  a  way  similar  to  that  explained  above  for  strut-beams. 
The  section  necessary  to  resist  the  transverse  stress  should  be  found  first,  then 
the  section-area  necessary  to  resist  the  tensile  stress,  and  the  two  added  together. 
!  Example  18.  Tie-Beam.  Combined  Bending  and  Tension.  One  span  of  a 
tie-beam,  10  ft  between  joints,  supports  a  load  of  6  000  lb  at  the  middle,  and  at 
the  same  time  is  under  a  tensile  stress  of  84  000  lb.  It  is  proposed  to  use  two 
steel  channels  for  the  tie-beam.  What  size  and  weight  are  required  for  the 
channels? 

Solution.  A  load  of  6  000  lb  applied  at  the  middle  of  a  beam  has  the  same 
effect  as  a  load  of  12  000  lb  uniformly  distributed,  or  6  000  lb  for  each  channel. 
From  Table  V,  page  584,  a  7-in,  9.75-lb  channel  will  be  required,  its  section- 
area  (Table  VIII,  page  359)  being  2.85  sq  in.  The  additional  area  required  to 
resist  the  tensile  stress  is  84  000  lb/ 16  000  lb  per  sq  in  =  5.25  sq  in,  or  2.63  for 
each  channel.  The  total  area  for  each  channel,  therefore,  should  be  2.85  -f-2.63 
B=  5,48  sq  in.  A  7-in,  19.75-lb  channel  has  a  section-area  of  5.81  sq  in,  and 
an  8-in,  18.75-lb  channel  has  a  section-area  of  5.5  sq  in.  Either  one  will  be 
sufficient,  but  the  8-in  channel  will  probably  be  more  economical,  as  it  weighs 
I  lb  per  ft  less. 

Example  19.  Channel,  Set  Flatwise.  W^hat  is  the  size  of  the  channel,  set 
flatwise,  required  to  support  a  uniformly  distributed  load  of  180  lb  per  ft  over 
a  span  of  10  ft,  or  1 20  in? 

Solution.  IF  =  180  X  10  =  I  800  lb.  From  Case  V,  page  326,  A/max  =  T^//8  =• 
I  800  X  1 20/8  =  :^  000  in-lb.    From   Formula  (3)',  page    557,  I/c=  M/S=* 


Oblique  Loading  of  I  Beams  and  Channels 


573 


27  000/16  000=  1.7.  From  Table  VIII,  page  359,  the  Ijc  about  the  axis  2-3 
corresponding  to  this  is  that  of  a  12-in,  20.5-lb  channel. 

Example  20.  Rectangiilar  Steel  Bar  with  Long  Side  Vertical.  In  a  suspended, 
plastered  ceiling  it  is  proposed  to  use  2  by  ^^-in  steel  bars,  4  ft  or  48  in  long,  to 
carry  the  plaster.  What  is  the  safe  load  each  bar  will  support,  if  set  with  the 
long  side  vertical? 

Solution.  From  Table  I,  page  346,  the  /  for  a  2  by  ^^-in  bar  is  o  250.  c  = 
one-half  the  depth  =  i  in.  Ijc  =  0.250/1  =  0.250.  Also,  from  Formula  (2)', 
page  557,  M^„^=  Sl/c.  Substituting,  lfni.x  =  16  oooX  0.250  =  4  000  in-lb. 
But,  from  Case  V,  page  326,  Mn,ax  =  H^//8,  and  hence,  4  ooo=PFX48/8  =■ 
6  W,  and  fF  =  4  000/6  =  666  lb. 

Oblique  Loading  of  I  Beams  and  Channels  * 

Oblique  Loading  of  Purlins  on  Sloping  Roofs.  (See,  also  pages  593, 
1 169  and  1 170.)  In  Tables  II  to  V  it  is  assumed  that  I  beams  and  channels 
are  set  with  webs  vertical  and  carry  vertical  loads.  This  is  not  the  case  when 
used  as  purlins  on  SLoriNG  roofs.  There  are  then  fiber-stresses  due  to  the 
components  of  the  bending  moment  both  at  right-angles  and  parallel  to  the 
plane  of  the  roof.  The  resultant  fiber-stress  may  be  calculated  from  the 
equation  on  page  11 70.  This  equation  is  used  in  determining  the  values 
given  in  Table  I  A.  It  may  be  noted  that  the  second  term  causes  the  fiber- 
stress  to  increase  rapidly  with  the  slope  of  the  roof.  If  purlins  were  propor- 
tioned according  to  the  equation  given  or  from  the  Table  I  A,  they  would  often 
be  much  larger  than  those  commonly  used.  For  small  slopes  the  second  term 
of  the  equation  may  be  reduced  or  eliminated  by  the  stiffness  of  the  roof- 
covering,  and  for  other  slopes  by  connecting  the  purlins  with  sag-rods  running 
up  the  sloping  sides  of  the  roof  to  an  unyielding  connection  at  the  peak. 


Table  I  A.     Ratio  of  Max  mum  F.ber-Stress  to  Bending  Moment  for  I-Beam 

and  Channel  Purlins  Set  of  Right-Angles  to  Rafters  and  Free  to  Move 

in  Any  Direction.     Loading  Vert'cal  and  Oblique  to  Web 


Purlin 


6-in  I  beam  12 K  lb. 

7 -in  I  beam  15  lb.  .  . 

8-in  I  beam  i8  lb. . . 

g-in  I  beam  21  lb. . . 
lo-in  I  beam  25  lb. . . 
12-in  I  beam  sil^lh. 

6-in  channel  8  lb .  . 
7-in  channel  9%  lb 
8-in  channel  11 34^  lb 
gin  channel  13H  lb 

to-in  channel  15  lb.  . 

12-in  channel  20H  lb 


0.14 
o.  10 
0.07 
0.05 
o  04 
0.03 

0.23 


0.08 
0.05 


Slope  of  roof  in  inches  per  foot 


o.is 

O.II 

cog 
0.07 
o  05 


0.40 
0.30 
0.23 
0.18 
0.15 
cog 


0.56 


0.33 
o.  26 


0.42 
0.31 
0.23 
0.18 
0.15 


0.8'; 
0.66 
0.52 
0.42 
0.34 
0.23 


o  47 
o  35 
o.  27 

O.  21 
0.17 
0.13 


0.76 
0.60 


0.40 

o.  26 


0.53 
0.39 
0.30 

o.  24 
o.ig 
0.14 

1. 10 

0.85 
0.68 
0.55 
0.45 
0.30 


0.61 
0.46 
0.3s 
0.28 
0.22 
0.17 

1.30 
1. 01 

0.80 
0.6s 
0.54 
0.36 


"  From  Notes  by  Robins  Fleming. 


574  Strength  of  Beams  and  Beam  Girders  Chap.  15 

Table  n.*t      Maximum  Beiiding  Moments  and  Web-Resistance  of  I  Beams 


Mm&x 

d 

V 

t 

V 

^ftt 

a 

R 

Maximum 

Depth 

Weight 

Thickness 

Allowable 

Allowable 

Minimum 

End- 

bending 

of 

per 

of 

web- 

buckling 

end- 

reaction 

moment 
ft-lb 

beam 

linft 

web 

shear 

resistance 

bearing 

a=3Hin 

in 

lb 

in 

lb 

lb  per  sq 
in 

in 

lb 

292  130 

27 

90.0 

0.524 

141  480 

10080 

20.0 

54140 

328  390 

115.0 

0.750 

180000 

13460 

II. 8 

95880" 

320390 

IIO.O 

0.688 

165  120 

12  960 

12.5 

84690 

312390 

105 . 0 

0.625 

150000 

12350 

13.4 

73  320 

264  400 

100. 0 

0.754 

180  960 

13490 

II. 8 

96  620 

256  560 

24 

95. 0 

0.693 

166  320 

13  000 

12.5 

85610 

248  710 

90.0 

0.631 

151  440 

12  410 

13.3 

74  4IO 

240  870 

85.0 

0.570 

136  800 

II  710 

14  5 

63410 

231  920 

80.0 

0.500 

1 20  000 

10  690 

16.5 

50  780 

216670 

74.0 

0.476 

114  240 

10  260 

17.4 

46  400 

156  930 

21 

60. 5 

0.428 

89880 

10500 

14.8 

39320 

220  750 

100.0 

0.884 

176  800 

15080 

8.3 

113  320 

214  210 

950 

o.8io 

162  000 

14720 

•8.6 

loi  370 

207  680 

90.0 

0.737 

147  400 

14300 

9.0 

89590 

201  140 

85.0 

0.663 

132  600 

13780 

9-5 

77630 

195  510 

20 

80.0 

0.600 

1 20  000 

13  230 

10. 1 

67  460 

169  170 

750 

0.649 

129  800 

13  660 

.<9.« 

75380 

162  640 

70.0 

0.575 

115  000 

12  980 

10.4 

63420 

155  930 

65.0 

0.500 

100  000 

12080 

II. 6 

51320 

186  720 

90.0 

0.807 

145  260 

15  140 

7.4 

97  730 
85  260 

180  840 

05.0 

0.725 

130  500 

14  700 

7-7 

174960 

80.0 

0.644 

115  920 

14  160 

8.2 

72940 

169  080 

75  0 

0.562 

loi  160 

13450 

8.9 

60480 

136  480 

18 

70.0 

0.719 

129  420 

14670 

7.8 

84350 

130  590 

65.0 

0.637 

114  660 

14  no 

8.3 

71890 

124710 
117  860 

60.0 

0.555 
0.460 

99900 

13380 

9.0 

59  420 
44980 

550 

82  800 

12  220 

10. 2 

109  200 

48.0- 

0.380 

68400 

10800 

12.2 

32830 

122  890 

750 

0.882 

132  300 

16  050 

5-6 

•102  660 

117  980 

70.0 

0.784 

117  600 

15690 

5-8 

89  160 

113  080 

65.0 

0.686 

102  900 

•15  210 

6.1 

75650 

108  270 

60.0 

0.590 

88500 

14600 

6.5 

6244X) 

90850 

IS 

55 -o 

0.656 

98  400 

15040 

6.2 

71  530 

85940 

50.0 

0.558 

83  700 

14340 

6.7 

58020 

81  040 

450 

0.460 

69  000 

13350 

7-5 

44520 

78  530 

42.0 

0.410 

61  500 

12  670 

8.1 

37660 

72  130 

37.5 

0.332 

49800 

II  180 

9.? 

26910 

V 

is  compute 

d  at  lo  000 

lb  per  sq  i 

n  of  gross  a 

irea  of  web 

-section. 

•FromT 

ocket  Com 

panion,  Ca 

rnegie  Stee 

1  Company 

,  Pittsburg 

h,  Pa. 

t  See,  als 

0,  foot-note 

on  page  5 

68,  with  pa 

ragraphs  n 

'lating  to  tl 

lis  table  ar 

d  to  Table 

III,  and  pa 

ragraphs  0 

n  page  567 

,  relating 

to  web-buc 

kling  of  st< 

iel  beams. 

See,  also, 

page  i8.«- 

Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


575 


Table  H  ♦ 

t  (Continued).     Maximum  Bending  Moments  and  Web-Resistances 

01  1  JBeams 

Mm&x 

d 

w 

t 

V 

So^ 

a 

R 

Maximum 

Depth 

Weight 

Thickness 

Allowable 

Allowable 

Minimum 

End- 

bending 

of 

per 

of 

web- 

buckling 

end- 

reaction 

moment 

beam 

linft 

web 

shear 

resistance 

bearing 

<J'=3Hin 

ft-lb 

in 

lb 

in 

lb 

lb  per  sq 
in 

in 

lb 

71  330 

5S.O 

0.821 

98520 

16470 

4.3 

87890 

67410 

50.0 

0.699 

83880 

16  030 

4.5 

73830 

63490 

45.0 

0.576 

69  120 

15390 

4.8 

57  620 

59  770 

12 

40.0 

0.460 

55  200 

14480 

5.3 

43300 

SO  730 

35-0 

0.436 

52320 

14230 

5-4 

40330 

47960 

31.5 

0.350 

42  000 

13  060 

6.2 

29  710 

44270 

28.0 

0.284 

34080 

II  680 

7.3 

21  560 

42320 

40.0 

0.749 

74900 

16690 

3.5 

75010 

39050 

350 

0.602 

60  200 

16  120 

3.7 

58  220 

35  780 

10 

30.0 

0.455 

45500 

15  190 

4-1 

41470 

.32  560 

25.0 

0.310 

31  000 

13  410 

5.0 

24940 

30  270 

22.25 

0.252 

25  200 

12  130 

5.7 

18340 

33  120 

35.0 

0.732 

65880 

16870 

3.1 

71  010 

30180 

9 

30.0 

0.569 

51  2IO 

16  260 

3-3 

S3  200 

27  240 

25.0 

0.406 

36540 

15  160 

3.7 

35390 

25  160 

21.0 

0.290 

26  100 

13  620 

4.4 

22  710 

22810 

25-5 

0.541 

43  280 

16  440 

2.9 

48920 

21  500 

23.0 

0.449 

35920 

15910 

30 

39290 

20  190 

8 

20. 5 

0.357 

28560 

15  120 

3.3 

29690 

18  960 

18.0 

0.270 

21  600 

13  870 

3.8 

20600 

19470 

17-5 

0.220 

17  600 

12  700 

4.3 

15370 

16  070 

20.0 

0.458 

32060 

16350 

2.5 

39310 

14  930 

7 

17.5 

0.353 

24  710 

15  570 

2.7 

28850 

13  800 

150 

0.250 

17500 

14  150 

3.2 

18580 

II  640 

17.25 

0.475 

28  500 

16  810 

2.1 

39930 

10660 

9 

14.75 

0.352 

21  120 

16050 

2.2 

28  250 

9680 

12.25 

0.230 

13800 

14480 

2.6 

16650 

8080 

14-75 

0.504 

25  200 

17  280 

1.6 

41370 

7  260 

5 

12.25 

0.357 

17850 

16580 

1.8 

28  120 

6450 

9.75 

0.210 

10  500 

14870 

2.1 

14  830 

4760 

10.5 

0,410 

16  400 

17310 

1.3 

31940 

4500 

4 

9-5 

0.337 

13480 

16  940 

1.4 

25690 

4240 

8.5 

0.263 

10  520 

16  360 

1.4 

19360 

3980 

7.5 

0.190 

7  600 

15360 

1.6 

13  130 

2  590 

75 

0.361 

10  830 

17  560 

I.O 

26940 

2390 

3 

6.5 

0.263 

7890 

17  020 

I.O 

19  020 

2  210 

5-5 

0.170 

5  100 

15950 

1.1 

II  530 

V  is  computed  at  10  000  lb  per  sq  in  of  gross  area  of  web-section. 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 

t  See,  also,  foot-note  on  page  568,  with  paragraphs  relating  to  this  table  and  to  Table 
III,  and  paragraphs  on  page  567,  relating  to  web-buckling  of  steel  beams.  See,  also, 
page  183. 


676  Strength  of  Beams  and  Beam  Girders  Chap.  15 

Table  III.*t     Maximum  Bending  Moments  and  Web-Resistances  of  Channels 


A/max 

d 

w 

/ 

V 

Soi 

a 

R 

Maximum 

Depth 

Weight 

Thick- 

Allowable 

Allowable 

Minimum 

End 

bending 

per 

ness  of 

web- 

buckling 

end- 

reaction, 

moment 

channel 

linft 

web 

shear 

resistance 

bearing 

c=3H  in 

ft-lb 

in 

lb 

in 

lb 

lb  per  sq 
in 

in 

lb 

76490 

55.0 

0.818 

122700 

15  820 

5.7 

93  830 

71590 

50.0 

0.720 

108  000 

15  390 

6.0 

80350 

66680 

15 

45.0 

0.622 

93300 

14  820 

6.4 

66840 

6i  780 

40.0 

0.524 

78600 

14  040 

6.9 

53  350 

56880 

35.0 

0.426 

63900 

12  900 

7.9 

39850 

55  570 

33.0 

0.400 

60000 

12  510 

8.2 

36270 

64360 

50.0 

0.791 

102  830 

16  150 

4.8 

86250 

60  no 

45.0 

0.678 

88  140 

15680 

5.0 

71  760 

55870 

13 

40.0 

0.565 

73450 

15  020 

5.4 

57260 

53320 

37.0 

0.497 

64  610 

14470 

5.7 

48540 

51  620 

35.0 

0.452 

58760 

14  020 

6.0 

42770 

48740 

32.0 

0.375 

48750 

13  000 

6.8 

32900 

43760 

40.0 

0.758 

90960 

16  260 

4.4 

80090 

39840 

35.0 

0.636 

76320 

15  730 

4.6 

6s  040 

35920 

12 

30.0 

0.513 

61  560 

14  950 

5.0 

49  850 

32000 

25.0 

0.390 

46800 

13  670 

5.8 

34  660 

28470 

20.5 

0.280 

33600 

II  570 

7.4 

21  060 

30800 

35.0 

0.823 

82300 

16  900 

3.4 

83  430 

27530 

30.0 

0.676 

67600 

16  440 

3.6 

66670 

24  260 

10 

25.0 

0.529 

52900 

15730 

3.9 

49  910 

20990 

20.0 

0.382 

38  200 

14470 

4-4 

33  160 

17840 

15.0 

0.240 

24  000 

II  780 

6.0 

16970 

20950 

25.0 

0.61S 

55350 

16  470 

3.2 

58  220 

18  010 

9 

20.0 

0.452 

40680 

15  550 

3.5 

40  420 

15070 

ISO 

0.288 

25920 

13590 

4.4 

22  500 

14  020 

13.25 

0.230 

20700 

12  220 

5.1 

16  170 

15920 

21.25 

0.582 

46560 

16  620 

2.8 

53200 

14  610 

18.75 

0.490 

39200 

16  170 

2.9 

43  580 

13  310 

8 

16.25 

0.399 

31  920 

15530 

3.2 

34070 

12000 

13. 75 

0.307 

24560 

14  490 

3.5 

24  460 

10770 

11.25 

0.220 

17600 

12  700 

4.3 

15370 

12640 

19-75 

0.633 

44  310 

17090 

2.3 

56780 

II  490 

17.25 

0.528 

36960 

i6  700 

2.4 

46300 

10  350 

7 

14.75 

0.423 

29610 

16  130 

2.6 

35830 

9  210 

12.25 

0.318 

22  260 

15  190 

2.9 

25360 

8030 

9.75 

0.210 

14700 

13230 

3.5 

14580 

8680 

15.5 

0.563 

33  780 

17  150 

2.0 

48  280 

7  700 

6 

13.0 

0.440 

26  400 

16640 

2.1 

36610 

6720 

10.5 

0.318 

19  080 

15730 

2.3 

25  010 

5780 

8.0 

0.200 

12  000 

13  810 

2.8 

13  810 

5  550 

II. 5 

0.477 

23  850 

17  180 

1.7 

38  920 

4730 

S 

9.0 

0.330 

16  500 

16  380 

1.8 

25  670 

3960 

6.5 

0.190 

9500 

14450 

2.2 

13040 

3050 

7.25 

0.325 

13000 

16870 

1.4 

24  670 

2790 

4 

6.25 

0.252 

10080 

16  250 

1.5 

18430 

2530 

5.25 

0.180 

7  200 

15  150 

1.6 

12  270 

I  840 

6.0 

0.362 

10860 

17560 

I.O 

27  020 

1640 

3 

5.0 

0.264 

7920 

17  030 

I.O 

19  no 

I  450 

4.0 

0.170 

5  100 

15940 

I.I 

II  520 

V  is  computed  at  lo  ooo  lb  per  sq  in  of  gross  area  of  web-section. 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 

t  See,  also,  foot-note  on  page  568,  with  paragraphs  relating  to  this  table  and  to  Table 
III,  and  paragraphs  on  page  567,  relating  to  web-buckling  of  steel  beams.  See,  also, 
page  183* 


Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


577 


Table  IV.*     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  for  Steel  I  Beams 

Maximum  bending  stress,  16000  lb  per  sq  in.    Beams  secured  against  yielding  sidewise 


Depth  and  weight  of  sections 

CoefR- 

Span, 
ft 

27-in 

24-in 

2i-in 

cient  of 
deflection  ' 

90 

IIS 

no 

105 

100 

95 

90 

85 

80 

74 

6o>i 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

"6    ' 

7 
8 

283.0 

36:).o 

330.2 

300.0 

3G1.9 

^32.6 

302.9 

273.6 

231.9 

228.S 

I7Q.8 

i 

0.60     ' 

0.81 

1.06 

352.5 
302.2 
264.4 

293.2 
256.6 

284.2 
248.7 

179.3 
156.9 

328.4 

320.4 

240.9 

216.7 

9 

259-3 

291.9 

284.8 

277.7 

235.0 

228.0 

221. 1 

214. 1 

206.1 

192.6 

139.5 

1.34 

10 
II 

2334 
212.2 

262.7 
238.8 

256.3 
233-0 

249-9 
227.2 

211. 5 
192.3 

205.2 
186.6 

199.0 

192.7 

185.5 
168.7 

173.3 
157.6 

125-5 

II4.I 

1.66 
2.00 

180.9 

175.2 

12 

194-5 

218.9 

213.6 

208.3 

176.3 

171. 0 

165.8 

160.6 

154.6 

144.5 

104.6 

2.38 

13 

179-5 

202.1 

197.2 

192.2 

162.7 

157.9 

153- 1 

148.2 

142.7 

133.3 

96.5 

2.80 

14 

166.7 

187.7 

183. 1 

178.5 

151 -I 

146.6 

142. 1 

137-6 

132.5 

123.8 

89.7 

3.24 

IS 

156.6 

175. 1 

170.9 

166.6 

141. 0 

136.8 

132.6 

128.5 

123.7 

1156 

83-7 

3.72 

16 

145-9 

164.2 

160.2 

156.2 

132.2 

128.3 

124.4 

120.4 

116. 0 

108.3 

78.4 

4.24 

17 

137-3 

154.  s 

150.8 

147-0 

124-4 

120.7 

117. 0 

113-4 

109. 1 

102.0 

73.8 

4.78 

18 

129.7 

146.0 

142.4 

138.8 

117-5 

;i4.o 

no. 5 

107. 1 

103. 1 

96.3 

69.7 

5.36 

19 

122.8 

138.3 

134-9 

131. 5 

111-3 

108.0 

104.7 

101.4 

97.6 

91.2 

66.1 

5.98 

20 

116. 7 

131. 4 

128.2 

125.0 

105.8 

102.6 

99-5 

96.3 

92.8 

86.7 

62.8 

6.62 

21 

III. I 

125. 1 

122. 1 

119. 0 

100.7 

97-7 

94.7 

91.8 

88.3 

82.5 

59.8 

7.30 

22 

106.1 

119. 4 

116. 5 

II3-6 

96.1 

93-3 

90.4 

87.6 

84.3 

78.8 

571 

8.01 

23 

101.5 

114. 2 

III. 4 

108.7 

92.0 

89.2 

86.5 

83.8 

80.7 

75-4 

54-6 

8.76 

24 

97-3 

109. S 

106.8 

104. 1 

88.1 

85.5 

82.9 

80.3 

77.3 

72.2 

52.3 

9.53 

25 

93-4 

105.1 

102.5 

100. 0 

84.6 

82.1 

79-6 

77-1 

74.2 

69.3 

50.2 

10.35 

26 

89-8 

lOI.O 

98.6 

96.1 

81.4 

78.9 

76.5 

74.1 

71.4 

66.7 

48.3 

II.  19 

27 

86.4 

97-3 

94-9 

92.6 

78.3 

76.0 

73.7 

71-4 

68.7 

64.2 

46.5 

12.07 

28 

83.4 

93-8 

91-5 

89-3 

75-5 

73-3 

71 -I 

68.8 

66.3 

61  9 

44-8 

12.98 

29 

80.S 

90.6 

88.4 

86.2 

72.9 

70.8 

68.6 

66.4 

64.0 

59.8 

433 

13.92 

30 

77.8 

87.6 

85-4 

83-3 

70.5 

68.4 

66.3 

64.2 

61.8 

57.8 

41-8 

14.90 

31 

75-3 

84-7 

82.7 

80.6 

68.2 

66.2 

64.2 

62.2 

59.8 

55-9 

40-5 

15.91 

32 

72.9 

82.1 

80.1 

78,1 

66.1 

64.1 

62.2 

60.2 

58.0 

542 

39-2 

16.9s 

33 

70.7 

79-6 

77.7 

75.7 

64.1 

62.2 

60.3 

58.4 

56.2 

52. 5 

38.0 

18.03 

34 

68.6 

77-3 

75-4 

73-5 

62.2 

60.4 

58.5 

56.7 

54.6 

51-0 

36.9 

19.13 

35 

66.7 

75.1 

73-2 

71-4 

60.4 

58.6 

56.8 

55.1 

53.0 

495 

35.9 

20.28       ; 

36 

64.8 

73-0 

71.2 

69-4 

58.8 

57.0 

55-3 

53-5 

51.5 

48.2 

34-9 

21.45          ; 

37 

63.1 

71.0 

69-3 

67-5 

57.2 

55-5 

53-8 

52.1 

50.1 

468 

33.9 

22.66 

38 

61.4 

69.1 

67-5 

65.8 

55-7 

54-0 

52.4 

50.7 

48.8 

456 

33.0 

23.90 

39 

59-8 

67-4 

65-7 

64.1 

54-2 

52.6 

51.0 

49-4 

47-6 

44.4 

32.2 

25.18 

40 

58.4 

65-7 

64.1 

62.5 

52.9 

51-3 

49-7 

48.2 

46.4 

433 

31.4 

26.48 

41 

56.9 

64.1 

62.5 

61.0 

51.6 

50.1 

48.5 

47.0 

45-3 

42.3 

30.6 

27.82 

42 

55.6 

62.6 

61.0 

59-5 

50.4 

48.9 

47.4 

45.9 

44.2 

41.3 

29.9 

29.20 

43 

54.3 

61. 1 

59-6 

58.1 

49-2 

47.7 

46.3 

44.8 

43.1 

40.3 

29.2 

30.60 

44 

53-0 

59-7 

58.3 

56.8 

48.1 

46.6 

45.2 

43-8 

42.2 

39.4 

28.5 

32.04 

45 

51-9 

58.4 

57-0 

55.5 

47-0 

45-6 

44.2 

42.8 

41.2 

38.5 

33.52 

46 

50.7 

57.1 

55.7 

54-3 

46.0 

44.6 

43.3 

41-9 

40.3 

37.7 

35.02 

47 

49-7 

55-9 

54.1 

53.2 

45.0 

43-7 

42.3 

41.0 

39.5 

36.9 

36.56 

48 
49 

48.6 
47.6 

54-7 

53^4 

52^1 

44-1 

42.8 

41.5 

40.1 

_38-7 

jA-}. 

38.14 

39-74 

ire" 

52.3 

51-0 

43.2 

4I-9 

40.6 

39.3 

37-9 

35.4 

50 

46.7 

52.5 

51 -3 

50.0 

42.3 

41.0 

39-8 

38.5 

37.1 

34.7, 

41.38 

Loads 

above  the  upper  heavy  lines  will  cause  maximum  allowable  j 

>hears  in 

webs.    S 

ee,  also,  paragraphs  in  text  and  foot-note  with  same,  page  567,  re 

iating  to 

web-buc 
Loads 

kling  in  beams 

below  the  lower  broken  lines  will  cause  excessive  deflections 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


Table  IV  *  (Continued).     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds 
for  Steel  I  Beams 


Maximum  bending  stress 

16  000  lb  per  sq 

in.    Beams  secured  against  yielding  sidewise 

Span, 

Depth  and  weight  of  sections 

Coeffi- 
cient of 

20-in 

i8-in 

ft 

deflec- 
tion 

100 

95 

90 

85 

80 

75 

70 

65 

90 

85 

80 

75 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

5 

35:^-6 

0.41 

353  2 

.-.. 

6 
7 

294 -3 
252.3 

324.0 

294.8 

265.2 

240.0 

259.6 

230.0 

200.0 

290.5 

261.0 

231.8 

202.3 

0.60 
0.81 

285.6 
244.8 

276.9 
237.7 

225.6 
193.3 

216.8 
185.9 

249.0 
213.4 

241. 1 
206.7 

229.9 

223.4 

178.2 

200.0 

193.2 

8 

220.7 

214.2 

207.7 

201. 1 

195.5 

169.2 

162.6 

155.9 

186.7 

180.8 

175.0 

169. 1 

1.06 

9 

196.2 

190.4 

184.6 

178.8 

173.8 

150.4 

144-6 

138.6 

166.0 

160.7 

155.5 

150.3 

1.34 

10 

176.6 

171. 4 

166. 1 

160.9 

156.4 

135.3 

130. 1 

124.7 

149.4 

144-7 

140.0 

135. 3 

1.66 

II 

160.5 

155.8 

151. 0 

146.3 

142.2 

123.0 

118. 3 

113. 4 

135.8 

131. 5 

127.2 

123.0 

2.00 

12 

147-2 

142.8 

138.5 

134. 1 

130.3 

112. 8 

108.4 

104.0 

124.5 

120.6 

116. 6 

112. 7 

2.38 

13 

135.8 

131. 8 

127.8 

123.8 

120.3 

104. 1 

100. 1 

96.0 

114. 9 

III. 3 

107.7 

104. 1 

2.80 

14 

126. 1 

122.4 

118. 7 

114. 9 

III. 7 

96.7 

92-9 

89.1 

106.7 

103.3 

100. 0 

96.6 

3.24 

15 

II7-7 

114. 2 

no. 8 

107.3 

104.3 

90.2 

86.7 

83.2 

99-6 

96.4 

93.3 

90.2 

3.72 

i6 

no. 4 

107. 1 

103.8 

100.6 

97.7 

84.6 

81.3 

78.0 

93.4 

90.4 

87-5 

84.5 

4.24 

17 

103.9 

100.8 

97.7 

94.1 

92.0 

79-6 

76.5 

73.4 

87.9 

85.1 

82.3 

79-6 

4.78 

i8 

98.1 

95.2 

92.3 

89.4 

86.9 

76.3 

72.3 

69.3 

83.0 

80.4 

77.8 

75.1 

5.36 

19 

92.9 

90.2 

87.4 

84.7 

82.3 

71.2 

68.5 

65.7 

78.6 

76.1 

73.7 

71.2 

5.98 

20 

88.3 

85. 7 

83.1 

80.5 

78.2 

67.7 

65. 1 

62.4 

74.7 

72.3 

70.0 

67.6 

6.62 

21 

84.1 

81.6 

79.1 

76.6 

74-5 

64.4 

62.0 

59-4 

71. 1 

68.9 

66.7 

64.4 

7.30 

23 

80.3 

77-9 

75.5 

73.1 

71. 1 

61.5 

59.1 

56.7 

67.9 

65.8 

63.6 

61.5 

8.01 

23 

76.8 

74.5 

72.2 

70.0 

68.0 

58.8 

56.6 

54.2 

64.9 

62.9 

60.9 

58.8 

8.76 

24 

73.6 

71.4 

69.2 

67.0 

65.2 

56.4 

54-2 

52.0 

62.2 

60.3 

58.3 

56.4 

9-53 

25 

70.6 

68.5 

66.5 

64.4 

62.6 

54-1 

52.0 

49.9 

59-8 

57-9 

56.0 

54.1 

10.35 

2« 

67.9 

65. 9 

63.9 

61.9 

60.2 

52.1 

50.0 

48.0 

♦57-5 

55.6 

53.8 

S2.0 

II. 19 

27 

65.4 

63.5 

61.5 

59  6 

57.9 

50.1 

48.2 

46.2 

55-3 

53-6 

51.8 

50.1 

12.07 

28 

63.1 

61.2 

59-3 

57.5 

55.9 

48.3 

46. 5 

44.6 

53.3 

51-7 

50.0 

48.3 

12.98 

29 

60.9 

59- 1 

57-3 

55.5 

53.9 

46.7 

44.9 

43-0 

51.5 

49  9 

48.3 

46.6 

13-92 

30 

58.9 

57.1 

55. 4 

53.6 

52.1 

45.1 

43.4 

41.6 

49.8 

48.2 

46.7 

45- 1 

14.90 

31 

57.0 

55.3 

53.6 

51.9 

50.5 

43.7 

42.0 

40.2 

48.2 

46.7 

45.2 

43.6 

15-91 

33 

55.2 

53.6 

51-9 

50.3 

48.9 

42.3 

40.7 

390 

46.7 

45.2 

43.7 

42.3 

16.95    . 

33 

53.5 

51.9 

50.4 

48.8 

47.4 

41.0 

39.4 

37.8 

45-3 

43.8 

42.4 

41.0 

18.03 

34 

51.9 

50.4 

48.9 

47.3 

46.0 

39-8 

38.3 

36.7 

43-9 

42.6 

41.2 

39-8 

19-13 

35 

50. 5 

49.0 

47.5 

46.0 

44.7 

38.7 

37.2 

35.6 

42.7 

41-3 

40.0 

38.6 

20.28 

36 
37 

49.1 
47.7 

47.6 
46.3 

46.2 
44.9 

44-7 
43. 5 

43.4 
42.3 

37.6 
36.6 

36.1 
35.2 

34-7 
33-7 

_4_i-S 

40.2 

38.9 

37.6 

21.45 
22.66 

46.4 

39-1 

37'8 

'36.6 

38 

46.5 

45.1 

43.7 

42.3 

41.2 

35.6 

34-2 

32.8 

39-3 

38.1 

36.8 

35.6 

23.90 

39 

45.3 

43.9 

42.6 

41.3 

40.1 

34.7 

33-4 

32.0 

25.18 

40 
41 

44-1 

42.8 

41^5 

40.2 

A^jI 

33.8 

3_2.5 

31.2 

26.48 
27.82 

43.1 

41.8 

40. 5 

39-2 

38.1 

33.0 

31.7 

30.4 

42 

42.0 

40.8 

39.6 

38.3 

37.2 

32.2 

31.0 

29.7 

29.20 

Loads  above  the  upper  heavy  lines  will  cause  maximum  allowable  shears  in 

webs.    See,  also,  paragraphs  in  text  and  foot-note  with  same,  page  567,  relating 

to  web-buckling  in  beams 

Loads  below  the  lower  broken  lines  will  cause  excessive  deflections                        , 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


Table  IV  *  (Continued).     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds 
for  Steel  I  Beams 


Maximum  bending  stress,  i6ooo  lb  per  sq  in. 

Beams  secured  against  yielding  sidewise 

a 

Depth 

and  weight  of  sections 

11 

•3  ^ 

— ■ — — 

i8-in 

15-in 

8-^ 

^ . 

70 

65 

60 

55 

48 

75 

70 

65 

60 

55 

50 

45 

42 

4 
5 

6 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

u 

258.8 

229.^ 

199.8 

136.8 

261.6 

235.2 

c'o^.'s 

177.0 

196.8 

167.4 

i^S.o 

12-^.0 

0.27 
0.41 

0.60 

245.8 
196.6 

163-8 

181. 7 
145.4 

121. 1 

218.4 
182.0 

208.9 

199-5 
166.3 

165.6 

188.8 
157.3 

180.9 

150.8 

173.2 
144.4 

137.5 

129.7 
108. 1 

114. 6 

174. 1 

157. 1 

104.7 

7 
8 

156.0  149-2 

142.5 
124.7 

134.7 
117. 9 

124.8 
109 . 2 

140.4 

134-8 
118. 0 

129.2 
113. 1 

123-7 
108.3 

103.8 
90.8 

98.2 
85.9 

92.6 
81.0 

89.8 
78.5 

0.81 
1.06 

136.5 

130.6 

122.9 

9 

121. 3 

116. 1 

no. 9 

104.8 

97.1 

109.2 

104.9 

100.5 

96.2 

80.8 

76.4 

72.0 

69.8 

1.34 

10 

109.2 

104.5 

99.8 

94.3 

87-4 

98.3 

94.4 

90.5 

86.6 

72.7 

68.8 

64.8 

62.8 

1.66 

II 

99.3 

950 

90.7 

85.7 

79-4 

89.4 

85.8 

82.2 

78.7 

66.1 

62.5 

58.9 

57.1 

2.00 

12 

91.0 

87.1 

83.1 

78.6 

72.8 

81.9 

78.7 

75.4 

72.2 

60.6 

57.3 

54.0 

52.4 

2.38 

13 

84.0 

80.4 

76.7 

72-5 

67.2 

75.6 

72.6 

69-6 

66.6 

55.9 

52.9 

49.9 

48.3 

2.80 

14 

78.0 

74.6 

71-3 

67-3 

62.4 

70.2 

67.4 

64.6 

61.9 

51.9 

49-1 

46.3 

44.9 

3.24 

15 

72.8 

69.6 

66.5 

62.9 

58.2 

65.5 

62.9 

60.3 

57.7 

48. 5 

45.8 

43.2 

41-9 

3.72 

i6 

68.2 

65.3 

62.4 

58.9 

54-6 

61.4 

590 

56.5 

54.1 

45.4 

43.0 

40.5 

39-3 

4.24 

17 

64.2 

61.5 

58-7 

55-5 

SI -4 

57-8 

55-5 

53-2 

50.9 

42.8 

40.4 

38.1 

37.0 

4.78 

i8 

60.7 

58.0 

55.4 

52.4 

48. 5 

54.6 

52.4 

50.3 

48.1 

40.4 

38.2 

36.0 

34.9 

5.36 

19 

57-5 

55.0 

52.5 

49.6 

46.0 

SI. 7 

49.7 

47.6 

45.6 

38.3 

36.2 

34.1 

33.1 

5.98 

20 

54.6 

52.2 

49. P 

47-1 

43.7 

49.2 

47.2 

45.2 

43.3 

36.3 

34.4 

32.4 

31.4 

6.62 

21 

52.0 

49-7 

47.5 

44.9 

4X.6 

46.8 

44-9 

43.1 

41.2 

34.6 

32.7 

30.9 

29.9 

7^0 

22 

49-6 

47.5 

45-3 

42.9 

39-7 

44.7 

42.9 

41 -I 

39.4 

33.0 

31-3 

29.5 

28.6 

8.01 

23 

47.5 

45.4 

43.4 

41.0 

38.0 

42.7 

41.0 

39-3 

37.7 

31.6 

29.9 

28.2 

27.3 

8.76 

24 

45.5 

43.5 

41.6 

39-3 

36.4 

41.0 

39.3 

37.7 

36.1 

30-3 

28.6 

27.0 

26.2 

9-53 

25 

43.7 

41.8 

39.9 

37.7 

34-9 

39.3 

37.8 

36.2 

34.6 

29.1 

27.5 

25-9 

25.1 

10.35 

26 

42.0 

40.2 

38.4 

36.3 

33-6 

37.8 

36.3 

34-8 

33.3 

28.0 

26.4 

24.9 

24-2 

II. 19 

27 

40.4 

38.7 

37-0 

34.9 

3^-4 

36.4 

35.0 

33-5 

32.1 

26.9 

25-S 

24.0 

23.3 

12.07 

28 

390 

37.3 

35.6 

33.7 

31-2 

35.1 

33-7 

32.3 

30.9 

26.0 

24.6 

23-2 

22.4 

12.98 

29 

37.6 

36.0 

34.4 

32-5 

30.1 

33.9 

32.5 

31.2 

29.9 

25.1 

23-7 

22.4 

21.7 

13.92 

30 
31 

36.4 
35.2 

34.8 
33.7 

33.3 
32.2 

31.4 
30.4 

29.1 
28.2 

_32_8 

31.5 

30^2 

28.9 

24^2 

22.9 

21.6 

20.9 

14.90 
15.91 

31.7 

30.4 

29.2 

27.9 

23.4 

22.2 

20.9 

20.3 

32 

34.1 

32.6 

31.2 

29.5 

27.3 

30.7 

29.5 

28.3 

27.1 

22.7 

21.5 

20.3 

19  6 

16.95 

33 

33.1 

31-7 

30.2 

28.6 

26.5 

18.03 

34 

32.1 

30.7 

29.3 

27.7 

25-7 

19  13 

35 

31.2 

29.8 

28.5 

26.9 

25.0 

20.28 

36 
37 

.3?i3 

29.0 

27.7 

26.2 

24-3 
23.6 

21.45 
22.66 

295 

~28".'2 

27.0 

25.5 

38 

28.7 

27.5 

26.3 

24.8 

230 

23.90 

Loads  above  the  upper  heavy  lines  will  cause  maximum  allowable  shears  in 

webs.     See,  also,  paragraphs  in  text  and  foot-note  with  same,  page  567,  relating 

to  web-buckling  in  beams 

Loads  below  the  lower  broken  lines  will  cause  excessive  deflections 

♦From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


580 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


Table  IV  *  (Continued).     S^fe  Uniform  Loads  in  Units  of  i  ooo  Pounds 
for  Steel  I  Beams 


Maximum  bending  stress,  i6  ooo  lb  per  sq  in. 

Beams  secured  against 

yield 

ing  sidewise 

Depth  and  weight  of  sections 

h 

i5-in 

i2-in 

lo-i.n 

CO 

8-0 
0 

37  Mi 

55 

50 

45 

40 

35 

31  Mi 

r28 

40 

35 

30 

25 

22  »4 

3 
4 
5 

6 

lb 

lb 

lb 
167.8 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

90-6 

197.0 

I'ss's 

1C4.6 

840 

f... 
68.2 

I4Q.8 

120.4 

91.0 

62.0 

so  .4 

0.15 
0.27 
0.41 

0.60 

190.2 
142.7 
114. 1 

95.1 

112. 8 
84.6 
67.7 

56.4 

104. 1 
78.1 
62.5 

52.1 

134.8 
107.9 

89.9 

127.0 

110.4 

101.5 
81.2 

67  6 

71.6 
57.2 

47.7 

I0I.6 
84.7 

95.6 
79.7 

76.7 
63.9 

52.1 

43.4 

48.5 
40.4 

96.1 

59  I 

7 

82.4 

81.5 

77.0 

72.6 

68.3 

58.0 

54.8 

50.6 

48.4 

44.6 

40.9 

37.2 

34.6 

0.81 

8 

72.1 

71.3 

67.4 

63. 5 

59-8 

50.7 

48.0 

44-3 

42.3 

39-0 

35.8 

32.6 

30.3 

1.06 

9 

64.1 

634 

59-9 

56.4 

53.1 

45.1 

42.6 

39.4 

37.6 

34.7 

31.8 

28.9 

26.9 

1.34 

10 

57. 7 

57.1 

53  0 

50.8 

47.8 

40.6 

38.4 

3S.S 

33.9 

31.2 

28.6 

26.0 

24.2 

1.66 

II 

52.4 

51.9 

49.0 

46.2 

43.5 

36.9 

34.9 

32.2 

30.8 

28.4 

26.0 

23.7 

22.0 

2.00 

12 

48.1 

47.6 

44.9 

42.3 

39.8 

33.8 

32.0 

29.5 

28.2 

26.0 

23.9 

21.7 

20.2 

2.38 

13 

44.4 

43.9 

41.5 

39- 1 

36.8 

31.2 

29s 

27.3 

26.0 

24.0 

22.0 

20.0 

18.6 

2.80 

14 

41.2 

40.8 

38.5 

36.3 

34.2 

29.0 

27.4 

25-3 

24.2 

22.3 

20.4 

18.6 

17-3 

3.24 

IS 

38.4 

38.0 

36.0 

33.9 

31.9 

27.1 

25.6 

23.6 

22.6 

20.8 

19. 1 

17.4 

16.2 

3.72 

i6 

36.0 

35.7 

33.7 

31.7 

299 

25.4 

24.0 

22.2 

21.2 

195 

17.9 

16.3 

15.1 

4-24 

17 

33-9 

33.6 

31.7 

29.9 

28.1 

23.9 

22.6 

20.9 

19.9 

18.4 

16.8 

IS. 3 

14.3 

4.78 

i8 

32.0 

31.7 

30.0 

28.2 

26.6 

22.5 

21.3 

19.7 

18.8 

17.4 

15.9 

14. 5 

13. 5 

5.36 

19 

30.4 

30.0 

28.4 

26.7 

25.2 

21.4 

20.2 

18.7 

17.8 

16.4 

15.1 

13.7 

12.8 

5.98 

20 
21 

28.8 
27 -S 

28.5 
27.2 

27.0 
25.7 

25.4 
24.2 

23.9 
22.8 

20.3 
19.3 

19.2 
18.3 

17.7 
16.9 

16.9 

15.6 

14.3 

13.0 

12. 1 
11.5 

6.62 
"  30 

16. 1 

14.9 

13.6 

12.4 

22 

26.2 

25.9 

24.5 

23.1 

21.7 

18.4 

17.4 

16. 1 

IS. 4 

14.2 

13.0 

II. 8 

II. 0 

8.01 

23 

25   I 

24.8 

23.4 

22.1 

20.8 

17.6 

16.7 

15.4 

8.76 

24 
25 

24.0 
23.1 

23.8 

22.5 

21.2 

19.9 

16.9 

16.0 

14.8 

9.53 
10.35 

22.8 

21.6 

20.3 

19. 1 

16.2 

15.3 

14.2 

26 

22.2 

21.9 

20.7 

19.5 

18.4 

IS. 6 

14.8 

13.6 

... 

II. 19 

27 

21  4 

12.07 

28 

20.6 

12.98 

29 

19.9 

13.92 

30 

19-2 

14.90 

31 

18.6 

15.91 

32 

18.0 

... 

16.95 

Loads  above  the  upper  heavy  lines  will  cause  maximum  allo^ 

vable  shears  in 

webs.      See,  also,  paragraphs  in  text  and  foot-note  with  same,  pa 

Lge  567,  relating 

to  web-buckling  in  beams. 

Loads  below  the  lower  broken  lines  will  cause  excessive  deflecti 

ons                       . 

j-:r 

From 

Pocke 

t  Con 

ipanio 

n,  Cai 

negie 

Steel 

Comp 

any,  1 

^ittsbi 

irgh,  ] 

^a. 

Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


581 


Table  IV  *  (Continued).     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds 
for  Steel  I  Beams 

Maximum  bending  stress  16  000  lb  per  sq  in.    Beams  secured  against  yielding  sidewise 


Span, 
ft 

Depth  and  weight  of  sections 

Coeffi- 
cient of 
deflec- 
tion 

9- 

n 

8-in 

7-in 

35 

lb 

30 
lb 

25 

lb 

21 
lb 

25>^ 
lb 

23 

lb 

2oy2. 
lb 

18 

lb 

I7H 
lb 

20 
lb 

17^^ 
lb 

IS 
lb 

3 

4 
5 
6 
7 
8 
9 
10 

II 
12 
13 
14 
IS 
16 

17 
18 

19 

20 

131.8 

102.4 

73.1 

52.2 

86.6 

71.8 

57.1 

64.1 

49.4 

35.0 

o.is 
0.27 
0.41 
0.60 
0.81 
1.06 
1.34 
1,66 

2.00 
2.38 
2.80 
3.24 
372 
4.24 
4.78 
5.36 

5.98 
6.62 

43.2 

88.3 
66.2 
53.0 

44.2 
37-9 
33.1 
29.4 
26.5 

24.1 
22.1 
20.4 
18.9 
17.7 
16.6 
15.6 
14.7 

80.5 
60.4 
48.3 
40.2 
34.5 
30.2 
26.8 
24.1 

22.0 
20.1 
18.6 
17.2 
16. 1 

15.1 
14.2 
13.4 

72.6 
54.5 
43.6 

36.3 
31. 1 
27.2 
24.2 
21.8 

19.8 
18.2 
16.8 
15.6 
14.5 
13.6 
12.8 
12. 1 

60.8 

45.6 
36.5 

30.4 
26.1 
22.8 
20.3 
18.2 

16.6 

15.2 

14.0 

13.0 

12.2 
II. 4 

57.3 
43.0 
34-4 

28.7 
24.6 
21.5 
19. 1 
17.2 

15.6 
14.3 
13.2 
12.3 
II. 5 
10.8 

S3. 9 
40.4 
32.3 

26.9 
23.1 
20.2 
18.0 
16.2 

14.7 
13.5 
12.4 
II. 5 
10.8 
10. 1 

3S.2 

42. Q 

39.8 
29.9 
23.9 

19.9 
17. 1 
14.9 
13.3 
11.9 
10.9 
10. 0 
9.2 
8.5 
'¥.0 

7.S 

50.3 
40.3 

33.6 
28.8 
25.2 
22.4 
20.1 

18.3 
16.8 
IS. 5 
14.4 
13.4 
12.6 
II. 8 
II. 2 

37.9 
30.3 

25.3 
21.7 
19.0 
16.9 
15.2 

13.8 
12.6 
11.7 
IQ.8 

10. 1 
9.5 

3 

2.1 
5.7 

C.4 
J. 4 
).i 

^.3 

2-9 

.7 

).7 
).9 

).2 

J.~6 

5.0 

27.6 
22.1 

18.4 
15.8 
13.8 
12.3 
II. 0 

10. 0 
9.2 
8.5 

_r9 

7.4 
6.9 

31. 1 

25.9 
22.2 
19-5 
17.3 
15.6 

14.2 
13.0 
12.0 
II. I 

10.4 

9.7 

2, 

2 
li 
l( 

i: 

I] 
ic 
( 
t 
~'i 
I 

10.7 
10. 1 

10. 1 
9.6 

9.5 
9.0 

8.9 
8.4 

9.2 
8.6 

13.9 
13.3 

12.7 
12. 1 

II. 5 
10.9 

10.6 
10. 1 

Span, 
ft 

Depth  and  weight  of  sections 

Coeffi- 
cient of 
deflec- 
tion 

6-in 

5-in 

4-in 

b 

3-in 

lb 

14% 
lb 

12H 
lb 

14% 
lb 

I2H 

lb 

m 
lb 

10V2 
lb 

9\^ 
lb 

27.0 
18.0 
12.0 
9.0 
7.2 
6.0 

S.I 
4.5 

8}/2 

lb 

21.0 
16.9 
II. 3 
8.5 
6.8 

5.6 
4.8 
4.2 

7 
1 

7K2 
lb 

61/2 
lb 

lb 

I 
2 
3 
4 
5 
6 

7 
8 

9 

10 

II 
12 

13 
14 

57.0 

42.2 

27.6 

50.4 

35-7 

21.0 

32.8 

15.2 
10.6 
8.0 
6.4 
5.3 

4.5 
4.0 

21.7 
20.7 
10.4 
6.9 
5.2 
4.1 
3.5 

15*8 

9.f 
6.-1 
4.8 
3.8 
3.2 

8.8 
59 
4.4 
3.5 

2.9 

0.02 
0.07 
0.15 
0.27 
0.41 
0.60 
0.81 
1.06 

1.34 
1.66 

2.00 
2.38 
2.80 
3.24 

46.6 
31.0 
23.3 
18.6 

iS-5 

13.3 
II. 6 

10.3 
9-3 

8.5 

7.8 

32.3 
21.5 
16.2 
12.9 
10.8 

9.2 
8.1 

7.2 
6.5 

29.1 
19.4 
14.5 
II. 6 

9-7 
8.3 
7.3 

6.5 

5.8 

19.0 
12.7 
95 
7.6 

6.3 

5.4 
4.8 

28.4 
21.3 
17. 1 

14.2 
12.2 
10.7 
9.5 
8.5 
7.8 
7.1 

25.8 
19-4 
IS. 5 
12.9 
II. I 
9.7 
8.6 
7.7 

17.2 
12.9 
.10:3 

8.6 

7.4 
6.4 

5-7 
5.2 

3.0 
2.6 

2.7 

2.4 

2.5 
2.2 

4.2 
3.8 

4.0 
3.6 

3.8 
3.4 

35 
3.2 

5.9 
5.4 

5.3 

4.8 

4.7 
4.3 

7.0 
6.5 

7.2 
6.7 

6.6 
6.1 

6.0 
5.5 

..   ■   .. 

Loads  at 
webs.     See 
to  web-buc 

Loads  be 

ove  t 

also, 

ding 

lowtl 

he  upper  h 
paragraphs 
in  beams 
le  lower  brc 

eavy 
in  te 

>ken  1 

lines  1 

xt  an 

nes  vi 

;vill  cj 
i  foot 

ill  cat 

luse  maximum  allowable  sh 
-note  with  same,  page  567,  r 

ise  excessive  deflections 

ears  in 
elating 

?From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


582  Strength  of  Beams  and  Beam  Girders  Chap.  15 

Table  V.*     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  for  Steel  Chaniaels 


Maximum  b< 

mding 

stress 

,  16  0 

00  lb 

per  sq  in.     Beams  secured  against  yielding 

I  sidewise 

Span, 
ft 

pth  and  weight  of 

Coeffi- 
cient of 
deflec- 
tion 

sections 

De 

15- 

in 

13- 

in 

55 
lb 

50 
lb 

45 
lb 

40 
lb 

35 

lb 

33 

lb 

50 
lb 

45 
lb 

40 
lb 

37 
lb 

35 

lb 

32 

lb 

3 
4 
S 

i  ;> 

^       7 
8 
9 

10 

II 

12 

13 
14 
15 

i6 
17 
i8 
19 

20 

21 
22 
23 
24 
25 

26 

27 
28 
29 

30 

31 
32 

245-4 

216.0 

186.0 

157-2 

127.8 

120.0 

205.7 

146.9 

129.2 

1175 

97-5 

0.15 
0.27 
0.41 

0.60 
0.81 
1.06 
1.34 
1.66 

2.00 
2.38 
>    2.80 
3.24 
3-72 

4.24 
4.78 
5.36 
5.98 
6.62 

7-30 
8.01 
8.76 
9-53 
10.35 

II.  19 

12.07 
12.98 
13.92 
14.90 

15.91 
16.95 

176.3 

204.0 
153.0 
122.4 

102.0 
87-4 
76.S 
68.0 
61.2 

55.6 
510 
471 
43-7 
40.8 

38.2 
36.0 
34.0 
32.2 
30.0 

29.1 
27.8 
26.6 
25.5 
24.5 

23.5 
22.7 
21.9 
21.1 
20.4 

19.7 
19.1 

190.9 
143.2 
114,5 

95.4 
81.8 
71.6 
63.6 
57.3 

52.1 

47-7 
44.1 
40.9 
38.2 

35.8 
33.7 
31.8 
30.1 
28.6 

27.3 
26.0 
24.9 
23.9 
22.9 

22.0 

21.2 
20.5 
19.7 
I9.I 

177.8 
133-4 
106.7 

88.9 
76.2 
66.7 
59-3 
53.3 

48.5 
44.5 
41.0 
38.1 
35.6 

33-3 
31.4 
29.6 
28.1 
26.7 

25.4 
24.3 
23.2 
22.2 
21.3 

20.5 
19.8 
19. 1 
18.4 
17.8 

171. 6 
128.7 
103.0 

85.8 
73.6 
64.4 
57-2 
51.5 

46.8 
42.9 
39-6 
35.8 
34.3 

32.2 
30.3 
28.6 
27.1 
25.7 

24.5 
23.4 
22.4 
21.5 

20.6 

19.8 

160.3 
120.2 
9S.2 

80.2 
68.7 
60.1 
53.4 
48.1 

43.7 
40.1 
37.0 
34.4 
32.1 

30.1 
28.3 
26.7 
25.3 
24.0 

22.9 
21.9 
20.9 
20.0 
19.2 

123.6 
98.9 

82.4 
70.6 
61.8 
54-9 
49-4 

44-9 
41.2 
38.0 
35-3 
33-0 

30.9 
29.1 
27.5 
26.0 
24.7 

23.5 

22.5 

21.5 

20.6 

19.8 

19.0 

18.3 
17.7 
17.0 
16.5 

113. 8 
91.0 

75.8 
65.0 
56.9 
50.6 
45.5 

41.4 
37.9 
35-0 
32.5 
30.3 

28.4 
26.8 
25.3 
239 
22.8 

21.7 
20.7 
19.8 
19.0 
18.2 

17.5 
16.9 
16.3 
15.7 
15.2 

III. I 
88.9 

74-1 
63. 5 
55.6 
49-4 
44.5 

40.4 
37.0 
34.2 
31.8 
29.6 

27.8 
26.1 
24.7 
23.4 
22.3 

21.2 
20.2 
19-3 
18.5 
17.8 

III. 7 
89-4 

74.5 
63.8 
55.9 
49-7 
44.7 

40.6 
37.2 
34.4 
31-9 
29.8 

27.9 
26.3 
24.8 
23.5 
22.3 

21.3 
20.3 
19.4 
18.6 
17.9 

17.2 

106.6 
85.3 

71. 1 
60.9 
53.3 

47-4 
42.7 

38.8 
35.5 
32.8 
30.5 
28.4 

26.7 
25.1 
237 
22.4 
21.3 

20.3 
19.4 
18.5 
17.8 
17. 1 

16.4 

103.2 
82.6 

68.8 
59-0 
51-6 
45.9 
41.3 

37-5 
34.4 
31-8 
29.5 

27-5 

25.8 
24.3 
22.9 
21.7 
20.6 

19-7 
18.8 
18.0 
17.2 

ir».5 
15.9 

97-5 
78.0 

65.0 
55.7 
48.7 
43.3 
39-0 

35.4 
32.5 
30. <9 
27-9 
26.0 

24.4 
22.9 
21.7 
20.5 
19-5 

18.6 
17.7 
17.0 
16.2 
15.6 

IS-O 

17. 1 
16.5 
15.9 
15.3 
14.8 

18.5 

19.1 
18.4 

17.8 
17.2 

16.6 
16.0 

.T5.8 
15.2 

15.3 
14.7 

14.4 
13.9 

18.5 
17.9 

17.2 
16.7 

15.9 
15.4 

14.7 
14.2 

14. J 
13.9 

Loads  at 
webs.     See 
to  web-buc 

Loads  be 

ove  t 

also 

kling 

lowtl 

he  up 

para 

in  bea 

le  low 

per  h 
graph 
ims 
er  bro 

2avy 
5  in  t 

kenl 

ines  will  c 
2Xt  and  foo 

nes  will  cai 

ause  maxim 
t-note  with 

ise  excessive 

um  a 
same 

jdefle 

llowable  sh 
,  page  567, 

actions 

ears  in 
relating 

•Fi 

■omP 

acket 

Comp 

mion, 

Carnegie  St 

eel  Compan 

y,  Pit 

tsburgh,  Pa. 

i"  a'l 

Tables  of  Safe  Loads  for  Steel  Reams  and  Girders 


583 


Table  V  *  (Continued).     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  for 
Steel  Channels 


Maxim 

am  bending  stress,  16  000  Ifc 

persq 

in.     Beams  secured  against  yielding  sidewise 

ight  of  sections 

Depth  and  we 

Span, 
ft 

Coeffi- 
cient of 
deflec- 
tion 

12-in 

lo-in 

40 

25 

20t4 

35 

30 

35 

30 

25 

20 

IS 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

2 

3 

4 

181.9 

152.6 

123.1 

93-6 

67.2 

164.6 

135.2 

105.8 

'76.4 

4^.0* 

0.07 
0.15 
0.27 

175. 1 
116.7 

87.5 

123.2 
82.1 
61.6 

no. I 
73.4 
55.1 

97.0 
64.7 
48.5 

106.2 
79-7 

95.8 
71.8 

85. 3 
64.0 

56.0 
42.0 

47.6 
35.7 

56.9 

5 

70.0 

63.7 

57.5 

51.2 

45.5 

49-3 

44.0 

38.8 

33.6 

28.5 

0.41 

6 

58.4 

53.1 

47.9 

42.7 

38.0 

41. 1 

36.7 

32.3 

28.0 

23.8 

0.60 

7 

50.0 

45.5 

41. 1 

36.6 

32.5 

35.2 

31.5 

27.7 

24.0 

20.4 

0.81 

8 

43.8 

39-8 

35.9 

32.0 

28. 5 

30.8 

27.5 

24.3 

21.0 

17.8 

1.06 

9 

38.9 

35.4 

31.9 

28.4 

25.3 

27.4 

24.5 

21.6 

18.7 

IS. 9 

1.34 

10 

35.0 

31.9 

28.7 

25.6 

22.8 

24.6 

22.0, 

19-4 

16.8 

143 

1.66 

II 

3'i.8 

29.0 

26.1 

23.3 

20.7 

22.4 

20.0 

17.6 

15.3 

13.0 

2.00 

12 

29.2 

26.6 

23.9 

21.3 

19.0 

20.5 

18.4 

16.2 

14.0 

11.9 

2.38 

13 

26.9 

24.5 

22.1 

19.7 

17.5 

19.0 

16.9 

14.9 

12.9 

II. 0 

2.80 

14 

25.0 

22.8 

20.5 

18.3 

16.3 

17.6 

15.7 

13.9 

12.0 

10.2 

3-24 

15 

23.3 

21.2 

19.2 

17. 1 

15.2 

16.4 

14.7 

12.9 

II. 2 

9.5 

3.72 

i6 

21.9 

19.9 

18.0 

16.0 

14.2 

15.4 

13.8 

12. 1 

10.5 

8.9 

4.24 

17 

20.6 

18.7 

16.9 

15. 1 

13.4 

14.5 

13.0 

II. 4 

9.9 

8.4 

4.78 

i8 

19-5 
18.4 

17.7 
16.8 

16.0 

14.2 

12.7 

13.7 

12.2 

10.8 

9-3 
8.8 

7.9 

5. 36 
5. 98 

19 

15. 1 

13. 5 

12.0 

13.0 

II. 6 

10.2 

7.5 

20 
21 

17.5 
16.7 

15.9 
15.2 

14.4 
13.7 

12.8. 

1 1. 4 

12^3 

II. 0 

._?iZ. 

8.4 

..111. 

6.62 
730 

12.2 

10.8 

II. 7 

10.5 

9.2 

8.0 

6.8 

22 

15.9 

14. 5 

13. 1 

II. 6 

10.4 

II. 2 

10. 0 

8.8 

7.6 

6.5 

8.01 

23 

IS. 2 

13.9 

12. 5 

II. I 

9-9 

8.76 

24 
25 

_Hl?. 

13.3 

12.0 

10.7 

__9A 

9.53 

10.35 

14.0 

'12'.  8" 

II. 5 

10.2 

9.1 

26 

13.5 

12.3 

II. I 

9.8 

8.8 

II. 19 

Loa 

ds  abc 

)ve  the  upper 

heavy 

lines  will  cause  rm 

ixirnum  allowable  a 

lears  in 

webs. 

See, 

also,  paragrap 

hs  in  t 

ext  and  foot-note  w 

ith  same,  page  567, 

relating 

to  we 
Loa 

b-buck 
dsbel 

ling  in  beams 
DW  the  lower 

broken 

lines  will  cause  exc 

essive  deflections 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


584 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


Table  V  *  (Continued).     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  for 
Steel  Channels 


Maximum  bending  stress,  i 

S  000 

lb  per  sq 

in. 

Beams  secured  against  yielding  sidewise 

Span, 
ft 

Depth  and  weight  of  sections 

Coeffi- 
cient of 
deflec- 
tion 

9-in 

8-in 

7-in 

25 

20 

IS 

I3V4 

21 H 

m 

V  16M 

13^^ 

11V4 

I9?4 

nVi 

14^4 

12H 

9H 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

no. 7 

81.4 

9^.1 

78.4 

63.8 

49.1 

88.6 

73.9 

59.2 

44.S 

2 

3 

83.8 

55. 9 

72.0 
48.0 

51.8 

41.4 

63.7 
42.5 

58.. 
39. < 

)S3.2 
)3S.S 

48.0 
32.0 

35-2 
28.7 

SO. 6 
33.7 

46.0 
30.7 

41.4 

27.6 

^6.8 

29-4 

0.07 
0.15 

40.2 

37.4 

24.621.4 

4 

41.9 

36.0 

30.1 

28.0 

31.8 

29.5 

J26.6 

24.0 

21.5 

25. 3 

23.0 

20.7 

18.4 

16. 1 

0.27 

5 
6 

33.5 
27.9 

28.8 
24.0 

24.1 
20.1 

22.4 
18.7 

25. 5 
21.2 

23.^ 
I9.i 

121.3 

17.7 

19.2 

17.2 

20.2 
16.9 

18.4 
15.3 

26.6 
13.8 

14.7 
12.3 

12.9 
10.7 

0.41 
0.60 

16.0 

14.4 

7 

23.9 

20.6 

17.2 

16.0 

18.2 

16.' 

IS  2 

13.7 

12.3 

14.4 

13.1 

II. 8 

10.5 

9.2 

0.81 

8 

20.9 

18.0 

IS. I 

14.0 

15.9 

14.^ 

13.3 

12.0 

10.8 

12.6 

11.5 

10.4 

9.2 

8.0 

1.06 

9 

18.6 

16.0 

13.4 

12.5 

14.2 

13.C 

II. 8 

10.7 

9.6 

II. 2 

10.2 

92 

8.2 

7.1 

I  34 

10 

16.8 

14.4 

12. 1 

II. 2 

12.7 

II. 7 

10.6 

9.6 

8.6 

10. 1 

9.2 

83 

7.4 

6.4 

1.66 

II 

IS  2 

13  I 

II. 0 

I0.2 

II. 6 

10.6 

9-7 

8.7 

7.8 

9.2 

8.4 

7.5 

6.7 

5.8 

2.00 

12 

14.0 

12.0 

10. 1 

9  3 

10.6 

9.7 

8.9 

8.0 

7.2 

8.4 

7.7 

6.9 

6.1 

5.4 

2.38 

13 

12.9 

II. I 

9.3 

8.6 

9.H 

9.C 

8.2 

7.4 

6.6 

7.8 

7.1 

6.4 

57 

4.9 

2.80 

14 
IS 

12.0 
II. 2 

10.3 
9.6 

8.6 
8.0 

8.0 
75 

9.1 
8.5 

8..1 
7.8 

7.6 
7.1 

6.9 
6.4 

6.2 

57 

7.2 

6.6 

5.9 

5.3 

4.6 

3.24 
3.72 

6.7 

6.1 

5.5 

4.9 

4.3 

i6 
17 

10.5 
9-9 

9.0 
8.5 

75 
7.1 

7.0 
6.6 

8.0 

7.3 

6.7 

60 

54 

6.3 

5-7 

5.2 

4.6 

4.0 

4.24 
4.78 

7.5 

6.9 

6.3 

5.6 

S.I 

i8 
19 

9  3 

8.0 

6.7 

6.2 

7.1 

6.5 

59 

5  3 

4.8 

5.36 
5.98 

8.8 

7.6 

6.3 

5.9 

20 

8.4 

7.2 

6.0 

5.6 

6.62 

Span, 

Depth  and  weight  of  sections 

Coeffi- 
cient of 

6-in 

S-in 

4-in 

3-in 

ft 

deflec- 

15^2 

13 

ioV{ 

8 

11!^ 

9 

6^2 

7M 

6M 

S»4 

6 

5 

4 

tion 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

47-7 

26.0 

21.7 

158 

I 

2 

67.6 

5=8 

38.2 

24.0 

44.4 
22.2 

33.0 

19.0 

24.4 
12.2 

W.2 
II.  I 

144 

14 
7 

7 
4 

13.1 
6.6 

10.2 
5.8 

0.02 
0.07 

34  7 

30.8 

26. 

?    23.1 

18.9 

10. 1 

3 

23.2 

20.5 

17. 

?    15.4 

14.8 

12.6 

10.5 

8.1 

7.4 

6.7 

4 

9 

4  4 

3.9 

0.15 

4 

17.4 

IS. 4 

13. 

1    II. 6 

II. I 

9.5 

79 

6.1 

5.6 

5.1 

3 

7 

3.3 

2.9 

0.27 

5 
6 

7 

13  9 
II. 6 
99 

12.3 
10.3 
8.8 

10. J 

9.< 

7. 

i     9.2 

3       7.7 

7     6.6 

8.9 
7.4 
6.3 

7.6 
6.3 
54 

6.3 

53 

4-5 

4.9 

4.5 

4.1 

2 

9 

2.6 

2.3 

1.9 

0.41 
0.60 
0.81 

4.1 
3.5 

3.7 
3.2 

3.4 
29 

2 

5 

2.2 

2 

I 

1.9 

1.7 

8 

8.7 

7.7 

6. 

1     5.8 

55 

4.7 

4.0 

3.0 

2.8 

2.5 

I 

8 

1.6 

1. 5 

1.06 

9 

7.7 

6.8 

6.< 

D       S.I 

4.9 

4.2 

3.S 

2.7 

2.5 

2.2 

1.34 

lO 

II 

6.9 
6.3 

6.2 

5.^ 

\       4.6 
)       4.2 

_4  4 
4.0 

3.4 

3.2 
7.9 

2.4 

2.2 

2.0 

1.66 
2.00 

5.6 

4.< 

12 
13 

5.8 

5.1 

4  . 

>      3  9 

3.7 

32 

2.6 

2.38 
2.80 

5  3 

4.7 

4- 

[      3.6 

14 

5.0 

4.4 

3.{ 

I      3.3 

3  24 

Loads  above  the  upper  heavy  lines  will  cause  maximum  allowable  sli 

ears  in 

wet>s.    See.  also,  paragraphs  in  text  and  foot-note  with  same,  page  567. 

relating 

to  web-buckling  in  beams 

Loads  below  the  lower  broken  lines  will  cause  excessive  deflections 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 


Tables  of  Safe  Loads  for  Steel  Beams  and  Girders  585 

Table  VI.*    Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  for  Steel  H  Beams 

Maximum  bending  stress,  i6  ooo  lb  per  sq  in.     Secured  against  yielding  sidewise 


Depth  and  weight  of  sections 

Coefficients 

of 
deflection 

Span, 
ft 

8-in 
34.0-lb 

6-in 
23.8-lb 

5-in 
18.7-lb 

4-in 
13.6-lb 

3 
4 

s 

7 
8 

9 

10 

II 

12 

13 
14 
IS 
i6 

17 
i8 

25.0 

3T.3 

19.0 
14-3 
11.4 

o.iS 
0.27 
0.41 

37-6 

25-4 
20.3 

32.1 

60.0 

51.3 

44.0 
38s 
34.2 
30.8 
28.0 
25.6 

23-7 
22.0 
20.5 
19.2 

26.7 

22.9 
20.1 

17.8 
16.0 
14.6 
13-4 

16.9 

14.5 
12.7 

11.3 
10. 1 

9-5 

8.1 
71 

0.60 

0.81 
1.06 

1.34 
1.66 
2.00 
2.38 

2.80 
3.24 
3.72 
4.24 
4.78 
5.36 

6.3 
5.7 

9.2 
8.5 

12.3 
11.5 

18. 1 
171 

Table  VH.  t    Safe  Uniform  Loads  in  Pounds  for  SmaU  Steel  Channels,  or 

Grooved  Steel 

Computed  for  a  fiber-stress  of  16  000  lb  per  sq  in 

Secured  against  yielding  sidewise 


Depth, 
in 

Weight 

Span  in  feet 

Section- 
number 

foot, 
lb 

2 

2.S 

3 

3.5 

4 

4.5 

5 

6 

2H 

3.80 

378s 

3028 

2523 

2  163 

I  892 

1682 

I  514 

I  261 

2 

2 

2.90 

2560 

2048 

I  706 

I  463 

I  280 

1 138 

I  024 

853 

3 

4 

2 

3.60 

2880 

2304 

I  920 

1643 

1440 

I  280 

I  152 

960 

2 

3.60 

3  120 

2496 

2080 

1783 

I  560 

138b 

I  248 

I  040 

2 

2.60 

1    2256 

1804 

IS04 

I  289 

I  128 

I  000 

902 

752 

6 

2 

2.00 

I  418 

II34 

945 

810 

709 

630 

5t>7 

472 

7 
g 

iH 

1. 13 

907 

726 

60s 

S18 

454 

403 

363 

302 
256 

iH 

1.32 

768 

614 

512 

439 

384 

341 

307 

9 
10 

iH 

1.46 

868 

694 

578 

496 

434 

386 

347 

289 

iM 

0.94 

47S 

380 

316 

271 

237 

211 

190 

II 

iH 

1. 12 

469 

375 

313 

268 

234 

208 

188 

12 

iH 

1. 00 

437 

350 

291 

250 

218 

194 

175 

13 

I 

0.83 

336 

268 

224 

192 

168 

.... 

14 

I 

0.68 

266 

212 

177 

152 

133 

IS 

li 

0.67 

224 

180 

149 

128 

112 

16 

li 

0.69 

229 

183 

152 

130 

.... 

17 

Va 

0.53 

133 

106 

88 

•  From  Pocket  Companion,  Carnegie  Steel 
t  Complied  by  F.  E.  Kidder.     See  note  on 


Company,  Pittsburgh,  Pa. 
page  570. 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


Table  VIII.*     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  for  Steel  Angles 

with  Equal  Legs.     (See  page  566.) 

Neutral  Axis  Parallel  to  Either  Leg 


Maximum  bendi 

ng  stress,  16  000  lb  per  sq  in.     Secured  against  yielding  side  wise 

Size,       \ 

hick- 

less, 

1-ft 
span 

Maximum 

span,  360 

X  deflection 

Size, 

Thick- 

i-ft 
span 

Maximum 

span,  360 

X  deflection 

in 

in 

Length, 

in 

in 

Safe 
load 

Safe 
load 

Length, 
ft 

Safe 
load 

Safe 

load 

ft 

8X8         I 

H 

186.99 

8.31 

22.5 

zHXsVi 

^Me 

24.00 

2.55 

9-4 

8X8         I 

Ha 

177.81 

7.87 

22.6 

s'AXiVz 

H 

22.51 

2.37 

^l 

8X8         I 

168.53 

7.43 

22.7 

3V^X3F2 

^Hg 

20.91 

2.18 

9.6 

8X8 

me 

159  15 

6.98 

22.8 

35^^X3'/^ 
3M2X3K2 

Me 

19.31 
17.60 

2.00 
1. 81 

9-7 
9.7 

8X8 

% 

149-55 

6.53 

22.9 

3HX3K2 

'/^ 

15.89 

1.62 

9.8 

8X8 

13/16 

139.84 

6.08 

23.0 

3/2X3^/2 

Me 

14.08 

1.42 

9-9 

8X8 

% 

130.03 

5.63 

23.1 

sHXsli 

H 

12.27 

1.23 

10. 0 

8X8 

Hie 

120.00 

5.18 

23.2 

3K2X3K2 

Me 

10.45 

1.04 

10. 1 

8X8 

H 

109.87 

4.73 

23.2 

s'AXsV^ 

H 

8.43 

0.83 

10.2 

8X8 

Me 

99  63 

4.28 

23.3 

3     X3 

% 

13.87 

1.69 

8.2 

8X8 

H 

89.28 

3.82 

23.4 

3     X3 

Me 

12.69 

I  53 

8.3 

3     X3 

Y' 

11.41 

1-37 

8.3 

6X6         1 

6X6 

6X6 

91.41 
86.51 
81.39 

5.48 
5-16 
4.84 

16.7 
16.8 
16.8 

3     X3 
3     X3 
3     X3 
3     X3 

Me 
% 
Me 

10.13 
8.85 
7.57 
6.19 

1. 21 

1.04 
0.88 
0.71 

8.4 
8.5 
8.6 

8.7 

6X6 

1^6 

76.27 

4.51 

16.9 

6X6 

% 

71.04 

4.18 

17.0 

2HX2V2 

Vi 

7.79 

1.15 

6.8 

6X6 
6X6 
6X6 

iMo 
Via 

65.81 
60.37 
54.83 

3.85 
3-51 
3.17 

17. 1 
17-2 
17-3 

2l/2X2^1j 
2l^^X2»-i 
2K2X2K2 
2K>X2H 

Me 
Me 

6.93 
6.08 
5.12 
4.16 

1. 01 
0.87 
0.72 
0.58 

6.9 
7.0 
7.1 
7.2 

6X6 

H 

49-17 

2.83 

17.4 

21^^X21/2 

Me 

3.20 

0.44 

7.3 

6X6 

Me 

43.41 
37  65 

2.48 
2.14 

17.5 

2}'^X2H 

H 

2.13 

0.29 

7.4 

6X6 

% 

17.6 

2      X2 

Me 

4.27 

0.79 

5.4 

2      X2 

3/i 

3.73 

0,68 

5.5 

5X5         1 

61.87 

4.55 

13.6 

2      X2 

Me 

3.20 

0.57 

5.6 

5X5 

^Me 

58.56 

4.28 

13.7 

2      X2 

M 

2.67 

0.46 

5.7 

5X5 

H 

55.15 

4.00 

13.8 

2      X2 

Me 

2.03 

0.35 

5.8 
5.8 

5X5 

me 

51.73 

3.73 

13.9 

2      X2 

78 

1.39 

0.24 

5X5 

y^ 

48.32 

3.45 

14 -O 

iHXiYi 

Me 

3.20 

0.68 

4.7 

5X5 

iMe 

44.80 

3.18 

14. 1 

I>tXl3/4 

3/i 

2.77 

0.60 

4.7 

5X5 

H 

41.17 

2.90 

14.2 

i%xm 

Me 

2.45 

0.51 

4.8 

5X5 

rie 

37,44 

2.62 

14.3 

iliXiM 

U 

2.03 

0.41 

4.9 

5X5 

M 

33-6o 

2.34 

14.4 

mxiH 

Me 

1.49 

0.30 

5.0 

5> 

:5 

Via 

29.76 

2.06 

14.5 

1^4X1^4 

H 

1.07 

0.21 

5.1 

5> 

:5 

% 

25.81 

1. 78 

14.5 

iHXi>^ 
I'/^Xii/^ 

Me 

2.03 
1. 71 

0.51 
0.42 

4.0 
4.1 

4> 

C4 

»M6 

32.11 

2.95 

10.9 

I'/^XiH 

M 

1.39 

0.33 

4.2 

4X4 

H 

29.97 

2.73 

II. 0 

iHXiV^ 

Me 

1.07 

0.25 

4.3 

4X4 

»He 

27.84 

2.51 

II. I 

IHXIK2 

H 

0.77 

0.17 

4.4 

4X4    . 

H 

25.60 

2.29 

II. 2 

iHXiH 

Me 

1. 17 

0.36 

3.3 

4X4 

Me 

23.36 

2.07 

II. 3 

iHXiH 

H 

0.97 

0.29 

3.4 

4X4 

H 

21.01 

1.85 

II.  4 

iHXiH 

Me 

0.76 

0.22 

3.5 

4X4 

Me 

18.67 

1.63 

11.4 

iHXiH 

H 

0.52 

0.14 

3.6 

4X4 

H 

16.21 

1. 41 

II. 5 

I    Xi 

M 

0.60 

0.22 

2.6 

4X4 

Me 

13.76 

1. 19 

II. 6 

I    XI 

Me 

0.47 

0.17 

2.7 

4X4 

H 

11.20 

0.96 

II. 7 

I    XX 

H 

0.33 

0.12 

2.8 

1 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


587 


Table  IX.*     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  of  Steel  Angles 
with  Unequal  Legs.       (See  page  566.) 

Neutral  Axis  Parallel  to  Shorter  Leg 

Maximum  bending  stress,  i6  000  lb  per  sq  in.     Secured  against  yielding  sidewise 


I-ft 

Maximum 

I-ft 

Maximum 

Size. 

Thick- 

span 

span,  360 
X  deflection 

Size, 

Thick- 

Span 

span,  360 
X  deflection 

in 

ness, 

in 

ness, 

in 

Safe 

Safe 

Length, 

in 

Safe 

Safe 

Length, 

load 

load 

ft 

load 

load 

ft 

8X6 

I 

161. 17 

7.49 

21.5 

6X3^2 

I 

83.52 

S.S7 

iS.o 

8X6 

1^6 

152.21 

7.04 

21.6 

6X3H 

15/6 

79.04 

5. 24 

IS.  I 

8X6 

% 

143.04 

6.59 

21.7 

6X3H 

% 

74.45 

4.90 

15.2 

8X6 

1^6 

133.87 

6.14 

21.8 

6X31^^ 

1^6 

69.87 

4.57 

IS. 3 

8X6 

% 

124.48 

5.68 

21.9 

6X3I/2 

H 

65.07 

4.23 

15.4 

8X6 

1M6 

114.88 

5.22 

22.0 

6X3H 

1H6 

60.27 

3.89 

IS. 5 

8X6 

•>i 

105.28 

4.76 

22.1 

6X3^^ 

^A 

55.36 

3.55 

IS. 6 

8X6 

Me 

95.47 

4.30 

22.2 

6X3K2 

Ha 

50.35 

3.21 

IS. 7 

8X6 

\^ 

85.55 

3.84 

22.3 

6X3Vi 

H 

45.23 

2.86 

15.8 

8X6 

ViO 

75.41 

3.37 

22.4 

6X3!/^ 

7/6 

40.00 

2.52 

15.9 

6X3i/i 

% 

34.67 

2.17 

16.0 

8X3'/^ 

I 

146.03 

7-53 

19-4 

■    6X3K2 

5/6 

29.23 

1.83 

16.0 

8X3H 

^Me 

138.03 

7.08 

19.5 

8X3'/^ 

% 

129.92 

6.63 

19.6 

8X3^^^ 

13/16 

121.60 

6.17 

19.7 

5X4 

I'i 

53.23 

4.00 

13  3 

8X3M2 

M 

113.17 

5.72 

19.8 

5X4 

13.i6 

50.03 

3.73 

13.4 

8X3^/^ 

iHe 

104.58 

5.23 

19.9 

5X4 

% 

46.61 

3.46 

13. 5 

8X3H 

H 

95.79 

4.78 

20.0 

5X4 

1/6 

43.20 

3.19 

13.5 

^XM 

9/16 

86.93 

4.32 

20.1 

5X4 

% 

39-79 

2.92 

13.6 

8X3H 

H 

77.97 

3.86 

20.2 

5X4 

Vie 

36.16 

2.64 

13.7 

8X3K2 

7/16 

68.80 

3.39 

20.3 

5X4 

H 

32.53 

2.36 

13.8 

5X4 

Vie 

28.80 

2.07 

13.9 

7X3>^ 

I 

112.85 

6.52 

17.3 

5X4 

H 

24.96 

1.78 

14.0 

7X3I/2 

iMe 

106.67 

6.13 

17.4 

7X3^/^ 

H 

100.48 

5. 75 

17.5 

7X3H 

13/6 

94.08 

5.36 

17.6 

5X3H 

% 

52.05 

4.04 

12.9 

7X3K2 

3/ 

87.68 

4.97 

17.6 

5X3H 

.     13/6 

48.85 

3.76 

13.0 

7X3H 

.Hie 

81.07 

4.58 

17.7 

5X3H 

% 

45.65 

3.49 

13.1 

7X3!'i 

H 

74.35 

4.18 

17.8 

5X3!/^ 

11/6 

42.35 

3.21 

13.2 

7X3H 

9/6 

67.52 

3.77 

17.9 

5X3  V^ 

% 

38.93 

2.93 

13.3 

7X3'/^ 

V2 

60.59 

3.37 

18.0 

5X31-^ 

M6 

35.41 

2.64 

13.4 

7X3H 

7/6 

53.44 

2.96 

18. 1 

5X3!/^ 

Vl 

31.89 

2.36 

13. 5 

7X3^/^ 

% 

46.19 

2.54 

18.2 

5X3I/2 

7/6 

28.16 

2.07 

13.6 

5X3\^ 

% 

24.43 

1.79 

13.7 

6X4 

I 

85.55 

5.56 

15.4 

sXsH 

5/6 

20.69 

1. 51 

13.7 

6X4 

15/6 

80.96 

5.22 

15. 5 

6X4 

7/i 

76.27 

4.89 

15.6 

SX3 

13/6 

47.47 

3.77 

12.6 

6X4 

1^6 

71.47 

4.55 

IS. 7 

5X3 

M 

44.37 

3.49 

.12.7 

6X4 

3/ 

66.67 

4.22 

15.8 

5X3 

iHe 

41.17 

3.22 

12.8 

6X4 

11/6 

61.65 

3.88 

IS. 9 

5X3 

% 

37.87 

2.94 

12.9 

6X4 

H 

56.64 

3.54 

16.0 

5X3 

9/6 

34.45 

2.65 

13.0 

6X4 

^6 

51.52 

3.20 

16. 1 

5X3 

H 

31.04 

2.37 

13.1 

6X4 

H 

46.19 

2.85 

16.2 

5X3 

7/6 

27.52 

2.09 

13.2 

6)^4 

M6 

40.85 

2.51 

16.3 

5X3 

% 

23.89 

1.80 

13.3 

6X4 

3/i 

35.41 

2.16 

16.4 

5X3 

5/6 

20.16 

1. 51 

13.4 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 


588 


Strength  of  Beams  and  Beam  Girders 


Table  IX  *  (Continued).     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds 

for  Steel  Angles  with  Unequal  Legs.     (See  page  566.) 

Neutral  Axis  Parallel  to  Shorter  Leg 

Maximum  bending  stress,  16  000  lb  per  sq  in.     Secured  against  yielding  side  wise 


i-ft 

Maximum 

i-ft 

Maximum 

Size, 

Thick- 

span 

span, 360 
X  deflection 

Size, 

Thick- 

span 

span,  360 
X  deflection 

ness. 

in 

. "  ' 

in 

in 

Safe 

Safe 

Length, 

in 

Safe 

Safe 

Length, 

load 

load 

ft 

load 

load 

ft 

4HX3 

13/16 

38.61 

3.36 

11.5 

3     X2I/2 

Me 

12.27 

1.53 

8.0 

4HX3 

H 

36.  OS 

3. II 

TI.6 

3     X2I/2 

Vi 

11.09 

1.37 

8.1 

4HX3 

I'/ie 

33-49 

2.87 

II. 7 

3     X2i/i 

Me 

9-92 

1.22 

8.1 

4HX3 

H 

30.83 

2.62 

II. 8 

3     X2K2 

% 

8.64 

1.06 

8.2 

4^^X3 

Me 

28.16 

2.38 

II. 8 

3     X2I/2 

Me 

7.36 

0.89 

8.3 

4HX3 

K2 

25.28 

2.13 

II. 9 

3     X2i^^ 

H 

5.97 

0.71 

8.4 

4HX3 

Me 

22.40 

1.87 

12.0 

4V^X3 

H 

19.52 

1. 61 

12. 1 

3     X2 

1/4 

10.67 

1.39 

7-7 

4HX3 

Me 

16.43 

1. 35 

12.2 

3     X2 

Me 

9-49 

1.22 

7.8 

4     X3I/2 

iMe 

31.15 

2.94 

10.6 

3      X2 

% 

8.32 

1.05 

7.9 

4     X33'^ 

H 

29  23 

2.73 

10.7 

3     X2 

Me 

7.04 

0.88 

8.0 

4     X3H 

iMe 

27 .  20 

2.52 

10.8 

3      X2 

M 

5.76 

0.71 

8.1 

4     X3^/^ 

H 

25 .  07 

2.3c 

10.9 

4     X3>^ 

^16 

22.93 

2.08 

II. 0 

2M2X2 

Vi 

7.47 

1. 15 

6.5 

4     X3'/^ 

1/^ 

20.69 

1.86 

II. I 

2HX2 

Me 

6.72 

1.02 

6.6 

4     X3H 

7/16 

18.35 

1.64 

II. 2 

2M2X2 

% 

5.87 

0.88 

6.7 

4     X3'/^ 

3/i 

16.00 

1. 41 

II. 3 

2I/2X2 

Me 

5.01 

0.74 

6.8 

4     X3H 

5/16 

13.44 

1. 18 

II. 4 

2^/^X2 

H 

4.05 

0.59 

6.9 

4     X3 

13/i6 

30.61 

2.97 

10.3 

2K2X2 

Me 

3.09 

0.44 

7.0 

4     X3 

M 

28.59 

2.75 

10.4 

21.4X2 

\^ 

2.13 

0.30 

7.1 

4     X3 

me 

26.56 

2.53 

10.5 

4     X3 

% 

24.53 

2.31 

10.6 

2\^X\V2 

Me 

4.69 

0.73 

6.4 

4     X3 

Me 

22.40 

2.09 

10.7 

2l/4Xll/2 

M 

3.84 

0.59 

6.5 

4     X3 

I'i 

20.16 

1.87 

10.8 

2V2Xll/i 

Me 

2.99 

0.45 

6.6 

4     X3 

Me 

17.92 

1.64 

10.9 

4     X3 

% 

15.57 

1.42 

II. 0 

2KX1I/2 

J'i 

5.76 

1.02 

5.6 

4     X3 

Me 

13.12 

1. 19 

II. 0 

2HX1I/2 

Me 

512 

0.90 

5.7 

4     X3 

H 

10.67 

0.96 

II. I 

2HX1H 

H 

4.48 

0.77 

5.8 

3HX3 

i^e" 

23.47 

2.57 

9.1 

2l/4Xll/2 

Me 

3.84 

0.65 

5.9 

3l'^X3 

% 

21.87 

2.38 

9.2 

2i/4Xii/i 

M 

3.20 

0.53 

6.0 

3^X3 

iMe 

20.37 

2.19 

9-3 

2HXI1/4 

Me 

2.45 

0.40 

6.0 

3HX3 

S/^ 

18.77 

2.00 

9.4 

3HX3 

9/ie 

17.17 

1. 81 

95 

2      Xll/4 

H 

3.63 

0.70 

5.2 

3^/^X3 

^^ 

15.47 

1.62 

9.5 

2      XlH 

Me 

3.09 

0.58 

5.3 

3HX3 

Me 

13.76 

1.43 

9.6 

2      Xll/i. 

M 

2.56 

0.47 

5.4 

3^X3 

% 

12.05 

1.24 

9.7 

2      X1K2 

Me 

1.92 

0..35 

5-5 

33'^X3 

Me 

10.24 

1.05 

9.8 

2      Xll/i 

\^ 

1.39 

0.24 

5.6 

3l'^X3 

H 

8.32 

0.84 

9.9 

2      Xll/i 

K 

2.45 

0.47 

5.2 

31/^X21/^ 

iMe 

19- 73 

2.19 

9.0 

2    XiH 

Me 

1.92 

0.36 

5.3 

3»/^X2i/^ 

5/i 

18.24 

2.00 

91 

3^/^X21.^ 

Me 

16.64 

1.82 

9.1 

I%Xll/4 

H 

1.92 

0.42 

4.6 

3HX2].i 

^ 

15.04 

1.63 

9.2 

iMXiH 

Me 

1.49 

0.32 

4.7 

3^^X2H 

Me 

13.44 

1.44 

9.3 

i3/4Xii/i 

H 

1. 00 

0.21 

4.8 

3V4X2i/^ 

34 

11.73 

I  24 

9-4 

ii/4Xii/4 

Me 

1. 71 

0.44 

39 

3*/^X2i/^ 

Me 

9.92 

1.04 

9-5 

iHXii/4 

M 

1.39 

0.35 

4.0 

3^X21/^ 

M 

8.00 

0.83 

9.6 

ii/4XiM 

Me 

1.07 

0.26 

4.1 

♦  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


689 


Table  X.*     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  for  Steel  Angles 

with  Unequal  Legs.     (See  page  s66.) 

Neutral  Axis  Parallel  to  Longer  Leg 

Maximum  bending  stress,  i6  ooo  lb  per  sq  in.     Secured  against  yielding  sidewise 


I-ft 

Max 

imum 

i-ft 

Maximum 

Size, 

Thick- 

Span 

span,  360 
X  deflection 

Size, 

Thick- 

span 

span,  360 
X  deflection 

in 

' 

in 

' 

in 

Safe 

Safe 

Length, 

in 

Safe 

Safe 

Length, 

load 

load 

ft 

load 

load 

ft 

8X6 

I 

95.15 

5.44 

17.5 

6X3I/2 

I 

30.93 

3.09 

10. 0 

8X6 

15/16 

89.92 

5. II 

17.6 

6X3H2 

15/6 

29.23 

2.90 

10. 1 

8X6 

H 

84.69 

4.79 

17.7 

6X3^^ 

% 

27.63 

2.71 

10.2 

8X6 

1M6 

79.36 

4.45 

17.8 

6X3H 

13/6 

25.92 

2.52 

10.3 

8X6 

H 

73.92 

4.13 

17.9 

6X3H 

% 

24.21 

2.33 

10.4 

8X6 

iMo 

68.37 

3.80 

18.0 

6X3H 

11/6 

22.51 

2.14 

lo.S 

8X6 

54 

62.72 

3.48 

18.0 

6X3H 

H 

20.69 

1.95 

10.6 

8X6 

^6 

56.96 

3.15 

18. 1 

6X3H 

9/6 

18.88 

1.76 

10.7 

8X6 

H 

SI. 09 

2.81 

18.2 

6X3K2 

l/i 

16.96 

1.57 

10.8 

8X6 

Ma 

45.12 

2.47 

18.3 

6X3»/^ 

7/6 

15.04 

1.38 

10.9 

6X3!/^ 

% 

13.12 

I  19 

II. 0 

8X35'^ 

I 

32.21 

3.10 

10.4 

6X3^^ 

Ma 

11.09 

1. 00 

II. I 

8X3I/2 

Me 

30.40 

2.90 

10.5 

8X3H 

H 

28.69 

2.71 

10.6 

8X3H 

me 

26.88 

2.52 

10.7 

5X4 

% 

35.31 

3.15 

II. 2 

8X3H 

94 

25.07 

2.33 

10.8 

5X4 

1^6 

33.17 

2.93 

11.3 

8X3K2 

11/16 

23.15 

2.13 

10.9 

5X4 

H 

30.93 

2.71 

II. 4 

SXsVi 

H 

21.33 

1.94 

II. 0 

5X4 

1/6 

28.69 

2.50 

II. 5 

8X3I/2 

ri6 

19.41 

1.74 

II. I 

5X4 

% 

26.45 

2.28 

II.  6. 

8X3V^ 

H 

17.49 

1.57 

II. 2 

5X4 

Vie 

24.11 

2.16 

II.  7 

8X3K2 

Vie 

15.57 

1.38 

II. 3 

5X4 

H 

21.76 

1.84 

II. 8 

5X4 

Vie 

19.31 

1.62 

11.9 

7X3'/2 

I 

31.57 

3.10 

10.2 

5X4 

% 

16.75 

1.40 

12.0 

7X3K2 

1^6 

29.87 

2.90 

10.3 

7X3K2 

% 

28.16 

2.71 

10.4 

SX3K2 

li 

26.88 

2.71 

9.9 

1X3^ 

1^6 

26.45 

2.52 

10.5 

5X3!/^ 

i-Me 

25.28 

2.53 

10. 0 

7X3K2 

% 

24.64 

2.33 

10.6 

5X3'/i 

% 

23.68 

2.34 

10.  r 

7X3K2 

iMe 

22.83 

2.14 

10.7 

5X3I/2 

11/6 

21.97 

2.15 

10.2 

7X3K2 

% 

21.01 

1.95 

10.8 

5X3K2 

H 

20.27 

1.97 

10.3 

7X3'/2 

Vie 

19.20 

1.76 

10.9 

5X3i/i 

9/6 

18.45 

1.78 

10.4 

7X3H 

¥2 

17.28 

1.57 

II. 0 

5X3I/2 

V2 

16.64 

1.60 

10.4 

7X3H 

7/16 

15.36 

1.38 

II. I 

5X3I/2 

lU 

14.83 

1. 41 

10.5 

iXs'A 

H 

13.44 

1. 19 

II. 2 

5X3K2 

H 

12.91 

1.22 

10.6 

5X3I/2 

5/6 

10.88 

1.02 

10.7 

6X4 

I 

40.43 

3.55 

II. 4 

6X4 

15/6 

38.29 

3.33 

II. 5 

6X4 

'A 

36.16 

3.12 

II. 6 

5X3 

13/6 

18.56. 

2.16 

8.6 

6X4 

13/6 

33.92 

2.90 

II. 7 

5X3 

H 

17.39 

2.00 

8.7 

6X4 

H 

31.68 

2.69 

II. 8 

5X3 

11/6 

16. II 

1.83 

8.8 

6X4 

11/6 

29.44 

2.47 

II. 9 

5X3 

% 

14.83 

1.67 

8.9 

6X4 

5/^ 

27.09 

2.26 

12.0 

5X3 

Vie 

13.55 

1. 51 

9.0 

6X4 

9/6 

24.64 

2.05 

12.0 

5X3 

\i 

12.27 

1.35 

9.1 

6X4 

H 

22.19 

1.84 

12. 1 

5X3 

Vie 

10.88 

1. 18 

9.2 

6X4 

7/6 

19-73 

1.62 

12.2 

5X3 

H 

9-49 

1.02 

9-3 

6X4 

H 

17.07 

1.39 

12.3 

5X3 

Vie 

8.00 

0.8s 

9.4 

?  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


590 


Strength  of  Beams  and  Beam  Girders 


Chap. 


Table  X  *  (Continued).     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  for 
Steel  Angles  with  Unequal  Legs.     (See  page  566.) 
Neutral  Axis  Parallel  to  Longer  Leg 
Maximum  bending  stress,  16  000  lb  per  sq  in.     Secured  against  yielding  sidewise 


4HX3 

4y2X3 

4HX3 

4V^X3 

4HX3 

4HX3 

4K2X3 

4HX3 

4K2X3 
X3H 
X33'^ 
X3H 

X3H 
X3H 
X33'^ 
X3H 
X33'^ 
X3 
X3 
X3 
X3 
X3 
X3 
X3 
X3 
X3 
X3 
3HX3 
3K2X3 
3K2X3 
3}'iX3 
31^^X3 
3HX3 
3M2X3 
3HX3 
3'AX3 
3V^X3 

3HX2y2 
3HX2H 
3HX2K2 

33'^X2H 
3V^X2i/i 

3MX2y2 
3yzX2M 

3\^X2\(i 


Thick- 
ness, 


% 

Vie 


'A 

1^6 


iHe 


y2 

7/16 


Ma 


i-ft 
span 


Safe 
load 


18.24 
17.07 
15.89 
14.61 
13.33 
12.05 
10.77 
9-39 
8.00 
24-53 
22.93 
21.33 
19  63 
17.92 
16.21 
14.40 
12.59 
10.67 
17.92 
16.7s 
15.57 
14.40 
13.12 
11.84 
10.56 
9.28 
7.89 
6.40 
17.60 
16.43 
15.36 
14.19 
12.91 
11.73 
10.45 
9.07 
7.68 
6.19 
10.56 
9.81 
8.96 
8. II 
7.25 
6.29 
5. 33 
4.37 


Maximum 

span,  360 

X  deflection 


Safe 
load 


2.15 
1.99 
1.83 
1.67 
1. 51 
1.35 
1. 19 
1.03 
0.87 
2.56 
2.37 
2.18 
1.98 
1.79 
1.60 
1.41 
1.22 
1.03 
2.15 
1.99 
1.83 
1.67 
1. 51 
1. 35 
119 
1.03 
0.87 
0.70 
2.17 
2.01 
1.85 
1.60 
1.52 
1.36 
1.20 
1.04 
0.87 
0.70 
1. 51 
1.39 
1.26 
1. 13 
0.99 
0.8s 
0.71 
0.58 


Length, 
ft 


Size, 


X2l/i 

X2I/2 

X2^ 

X2H 

X2\i 

X2K2 


3  X2 
3     X2 

3      X2 

3     X2 

3      X2 

2KX2 
2M2X2 

2l/^X2 

2K2X2 

2 1/2X2 
2I/2X2 
2l/^X2 

•2i/iXi3'^ 

21/2XI/2 

2j'iXll/2 

2HX1K2 
2}4Xl/2 
2/4Xll/i 
2HX1K2 
2MX1/2 
2l/Xl}'i 

2      X1/2 

2  XiH 

2  XiH 

2  X1/2 

2  X1/2 

2  XiH 

2  XiH 

1^4  XiM 
iMXiH 
i%XiH 

iMXiH 

l/2XlH 

iHXiH 


Thick- 
ness, 


y2 
7/6 


Vie 

Me 

3/8 


Via 

H 


Me 


I-ft 

span 


Safe 
load 


8.75 
7.89 
7.04 
6.19 
5.23 
4.27 

5.01 
4.48 
3.95 
3.41 

2.77 

4.91 
4.37 
3.84 
3-31 
2.67 
2.13 
1.49 

1. 81 
1.49 
1. 17 

2.77 
2.4s 
2.13 
1. 81 
1.49 
1. 17 

2.13 
1. 81 
1.49 
117 
0.80 
1.04 
0.80 

.1.01 

0.80 
0.56 

1. 17 
0.99 
0.78 


•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


591 


i|)l(B  XI.  *    Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  for  Steel  Tees  with 
.  Neutral  Axis  Parallel  to  Flange.     (See  page  566.) 
Maximum  bending  stress,  16  000  lb  per  sq  m.     Secured  against  yielding  sidewise 

EQUAL   FLANGE    AND    STEM 


• 

Maximum 

Maximum 

i-ft 

span, 360 

i-ft 

span,  360 

Size 

Weight 

span 

X  deflec- 

Size 

Weight 

span 

X  deflec- 

per 

tion 

per 

tion 

foot, 
lb 

foot, 
lb 

Flnge 

Stem 

Safe 

Safe 

L'gth 

Flnge 

Stem 

Safe 

Safe 

L'gth 

in 

in 

load 

load 

ft 

in 

in 

load 

load 

ft 

6H 

6H 

19.8 

52.80 

2.77 

19-1 

2^4 

2M 

4.9 

4-37 

0.69 

6.3 

4 

4 

13. 5 

21.55 

1.89 

II. 4 

2M- 

21/4 

4-1 

3.41 

0.53 

6 

4 

4 

4 

10.5 

16.85 

1.45 

II. 6 

2 

2 

4.3 

3.31 

0.59 

5 

6 

z\^ 

3K2 

II. 7 

16.32 

1.65 

9.9 

2 

2 

3.56 

2.77 

0.49 

5 

7 

3K2 

ZVi 

9.2 

12.69 

1.27 

10. 0 

1% 

1% 

3.09 

2.03 

0.41 

4 

9 

3 

3 

9-9 

11.73 

1. 41 

8.3 

iH 

1 1/2 

2.47 

1.49 

0.36 

4 

I 

3 

3* 

8.9 

10.45 

1.24 

8.4 

l'/2 

l'/^ 

1.94 

1. 17 

0.27 

4 

3 

3 

3 

7.8 

917 

1.08 

8.S 

1 1/4 

iM 

2.02 

I.  CI 

0.30 

3 

4 

3 

3 

6.7 

7.89 

0.92 

8.6 

iH 

iH 

1. 59 

0.78 

0.22 

3 

5 

2Y2 

2K> 

6.4 

6.29 

0.90 

7.0 

I 

I 

I. 25 

0.49 

o.i8 

2 

7 

2V1 

2V1 

5.5 

5.33 

0.75 

7.1 

I 

I 

0.89 

0.35 

0.12 

2 

9 

2H 

2V4 

4.9 

4-37 

0.69 

6.3 

.,::H7/ 

^lA^V- 

UN 

EQUAL   FLA^ 

fGE   AN 

D   Sl^E 

%A'.AiW. 

ff     y 

Maximum 

Maximum 

Si 

ze 

Weight 

per 

foot, 

lb 

l-ft 
span 

span,  360 
X  deflec- 
tion 

Si 

ze 

Weight 

per 

foot, 

lb 

I-ft 

span 

span,  360 
X  deflec- 
tion 

Flnge 

Stem 

Safe 

Safe 

L'gth 

Flnge 

Stem 

Safe 

Safe 

L'gth 

in 

in 

load 

load 

ft 

in 

in 

load 

load 

ft 

5 

3 

13.4 

11. 41 

1.25 

9-1 

3^2 

3 

10.8 

12.05 

1.42 

8.5 

5 

2V1 

10 

9 

8.96 

1.20 

7.5 

3M2 

3 

8.5 

9-49 

1.09 

8.7 

4M2 

3V2 

15 

7 

22.72 

2.37 

9.6 

3'/^ 

3 

7.5 

9.07 

1.04 

8.7 

43^^ 

3 

9 

8 

9.71 

1.07 

9-1 

3 

4 

II. 7 

20.69 

1.92 

10.8 

4K2 

3 

8 

4 

8.32 

0.90 

9.2 

3 

4 

10.5 

18.35 

1.68 

10.9 

4H 

2yi 

9 

2 

6.72 

0.87 

7.7 

3 

4 

9.2 

16. II 

1.47 

II. 0 

^V^ 

2H 

7 

8 

5.76 

0.74 

7.8 

3 

3K2 

10.8 

15.89 

1.66 

9.6 

4 

5 

IS 

3 

33.39 

2.40 

13.9 

3 

3M2 

9.7 

14.19 

1.46 

9-7 

4 

S 

II 

9 

25.92 

1.84 

14. 1 

3 

sVz 

8.5 

12.37 

1.26 

9.8 

4 
4 

4^^ 
4H 

14 

4 

27.09 
21.12 

2. IS 
1.65 

12.6 

3 
3 

2^/2 

7.1 
6.1 

6.40 
5.55 

0.89 
0.76 

7.2 

II 

2 

12.8 

2K2 

7.3 

4 

3 

9 

2 

9.60 

1.08 

8.9 

2K2 

3 

7.1 

8.96 

1.08 

8.3 

4 

3 

7 

8 

8.21 

0.90 

91 

2I/2 

3 

6.1 

7.68 

0.91 

8.4 

4 

2\^ 

8 

5 

6.61 

0.87 

7.6 

2^/2 

iH 

2.87 

0.93 

0.2S 

3.7 

4 

2H 

7 

2 

5.65 

0.73 

7.7 

2 

1 1/2 

3.09 

1.60 

0.36 

4.4 

4 

2 

7 

8 

4.27 

0.70 

6.1 

iH 

2 

2.45 

2.03 

0.37 

5.5 

4 

2 

6 

7 

3.63 

0.59 

6.2 

l\i 

iM 

1. 25 

0.57 

0.15 

6-1 

33^^ 

4 

12 

6 

21.12 

1.90 

II. I 

iH 

% 

0.88 

0.14 

0.07 

1-9 

Z\^ 

4 

9 

8 

16.  S3 

1.46 

II. 3 

... 

*  From  Pocket  Companion,  Carnegie  Steel  Coiripany,    Pittsburgh,  Pa. 


692  Strength  of  Beams  and  Beam  Girders  Chap.  15 

Bethlehem  I  Beams.*  Bethlehem  I  beams  from  8  to  24  in  in  depth,  in- 
clusive, have  the  same  strength,  or  section-modulus,  as  Standard  beams  of  the 
same  depth.  Bethlehem  beams,  due  to  the  proportions  of  the  sections,  weigh 
generally  10%  less  than  standard  beams  of  the  same  depth  and  strength.  For 
example  (Table  VI,  page  357),  a  Bethlehem  15-in  I  beam,  weighing  54  lb  per 
ft,  has  a  section-modulus  of  81.3.  The  corresponding  standard  section  (Table 
IV,  page  354)  is  a  15-in  I  beam  weighing  60  lb  per  ft,  with  a  section-modulus  of 
81.2.  Therefore,  for  equal  strength,  the  Bethlehem  beam  weighs  6  lb  per  ft 
less  than  the  standard  beam,  or  a  saving  of  10%  in  weight.  Similar  com- 
parisons with  other  sizes  of  the  standard  beams  previously  rolled  by  the  mills 
of  this  country  show  that  the  Bethlehem  I  beams  afford  an  equal  carrying 
capacity,  but  with  practically  10%  less  weight  of  metal. 

Thickness  of  Webs  and  Flanges.  It  is  claimed  that  the  webs  of  standard 
beams  are  much  thicker  than  required  for  a  scientifically  proportioned  section. 
It  is  impossible  to  reduce  the  web-thickness  in  the  ordinary  mill,  but  with 
the  Grey  Mill  webs  of  the  desired  thickness  can  be  produced.  By  adding  to 
the  FLANGES  part  of  the  metal  thus  saved,  the  strength  of  the  beam  is  main- 
tained, thereby  affording  a  lighter  section  of  the  same  strength.  The  wide 
FLANGES  give  increased  lateral  stiffness,  which  commends  the  use  of  such  beams 
in  many  cases,  where  the  narrow  flanges  and  lack  of  sufficient  lateral  rigidity 
prevent  the  use  of  ordinary  standard  beams. 

Depth  and  Weight  of  Bethlehem  Beams.  Formerly  the  heaviest  beams 
rolled  in  this  country  were  24  in  deep,  weighed  115  lb  per  ft,  and  had  a  section- 
modulus  of  246.3.  Whenever  greater  strength  was  required,  a  riveted  girder 
was  necessary.  Bethlehem  beams  are  rolled  to  a  maximum  depth  of  30  in, 
weigh  200  lb  per  ft,  and  have  a  section-modulus  of  610,  or  two  and  one-half 
times  the  strength  of  the  largest  beam  previously  rolled.  The  opportunity  for 
using  ROLLED  BEAMS  instead  of  built-up  riveted  girders  is,  therefore,  greatly 
increased.  These  rolled  beams  and  girders  afford  a  saving  in  weight  of  metal 
and  also  a  large  economy  in  cost  of  fabrication,  as  they  do  not  require  the 
punching,  assembling  and  riveting  necessary  for  building  a  riveted  girder. 

Bethlehem  Girder  Beams.*  Bethlehem  girder  beams,  from  8  to  24  in 
in  depth,  inclusive,  have  a  strength,  or  section-modulus,  equal  to  that  of  two 
minimum-weight  standard  I  beams  of  the  same  depth.  The  girder  beam, 
however,  weighs  generally  i2V2%  less  than  the  combined  weight  of  the  two 
standard  beams,  not  considering  the  saving  in  weight  of  separators  needed  for 
assembling  the  standard  beams  into  a  girder.  For  example,  a  Bethlehem  15-in 
girder  beam,  weighing  73  lb  per  ft  has  a  section-modulus  of  11 7. 8  (Table  VII, 
page  358).  Two  standard  15-in  I  beams,  each  weighing  42  lb  per  ft,  have 
together  a  like  section-modulus  of  117. 8  (Table  IV,  page  354).  Thus,  for  equal 
depth  and  strength,  the  girder  beam  weighs  11  lb  per  ft  less  than  the  two 
standard  beams.  This  is  a  saving  of  13%  in  weight,  not  including  separators, 
which  would  add  at  least  2},^  lb  per  ft  more  to  the  weight  of  the  assembled 
girder.  In  this  case  a  total  saving  of  16%  in  weight  is  afforded  by  the  Bethle- 
hem girder  beam,  besides  the  saving  in  the  cost  of  assembling  the  standard 
beams  into  a  girder. 

Safe  Uniformly  Distributed  Loads  for^ethlehem  I  Beams  and  Girder 
Beams.  Tables  XII  *  and  XIII,*  pages  594  to  602,  give  the  safe  uniformly 
distributed  loads  in  tons  of  2  000  lb,  on  Bethlehem  girder  beams  and  I  beams 
for  a  maximum  fiber-stress  of  16  000  lb  per  sq  in.    The  tabular  loads  include 

•  Adapted  by  permission  from  the  Catalogue  of  Bethlehem  Structural  Shapes,  Bethlc 
hesn  Steel  Company,  South  Bethlehem,  Pa. 


Oblique  Loading  of  Angles  Used  as  Beams 


603 


the  weight  of  the  beam,  which  must  be  deducted  to  obtain  the  net  load  a  beam 
will  support.  Safe  loads  for  intermediate  or  heavier  weights  of  beams  can 
be  obtained  from  the  separate  column  of  corrections,  given  for  each  size. 
This  last  column  of  the  table  states  the  increase  in  safe  load  for  each  pound 
of  increase  in  weight  per  foot  of  beam.  If  the  load  is  concentrated  at  the 
middle  of  the  span,  the  safe  load  is  one-half  the  safe  uniformly  distributed 
load  for  the  same  span.  The  safe  loads  on  short  spans  may  be  limited  by 
the  shearing  strength  of  the  web,  instead  of  by  the  maximum  fiber-stress 
allowed  in  the  flanges.  This  limit  is  indicated  in  the  tables  by  the  heavy  hori- 
zontal lines.  The  loads  given  above  these  lines  are  greater  than  the  safe  crip- 
pling or  buckling  strength  of  the  web,  and  must  not  be  used  unless  the 
webs  are  stiffened*  In  such  cases  it  will  generally  be  advisable  to  select  a 
heavier  beam  with  a  thicker  web.  To  use  these  tables  for  other  spans,  or  for 
other  distribution  of  the  loading,  see  explanation,  page  566.  To  use  these  tables 
for  beams  yielding  laterally,  see  Lateral  Deflection,  pages  566  and  670. 


Oblique  Loading  of  Angles  Used 
as  Beams  f 

Oblique  Loading  of  Purlins  on 
Sloping  Roofs.  (See,  also,  pages 
573,  1169  and  II 70.)  The  preceding 
Tables  VIII,  IX  and  X  for  safe  loads 
on  angles  are  based  on  the  neutral 
axis  being  parallel  to  one  of  the  legs. 
When  this  is  not  the  case,  as  in  roof- 
purlins  (Fig.  10),  the  strength  of  a 
given  angle  may  be  found  by  taking 
its  section-modulus  from  Table  XI  A 
and  using  the  fundamental  formula 
for  flexure  (page  557).  It  should  be 
noted  that  purlins  set  as  at  (a)  are 
stronger  than  {b),  Fig.  9a. 


Fig.  9a.     Strong    and  Weak    Setting    of 
Angle-Purlins  on  Sloping  Roofs 


Table  XI  A.     Section-Moduli  of  Angle-Purlins   Set  at   Right-Angles  to  Rafters, 
as  in  (a)  Fig.  9a,  and  Free  to  Move  in  Any  Direction.     Loading  Vertical. 


Purlin 


2  X 

2H  X 

2HX 
2HX 

3  X 
3       X 

3HX 


2         X 

2  X 
2HX 
2MX 

2MX 
2H  X 
2^  X 
2^X 

3  X 

3  X 

3HX 

s'AX 

4  X 
4       X 


M  angle.. 
}4  angle.. 
H  angle.. 
H  angle.. 
14  angle . . 
%  angle.. 
H  angle.. 
%  angle.. 
li  angle.. 
%  angle.. 
•)1o  angle. 
?/8  angle . . 
Vs  angle.. 
J^^  angle . . 


Slope  of  roof  in  inches  per  foot 


0.18 
0.30 
0.31 
0.42 
0.44 
0.64 
0.56 
0.84 
0.7S 
I. II 
1.48 
1.76 
2.50 
3  •  30 


c.  19 
0.31 
0.32 
0.44 
0.46 
0.67 
O.S9 
0.89 
0.80 
1. 18 
1-55 
1.86 
2.66 
3-52 


0.22 
0.38 
0.37 
0.52 
0.56 

D.82 
3.76 
I.  14 
I  .02 
1.47 
1.96 
2.34 
3.41 
^•52 


0.24 
0.41 

0.39 
0.55 

0.60 

0.89 
0.83 


1.58 

2.  12 
2.52 

3   70 

4.84 


0.26 
0.44 
0.42 
0.60 
0.65 
0.95 
0.89 
1.29 
I.  18 
I  .70 
2.30 
2.71 
4.00 
5.18 


0.31 
0.49 
0.48 
0.68 
0.74 
I  .06 
0.84 
I.  19 
1.27 
1.76 
2.06 
2.42 
317 
4.09 


*  See  pararaphs  and  foot-note,  page  567 
t  From  Notes  by  Robins  Fleming. 


relating  to  web-buckling  of  beams. 


594 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


Table  XII.     Safe  Uniform  Loads  in  Tons  of  2  000  Pounds  for  Bethlehem 
Girder  Beams 

Beams  secured  against  yielding  sidewise 


30-in  G 

28-in  G 

26-in  G 

Span, 
ft 

Add  for 
each  lb 

Add  for 
each  lb 

Add  for 
each  lb 

G3oa 

G30 

increase 

G28a 

G28 

increase 

G26a 

G26 

increase 

in 
weight 

in 
weight 

in 
weight 

200  lb 

180  lb 

180  lb 

165  lb 

160  lb 

150  lb 

18 

180.75 

161.87 

0.44 

153.75 

138.89 

0.41 

128. II 

117.47 

0.38 

19 

171.24 

153.35 

0.41 

145.66 

131.58 

0.39 

121.37 

III. 29 

0.36 

20 

102.68 

145.68 

0.39 

138.38 

125.00 

0.37 

115.30 

105.72 

0.34 

21 

154.93 

138.74 

0.37 

131.79 

119. OS 

0.35 

109.81 

100.69 

0.32 

22 

147.89 

132.44 

0.36 

125.80 

113.64 

0.33 

104.82 

96.11 

0.31 

23 

141.46 

126.68 

0.34 

120.33 

108.70 

0.32 

100.26 

91-93 

0.30 

24 

135.56 

121.40 

0.33 

115. 31 

104.17 

0.31 

96.08 

88.10. 

0.28 

25 

130.14 

116.55 

0.31 

110.70 

100,00 

0.29 

92.24 

84.58 

0.27 

26 

125.14 

112.06 

0.30 

106.44 

96.16 

0.28 

88.69 

81.32 

0.26 

27 

120.50 

107.91 

0.29 

102.50 

92.60 

0.27 

85.41 

78.31 

0.25 

28 

116.20 

104.06 

0.28 

9S.84 

89.29 

0.26 

82.36 

75.52 

0.24 

29 

112. 19 

100.47 

0.27 

95.43 

86.21 

0.25 

79-52 

72.91 

0.23 

30 

108.45 

97.12 

0.26 

92.25 

83.34 

0.24 

76.87 

70.48 

0.23 

31 

104.95 

93.99 

0.2s 

89.27 

80.65' 

0.24 

74.39 

68.21 

0.22 

32 

101.67 

91  05 

0.25 

86.48 

78.13 

0.23 

72.06 

66.08 

0.21 

33 

98-59 

88.29 

0.24 

83.86 

75.76 

0.22 

69.88 

64.07 

0.21 

34 

95.69 

85.70 

0.23 

81.40 

73-53 

0.22 

67.82 

62.19 

0.20 

35 

92.96 

83.25 

0.22 

79.07 

.  71.43 

0.21 

65.88 

60.41 

0.19 

36 

90.38 

80.93 

0.22 

76.88 

69.45 

0.20 

64.05 

58.73 

0.19 

37 

87.93 

78.75 

0.21 

74.80 

67.57 

0.20 

62.32 

57.15 

0.18 

38 

85.62 

76.67 

0.21 

72.83 

65.79 

0.19 

60.68 

55.64 

0.18 

39 

83.42 

74.71 

0.20 

70.96 

64.10 

0.19 

59.13 

54.22 

0.17 

40 

81.34 

72.84 

0.20 

69.19 

62.50 

0.18 

57.65 

52.86 

0.17 

41 

79-35 

71.06 

0.19 

67.50 

60.98 

0.18 

56.24 

51.57 

0.17 

42 

77.47 

69.37 

0.19 

65.89 

59.53 

0.17 

54.90 

50.34 

0.16 

43 

75.66 

67.76 

0.18 

64.36 

58.14 

0.17 

53.63 

49.17 

0.16 

44 

73.94 

66.22 

0.18 

62.90 

56.82 

0.17 

52.41 

48.06 

0.15 

45 

72.30 

64.75 

0.17 

61.50 

55.56 

0.16 

51.24 

46.99 

0.15 

46 

70.73 

63.34 

0.17 

60.16 

54.35 

0.16 

50.13 

45.97 

0.15 

47 

69.22 

61.99 

0.17 

58.88 

53.19 

0.16 

49.06 

44.99 

0.14 

48 

67.78- 

60.70 

0.16 

57.66 

52.09 

o.is 

48.04 

44.05 

0.14 

Safe  loads  given  inc 

ude  weigl 

it  of  beam 

Maximum  fiber-stre 

ss,  16  000  1 

b  per  sq  in 

The  section-numbe 

rs  are  give 

m  for  convenie 

nee  in  ide 

ntificati 

on  and 

ordering   . 

Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


595 


Table  XII  (Continued).     Safe  Uniform  Loads  in  Tons  of  2  000  Pounds 
for  Bethlehem  Girder  Beams 

Beams  secured  against  yielding  sidewise 


24-in  G 

20-in  G 

i8-in  G 

Add  for 
each  lb 

Add  for 
each  lb 

Add  for 
each  lb 

1    Span, 
ft 

G24a 

G24 

increase 

G2oa 

G20 

increase 

G18 

increase 

in 

weight 

in 
weight 

in 
weight 

140  lb 

120  lb 

140  lb 

112  lb 

92  lb 

12 
13 

ISS.61 
143.64 

133.60 
123.33 

•    0.52 
0.48 

130.43 

104.09 

0.44 
0.40 

78.59 

0.39 
0.36 

120.40 

96.09 

72.54 

14 

133.38 

114.52 

0.45 

III. 80 

89.23 

0.37 

67.36 

0.34 

IS 

16 
17 

124.48 

106.88 
100.20 

0.42 

0.39 
0.37 

104.34 

97.82 
92.07 

83.28 

78.07 
73.48 

0.3S 

0.33 
0.31 

62.87 

58.94 

55.47 

0.31 

0.29 
0.28 

116. 71 
109.84 

94.31 

18 

103.74 

89.07 

0.35 

86.95 

69.40 

0.29 

52.39 

0.26 

19 

98.28 

84.38 

0.33 

82.38 

65.74 

0.28 

49.63 

0.25 

20 

93.37 

80.16 

0.31 

78.26 

62.46 

0.26 

47.15 

0.24 

21 

88.92 

76.3s 

0.30 

74.53 

59  48 

0.25 

44.91 

0.22 

22 

84.88 

72.88 

0.29 

71.14 

56.78 

0.24 

42.87 

0.21 

23 

81.19 

69.71 

0.27 

68.05 

54.31 

0.23 

41.00 

0.20 

24 

77.80 

66.80 

0.26 

65.22 

52.05 

0.22 

39 .29 

0.20 

25 

74.69 

64.  IS 

0.25 

62.61 

49.97 

0.21 

37.72 

0.19 

26 

71.82 

61.66 

0.24 

60.20 

48.04 

0.20 

36.27 

0.18 

27 

69.16 

59-38 

0.23 

57. 97 

46.26 

0.19 

34.93 

0.17 

28 

66.69 

57.26 

0.22 

55.90 

44.61 

0.19 

33.68 

0.17 

29 

64.39 

55.29 

0.22 

53.97 

43.07 

0.18 

32.52 

0.16 

30 

62.24 

53.44 

0.21 

52.17 

41.64 

0.17 

31.43 

0.16 

31 

60.24 

51.72 

0.20 

50.49 

40.30 

0.17 

30.42 

O.IS 

32 

58.35 

50.10 

0.20 

48.91 

39.04 

0.16 

29 -47 

0.15 

33 

56.58 

48.58 

0.19 

47-43 

37.8s 

0.16 

'   28.58 

0.14 

34 

54.92 

47.  IS 

0.18 

46.04 

36.74 

0.15 

27.74 

0.14 

35 

53.35 

45.81 

0.18 

44.72 

35.69 

0.15 

26.94 

0.13 

36 

51.87 

44.54 

0.17 

43.48 

34.70 

o.is 

26.20 

0.13 

37 

50.47 

43.33 

0.17 

42.30 

33.76 

0.14 

25.49 

0.13 

38 

49.14 

42.19 

0.17 

41.19 

32.87 

0.14 

24.82 

0.12 

39 

47.88 

41.  II 

0.16 

40.13 

32.03 

0.13 

24.18 

0.12 

40 

46.68 

40.08 

0.16 

39-13 

31.23 

0.13 

23.58 

0.12 

Safe  loads  giv 

en  incluc 

ie  weight 

of  beam 

.     Maxirr 

um  fiber-s 

tress,  16 

000  lb  per 

sq  in 

Loads  given  a 

bove  the 

heavy  lin 

es  are  grc 

^ater  thai 

1  safe  loads 

for  web 

-crippling. 

See  paragraphs 

and  accc 

)mpanyin{ 

I  foot-no 

te,  page 

567,  relatin 

g  to  web 

-buckling 

of  beams 

Safe  loads  giv 

en  belo\i 

T  the  lowe 

r,  broker 

1  line  cat 

ise  deflecti 

ons  excee 

;ding  Heo 

of  the  span 

The  section-n 

umbers  £ 

ire  given  : 

or  conve 

nience  in 

identifical 

ion  and 

ordering 

S96 


Strength  of  Beams  and  Beam  Girders 


Table  XII  (Continued).     Safe  Uniform  Loads  in  Tons  of  2  000  Pounds 
for  Bethlehem  Girder  Beams 

Beams  secured  against  yielding  sidewise 


15-in  G 

i2-in  G 

Span, 
ft 

Add  for 
each  lb 

Add  for 
each  lb 

Gisb 

Gisa 

G15 

increase 

Gi2a 

G12 

increase 

in 
weight 

in 
weight 

140  lb 

104  lb 

73  lb 

70  lb 

55  lb 

10 
II 

113.26 
102.96 

86.76 
78.88 

62.83 

0.39 
0.36 

47.89 
43.54 

38.40 
34.91 

0.31 

0.29 

57.12 

12 

94  38 

72.30 

52.36 

0.33 

39-91 

32.00 

0.26 

13 

87.12 

66.74 

48.33 

0.30 

36.84 

29.54 

0.24 

14 
15 

80.90 
75.51 

61.97 
57.84 

44.88 
41.89 

0.28 
0.26 

34-21 

27-43 

0.22 
0.21 

31.93 

25.60 

16 

70.79 

54-23 

39-27 

0.25 

29.93 

24.00 

0.20 

17 

66.62 

51  04 

36.96 

0.23 

28.17 

22.59 

0.19 

18 

62.92 

48.20 

34.91 

0.22 

26.61 

21.33 

0.18 

19 

59-61 

45-67 

33  07 

0.21 

25.21 

20.21 

0.17 

20 

56.63 

43-38 

31.42 

0.20 

23.95 

19.20 

o.i6 

21 

53.93 

41-32 

29.92 

0.19 

22.81 

18.28 

0.15 

22 

51.48 

39-44 

28.56 

0.18 

21.77 

17.45 

0.14 

23 

49  24 

37-72 

27.32 

0.17 

20.82 

16.69 

0.14 

24 
25 

47-19 
45  30 

36.15 
34.71 

26.18 
25.13 

0.16 
0.16 

19.95 

16.00 

0.13 
0.13 

19.16 

15.36 

26 

43-56 

33.37 

24-17 

0.15 

18.42 

14.77 

0.12 

27 

41.95 

32.13 

23.27 

0.15 

17.74 

14.22 

0.12 

28 

40.45 

30.99 

22.44 

0.14 

17.10 

13.71 

O.II 

29 

39-05 

29.92 

21.67 

0.14 

16.51 

13.24 

O.II 

30 
31 

37J5  _ 

28.92 

_20^94_ 

0.13 
0.13 

15.96 
15.45 

12.80 
12.39 

O.IO 
0.10 

36.54 

27.99 

20.27 

32 

35.39 

27.11 

19.63 

0.12 

14.97 

12.00 

O.IO 

33 

34.32 

26.29 

19  04 

0.12 

14.51 

11.64 

O.IO 

34 

33.31 

25.52 

18.48 

0.12 

14.09 

11.29 

0.09 

35 

32.36 

24.79 

17.95 

O.II 

13.68 

10.97 

0.09 

Safe  loads  given  include  w 

eight  of  be 

am.     Maxi 

mum  fiber-stress,  16 

Doo  lb  per 

sq  in 

Load  given  above  the  hea 

vy  line  is 

greater  tha 

n  a  safe  load  for  web- 

crippling. 

See  paragraphs  and  accompa 

nying  foot 

-note,  page 

567,  relating  to  web 

-buckling 

of  beams. 

Safe  loads  given  below  the 

lower,  bro 

<en  lines  c 

ause  deflections  excee 

ding  I'Uo 

of  the  span. 

The  section-numbers  are  g 

ven  for  coi 

ivenience  i 

n  identification  and  c 

)rdering 

1 

t 

Tables  of  Safe  Loads  for  Steel  Beams  and  Girders          697 

Table  XII  (Continued).     Safe  Uniform  Loads  in  Tons  of  a  ooo  Pounds 

for  Bethlehem  Girder  Beams 

Beams  secured  against  yielding  sidewise 

lo-in  G 

9-in  G 

8-in  G 

Span, 
ft 

Add  for 
each  lb 

Add  for 
each  lb 

Add  for 
each  lb 

Span, 
ft 

Gio 

increase 

G9 

increase 

G8 

increase 

in 
weight 

in 
weight 

in 

weight 

44  lb 

38  1b 

32.5  lb 

10 

26.05 

0.26 

5 

40.50 

0.47 

30.  SI 

0.42 

II 

12 

13 

23.68 
21.71 
20.04 

0.24 
0.22 
0.20 

6 

7 
8 

33.75 
28.93 

0.39 
0.34 
0.29 

25.42 

0.35 
0.30 
0.26 

21.79 
19.07 

25.31 

14 

18.61 

0.19 

9 

22.50 

0.26 

16.95 

0.23 

15 

17.37 

0.17 

10 

20.25 

0.23 

15.2s 

0.21 

i6 

16.28 

0.16 

II 

18.41 

0.21 

13.87 

0.19 

17 

15.32 

0.15 

12 

16.88 

0.20 

12.71 

0.17 

i8 

14.47 

0.15 

13 

15.58 

0.18 

11.73 

0.16 

19 

13.71 

0.14 

14 

14.47 

0.17 

10.90 

o.is 

20 
21 

_i3^o3_ 

0.13 
0.12 

15 
16 

13.50 
12.66 

0.16 
0.15 

10.17 
__9.53 

0.14 
0.13 

12.40 

22 

11.84 

0.12 

17 

II. 91 

0.14 

8.97 

0.12 

23 

11.33 

O.II 

18 

11.25 

0.13 

8.47 

0.12 

24 

10.85 

C.II 

19 

10^66  " 

0.12 

8.03 

O.II 

25 

10.42 

O.IO 

20 

10.13 

0.12 

7.63 

O.IO 

26 

10.02 

O.IO 

21 

9.64 

O.II 

7.26 

O.IO 

27 

9.6s 

O.IO 

22 

9.21 

O.II 

6.93 

0.09 

28 

9- 30 

0.09 

23 

8.80 

O.IO 

6.63 

0.09 

29 

8.98 

0.09 

24 

8.44 

O.IO 

6.36 

0.08 

30 

8.68 

0.09 

25 

8.10 

0.09 

6.10 

0.08 

31 

8.40 

0.08 

26 

7-79 

0.09 

"••••• 

32 

8.14 

0.08 

27 

7.50 

0.09 

33 

7.89 

0.08 

28 

7.23 

0.08 

34 

7.66 

0.08 

29 

6.98 

0.08 

35 

7.44 

0.07 

30 

6.75 

0.07 



Safe  loads  given  include  weight  of  beam.    Maximum  fiber-stress,  i6  coo  lb  per 

sq  in 

Loads  given  above  the  heavy  lines  are  greater  than  safe  loads  for  web-crippling. 

See  paragraphs  and  accompanying  foot-note,  page  567,  relating  to  web-buckling 

of  beams 

Safe  loads  given  below  the  lower,  broken  lines  cause  deflections  exceeding  J'^eo 

of  the  span. 

The  section-numbers  are  given  for  coi 

ivenience  in  identification  and  ordering 

598 


Strength  of  Beams  and  Beam  Girders 


Table  XIII.     Safe  Uniform  Loads  in  Tons  of  2  000  Pounds  for  Bethlehem 
I  Beams 

Beams  secured  against  yielding  sidewise 


30-in  I 

28-in  I 

26-inI 

Span, 
ft 

Add  for 
each  lb 

Add  for 
each  lb 

Add  for 

each  lb 

B30 

increase 

B28 

increase 

B26 

incf-ease 

in 
weight 

in 
weight 

in 

weight 

120  lb 

1051b 

90  lb 

18 

103.50 

0.44 

84.95 

0.41 

67.86 

0.38 

19 

98.05 

0.41 

80.48 

0.39 

64.29 

0.36 

20 

93.15 

0.39 

76.46 

0.37 

61.07 

0.34 

21 

88.71 

0.37 

72.82 

0.35 

58.16 

0.32 

22 

84.68 

0.36 

69.51 

0.33 

55-52 

0.31 

23 

81.00 

0.34 

66.49 

0.32 

53.11 

0.30 

24 

77-62 

0.33 

63.72 

0.31 

50.89 

0.28 

25 

74.52 

0.31 

61.17 

0.29 

48.86 

0.27 

26 

71.65 

0.30 

58.81 

0.28 

46.98 

0.26 

27 

69.00 

0.29 

56.64 

0.27 

45.24 

0.25 

28 

66.54 

0.28 

54-61 

0.26 

43.62 

0.24 

29 

64.24 

0.27 

52.73 

0.25 

42.12 

0.23 

30 

62.10 

0.26 

50.97 

0.24 

40.71 

0.23 

31 

60.10 

0.25 

49-33 

0.24 

39.40 

0.22 

32 

58.22 

0.25 

47  "79 

0.23 

38.17 

0.21 

33 

56.45 

0.24 

46.34 

0.22 

37-01 

0.21 

34 

54.79 

0.23 

44.98 

0.22 

35.92 

0.20 

35 

53.23 

0.22 

43.69 

0.21 

34.90 

0.19 

36 

51.75 

0.22 

42.48 

0.20 

33.93 

0.19 

37 

50.35 

0.21 

41.33 

0.20 

33.01 

0.18 

38 

49-03 

0.21 

40.24 

0.19 

32.14 

0.18 

39 

47.77 

0.20 

39.21 

0.19 

31.32 

0.17 

40 

46.57 

0.20 

38.23 

0.19 

30.54 

0.17 

41 

45.44 

0.19 

37.30 

0.18 

29.79 

0.17 

42 

44-36 

0.19 

36.41 

0.18 

29.08 

0.16 

43 

43.33 

0.18 

35.56 

0.17 

28.41 

0.16 

44 

42.34 

0.18 

34.75 

0.17 

27.76 

0.15 

45 

46 

41.40 
40.50 

0.17 
0.17 

33.98 

0.16 

27.14 

0.15 

33.24 

0.16 

26.55 

0.15 

47 

39.64 

0.17 

32.54. 

0.16 

25.99 

0.14 

48 

38.81 

0.16 

31.86 

0.15 

25.45 

0.14 

Safe  loads  given  include  weight  of  beam.    Maximum  fiber-stress,  i6  000  lb  per 
q  in 
The  section-numbers  are  given  for  convenience  in  identification  and  ordering 


Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


599 


Table  XIII  (Continued).     Safe  Uniform  Loads  in  Tons  of  2000  Pounds 

for  Bethlehem  I  Beams 

Beams  secured  against  yielding  sidewise 


24-in  I 


B24  a 


841b 


81.43 
75.62 


B24 


73  lb 


70.58 

66.16 
62.27 
S8.81 
55  72 
52.93 

50.41 
48.12 
46.03 
44.11 
42.35 

40.72 
39.21 
37.81 
36.50 
35.29 

34.15 
33.08 
32.08 
31.14 
30.2s 

29.41 
28.61 
27.86 
27.14 
26.47 


77.45 

71-49 
66.38 

61.96 

58.08 
54.67 


51.63 
48.91 
46.47 

44.26 
42.24 
40.41 
38.72 
37.17 

35.74 
34-42 
33.19 
32.05 
30.98 

29.98 
29.04 
28.16 
27.33 
26.55 

25-82 
25.12 
24.46 
23.83 
23.23 


Add  for 
each  lb 
increase 

in 
weight 


0.52 
0.48 
0.45 
0.42 

0.39 
0.37 
0.35 
0.33 
0.31 

0.30 
0.29 
0.27 
0.26 
0.25 

0.24 
0.23 
0.22 
0.22 
0.21 

0.20 
0.20 
0.19 
0.19 
0.18 

0.17* 
0.17 
0.17 
0.16 
0.16 


20-in  I 


B20  a 


82  lb 


69 -33 

63.99 
59.42 

55.46 

51.99 
48.94 
46.22 
43.78 
41.60 

39.61 
37.81 
36.17 
34.66 
33.28 


72  lb 


65.18 


60.17 
55.87 
52.14 

48.88 
46.01 

43.45 
41.17 
39  II 

37.25 
35.55 
3401 
32.59 
31.29 


B20 


32.00  30.08 

30.81  28.97 

29.71  27.93 

28.69  26.97 

27.73  26.07 


26.84 
26.00 
25.21 
24.47 
23.77 

23.11 
22.48 
21.89 
21.33 
20.80 


25.23 
24.44 
23.70 
23.00 
22.35 

21.73 
21.14 
20.58 
20.06 
19.55 


69  lb      64  lb 


56.40 
52.06 
48.34 
45.12 

42.30 
39-81 
37.60 
35.62 
33.84 

32.23 
30.76 
29  42 
28.20 
27.07 

26.03 
25.07 
24.17 
23.34 
22.56 

21.83 
21.15 
20.51 
19-90 
19.34 

18.80 
18.29 
17.81 
17-35 
16.92 


54.32 

50.14 
46.56 

43.45 


40.74 
38.34 
36.21 
34.31 
32.59 

31  04 
29.63 
28.34 
27.16 
26.07 

25-07 
24.14 
23-28 
22.48 
21.73 

21.03 
20.37 
19.75 
1917 
18.62 

18.11 
17.62 
17-15 
16.71 
16.30 


59  lb 


52.10 


Add  for 

each  lb 

increase 

in 

weight 


48.09 
44.65 
41.68 

39  07 
36.77 
34 .  73 
32.90 
31.26 

29.77 
28.42 
27.18 
26.05 
25.01 

24.04 
23.15 
22.33 
21.56 
20.84 

20.17 
19.54 
18.94 
18.39 
17.86 

17.37 
16.90 
16.45 
16.03 
15.63 


0.44 
0.40 
0.37 
0.35 

0.33 
0.31 
0.29 
0.28 
0.26 

0.25 
0.24 
.  0.23 
0.22 
0.21 

0.20 
0.19 
0.19 
0.18 
0.17 

0.17 
0.16 
0.16 
o.is 
o.is 

O.IS 
0.14 
0.14 
0.13 
0.13 


Safe  loads  given  include  weight  of  beam.    Maximum  fiber-stress.  t6  000  lb  per 

'\oads  given  above  the  heavy  lines  are  greater  than  safe  loads  for  web-crippling 
See  paragraphs  and  accompanying  foot-note,  page  567.  relating  to  web-bucklmg 

°  The'^ection-numbers  are  given  for  convenience  in  identification  and  ordering 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


Table  XIII  (Continued) .     Safe  Uniform  Loads  in  Tons  of  2  000  Pounds 
for  Bethlehem  I  Beams 

Beams  secured  against  yielding  sidewise 


i8-in  I 

15-in  I 

Span, 
ft 

Add  for 
each  lb 
increase 

in 
weight 

Add  for 
each  lb 
increase 

in 
weight 

B18 

Bisb 

Bi5a 

Bis 

59  lb 

54  lb 

48.51b 

71  lb 

54  lb 

461b 

41  lb 

381b 

12 
13 

43.62 

41.58 

39  42 

0.39 
0.36 

47.18 
43.55 

36.15 
33  37 

28.73 
26.52 

27.06 
24.98 

26.23 
24.21 

0.33 
0.30 

40.26 

38.38 

36.39 

14 

37.39 

35  64 

33.79 

0.34 

40.44 

30.99 

24.62 

23.19 

22.48 

0.28 

15 

34.90 

33.26 

31-54 

0.31 

37.75 

28.92 

22.98 

21.65 

20.98 

0.25 

16 

32.71 

31.18 

29.56 

0.29 

35.39 

27.11 

21.55 

20.30 

19.67 

0.26 

17 

30.79 

29.35 

27.83 

0.28 

33.30 

25.52 

20.28 

19.10 

18.51 

0.23 

18 

29.08 

27.72 

26.28 

0.26 

31.45 

24.10 

19.15 

18.04 

17.49 

0.22 

19 

27.55 

26.26 

24.00 

0.25 

29.80 

22.83 

18.14 

17.09 

16.56 

0.21 

20 

26.17 

24.95 

23.65 

0.24 

28.31 

21.69 

17.24 

16.24 

IS. 74 

0.20 

21 

24.93 

23.76 

22.53 

0.22 

26.96 

20.66 

16.42 

15.46 

14.99 

0.19 

22 

23.79 

22.68 

21.50 

0.21 

25-74 

19.72 

15.67 

14.76 

14.31 

0.18 

23 

22.76 

21.70 

20.57 

0.21 

24.62 

18.86 

14-99 

14.12 

13.68 

0.17 

24 

21.81 

20.79 

19.71 

0.20 

23.59 

18.07 

14.36 

13.53 

13. II 

0.16 

25 

20.94 

19.96 

18.92 

0.19 

22.65 

17.35 

13.79 

12.99 

12.59 

0.16 

26 

20.13 

19.19 

18.19 

0.18 

21.78 

16.68 

13  26 

12.49 

12. II 

O.IS 

27 

19.39 

18.48 

17.52 

0.17 

20.97 

16.07 

12.77 

12.03 

11.66 

0.15 

28 

18.69 

17.82 

16.89 

0.17 

20.22 

15-49 

12.31 

11.60 

11.24 

0.14 

29 

18.05 

17.21 

16.31 

0.16 

19.52 

14.96 

11.89 

11.20 

10.85 

0.14 

30 
31 

17.45 
16.88 

16.63 
16.10 

15.77 
15.26 

0.16 

o.is 

18.87 

14.46 

11.49 

10.82 

10.49 

0.13 
0.13 

18.26 

13-99 

11.12 

10.47 

10.  IS 

32 

16.36 

15-59 

14.78 

0.15 

17.69 

13-56 

10.77 

10.15 

9.84 

0.12 

33 

15.86 

15.12 

14.33 

0.14 

17.16 

13.15 

10.45 

9.84 

9.54 

0.12 

34 

15.40 

14.68 

13.91 

0.14 

16.65 

12.76 

10.14 

9.55 

9.26 

0.12 

35 

14.96 

14.26 

13.52 

0.13 

16.18 

12.39 

9.85 

9.28 

8.99 

O.II 

36 
37 

I4._5_4 

13.86 

13.14 

0.13 
0.13 

15-73 
15.30 

12.05 
11.72 

9.58 
9.32 

9.02 
8.78 

8.74 
8.SI 

O.II 
O.II 

14.15 

13.49 

12.78 

38 

13.77 

13.13 

12.45 

0.12 

14.90 

11.42 

9.07 

8.55 

8.28 

O.IO 

39 

13.42 

12.79 

12.13 

0.12 

14-52 

II. 12 

8.84 

8.33 

8.07 

O.IO 

40 

13.09 

12.47 

11.83 

0.12 

14.15 

10.84 

8.62 

8.12 

7.87 

O.IO 

Safe 

.cads  given  include 

weight  of 

)eam. 

Maxir 

num  fiber-str 

2SS,   16 

000  lb  per 

sq  in 

Load 

given  above  the  h 

savy  line  i 

s  great 

er  tha 

n  safe  load  fc 

r  web- 

<:rippling. 

See  par 

agraphs  and  accomi 

lanying  foe 

)t-note 

page 

567,  relating 

to  web 

-buckling 

of  bean 

IS 

Safe 

oads  given  below  th 

e  broken  1 

nes  ca 

use  del 

lections  excee 

ding  }> 

^00  of  the 

span 

given  for  c 

Thes 

>ection 

numb 

2rs  are 

onveni 

ence  in 

identifacatio 

a  and  c 

jrdering 

Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


601 


Table  XIII  (Continued).     Safe  Uniform  Loads  in  Tons  of  2000  Pounds 
for  Bethlehem  I  Beams 


Beams  secured  against  yielc 

ing  sidewise 

i2-in  I 

lo-in  I 

Span, 
ft 

Addfo 
each  It 

r 

Add  for 
each  lb 

■ 

B120 

B12 

increas 

e                   Bio 

increase 

in 

weight 

in 
weight 

36  1b 

32  lb 

28.5  lb 

28.S  lb 

23.5  lb 

9 

26.59 

22.57 

21.36 

0.35 

15.95 

14.57 

0.29 

10 

23.93 

20.31 

19.22 

0.31 

14.35 

13  II 

0.26 

II 

21.76 

18.46 

17.47 

0.29 

13.05 

11.92 

0.24 

12 

19-94 

16.92 

16.02 

0.26 

11.96 

10.92 

0.22 

13 

18.41 

15.62 

14.79 

0.24 

11.04 

10.08 

0.20 

14 

17.09 

14.51 

13.73 

0.22 

10.25 

9.36 

0.19 

15 

15.95 

13.54 

12.81 

0.21 

9.57 

8.74 

0.17 

16 

14.96 

12.69 

12.01 

0.20 

8.97 

8.19 

0.16 

17 

14.08 

11.95 

II. 31 

0.19 

8.44 

7.71 

o.is 

18 

13.30 

11.28 

10.68 

0.17 

7.97 

7.28 

o.is 

19 

12.60 

10.69 

10.12 

0.17 

7.55 

6.90 

0.14 

20 
21 

11.97 
11.40 

10.15 
967 

9.61 
9.15 

0.16 
0.15 

___7_.i_8__ 

__.AAS__ 

0.13 
0.12 

6.84 

6.24 

22 

10.88 

9.23 

8.74 

0.14 

6.52 

S.96 

0.12 

23 

10.41 

8.83 

8.36 

0.14 

6.24 

5. 70 

O.II 

24 
25 

__9.97_ 

8.46 

8.01 

0.13 
0.13 

5. 98 
5.74 

5.46 
5.24 

O.II 
O.IO 

■      9-57 

'""¥.'12" 

""'"7."69" 

26 

9.20 

7.81 

7.39 

0.12 

5.52 

5.04 

O.IO 

27 

8.86 

7.52 

7.12 

0.12 

5.32 

4.86 

O.IO 

28 

8.55 

7.25 

6.86 

O.II 

5-13 

4.68 

0.09 

29 

8.25 

7.00 

6.63 

O.II 

4.95 

4-52 

0.09 

30 

9.98 

6.77 

6.41 

O.II 

4.78 

4.37 

0.09 

31 

7.72 

6.55 

6.20 

O.IO 

32 

7.48 

6.35 

6.01 

O.IO 

33 

7.25 

6.15 

5.82 

O.IO. 

34 

7.04 

5.97 

5.65 

0.09 

35 

6.84 

5.80 

5.49 

0.09 

Safe  loads  giver 

include  weight  of  beam.     M 

aximum  fiber-stress,  16 

000  lb  per 

sq  in 

Safe  loads  giver 

I  below  the  broken  lines  cause 

deflections  exceeding  I 

^60  of  the 

span 

The  section-nur 

nbers  are  given  for  convenien 

ce  in  identification  and 

ordering 

602' 


Strength  of  Beams  and  Beam  Girders 


Table  XIII  (Continued).      Safe  Uniform  Loads  in  Tons  of  2  000  Pounds 

for  Bethlehem  I  Beams 

Beams  secured  against  yielding  sidewise 


Span, 
ft 

9-in  I 

Add- for 

each  lb 

increase 

in  weight 

8-inI 

Add  for 

each  lb 

increase 

in  weight 

B9 

B8 

24  lb 

20  lb 

17.S  lb 

19-5  lb 

5 

6 
7 
8 
9 
10 

II 
12 
13 
14 
15 

16 

17 
18 

19 

20 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

21.83 

18.19 
15  60 
13.6s 
12.13 
10.92 

9.92 
9.10 
8.40 
7.80 
7.28 

6.82 
6.42 
6.07 

20.18 

16.81 
14-41 
12.61 
II. 21 
10.09 

917 
8.41 
7.76 
7.21 
6.73 

6.31 

593 
5. 61 

0.47 

0.39 
0.34 
0.29 
0.26 
0.24 

0.21 
0.20 
0.18 
0.17 
0.16 

0.15 
0.14 
0.13 

0.13 
0.12 

O.II 
O.II 
O.IO 
O.IO 
O.IO 

0.09 
0.09 
0.09 
0.08 
o.oS 

16.16 

13.46 
11.54 
10.10 
8.98 
8.08 

7  34 
6.73 
6.21 
5.77 
5.39 

5.05 

15.30 

12.75 
10.93 
9-57 
8.50 
7.65 

6.96 
6.38 
5.89 
5. 47 
5.10 

4.78 

0.42 

0.35 
0.30 
0.26 
0.23 

0.21 

0.19 
0.17 
0.16 
0   15 
0.14 

0.13 
0.12 
0.12 
0   II 
O.II 

•    O.IO 
O.IO 
0.09 
0.09 
0.08 

4.75 
4-49 
4.25 
4.04 

3.85 
3.67 
3.51 
3.37 
3.23 

4.50 
4-25 
4.03 
3.83 

3.64 
3.48 
3.33 
3.19 
3.06 

5.75 
5.46 

5. 20 
4.96 
4.75 
4.55 
4-37 

4.20 
4.04 
3.90 
3.76 
3.64 

5.31 
5.04 

4.80 
4-59 
4.39 
4.20 
4.04 

3.88 
3-74 
3.60 
3  48 
3.36 

1 

Safe  lo£ 
sq  in 

Safe  lo£ 
span 

The  sec 

ids  given  include  weight  of  beam.     Maximum  fiber-stress,  16  000  lb  per 
ids  given  below  the  broken  lines  cause  deflections  exceeding  Hso  of  the 
tion-numbers  are  given  for  cdnvenietKe  in  identification  and  ordering 

Tables  of  Safe  Loads  for  Steel  Beams  and  Girders  603 

Riveted  Single-Beam  and  Double-Beam  Girders.*  Where  a  single 
ROLLED  BEAM  is  insufficient  to  carry  a  load,  the  required  capacity  may  be  secured 
by  fabrication  in  various  ways.  Two  beams  can  be  used,  connected  by  bolts 
and  separators.  The  total  strength  of  these  is  twice  that  of  the  single  beam 
of  the  same  depth  and  weight.  Care  should  be  taken,  however,  to  see  that 
the  loads  are  apportioned  to  them  equally,  and  where  it  is  necessary  for  the 
beams  to  act  as  a  unit,  the  separators  should  consist  of  plates  and  angles  and  not 
be  made  of  cast  iron.  If  the  loading  is  not  uniformly  distributed  over  the  two 
beams,  the  strength  of  each  must  be  computed  separately.  The  use  of  a  single- 
beam  GIRDER  with  plates  at  top  and  bottom  to  sustain  a  given  load  is  often  more 
economical  in  material  than  the  use  of  two  beams  connected  by  bolts  and 
separators.  The  beam  girders  in  Table  XIV,  pages  605-6,  have  about  twice 
the  carrying  capacity  of  the  single  beams  of  which  they  are  built. 

Tables  XIV  and  XV  give  the  safe  loads  for  the  single  and  double -beam 
GIRDERS  commonly  used.  The  values  given  in  the  tables  are  founded  upon 
the  moments  of  inertia  of  the  various  sections,  deductions  being  made  for  the 
rivet-holes  in  both  flanges.  In  Table  XIV,  taken  by  permission  from  Carnegie's 
Pocket  Companion,  the  safe  loads  are  based  upon  a  fiber-stress  for  flange-bend- 
ing of  16  000  lb  per  sq  in,  and  in  Table  XV,  retained  from  the  former  edition  of 
Kidder's  Pocket-Book,  upon  a  fiber-stress  of  13  000  lb  per  sq  in.  For  other  fiber- 
stresses,  as  14  000  or  15  000  lb  per  sq  in,  the  safe  loads  in  Tables  XIV  or  XV 
may  be  decreased  or  increased  by  proportion  as  the  loads  vary  as  the  fiber- 
stresses. f 

*  For  tables  of  riveted  plate  girders,  see  Chapter  XX. 

t  The  editors  decided  to  retain  Table  XV  for  the  safe  uniformly  distributed  loads  for 
riveted  steel-beam  box  girders,  based  upon  a  bending  fiber-stress  of  13  000  lb  per  sq  in. 
To  use  this  table  for  fiber-stresses  of  14  000,  15  000  or  16  000  lb  per  sq  in,  divide  the 
tabular  loads  by  13  and  multiply  the  quotients  by  14,  15  or  16,  respectively,  for  the  safe 
load  at  the  required  fiber-stress.  In  regard  to  Table  XV,  Mr.  Kidder  said,  in  the 
preceding  editions  of  this  pocket-book,  "in  order  to  amply  compensate  for  the  deteriora- 
tion of  the  metal  around  the  rivet-holes  from  punching,  and  also  because  these  girders 
are  more  often  used  to  support  permanent  loads,  such  as  brick  or  stone  walls,  the  maximum 
fiber-stress  [for  riveted  double-beam  girders]  was  limited  to  13  000  lb  per  sq  in,  although 
it  is  but  right  to  state  that  most  of  the  latest  handbooks  of  the  steel-manufacturers  give 
tables  of  safe  loads  for  such  girders  based  upon  a  fiber-stress  of  15  000  lb  per  sq  in. 
The  author  advises  that  for  loads  of  masonry,  which  usually  come  very  close  to  the 
estimated  loads,  and  which  are  constantly  applied,  the  girders  be  not  loaded  beyond  the 
values  given  in  the  following  tables  (that  is,  based  upon  13  000  lb  per  sq  in),  while  for 
ordinary  floor-loads,  which  seldom  reach  the  estimated  loads,  an  addition  of  Hth  may  be 
added  to  the  values  given  in  the  tables." 

Girders  fabricated  of  single  steel  I  beams  and  plates  riveted  to  the  upper  and  lower 
flanges,  as  shown  in  Table  XIV,  are  not  often  used  to  support  masonry  walls,  because  of 
their  relatively  narrow  flange-width  and  lack  of  lateral  stiffness.  In  case  they  are  used 
to  support  masonry  walls  and  are  not  thoroughly  braced  laterally,  it  is  recommended  that 
the  safe  loads  be  reduced  as  explained,  from  those  given  in  Table  XIV,  to  agree  with 
a  fiber-stress  of  13  000  or  14  000  lb  per  sq  in,  according  to  the  span,  bracing,  character 
of  loading,  etc.  It  is  recommended,  also,  that  for  girders  fabricated  of  two  steel  I  beams 
and  plates  riveted  to  the  flanges,  as  shown  in  Table  XV,  and  carrying  masonry  walls,  the 
safe  loads,  given  in  this  table  and  computed  for  a  fiber-stress  of  13  000  lb  per  sq  in,  be  used, 
or,  if  increased,  that  the  fiber-stress  be  taken  not  greater  than  14  000  lb  per  sq  in. 

Recent  handbooks  have  contained  tables  of  safe  uniformly  distributed  loads  for  fabri- 
cated steel  girders  computed  from  safe  unit  fiber-stresses,  in  pounds  per  square  inch, 
for  flange-bending  as  follows.  For  riveted  single-beam  girders:  Carnegie  Steel 
Company,  1903  Edition,  no  tabks;  Carnegie,  1915  Edition,  16000,  based  upon  t!he 
section-modulus  of  the  gross  area  of  the  cross-section;  Cambria  Steel  Company,  191 2 
Edition,  no  tables;  (former)  Passaic  Steel  Company,  1903  Edition,  no  tables;  Kidder's 
Pocket-Book,  previous  editions,  no  tables.    For  riveted   double-beam  girders:  Car- 


604  Strength  of  Beams  and  Beam  Girders  Chap.  15 

Example  21.  A  13-in  brick  wall,  15  ft  high,  is  to  be  built  over  an  opening  of 
24  ft.     What  is  the  size  of  the  double-beam  girder  required? 

Solution.  Assuming  25  ft  as  the  distance,  center  to  center  of  bearings  and  121 
lb  per  cu  ft  as  the  weight  of  brickwork,  the  weight  of  the  wall  is25XiSXi2i  = 
45  375  ib,  or  about  22.68  tons.  From  Table  XV,  page  610,  a  girder  composed  of 
two  i2-in  steel  beams,  each  weighing  31.5  lb  per  ft,  and  two  14  by  \^-m  flange- 
plates  will  carry  safely,  for  a  span  of  25  ft,  a  uniformly  distributed  load  of  23.23 
tons,  including  its  own  weight.  Deducting  the  latter,  1.42  tons,  given  in  the 
next  column,  the  result  is  21.81  tons  for  the  safe  net  load,  which  is  0.87  ton  less 
than  required.  From  the  following  column  of  the  table  it  is  seen  that  by  in- 
creasing the  thickness  of  the  flange-plates  He  in  it  is  safe  to  add  1.52  tons  to  the 
allowable  load.  This  will  more  than  make  up  the  difference.  Hence  the  re- 
quired DOUBLE-BEAM  GIRDER  will  be  composcd  of  two  i2-in  31.5-lb  beams, 
and  two  14  by  ^le-in  steel  flange-plates. 

A  SINGLE-BEAM  GIRDER  (according  to  Table  XIV,  page  606),  composed  of 
one  15-in  42-lb  I  beam  and  two  8  by  J^i-in  flange-plates  will  carry,  at  16000 
lb  per  sq  ft,  49  000  lb  over  a  span  of  25  ft,  and  as  it  is  lighter,  weighing  but 
69.2  lb  per  ft  to  the  others  113.6  lb,  it  would  be  more  economical.  The 
DOUBLE-BEAM  GIRDER  is,  however,  more  suitable  in  this  particular  case,  as  the 
13-in  wall  should  have  a  wider  bearing  than  8  in,  and,  also,  the  safe  load  should 
be  decreased  from  the  tabular  load  to  correspond  to  a  fiber-stress  of  13  000  or 

14  000  lb  per  sq  in  because  of  the  nature  of  the  loading,  the  long  span,  etc., 
or,  what  amounts  to  the  same  thing,  the  strength  of  the  girder  should  be 
increased  to  correspond  to  the  decreased  fiber-stress.  (See  foot-note,  page  603.) 
A  49  000-lb  load  at  16  000  lb  per  sq  in  fiber-stress  corresponds  to  a  49  000  X 
i^ia  =  60307-lb  load  at  13  000  fiber-stress,  as  far  as  selecting  a  corresponding 
girder  from  table  is  concerned.  A  single-beam  girder  (Table  XIV)  com- 
posed of  one  15-in  60-lb  I  beam  and  two  9  by  %-m  flange-plates  will  carry 
68  000  lb  and  weighs  only  98.3  lb  per  ft.  Therefore,  as  far  as  strength  is  con- 
cerned, to  suit  the  conditions  of  loading,  this  would  be  the  proper  single-beam 
GIRDER  to  use,  and  it  would  also  be  cheaper  than  the  double-beam  girder 
determined  by  Table  XV;  but  the  width  of  bearing  for  the  13-in  wall  is  still 
only  9  in  compared  to  14  in  with  the  double-be.\m  girder. 

negie,  1903,  15000,  ^Me-in  rivet-holes  deducted;   Carnegie,  191.5,  no  tables;    Cambria, 

15  000,  i^e-in  rivet-holes  deducted;  Passaic,  15  000, 1  Vie  or  ^yio-in  rivet-holes  deducted; 
Kidder,  previous  and  new  editions,  13  000,  i^^ie-in  rivet-holes  deducted.  For  riveted 
siNGLE-WEB,  PLATE-AND-ANGLE  GIRDERS  (see  Chapter  XX):  Carnegie,  1903.  15000, 
i^lfi-in  rivet-holes  deducted;  Carnegie,  191S,  16  000,  based  upon  section-modulus  of  the 
gross  area  of  cross-section;  Cambria,  15000,  i^e  or  i4,^6-in  rivet-holes  deducted; 
Passaic,  15  000,  ^Me  or  ^Yia-in  rivet-holes  deducted;  Kidder,  previous  editions,  12  000 
and  13000  for  flanges,  ^ie  or  ^^--le-in  rivet-holes  deducted  (also  contained  the  Passaic 
tables).  For  riveted  multiple-web,  plate-and-angle  girders  (see  Chapter  XX): 
Carnegie,  1903.  15000,  ^  Me -in  rivet-holes  deducted;  Carnegie,  1915.  16000,  based  upon 
section-modulus  of  the  gross  area  of  cross-section  (the  elements,  only,  of  these  girders, 
and  not  the  loads,  are  given):  Cambria,  no  tables;  Passaic.  15000,  ^Me  or  '"^'Ifi-in 
rivet -holes,  deducted;  Kidder,  previous  editions,  same  as  for  single-web  plate-and- 
girders. 

The  revised  edition  of  Kidder's  Handbook  uses,  by  permission,  the  Carnegie  tables 
for  all  but  the  riveted  double-beam  girders,  for  which  the  old  Kidder  tables  are  retained. 

The  limiting  conditions  of  use  are  fully  explained  in  the  te.xt  and  foot  notes.  Editor- 
in-chief. 


Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 


605 


Table  XIV.*     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds  for  Riveted 

Steel-Beam  Girders 

Maximum  bending  stress,  i6  ooot  lb  per  sq  in 


_.4_4i-— o-J 

_,^7^^-1 

r-fio;:,--; 

._J ^        A 

i^ 

r 

\% 

'T\ 

^  L 

^ 

1 

':^i.. 

^ 

_.L 

x^  1 

-.1 

%^  1 

_t 

'± 

!.._ 

_t 

^  "■" 

^  "~ 

5J 

Span , 

J^ 

1 

.i-c 

iJ 

k 

.1^ 

--ti 

k, 

Co- 

efH- 

cients 

of 

1      ; 

•      • 

27-in90-rDbeam 

24-in  8o-lb  beam 

24-in  8o-lb  beam 

20-in  8o-lb  beam 

ft 

12  by  %-in 

12  by  %-in 

10  by  ^^-in 

10  by  %-in 

de- 

plates 

plates 

plates 

plates 

flec- 

tion 

Increase 

Increase 

Increase 

Increase 

in  safe 

in  safe 

in  safe 

in  safe 

loads  for 

loads  for 

loads  for 

loads  for 

Safe 

He-in 

Safe 

Me-in 

Safe 

He-in 

Safe 

He-in 

loads 

increase 
in  thick- 
ness of 
flange- 
plates 

loads 

increase 
in  thick- 
ness of 
flange- 
plates 

loads 

increase 
in  thick- 
ness of 
flange- 
plates 

loads 

increase 
in  thick- 
ness of 
flange- 
plates 

13 

14 

370 

343 

IS. 9 

14.8 

312 

289 

14.2 
13.2 

259 

II. 7 

10.9 

9.7 

9-0 

2.80 
3-24 

235 
218 

240 

15 

321 

13.8 

270 

12.3 

224 

10. 1 

204 

8.4 

3.72 

16 
17 

301 

130 
12.2 

253 

"5 
10.9 

210 

198 

9-5 
9.0 

191 
180 

7.9 

7.4 

4.24 
4.78 

283 

238 

18 

267 

II. 5 

225 

10.3 

187 

8.4 

170 

7.0 

5.36 

19 

253 

10.9 

213 

9-7 

177 

8.0 

161 

6.6 

5  98 

20 

240 

10.4 

203 

9.2 

168 

7.6 

153 

6.3 

6.62 

21 

229 

9-9 

193 

8.8 

160 

7.2 

146 

6.0 

7.30 

22 

219 

9-4 

184 

8.4 

153 

6.9 

139 

5-7 

8.01 

23 

209 

90 

176 

8.0 

146 

6.6 

133 

5-5 

8.76 

24 

200 

8.6 

169 

7-7 

140 

6-3 

127 

5-3 

9.53 

25 

192 

8.3 

162 

7-4 

135 

6.1 

122 

S.o 

10.35 

26 

185 

8.0 

156 

7-1 

129 

5-9 

118 

4.8 

II. 19 

27 

178 

7.7 

150 

6.8 

125 

5.6 

113 

4-7 

12.07 

28 

172 

7-4 

145 

6.6 

120 

5.4 

109 

4-5 

12.98 

29 

166 

7-1 

140 

6.4 

116 

5.2 

105 

4-3 

13.92 

30 

160 

6.9 

135 

6.2 

112 

S-i 

102 

4.2 

14.90 

31 

155 

6.7 

131 

6.0 

109 

4-9 

99 

4.1 

15.91 

32 

150 

6.5 

127 

5.8 

lOS 

4.8 

96 

3.9 

16.95 

SZ 

146 

6.3 

123 

5.6 

102 

4.6 

93 

3.8 

18.03 

34 

T41 

6.1 

119 

•     5-4 

99 

4-5 

90 

3-7 

19   13 

35 

137 

5.9 

116 

5-3 

96 

4-3 

87 

3.6 

20.28 

Area 

44-33  in^ 

41.32  in2 

35.82  in2 

38.7 

3  in^ 

/Ai-it 

450.8    in' 

380.0    in' 

315-5    in' 

•286.7 

in' 

Wgt 

152.2    lb  per  ft 

141 . 2    lb  per  ft 

122.5    lb  per  ft 

131. 0 

lb  per  ft 

Saf( 

I  loads  above  the  1 

leavy,    horizontal 

lines  exceed  the  re 

sistanc 

e  of  the  we 

)    and 

girder 

s  should  be  provi< 

led  with  stiflFeners 

;    for  limiting  cor 

iditions 

,  see  expla 

natory 

notes 

on  page  567.     See 

Pocket  Companio 

n  for  13  and  14-ft 

spans. 

We 

ghts  given  for  girc 

!ers  do  not  include 

stiffeners,  rivet-h 

sads  or 

other  deta 

Is 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 

t  See  paragraph  on  Riveted  Single-Beam  and  Double-Beam  Girders,  page  603,  and  the 
foot-note  for  same  regarding  fiber-stresses. 

t  I/c  is  the  section-modulus  or  section-factor  of  the  cross-section  with  reference  to  the 
axis  i-i. 


606 


Strength  of  Beams  and  Beam  Girders 


Chap. 


Table  XIV*  (Continued).     Safe  Uniform  Loads  in  Units  of  i  ooo  Pounds 
for  Riveted  Steel-Beam  Girders 

Maximum  bending  stress,  16  coot  lb  per  sq  in 


i  J<-rio'--: 

r"T'^'"'T"^; 

U-9"-^ 

t^ 

Y" 

:  ^ 

^ 

t  ^ 

r 

T^ 

r^ ' 

L 

._i 

|.„ 

.1 

U  i._ 

_.L 

Span, 

._ix 

J 

Vi^ 

1  /^ 

V«k 

.            jsJ 

w 

: 

Co- 

efB- 

cients 

of 

f  1 

tS  , 

;     r-CZ- uJ_, 

-^-■C  0^ 

■  AH^g-C^ 

20-in  65-lbbeam, 

i8-in  55-lb  beam, 

15-in  6o-lbbeam, 

15-in  42-lb  beam, 

ft 

10  by  %-\n 

9  by  H-in 

9  by  ^^-in 

8  by  Vi2-in 

de 

plates 

plates 

plates 

plates 

flec- 
tion 

Increase 

Increase 

Increase 

Increase 

in  safe 

in  safe  , 

in  safe 

in  safe 

loads  for 

loads  for 

loads  for 

loads  for 

Safe 

He -in 

Safe 

He-in 

Safe 

Mo-in 

Safe 

Htj-in 

loads 

increase 
in  thick- 
ness of 
flange- 
plates 

loads 

increase 
in  thick- 
ness of 
flange- 
plates 

loads 

increase 
in  thick- 
ness of 
flange- 
plates 

loads 

increase 
in  thick- 
ness of 
'  flange- 
plates 

9 
10 

279 
251 

14.2 
12.7 

218 
196 

II-5 
10.3 

189 
170 

9-4 
8.5 

137 

8.5 
7.6 

1-34 
1.66 

123 

II 
12 
13 

228 
209 

II. 6 
10.6 
9.8 

178 

9.4 
8.6 
7.9 

155 
142 
1.31 

7.7 
7.1 
6.5 

112 
102 
95 

6.9 
6.4 
5.9 

2.00 
2.38 
2.80 

164 
151 

193 

14 

179 

91 

140 

7.4 

122 

6.1 

88 

5.5 

3.24 

IS 

167 

8.5 

131 

6.9 

113 

5.7 

82 

5.1 

3.72 

16 

157 

8.« 

123 

6.5 

106 

5.3 

77 

4.8 

4.24 

17 

148 

7.5 

IIS 

6.1 

100 

5.0 

72 

4.5 

4.78 

18 

139 

7.1 

109 

5.7 

95 

4.7 

68 

4.2 

5.36 

19 

132 

6.7 

103 

5.4 

90 

4.5 

65 

4.0 

5. 98 

20 

125 

6.4 

98 

5.2 

85 

4.3 

61 

3.8 

6.62 

21 

119 

6.1 

93 

4.9 

81 

4.0 

59 

3.6 

7.30 

22 

114 

5.8 

«9 

4.7 

77 

3.9 

56 

3.5 

8.01 

23 

109 

55 

85 

4.5 

74 

3.7 

53 

3.3 

8.76 

24 

105 

5.3 

82 

4.3 

71 

3.5 

51 

3.2 

9.53 

25 

100 

S.I 

79 

4.1 

68 

3.4 

49 

3.1 

10.35 

26 

97 

4.9 

76 

4.0 

65 

3.3 

47 

2.9 

II. 19 

27 

93 

4.7 

73 

3.8 

63 

3.1 

46 

2.8 

12.07 

28 

90 

4.6 

70 

3-1 

61 

*.  3.0 

44 

2.7 

12.98 

29 

87 

4.4 

68 

3.6 

59 

2.9 

42 

2.6 

13.92 

30 

84 

4.2 

65 

3.4 

•57 

2.8 

41 

2.5 

14.90 

Area 

31.58  in2 

27.18  in2 

28.92  in2 

20.48 in^ 

Ilc^-xX 

235.2    in3 

184. 1    in3 

159-5  m' 

1 15. 3    ni3 

Wgt 

107. 5    lb  per  ft 

93.3    lb  per  ft 

98.3    lb  per  ft 

69.21b  per  ft 

Safe 

I  loads  above  the  1 

leavy,  horizontal : 

ines  exceed  the  res 

>istance  of  the  wet 

3,  and 

girder 

s  should  be  provi 

led  with  stiffenen 

,;  for  limiting  con 

ditions,  see  explan 

atory 

notes 

on  page  567.     See 

Pocket  Companu 

jn,  1915  for  9-ft.  SI 

)an 

Wei 

ghts  given  for  gir 

ders  do  not  incluc 

ie  stifTeners,  rivet 

-heads  or  other  d 

etails 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pitsburgh,  Pa. 

t  See  paragraph  on  Riveted  Single-Beam  and  Double-Beam  Girders,  page  603,  and  the 
foot-note  for  same  regarding  fiber-stresses. 

\  I/c  is  the  section-modulus  or  section-factor  of  the  cross-section  with  reference  to  the 
axis  I -I. 


Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 

60? 

Table  XV.     Safe  Uniform  Loads  in 

Tons  of  2  000  Pounds  for  Riveted 

Steel-Beam  Box  Girders 

Two  20-In  steel  I  beams  and  two  16  by  H-in  steel  plates 

Two  steel 

.U-7^^. 

Two  steel" '^lr-"-.r<»''     ^"^P 

Dis- 

plates, 

i6by  H 

in 

d 

20-m 
beams, 
80.0  lb 
L^^l^     perft 

plates, 

i6by  H 

in 

4 

20-1  n 
beams, 
6s.o  lb 

Increase 
in  weight 
of  girder 

center  to 
center 
of  bear- 
ings, ft 

Safe 
loads, 
uniformly 
distrib- 
uted (in- 

Weight of 

girder 
(includ- 
ing rivet- 

Increase 

in  safe 

loads  for 

He-in  in- 

Safe 
loads, 
uniformly 
distrib- 
uted (in- 
cluding 
weight  of 

Weight  of 
girder 
(includ- 
ing rivet- 

Increase 

in  safe 

loads  for 

Mo-in  in- 

for He-in 
increase 
in  thick- 
ness of 
flange- 
plates 

cluding 
weight  of 

heads),  in 

crease  in 
thickness 

heads),  in 
tons  of 

crease  in 
thickness 

girder), 

2  000  lb 

of  flange- 

girder), 

of  flange- 

in  tons  of 

plates 

in  tons  of 

plates 

2  000  lb 

2  000  lb 

10 

199.67 

1.22 

1.06 

7.34 

0.03 

7.22 

176.72 

II 

181. 51 

1.34 

6.56 

160.66 

1. 16 

6.68 

0.04 

12 

166.39 

1.46 

6.02 

147.26 

1.27 

6.12 

0.04 

13 

153  60 

1.58 

5.56 

135. "^5 

1.37 

5.65 

0.04 

14 

142.64 

1.70 

5.16 

126.24 

1.48 

5.2s 

0.05 

15 

133.12 

1.83 

4.81 

117.82 

1.58 

4.90 

0.05 

i6 

124.80 

1.95 

4.51 

110.45 

1.69 

4.59 

0.05 

17 

117.47 

2.07 

4.25 

103.96 

1.79 

4.32 

0.06 

i8 

110.94 

2.19 

4.01 

98.18 

1.90 

4.08 

0.06 

.19 

105.10 

2.31" 

3.80 

93  01 

2.01 

3.86 

0.06 

20 

99.83 

2.43 

3.6i 

88.36 

2. II 

3.67 

0.07 

21 

95.08 

2.56 

3.44 

84.15 

2.22 

3.50 

0.07 

22 

90.77 

2.68 

3'.  28 

80.33 

2.32 

3.34 

0.07 

23 

86.82 

2.80 

3.14 

76.84 

2.43 

3.19 

0.08 

24 

83.20 

2.92 

3.01 

73.64 

2.53 

3.06 

0.08 

25 

79.87 

3.04 

2.89 

70.69 

2.64 

2.94 

0.08 

26 

76.80 

3.16 

2.78 

67.97 

2.75 

2.82 

0.09 

27 

73.96 

3.29 

2.68 

65.46 

2.85 

2.72 

0.09 

28 

71.32 

3.41 

2.58 

63.12 

2.96 

2.62 

0.09 

29 

68.86 

3.53 

2.49 

60.94 

3.06 

2.53 

o.io 

30 

66.56 

3.65 

2.41 

58.91 

3.17 

2.45 

O.IO 

31 

64.41 

3.77 

.    2.33 

57.01 

3.27 

2.37 

0.10 

32 

62.41 

3.89 

2.26 

55.22 

3.38 

2.29 

O.II 

33 

60.51 

4.02 

2.19 

53.56 

3.48 

2.22 

O.II 

34 

58.73 

4.14 

2.12 

51.98 

3.59 

2.16 

O.H 

35 

57.05 

4.26 

2.06 

50.50 

3.70 

2.10 

0.12 

36 

55.46 

4.38 

2.01 

49-09 

3.80 

2.04 

0.12 

37 

53.96 

4.50 

1.95 

47.77 

3.91 

1.98 

0.12 

38 

52.54 

4.62 

1.90 

46.51 

4.01 

1.93 

0.13 

39 

51.20 

4.75 

1.8s 

45.32 

4.12 

1.88 

0.13 

The  above  values  are  based  on  a  maximum  fiber-stress  of  13  000  lb  per  sq  in,  rivet-holes 
in  both  flanges  deducted.  See  paragraph  on  Riveted  Single-Beam  and  Double-Beam 
Girders,  page  603,  and  the  foot-note  for  same  regarding  fiber-stresses.  Weights  of  girders 
correspond  to  lengths,  center  to  center  of  bearings. 


608 


Strength  of  Beams  and  Beam  Girders  Ckap.  1$ 


Table  XV  (Continued).     Safe  Uniform  Loads  in  Tons  of  2  000  Pounds 
for  Riveted  Steel-Beam  Box  Girders 


Two  i8-iri  steel  I  beams  and  two 

16  by  5 

t-in 

iteel  plates 

■  JK-T-V^                  1 

Two 
i8-iri 

'.      -o//' 

Two 

^ 

lii^S 

^     Two 

i8-in 

^ 

beams. 

beams 

i6by?4-in 

70  lb 

55  lb 

steei 

plates 

Add  to 

Dis- 

^ 

^Sr^ 

0       per  ft 

per  ft 

/^l 

:^ 

^ 

weight 

tance, 

center 

to 

t=^ CT- 

Two  i^by  ^4-in  steel  plates 

=^ 

of  gird- 
er for 
He-in 

center 

increase 

of  bear- 
ings, 
ft 

Safe 
loads  in 

tons, 
includ- 

Weight 
of 

Add  to 
safe  loads 
for  Mo-in 

Safe 
loads  in 

tons, 
includ- 

Weight 
of 

Add  to 

safe 
loads  for 

Add  to 
safe  loads 
for  yi  6-ia 

in 
thick- 
ness of 
plates 

ing 
weight 

girder, 
lb 

increase 
in  thick- 

ing 
weight 

girder, 
lb 

5  pounds 
increase 

increase 
in  thick- 

of 
girder 

ness  of 

of 
girder 

in  weight 

ness  of 

plates 

of  beam 

plates 

12 

132.2 

2712 

5.43 

123.0 

2  352 

2.81 

.  5.43 

82 

13 

122.0 

2933 

5.01 

113. 5 

2548 

2.61 

5.01 

88 

14 

113-3 

3  164 

4.66  • 

105.3 

2  744 

2.43 

4.66 

95 

15 

105.7 

3390 

4.35 

98.3 

2  940 

2.27 

4.35 

102 

16 

99.1 

3616 

4.07  . 

92.2 

3136 

2.12 

4.07 

109 

17 

93.3 

3842 

3.83 

86.8 

3332 

2.00 

3.83 

116 

18 

88.1 

4068 

3.62 

82.0 

3528 

1.90 

3.62 

122 

19 

83.5 

4294 

3.43 

77.6 

3724 

1.80 

3.43 

129 

20 

79-3 

4  520 

3.26 

73.8 

3920 

I.  70 

3.26 

136 

21 

75.5 

4746 

3.10 

70.2 

4  116 

1.62 

3.10 

143 

22 

72.1 

4972 

2.96 

67.0 

4312 

1.54 

2.96 

150 

23 

69.0 

5198 

2.83 

64.1 

•4508 

1.47 

2.83 

156 

24 

66.1 

5424 

2.72    . 

61.5 

4  704 

1. 41 

2.72 

163 

25 

63. 5 

5650 

2.61 

590 

4900 

1.36 

2.61 

170 

26 

61.0 

5876 

2.51 

56.7 

■   5096 

1.30 

2.51 

177 

27 

58.8 

6  102 

2.41 

54.6 

5292 

I. 26 

2.41 

184 

28 

56.6 

6328 

2.33 

52.7 

5488 

1. 21 

2.33 

190 

29 

54.7 

6554 

2.25 

50.9 

5684 

1. 17 

2.25 

197 

30 

52.9 

6780 

2.17 

49-2 

5880 

1. 13 

^      2.17 

204 

31 

51.8 

7006 

2.10 

47.6 

6  076 

1. 10 

2.10 

211 

32 

49-6 

7232 

2.04 

46.1 

6272 

1.06 

2.04 

218 

33 

48.1 

7458 

1.98 

44-7 

6468 

1.03 

1.98 

224 

34 

46.7 

7684 

1.92 

43-4 

6664 

1. 00 

1.92 

231 

35 

45.3 

7910 

1.86 

42.1 

6860 

0.97 

1.86 

238 

36 

44.1 

8  136 

1. 81 

41.0 

7056 

0.94 

1. 81 

245 

37 

42.9 

8362 

1.76 

39.9 

7  252 

0.92 

1.76 

252 

38 

41.2 

8588 

1.72 

38.8 

7448 

0.90 

1.72 

258 

The  above  values  are  based  on  a  maximum  fiber-stress  of  13  000  lb  per  sq  in,  rivet-holes 
iti  both  flanges  deducted.  See  paragraph  on  Riveted  Single-Beam  and  Double-Beam 
Girders,  page  603,  and  the  foot-note  for  same  regarding  fiber-stresses.  Weights  of  girders 
correspond  to  lengths,  center  to  center  of  bearings. 


^ 


i 

Tables  of  Safe  Loads  for  Steel  Beams  and  Girders 

609 

Table  XV  (Continued 

.     Safe  Uniform  Loads  in 

Tons  ol 

2  000  Pounds 

for  Riveted  Steel-Beam  Box  Girders 

Two  15-in  steel  I  beams  and  two  14  by  ^s 

-in  steel  plates 

Twoi5-inbeams, 

T-o  15-in  benmsj 

1* 

75.0  lb  per  ft 

60.0  lb  per  ft 

r.-^'^- 

^l- 

^^^-GX^'  ^ 

^ 

j^<. 

r 

s 

r'r 

Dis- 

r^ 

^r^ 

i^ 

r^ 

^r-'^ 

A- 

M    0 

Increase 
in  safe 
load  for 
He-in 
increase 
in  thick- 
ness of 
flange- 
plates 

Increase 
in  weight 

«=^F 0- 

^ o-* 

^-^ — 

^^o=»  '^ 

tance, 

Steel  Plates, 

Steel  Plates, 

Steel  Plates, 

of  gird- 

center 

to 
center 
of  bear- 

14 by  %  in 

14  by  Vh  in 

14  by 

V%  in 

er  for 

He-in 

increase 

in  thick- 

Safe 
loads, 
uni- 

Weight 

Safe 
loads, 

Weight 

Safe 
loads, 

Weight 

ings, 

formly 

of  gird- 

formly 

of  gird- 

formly 

of  gird- 

ness of 

ft 

distrib- 

er (in- 

distrib- 

er (in- 

distrib- 

er (in- 

flange- 

uted  (in- 
cluding 

weight  of 
girder). 

cluding 
rivet- 
heads), 
in  tons 
of  2  000 
lb 

uted  (in- 
cluding 

weight  of 
girder) , 

cluding 
rivet- 
heads), 
in  tons 

uted  (in- 
cluding 

weight  of 
girder). 

cluding 
rivet- 
heads), 
in  tons 

plates 

in  tons 

in  tons 

of  2  000 
lb 

in  tons 

of  2  000 
lb 

of  2  000 

of  2  000 

of  2  000 

lb 

lb 

lb 

10 

122.33 

1.06 

III. 01 

0.91 

90.29 

0.72 

4.63 

0.03 

II 

III. 21 

1.17 

100.92 

1. 00 

82.08 

0.79 

4.21 

0.03 

12 

101.95 

1.27 

92.51 

1-09 

75.24 

0.86 

3.86 

0.03 

1.3 

94  10 

1.38 

85.40 

1. 18 

69.45 

0.93 

3.57 

0.04 

14 

87.38 

1.48 

79-30 

1.27 

64.50 

1. 00 

3.31 

0.04 

IS 

81.56 

1-59 

74-01 

1.36 

60.19 

1.08 

3.09 

0.04 

i6 

76.46 

1.70 

69.38 

1-45 

56.43 

1. 15 

2.90 

0.05 

17 

71.96 

1.80 

65-30 

1.54 

53.11 

1.22 

2.72 

0.05    ^ 

i8 

67.96 

1. 91 

61.67 

1.63 

50.16 

1.29 

2.57 

0.05 

19 

64.39 

2.01 

58.43 

1.72 

47.52 

1.36 

2.43 

0.05 

20 

61.17 

2.12 

55.50 

1. 81 

45-14 

1.44 

2.32 

0.06 

21 

58.25 

2.22 

52.86 

1.90 

42.99 

1. 51 

2.21 

0.06 

22 

55.60 

2.33 

50.46 

2.00 

41.04 

1.58 

2. II 

0.06 

23 

53.19 

2.43 

48.27 

2.09 

39-25 

1.65 

2.02 

0.07 

24 

50.97 

2.54 

46.25 

2.18 

37.62 

1.72 

1.93 

0.07 

25 

48.93 

2.65 

44.40 

2.27 

36.12 

1.79 

1.85 

0.07 

26 

47.05 

2.76 

42.70 

2.36 

34.72 

1.87 

1.78 

0.08 

27 

45-31 

2.86 

41.12 

2.45 

33.44 

1.94 

1. 71 

0.08 

28 

43.69 

2.96 

39-65 

2.54 

32.25 

2.01 

1.66 

0.08 

29 

42.18 

3.07 

38.28 

2.63 

31.13 

2.08 

1.60 

0.08 

30 

40.78 

3-17 

37-00 

2.72 

30.09 

2.15 

1.54 

0.09 

31 

39.46 

3.28 

35.81 

2.81 

29.12 

2.23 

1.49 

0.09 

32 

38.23 

3.38 

34.69 

2.80 

28.21 

2.30 

1.45 

0.09 

33 

37-07 

3.46 

33.64 

2.99 

27.36 

2.37 

1. 41 

O.IO 

34 

35.98 

3- 60 

32.65 

3-08 

26.55 

2.44 

1.37 

O.IO 

35 

34.95 

3.70 

31.72 

3-17 

25.80 

2.51 

1.33 

O.IO 

36 

33-98 

3.81 

30.84 

3.27 

25-08 

2.58 

1.29 

O.IO 

37 

33 -06 

3.91 

30.00 

3.36 

24.40 

2.66 

1.25 

O.II 

38 

32.20 

4.02 

29.*2I 

3.4s 

23-76 

2.73 

1.22 

O.II 

39   • 

31.37 

4.13 

28.47 

3-54 

23.15 

2.80 

1. 19 

O.II 

The  above  values  are  based  on  a  maximum  fiber-stress  of  13  000  lb  per  sq  in,  rivet-holes 
in  both  flanges  deducted.  See  paragraph  on  Riveted  Single-Beam  and  Double-Beam 
Girders,  page  603,  and  the  foot-note  for  same  regarding  fiber-stresses.  Weights  of  girders 
correspond  to  lengths,  center  to  center  of  bearings. 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


Table  XV  (Continued).     Safe  Uniform  Loads  in  Tons  of  2  ooo  Pounds 

for  Riveted  Steel-Beam  Box  Girders 

Two  i2-in  steel  I  beams  and  two  14  by  H-in  steel  i)lates 


,-^3- 

K^C'^^^ 

Fwo  i2-in 

rr'i^ 

0  i2-in 

"^ 

"r^    " 

r  ' 

'CU^]y  T. 

beams, 

beams, 

40.0  lb 

31.S  lb 

per  ft 

per  ft 

r^ 

^r^ 

i^ 

.i^Sr^-^. 

Increase 

Dis- 

'=^ 

57^ 

«-o cr-' 

in  weight 

tance, 

[  Two  steel  plai 

es, 

Two  steel  plates 

, 

of  girder 

center  to 

14  by  ]^i  in 

14  by  H  in 

for  Me-in 

center 

increase 

of  bear- 
ings, 

Safe  loads, 
uniformly 

Weight 

Increase 

in  safe 

loads  for 

Safe  loads, 
uniformly 

Weight       ^l 

icrease 

in  thick- 
ness of 

ft 

distrib- 

of girder 

distrib- 

of girder     ^^ 

ads  for 

flange- 

uted  (in- 
cluding 
weight  of 

(includ- 
ing rivet- 
heads),  in 

Me-in  in- 
crease in 
thickness 

uted  (in- 
cluding 
weight  of 

(includ-     1/ 
ing  rivet-    ^^ 
heads),  in  ^^ 

6-in  in- 
ease  in 
ickness 

plates 

girder), 
in  tons  of 

tons  of 
2  000  lb 

of  flange- 
plates 

girder), 
in  tons  of 

tons  of      ^f 
2  000  lb 

flange- 
plates 

2  000  lb 

2  000  lb 

10 

64.94 

0.65 

3.75 

58.08 

0.57 

3.81 

0.03 

II 
12 

59.02 
54.12 

0.71 
0.78 

3.40 

52.80 

0.63 
0.68 

3.45 
3.17 

0.03 
0.03 

3.12 

48.40 

13 

49.95 

0.84 

2.88 

44.68 

0.74 

2.93 

0.04 

14 

46.39 

0.91 

2.68 

41.48 

0.80 

2.72 

0.04 

IS 

43.29 

0.97 

2.50 

38.72 

0.85 

2.53 

0.04 

16 

40.59 

1.04 

2.34 

36.30 

0.91 

2.38 

0.05 

17 

38.20 

1. 10 

2.21 

34.16 

0.97 

2.24 

0.05 

18 

36.08 

1. 17 

2.08 

32.27 

1.03 

2. II 

0.05 

19 

34.18 

1.23 

1.97 

30.57 

1.08     ~ 

2.00 

0.05 

20 

32.47 

1.30 

1.87 

29.04 

1.14 

1.90 

0.06 

21 

30.93 

1.36 

1.78 

27.66 

1.20 

1. 81 

0.06 

22 

29  52 

1.43 

1.70 

26.40 

1.25 

1.73 

0.06 

23 

28.23 

1.49 

1.63 

25.25 

1.31 

1.65 

0.07 

24 

27.06 

1.56 

1.56 

24.20 

1.37 

1.58 

0.07 

25 

25.98 

1.62 

1.50 

23.23 

1.42 

1.52 

0.07 

26 

24.98 

1.69 

1.44 

22.34 

1.48 

1.46 

0.08 

27 

24.05 

1.75 

1.38 

21.51 

1.54 

1. 41 

0.08 

28 

23.19 

1.82 

1.34 

20.74 

1.60 

1.36 

0.08 

29 

22.39 

1.88- 

1.29 

20.03 

1.65 

1. 31 

0.08 

30 

21.65 

1.95 

1.25 

19.36 

1. 71 

1.27 

0.09 

31 

20.95 

2.01 

1. 21 

18.73 

1.77 

1.23 

0.09 

32 

20.29 

2.08 

1. 17 

18.15 

1.82 

1. 19 

0.09 

33 

19.68 

2.14 

1. 14 

17.60 

1.88 

1. 15 

O.IO 

34 

19.10 

2.21 

1. 10 

17.08 

1.94 

1. 12 

O.IO 

35 

18.5s 

2.27 

1.07 

16. 59 

1.99 

1.09 

O.IO 

36 

18.04 

2.34 

1:04 

16.13 

2 '05 

1.06 

O.IO 

37 

17. 55 

2.40 

1. 01 

15.70 

2. II 

1.03 

O.II 

38 

17.09 

2.47 

0.99 

15.28    * 

2.17 

1. 00 

©.II     1 

39 

16.65 

2.53 

0.96 

14.89 

2.22 

0.98 

O.II     1 

The  above  values  are  based  on  a  maximum  fiber-stress  of  13  000  lb  per  sq  in,  rivet-holes 
in  both  flanges  deducted.  See  paragraph  on  Riveted  Single-Beam  and  Double-Beam 
Girders,  page  603,  and  the  foot-note  for  same  regarding  fiber-stresses.  Weights  of  girders 
correspond  to  lengths,  center  to  center  of  bearings. 


Tables 

of  Safe  Loads  for  Steel  Beams  and  Girders 

611 

Table  XV  (Continued). 

Safe  Uniform  Loads  in  Tons  of  2  000  Pounds 

for  Riveted  Steel-Beam  Box  Girders 

Two  lo-in  steel  I  Beams  and  two  12  by  ^^-in  steel  plates 

r-Q 

MK^ 

-Q-, 

Two  lo-in 

r^ 

Wk^ 

Two  lo-in 

"^ 

^^ 

r 

%^ 

r 

beams. 

beams, 

35.0  lb 

25.0  lb 

^ 

^r^ 

1^ 

per  ft 

^U 

K 

per  ft 

Increase 

Dis-, 
tance, 
center  to 
center 
of  bear- 
ings, ft 

Tw 

0  steel  plat 
12  by  ]ri  ir 

es, 

I 

Two  steel  plates, 
12  by  }ri  in 

in  weight 
of  girder 

for  He-in 
increase 

in  thick- 
ness of 

Safe  loads, 
uniformly 

Weight 

Increase 

in  safe 

Safe  loads, 
uniformly 

Weight 

Increase 
in  safe 

distrib- 
uted (in- 
cluding 
weight  of 

of  girder 
(includ- 
ing rivet- 
heads),  in 

loads  for 
He-in  in- 
crease in 
thickness 

distrib- 
uted (in- 
cluding 
weight  of 

of  girder 
(includ- 
ing rivet- 
heads),  in 

loads  for 
M  6-in  in- 
crease in 
thickness 

flange- 
plates 

girder), 
in  tons^of 
2  000  lb 

tons  of 
2  000  lb 

of  flange- 
plates 

girder) , 
in  tons  of 
2  000  lb 

tons  of 
2  000  lb 

of  flange- 
plates 

ID 

44.35 

0.55 

2.59 

39-23 

0.47 

2.64 

0.02 

II 

40.32 

0.60 

2.36 

35.66 

0.52 

2.40 

0.03 

12 

3(3.96 

0.65 

2.16 

32.69 

0.56 

2.20 

0.03 

13 

34.12 

0.71 

1.99 

30.18 

0.61 

2.03 

0.03 

14 

31.68 

0.76 

1.85 

28.02 

0.66 

1.89 

0.03 

15 

29.57 

0.82 

1.73 

26.15 

0.71 

1.76 

0.04 

i6 

27.72 

0.87 

1.62 

24.52 

0.75 

1.65 

0.04 

17 

26.09 

0.93 

1.52 

23.08 

0.80 

1.55 

0.04 

i8 

24.64 

0.98 

1.44 

■21.79 

0.85 

1.47 

0.04 

19 

23.34 

1.04 

1.36 

20.65 

0.89 

1.39 

0.05 

20 

22.18 

1.09 

1.30 

19.62 

0.94 

1.32 

0.05 

21 

21.12 

i.i5 

1.23 

18.68 

0.99 

1.26 

0.05 

22 

20.16 

1.20 

1. 18 

17.83 

1.04 

1.20 

0.05 

23 

19.28 

1.26 

1. 13 

17.06 

1.08 

1. 15 

0.06 

24 

18.48 

1. 31 

1.08 

16.3s 

1. 13 

1. 10 

0.06 

25 

17.74 

1.36 

1.04 

15.69 

1. 18 

1.06 

0.06 

26 

17.06 

1.42 

1. 00 

15.09 

1.22 

1.02 

0.06 

27 

16.43 

1.47 

0.96 

14.53 

1.27 

0.98 

0.07 

28 

15.84 

1.53 

0.93 

14.01 

1.32 

0.94 

0.07 

29 

15.29 

1.58 

0.89 

13-53 

1.37 

0.91 

0.07 

30 

14.78 

1.64 

0.86 

13.08 

1. 41 

0.88 

0.07 

'       31 

14.31 

1.69 

0.84 

12.65 

1.46 

0.8s 

0.08 

32 

13.86 

1. 75 

0.81 

12.26 

1. 51 

0.82 

0.08 

33 

13-44 

1.80 

0.78 

11.89 

1. 55 

0.80 

0.08 

34 

13.04 

1.86 

0.76 

11.54 

1.60 

0.78 

0.08 

35 

12.67 

1. 91 

0.74 

II. 21 

1.65 

0.75 

0.09 

36 

12.32 

1.96 

0.72 

10.90 

1.70 

0.73 

0.09 

37 

11.99 

2.02 

0.70 

10.60 

1.74 

0.71 

0.09 

38 

11.67 

2.07 

0.68 

10.32 

1.79 

0.69 

0.09 

39 

11.37 

2.13 

0.66 

10.06 

1.84 

0.67 

O.IO 

The  above  values  based  on  a  maximum  fiber-stress  of  13  000  lb  per  sq  in,  rivet-holes 
in  both  flanges  deducted.  See  paragraph  on  Riveted  Single-Beam  and  Double-Beam 
Girders,  page  603,  and  the  foot-note  for  same  regarding  fiber-stresses.  Weights  of  girders 
correspond  to  lengths,  center  to  center  of  bearings. 


6i2 


Strength  o(  Beams  and  ISeam  Girders  Chap.  15 


Beams  Supporting  Brick  Walls.  In  calculating  the  size  of  a  girder  to  sup- 
port a  brick  wall,  the  structuie  of  the  wall  should  be  carefully  considered.  If 
the  wall  is  without  openings  and  does  not  support  floor-beams,  only  that  part 
of  the  wall  included  within  the  dotted  lines,  Fig.  10,  need  be  considered  as  being 
supported  by  the  girder.  The  beams  in  that 
case,  however,  should  be  made  very  stiff,  so 
as  to  have  little  deflection.  If  there  are 
several  openings  above  the  girder,  and  especi- 
ally if  there  is  a  pier  over  the  middle  part  of 
it,  as  shown  in  Fig.  11,  then  the  manner  in 
wliich  the  loading  is  distributed  should  be 
carefully  considered.  In  a  case  of  this  kind, 
only  the  dead  weight  included  between  the 
dotted  lines  A  A  and  BB  should  be  considered 


Fig.  10.    Triangular  Loading  of  Beams 
under  Brick  Walls 


Fig.  11.     Loading  of  Beams  under 
Walls  with  Openings 


as  coming  upon  the  girder,  and  proper  allowance  made  for  the  concentration 
of  the  greater  part  of  the  load  at  or  near  the  middle.  If,  however,  the  lower 
windows  are  two-thirds  their  total  width,  or  more,  above  the  girder,  then  it 
is  more  reasonable  to  suppose  that  the  wall  included  between  the  lines  CC 
rests  upon  the  girder,  and  also  to  consider  that  this  load  is  uniformly  dis- 
tributed over  it.  When  beams  extend  under  the  entire  length  of  a  wall 
which  is  more  than  i6  or  i8  ft  long,  the  weight  of  the  entire  wall  rather  than 
the  weight  of  a  triangular  part  of  it  should  be  taken  as  coming  upon  the 
beams;  for,  if  they  should  bend,  the  wall  would  settle,  and  might  push  out 
the  supports  and  cause  the  whole  structure  to  fall.      (See,  also,  page  318.) 


5.   Framing  and  Connecting  Steel  Beams  and  Girders 

Standard  Separators.  When  beams  are  used  to  support  walls,  or  as  girders 
to  carry  floor-beams,  they  are  often  placed  side  by  sifie;  and  should  in  such 
cases  be  connected  by  means  of  bolts  and  cast-iron  separators  fitting 
closely  between  the  flanges  of  the  beams.  The  office  of  these  separators  is,  in  a 
measure,  to  hold  in  position  the  compression-flanges  of  the  beams  by  preventing 
SIDE  deflection  or  BUCKLING,  and  also  to  unite  the  beams  so  as  to  cause 
them  to  act  in  unison  as  regards  vertical  deflection.  Separators  should 
be  provided  at  the  supports,  at  points  where  heavy  concentrated  loads  are 
imposed,  and  at  regular  intervals  of  from  5  to  6  ft  between.  TRe  illustra- 
tions, dimensions,  etc.,  given  in  Table  XVI,  are  for  the  standard  separaxj 
in  common  use. 


ixaii 

I 


Framing  and  Connecting  Steel  Beams  and  Girders  613 


Table  XVI.*     Separators  for  Steel  Beams 

AMERICAN    BRIDGE    COMPANY    STANDARD 


Beams 

Separators 

•>4-in  bolts 

d 

"A 

Dimensions 

-£ 

11 

.s 

^£ 

1% 

Diagrams 

-:      Weight 
-^     per  foot. 

0  W 

2i 

0  S 

0  ti 

-J 

&           lb 

J 

w 
in 

h 
in 

d      t 
in    ii 

1 1^ 

G 

24  II5-II0-I0S 

8^4 

16% 

8 

20 

12      •) 

631 

^•^ 

I0>^ 

3.4 

0.25 

100 

8 

151/2 

7H 

20 

12      ■) 

^28 

3.6 

10 

3.2 

0.25 

24    95  and  90 
85 
80 

..  100  and  95 

8 
8 
8 
8 

15I/4 
I5M 
15 
15H 

7V4 
7/2 

7 

20 
20 
20 

12      5^ 
12      •} 
12      -^ 

i28 

<^29 

ii  29 

3.6 
3.6 
3.6 

10 

9VC> 
9K2 

3.2 
3.1 
3.1 
3.2 

0.25 
0.25 

0.25 

1 

t 

16 

12      •) 

^  22 

2.9 

10 

0.25 

^ 

20          90 

7K2 

14% 

6% 

16 

12      •> 

^22 

2.9 

9V1 

3.1 

0.25 

v 

_..  _  : 

_ 

85  and  80 

7Vz 

14H 

6-)<i 

16 

12      •) 

<<.  22 

2.9 

9 

3.0 

0.25 

\ 

'..           75 

7 1/2 

14 

63/, 

16 

12      •) 

^8  22 

2.9 

9 

3.0 

0.25 

j     — 

20          70 

7 

13V2 

61/2 

16 

12      •) 

^  21 

2.9 

9 

3.0 

0.25 

I 

65 

7 

I3'/4 

61/^ 

16 

12      ^) 

^8  21 

2.9 

Wi 

3.0 

0.25 

4  l^" 

i 

90 

8 

15  H 

7 

14 

9     '. 

^20 

2.5 

10 

.3.2 

0.25 

^  V^\ 

18    85  and  80 

8 

15H 

7H 

14 

9     V 

i2I 

2.5 

10 

3.2 

0.25 

Ji" 

\ 

I 

j 

75 
. .    70  and  65 

8 
7 

15 

7V^2 

6H 

14 
14 

9     V 
9     V 

<*2I 

/si8 

2.5 
2.5 

10 

3.2 

3.0 

0.25 
0.25 

--^- 

-i-  L 

18           60 

7 

13  V4 

6K2 

14 

9     ' 

ii  19 

2.5 

8I/2 

3.0 

0.25 

^i 

55 

7 

13 

61/2 

14 

9     ' 

^  19 

2.5 

8I/2 

3.0 

0.25 

*— 

-• 

75 
I  c    70  and  65 

7 

7 

13M 
13K1 

6 

II 

7K2I 
7K2 

412 

/2  12 

1.6 
1.6 

9 
9 

3.0 
3.0 

0,25 
0.25 

J     j 

1 

..i. 

6U 

II 

1     ■    ■ 

..           60 

m 

12K2 

5% 

II 

7K2 

/2II 

1.6 

8 

2.7 

0.25 

.[tl^-.;,,   k— -m  — ->; 

55 

m 

1 2 1/4 

5% 

II 

7K2 

/2  II 

1.6 

8 

2.7 

0.25 

l^V/«' 

15    50  and  45 

42 

6K2 

12^ 
12 

6 
6 

II 
II 

7K2 
7H 

/2  12 
.^  12 

1.6 
1.6 

8 
8 
8 

2.7 
2.7 

0.25 
0.2s 

5^' cored  holes 

55 

6 

11% 

5M 

m 

5 

/2    9 

1.3 

2.7 

0.25 

12           50 

6 

II 1/2 

5I/J 

m 

5 

'4    9 

1.3 

8 

2.7 

0.25 

45 

6 

iiKi 

5V4 

SYa 

5 

/^2     9 

1.3 

1Y 

2.6 

0.25 

12    40  and  35 
31.5 

6 
6 

iiH 
II 

5K2 
5Ki 

8% 

5 
5 

/2     9 

l'^    9 
l^    6 

1.3 
1.3 

I.I 

1V2 
7K2 

2  6 

0.25 

216 

1.3 

0.25 

40 

sVi 

10% 

4% 

7V2 

0.13 

10           35 

sVi 

loH 

4% 

7'/2 

'/2     6 

I.I 

7 

1.3 

0.13 

f^'  ^^" 

30 

sVi 

I0K2 

5 

7K2 

M2    7 

I.I 

7 

1.3 

0.13 

25 

5H 

10 

5 

7/2 

H    7 

I.I 

7 

1.3 

0.13 

35 

5 

10 

4H 

6^2 

K2    5 

0.9 

7 

1.3 

0.13 

1  '' 

—  ■*• 

9           30 

5 

9VC 

4Kt 

6H 

^2     5 

0.9 

6K2 

1.2 

0.13 

ill" 

1 

25 

5 

9K 

4K 

6K2 

H   5 

0.9 

6K 

1.2 

0.13 

^i^ 

I 

21 
25.5 

\v. 

9W 
9 

4K 
4 

6H 

/'    5 

0.9 
0.8 

6K 

1.2 

0.13 

^ 

5^^ 

'/i    ^ 

6 

I.I 

0.13 

8           23 

4'/2 

8% 

4 

5H 

/2      4 

0.8 

6 

I.I 

0.13 

— 

] 

. .  20.5  and  18 
20 

4H 
411 

8K 

8H 

4 
4 

5K 
5 

K2    4 

0.8 
\   o.-j 

6 
6 

i.i 
I.] 

0.13 
0.13 

l.A. 

\\    i 

7          17-5 

\\i 

8V. 

4 

5 

Vi   I 

\    0.' 

6 

I.] 

0.13 

^-*'kii"^/   H" — '*^ — ^^ 

15 

4K 

8M 

41^^ 

5 

Vi   i 

\    0.- 

6 

I.] 

0.13 

^f 

17.25 
6         14-75 

4 
4 

73/ 

J3V 

i  aV 

\   oX 

)    5M 

I.] 
I    I. 

0.13 
[  0.13 

%''cored'  hole 

12.25 

4 

nv 

r 

I   aV 

Vi    4|  o.( 

5    5V 

I    I. 

[  0.13 

For  5-in,  4-in  and  3-in  beams.'use  i-in gas-pipes,  3H,  3 and  2^^tn long,  respectively 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


614 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


Gas-Pipe  Separators.  Separators  formed  of  pieces  of  gas-pipe,  cut  to  the 
desired  lengths  and  slipped  over  the  bolts  are  often  used  by  contractors.  (See 
bottom  of  Table  XVI.)  Such  separators  permit  the  beams  to  act  independently 
of  each  other,  and  should  not  be  used  in  any  place  where  one  beam  is  liable  to 
receive  a  greater  load  than  the  other;  and  as  this  condition  exists  in  almost 
every  case  where  two  or  more  beams  are  used  together,  it  follows  that  "cast- 
iron  separators,  made  to  fit  the  space  between  the  beams,"  should  be  specified 
in  almost  every  instance.  As  noted  in  Table  XVI,  gas-pipe  may  sometimes  be 
used  for  5,  4  and  3-in  beams.  Separators  with  two  bolts  should  be  used  for 
beams  1 2  in  or  more  in  depth.  For  1 2-in  beams  one  bolt  is  sometimes  used  when 
the  load  is  light;  for  beanis  under  12  in  in  depth  one  bolt  is  sufficient. 


FRAMING 

DETAILS  OF  FRAMING  BETWEEN  COLUMNS 


SHOP-DRAWING  OF  GIRDER      (STANDARD  CONNECTIONS  FOR  9  BEAMS] 


.m^ 

•  c 

< 

•  ( 

>• 

) 
>• 

■■1 

-fo 

o 
-  o 


SECTION  A  B 


}4  Clearance-^  SECTION  C  D 


IF 


PUN  OF  ABOVE  WITH  UPPER  FLANGES  REMOVED  ELEVATION  SHOWING  THE  COPING  OF  BEAMS 

CONNECTIONS   FOR    BEAMS   AND    GIRDERS 

"  Connection-angles  shall  in  no  case  be  less  in  thickness  than  the  web  of  the  beam 
or  girder  to  which  they  are  fastened,  nor  shall  the  width  be  less  than  H  the  depth  of 
the  beam,  except  that  no  angle-knee  shall  be  less  than  2y/'  wide  nor  required  to  be 
more  than  6  wide.  Web-angles,  the  full  depth  of  the  web,  must  be  used  for  all  girder- 
connections.  " 

Fig.  12.     Framing  of  Steel  I  Beams  and  Girders 

Beam-Connections.  Steel  beams  and  channels  are  framed  together  by 
means  of  short  pieces  of  angles,  which  are  usually  riveted  to  the  floor-beam  or 
tail-beam  and  bolted  to  the  girder.  The  angles  are  always  used  in  pairs,  one  on 
each  side  of  the  beam.  If  the  floor-beam  is  framed  flush,  either  with  the  top  or 
bottom  of  the  girder,  or  if  two  beams  of  the  same  height  are  framed  together,  the 
end  of  the  beam  supported  should  be  coped,  or  cut  to  fit  the  shape  of  the  girder 
or  supporting  beam.    The  maximum  clearance-space  allowed  between  the  end 


Framing  and  Connecting  Steel  Beams  and  Girders  615 


Fig.  13.     Framing  to  Riveted  Plate  Girder 

of  the  beam  and  the  web  varies  from  Me  in  in  the  smaller  beams  to  H  in  in  the 
larger  ones.  Figs.  12  and  13  show  various  details  of  beams  framed  together 
and  also  to  girders.  When  a  floor-beam  rests  on  top  of  another  beam  or  girder, 
as  in  Fig.  15.  the  beam  should  be  secured  by  means  of  a  pair  of  wrought-iron 


616 


Strength  of  Beams  and  Beam  Girders 


Chap.  15 


CLIPS,  shown  in  Fig.  14,  shaped  so  as  to  fit  closely  the  top  flange  of  the  girder, 
and  either  bolted  or  riveted  to  the  opposite  sides  of  the  lower  flange  of  the  floor- 
beam. 

Fig.  16  shows  one  method  of  framing  the  ends  of  wooden  floor-joists  to  steel 
beams,  a  4  by  3  by  %-in  angle  being  riveted  the  whole  length  of  the  steel  beam, 
by  %-in  rivets,  about  6  in  apart.    The  joists  are  usually  secured  by  iron  or 


^  \\^x  S/^ Anchor 


rig.  14.  Clip  for  Fas- 
tening Steel  Beam  on 
Top  of  Another 


Fig.  15.  Steel  Beams 
Fastened  One  on  the 
Other  by  Clips 


Fig.  1 6.     Framing  of  Wooden 
Joists  to  Steel  I  Beam 


•CLAMPS  or  ANCHORS,  and  framed  about  i  in  above  the  upper  flange  of  the  beam 
to  allow  for  settlement.  If  these  joists  are  over  3  ft  apart,  short  lengths  of  angles 
may  be  placed  under  each  one.* 

Standard  Connection-Angles  for  I  Beams  and  Channels.  The  size  of 
the  angles  and  the  number  of  rivets  used  for  connecting  steel  beams,  vary 
somewhat  with  different  shops  and  with  different  structural  engineers,  so  that 
there  cannot  be  said  to  be  a  universal  standard.  The  variations  in  the  differ- 
ent STANDARDS,  however,  are  not  very  great,  and  as  the  connections  adopted 
by  the  Carnegie  Steel  Company  are  perhaps  the  most  used,  the  author  has  se- 
lected them  for  illustration  in  Table  XVII.  The  connections  have  been  pro- 
portioned with  a  view  to  covering  most  cases  occurring  in  ordinary  practice, 
with  the  usual  relations  of  depth  of  beam  to  length  of  span.  In  extreme  in- 
stances, however,  where  beams  of  short  relative  span-lengths  are  loaded  to  their 
full  capacity,  or  when  beams  frame  opposite  each  other  into  another  beam  with 
web-thickness  less  than  %t  in,  it  may  be  found  necessary  to  make  provision  for 
additional  strength  in  the  connections.  The  limiting  span-lengths,  also, 
at  and  above  which  the  standard  connection-angles  may  be  used  with  perfect 
safety,  are  also  given  in  Table  XVIII. 

•  For  details  of  the  framing  of  floor-beams  and  girders,  see  Chapters  XXI  and  XXII 
and  also  Professor  Nolan's  revised  Chapters  II  and  VII  of  Kidder's  Building-Construction 
and  Superintendence,  Part  II,  Carpenters'  Work, 


Framing  and  Connecting  Steel  Beams  and  Girders 


617 


Table  XVII.*    Connections  for  Steel  Beams 

AMERICAN   BRIDGE    COMPANY   STANDARD 


2Ls4'x4''xi^xl'8i^'' 
Weight  46  lb 

21" 


2Ls4"x4"xi^"xl'2i^* 
Weight  33  lb 


12" 


*5^-* 


^H} 


-& 


2Ls4".x4'x>{'^xO'8i4- 
Weight  IT  lb 

r;  6'/  5" 


Weight  39  lb 


2o;'i8;'i^" 


2)^' 


.2Ls4x4'xy6X0ai^' 
Weight  23  lb 

io;'9;'8" 


^^ 

2H 

^ 

^ 

2H' 

P 

Jl 

1 

^ 

H 

r-'^ 



2.Ls6x4"x%"xO'5>^" 
Weight  13  lb 


4';  3" 


2J^fHH2)^' 


2  Ls  6"x.4"x  %  X  0'3'  2  Ls  G^x  4"x  %"x  0'2* 

Weight  7  lb  Weight  5  lb 

Rivels  andbolts '>^ diameter 

Weiglits  given  are  for  %"shop  rivets  and  angle-connection^;  abouf 

20  per  cent  should  be  added  for  field-rivets  or  bolts 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 


618  Strength  of  Beams  and  Beam  Girders  Chap.  15 

Table  XVin.*     Limiting  Values  of  Connections  for  Steel  Beams 


Value  of 

VnliiP*^  of  niit^t^tirliTiP'  1pp*<n  nf  mnnppf  ion-anp^lp*; 

I  bea.ms 

web-con- 

»   C4AC4.^0    \JL,    V^k^UObC4>XX\^lXX^    JLV^^O    KJi.    \^\Jl.LXX\^\^\i k\JX,X    CLXX^X^Aj 

nection 

Field-rivets 

Field-bolts 

Shop; 

•>4-in  rivets 

or  turned 

bolts, 

single 

shear, 

lb 

Min.  allow- 

;^4-in rough 

Min.  allow- 

_ 

Depth, 

Weight, 

rivets  in 

able  span, 

bolts, 

able  span, 

lb  per 

enclosed 

uniform 

t. 

single 

uniform 

I, 

in 

in 

ft 

bearing, 
lb 

load, 
ft 

in 

shear, 
lb 

load, 
ft 

tT 

27 

90 

82  530 

61  900 

18.9 

~w 

49500 

23. b 

(  80 

67  500 

S3  000 

17 

S 

ti 

42  400 

21.9 

y% 

24 

'  74 

64  260 

S3  000 

16 

4 

H 

42  400 

20  4 

li 

21 

60 1^ 

48150 

44200 

14 

2 

% 

35300 

17.8 

Vs 

20 

6S 

45  000 

35300 

17 

6 

% 

28300 

22  I 

'6 

18 

1  55 

41  400 

35300 

13 

3 

t' 

28300 

16.7 

Ys 

I  48 

34  200 

35300 

12 

8 

He 

28300 

15-4 

V^ 

15 

[  42 
I  37^ 

36900 

35300 

% 

9 

f5 

28300 

II. I 

Ys 

29880 

35300 

"9 

7 

'A 

28300 

10.2 

91 6 

1  31 K2 

23  600 

26  soo 

8 

I 

VlG 

21  200 

90 

Ys 

12 

i  28 

19  170 

26  500 

9 

2 

VX6 

21  200 

9-2 

H 

(  25 

27  900 

17  700 

7 

4 

Vs 

14  100 

9.2 

Ys 

10 

i  221^ 

22  680 

17  700 

6 

8 

Vs 

14  100 

8.6 

Ys 

9 

21 

26  100 

17  700 

5 

7 

Vs 

14  100 

71 

5g 

g 

^17^ 

24300 

17  700 

4 

3 

'A 

14  100 

5  4 

H 

18900 

17  700 

4 

4 

y% 

14  100 

5-5 

% 

7 

15 

II  300 

8800 

6 

2 

% 

7  100 

78 

Ys 

6 

12H 

10  400 

8800 

4 

4 

% 

7  100 

5  5 

Ys 

5 

9H 

9  Soo 

8800 

2 

9 

v% 

7  100 

36 

Ys 

4 

lY^ 

8600 

8800 

2 

2 

^6 

7  100 

2.7 

Ys 

3 

SV2 

7  700 

8800 

I 

3 

Yi 

7  100 

1-4 

Ys 

1 

Allowable  Unit  Stress  in  Pounds  per  Square  Inch  t                     ( 

Rivets shop   12  000 

Rivets,  enclosed.. shop   30000 

Single 
shear 

Rivets  and  turned 

Rivets,  one  side,  .shop    24000 

bolts field   10  000 

Bearing 

Rivets  and  turned 

Rough  bolts field     8  000 

bolts...; field   20000 

Rough  bolts field    16  000 

/  =  Web-thickness,  in  bearing,  to  develop  maximum  allowable  reactions,  when 

beams  frame  opposite 

Connections  are  figured  for  bearing  and  shear  (no  moment  considered) 

The  above  values  agree  with  tests  made  on  beams  under  ordinary  conditions  of 

Where  the  web  is  enclosed  between  connection-angles  (enclosed  bearing),  values 

are  greater  because  of  the  increased  efficiency  due  to  friction  and  grip 

Special  connections  must  be  used  when  any  of  the  limiting  conditions  given 

above  are  exceeded,  as  when  an  end-reaction  from  a  loaded  beam  is  greater  than 

the  value  of  the  connection  of  the  shorter  span  with  the  beam  fully  loaded;  or  a  less 

thickness  of  web  when  maximum  allowable  reactions  are  used 

*From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 
t  For  slight  variations  from  these  values,  see  Chapter  XXVIII.  Table  I  and  Chapter 
XXX,  4,  Stresses. 


Tie-Rods  and  Anchors  for  Steel  Beams  and  Girders 


619 


'     Table  XIX.*      Lengths  and  Weights  of  Tie-Rods  and  Anchors  for  Steel 

Beams 


AMERICAN    BRIDGE    COMPANY    STANDARD 


2K'toiK    ^'toiy/  ' 

[^"""H^~""^c. tocof  '^ir/ii                              •         uL^ff^-tni  \ 

Hl^---:^-  beams 

s 

/ — !'•            ' 

%-INCH  TIE-RODS 
i 

B*i« 

!<---3'--->j 

Lengths  and  Weights  tor  Various  Distances  Center  to  Center  of 

Beams 

Weights  include  two  nuts 

CtoC 

L'th 

Wgt 

CtoC 

L'th 

Wgt 

CtoC 

L'th 

Wgt 

CtoC 

L'th 

Wgt 

ft  in 

ft  in 

lb 

ft  in 

ft  in 

lb 

ft  in 

ft  in 

lb 

ft  in 

ft  in 

lb 

I      0 

I     3 

2.30 

I     3 

I    6 

2.67 

I    6 

I    9 

3.05 

I    9 

2    0 

3.42 

2      0 

2     3 

3.80 

2     3 

2    6 

4.17 

2    6 

2    9 

4.55 

2    9 

3     0 

4.92 

3    0 

3    3 

5.30 

3     3 

3    0 

5.07 

3    b 

3    9 

6.05 

3    9 

4     0 

6.42 

4    0 

4    3 

6.80 

4     3 

4    t 

7.17 

4    b 

4    9 

7.55 

4950 

7.92 

5    0 

5     3 

8.30 

5     3 

5    6 

8.67 

5    b 

5    9 

9  05 

5960 

9.42 

6    0 

6    3 

9.80 

6    3 

6    6 

10.17 

6    6 

b    9 

TO.  55 

6    Q 

7    0 

10.92 

7    0 

7    3 

11.30 

7    3 

7    0 

11.67 

7    b 

7    9 

12.05 

7    9 

8    0 

12.42 

8    0 

8    3 

12.80 

8    3 

8    6 

13.17 

8    6 

8    9 

13.55 

8    9 

9    0 

13.92 

For  strength  of  rods,  see  Table  II,  page  ; 
Anchors  * 


Swedge-Bolt 


Weight  includes  nut 
Built-In  Anchor-Bolts 


Government  Anchor 


M 


^^^^mm^ 


Diameter 

Length 

Weight 

in 

.  ft  In 

lb 

VA 

0  9 

1  0 
1    0 
1    3 

1.3 
2.3 
3.1 
6.1 

[-in  rod,  i  ft  9  in  long.    Wt.,  3  lb 
Angle-Anchor 


OH 


When  center  to  center  of  anchors  is  less  than    Two  angles,  6  by  4  by  Me  by  2H  in 
width  of  washer,  use  washer  with  two  holes  Weight  with  M-in  bolts,  7  lb 


For  bearing-plates,  bases,  etc.,  see  Chapter  XIII. 

♦  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 


620        Strength  of  Cast-iron  Lintels  and  Wooden  Beams    Chap.  16 


CHAPTER  XVI 

STRENGTH    OP    CAST-IKON    LINTELS    AND    WOODEN 

BEAMS 

By 
F.  H.  KINDL 

LATE  CORRESPONDING  MEMBER  AMERICAN  INSTITUTE   OF  ARCHITECTS 

1.    Cast-iron  Lintels 

Form  of  Cross-Section.  Owing  to  the  fact  that  the  resistance  of  cast  iron 
to  tension  is  only  about  one-fifth  of  its  resistance  to  compression,  the  shapes  of 
beams  most  economical  for  wrought  iron  or  steel  would  be  wasteful  for  cast 
iron.  The  extreme  brittleness  of  cast  iron,  and  the  danger  of  flaws  in  castings, 
render  it  an  undesirable  material  for  resisting  transverse  stress.  About  the 
only  form  in  which  cast-iron  beams  are  now  used  in  building-construction  in 
this  country  is  in  the  shape  of  lintels  for  supporting  brick  or  stone  walls,  in 
t)M>n??//}%  places  where  a  flat  soffit  is  desired,  and  the  walls  are 

^%^  not  to  be  plastered.    Cast-iron  lintels  are  also 

i  -  -    -  - 


occasionally  used  over  store-fronts,  the  face  of  the 

lintel  being  paneled  and  molded  for  architectural 

effect. 
Experiments    on    Cast-iron   Beams.    Before 

wrought-iron  I  beams  were  manufactured,  cast- 
i  •  ^  Tssm   BEAMS  were   frequently   used   as   the   only 

available  ones,  other  than  those  of  wood  or  stone. 

Early  in  the  nineteenth  century  Eaton  Hodgkin- 

^i^^%M^^^^%%m%%^       son,  an  English  engineer,  made  a  series  of  experi- 

Fig.l.    Cross-section  of  Cast-    "^^^^s  with  cast-iron  beams,  from  which  he  found 

iron  Lintel  of  Ideal  Form       ^^^  the  form  of  cross-section  of  a  beam  of  that 

material  which  will  resist  the  greatest  transverse 
stress  is  that  shown  in  Fig.  1,  in  which  there  is  six  times  more  metal  in  the 
bottom  than  in  the  top  flange.  The  relative  thicknesses  of  the  three  parts,  the 
web,  the  top  flange  and  the  bottom  flange,  may  be,  with  advantage,  as  5,  6  and 
8,  respectively. 

Strength  of  Cast-Iron  Beams.  If  made  with  these  proportions,  the  width 
of  the  top  flange  will  be  equal  to  one-third  that  of  the  bottom  flange.  As  the 
result  of  his  experiments,  Hodgkinson  gave  the  following  rule  for  the  breaking- 
weight  at  the  middle  for  a  cast-iron  beam  of  this  form: 

I  area  of  bottom  flangeX     /   depth   \ 
I       .  -uX'-u        X  2.426 

_,,.,,.  \      m  square  inches      /      V  in  inches/  ,  ^ 

Breakmg-load  m  tons  =  -^ ^^ — ^ (i) 

clear  span  in  feet 

This  rule,  although  largely  empirical,  agreed  very  well  with  the  few  experi- 
ments that  were  made.  Structural  engineers,  however,  use  the  general  formu- 
las for  the  strength  of  beams,  as  given  in  Chapter  XV,  except  that  the  section- 
modulus  is  found  by  dividing  the  moment  of  inertia  by  the  distance  of  the 
neutral  axis  from  the  bottom  of  the  beam,  and  the  safe  tensile  strength  is 


Cast-iron  Lintels 


621 


used  in  the  flexure-formula.  Thus  the  general  formula  for  a  beam  supported 
at  both  ends  and  with  the  load  uniformly  distributed,  as  given  in  Chapter  XV, 
page  560,  is: 

Safe  load  in  pounds  =  2^^  __  x  5^     As  St,  the  safe  tensile  strength  for  cast 

iron  should  be  taken  at  3  000  lb,  this  formula  becomes 

2  000  l/c 


Safe  load  in  pounds  =  ■ 


(2) 


and,  for  either  section  given  below, 
I/c  = 


Moment  of  inertia 


A  h  lb  ib  ib 

"^     "     I    '    "   ^    I  I  NPUTRAL  AXIS' 


NEUTRAL  AXIS' 


The  MOMENT  OF  INERTIA  is  computed  by  the  formula  (see  page  33s) 


(3) 


in  which  b  denotes  the  combined  thickness  of  the  webs,  and  the  distances  d, 
d\,  and  J2  are  measured  from  the  neutral  axis,  which  must  pass  through  the 
CENTER  OF  GRAVITY  of  the  Section.  The  center  of  gravity  may  be  found  by  the 
method  explained  in  Chapter  VI.  This  formula  may  be  used  for  any  of  the 
above  sections  when  the  depth  does  not  exceed  the  width,  and  the  thickness  of 
each  web  is  at  least  equal  to  the  thickness  of  the  flange.  In  lintels  with  a  singlf 
web  it  is  well  to  make  the  thickness 


r 


1 


_L.. 


r 


_^ 


-6=2 


1 


Fig.  2.    Cross-section   of   Cast-iron  Lintel 
with  Three  Webs 


of  the  web  V4,  or  Vs  in  greater  than 
the  thickness  of  the  flange.  For  a 
beam  with  a  cross-section  like  that 
shown  in  Fig.  1,  Formula  (2)  agrees 
very  closely  with  Formula  (i),  when 
a  factor  of  safety  of  six  is  used. 

Example.  The  following  example 
illustrates  the  application  of  Formula 
(2) :  It  is  required  to  compute  the  safe 
load  for  a  cast-iron  lintel  having  the 
section  shown  in  Fig;  2  and  a  clear  span  of  10  ft.  The  load  is  uniformly  dis- 
tributed, and  the  thickness  of  the  metal  i  in. 

Solution.  The  first  step  is  the  finding  of  distance  d,  that  the  center  of  gravity, 
through  which  the  neutral  axis  of  the  cross-section  passes,  is  below  the  top- 
surface  of  the  beam.  This  is  found  by  taking  the^moments  of  the  areas  of  the 
cross-sections  of  webs  and  flange  about  the  line  XY,  and  dividing  their  sum  by 
the  area  of  the  entire  section.  (See  page  294.)  Each  web-section  is  11  in 
deep  and  i  in  thick;  hence  the  area  of  each  is  11  sq  in.  The  moments  of  the 
THREE  WEBS  about  XY  will  then  be  3X11X5^/^=  181. 5 

The  moment  of  the  flange  about  XY  =  28  X  iiV^  =  322 

503.5 


622        Strength  of  Cast-iron  Lintels  and  Wooden  Beams    Chap.  16 


The  area  of  the  entire  cross-section  =  6i  sq  in 

503.54-61  =  8.25  =  i  in 
Then  d  =  8.25  in  d^  =  561.5 

^i  =  3-75ii^  ^1^=    52.7 

di  =  2.75  in  d'>}  =    20.8 

The  MOMENT  OF  INERTIA  is  next  found  by  Formula  (3) : 

r        3X561.5+28X52.7-25X20.8 


&  =    3  in 

h'  =  28  in 


l/c  =  880/3.75.     From  Formula  (2)  the  safe  load  =  (2  000  X  234.6)/io  =  46  920 
lb,  or  23.4  tons. 

Ends  and  Brackets  of  Cast-iron  Lintels.     When  a  lintel,  the  cross-sec- 
tion of  which  has  the  shape  of  an  inverted  T  (-L),  is  used  over  a  single  opening,  the 


Fig.  3.     Cast-iron  Lintel  with  Tapering  Web 

web  may  be  tapered  towards  the  ends,  as  in  Fig.  3,  without  affecting  the  strength. 
If  the  flange  is  more  than  8  in  wide,  brackets  should  be  cast  in  the  middle,  as  at 
A,  Fig.  3. 

When  CONTINUOUS  lintels  are  used  over  store- fronts  or  similar  places, 
ends  should  be  cast  on  the  lintels,  as  in  Fig.  4,  and  the  ends  of  abutting  lintels 


Fig.  4.     Cast-iron  Lintel  with  Ends  for  Bolting 

bolted  together.     All  lintels  with  two  or  three  webs  should  haveCsolid  ends  con- 
necting the  webs. 

Tables  of    Strength  of  Cast-iron  Lintels.    The  tables  on  the  following 
pages  have  been  computed  in  accordantce  with  Formula  (2)^  ^The  weight  of  the 


Cast-Iron  Lintels 


623 


lintel  itself  should  be  deducted  from  the  safe  load.  In  using  these  tables  it 
should  be  remembered  that  the  values  are  for  loads  uniformly  distributed. 
If  the  load  is  concentrated  at  the  middle,  it  should  be  multiplied  by  2.  If 
at  some  other  point  than  the  middle,  the  load  should  be  multiplied  by  the  value 
given  on  pages  566  and  632,  which  most  nearly  corresponds  with  the  position 
of  the  load.  For  other  spans  than  those  given,  the  distributed  load  should  be 
multipHed  by  the  span,  and  the  lintel  used  which  has  acoEmciENT  of  strength 
C  (Table  I)  just  above  the  product  thus  obtained.  (For  explanation  of  coeffi- 
cient of  strength,  see  Chapter  XV,  page  556.) 

Example.  It  is  required  to  support  a  12-in  brick  wall,  10  ft  high,  over  an 
opening  5  ft  6  in  wide,  with  a  cast-iron  lintel.  At  a  distance  of  22  in  from  one 
support,  a  girder,  which  may  bring  a  load  of  9  600  lb  on  the  lintel,  enters  the 
wall.     What  should  be  the  dimensions  of  the  lintel? 

Solution.  At  no  lb  per  cu  ft,  the  wall  above  the  lintel  weighs  10  X  5^/^  X  no 
=  6050  lb.  As  22  in  is  one-third  of  the  span,  the  concentrated  load  is  multi- 
plied by  1.78  (page  632),  making  the  load  17  088  lb.  The  total  equivalent  dis- 
tributed load  is  then  23  138  lb.  Multiplying  this  by  the  span  there  results 
127  259  lb,  or  63.6  tons,  as  the  least  value  for  the  coefficient  of  strength  C.  From 
the  table,  it  is  found  that  a  12  by  lo-in  lintel,  i  in  thick,  with  one  web,  has  a 
coefficient  of  strength  of  72.2;  and  that  a  12  by  8  by  ii4-in  lintel  with  two  webs, 
has  a  coefficient  of  strength  of  69.9.  A  lintel  with  two  webs  is  best  for  a  12-in 
wall,  and  interpolating  between  the  values  of  C  for  the  i-in  and  2-in  thicknesses 
of  the  12  by  8-in  lintel,  65.4  is  found  to  be  the  value  of  C  for  a  thickness  of  iVs 
in.  This  exceeds  the  required  value  by  enough  to  more  than  compensate  for 
the  weight  of  the  hntel  itself;  hence  a  12  by  8  by  iV^-in  lintel  with  two  webs 
is  used. 

Flaws  in  Castings.  Owing  to  the  Hability  of  flaws  in  the  castings,  cast-iror 
beams  should  always  be  carefully  inspected  before  being  accepted. 


624        Strength  of  Cast-iron  Lintels  and  Wooden  Beams    Chap.  16 
Table  I.     Safe  Distributed  Loads  in  Tons  for  Cast-iron  Lintels 


Lintels  of 


1-^-4=^ 


Shapes 


K- WIDTH ->j  U_wiOTH->l 

J  »       •  » 

Loads  include  weights  of  lintels.     Maximum  tensile  stress  3  ooo  lb  per  sq  in.    See 
remarks,  pages  622  and  623. 


Size, 
width 

by 

depth, 

in 

Thick- 
ness of 
metal. 

Weight 
per 
foot. 

c, 

tons 

Span  in  feet 

in 

lb 

5 

6 

7 

8 

9 

10 

II 

12 

H 

26.3 

15.9 

3.18 

2.65 

2.27 

1.98 

1.76 

1.59 

1.44 

1.32 

6x  6 

I 

34.4 

19.0 

3.80 

3.16 

2.71 

2.37 

2. II 

1.90 

1.72 

1.58 

iH 

42.0 

21.5 

4-30 

3.58 

3.07 

2.68 

2.39 

2. IS 

1.95 

1.79 

% 

28.6 

17.8 

3.56 

2.96 

2.54 

2.22 

1.98 

1.78 

1. 61 

1.48 

7X  6 

I 

37. 5 

21.3 

4.26 

3.55 

3.04 

2.66 

2.36 

2.13 

1.93 

1.77 

iH 

45-9 

24.0 

4.80 

4.00 

3.43 

3.00 

2.66 

2.40 

2.18 

2.00 

% 

31.0 

22.6 

4-52 

3.76 

3.23 

2.82 

2.51 

2.26 

2.0s 

1.88 

7X  7 

I 

40.6 

27.5 

5. SO 

4.58 

3.93 

3.43 

3.05 

2.75 

2.50 

2.29 

iM" 

49-8 

31.4 

6.28 

5.23 

4.49 

3.92 

3.49 

3.14 

2.85 

2.62 

H 

31.0 

19.6 

3.92 

3.26 

2.80 

2.45 

2.18 

1.96 

1.78 

1.63 

8X  6 

I 

40.6 

23.4 

4.68 

3.90 

3.34 

2.92 

2.60 

2.34 

2.12 

1.9s 

iH 

49-8 

26.4 

5.28 

4.40 

3.77 

3.30 

2.93 

2.64 

2.40 

2.20 

' 

H 

33.3 

25.0 

5.00 

4.16 

3.57 

3.12 

2.77 

2.50 

2.27 

2.08 

8X  7 

I 

43.7 

30.3 

6.06 

5.05 

4.33 

3.79 

3.36 

3.03 

2.75 

2.52 

iH 

53.7 

34.8 

6.96 

5.80 

4.97 

4.35 

3.86 

3.48 

3.16 

2.90 

?4 

35. 6 

30.6 

6.12 

5.10 

4.37 

3.82 

3.40 

3.06 

2.78 

2.55 

8X  8 

I 

46.8 

37.6 

7.52 

6.26 

5.37 

4.70 

4.18 

3.76 

3.41 

3.13 

iH 

57.6 

43.4 

8.68 

7.23 

6.20 

5. 42 

4.82 

4.34 

3.94 

3.61 

H 

38.0 

36.5 

7.30 

6.08 

5.21 

4.56 

4.05 

3.65 

3.31 

3.04 

8X  9 

I 

50.0 

45.2 

9.04 

7.53 

6.45 

5.65 

5.02 

4.52 

4. II 

3.76 

iH 

61. 5 

52.6 

10.52 

8.76 

7.51 

6.57 

5.84 

5.26 

4.78 

4.38 

H 

40.4 

26.S 

5.30 

4.41 

3.78 

3.31 

2.94 

2.65 

2.41 

2.21 

I2X   6 

I 

53.1 

31.6 

6.32 

5. 26 

4.51 

3.95 

3.51 

3.16 

2.87 

2.63 

iH 

65.4 

34.8 

6.96 

5.80 

4.97 

4.35 

3.86 

3.48 

3.16 

2.90 

H 

45.0 

41.7 

8.34 

6.95 

5.95 

5.21 

4.63 

4.17 

3.79 

3.48 

I2X  8 

I 

59-4 

51.2 

10.24 

8.53 

7.31 

6.40 

5.69 

5.12 

4.6s 

4.26 

iH 

73.2 

58.5 

11.70 

9.75 

8.35 

7.31 

6.50 

5.85 

5. 32 

4.87 

% 

49-8 

58.0 

11.60 

9.66 

8.28 

7.25 

6.44 

5.80 

5.27 

4.83 

12X10 

1 

65.6 

72.2 

14.44 

12.03 

10.31 

9.02 

8.02 

7.22 

6.56 

6.01 

iH 

81.0 

83.8 

16.76 

13.96 

11.97 

10.47 

9.31 

8..^8 

7.62 

6.98 

H 

54.4 

75.2 

15.04 

12.53 

10.74 

9.40 

8.35 

7.52 

6.83 

6.26 

12x12 

I 

71.9 

94.8 

18.96 

15.80 

13.54 

11.85 

10.53 

9.48 

8.62 

7.90 

iH 

88.9 

III. 5 

22.30 

18.58 

15.92 

13.93 

12.39 

II. IS 

10.12 

9.29 

Cast-iron  Lintels  625 

Table  I  (Continued).    Safe  Distributed  Loads  in  Tons  for  Cast-Iron  Lintels 

1" 


Lintels  of 


1 

1 

'1 

.Shapes 


Loads  include  weights  of  lintels.    Maximum  tensile  stress  3  ooo  lb  per  sq  in.     See 
remarks,  pages  622  and  623. 

Size, 
width 

by 

depth., 

in 

Thick' 

ness  of 

metal, 

in 

Weight 

per 

foot, 

lb 

c, 

tons 

Span  in  feet 

5 

6 

7 

8 

9 

10 

11 

12 

I2X  6 

2/4 

I 

52. 7 
68.8 
84.0 

31.7 
37.6 
43.0 

6.34 
7.52 
8.60 

5.28 
6.26 
7.16 

4.53 
5.37 
6.14 

3.96 
4.70 
5.37 

3. 52 
4.18 
4.77 

3.17 
3.76 
4.30 

2.88 
3.42 
3.91 

2.64 
3.13 
3.58 

I2X  8 

I 

62.1 
81.3 
99.6 

49-5 
60.9 
699 

990 
12.18 
13.98 

8.25 
10.15 
11.65 

7.07 
8.70 
9.98 

6.19 
7.61 
8.73 

5.50 
6.76 
7.76 

4.95 
6.09 
6.99 

4.50 
5.53 
6.35 

4.12 
5.07 
5.82 

14X  6 

I 

57.4 

75:0 

91.8 

35.5 
42.0 
48.0 

7.10 
8.40 
9.60 

5-91 
7.00 
8.00 

5.07 
6.00 
6.85 

4.43 
5.25 
6.00 

3.94 
4.66 
5.33 

3.55 
4.20 
4.80 

.3.22 
3.82 
4.36 

2.96 
3.50 
4.00 

I4X  8 

I 

66.8 
87.5 
107.4 

55.4 
68.1 
78.8 

11.08 
13-62 
15.76 

9.23 
11.35 
13.13 

7.91 
9.73 
11.25 

6.92 
8.$i 
9.85 

6.15 
7.56 
8.75 

5.54 
6.81 
7.88 

5. 03 
6.19 
7.16 

4.61 
5.67 
6.56 

i6x  6 

I 

62.1 
81.3 
99-6 

39- 1 
46.8 
52.9 

7.82 
9.36 
10.58 

6.51 
7.80 
8.81 

5. 58 
6.68 
7.55 

4.88 
5.85 
6.61 

4.34 
5.20 
5.88 

3.91 
4.68 
5.29 

3.55 

4.25 
4.81 

3.25 
3.90 
4.40 

i6x  8 

I 

1K4 

71.5 
93.8 
115. 2 

61.4 
74.6 
86.8 

12.28 
14.92 
17.36 

10.23 
12.43 
14.46 

8.77 
10.65 
12.40 

7.67 
9-32 
10.85 

6.82 
8.29 
9.64 

6.14 
7.46 
8.68 

5.58 
6.78 
7.89 

5. II 
6.21 
7.23 

20X  6 

I 

71. 5 
93.8 
115. 2 

47-2 
55.1 
62.0 

9.44 
11.02 
12.40 

7.86 
9.18 
10.33 

6.74 
7.87 
8.85 

5.90 
6.88 
7.75 

5.24 
6.12 
6.88 

4.72 
5.51 
6.20 

4.29 
5. 01 
5. 63 

3.93 
4.59 
5.16 

20X  8 

I 

80.8 
106.2 
130.8 

72.6 
89.5 
102. s 

14.52 
17.90 
20.50 

12.10 
14.91 
17.08 

10.37 
12.78 
14.64 

9.07 
11.18 
12.81 

8.06 
9.94 
11.39 

7.26 
8.95 
10.25 

6.60 
8.13 
9.31 

6.05 
7.45 
8.54 

20X10 

I 

90.2 
118. 8 
146.5 

100.5 
125.4 
146.8 

20.10 
25.08 
29.36 

16.75 
20.90 
24.46 

14.35 
17.91 
20.97 

12.56 
15.67 
18.35 

11.16 
13.93 
16.31 

10.05 
12.54 
14.68 

9-13 
11.40 
13.34 

8.37 
10.45 
12.23 

20X12 

I 

99.6 
131. 3 
162. 1 

122.6 
158.0 
189.5 

24.52 
31.60 
37.90 

20.43 
26.33 
31.58 

17.51 
22.57 
27.07 

15.32 
19.75 
23.68 

13.62 
17.55 
21.05 

12.26 
15.80 
18.95 

11.14 
14.36 
17.22 

10.21 
13.16 
15.79 

24X  8 

I 

90.2 
118. 8 
146.5 

83.4 
102.4 
117. 0 

16.68 
20.48 
23.40 

13.90 
17.06 
19.50 

11.91 
14.63 
16.71 

10.42 
12.80 
14.62 

9.26 
11.37 
13.00 

8.34 
10.24 
11.70 

7.58 
9-31 
10.63 

6.95 
8.53 
9.75 

626         Strength  of  Cast-iron  Lintels  and  Wooden  Beams     Chap.  16 
Table  I  (Continued).     Safe  Distributed  Loads  in  Tons  for  Cast-Iron  Lintels 


Lintels  at 


"T' 


Shapes 


->j     r^    ^- 


Loads  include  weights  of  lintels.     Maximum  tensile  stress  3  ooo  lb  per  sq  in.     See 
remarks,  pages  622  and  623. 


Size, 
width 

by 

depth, 

in 

Thick- 
ness of 
metal, 
in 

Weight 

per 

foot, 

lb 

c, 

tons 

Span  in  feet 

5 

6 

7 

8 

9 

10 

II 

12 

24X10 

I 

99.6 
131. 3 
162. 1 

116. 
144. 
167. 

0    23.20 
4    28.88 
6    33.52 

19-33 
24.06 
27-93 

16.5 
20.6 
23.9 

7    14-50 

3  18.05 

4  20.95 

12.88 
16.04 
18.62 

11.60 
14-44 
16.76 

10.54 
13.12 
15.23 

9.66 
12.03 
13.96 

24X12 

1 

109.0 
143.8 
177.7 

150. 
189. 
223. 

4    30.08 
6    37.92 
0    44.60 

25.06 
31.60 
37.16 

21.4 
27.0 
31.8 

8    18.80 
6    23.70 
5    27.87 

16.71 
21.06 
24.77 

15 -04 
18.96 
22.30 

13-67 
17.23 
20.27 

12.53 
15.80 
18.58 

28X  8 

I 

99-6 
131. 3 
162. 1 

95. 
115. 
130. 

5    19.10 
0    23.00 
5    26.10 

15-91 
19.16 
21.75 

13-6 
16.4 
18.6 

4    11.93 

3  14.37 

4  16.31 

10.61 
12.77 
14.50 

9.55 
11.50 
13.05 

8.68 
10.45 
11.86 

7.98 
9-58 
10.87 

28X10 

I 

109.0 
143.8 
177.7 

130. 
164. 
188. 

0    26.00 
8    32.96 
5    37.70 

21.67 
27.46 
31.41 

18.5 
23-S 
26.9 

7    16.25 
4    20.60 
3    23.56 

14.44 
18.31 
20.94 

13.00 
16.48 
18.85 

11.82 
14.98 
17.14 

10.83 
13-73 
15.70 

28X12 

H 

I 

118. 3 
156.3 
193.3 

162. 
211. 
252. 

5    32.50 
8    42.36 
0    50.40 

27.68 
35.30 

42.00 

23.2 
30.2 
36. c 

1    20.31 
6    26.48 
0    31.50 

18.06 
23.53 
28.00 

16.25 
21.18 
25.20 

14.77 
19  25 
22.91 

13.54 
17.6s 
21.00 

I 

.INTELS 

OF 

Shape 

s 

t 

DEPTH 
i 

fe WIDTH 

-M 

16X  6 

H 

I 

74.4 
96.9 
118. 1 

43. 
52. 
59. 

3  8.66 

4  10.48 
3    11.86 

7.21 
8.73 
9.88 

6.1 

7.4 
8.4 

8      5.41 
8      6.55 

7      7.41 

4.81 
5-82 
6.59 

4-33 
5.24 
5.93 

3.93 

4.76 
5.39 

3.60 
4.36 
4.94 

i6x  8 

I 

88.5 
115. 6 
141. 6 

68. 
83. 
97. 

1    13.62 
9    16.75 
0    19.40 

11.35 
13.98 
16.16 

9-7 
11.9 
13.8 

3      8.51 
8    10.48 
5    12.12 

7.56 
9.32 
10.77 

6.81 
8.39 
9.70 

6.19 
7.62 
8.81 

5.67 
6.99 
8.08 

20X  8 

I 

97.8 
128. 1 

157.2 

80. 
98. 
113. 

2    16 . 04 
7    19.74 
9    22.78 

13.36 
16.45 
18.98 

II. 4 
14.1 
16.2 

5    10.02 
0    12.33 
7    14.23 

8.91 
10.96 
12.65 

8.02 

9-87 
11.39 

7.29 
8.97 
10.35 

6.68 
8.22 
9-49 

Sections,  Stresses,  Buckling  and  Deflection  of  Wooden  Beams     627 
Table  I  (Continued).     Safe  Distributed  Loads  in  Tons  for  Cast-iron  Lintels 


Lintels  or 


Loads  include  weights  of  lintels.     Maximum  tensile  stress  3  000  lb  per  sq  in.    See 
remarks,  pages  622  and  623. 


Size, 
width 

by 
depth, 


Thick- 
ness of 
metal, 


Weight 

per 

foot 

lb 


C, 

tons 


Span  in  feet 


24  X  8 


iH 

I 
iH 


III. 9 
146.9 
180.7 

126.0 
165.6 
204.1 

107.2 
140.6 
172.6 

121. 3 
159-4 
196.3 

135.3 
178. 1 
219-7 

130.7 
171-9 
211. 9 

144-7 
190.6 
235-3 


112. o 
139-7 
163. 5 

146.7 
184.8 
218.8 

91  9 

112. 8 
130.2 

127.8 
159.5 
183.6 

166.6 
209.3 

247-7 

141. 4 
177.4 
207.8 

186.0 
234.6 
277.9 


22.40 
27.94 
32.70 

29.34 
36.96 
43.76 

18.38 
22.  SC 
26.04 

25.56 
31.90 
36.72 

,33.32 
41.86 
49.54 

28.28 
35.48 
41.56 

37.20 
46.92 
55.58 


18.66 

23. 

27.25 

24.45 
30.80 
36.46 

15.31 

18.80 
21.70 

21.30 
26.58 
30.60 

27.76 
34.88 
41.28 

23.57 
29.57 
34.63 

31.00 

39-10 
46.31 


16.00 
19.95 
23.35 

20.95 
26.40 
31.25 

13.12 
16. II 
18.57 

18.25 
22.78 
26.23 

23.80 
29.90 
35.39 

20.20 
25.34 
29.68 

26.57 
33.51 
39.70 


14.00 
17.46 
20.43 

18.33 
23.10 
27.35 

11.49 
14.10 
16.27 

15.97 
19.94 
22.95 

20.82 
26.16 
30.96 

17.67 
22.17 
25-97 

23.25 
29.32 
34.74 


12.44 
15.52 
18.16 

16.30 
20.53 
24.31 

10.21 
12.53 

14.47 

14.20 

17. 72 
20.40 

18.51 
23.2s 
27.52 

15.71 
19.71 
23.09 

20.66 
26.06 
30.88 


13.97 
16. 35 

14.67 
18.48 
21.88 

9-19 
11.28 
13.02 

12.78 
15.95 
18.36 

16.66 
20.93 
24.77 

14.14 
17.74 
20.78 

18.60 
23.46 
27.79 


10.18 
12.70 
14.86 

13.33 
16.80 
19-89 

8.35 
10.25 
11.83 

II. 61 
14.50 
16.69 

15.14 
19.02 
22.51 

12.85 
16.12 
18.89 

16.91 
21.32 
25.26 


9.33 
11.64 
13.62 

12.22 
15.40 
18.24 

7.66 
9-40 
10.85 

10.65 
13.29 
15.30 

13.88 

17.44 
20.64 

11.78 
14.78 
17.31 

15.  SO 
19. 55 
23.16 


2.     Sections,  Stresses,  Buckling  and  Deflection  of  Wooden  Beams  and 

Girders 
Sections  and  Fiber-Stresses.  The  cross-sections  of  wooden  beams  are 
almost  invariably  square  or  rectangular,  and  those  shapes  only  are  con- 
sidered in  the  following  rules  and  formulas.  Beams  should  have  such  a  cross- 
section,  that  the  maximum  fiber-stress  due  to  transverse  bending,  the  maximum 
horizontal  shear  and  the  compression  across  the  grain  at  the  end-bearings  do  not 
exceed  the  average  allowable  unit  stresses  as  set  forth  in  Table  XVI. 

Buckling.  Wooden  girders  should  be  braced  laterally  to  prevent  buckling 
when  the  ratio  of  length  to  breadth  exceeds  twenty,  or  designed  with  a  reduced 
fiber-stress  from  that  allowable,  where  this  ratio  is  exceeded.  Tables  VII  to 
XV  assume  such  bracing.  Joists  should  have  bridging  not  over  8  ft  on  centers. 
The  percentage  of  reduction  of  fiber-stress  for  girders  should  be  as  follows: 


628 


Strength  of  Cast-iron  Lintels  and  Wooden  Beams    Chap.  16 


Ratio  of  length  to  width 20  to  30 

Percentage  of  reduction 25 


30  to  40    40  to  50     50  to  60 
34  42  50 

Deflection.  It  is  also  important  that  beams  carry  the  loads  without  deflect- 
ing beyond  a  limit  fixed  by  the  use  to  which  the  structure  is  applied;  this  limit 
is  generally  taken  at  Vso  of  an  inch  per  foot  of  span  for  plastered  ceilings. 

3.    Constants  and  CoeflSicients  for  Beams 

Value  of  the  Constant,  A.  The  letter  A  in  the  following  formulas  (4)  to 
(16),  denotes  the  safe  load  for  a  unit  beam,  i  in  square  in  section  and  i  ft  in 
span,  loaded  at  the  middle  of  the  span.  This  is  also  one-eighteenth  of  the 
ALLOWABLE  FIBER-STRESS  in  pounds  per  square  inch.  (See  Table  I,  on  page 
557.)  The  following  are  the  values  of  A,  obtained  by  dividing  by  eighteen  the 
RECOMMENDED  UNIT  STRESSES  for  TRANSVERSE  BENDING,  and  those  given  in  the 
building  laws  of  New  Ybrk,  Chicago,  Baltimore  and  Boston. 


Table  II.* 


Coefficients  for  Iron,  Steel  and  Wooden  Beams. 
Formulas 


Values  for  A  in 


Materials 

New  York 

Chicago 

Baltimore       Boston 

Recom- 
mended t 

Cast  iron 

167 
667 
889 

90 
67 
67 
44 

167 
667 
889 

72 
44 
44 
33 

167 
667 
889 

100 
56 

75 

167 
667 

889 

83 
56 
56 

167 

667 
889 

67 
39 
39 
33 
44 
67 
S6 

Wrought  iron  .... 

Steel 

Yellow  pine 

White  pine 

Spruce 

Hemlock 

Chestnut 

* 

Oak                        .    .      . 

67 
67 

67 
72 

83 

56 

Douglas  fir 

•  For  safe  allowable  working  unit  stresses  for  other  'woods,  see  Table  XVI,  page  647. 
From  these  values,  A  may  be  determined  by  dividing  them  by  eighteen.  See  Table 
XVII,  page  648,  for  other  stresses  for  woods,  taken  from  various  building  laws.  See 
Tables  XVIII  and  XIX,  pages  650  and  651,  for  the  ultimate  strength  of  woods. 

t  The  values  of  A  for  wo(*den  beams  may  be  increased  from  30  to  40%  for  temporary 
structures,  and  for  commercially  dry  and  protected  timber,  not  subject  to  impact,  or  for 
ideal  conditions. 


Table  III.     Coefficients  Recommended  for  Stone  J  and  Concrete  Beams. 
Values  of  A 


Materials 

Values  of 
A 

Materials 

Values  of 
A 

Granite 

10 
8 
7 
6 

Bluestone 

17 

22 
1-7 
I.I 

Limestone 

Slate. 

Marble 

Sandstone 

Concrete  1:2:4 

Concrete  1:2:5 

t  Values  of  A  for  stone  beams  were  taken  from  former  Building  Laws  of  New  York 
ancl  from  the  rec^uirements  of  the  Board  of  Fire  Underwriter^. 


FlexUral  Strength  of  Wooden  Beams 


m 


4.   Flexural  Strength  of  Wooden  Beams 

Section-Modulus.  For  beams  with  a  rectangular  cross-section,  the  formulas 
for  strength  can  be  simplified  by  substituting  for  the  section-modulus  its 
Value  Va  bd-,  where  b  is  the  breadth  and  d  the  depth  of  the  section. 

Substituting  this  value  in  the  general  formulas  for  beams  with  rectangular 
cross-sections  arid  of  any  material,  the  following  formulas  result: 

Beams  Fixed  at  One  End  and  Loaded  at  the  Other  (Fig.  5). 

^  ,    ,      ,   .              ,        breadth  X  square  of  depth  X^*  ,  , 

bate  load,  m  pounds  = 7—. — 7 — ^  (4) 


or 


Breadth,  in  inches 


4  X  length  in  feet 

4  X  load  X  length  in  feet 
square  of  depth  XA* 


(5) 


-Z— 


w 


Fig.  5.     Cantilever  Beam.     Load 
near  Free  End 


Fig.  6.     Cantilever  Beam.     Distrib- 
uted Load  over  Entire  Span 


Beams  Fixed  at  One  End  and  Loaded  with  a  Uniformly  Distributed  Load 
(Fig.  6). 

breadth  X  square  of  depth  X  A* 


Safe  load,  in  pounds  =. 
Breadth,  in  inches 


2  X  length  in  feet 

2  X  load  X  length  in  feet 
square  of  depth  X  ^* 
P 


(6> 
(7) 


-Z- 


Fig.  7.    Simple  Beam.    Load  at  Aliddle  of  Span 
Beams  Supported  at  Both  Ends  and  Loaded  at  the  Middle  (Fig.  7). 

^  -    ,      ,   ,              ,       breadth  X  square  of  depth  Xyl* 
bare  load,  m  pounds  = 


Breadth,  in  inches 


span  in  feet 

span  in  feet  X  load 
square  of  depth  X  ^  * 
*  For  values  of  A,  see  Tables  II  and  III. 


(8) 
(9) 


630        Strength  of  Cast-iron  Lintels  and  Wooden  Beams    Chap.  16 


Beams  Supported  at  Both  Ends  and  Loaded  with  a  Uniformly  Distributed 
Load  Over  Entire  Span  (Fig.  8). 


Fig.  8.    Simple  Beam.     Distributed  over  Entire  Span 

2  X  breadth  X  square  of  depth  XA* 


Safe  load,  in  pounds  = 


Breadth,  in  inches 


span  in  feet 
span  in  feet  X  load 


(lo) 


(ii) 


2  X  square  of  depth  X  ^  * 
Beams  Supported  at  Both  Ends   and  Loaded  with  a  Uniformly  Distributed 
Load  Over  Only  a  Portion  of  the  Span  (Fig.  9). 

-m- 


Fig.  9.    Simple  Beam.     Distributed  Load  over  Part  of  Span 

In  this  case  the  dimensions  of  the  beam  required  to  carry  the  load  can  be 
accurately  determined  only  by  computing  the  maximum  bending  moment,  as 
explained  in  Chapter  IX,  and  substituting  the  value  thus  found  in  Formula  (i6), 
following.  If,  however,  the  length  /i  is  very  short  in  comparison  with  /,  and 
near  the  middle,  then  the  load  may  be  considered  as  concentrated  at  the  middle 
of  the  span  and  the  breadth  of  the  beam  may  be  found  by  Formula  (9).  For- 
mula (13)  is  used  if  the  load  is  at  one  side  of  the  middle.  The  error  will  be  on 
the  safe  side. 

Beams  Supported  at  Both  Ends  and  Loaded  with  Concentrated  Load,  not 
at  the  Middle  of  the  Span  (Fig.  10). 


Fig.  10.     Simple  Beam.     Concentrated  Load  at  Any  Point 

breadth  X  square  of  depth  X  span  X  ^  * 


Safe  load,  in  pounds  = 


Breadth,  in  inches     =  • 


4XfnXn 
4  X  load  XmXn 


square  of  depth  X  span  XA* 
'  For  values  of  .4,  see  Tables  II  and  III. 


(12) 
(13) 


Application  of  Formulas  for  Flexural  Strength  of  Wooden  Beams    631 


Beams  Supported  at  Both  Ends  and  Loaded  with  P  Pounds  at  a  Distance 
m,  from  each  End  (Fig.  11).  ^^ 


Pa  ^P 

Fig.  11.     Simple  Beam.    Two  Equal  Concentrated  Loads  Symmetrically  Placed 

Safe  load,  P,  in  pounds )       breadth  X  square  of  depth  X  A* 


at  each  point 


Breadth,  in  inches 


4X  w 
4  X  load  at  one  point  X  m 


(14) 


(15) 


square  of  depth  XA* 

Note.    In  the  last  two  cases  the  lengths  denoted  by  m  and  n  should  be  in 
feet,  as  the  spans  are  in  feet. 


5.   Application  of  Formulas  for  Flexural  Strength  of  Wooden  Beams 

Example  i.  What  load,  6  ft  out  from  the  wall,  will  an  8  by  14-in  long-leaf 
yellow  pine  beam,  securely  fastened  at  one  end  into  a  brick  wall>  sustain  with 
safety? 

Solution.    The  safe  load  in  pounds  (Formula  4)  =  ■ =  4377  lb 

4X6 

Example  2.  It  is  desired  to  suspend  tw.o  loads  of  10  000  lb  each,  4  ft  from 
each  end  of  an  oak  beam,  20  ft  long.     What  should  be  the  size  of  the  beam? 

Solution.  Let  the  depth  of  the  beam  be  assumed  to  be  16  in.  Then  (For- 
mula 15) 

4  X  10  000  X  4 


The  breadth  =  ■ 


=  9.3  in,  nearly 


256  X  67 
The  beam,  therefore,  should  be  10  by  16  in  in  cross-section. 

Beam  with  Several  Loads.  It  is  required,  next,  to  determine  the  size  of  a 
beam  which  is  supported  at  both  ends,  and  which  will  safely  support  several 
concentrated  loads,  or  a  distributed  load  and  one  or  more  concentrated  loads. 
The  correct  method  of  finding  the  least  size  of  a  beam  that  will  safely  support 
a  combination  of  loads,  is  to  first  find  the  maximum  bending  moment,  as  ex- 
plained in  Chapter  IX,  page  329,  and  then  substitute  the  value  thus  found  for 
this  BENDING  MOMENT  in  the  following  formula: 

4  X  maximum  bending  moment  in  f  t-lb 


Breadth,  in  inches  =  ■ 


(16) 


square  of  depth  X  A 

A  shorter  and  easier  method  is  to  find  the  equivalent  distributed  load  for 
each  concentrated  load,  and  then  find  the  size  of  a  beam  required  to  support 
the  total  equivalent  distributed  load  thus  found.  The  equivalent  distributed 
loads  for  concentrated  loads  applied  at  different  proportions  of  the  span  from 
either  end,  may  be  obtained  by  multiplying  the  concentrated  loads  by  the  follow- 
ing factors: 

*  For  values  of  A,  see  Tables  II  and  III. 


632        Strength  of  Cast-iron  Lintels  and  Wooden  Beams    Chap.  16 
Table  IV.    Factors  for  Equivalent  Distributed  Loads 


Factor 

Position  of  load 

For  a  concentrated  load 
For  a  concentrated  load 
For  a  concentrated  load 
For  a  concentrated  load 
For  a  concentrated  load 
For  a  concentrated  load 
For  a  concentrated  load 
For  a  concentrated  load 
For  a  concentrated  load 

Applied  at  middle  of  span 
Applied  at  one-third  the  span 
Applied  at  one-fourth  the  span 
Applied  at  one-fifth  the  span 
Applied  at  one-sixth  the  span 
Applied  at  one-seventh  the  span 
AppHed  at  one-eighth  the  span 
Applied  at  one-ninth  the  span 
Applied  at  one-tenth  the  span 

Multiply  by  2. 
Multiply  by  1.78 
Multiply  by  1.5 
Multiply  by  1.28 
Multiply  by  1^6 
Multiply  by  0.98 
Multiply  by    % 
Multiply  by  0.79 
Multiply  by  0.72 

*  (See,  also,  Chapter  XV,  Safe  Loads  for  Steel  Beams,  page  566.) 

Thus,  a  concentrated  load  of  900  lb,  applied  at  one-sixth  the  span  from  one 

support,  will  result  in  the  same  maximum  bending  moment  as  a  distributed 

load  of  900  X  1%,  or  i  000  lb. 

The  above  method  for  finding  the  size  of  a  beam  for  a  combination  of  several 

loads  gives  a  larger  beam  than  the  correct  method,  by  Formula  (16),  for  the 

reason  that  the  maximum  bending  moment 
will  not  be  equal  to  the  sum  of  the  in- 
dividual bending  moments.  Hence,  when 
there  are  several  heavy  loads  to  be  sup- 
ported, it  is  economical  to  compute  the 
maximum  bending  moment  by  the  graphic 
METHOD    explained    in   Chapter   IX,   page 

3k    n      I  I 1  I 1  h- 4t—      329. 


^-4- 


^^5- 


k-y^^ 


\ 


tH 


•      . .  Example  3.    The  girder  G,  Fig.  12,  sup- 

r  \  ports  the  rafters  of   a   flat  roof,  and  also 

Fig.  12.    Girder  with  Three  Concen-    three  heavy  beams,  A,  B  and  C,  blocked  up 
trated  Loads  above  the  roof  and  supporting  a  large  tank 

filled  with  water.  The  timber  is  to  be 
long-leaf  yellow  pine.  The  weight  of  the  roof  and  allowance  for  snow  is  7  500 
lb.  Each  of  the  beams  A,  B  and  C,  impose  a  load  on  the  girder,  due  to  the 
weight  of  the  tank  and  its  contents,  of  3  000  lb.  What  should  be  the  size  of  the 
girder? 

Solution.  The  roof-load  may  be  considered  to  be  uniformly  distributed. 
The  load  from  beam,  A,  is  applied  at  one-third  the  span  from  one  end;  the  load 
from  B,  five-twelfths  the  span  from  the  other  end;  and  the  load  from  C,  one- 
sixth  the  span.  The  fraction  five-twelfths  is  the  mean  of  one-half  and  one-third; 
hence  the  load  from  B  should  be  multiplied  by  1.89.  Multiplying  the  con- 
centrated loads  by  their  proper  factors,  the  equivalent  distributed  load  is  found 
to  be  as  follows: 

Roof-load,  distributed. 
Load  from  A,  3  000 X  1.78 
Load  from  By  3  000  X  1-89 
Load  from  C,  3  ocjo  X  iV^ 

figuivalent  distributed  load  =21  843  lb 


Relative  Strengths  of  Beams  635 

Assuming  i6  in  as  the  depth  of  the  beam,  and  using  Formula  (ii), 

The  breadth  =  ''"""l^^!   =  7-6  in 
2X256X67      ' 

Assuming  14  in  for  the  depth,  10  in  is  obtained  for  the  breadth;  hence,  the 
girder  must  be  10  by  14  in,  or  8  by  16  in  in  cross-section. 

Strut-Beams  and  Tie-Beams.  A  strut-beam  is  a  beam  that  is  subject 
to[both  a  transverse  and  a  compressive  stress.  A  tie-beam  is  one  that  is  subject 
to  direct  tension  in  addition  to  the  transverse  stress.  To  find  the  strength  of 
either,  first  find  the  size  of  a  beam  required  to  resist  the  transverse  stress,  and 
then  the  size  of*  a  timber,  of  the  same  depth  as  the  beam,  to  resist  the  direct 
tension  or  compression,  and  add  the  two  breadths  together. 

Example  4.  A  spruce  tie-beam,  10  ft  long  between  joints,  sustains  a  ceiling- 
load  of  2  000  lb  and  a  direct  tensile  stress  of  40  000  lb.  What  should  be  th^ 
dimensions  of  the  beam? 

Solution.  As  a  ceiling-load  is  uniformly  distributed,  the  size  of  the  beam  is 
determined  by  Formula  (11),  page  630.     Assuming  the  depth  to  be  10  in 

10  X  2  000 

The  breadth  = ,     or     2 1/^  in,  nearly 

2  X  100  X  39 

The  resistance  of  spruce  to  tension  (see  Table  XVI,  page  647)  is  800  lb  per 
sq  in.  40  000/800  =  50  sq  in,  which  is  equivalent  to  a  5  by  lo-in  section.  It  will 
require,  therefore,  a  beam  7^/^  by  10  in  in  cross-section  to  resist  both  the  trans- 
verse stress  and  the  direct  tension.  If  the  tie-beam  is  cut  in  any  way  so  as  to 
reduce  the  section,  except  over  a  support,  the  dimensions  must  be  increased 
accordingly. 

Example  5.  A  strut-beam  of  white  pine,  10  ft  long,  supports  a  distributed 
roof-load  of  6  000  lb,  and  is  also  subject  to  a  direct  compression  of  64  000  lb. 
What  should  be  the  size  of  the  beam? 

Solution.  Assuming  14  in  for  the  depth,  the  breadth  for  the  transverse  load 
is  found  by  Formula  (11),  page  630 

rr^,     1        11         10  X  6  000  .  , 

The  breadth  = •  =3.9  m,  nearly 

2X196X39 

Using  Formula  (4),  page  450,  from  which  is  computed  Table  IV,  page  452, 
giving  the  safe  loads  for  white-pine  posts,  it  is  found  that  a  ^V2  by  14-in  post, 
10  ft  long  will  safely  carry  the  compressive  stress,  64  000  lb.  Hence  it  will  re- 
quire a  7V2  by  14-in  beam  to  resist  the  compressive  stress,  and  a  4  by  14-in 
beam  to  resist  the  transverse  load.  The  beam,  therefore,  should  be  12  by  14 
in  in  cross-section  to  resist  them  both. 

6.   Relative  Strengths  of  Beams 

Relative  Strengths  of  Rectangular  Beams.  From  an  inspection  of  the 
foregoing  formulas  it  is  found  that  the  relative  strengths  of  beams  of  rec- 
tangular cross-sections,  for  the  different  cases  is  as  shown  in  Table  V. 

Strengths  of  Beams  of  Any  Constant  Cross-Section.  The  strength- 
ratios  given  in  Table  V  are  true  for  beams  of  any  constant  cross-section  ol 
whatever  form. 

Beam  on  Edge.  When  a  beam  of  square  cross-section  is  supported  on  its 
edge,  that  is,  when  one  of  its  diagonals  is  vertical,  it  will  bear  about  seven-tenths 
as  great  a  breaking-load  as  it  will  when  it  is  supported  on  one  side. 


634         Strength  of  Cast-iron  Lintels  and  Wooden  Beams     Chap.  16 
Table  V.    Relative  Strengths  of  Rectangular  Beams 


Kind  of  load 

Position  of  load 

Strength  ratios 

Beam  supported  at  both  ends 

Uniformly  distributed 
Concentrated 
Concentrated 
Concentrated 
Concentrated 
Concentrated 
Concentrated 
Concentrated 
Concentrated 
Concentrated 

Over  entire  span 
At  middle  of  span 
At  one-third  the  span 
At  one-fourth  the  span 
At  one-fifth  the  span 
At  one-sixth  the  span 
At  one-seventh  the  span 
At  one-eighth  the  span 
At  one-ninth  the  span 
At  one-tenth  the  span 

I 
Yxfs 

.    25^2 

81/64 
2^8 

Beam  fixed  at  one  end,  or  cantilever  beams 

Uniformly  distributed 
Concentrated 

Over  entire  span 
At  the  free  end 

Beam  supported  at  one  end  and  fixed  at  the  other  end 

Uniformly  distributed 
Concentrated 

Over  entire  span 

Near  the  middle  of  span 

I 

mo 

Beam  fixed  at  both  ends 

Uniformly  distributed 
Concentrated 

Over  entire  span 
At  middle  of  span 

I 

The  Strongest  Beam  Cut  From  a  Cylindrical  Log  is  one  in  which  the 
breadth  is  to  the  depth  as  5  is  to  7,  very  nearly,  and  the  dimensions  of  such  a  beam 
can  be  found  graphically,  as  shown  in  Fig.  13.  Any  diagonal,  as  ab,  is  drawn 
and  divided  into  three  equal  parts  by  the  points  c  and 
d;  from  these  points- lines  perpendicular  to  ab  are  drawn, 
and  the  points  e  and  /  connected  with  a  and  b,  as 
shown. 


Cylindrical  Beams.  A  cylindrical  beam  is  only 
ten-seventeenths  as  strong  as  a  beam  with  a  square 
cross-section,  the  side  of  the  square  being  equal  to  the 
diameter  of  the  circular  section  of  the  cylindrical  beam. 
Hence,  to  find  the  safe  load  for  a  cylindrical  beam,  first 
find  the  proper  load  for  the  corresponding  square- 
section  beam,  and  divide  this  load  by  1.7. 
The  Bearing  of  the  Ends  of  a  Beam  on  a  wall 
beyond  a  certain  distance  does  not  strengthen  the  beam.  In  general,  a  beam 
should  have  a  bearing  of  4  in,  or  if  it  is  very  long,  6  in. 

The  Weight  of  the  Beam  Itself.  The  formulas  given  for  the  strength  of 
beams  do  not  take  into  account  the  weight  of  the  beams  themselves,  and 
hence  the  safe  loads  of  the  formulas  include  both  the  external  loads  and  the 
weights  of  the  material  in  the  beams.    In  small  wooden  beams,  the  weight  of 


Fig.  13.  Strongest  Beam 
of  Rectangular  Section 
Cut  from  Log 


Tables  for  Strength  and  Stiffness  of  Wooden  Beams         635 ^ 

each  beam  is  generally  so  small,  compared  with  the  external  load,  that  it  need 
not  be  taken  into  account.  But  for  larger  wooden  beams,  and  for  metal  and 
stone  beams,  the  weight  of  the  beam  should  be  subtracted  from  the  safe  load 
if  the  load  is  distributed;  and  if  the  load  is  applied  at  the  middle,  one-half  the 
weight  of  the  beam  should  be  subtracted. 

The  Weight  of  Timber.  The  weight  per  cubic  foot  for  different  kinds  of 
timber  may  be  found  in  the  table  in  Part  III,  pages  1501  to  1508,  giving  the 
Weights  of  Various  Substances. 


7.   Tables  for  Strength  and  Stiffness  of  Wooden  Beams 

Tables  VII  to  XV  for  the  Strength  and  Stiffness  of  Wooden  Beams 

are  given  on  pages  638  to  646,  for  beams  one  inch  in  breadth.  To  find  the 
strength  for  any  other  breadth,  multiply  the  proper  tabular  value  by  the  breadth 
of  the  beam  in  inches.  To  obtain  the  required  breadth  for  any  load,  divide  the 
given  load  in  pounds  by  the  proper  tabular  value.  In  heading  the  tables,  prom- 
inence has  been  given  to  the  values  used  for  S,  and  the  corresponding  values 
of  ^,  so  that  those  who  prefer  to  use  for  any  wood  a  value  different  from  that 
recommended,  need  only  to  look  up  the  table  based  on  the  value  they  desire 
to  employ.  For  certain  cases  and  in  some  cities,  the  building  laws  specify  i  300, 
I  500  and  I  800  pounds  as  values  of  S  to  be  used  for  long-leaf  yellow  pine; 
hence  Tables  XIII,  XIV  and  XV,  based  on  these -values,  are  added. 

Since  timber  is  weak  Li  horizontal  shear  compared  with  its  strength  in 
tension  and  compression,  the  safe  load  a  beam  of  short  span  can  carry  is 
governed,  not  by  its  resistance  to  cross-breaking,  but  by  its  resistance  to 
shearing  along  the  neutral  surface.  Wooden  beams  and  joists,  therefore, 
should  be  dimensioned  to  safely  withstand  this  shearing  action.  The  ratio 
of  the  shearing  to  the  flexural  strength  is  not  exactly  the  same  for  different 
kinds  of  wood,  but  for  practical  use  and  in  the  tables  it  has  been  assumed  to 
be  one-twelfth  of  the  working  unit  fiber-stre'ss.  As  it  can  be  shown  *  that 
the  ratio  of  the  span  to  the  depth  of  a  rectangular  beam,  uniformly  loaded, 
is  directly  proportional  to  its  cross-breaking  stress  and  shearing  working 
stress,  the  tabular  loads  are  figured  for  the  permissible  unit  fiber-stress, 
where  the  length  of  the  span  is  twelve  or  more  times  the  depth  of  the  beam; 
while  for  shorter  lengths,  the  tabular  loads  are  governed  by  the  shear.  To 
determine  the  safe  load  on  beams  for  a  deflection  not  exceeding  Vaeo  of  the 
span,  tabular  values  have  been  placed  directly  underneath  the  safe  loads  for 
strength.  These  values  are  based  on  the  modulus  of  elasticity,  E,  given  in 
the  tables. 

The  formula  for  flexure  used  in  determining  the  safe  uniformly  distributed 
loads  in  the  tables  is  (see  Formulas  (i),  page  S33  ^i^d  (2)',  page  557) 

,,     SI      Shd^     Wl 

Hence  W ,  in  which  /  is  the  span  in  inches        ' 

3I  .r. 

The  formula  for  shear  is  ■^'  ' 


*  Materials  of  Construction,  J.  B.  Johnson,  page  55. 


636         Strength  of  Cast-iron  Lintels  and  Wooden  Beams     Chap.  16 

The  FORMULA  FOR  DEFLECTION  is  (sec,  also,  Formulas  (i)  to  (17)  and  Table  I, 
Chapter  XVIII) 

Ed? 

W  = in  which  /  is  the  span  in  feet; 

8100/2 

M  =  maximum  bending  moment  in  inch-pounds; 

/  =  moment  of  inertia  of  the  cross-section  of  the  beam  in  biquadratic 

inches; 

c  =  d/2  =  one-half  the  depth  of  the  beam  in  inches; 

SI/c  =  resisting  moment  of  the  cross-section  in  inch-pounds; 

W  =  total  safe  load  in  pounds,  uniformly  distributed; 

h  =  breadth  of  the  beam  in  inches;  * 

d  =  depth  of  the  beam  in  inches; 

/  =  span,  in  feet  or  inches,  as  noted  for  the  dififerent  formulas; 

S  =  unit  flexural  fiber-stress  in  pounds  per  square  inch; 

S3  =S/i2  =  horizontal  unit  shearing-stress,  in  pounds  per  square  inch,  along  the 

neutral  surface; 

E  =  modulus  of  elasticity  in  pounds  per  square  inch. 

Example  6.  What  is  the  safe,  uniformly  distributed  load,  corresponding  to 
a  fiber-stress  of  i  500  lb  per  sq  in,  for  an  S  by  14-in  long-leaf  yellow-pine  beam 
supported  at  both  ends,  and  having  a  24-ft  clear  span? 

Solution.  From  Table XIV,  the  load  for  a  i-in  thickness  is  1362  lb.  Hence, 
I  362  X  8  =  10896  lb,  the  total  load  for  the  beam.  If  the  deflection  of  this 
beam  should  not  be  more  than  J-^co  of  the  span,  the  safe  load  for  i -in  thickness 
should  not  exceed  882  lb.  Hence,  882  X  8  =>  7  056  lb,  is  the  maximum  load  to 
be  used  in  this  case.    It  is  assumed  that  i  500  lb  per  sq  in  is  allowed  for  S. 

Example  7.  What  should  be  the  size  of  a  Norway-pine  beam  required  to  carry 
a  distributed  load  of  6  400  lb  over  a  clear  span  of  18  ft? 

Solution.  From  Table  X,  it  is  found  that  a  beam  12  in  deep  and  i  in  thick 
and  with  an  i8-ft  span,  will  support  711  lb.  Dividing  the  load,  6400  lb,  by 
711,  the  result  is  9  for  the  breadth  of  the  beam  in  inches.  Hence  the  beam 
should  be  9  by  12  in,  to  carry  a  distributed  load  of  6  400  lb  over  a  span  of  18  ft. 
As  the  deflection-load  of  593  lb  can  be  increased  20%  for  Norway  pine,  the  beam 
is  safe  for  deflection;  if,  however,  cypress  is  used,  593  must  be  taken  in  place  of 
711,  to  determine  the  breadth  of  the  beam.  This  would  result  in  a  beam  11 
by  12  in. 

Different  Positions  of  Loads.  To  find  the  safe  load,  concentrated  at  the 
middle  of  the  span  of  a  given  beam,  find  the  safe  distributed  load,  as  in  Example 
6,  and  divide  this  load  by  2.  To  find  the  safe  load  concentrated  at  some 
point  other  than  the  middle  of  the  span,  find  the  safe  distributed  load  for  the 
given  span,  and  divide  this  load  by  the  proper  factor  taken  from  Table  IV, 
page  632.  To  find  the  size  of  a  beam  to  support  a  given  concentrated  load, 
multiply  the  given  load  by  the  factor  corresponding  to  the  position  of  the  load, 
as  given  in  Table  IV,  and  then  proceed  as  in  Example  7. 

Use  of  Formulas.  If  in  doubt  as  to  the  application  of  the  tables,  in  special 
cases,  use  one  of  the  formulas,  from  (4)  to  (16),  applying  to  the  case.  The 
formulas  and  tables  should  always  give  the  same  result. 

Nominal  and  Actual  Sizes  of  Beams.  The  tables  may  be  used  for  beams 
the  dimensions  of  which  are  less  than  the  nominal  dimensions.  Dressed 
beams,  and,  in  many  localities,  floor-joists  carried  in  stock,  are  more  or  less 
scant  of  the  nominal  dimensions,  and  for  such  beams  and  joists  a  reduction  in 
the  safe  load  must  be  made  to  correspond  with  the  reduction  in  size.    The 


Tables  for  Strength  and  Stiffness  of  Wooden  Beams  63T 

DRESSED  SIZES  are  generally  i/4  in  scant,  up  to  4  in  in  breadth,  above  which  they 
are  V2  in  scant;  while  in  depth  they  are  all  generally  V2  in  less  than  the  nominal 
size.  The  safe  loads  may  be  obtained  by  multiplying  the  safe  loads  for  the 
corresponding  nominal  sizes,  as  given  in  Tables  VII  to  XV,  by  the  factors  given 
in  the  following  table. 

Table  VI.     Conversion  Factors  for  Actual  Sizes  of  Wooden  Beams 


Cross-sections 

of  beams  in 

inches 

Factors 

Cross-sections 

of  beams  in 

inches 

Factors 

1%  X5'/2 
2'>;i  X5V2 
1%  x6H 
2%  xey^ 
m  xiYz 

2%X7K2 

1%  X9V2 
2)  i  X9K2 

1.47 
2.31 
1. 51 
2.51 
1.54 
2.42 
1.58 
2.48 

1^4X11^2 

2MX11V2 

ly^xizVi 
2y^xizVi 

•      i^4Xi5K2 
2^4X15^2 
i^4xi7H 
2MX17K2 

1. 61 
2.53 
1.63 
2.56 
1.65 
2.58 
1.65 
2.60 

Example  8.  What  is  the  safe  load  for  a  2%  by  13^/^-in  spruce  beam,  with 
an  i8-ft  span? 

Solution.  From  Table  VIII,  the  safe  load  for  a  i  by  14-in  beam  is  847  lb. 
Multiplying  this  by  2.56,  we  have  2  178  lb  as  the  safe  distributed  load  for  a 
beam  2%  by  13!/^  in  in  cross-section.  For  a  full  3  by  14-in  cross-section,  the 
safe  load  would  be  2  541  lb. 

Stone  Beams.  The  above  formulas  may  be  used  for  rectangular  stone 
beams  when  the  proper  coefficients,  recommended  in  Table  III,  page  628,  are 
inserted.  Sandstone  beams  should  never  be  subjected  to  any  heavy  loads  and 
sandstone  lintels  should  be  relieved  by  steel  beams  or  by  brick  arches  over  them 
or  back  of  them. 

Concrete  Beams  are  generally  reinforced  with  steel  rods,  but  when  used 
without  reinforcement,  the  coefficient,  A,  given  in  Table  III,  is  recommended. 
Use  of  Tables  VII  to  XV.  The  safe  loads  given  in  Tables  VII  to  XV 
are  correct  for  the  fiber-stresses  indicated;  but  for  greater  convenience  in  using 
the  tables,  each  figure  in  the  units-place  of  each  value  may  be  made  a  cipher, 
and  each  figure  in  the  tens-place  may  be  increased  by  one  when  the  unit-figure 
is  six  or  greater.     Thus,  505  would  be  500,  506  would  be  510,  etc. 

Important  Notes  on  Stresses  and  Loads  for  Wooden  Beams.  In  compiling  and 
using  the  tables  of  safe  loads  for  wooden  beams,  the  following  important  considerations 
must  be  kept  in  mind: 

(i)  Unseasoned  timber  is  very  much  weaker  than  commercially  dry  timber,  that  is, 
timber  containing  from  10  to  15%  of  moisture. 

(2)  Timber  containing  large  or  loose  knots  is  much  weakened. 

(3)  When  impact  has  to  be  considered,  the  stresses  should  be  reduced. 

(4)  For  continuous,  heavy  loading,  relatively  low  stresses  should  be  used. 

(5)  Commercial  dimensions  are  smaller  than  nominal  dimensions. 

(6)  Timbers  deteriorate  and  the  factors  of  safety  for  strength  grow  smaller  with  time. 

(7)  The  modulus  of  elasticity,  E,  for  unseasoned  timber,  should  be  reduced  50%  from 
its  value  given  for  thoroughly  seasoned  timber. 

(8)  It  is  better  engineering  practice  to  compute  tables  of  safe  loads  based  on  conserva- 
tive stresses  for  average  or  poor  conditions,  increasing  the  values  given  when  conditions 
are  ideal,  than  to  recommend  values  for  ideal  conditions  which  usually  do  not  exist. 
(See  notes,  pages  628  and  647,  regarding  increase  in  the  table-values.)     Editor-in-Chief. 


638        Strength  of  Cast-iron  Lintels  and  Wooden  Beams 


Table  VII.     Safe  Distributed  Loads  *  in  Pounds  for  Rectangular  Wooden  Beams 
For  Average  Hemlock.     Maximum  Fiber-Stress,  S  =  600  lb  per  sq  in. 
E  =  900  000  lb  per  sq  in.     il  »  33 


Span 
in 
feet 

The  first  horizontal  line  gives  the  depth  of  the  beam  in  inches     ' 

The  loads  are  for 

beams  one  inch  wide  and  supported  at  both  ends 

6 

7 

6 

8 

10 

12 

14 

16 

18 

400 

533   ■ 

533 

666 
666 

800 
800 

933 
933 

1066 
1066 

I  200 
I  200 

343 

8 
9 

300 
266 

533 

666 

666 

800 
800 

933 
933 

I  066 
1066 

I  200 

I  200 

474 

10 
II 

I   240  j 

427 
388 

666 

800 
800 

933 
933 

1066 
1066 

I  200 
I  200 

60S 

12 
13 

{    7e\ 
\    143  ) 

356 
328 

555 
513 

800 

933 
933 

1066 
1066 

I  200 
I  200 

738 

14 
15 

1  171 
I  122 

(  t6o 

305  } 
291  j 

285  j 

477 
445 

686 
640 

933 

106Q 
1066 

I  200 
I  200 

871 

\     107 

253  1 

16 
17 

(  150 
\       94 

267  ) 

222  ) 
j   251 
I   197 

417 

392  ) 

384  ) 

600 
565 

817 
762 

1066 

I  200 
I  200 

I  003 

18 
19 

1   237 
I   175 
f   225 

(   157 

371  j 
343  i 

351  } 
308  j 

534 
505 

726 
688 

948 
898 

I  200 

I  137 

20 

{   213 
I   142 

333 

480  ) 
480  ) 

653 

854 

I  080 

277 

21 

I   317 
1   252 

462  ) 
435  ) 

623 

813 

I  029 

22 

j   303 
\      229 

436  ( 

594 

776 

982 

397  ) 

23 



(   290 

1   211 

417  \ 
363  ) 

568 

742 

939 

24 

j   278 
\        193 

400 

545  ) 
529  ) 

712 

900 

334 

25 

1   384 
1   308 

523  j 
488  j 

683 

864 

26 

1   369 
1   284 

503  ( 
452  j 

657 

831 

27 

(   356 

1   264 

482 

633  ) 
625  j 

800 

418 

28 

{   343 
1   245 

467 

609  ) 
582  ( 

772 

389 

29 

{ 

451 
353 

589  ) 
542  j 

745 

30 

1 

436 

569 

720  ) 
720  ) 

339 

50s 

Loads  above  zigzag  lines  calculated  for  horizontal  shear, 
the  upper  is  calculated  for  strength,  the  lower  for  deflection 


Where  two  loads  are  given, 
not  to  exceed  ^eo  the  span. 


*  Add  30  to  40%  to  strength-values  for  ideal  conditions.     See  notes,  pages  6^8,  637-  647. 


Tables  for  Strength  and  Stiffness  of  Wooden  Beams        639 

Table  VIII.     Safe  Distributed  Loads  *  in  Pounds  for  Rectangular  Wooden  Beams 
For  Average  White  Pine,  Spruce  and  Eastern  Fir.     Maximum  Fiber- 
Stress,  iS  =  700  lb  per  sq  in.    £  f  =  1 000  000  lb  per  sq  in.    A  "  39 


Span 
in 
feet 


13 

14 

IS 
16 

17 
18 


23 
24 
25 
26 
27 
28 
29 
30 


The  first  horizontal  line  gives  the  depth  of  the  beam  in  inches 
The  loads  are  for  beams  one  inch  wide  and  supported  at  both  ends 


467 


400 
350 

311 

f     280 
I     267 

(  255 

1  221 

(  233 

I  185 

(  216 

(  158 

(  200 

1  136 

f  187 

\  119 

{  175 

I  104 


622 
622 


552 

497 


383 
374 
356 
323 
332 
281 
311 
247 

293 
219 
276 
195 
262 
175 


777 
777 
777 
777 


707 
648 
598 
556 

518 

486 
482 

458 

427 

433 

381' 

410 

342 

389 

308 

370 

280 

354 

255 

338 

234 

324 

215 


933 
933 
933 
933 
933 

933 
933 


861 
800 

747 
700 

660 
623 


560 
534 
534 
484 
509 
441 
487 
403 
468 
371 
448 
342 
430 
316 
415 
293 
400 
272 


089 


089 


089 


952 
897 
847 
802 
762 
726 

692 

662 
641 
635 
588 
610 
542 
586 
502 
565 
465 
544 
432 
526 
403 
508 
377 


I  244 
I  244 

I  244 

1244 

I  244 

I  244 

I  244 

I  244 

I  244 

I  244 


I  172 
I  107 
I  048 
996 
948 
906 
866 
830 

796 

766 
750 
738 
695 
711 
646 
687 
602 
664 
562 


*  Add  30  to  40%  to  strength- values  for  ideal  conditions.  See  notes,  pages  628,  637, 
6V7. 

t  For  first-class,  dry  spruce  and  Eastern  fir,  £  =  i  200  00  could  safely  be  used,  making 
the  safe  deflection-loads  those  given  in  Table  XI.     See,  also,  foot-note  with  Table  VII. 


640 


Strength  of  Cast-iron  Lintels  and  Wooden  Beams     Chap. 


Table  IX.     Safe  Distributed  Loads  *  in  Pounds  for  Rectangular  Wooden  Beams 

For  Average  California  Red  Wood  and  Cedar.     Maximum  Fiber-Stress, 

iS  =  750  lb  per  sq  in.     E  =  700000  lb  per  sq  in.     A  =  41.7 


Span 
in 
feet 


13 
14 

15 
16' 

17 
18 


23 

24 
25 
26 

% 
28 
29 
30 


The  first  horizontal  line  gives  the  depth  of  the  beam  in  inches 
The  loads  are  for  beams  one  inch  wide  and  supported  at  both  ends 


(      292    j 


428 
382 
375 
292 

333 
231 
300 
187 
274 
155 
250 
130 

231 
no 
214 
95 


667 
667 
667 


592 
547 
533 
443 

485 
366 
445 
307 
410 
262 
382 
226 
356 
197 
333 
173 


833 
833 
833 
833 
833 


757 
714 
641 
600 

641 
512 

595 
441 
556 
384 
521 
337 
491 
299 
463 
267 

439 
240 


I  000 

I  000 


923  ) 

885  I 

857  1 

763  I 

800 

665 

750 

584 

706 

518 

667 

462 

632 
414 

{600 
374 
(  572 
\  339 
(  547 
1  309 
(  522 
(  282 
i  500 
1  260 
I  480 
I  239 
I  463 
\  221 
(  444 
I  205 
I  428  . 
I  190 


14 


I  167 
I  167 
I  167 
I  167 
I  167 
I  167 
I  167 
I  167 
I  167 


I  060 
I  020 
929 
961 
822 
908 
733 
860 
658 
816 
594 
778 
526 
742 
491 
710 
448 
681 
412 
653 
380 
628 
351 
605 
326 
583 
203 
563 
282 
544 
264 


1333 
I  333 
1333 
1333 
1333 
1333 
1333 
1333 
1333 
I  333 
1333 


1254 

I  223 

I  184 

I  090 

I  122 

982 

I  066 

886 

I  oi6 

803 

970 

732 

928 

670 

890 

616 

854 

567 

821 

525- 

791 

487 

762 

452 

736 

421 

712 

393 


*  Add  30  to  40%  to  strength -values  fpr  ideal  conditions.     See  notes,  pages  628,  637, 
647.     See,  also,  foot-note  with  Table  VlL 


Tables  for  Strength  and  Stiffness  of  Wooden  Beams 


Table  X.     Safe  Distributed  Loads  *  in  Pounds  for  Rectangular  Wooden  Beams 

For  Average  Norway  Pine,  Cypress  and  Chestnut. 
Maximum  Fiber-Stress,  S  =  800  lb  per  sq  in.    £  f  =  900  000  lb  per  sq  in,    A  =  44 


Span 
in 
feet 

The  first  horizontal  line  gives  the  depth  of  the  beam  in  inches     \ 
The  loads  are  for  beams  one  inch  wide  and  supported  at  both  ends 

6 

8 

10 

12 

14 

16 

18 

6 

7 
8 

9 

10 

II 
12 

13 
14 

15 
16 

17 
18 

19 

20 
21 
22 
23 

,  24 

1  ^-^ 

.26 

27 
28 
29 
30 

533 

711 
711 
711 

889 
889 
889 

889 
889 

1066 
1066 
1066 

1066 

1066 
1066 

I  244 
1244 
I  244 

I  244 
I  244 
1244 
1244 
1  244 
1244 

I  422 
I  422 
I  422 

1422 

I  422 

I  422 

1422. 

I  422 

1422 

I  422 

I  422 

I  600 
I  600 
I  600 

1600 

I  600 

I  600 

I  600 

1 600  : 

I  600 

I  600 

I  600 

I  600 

I  600 

{ 

457 

400  ) 

375  ) 

356  ) 

296  i 

320 

240 

291 

199 

267 

166 

246 

142 

229 

122 

214 

107 
200 
94 

632 

569  ) 
569  ) 

517  1 

470  j 

474  } 

395  i 

438 

337 

407 

291 

800 
742 

684  ) 
658  j 
635  I 
567  ( 

593 

494 

556 

432 

524 

384 

494 

343 

468 

308 

445 

277 
1   423 
\      252 
(   404 
\      229 
{   387 
(   211 
{   371 
1   193 

985 

914 

854  \ 
854  ) 
800  ) 
750  j 

754  1 
66s  ) 
7it 
593 

674 

532 

640 

4«o 

609 

435 

5;«2 

397 

557 

363 

534 

334 
f  512 
(  308 
1  492 
\     284 
(  474 
»  264 
(  457 
I  245 

379 
253 
356 
222 

(   335 
1   197 
I   316 
I   175 
1   300 
\      157 
(   284 
1   142 

I  161 
I  089 

I  02s 

968  1 
914  ) 

917  1 

846  i 

871 

752 

830 

692 

792 

630 

758 

577 

726 

529 

697 

488 

670 

452 

646 

418 

622 

389 
i     601 
I     353 
1  581 
i  339 

1339 
I  264 

I  198 

I  138  1 
I  138  1 
1084  ) 
1032  j 
1035  ) 

941  i 

990 

860 

949 

790 

9" 

728 

876 

675 

843 

625 

813 

582 

785 

542 

759 

506 

1 441 
1372 

1309 

I  253  ) 
1225  } 
I  200  ] 
II26  } 

1 152  i 

1037  ( 

I  108  1 

960  } 

1068  i 

890  } 

1029  1 

827  { 

993  ) 

770  I 

960  1 

720  } 

.  ^ , . . . 

1 

*  Add  30  to  40%  to  strength- values  for  ideal  conditions.     See  notes,  pages  628, 637, 647. 
See,  also,  foot-note  with  Table  VII. 

t  For  safe  deflection-loads,  for  Norway  pine,  add  20%  to  the  above  values. 


I  : 


642        Strength  of  Cast-iron  Lintels  and  Wooden  Beams     Chap.  16 


Table  XI.     Safe  Distributed  Loads  *  in  Pounds  for  Rectangular  Wooden  Beams 

For  Average  Douglas  Fir  and  Short-Leaf  Yellow  Pine.    Fiber-Stress,  S  =  i  ooo  lb 

per  sq  in.     E  i  =  i  200  000  lb  per  sq  in.     A  =  55-6 


Span 
in 
feet 

The  first  horizontal  line  gives  the  depth  of  the  beam  in  inches 
The  loads  are  for  beams  one  inch  wide  and  supported  at  both  ends 

6 

8 

10 

12 

14 

16 

18 

6 
7 
8 

9 
10 

II 

1   " 
13 

14 

15 
16 

17 
18 
yg 

21 
22 

1   ^^ 

\    ^' 
I   26 

{  27 

'  28 

29 

30 

667 

889 
889 
889 

I  III 
I  III 
I  III 

I  III 

I  III 

I  333 
1333 
1333 

1333 
1333 

1556 
1556 
1556 

1556 
1556 

1778 
1778 
1778 

1778 

1778 

1778 

1778 

1778 

1778 

1778 

1778 

2  000 
2  000 
2000 

2  000 

2  000 

2  000 

2  000 

2  000 

2  000 

2  000 

2000 

2  000 

2  000 

( 
I 

1 
{ 
{ 
{ 
{ 
{ 
{ 
1 

..) 
;•'• 

i.. 

571 
500  ) 
500  ) 

444  ) 
395  J 
400  j 
320  j 

364 
265 
333 
222 

308 
190 
286 
163 
267 
143 
250 
125 

790 

711 

647  ) 
628  f 
593  ) 
527  j 
547  ) 
449  i 
508 
388 

474 
337 
445 
296 

f  419 
1   263 
(  395 
I   234 

f  374 
1  210 
1   356 
I   190 

1 

I  010 
926 

1333 
1333 

1556 
1556 
1556 
I  556 

855 

794  ) 
757  3 
741  1 
659  3 
695 
578 

654 
512 
618 
457 

585 

410 

556 

370 
(  528 
i  336 
1  50s 
(  306 
(  483 
\     281 

r  463 
\  258 

I  231 

II43 

I  067 
I  000  ) 

I  000  j 
942  1 

886  f 
890  ) 
790  j 

843 

710 

800 

641 

762 

581 

727 

529 

696 

484* 

667 

445 
1  640 
\     410 
(  61S 
\     386 
f  593 
\     352 
(  572 
1  327 

1452 

I  361 

I  281 

I  210 

I  146  ) 
I  126  1 
I  088  ) 
I  016  ) 
I  037  ) 
922  j 
990 
841 
947 
770 
908 
706 
871 
650 
838 
602 
807 
558 
778 
518 
{  751 
\     484 
(  726 
1  452 

1674 
I  581 
1498 
1423 

1355 

1293  ) 
I  254  i 
1237  ) 
I  147  ) 
I  186 
1053 
I  138 

972 
1094 

900 
1054 

834 
I  016 

776 

982 

725 

949 

674 

1895 
I  800 
I  714 
1636 

1565 

1500  1 
1500  } 
I  440  ) 

1384  } 

1385  1 
1286  ] 
1334  ) 
I  186  ( 
1286  J 
I  103  } 
I  241  ) 
I  027  { 
I  200  1 

960  1 

•iw* 

JH>  ■ 

♦Add 
tFor 


30  to  40%  to  strength -values  for  ideal  conditions, 
deflection-loads  for  Douglas  fir,  add  25%.     See, 


See  notes,  pages  628,  637,  647. 
also,  foot-note  with  Table  VIL 


Tables  for  Strength  and  Stiffness  of  Wooden  Beams  643 

Table  XII.     Safe  Distributed  Loads  *  in  Pounds  for  Rectangular  Wooden  Beams 
For  Average  White  Oak  and  Long-Leaf  Yellow  Pinef.     Maximum  Fiber- 
Stress,  S  =  i2od  lb  per  sq  in.    E  =  i  500  000  lb  per  sq  in.    A  «  66.7 


Span 
in 
feet 


9 
10 


13 

14 

15 
16 

17 
18 

19 


23 
24 
25 
26 
27 
28 
29 
30 


The  first  horizontal  line  gives  the  depth  of  the  beam  in  inches 
The  loads  are  for  beams  one  inch  wide  and  supported  at  both  ends 


686 
600 

(  533 

\  495 

i  480 

I  400 

f  437 

(  332 

(  400 

\  278 

(  369 

I  247 

I  343 

I  204 

f  320 

(  179 

J  300 

\  156 


I  067 
I  067 

I  067 


854 

776 

711 
658 
656 
561 
610 
485 

569 
422 
533 
371 
502 
329 
474 
293 

449 
263 


10 


1333 
1333 
1333 

1333 
1333 


I  212 
I  III 

I  026 

953 
946 
890 
824 
834 
724 

785 
642 
741 
572 
702 
513 
666 
462 
634 
420 
606 
383 
579 
351 
556 
322 


I  600 
I  600 
I  600 

I  600 
I  600 
I  600 
I  600 


1477 

I  371 

1280 

I  200 

I  130 
I  108 

I  067 
990 

I  010 
886 
960 
802 
914 
726 
872 
662 
835 
605 
800 
557 
768 
513 
738 
473 
711 
440 
636 
410 


14 


1867 
1867 
1867 

1867 
1867 
1867 
1867 
1867 
1867 


I  741 
1633 

1537 
1452 

1375 

1306 

I  272 

1245 

I  154 

I  188 

I  051 

I  136 

962 

I  090 

882 

1045 

813 

I  006 

753 

969 

698 

933 

648 

902 

605 

871 

566 


16 


2  133 
2  133 
2  133 

2  133 
2133 
2  133 

2  133 
2133 
2133 
2133 
2133 


2  009 
1898 

179s 
1708 
I  626 

1552 
1484 

I  435 
1423 
I  318 
1366 
I  215 
I  313 

I  125 

1265 
1043 
I  218 

970 
I  178 

903 
I  138 

843 


•  ideal  conditions.     See  notes,  pages  628,  637, 
,  1500  and  1800  lb  per  sq  in,  see  Tables  XIII, 


644         Strength  of  Cast-iron  Lintels  and  Wooden  Beams     Chap.   16 

Table  XIII.     Safe  Distributed  Loads  in  Pounds  for  Rectangular  Wooden  Beams 
Maximum  Fiber-Stress,  S=  i  300  lb  per  sq  in.     A  =  72.2 


Span 


feet 


13 
14 
15 
16 

17 
18 

-19 

(20 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 


The  first  horizontal  line  gives  the  depth  of  the  beam  in  inches 
The  loads  are  for  beams  one  inch  wide  and  supported  at  both  ends 


867 


743 
650 

567 
520 

473 
433 
400 
371 
347 
325 


I  155 
I  155 
I  155 


I  027 
924 
840 
770 
711 
660 

616 
578 
544 
514 

487 
462 


1444 
1444 
1444 
1444 
I  444 


I  311 
I  200 

I  III 
I  032 

963 
903 

849 
802 

760 
722 
688 
6S7 
628 
602 


1733 
1733 
1733 
1733 
1733 
1733 
I  733 


I  600 
i486 

1387 
1300 

I  224 
I  156 

1095 
I  040 
990 
945 
904 
867 
832 
800 
770 
743 


2  022 
2  022 
2  022 
2  022 
2  022 
2  022 
2  022 
2  022 
2  022 


1887 
1770 

I  664 
1572 
1490 
I  415 
1348 
1286 
I  230 
I  179 
I  132 
1088 
I  048 
I  on 
-  976 
943 


2  311 

2  311 
2  311 
2  311 
2  311 

2  311 
23H 

2  311 
2  311 

2  311 
2  311 


2  175 
2054 
1946 
1849 
I  761 
I  681 
1608 

I  541 
1479 
I  422 
1369 
I  321 
I  275 
I  232 


2600 

2  600 
2  600 
2  600 
2  600 
2  600 
2  600 
2  600 
2  600 
2  600 
2  600 
2  600 
2  600 


2463 
2340 
2  229 
2  127 
2035 
1950 
1872 
I  800 
I  733 
I  671 
I  614 
I  560 


Loads  above  the  heavy,  black  zigzag  lines  are  calculated  for  resistance  to  shear. 
For  safe  deflection-loads,  see  values  in  Tables  VII  to  XII,  according  to  the  value  of  E 
lused,  and  determined  by  the  deflection-formula,  page  636. 


\    8if.  I 


Tables  for  Strength  and  Stiffness  of  Wooden  Beams 


645 


Table  XIV.     Safe  Distributed  Loads  in  Pounds  for  Rectangular  Wooden  Beams 
Maximum  Fiber-Stress,  S=  i  500  lb  per  sq  in.    A=  83.3 


Span 
in 
feet 

The  first  horizontal  line  gives  the  depth  of  the  beam  in  inches 
The  loads  are  for  beams  one  inch  wide  and  supported  at  both  ends 

6. 

8 

10 

12 

14 

16 

18 

6 

7 
8 

9 

10 

II 
12 

13 
14 

15 
16 

17 
18 

19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

I  000 

1333 
1333 
1333 

1667 
1667 
1667 
1667 
1667 

2  000 
2  000 
2  000 
2  000 
2  000 
2  000    • 
2  000 

2333 
2333 
2333 

2667 
2667 
2667 

3000 
3000 
3  000 
3  000 
3000 
3000 
3000 
3000 
3  000 
3  000 
3000 
3000 
3  000 

857 
750 

667 
600 

548 
500 
462 
428 

I  18S 
I  067 
970 
890 
820 
764 
712 
667 

2333 
2333 
2333 
2333 
2333 
2333 

2667 
2667 
2667 
2667 
2667 
2667 
2667 
2667 

I  515 

1390 

I  282 

I  190 

I  112 

I  042 

982 

926 

878 

1846 

I  714 

I  600 

isoo 

I  412 

1334 

I  264 

I  200 

I  144 

1094 

I  044 

I  000 

960 

926 

888 

856 



2178 
2  042 

1974 
I  815 
I  720 
1632 
1556 
1484 
I  420 
1362 
I  306 
I  256 
I  210 
I  166 
I  126 
1088 

2  510 
2370 
2246 
2133 
2  032 
I  940 
1856 
I  780 
I  708 
1642 
I  582 
1524 
1472 
I  422 

2842 
2  700 
2  571 
2  455 
2348 
2250 
2  lOo 
2  076 
2.000 
1930 
1862 
1800 

Loads  above  the  heavy,  black  ziezac  liness  are  calculated  for  resistance  to  shear. 
For  safe  deflection-loads,  see  values  in  Tables  VII  to  XII,  according  to  the  value  of  i 
used,  and  determined  by  the  deflection-formula,  page  636. 


646 


Strength  of  Cast-iron  Lintels  and  Wooden  Beams     Chap.  16 


Table  XV,    Safe  Distributed  Loads  in  Pounds  for  Rectangular  Wooden  Beams 
Maximum  Fiber-Stress,  S  =  i  800  lb  per  sq  in.    A  =  100 


Span 
in 
feet 

The  first  horizontal  line  gives  the  depth  of  the  beam  in  inches 
The  loads  are  for  beams  one  inch  wide  and  supported  at  both  ends 

6 

8 

10 

12 

14 

16 

18 

6 

7 
8 

9 

10 

II 
12 

13 
14 

15 
16 

17 

19 
20 

!    21 

22 
23 
24 
25 
26 
27 
•   28 
29 
30 

I  200 

I  600 
1600 
I  600 

2  000 
2  000 
2  000 
2  000 

2  000 

2  400 
2  400 
2  400 
2  400 

2400 
2  400 
2  400 

2800 
2800 
2800 
2800 
2800 
28CO 

2800 

0 

2800 
2800 

3  200 
3  200 
3200 
3200 
3  200 
3200 
3200 
3  200 
3200 
3200 
3  200 

3600 
3600 
3600 
3600 
3  600 
3600 
3600 
3600 
3600 
3600 
3600 
3600 
3600 

I  030 
900 
800 
720 

655 
600 

554 
514 
480 
450 

I  422 
I  280 

I  164 
I  067 

98s 
914 

I  818 
1667 

1539 
1428 

2215 
2057 
1920 
1800 

1694 
I  600 

I  516 
1440 
I  371 
1309 
1252 
I  200 
I  152 
IIO8 
I  067 
I  029 

853 
800 

1333 
I  250 

I  176 
I  in 

1053 

I  000 

2613 
2450 
2306 
2  178 

2063 
i960 
1867 
I  782 
1704 
1633 
1568 
I  508 
1452 
I  400 
1352 
1307 

753 
711 

674 
640 

3  012 
2844 
269s 

2  560 
2438 
2327 
2  226 
2  133 
2  048 
1969 
1896 
I  829 
1766 
1707 

3  411 
3240 
3086 
2945 
2817 
2  700 

2592 
2492 

2  400 
2314 
2235 
2  160 

Loads  above  the  heavy,  black  zigzag  lines  are  calculated  for  resistance  to  shear. 
.  For  safe  deflection-loads,  see  values  in  Tables  VII  to  XII,  according  to  the  value  of  E 
used,  and  determined  by  the  deflection-formula,  page  636.  • 


Working  Unit  Stresses  for  Woods.    Taken  from  Building  Laws     647 

8.  Working  Unit  Stresses  for  Average,  Unseasoned  Woods 

Safe  Working  Unit  Stresses  for  unseasoned  woods  (except  for  E)  are  given 
in  Table  XVI.  They  are  compiled  and  adapted  largely  from  recommended 
UNIT  STRESSES  adopted  by  the  Association  of  Railway  Superintendents  of  Bridges 
and  Buildings  and  by  the  American  Railway  Engineering  Association.  (See, 
also,  page  449.) 


Table  XVI.     Safe  Working  *  Unit  Stresses  for  Unseasoned  Woods,  in  Pounds 
per  Square  Inch 


Kind  of  wood 


Factor  of  safety      Ten 


Tension 


Compression 


With 

the 

grain  § 


Across 
the 
grain 


Ten 


With  the 
grain 


End- 
bear- 
ing 


Five 


Col 

umnst 
under 

IS 
diams 


Five 


Across 
the 
grain 


Four 


Bending  f  Shearing 


Ex- 
treme 
fiber- 
stress  § 


Six 


Modu- 
lus ol 
"elasti- 
city,! I 
£/i  000 


One 


With 

the 

grain 


Four 


Across 
the 
grain 


Four 


White  oak 

White  pine 

Long-leaf  yellow 
pine 

Douglas  fir 

Short-leaf  yellow 
pine 

Red  pine  and 
Norway  pine . . 

Spruce  and  east- 
ern fir 

Hemlock 

Cypress 

Cedar 

Chestnut 

Cal.  red  wood . . . 

Cal.  spruce 


T  200 
7t)o 


I  200 
800 


900 

800 

800 
600 
600 
TOO 
850 
700 


200 
50 


60 


SO 
SO 


I  400 
I  100 


I  400 
I  200 


12  00 
I  100 
I  000 

I  I  100 


900 


I  000 
800 

I  000 
900 

800 

750 

900 
800 
75c 
750 
800 
800 
800 


SCO 
200 

3SO 
200 

250 

200 

200 
150 
200 
200 
250 
ISO 


I  200 

700II 

I  200 

8001 

I  000 

800 

7oolf 
600 
800 
700 
800 
7SO 
800 


I  SCO 
I  000 

I  Soo 
1  SCO 

z  200 

I  100 

z  200 
900 
900 
700 

z  000 
700 

z  200 


2CO 
ZOO 


ISO 

Z30 


zoo 
zoo 

zoo 

150 

zoo 


z  coo 
soo 


I  250 
900 


z  000 

7SO 


7SO 
600 


400 
soo 


*  The  stresses  given,  except  for  E,  may  be  increased  30%  for  protected,  commercially 
dry  timber,  not  subject  to  impact,  as  in  most  buildings. 

t  See  also,  Table  I,  page  557,  Table  XVII,  page  648,  and  Table  I,  page  ZZ38. 

i  The  larger  end-bearing  stresses  are  frequently  used  for  short  columns  and  for  column- 
formulas.     (See  tables,  pages  449,  1138.)     Lower  factors  of  safety  give  higher  stresses. 

§  Some  of  these  values  are  considered  too  low,  relatively,  by  some  building  codes. 

II  These  values  of  E  are  for  seasoned  timber.  For  unseasoned  timber,  reduce  E 
50%. 

H  The  New  York  Building  Code  (i^tV)  stresses  ifcr  these  are  z  200  lb  per  sq  in. 

9.  Working  Unit  Stresses  for  Woods.    Taking  from  Building  Lawtf.  '• 

The  Allowable  Working  Unit  Stresses  for  different  woods,  taken  from  the 
building  laws  of  four  cities,  are  given  in  Table  XVII.  The  UNIT  STRESSES 
are  for  tension,  compression,  bending  and  shear.  ,  ^    .    .   ^  _  ^ 


648  Strength  of  Cast-iron  Lintels  and  Wooden  Beams      Chap.  16 


Table  XVII. 

Working  Unit  Stresses  for  Woods,  in  Pounds  rer  Square  Inch 

Kind  of  stress 

Kind  of  wood 

New 
York  * 

Chicago 

Baltimore  § 

Boston  H 

Tension 

Yellow  pinet .  • 
White  pine. .  .  . 

SpruceJ 

Hemlock 

Douglas  fir. .  .  . 
Oak. .  .  .  AmV.  -} 
Locust /'V 

I  200 

700 
8oo 
6oo 
8oo 

1300 

800 

800 

800 
I  300 

ll'i ■ 

I  oooSLYP 

1  800LLYP 

I  000 

I  200 

800 

oV/  I  500 

I  200VP 

Compression 

with  the 

grain 

Yellow  pinet  •  • 
White  pine. .  .  . 

SpruceJ 

Hemlock 

Douglas  fir. .  .  . 
Oak 

I  6oo 

I  000 
I  200 

8oo 

I  200 

I  400 

I  200 

I  100 

700 

700 

500 
I  100 

900 

800SLYPI! 

I  oooLLYP 
800 
800 
600 

I  600 
1  000 

1  OGO 

I  500 
1400 

I  000 

I  200 

800NC  or  YP 

Locust 

Compression 

across  the 

grain 

Yellow  pinet  •  • 
White  pine. .  .  . 

SpruceJ 

Hemlock 

Douglas  fir. .  .  . 
Oak 

350 

250 
200 
150 
200 

500 

250 
200 
200 
150 

600LLYP 
400 
400 
500 

500 
250 
250 

400 
600 

I  600 
1  000 
1000 

I  500 
I  400 

500 

600 

I  000 

40oNCorVP 

Locust 

250SLYP!! 

Transverse 
bending 

Yellow  pinet  •  • 
White  pine. .  .  . 

SpruceJ 

Hemlock 

Douglas  fir. .  .  . 

Oak 

Locust 

J  6oo 

I  200 
I  200 

8oo 

I   200 

I   200 

I  300 

800 

800 

600 

I  300 

I  200 

I  800LLYP 
I  000 
I  350 
I  000 

I  500 

I  oooSLYPit 

Shear  with 
the  grain 

Yellow  pinet  •  • 
W^hite  pine. .  .  . 

Sprucet 

Hemlock 

Douglas  fir. .  .  . 
Oak 

150 

lOO 
100 
100 
100 
200 

130 

80 

80 

60 

130 

200 

looLLYP 
85 
90 

75 

150 
100 
100 

120 
ISO 

100 

Locust 

i2oSLYPi| 

90VP 

Shear  across 
the  grain 

Yellow  pinet.  • 
White  pine. .  .  . 

Spruce  J 

Hemlock 

Douglas  fir. .  .  . 
Oak 

I  ooo 
500 
500 
600 

1000 

I  000 

500LYP 

350 
350 
350 

I  200 

800 

800 

I  000 
I  200 

720 

Locust 

400VP 

•  Stresses  named  by  N.  Y.  are  given  in  the  191 7  Building  Code  of  the  Borough  of 
Manhattan.  Exception:  Dist.  of  Columbia  omits  hemlock,  omits  chestnut  in  shear 
across,  grain  and  puts  spruce  and  Virginia  pine  under  one  caption;  Cincinnati  makes 
caption  of  white  pine  and  spruce,  with  N.  Y.  white-pine  values,  and  gives  270  for  hemlock, 
for  shear  across  grain,  t  Chicago,  "Douglas  fir  and  long-leaf  yellow  pine."  tChicago, 
no  values  for  spruce;  spruce-values  apply  to  Norway  pine.  |I  Chicago,  values  given 
for  short-leaf  yellow  pine,  SLYP.  §  Baltimore,  LLYP  is  long-leaf  yellow  pine;  NC 
or  VP,  N.  Carolina  or  Virginia  pine.     If  Boston,  yellow  pine  is  "yellow  pine  (long-leaf).'* 


Ultimate  Unit  Stresses  for  Woods 


649 


10.   Ultimate  Unit  Stresses  for  Woods 

The  Average  Ultimate  Unit  Stresses  for  the  coniferous  or  softwoods 
and  for  the  broad-leaved  or  hardwoods,  together  with  the  average  weights 
of  the  woods  per  cubic  foot  arc  given  in  Tables  XVIII  and  XIX.  The  values 
given  are  compiled  from  many  tests  on  numerous  species  of  timber.  In  regard 
to  the  range  of  vahies  for  the  same  kind  of  wood,  it  may  be  stated  that  the 
higher  values  are  for  specimens  which  contained  a  percentage  of  water  varying 
from  15  to  20%;  and  that  tests  on  laboratory  specimens  showed  greater  strength 
than  the  actual  pieces  used  in  construction.  The  weights  per  cubic  foot  are 
averages  of  the  weights  of  many  specimens  tested  and  agree  generally  with 
average  values  given  in  other  tables  of  weights  of  materials. 


650        Strength  of  Cast-iron  Lintels  and  Wooden  Beams     Chap.  16 

Table  XVm.*    Average  Ultimate  Unit  Stresses  for  the  Coniferous 
or  Softwoods,  in  Pounds  per  Square  Inch 


Kind  of  wood 


Cedar  (white) 

Cedar  (red) 

Cypress 

Hemlock 

Pine  (white) 

Pine  (red),  (Norway 
pine) 

Pine  (yellow),  (long- 
leaf) 

Pine  (yellow),  (short- 
leaf) 

Douglas  fir  (Oregon 
pine) 

Redwood  (California) 

Spruce  (black) 

Spruce  (white) 


Weight 
in  lb 
per  cu 
ft,  dry 

Tension 

Compression 

Bend- 
ing 
(mod- 
ulus of 
rup- 
ture) 

With 
the 
grain 

Across 
the 
grain 

19.72 

8  000 

4  000 

700 

5  000 

to 

to 

to 

20.70 

II  400 

6  000 

23.66 

8  000 

4  000 
to 
7  000 

700 

5  000 

29.80 

4  000 

4  000 

700 

5  000 

to 

to 

to 

to 

6000 

8  000 

800 

II  700 

26.42 

6  000 

4  000 

600 

3500 

to 

to 

to 

to 

32.29 

8  700 

7420 

700 

25.55 

3000 

3000 

700 

4  000 

to 

to 

to 

to 

12  000 

6  650 

I  000 

10  000 

30.25 

5  000 

6  000 

800 

5  000 

to 

to 

to 

to 

13  000 

8000 

I  000 

12  300 

43.62 

6000 

5  000 

I  000 

7  000 

to 

to 

to 

to 

13  000 

9500 

I  400 

14  200 

38.40 

5  000 

4  000 

900 

6  000 

to 

to 

to 

to 

10  000 

9000 

I  000 

12  400 

32.14 

9  000 

4880 

800 

6500 

to 

to 

to 

to 

14000 

9800 

I  200 

12  100 

26.23 

7  000 
to 

10853 

3000 
to 
4  000 

800 

4500 

28.57 

5  000 

4  000 

700 

4  000 

to 

to 

to 

19500 

7850 

12  000 

25.25 

5  000 

4  000 

700 

4  000 

to 

to 

to 

19500 

7850 

12  000 

Shear 


With 
the 
grain 


400 


225 
to 
423 


300 

to 

700 

400 

to 

700 

500 
to 
600 
400 


250 

to 

400 

250 

to 
400 


*  The  higher  values  of  tensile  and  compressive  strengths  are  for  "  dry  "  or  "  sea- 
soned "  timber  containing  from  10  to  15%  of  water.  For  safe  fiber-stresses  for 
flexure,  .see  Table  I,  page  557. 


Ultimate  Unit  Stresses  for  Woods  6 

Table  XIX.*    Average  Ultimate  Unit  Stresses  for  the  Broad-Leaved  or 
Hardwoods,   in  Pounds   per  Square  Inch 


Kinds  of  wood 


Weight 
in  lb 
per  cu 
ft,  dry 


Tension 


Compression 


With 
the 
grain 


Across 
the 
grain 


Bend- 
ing 
(mod- 
ulus of 
rup- 
ture) 


Shear 


With 
the 
grain 


Ash  (white). 


Ash  (red) . . . 
Ash  (green). 


Chestnut 

Elm  (white) . 

Gum , 

Hickory 

Locust 


Lignum-vitae  . 
Maple  (hard). 


Maple  (white) . 


Mahogany   (Central 
America) 


Oak  (white). 


Oak  (chestnut) 

Oak  (live) 

Oak  (red  and  black) 


Poplar  (whitewood) 


Walnut  (white)  (but- 
ternut)  


Walnut  (black). 


38.96 
44.35 


41.00 
45-26 
36.83 


46.16 
to 

52.17 
45.70 


77.12 
43.08 


32.84 


46.35 


53  63 
59-21 

40.75 


30.00 

25.46 
38.11 


II  000 

to 
17  000 


9  000 
to 
13  000 
8  000 
to 
13  000 
15  000 

to 
18  000 

12  800 
to 

18  000 

10  500 
to 

24  800 

11  000 
8  000 

to 
10  000 
8  000 

to 
10  000 

2300 

to 
17  900 
10  000 

to 
19500 

10  000 

13  000 

10  000 


4  000 
to 

9  000 
6800 

8  000 
to 

9  800 

5  000 


6  000 
to 

10  000 

5  600 
to 

8500 

7  000 
to 

10  000 
7  000 

to 

11  700 

8800 

7  000 
to 
9940 

6  000 
to 

7500 

6  000 


4500 

to 
II  300 
7500 
9  000 
4  000 

to 
8500 

4  000 
to 

5700 

5  000 
to 

6800 
7  .500 


I  900 


900 


2  700 
to 
3200 


I  700 
to 
I  900 


6300 

to 

14  200 

5  100 

to 

16  000 

5  000 


7300 

to 

13  600 

6  000 

to 

12  700 

5400 

to 

24300 


6  000 


9  100 

to 

15  400 


450 
to 

I  100 


I  000 
to. 

I  200 


399 
to 
537 


750 
to 
I  000 


*  The  higher  values  of  the  tensile  and  compressive  strengths  are  for  "  dry  "  or 
"  seasoned  "  timber  containing  from  lo  to  is%  of  water.  For  safe  fiber-stresses  for 
flexure,  see  Table  I,  page  557. 


652  Built-Up,  riitched  and  Trussed  Wooden  Girders    Chap.  17 


CHAPTER  XVII 

STRENGTH    OF    BUILT-UP,    FLITCHED    AND    TRUSSED 
WOODEN   GIRDERS 

By 
F.  H.  KINDL 

LATE   CORRESPONDING  MEMBER  AMERICAN  INSTITUTE   OF  ARCHITECTS 

1.   Built-Up  Wooden  Girders 

Built-Up  Wooden  Beams.  Wooden  beams  or  girders  built  up  of  planks, 
spiked  or  bolted  together  side  by  side,  will  generally  be  somewhat  stronger 
•than  solid  girders  of  the  same  dimensions,  because  the  planks  will  be  better 
seasoned  and  freer  from  check-cracks  and  other  defects.  For  beams  or  girders 
ID  in  or  less  in  depth,  spikes  will  usually  be  sufficient  to  bind  the  planks  together; 
but  for  deeper  beams,  bolts  should  be  used  in  addition  to  the  spikes,  to  prevent 
the  planks  from  separating  and  the  outer  planks  from  warping  or  curling  away 
Ifrom  the  others. 

Bolts.  Two  bolts  should  be  placed  at  each  end  of  the  beam  and  every  four 
feet  of  its  length. 

Lengths  of  Planks.  When  a  beam  is  built  up  in  this  way  each  plank 
_  should  extend  the  full  length  of  the  beam.  In  a  continuous  bbam,  the  planks 
should  break  joints  over  the  supports.  The  planks  of  built-up  beams  should 
■  always  be  set  on  edge,  never  flatwise. 

Compound  Wooden  Beams.  It  is  sometimes  necessary  to  use  a  wooden 
beam  for  a  longer  span  or  greater  load  than  is  safe  for  the  deepest  single  beam 
that  can  be  obtained,  or  for  a  beam  built  up  of  planks.  In  such  cases  compound 
WOODEN  BEAMS  may  be  used. 

Definition.  By  a  compound  wooden  beam  or  girder  is  meant  a  beam 
built  up  by  placing  two  or  more  single  beams  over  another  one,  with  the  view 

of  having  them  act  as  a 
single  BEAM  having  the 
depth  of  the  combined 
beams. 

Strength     of     Com- 
pound Beams.     If  two 
Fig.  1.    Two  Simple  Wooden  Beams,  One  Over  the  Other,    lo  by  lo-in  beams  were 
Loaded  in  Middle  placed  one  on  top  of  the 

other,  and  the  upper  one 
loaded  at  the  middle,  the  beams  would  act  as  two  separate  beams  (Fig.  1)  and 
their  combined  strength  would  be  no  greater  than  if  the  two  Ueams  were  placed 
side  by  side.  If,  however,  the  two  beams  can  be  joined  so  that  the  libers  of 
the  lower  beam  will  be  extended  as  much  as  would  be  the  case  in  a  single 
beam  of  the  same  depth,  or,  in  other  words  so  that  the  two  beams  will  not 
slip  on  each  other,  the  compound  beam  will  have  four  times  the  strength  of 

the  SINGLE  BEAM. 

Tests  of  Compound  Beams.  Various  attempts  have  been  made  to  join 
beams  thus  placed  so  as  to  prevent  the  two  parts  slipping  on  each  other,  and 


Bullt-Up  Wooden  Girders 


653> 


during  the  years  1896-7,  Edgar  Kid  well,  of  the  Michigan  College  of  Mines, 
made  an  extended  series  of  tests  of  the  efficiency  of  compound  beams  of  differ- 
ent patterns.  From  these  tests  much  valuable  data  was  obtained.  A  full 
description  of  the  tests,  accompanied  by  the  conclusions  of  the  author,  and  the 
rules  and  data  for  proportioning  the  bolts  and  keys,  of  keyed  beams,  is  pub- 
lished in  the  Trans.  Am.  Soc.  M.  E.,  vol.  27. 

Simple  Form  of  Compound  Beam.  A  form  of  compound  beam,  some-; 
times  used  in  American  building-construction,  is  shown  in  Fig.  2,  diagonal 
.boards  in  opposite  directions  being  nailed  to  each  side  of  the  two  timbers  to 
prevent  their  slipping  on  each  other.  T.  M.  Clark,  in  his  Building  Superin- 
tendence, advocates  this  as  one  of  the  best  forms  of  compound  beams,  and 


Fig.  2.     Simple  Form  of  Compound  Wooden  Beam 

places  its  efficiency  at  about  95%  of  that  of  a  solid  beam  of  the  same  depth. 
Professor  Kidwell  made  nine  tests  of  this  type  of  beam.  In  six  of  the  beams 
the  ratio  of  span  to  depth  was  as  12  to  i,  and  in  three  of  the  beams,  as  24  to  i. 
The  shorter  beams  gave  an  average  efficiency,  without  much  variation,  of 
71.4%,  and  the  longer  beams  an  efficiency  of  80.7%. 

It  was  found  that  the  beams  failed  by  the  splitting  of  the  diagonal  pieces  or 
the  drawing  of  the  nails;  "in  every  case,  long  before  the  beam  broke,  the  struts 
split  open  or  the  nails  were  partly  drawn  out  or  bent  over  in  the  wood,  thereby 
permitting  the  component  beams  to  slide  on  each  other."  When  built  with 
diagonal  boards,  iM  in  thick,  nailed  with  tenpenny  nails,  as  in  Fig.  2,  the 
working  strength  of  such  a  beam  may  be  taken  at  65%  of  the  strength  of 


-Spruee-Beam-28-fti-Span- 

Fig.  3.     Compound  Keyed  and  Bolted  Wooden  Beams 

a  solid  beam  of  the  same  depth  and  of  a  breadth  equal  toijthe  breadth  of.  the 
timbers.  The  deflection  of  the  beam,  however,  will  be  about  double  that  of 
a  solid  beam  of  the  same  size,  and  on  that  account  this  type  of  beam  is  not 
to  be  recommended  for  supporting  floors  with  plastered  ceilings  or  for  carrying 
plastered  partitions. 

Keyed  Beams.  Professor  Kidwell  tested,  also,  several  types  of  keyed 
BEAMS,  and  found  that  a  compound  beam  keyed  and  bolted  together,  as  shown 
in  Fig.  3,  is  the  most  efficient  form  that  it  is  practical  to  build.  ■  - 


654 


BuUt-Up,  Flitched  and  Trussed  Wooden  Girders     Chap.  17 


It  was  found  that  with  oak  keys  it  was  possible  to  obtain  an  efficiency  for 
spruce  beams  of  95%,  while  the  deflection  varied  from  20  to  25%  more  than 
would  be  expected  in  a  soUd  beam. 

Cast-iron  Keys.  By  using  cast-iron  keys  the  deflection  was  found  to  be 
but  little,  if  any,  greater  than  for  a  solid  beam. 

Shape  of  Keys.  The  keys  must  be  wedge-shaped,  as  shown  in  Fig.  4,  so 
that  they  can  be  driven  tightly  against  the  end-wood. 

Efficiency  of  Keyed  Beams.  Professor  Kidwell  recommends  that  for 
ordinary  purposes  an  efficiency  of  75%  be  allowed  when  oak  keys  are  used 
and  of  80%  when  the  keys  are  of  cast  iron.  The  width  of  an  oak  key  should 
be  twice  its  height.  Numerous  small  keys  closely  spaced  gave  better  results 
than  fewer  large  keys.  In  his  report,  Professor  Kidwell  gives  formulas,  also, 
for  the  number  and  spacing  of  the  keys. 

Keys,  Bolts  and  Washers  for  Compound  Beams.  As  compound  beams, 
when  used,  are  generally  built  up  of  8,  10,  12  or  14-in  timbers,  Mr.  Kidder, 
some  years  ago,  prepared  a  table  giving  the  sizes  of  keys,  the  number  required 
on  each  side  of  the  middle  of  the  span,  their  minimum  spacing  and  the  sizes  of 
the  bolts  and  washers  to  be  used  for  such  beams  of  from  20  to  36-ft  spans. 
He  noted  that  the  maximum  safe  loads  for  such  beams  should  be  75%  of  the 
loads  computed  by  Formula  (10),  page  630,  for  a  beam  supported  at  both  ends, 
and  loaded  with  a  uniformly  distributed  load. 

Table  I.     Keys,  Bolts  and  Washers  for  Compound,  Keyed  Wooden  Beams 


Size  of 

beams 

Size  of  keys 

JBolts 

Washers 

Number  of  keys  each  side 
of  center  line 

White 
pine 

Spruce 

Doug- 
las 
fir 

Long- 
leaf 

yellow 
pine 

i6-in  beams 
20-in  beams 
24-in  beams 
28-in  beams 

iH  by  3    -in  oak  keys 
i^^  by  3    -in  oak  keys 
2     by  4    -in  oak  keys 
2H  by  4^^-in  oak  keys 

%-in 
H-in 
?i-in 
7:i-in 

3    -in 
3    -in 

35'^-in 
3H-in 

7 
9 
8 
9 

8 
II 

9 
10 

II 
13 
12 
12 

12 
15 
14 
14 

Size  of  keys 

Bolts 

Washers 

Minimum  spacing  of'keys 

ii/^by3    -i 
2     by  4    -i 
2H  by  4H-i 

n  oak  keys 

^-in 
li-in 

3-in 
3-in 
3-in 

1 1  H-in 
IS    -in 
17    -in 

iiKi-in 
15    -in 
17    -in 

9    -in 
ii^^-in 
13    -in 

9    -in 
iij'^-in 
13    -in 

ti  oak  keys 

n  pak  keys    .... 

The  Breadth  or  Thickness  of  Compound  Beams  should  be  not  less  than 
two-fifths  of  the  depth. 

The  Number  of  Keys  required  is  not  affected  by  the  length  or  breadth  of 
the  beam,  if  the  beam  is  figured  for  the  full  safe  load. 

In  Spacing  the  Keys  (Figs.  3  and  4)  they  should  not  be  closer  than  the 
minimum  spacing  given  in  Table  I.  For  beams  loaded  at  the  mid  lie,  the  spac- 
ing of  the  keys  should  be  uniform  from  X  to  Y,  Fig.  3,  V  being  one-eighth  the 
span  from  the  center  lia&.  ^jlt  Jj^j^^i^tj^  Rcg. Jbpty^ai  the  keys,  center  to  cea- 


Flitched  Beams  or  Flitch-Plate  Girders 


655 


ter,  works  out  less  than  the  minimum  spacing,  the  safe  load  should  be  cor- 
respondingly reduced  or  the  thickness  of  the  beam  increased. 

For  Beams  Uniformly  Loaded,  the  first  four  or  five  keys  from  the  end 
should  be  spaced  for  minimum  spacing,  and  the  spacing  of  the  remaining  keys 
increased  toward  the  point  Y.  When  the  ratio  of  depth  to  span  is  greater  than 
I  to  1 6,  the  inner  key  may  be  a  Httle  more  than  one-eighth  the  span  from  the 
center  line,  for  distributed  loads.  Fig.  3  shows  the  proper  spacing  for  a  20-in 
spruce  beam  of  28-ft  span  and  for  a  long-leaf  yellow  pine  beam  of  30-ft  span; 
and  the  tabulation  below  gives  the  proper  spacing  of  keys  for  spruce  beams  of 


B  PLAN  OF  14" X  24" SPRUCE  BEAIVI-36'  SPAN 
Fig.  4.    Details  of  Keyed  and  Bolted  Wooden  Beam 

longer  spans,  figured  from  the  end  of  the  beam  in  each  case.  For  other  woods 
and  spans  the  spacing  should  be  made  as  near  like  these  as  the  fixed  condi- 
tions will  permit.  Four  examples  of  spacing  are  given  below.  The  sizes  of 
bolts  and  washers  to  be  used  are  given  in  Table  I.  If  the  beam  is  not  over 
10  in  wide,  the  bolts  may  be  arranged  as  for  the  spruce  beam  (Fig.  3);  if  12  in 
wide  or  over,  the  bolts  should  be  staggered  as  shown  for  the  hard-pine  beam. 
In  a  very  wide  beam  the  bolts  might  be  spaced  as  in  detail  B,  Fig.  4. 

Spacing  of  keys  in  inches  for  spruce  beams,  commencing  at  end,  for  uniformly 
distributed  loads: 


16 


Au-in  spruce  beam,  32-ft  span,  10,  12,  12,      16,      19,  24,  32 

20-in  spruce  beam,  32-ft  span,  10,  ii^^,  iiV^,  11^,  12,  12,  12,  13, 15,  18,  24 

24-in  spruce  beam,  36-ft  span,  13,  15,  15,      15,      15,  16,  :  " 

28-in  spruce  beam,  36-ft  span,  15,  17,  17,      17, 


IS,  16,  18,  20,  30 
17,17,17,17,17,17 


3.   Flitched  Beams  or  Flitch-Plate  Girders 

Flitch-Plate  Beams  (Fig.  5)  were  at  one  time  much  used,  but  with  the 
present  prices  of  steel  it  is  cheaper  and  better  to  use  steel  beams. 

The  following  explanation  and  formulas  are  given,  however,  for  the  benefit 
of  those  who  might  have  occasion  to  use  a  beam  of  this  kind.  It  has  been 
found  in  practice  that  the  thickness  of  the  wood  should  be  sixteen  times  the 
thickness  of  the  steel    As  the  steel  is  so  much  suffer  than  the  wood,  we  must 


656  Built-Up,  Flitched  and  Trussed  Wooden  Girders     Chap.  17 

proportion  the  load  on  the  wood  so  that  the  latter  will  bend  as  much  as  the 
steel  plate  bends:  otherwise  the  whole  load  might  be  thrown  on  the  steel  plate. 
The  MODULUS  OF  ELASTICITY  of  Steel  is  about  twenty  times  that  of  long-leaf 
yellow  pine;    so  that  a  beam  of  this  wood,  i  in  wide,  will  bend  twenty  times 

as  much  as  a  plate  of  steel  of  the  same 

^T^^^  P^^"*"^ ^^         _         size  and  under  the  same  load.     Plence, 

:®         ^     --'-^-^^^y^^^^f^f^       if  we  want  this  beam  to  bend  just  as 


{rO  _  :   :   o        -        -    -  - ^' - '  }        much  as  the  steel  plate,  we  must  put 

Fig.  5.    Flitch-plate  Girder  ^^^y  one-twentieth  the  load  on  it.     If 

the   wooden  beam   is   sixteen  times  as 

thick  as  the  steel  plate,  we  should  put  sixteen-twentieths  of  its  safe  load  on  it, 

or,  what   amounts  to  the  same  thing,  use  a  constant  only  four-fifths  of  the 

strength  of  the  wood. 

Formulas  for  Flitch-Plate  Girders.  On  this  basis  the  following  formulas 
have  been  derived  for  the  strength  of  flitch-plate  girders,  in  which  the  thick- 
ness of  the  wood  is  sixteen  times  the  breadth  of  the  steel,  approximately: 

Let  d  =  depth  of  beam  in  inches 

b  =  total  thickness  of  wood  in  inches 
/  =  clear  span  in  feet 
/  =  thickness  of  steel  plate  in  inches 
(  53.6  for  long-leaf  yellow  pine 
^'  *  =   \  4S  for  Douglas  fir 
(31  for  spruce 
P  =  total  load  at  middle  in  pounds 
W  =  distributed  load  in  pounds 

Then,  for  beams  supported  at  both  ends, 

Safe  load  at  middle  in  pounds  =  -~  (A'b  -{-  889  /)  (i) 

Safe  distributed  load  in  pounds  =  -—  (A'b  +  889  /)  (2) 


(3) 


4  /      wi 

For  distributed  load,  ^  =  V  — ; • 

For  load  at  middle,  d=\/-—' (4) 

V^'^, -1^889/  ^ 

The  bolts  should  be  %  in  in  diameter,  and  spaced  2  ft  on  centers.  Each 
end  should  have  two  bolts,  as  in  Fig.  5. 

Example.  What  is  the  safe  load,  uniformly  distributed,  for  a  girder  composed 
of  three  4  by  14-in  Douglas-fir  timbers  and  two  %  by  14-in  flitch-plates,  with  a 
span  of  25  ft? 

Solution.     By  Formula  (2), 

Safe  load  = ^(45  X  12  -f  889  X  3/4)  =18  922  lb 

25 

3.  Trussed  Beams  and  Girders 
Use  of  Trussed  Beams  and  Girders.    Whenever  we  wish    to    support    a 
floor  upon  girders  having  a  span  of  more  than  30  ft,  we  must  use  a  trussed 
GIRDER,  a  riveted  steel-plate  girder,  or  two  or  more  steel  beams.     Under 

*  For  commercially  spasoned  timber  and  for  ideal  conditions  these  values  may  increase 
about  30%. 


Trussed  Beams  and  Girders 


657 


some  circumstances  and  in  some  parts  of  the  country  it  may  be  cheaper  or 
more  convenient  to  use  a  large  wooden  girder,  and  truss  it,  as  in  Figs.  6,  7,  8  or  9. 

Depth  of  Trussed  Girder.  For  all  these  forms  it  is  desirable  to  give  the 
girders  as  much  depth  as  the  conditions  allow;  as,  the  deeper  the  girder,  the 
smaller  the  stresses  in  the  pieces. 

In  the  Single-Strut  Trussed  Girder,  we  either  have  two  beams,  and  one 
rod  which  runs  up  between  them  at  the  ends,  or  three  beams,  and  two  rods 
running  up  between  the  beams  in  the  same  way.  The  beams  should  be  in  one 
continuous  length  for  the  whole  span,  if  they  can  be  obtained  in  that  length. 
The  requisite  dimensions  of  the  tie-rod,  struts  and  beams,  in  any  given  case, 
must  be  determined  by  first  finding  the  stresses  developed  in  these  pieces,  and 
then  the  areas  of  cross-sections  required  to  resist  these  stresses. 

For  a  Single-Strut  Truss  (Fig.  6),  the  stresses  in  the  pieces  may  be  deter- 
mined by  the  following  formulas: 

For  a  Distributed  Load  W  Over  the  Whole  Girder  (Fig.  6) 


Fig,  6.    Trussed  Wooden  Girder,    One  Vertical  Strut 


Tension  in  T 
Compression  in  C 


_   W       length  of  T 
2         length  of  C 


iW. 


W 


Compression  in  B=  — ,X 


(See  Note.) 
length  of  B 


(5) 
(6) 
(7) 


length  of  C 

Note.    When  the  beam  B  is  in  one  piece,  the  full  length  of  span.     If  B  is 
jointed  over  the  strut  then  compression  in  C  or  tension  in  R  =  V2  W. 

For  a  Concentrated  Load  P  Over  C  (Fig.  6) 
Tension  in  T 


P      length  of  r 
=  -X: 


2      length  of  C 


(8) 


Compression  in  C  =  P 
P 


Compression  in  B  = 


length  of  B 


2      length  of  C 


(9) 


For  a  Girder  Trussed  as  in  (Fig.  7),  Under  a  Distributed  Load   W  Over  the 
Whole  Girder 


Compression  in  5  = 
Tension  in  R 
Tension  in  B 


W  length  of  S 

2  length  of  R 

=  %  W.  (See  Note.) 

W  length  of  B 

2  length  of  R 


bTJO  dIodV- 


(10) 


(11) 


Note.     When  the  beam  B  is  in  one  piece,  the  full  length  of  span.     If  B  is 
jointed  over  the  strut  then  compression  in  C  or  tension  in  R  =  V2W. 


658    •        Built-Up,  Flitched  and  Trussed  Wooden  Girders     Chap.  17 
For  a  Concentrated  Load,  P  at  the  Middle  (Fig.  7) 


Fig.  7.    Trussed  Wooden  Girder.     One  Vertical  Tie 

^  ■       .     e      ^^  length  of  5 

Compression  in  6  =  —  X  ; 


2      length  of  R 


Tension  in  R 
Tension  in  B 


=  P 


P      length  of  B 
2      length  of  R 


(I2) 


(i3) 


For  a  Double-Strut  Trussed  Beam  (Fig.  8)  with  a  Distributed  Load   W  Over 
the  Whole  Girder  (Beam  B  Divided  into  Three  Equal  Spans) 


Fig.  8.    Trussed  Wooden  Girder.    Two  Vertical  Struts 
Tension  in  T 
Compression  in  C  =  — 


W^      length  of  T 
3       length  of  C 


^  '      '     T,       ,      ■      .     y^      W      length  of  5 

Compression  in  B  or  tension  in  D  =  —  X ,: — 

3       length  of  C 

For  a  Concentrated  Load  P  Over  Each  of  the  Struts  C  (Fig.  8) 

.  length  of  T 


Tension  in  T 


=  PX 


length  of  C 


Compression  in  C  =  P 


Compression  in  B  or  tension  in  Z>  =  P  X 


length  of  B 
length  of  C 


(14) 


(^5) 


(16) 


(17) 


For  a  Girder  Trussed  as  in  Fig.  9,  and  Under  a  Distributed  Load  W  Over 
the  Whole  Girder  (Beam  B  Divided  into  Three  Equal  Spans) 


.      .     ^      W      length  of  S 

Compression  in  5  =  —  X  , — 7-=: 

3       length  of  R 


(18) 


Tension  in  R 


W 
3 


,,,..„  .      .     ^    W     length  of  5  ,     , 

Tension  m  B  or  compression  in  D  =—  X  , ; — ;-;:  (19) 

3       length  of  R 


Trussed  Beams  and  Girders 


65^ 


For  Concentrated  Loads  P  Applied  at  Joints  2  and  3  (Fig.  9) 
2  3 


Fig.  9.    Trussed  Wooden  Girder.    Two  Vertical  Ties 


Compression  in  6"  =  P  X 


length  of  S 
length  of  R 


Tension  m  R         =  P 

Tension  in  B  or  compression  in  D  = 


PX 


length  of  B 
length  of  R 


(20) 


(21) 


Trusses  constructed  as  shown  in  Figs.  8  and  9  should  be  divided  so  that  the 
rods  R,  or  the  struts  C,  will  divide  the  lengths  of  the  girder  into  three  equal  or 
nearly  equal  parts.  The  lengths  of  the  pieces  T,  C,  B,  R,  S,  etc.  should  be 
measured  on  the  axial  lines  of  the  pieces.  Thus,  the  length  of  R  should  be 
measured  from  the  center  line  or  axis  of  the  tie-beam  B  to  the  center  line 
OR  AXIS  of  the  strut  D;  and  the  length  of  C  should  be  measured  from  the  axis 
of  the  rod  to  the  axis  of  the  strut-beam  B. 

After  determining  the  stresses  in  the  pieces  by  these  formulas,  we  may  com- 
pute the  areas  of  the  cross-sections  by  the  following  rules: 

compression  in  strut 
(22) 


Area  of  cross-section  of  a  short  strut  = 


in  which  Sc  for  cast  iron  may  be  taken  at  from  13  000  or  14  000  lb  per  sq  in, 
and  for  wood  as  given  in  Table  XVI,  page  647. 

The  size  of  the  long  strut  D  (Fig.  9)  should  be  determined  by  means  of 
Tables  451  and  452  for  wooden  columns,  Chapter  XIV. 

The  diameters'  of  the  tie-rods  may  be  obtained  from  Table  II,  page  388. 

For  the  beam  B  (Figs.  8  and  9)  when  the  load  is  distributed,  we  must  compute 
its  necessary  area  of  cross-section  as  a  strut  (Fig.  8)  or  a  tie  (Fig.  9),  and  also 
the  area  of  its  cross-section,  as  a  beam,  required  to  support  its  load,  and  use 
a  beam  with  a  section  equal  to  the  sum  of  the  two  sections  thus  obtained. 

Area  of  cross-section  of  B  to  resist  )       tension        compression 

>  = or  (23) 

tension  or  compression  )  St  Sc  v^' 

In  the  trusses  shown  in  Figs.  6  and  7,  with  distributed  loads, 

Wxl 

4Xd^XA 

In  the  trusses  shown  in  Figs.  8  and  9,  with  distributed  loads, 

Wxl 
Breadth  of  B  (as  a  beam)  =  - — — — -  (25) 

(Compare  Equation  (24)  and  (25)  with  Equation  (11),  page  630.) 

W  denotes  the  total  distributed  load  in  pounds  on  the  girder,  and  /  the  length 
in  feet  of  one  section  of  the  beam.  When  the  loads  are  concentrated  over  the 
struts  C  (Fig.  8)  or  at  the  joints  R  (Fig.  9)  then  there  will  be  no  transverse 


Breadth  of  B  (as  a  beam)  =  - 


(24) 


660  Built-Up,  Flitched  and  Trussed  Wooden  Girders     Chap.  17 

STRESS  on  the  beams  B,  and  they  need  be  proportioned  for  the  compressiv^e 
or  TENSILE  STRESS,  Only,  as  the  case  may  be. 

In  Formulas  (23),  (24)  and  (25),  for  Sc  and  St,  substitute  the  values  for 
safe  unit  stresses  for  compression,  Table  XVI,  page  647,  and  for  tension,  Table 
II,  page  388,  and  for  A  substitute  the  values  recommended  in  Tables  II  and 
XVI,  pages  628  and  647. 

Illustrative  Examples.  To  illustrate  the  method  of  computing  the  dimen- 
sions of  the  different  parts  of  girders  of  this  kind,  two  examples  are  given. 

Example  1.  It  is  required  to  design  a  trussed  girder  of  the  form  shown  in 
Fig.  6,  for  a  span  of  30  ft.  The  girders  are  to  be  12  ft  on  centers,  and  are  to 
carry  a  floor  loaded  with  100  lb  per  sq  ft.  The  girder  consists  of  three  strut- 
beams  B,  side  by  side,  and  two  rods.  We  can  allow  the  rod  T  to  come  two  feet 
below  the  beams  B,  and  we  will  assume  that  the  depth  of  the  beams  B  will 
be  12  in;  then  the  length  of  C,  measured  from  the  center  line  of  the  beam,  will 
be  30  in.  The  length  of  iJ  is  15  ft,  and  by  computation,  or  by  scaling,  we  find 
the  length  of  T  to  be  15  ft  2M  in. 

Solution.    The  total  load  on  the  girder  equals  100  lb  multiplied  by  the  span 

multiplied  by  the  distance  of  the  girders  on  centers,  or,  100  X  30  X  12  =  36  000  lb. 

From  Formula  (5), 

„      .      .    ^     36000      1821/2  in 

Tension  m  T  =  X : — -  =  109  500  lb 

2  30  m    . 

or  54  750  lb  on  each  of  the  two  rods.  For  such  a  large  stress  it  is  best  to  upset 
the  ends  of  the  rods,  and  allowing  16  000  lb  per  sq  in  for  steel  rods,  we  find  from 
Table  II,  Chapter  XI,  that  we  must  use  two  2li-\n  steel  rods. 

The  strut-beam  we  will  make  of  long-leaf  yellow  pine.  From  Formula  (7)  we 
find  the  compressive  stress  in  ^  =  (36  000/2)  X  (180/30)  =  108  000  lb.  As  we  are 
to  use  three  beams  side  by  side,  there  will  be  36  000  lb  compression  in  each  beam. 

To  resist  the  compression  there  is  required  an  area  of  36  ooo/i  000  or  36  sq  in, 
which  is  equal  to  3  by  12  in. 

From  Formula  (24)  we  find  the  total  breadth  required  to  resist  the  transverse 

36  000  X  IS  .  ,   ,  ,  ,  ... 

stress  = : =  14  m;  or  each  beam  must  be  4^^  by  12  m  in  section  to 

4X144X67 
resist  the  transverse  stress,  and  3  by  12  in  to  resist  the  compressive  stress. 
Consequently  each  beam  must  be  7^^  by  12  in  in  cross-section. 
[     As  this  would  make  the  girder  very  wide,  27 14  in,  we  will  use  beams  14  in 
deep,  increasing  the  depth  of  the  girder  i  in,  so  that  the  height  on  centers  will 
still  be  30  in. 

The  area  required  to  resist  the  compressive  stress  will  be  the  same  as  before, 
36  in,  but  as  the  beam  is  14  in  deep  the  breadth  will  be  only  2.57  in. 

36  000  X  I") 

The  total  breadth  to  resist  the  transverse  stress  will  be  -^ ~  =  10.28  in, 

4X196X67 

or  3.43  in  for  each  beam.  The  total  breadth  for  each  beam  will  therefore  be 
6  in.  A  beam  with  a  cross-section  of  6  by  14  in  will  meet  the  requirements. 
The  total  width  of  the  girder  will  then  be  22H  in.  The  load  on  C=  %  IF  = 
22  500  lb,  or  II  250  lb  over  each  rod.  The  theoretical  sectional  area  in  square 
inches  necessary  to  resist  this  load  =11  250/13  000  for  cast  iron  and  1 1  250/1  000 
for  oak.  As  the  struts  must  be  the  full  width  of  the  girder,  however,  it  will 
be  necessary  to  make  the  sectional  area  much  greater  than  the  theoretical  re- 
quirements. If  made  of  cast  iron  the  strut  should  be  of  the  shape  shown  in 
Fig.  10,  and  if  of  oak,  of  the  shape  shown  in  Fig.  11.  The  cast-iron  strut  will 
be  the  best,  but  an  oak  strut  will  answer. 


Trussed  Beams  and  Girders 


661 


Example  2.  It  is  required  to  support  a  floor  over  a  lecture-room  40  ft  wide, 
by  means  of  trussed  girders;  and  as  the  room  above  is  to  be  used  for  electrical 
purposes,  it  is  desired  to  have  a  truss  with  very  httle  iron  in  it.  It  is  decided^ 
therefore,  to  use  a  truss  such  as  is  shown  in  Fig.  9. 

Solution.  Where  the  girders  rest  on  the  wall,  there  will  be  brick  pilasters 
having  a  projection  of  6  in,  which  will  make  the  span  of  the  truss  39  ft,  and 
the  rods  RR  will  be  placed  so  as  to  divide  the  tie- 
beam  into  three  equal  spans  of  13  ft  each.  The  tie- 
beam  B  will  consist  of  two 

long-loaf  yellow  pine  beams, 

with    the    struts  S    coming 

between    them.     There    are 

two  rods,  instead  of  one,  at 

RR,  coming  down  on  each  side 

of  the  struts  S,  and  passing 

through  iron  castings  below 

the   beams   B,  and   forming 

supports     for     them.      The 

height    of    the    truss    from 

center  to  center  of  timbers 

must  be   limited  to   18   in. 

The    trusses    arc    8    ft    on 

centers. 

The  total  floor-area  supported  by  one  girder  is  8  by  39  ft,  or  312  sq  ft.  The 
heaviest  load  to  which  the  floor  will  be  subjected  is  the  weight  of  the  people 
in  the  room,  for  which  75  lb  per  sq  ft  is  an  ample  allowance;  and  the  weight 
of  the  floor  itself  is  about  100  lb  per  sq  ft.  This  makes  the  total  weight  ^liable 
to  come  on  one  girder  31  200  lb.  M  '-y^^uM 

W    . 157  m 


Fig.  10.     Cast-iron  Strut 
for  Two  Tie -rods 


Fig.  11.    Wooden  Strut  for 
Two  Tie-rods 


Compression  in  S,  from  Formula  (18)  =  —  X  - 

3 


:  90  7oo'lb>''>^l'l' 


Tension  in  one  pair  of  rods 


W 

■■  —  =  10  400  lb 
3 


rr      .       .      „  .       .      ^      PF      156  in 

lension  m   B  or  compression  m  D  =  — X =  90  130  lb 

3        18  m 

As  the  unsupported  length  of  D  is  greater  than  that  of  S,  a  beam  that  will 
resist  the  compression  in  D  will  be  ample  for  S.  We  find  from  Table  II,  Chap- 
ter XIV,  that  it  will  require  a  post  10  by  12  in  in  cross-section  to  resist  the  com- 
pression in  D,  which  is  13  ft  in  length.  The  tension  in  each  rod  is  only  5  200  lb; 
but  as  the  rods  must  support  a  larger  washer  at  the  bottom,  they  are  made 
I  in  in  diameter,  not  upset.  The  tension  in  each  of  the  beams  B  is  45  065  lb. 
This  divided  by  i  200,  the  safe  unit  tensional  stress  for  long-leaf  yellow  pine 
=  37-6  sq  in,  or  about  2%  by  14  in. 

The  total  breadth  of  the  tie-beam  to  resist  the  transverse  load  is  found  from 
Formula  (25).    Assuming  14  in  for  the  depth  of  B 


Breadth  oi  B  = 


31  200  X  13 


=  5.15  in,  or  about  2H  in  for  each  beam 


6  X  196  X  67 

The  breadth  of  each  tie-beam  must  therefore  be  2%  'm+  2\i  in  =  5H  in. 
Hence  the  tie-beams  must  be  5  by  14  in  in  section.  The  girder,  therefore,  must 
be  built  with  10  by  i4-in  strut-beams  and  two  5  by  14-in  tie-beams,  each  42  ft 
Jong.    The  i-in  rods  may  be  cut  H  in  into  the  strut->beams,  and  I'i  in  into  the  tie- 


662  Built-Up,  Fiitched  and  Trussed  Wooden  Girders    Chap.  17 

beams,  so  that  the  latter  will  come  close  against  the  struts  S.  The  thrust  of 
the  strut  S  is  equal  to  its  compressive  stress,  and  a  connection  between  the  tie- 
beams  and  the  struts  must  be  designed  that  will  resist  this  thrust,  which  in  this 
case  is  90  700  lb.  As  the  inclination  of  the  strut  is  very  slight,  there  is  ample 
room  for  bolts.  It  is  best  to  use  bolts  which  are  at  least  iH  in  in  diameter. 
As  they  are  in  double  shear,  the  resistance  to  shearing  of  one  bolt  is  35  340  lb. 
(See  Table  IX,  page  431.)     Steel  bolts  are  used. 

The  bearing  area  of  a  iH-in  bolt  in  a  timber  10  in  wide  is  15  in.  For  the 
bearing  resistance  of  long-leaf  yellow  pine,  we  may  allow  i  400  lb  per  sq  in 
(Table  XVI,  page  647),  which  will  give  21  000  lb  as  the  bearing  resistance  of 
one  i^^-in  steel  bolt.  As  the  force  to  be  resisted  is  90  700  lb,  it  will  require 
five  ii'i-in  steel  bolts  to  sustain  this  bearing  pressure,  the  resistance  to  shearing 
being  greater  than  this  stress. 

The  number  of  bolts  required  to  resist  the  bending  moment  must  now  be 
determined.  The  total  bending  moment  to  be  resisted  (see  page  434,  Chap- 
ter XII)  =  90  700  times  the  distance,  in  inches,  between  the  centers  of  the  tie- 
beams  divided  by  12,  or  90  700  X  ^%2  =  113  375  in-lb. 

From  Table  IX,  page  431,  we  find  that  the  maximum  bending  moment, 
at  a  fiber-stress  of  20000  lb  per  sq  in,  for  a  iH-in  steel  bolt  is  6  630  in-lb. 
Hence  it  will  require  seventeen  iH-in  bolts  to  resist  the  thrust  in  5  without 
bending  the  bolts.  As  it  is  impracticable  to  put  in  so  many  bolts,  larger  ones 
must  be  used.  For  a  2H-in  steel  bolt,  the  maximum  bending  moment  is 
30700  in-lb  (Table  IX,  page  431),  and  four  times  this  is  122800  in-lb; 
hence  four  2H-in  steel  bolts  will  be  suflacient  to  resist  the  bending  stress,  and 
also  the  shearing  and  bearing-stresses.  It  will  be  seen  from  this  example  that 
it  is  much  more  difficult  and  expensive  to  make  satisfactory  end-joints  for 
girders  trussed  as  in  Figs.  7  and  9  than  it  is  for  the  single  and  double-strut 
trusses  like  those  shown  in  Figs.  6  and  8.  The  latter  forms  are  to  be  preferred 
when  the  conditions  will  admit  of  their  use. 

These  four  cases  of  trussed  girders  are  but  special  examples  of  trusses. 
The  stresses  in  them  may  also  be  determined  by  the  methods  explained  in 
Chapter  XXVII;  and  where  the  divisions  of  the  girder  cannot  be  made  uni- 
form, the  stresses  should  be  computed  by  the  general  methods  there  explained. 


General  Principles  of  the  Deflection  of  Beama  663 

CHAPTER  XVIII 
STIFFNESS  AND  DEFLECTION  OF  BEAMS 

By 
CHARLES  P.  WARREN 

LATE  ASSISTANT  PROFESSOR   OF  ARCHITECTURE,   COLUMBIA  UNIVERSITY 

1.   General  Principles  of  the  Deflection  of  Beams* 

Strength  and  Stiffness.  In  many  structures  it  is  necessary  that  beams  and 
girders  shall  be  not  only  strong  enough  but  stiff  enough;  that  is,  not  only 
must  RUPTURE  be  prevented,  but  the  beams  must  not  bend  so  much  as  to  ap- 
pear unsightly,  or  to  crack  the  ceiling.  Therefore,  in  many  cases,  deflection, 
rather  than  absolute  strength,  may  become  the  governing  consideration  in 
determining  the  size  of  a  beam.  Unfortunately,  there  is  no  method  at  present 
of  combining  the  two  calculations  for  strength  and  for  stiffness  in  one.  A 
beam  properly  proportioned  for  strength  will  not  bend  enough  to  stress  the 
fibers  beyond  the  elastic  limit,  but  it  may  in  some  cases  bend  more  than  a 
due  regard  for  appearances  will  justify.  The  distance  that  a  beam  bends 
under  a  given  load  is  called  its  deflection,  and  its  resistance  to  deflection  is 
called  its  stiffness. 

A  General  Formula  for  the  Maximum  Deflection  of  any  beam  under  a 
concentrated  or  uniformly  distributed  load  not  stressed  beyond  the  elastic 
LIMIT  is: 

^  ^      .      .    .     ,  load  in  pounds  X  cube  of  span  in  inches  X  c  . 

Deflection  m  mches  =  — 7—,^ — 7-. tz : —  U} 

modulus  of  elasticity  X  moment  01  inertia 

The  values  of  c  are  as  follows: 

For  beam  supported  at  both  ends,  loaded  at  the  middle 0.021 

For  beam  supported  at  both  ends,  uniformly  loaded 0.013 

For  cantilever  beam,  loaded  at  free  end 0.333       ' 

For  cantilever  beam,  uniformly  loaded o.  125 

Deflection  of  Beam  with  Rectangular  Section.     By  making  the  proper 

substitutions  in  Formula  (i),  the  following  formula  for  a  rectangular  beain 

supported  at  both  ends  and  loaded  at  the  middle  may  be  derived: 

^  ^      .      .    .     ,  load  in  pounds  X  cube  of  span  in  feetX  i  728 

Deflection  in  inches  = — r 7- — .  ^^  ^ (2) 

4  X  breadth  X  cube  of  depth  X  E 

Modulus  of  Elasticity.  From  this  formula  the  value  of  the  modulus  of 
ELASTICITY,  £,  for  different  materials,  has  been  calculated  by  accurately  measur- 
ing the  actual  deflection  of  known  beams  under  given  loads  applied  at  the 
middle  and  then  substituting  these  known  quantities  in  Formula  (2). 

Simple  Formula  for  Deflection.  Formula  (2)  may  be  simplified  some- 
what by  representing  i  728 /4E  by  i/F,  which  gives  the  formula 

Deflection  in  inches  =  ^        — — ;  (3) 

bXd^XF'] 

For  a  DISTRIBUTED  LOAD  the  deflection  will  be  five-eighths  of  this. 

*  See,  also,  in  Chapter  XVI,  formula  on  page  636  and  Table  XVI,  page  647. 

t  Tke  constant  F  corresponds  to  Hatfield's  F,  in  his  treatise  on  "Transverse  Strains." 


664 


Stiffness  and  Deflection  of  Beams 


Chap.  18 


To  Find  the  Load  at '  the  Middle  that  will  cause  a  given  deflection, 
transpose  Formula  (2)  so  that  the  load  becomes  the  left-hand  r^ember  of  the 
equation.     Thus:  1  >  . 

Load  at  middle      4  X  breadth  X  cube  of  depth  X  deflection  in  in  X  E 
in  pounds 


(4) 


^  culpe  o^  span  X  i  728   /  j ;;  ?  ,  ^ 
Limit  of  Deflection.     In  order  that  this  formula  may  be  of  use  in  deter- 
mining the  maximum  load  which  may  be  placed  upon  a  beam,  the  limit  of  the 
DEFLECTION  must  in  some  way  be  tixed.     This  is  generally  done  by  making  it  a 
certain  proportion  of  the  span. 

Allowable  Deflection  of  Floor-Beams.  Trcdgold  and  other  authorities 
state  that  if  a  floor-beam  detiects  more  than  one-fortieth  of  m  inch  for 
EVERY  FOOT  OF  SPAN,  it  is  liable  to  crack  the  ceiling  on  the  under. side;  and  hence 
this  is  the  limit  which  is  often  set  for  the  deflection  of  beartis  in  fiirst-class 
buildings. 

Formulas  for  Deflection  of  Floor-Beams.  If  the  length  in  feet  divided 
by  40 ;^  substituted  for  the  deflection  in  inches,  Formula  (4)  becomes 

breadth  X  cube  of  depth  X  & 


Load  at  the  middle  =  - 


square  of  span  in  feet 


(5) 


in  which  e— — 

17  2S0 

Most  engineers  and  architects,  however,  think  that  one-thirtieth  of  an 
inch  per  foot  of  span,  that  is,  Hoo  of  the  span,  is  not  too  much  to  allow  for 
the  deflection  of  floor-beams,  as  a  floor  is  seldom  subjected  to  its  full  estimated 
load,  and  then  only  for  a  short  time. 

Table  I.     Values  of  Constants  for  Stiffness  or  Deflection  on  Beams* 


Material 


Cast  iron 

Wrought  iron 

Steel 

Ash......... 

Calif  orilia  redwood. .......... 

Cedar.. 

Chestnut 

Cypress 

Douglas  fir.  :iXtA  /ll  liWViX^ 

Hemlock .-\.v  '^-m  »"<h~  »<•,  •  i"-' 

Long-leaf  yellow  pine 

Maple. 

Norway  pine. 

Short-leaf  yellow  pine 

Spruce. 

White  oak 

White  pine 


^t 


15  000  000 

26  000  000 

29  00c  000 

I  482  000 

700  000 

700  000 

•900  000 

900  000 

I  500  000 

900  000 

I  500  000 

I  902  000 

I  100  000 

I  200  000 

I  200  000 

I  500  000 

I  000  000 


34  722 
60  000 
67  130 
3430 
I  620 

1  (320 

2  080 
2  080 
3472 
2  080 
3472 

4  400 
2546 
2777 
2777 
3472 
231S 


17280 


862 
I  Soo 
1  678 
87 
40 
40 
52 
52 
87 
52 
87 
iro 
64 
69 
6c) 
87 
58 


1  157 

2  000 
2238 

114 
54 
54 
69 
69 

1x6 
69 

116 

146 
85 
92 
92 

116 
77 


E  =  modulus  of  elasticity,  pounds  per  square  inch;   seasoned  timber; 

F  =  constant  for  deflection  of  beam,  supported  at  both  ends,  loaded  at  middle; 

e  =  constant,  allowini^  a  d.^flection  of  one-forlicth  of  an  inch  per  foot  of  span- 

ci  =  constant,  allowing  a  defection  of  one-tliirtieth  of  an  inch  per  foot  of  span; 
*  See,  also,  in  Chapter  XVI    formula  on  page  636,  and  Table  XVI,  page  647. 
t  See  Notes,  page  637,  regarding  reductions  ia  value  for  E,  for  unseasoned  timber. 


Formulas  for  Loads,  Based  Upon  the  Stiffness  of  Beams      665 

If  this  ratio  is  adopted,  the  constant  for  deflection  becomes 

E 
ei= —■ 

12  960 

Constants  for  Stiffness  or  Deflection  of  Beams.  In  either  of  the  above 
cases  it  is  evident  that  the  values  used  for  E,  F,  e,  or  ei,  should  be  derived  from 
tests  on  timbers  of  the  same  size  and  quality  as  those  to  be  used.  The  values 
for  the  various  woods  given  in  the  preceding  table  have  been  adopted  by  the 
editors  after  careful  comparison  with  the  results  of  numerous  tests  on  large 
timbers  and  with  values  given  by  ditTerent  authorities.  The  editors  beheve 
that  they  are  perfectly  rcHable  for  first-class,  seasoned,  merchantable  timber. 

2.   Formulas  for  Loads,  Based. Upon  the  Stiffness  of  Beams 

Safe  Loads  for  Limited  Deflections  for  Rectangular  Beams.  Knowing 
the  deflection  caused  by  a  load  concentrated  at  the  middle  of  a  beam,  and  the 
ratio  of  other  deflections,  caused  by  different  modes  of  loading  and  support- 
ing, formulas  for  Cases  I  to  VIII,  Figs.  1  to  <S,  considered  under  the  strength  of 
rectangular  beams  (Chapter  XVI),  can  be  easily  deduced.  These  cases,  ar- 
ranged in  a  different  order,  are: 

For  Beams  Supported  at  Both  Ends* 
Load  at  the  middle 

^  ^    ,      ,      breadth  X  cube  of  depth  X  ^1 

Safe  load  =  : (6) 

square  of  span 
or, 

^       ,  ,         load  X  square  of  span  ,  , 

Breadth   =  — ,       rv—r (?) 

cube  of  depth  X  ei 

Load  at  a  point  other  than  at  the  middle,  m  and  n  being  the  segiments  into 

which  the  beam  is  divided 

^   .    ,      ,      breadth  X  cube  of  depth  X  square  of  span  X  ^1 

Safe  load  = (8) 

i6Xw2X«2 

or, 

^       ,  ,  loadXw-Xw^XiG 

Breadth    =  — 7~T~~^ T" (9) 

cube  01  depth  X  square  01  span  X  ei 

Load  uniformly  distributed 

^   -    ,      ,      8  X  breadth  X  cube  of  depth  X  ei  ,     .^ 

Safe  load  = (10)  f 

5  X  square  of  span 
or, 

_       ,  .         5  X  load  X  square  of  span  ,     . 

Breadth    = — — , — (11) 

8  X  cube  of  depth  X  ci' 

Inclined  beam,  loaded  at  the  middle  t 

^   .    ,      ,  breadth  X  cube  of  depth  X  ei  ,     . 

Safe  load  = (12) 

span  X  horizontal  distance  between  supports 

or, 

^       ,  ,         load  X  span  X  horizontal  distance  between  supports         ,     . 

Breadth   = -{^'7~, — --— — (13) 

cube  of  depth  X  ei 

*  In  Formulas  (6)  to  (17)  the  breadth  and  depth  are  to  be  taken  in  inches,  and  the 
length  or  span  in  feet.     The  load  is  always  in  pounds. 

The  values  given  in  either  of  the  last  two  columns  of  Table  I  may  be  used  for  e  or  Cy, 
according  to  the  degree  of  stiffness  desired,  but  the  values  e^  i^  the  last  column  arq 
ample  under  ordinary  conditions. 

t  See,  also,  formula  in  Chapter  XVI,  page  636, 

%  Tredgold's  Eleraents  of  Carpentry,  page  65, 


666  Stiffness  and  Deflection  of  Beams  Chap.  18 

For  Beams  Fixed  at  One  End,  or  Cantilever  Beams 

Load  at  the  free  end 

^  ,    ,      ,      breadth  X  cube  of  depth  Xei  ,    ^ 

Safe  load  = ;: (14) 

16  X  square  of  span 

or, 

^       ,  ,         16  X  load  X  square  of  span  ,    , 

Breadth   =  ; — ; (15) 

cube  of  depth  Xei 

Load  uniformly  distributed 

^  ,   .     .      breadth  X  cube  of  depth  Xei  ,  ^^ 

Safe  load  = ;: (16) 

6  X  square  of  span 

or, 

^       ,  ,         6  X  load  X  square  of  span  ,    ^ 

Breadth   = (17) 

cube  of  depth  X  ei 

Note.  When  the  span  in  feet  is  less  than  the  depth  in  inches,  the  beams 
should  not  be  calculated  by  the  formulas  for  stiffness,  but  by  those  for  hori- 
zontal SHEAR.     (See  Chapter  XVI,  page  635.) 

3.  Relative  Stiffness  of  Beams 

Beam  supported  at  both  ends  and  loaded  at  the  middle i 

Beam  supported  at  both  ends  and  uniformly  loaded % 

Beam  fixed  or  restrained  at  both  ends  and  loaded  at  the  middle, . .  4 

Beam  fixed  or  restrained  at  both  ends  and  uniformly  loaded 8 

Cantilever  beam  loaded  at  the  free  end Me 

Cantilever  beam  uniformly  loaded H 

The  Stiffest  Rectangular  Beam  containing  a  given  amount  of  material  is 
that  in  which  the  ratio  of  depth  to  breadth  is  as  10  is  to  6;  hence,  in  designing 
beams,  the  depth  and  breadth  should  be  made  to  approach  as  near  this  ratio  as 
is  practicable. 

Example  i.  What  is  the  greatest  distributed  load  that  an  8  by  10  in  white- 
pine  girder,  20  ft  in  span,  will  support,  without  deflecting  at  the  center  more 
than  one-thirtieth  of  an  inch  per  foot  of  span? 

Solution.  This  girder  comes  under  the  case  of  a  beam  supported  at  both 
ends  and  loaded  with  a  uniformly  distributed  load,  and  hence  should  be  calcu- 
lated by  Formula  (10).     Substituting  the  given  dimensions  in  Formula  (10), 

c  (    ^     A      8X8X1000X77  -    ,, 

Safe  load  = =  2  464  lb 

5X400 

Example  2.  What  should  be  the  dimensions  of  a  long-leaf  yellow-pine  beam, 
10  ft  in  span,  to  support  a  concentrated  load  of  4  250  lb  at  the  middle  without 
deflecting  more  than  one-third  of  an  inch  at  the  center? 

Solution.  A  deflection  of  one- third  of  an  inch  in  a  span  of  10  ft  is  in  the  pro- 
portion of  one-thirtieth  of  an  inch  per  foot  of  span;  and  as  the  load  is  concen- 
trated at  the  middle.  Formula  (7)  should  be  used,  with  ei,  the  value  given  in  the 
fourth  column  opposite  long-leaf  yellow  pine. 

Formula  (7)  gives  the  dimensions  of  the  breadth,  but  in  order  to  obtain  it, 
a  value  for  the  depth  must  first  be  assumed.  For  such  a  short  span,  10  inches 
would  seem  to  be  a  proper  depth. 

Substituting  in  Formula  (7) 

4  250  X  100 

Breadth  =« =  3.6  m 

I  oooX  116 


Cylindrical  Beams.     Safe  Loads.     Nominal  Sizes  667 

Hence  it  will  be  necessary  to  use  a  4  by  lo-in  beam.  As  the  span  of  this 
beam  in  feet  is  the  same  as  its  depth  in  inches,  it  should  be  tested  to  see  if  it 
meets  the  requirements  for  strength  also.  From  Table  XII,  page  643,  it 
is  found  that  the  safe  distributed  load  for  a  i  by  lo-in  beam,  10  ft  in  span,  is 
I  33S  lb,  and  for  a  4  by  lo-in  beam  the  safe  load  would  be  four  times  as  much, 
or  5  332  lb.  The  load  in  this  example,  however,  is  applied  at  the  middle; 
hence  the  safe  distributed  load  must  be  divided  by  2,  which  gives  2  666  lb  for 
the  safe  load  at  the  middle.  As  this  is  much  less  than  the  load  to  be  carried, 
the  size  of  the  beam  should  be  increased  to  4  by  16  in.  In  general  it  is  not  safe 
to  use  the  formulas  for  stiffness  when  the  span  in  feet  does  not  exceed  the 
depth  in  inches. 

Example  3.  What  is  the  largest  load  that  an  inclined  spruce  beam  8  by  12  in 
in  cross-section  and  16  ft  in  length  between  the  supports  will  carry  at  the 
middle,  consistent  with  stiffness,  the  horizontal  distance  between  the  supports 
being  14  ft? 

Solution.  Formula  (12)  is  the  one  to  be  used  in  this  case.  Assuming  the 
limit  of  deflection  at  one-thirtieth  of  an  inch  per  foot  of  span,  the  value  of  ei 
is  found  opposite  spruce  in  the  last  column  of  Table  I,  Making  the  proper 
substitutions, 

^  .,,      8X1728X92         ^'      „ 

Safe  load  = —  =  5  678  lb 

16  X  14 

4.    Cylindrical  Beams 

Formulas.  The  formulas  for  beams  with  square  cross-sections  may  be 
used  for  beams  with  circular  cross-sections,  if  1.7  X  e  is  substituted  for  e. 
That  is,  other  conditions  being  equal,  a  cylindrical  beam  bends  or  deflects 
1.7  times  as  much  as  a  beam  the  cross-section  of  which  is  the  square  circum- 
scribing the  circular  cross-section  of  the  cylindrical  beam. 

5.   Safe  Loads  for  Wooden  Beams  for  a  Given  Deflection 

Use  of  Tables  and  Formulas.  Tables  VII  to  XV,  inclusive,  pages  638  to 
646,  giving  the  safe  loads  for  beams,  give,  also,  the  maximum  loads  for  beams, 
I  in  thick,  that  will  cause  a  deflection  not  exceeding  Mgo  of  the  span,  that  is, 
Vii)  in  per  foot  of  span.  Where  two  loads  are  given  for  any  span  or  depth  the 
upper  load  is  calculated  for  strength  and  the  lower  load  for  deflection. 
Where  one  load  is  given  the  calculation  is  for  strength,  as  the  calculation  for 
deflection  in  those  particular  beams  would  give  an  excessive  load  (Example  2). 
To  find  the  corresponding  load  for  any  thickness,  multiply  the  load  given  in 
the  table  by  the  breadth  of  the  beam  in  inches.  Suppose,  for  example,  that  it 
is  required  to  find  the  greatest  distributed  load  that  an  8  by  10-in  white-pine 
girder,  20  ft  in  span,  will  support,  without  deflecting  at  the  center  more  than 
one-thirtieth  of  an  inch  per  foot  of  span.  Referring  to  Table  VIII,  page  639, 
giving  the  safe  loads  in  pounds  for  white-pine  beams,  two  values  are  found 
opposite  the  20-ft  span,  389  and  308,  the  latter  being  the  safe  load  for  deflection. 
The  safe  load,  therefore,  for  an  8  by  lo-in  girder  will  be  eight  times,  or 
308  X  8  =  2  464  lb,  which  agrees  with  the  safe  load  for  the  same  girder  calcu- 
lated for  deflection  by  Formula  10,  Example  i. 

6.   Nominal  and  Standard  Sizes  of  "Wooden  Beams 

Conversion  Factors  for  Wooden  Beams  of  Standard  Size.  Table  II 
may  be  used  for  beams  that  measure  less  than  the  nominal  dimensions. 
Dressed  beams,  and  in  many  localities  floor-joists  carried  in  stock,  are  more 


668 


Stiffness  and  Deflection  of  Beams 


Chap.  18 


or  less  SCANT  of  the  nominal  dimensions,  and  for  such  joists  a  reduction  in  the 
safe  load  must  be  made  to  correspond  to  the  reduction  in  size.  The  dressed 
SIZES  are  generally  H  in  scant  up  to  4  in  in  breadth,  above  which  they  are  V2  in 
scant;  while  in  depth  they  are  all  generally  H  in  less  than  the  nominal  sizes. 
The  safe  loads  may  be  obtained  by  multiplying  the  safe  loads  as  given  in 
Tables  VII  to  XV,  pages  638  to  646,  by  the  factors  given  in  the  following 
table: 

Table  11.    Conversion  Factors  for  Beams  of  Commercial  or  Standard  Sizes 


Cross-sections 

Cross-sections 

of  beams  in 

Factors 

of  beams  in 

Factors 

inches 

inches 

iHxs'A 

1.47 

1HX11V2 

1. 61 

2MXSK2 

2.31 

2%  XII 1/2 

2.53 

i%X6i/2 

1.51 

1HXIZV2 

iM 

2%X6K2 

2. SI 

2HX13H 

2.56 

1MX7K2 

1.54 

1HX15V2 

1.6s 

2%x7y2 

2.42 

2y4XisH 

2.58 

mxgyz 

1.58 

1MX17H 

1.6^ 

2%  X9H 

2.48 

2^^1x17'/^ 

2.60 

Example  4.  What  is  the  safe  load  for  a  2%  by  isH-in  spruce  beam,  18 -ft 
span? 

Solution.  From  Table  VIII,  page  639,  the  safe  load  for  a  i  by  14-in  beam 
is  847  lb.  Multiplying  this  by  2.5^6  the  product  is  2  168  lb,  the  safe  distributed 
load  for  a  beam  2%  by  13'/^  in  in  cross-section.  For  a  full,  "nominal"  size, 
3  by  14-in,  the  safe  load  would  be  2  541  lb. 


7.  Deflection  of  Steel  Beams 

General  Formula.  The  deflection  of  any  steel  beam  may  be  found  by 
means  of  Formula  (i),  page  663. 

Example  5.  It  is  required  to  determine  the  deflection  of  a  12-in  31.5-Ib 
beam,  20  ft  in  span,  under  its  maximum  uniformly  distributed  load  of 
9.59  tons. 

Solution.  The  load  in  pounds  =9.59  tonsX  2  000  =  19  180  lb;  the  span  in 
inches  =  20  f t  X  12  =  240  in;  c,  for  a  beam  supported  at  both  ends  and  uni- 
formly loaded,  from  the  values  given  under  Formula  (i),  is  0.013;  E,  for  steel  is 
29000000  lb  per  sq  in  (Table  I,  page  664);  and  the  moment  of  inertia,  from 
the  properties  of  steel  I  beams,  page  355,  is  215.8.  Substituting  these  values 
in  Formula  (i),  page  663, 


Deflection  in  inches  = 


19  180  X  240'  X  0.013 
29  000  000  X  215.8 


=  0.551  m 


The  allowable  deflection  is  1^0  of  an  inch  per  foot  of  span,  or  2%o  =  0.666  in. 

Coefficients  of  Deflection.  In  order  to  save  the  time  required  to  use  the 
deflection-formula,  coefficients  of  deflection  have  been  worked  out  f<?r 
different  spans  and  are  given  in  Table  III. 


Deflection  of  Steel  Beams  669 

Table  in.     Coefficients  of  Deflection  for  Uniformly  Distributed  Loads* 


Fiber-stress,  pounds  per 

Fiber-stress,  pounds  per 

Span  in 

square  inch 

Span  in 

square  inch 

feet 

feet 

i6  ooo 

14  000 

12500 

16  000 

14  000 

12500 

I 

0.017 

0.014 

0.013 

26 

II. 189 

9  790 

8.741 

2 

0.066 

0.058 

0.052 

27 

12.066 

10.558 

9  427 

3 

0.149 

0.130 

0.116 

28 

12.977 

11.354 

10.138 

4 

0.265 

0.232 

0.207 

29 

13.920 

12.180 

10.875 

5 

0.414 

0.362 

0.323 

30 

14.897 

13.034 

11.638 

6 

0.596 

0.521 

0.466 

31 

IS. 906 

13.918 

12.427 

7 

0.811 

0.710 

0.634 

32 

16.949 

14.830 

13.241 

8 

1.059 

0.927 

0.828 

33 

18.025 

15.772 

14.082 

9 

1. 341 

1.173 

1.047 

34 

19  134 

16.742 

14.948 

10 

1.65s 

1.448 

1.293 

35 

20.276 

17.741 

15.841 

II 

2.003 

1.752 

1.565 

36 

21.451 

18.770 

16.759 

12 

2.383 

2.086 

1.862 

37 

22.659 

19.827 

17.703 

13 

2.797 

2.448 

2.18s 

38 

23.901 

20.913 

18.672 

14 

3.244 

2.839 

2.534 

39 

25.175 

22 . 028 

19.668 

IS 

3.724 

3.259 

2.909 

40 

26.483 

23.172 

20 . 690 

i6 

4.237 

3.708 

3.310 

41 

27.823 

24.346 

21.737 

17 

4.783 

4.186 

3  737 

42 

29.197 

25.548 

22.810 

18 

5. 363 

4.692 

4.190 

43 

30.604 

26.779 

23.909 

19 

5.975 

5.228 

4.668 

44 

31.954 

28.039 

25.034 

20 

6.621 

5.793 

5.172 

45 

33.517 

29.328 

26.18s 

21 

7.299 

6.387 

5. 703 

46 

35.023 

30.646 

27.362 

22 

8. on 

7.010 

6.269 

47 

36.562 

31.992 

28.56s 

23 

8.756 

7.661 

6.841 

48 

38.135 

33.368 

29.793 

24 

9  534 

8.342 

7.448 

49 

39-741 

34-773 

31.047 

25 

10.345 

9  052 

8.082 

1 

50 

41.379 

36.207 

32.328 

*  Taken  by  permission  from  Pocket  Companion,  191 5,  Carnegie  Steel  Company. 

To  find  the  deflection  in  inches  of  a  section  symmetrical  about  the  neutral 
AXIS,  such  as  the  section  of  an  I  beam,  channel,  zee,  etc.,  divide  the  coefficient 
in  the  table  corresponding  to  the  given  span  and  fiber-stress  by  the  depth  of  the 
section  in  inches.  To  find  the  deflection  in  inches  of  a  section  not  symmetrical 
ABOUT  THE  NEUTRAL  AXIS,  such  as  the  section  of  an  angle,  tee,  etc.,  divide  the 
coefficient  corresponding  to  the  given  span  and  fiber-stress  by  twice  the  distance 
of  the  extreme  fiber  from  the  neutral  axis,  obtained  from  the  tables  of  Chapter  X. 
To  find  the  deflection  in  inches  of  a  section  for  any  other  fiber-stress  than 
the  fiber-stresses  given,  multiply  this  fiber-stress  by  any  of  the  coefiicients  in 
Table  III,  for  the  given  span,  and  divide  by  the  fiber-stress  corresponding  to  the 
coefiicient  used. 

Example  6.  Required  the  deflection  of  a  lo-In  25-lb  beam  of  lo-ft  span,  under 
its  maximum  distributed  load  of  13  tons,  the  fiber-stress  being  taken  at  16  000  lb 
per  sq  in.  Table  III  gives  1.655  ^.s  the  deflection-coefficient,  and  dividing  this 
by  10,  the  depth  of  the  beam  in  inches,  the  result  is  1.655/10=0.1655,  for 
the  deflection  at  the  middle.     By  Formula  (i),  page  663,  the  deflection  for 

,,         ,  26  000  X   I   728  000  X  0.013  r  '  .lU 

the  same  beam,  span,  and  load  = =  0.1649   m,  the 

29  ooooooX  122. 1 


670 


Graphical  Determination  of  Deflection  of  Beams      Chap.  18 


two  results  being  nearly  identical.  For  the  same  beam,  a  span  of  i8  ft  and  a 
load  of  7.2  tons,  the  deflection  by  the  table  is  0.5363  in;  and  by  Formula  (i), 
0.5328  in,  practically  the  same  result. 

Safe  Loads  and  Deflection.  In  the  tables  of  Chapter  XV,  giving  the  safe 
loads  for  I  beams,  channels  and  rolled  beams  of  other  cross-sections,  the  loads 
given  are  for  the  safe  limit  of  deflection;  and  the  safe  loads,  also,  are  given 
which  will  cause  deflections  of  more  than  yUo  of  the  span-length  in  inches. 

Lateral  Deflection  of  Beams.  When  the  unbraced  length  exceeds  ten 
times  the  width,  the  tabular  safe  loads  should  be  reduced  in  accordance  with 
the  ratios  given  in  the  following  table  in  order  to  insure  that  the  stresses  in  the 
compression-flanges  should  not  exceed  the  allowed  safe  unit  stress: 


Length  of  span       Allowable  safe  load        Length  of  span       Allowable  safe  load 


5  X  flange-width 
10  X  flange-width 
15  X  flange-width 
20  X  flange-width 


Full  tabular  load 
Full  tabular  load 
9o.G%  tabular  load 
81.2%  tabular  load 


25  X  flange-width 
30  X  flange-width 
35  X  flange-width 
40  X  flange-width 


71.9%  tabular  load 
62.5%  tabular  load 
53.1%  tabular  load 
43.8%  tabular  load 


"  In  addition  to  this  lateral  deflection  which  is  induced  within  the  beam  by 
the  action  of  pure  bending-stresses,  lateral  deflection  may  be  induced  by  the 
thrust  of  floor-arches  or  other  loading  acting  on  an  axis  perpendicular  to  the 
line  of  principal  bending-stress.  The  thrust  of  these  arches  should  either  be 
neutralized  by  tie-rods,  or  the  safe  carrying  capacity  of  the  beam  should  be 
computed  in  accordance  with  the  general  formulas  of  flexure  to  provide  for 
the  combined  stresses  due  to  the  action  of  both  vertical  and  horizontal  forces; 
that  is  to  say,  the  safe  loads  should  be  figured  around  both  the  axes  i-i  and 
2-2,  and  the  unit  stress  computed  so  as  no^  to  exceed  16  000  lb  per  sq  in." 


8.  Graphical  Determination  of  Deflection  of  Beams 

The  Deflection  of  a  Beam  with  parallel  flanges  and  constant  moment  of 
inertia  may  be  determined  graphically.     The  deflected  form  is  identical 

with  the  bending-moment  curve  for  the 
beam  with  a  load  distributed  in  a  form 
similar  to  that  of  the  bending-moment 
diagram.     Fig.  1  is  a  beam  of  length  /. 

The  moment-curve  due  to  loading 
ABC  is  the  deflection-curve  due  to 
concentrated  load  P.  The  deflection- 
curve  is  obtained  graphically  by  divid- 
ing area  ABC  into  thin  vertical  strips 
and  constructing  force  and  equilibrium- 
polygons  (page  296).  If  a  pole-distance 
be  chosen  bearing  a  convenient  ratio 
to  EI  {E  is  the  Modulus  of  Elasticity 
of  the  material  and  /  the  Moment  of 
Inertia  of  the  cross-section  of  the  beam), 
the  deflection  at  any  point  of  the  beam 
will  have  the    same  ratio  to  the  scaled 


Fig.  1.  Moment  and  Deflection-diagrams 
of  Beam  Loaded  at  the  Middle 


ordinate  at  that  point  of  the  equilibrium-polygon. 


Supporting-Forces  or  Reactions  of  Continuous  Girders       671 


CHAPTER  XIX 

STRENGTH  AND   STIFFNESS  OF  CONTINUOUS 
GIRDERS 

BY 

CHARLES  P.  WARREN 

LATE   ASSISTANT   PROFESSOR   OF   ARCHITECTURE,   COLUMBIA   UNIVERSITY 

1.    General  Considerations 

Continuous  Versus  Single-Span  Girders.  A  continuous  girder  is  one 
resting  upon  three  or  more  supports,  as  distinguished  from  a  simple  girder 
which  rests  upon  two  supports.  Continuous  girders,  except  in  reinforced-con- 
crete  construction,  and  in  some  types  of  grillage-foundations,  are  of  rare  occur- 
rence in  building-construction.  While  in  almost  every  building  of  importance 
it  is  necessary  to  employ  girders  resting  upon  piers  or  columns,  placed  from  15 
to  20  ft  apart,  and  while  in  many  cases  steel  girders  could  conveniently  be  ob- 
tained which  would  span  two  and  even  three  of  the  bays  between  the  supports, 
they  are  practically  limited  to  one-story  buildings,  because  in  tall  buildings  it  is 
better  construction  to  have  the  vertical  rather  than  the  horizontal  supports 
continuous.  Many  different  opinions  are  held  as  to  the  relative  strength 
and  stiffness  of  continuous  and  non-continuous  girders,  and  different  formulas 
have  been  proposed  from  time  to  time;  but  in  this  chapter  the  mathematical 
discussions  will  not  be  given.* 

Continuous  Girders  and  Overhanging  Girders.  In  all  continuous 
GIRDERS,  the  end-spans  (Fig.  2)  are  somewhat  in  the  condition  of  a  simple 
girder  with  one  overhanging  end,  while  the  other  spans  are  somewhat  in 
the  condition  of  a  simple  girder  with  two  overhanging  ends.  At  each  inter- 
mediate support  there  is  a  negative  bending  moment,  the  effect  of  which 
is  to  reduce  the  bending  moments  between  the  supports. 

2.   Supporting  Forces  or  Reactions  of  Continuous  Girders 

Continuous  Girder  of  Two  Equal  Spans.  Concentrated  Load  at  the 
Middle  of  Each  Span.  If  a  girder  of  two  spans,  each  equal  to  /  (Fig.  1),  be 
loaded  at  the  middle  of  the  left  span  with  P  lb,  and  at  the  middle  of  the  right 
span  with  Pi  lb,  the  reaction  at  the  support  Ri  is  determined  by  the  formula 

R.^^-^^^^  (X) 

the  reaction  at  the  support  Ri  by 

i22=Hi6(P  +  Pi)  (2) 

and  the  reaction  at  the  support  R3  by  the  formula 

Ri  = (3) 

32 

*  For  the  derivation  of  the  following  formulas,  see  an  article  by  F.  E.  Kidder  on  this 
subject,  in  Van  Nostrand's  Engineering  Magazine,  July,  i88i. 


672 


Strength  and  Stiffness  of  Continuous  Girders       Chap.  19 


If  P  =  Pi,  then  each  of  the  end-supports  must  support  Yie  P  and  the  middle 
support  2^ie  P.  If  the  girder  is  cut  so  as  to  make  two  girders  ^pf  one  span 
each,  then  the  end-supports  will  carry  y2  P  or  Mo  P,  and  the  middle  support 

i^-ib  P.  Hence,  it  is  seen  that  by  using 
the  continuous  girder  of  three  spans,  the 
reactions  of  the  end-supports  are  dimin- 
ished, while  the  reaction  at  the  middle 
support  is  increased. 

Continuous  Girder  of  Two  Spans. 
Uniformly  Distributed  Load  Over  Each 
Span  (Fig.  1).  Load  over  each  span  equals  w  lb  per  unit  of  length.  Let  / 
be  the  length  of  the  left  span  and  /i  the  length  of  the  right  span.  Reaction  of 
left  support 


Fig.  1.     Continuous  Girder  of  Two  Spans 


Ri  = 


L       4/(^  +  /i)J 


Reaction  of  middle  support, 

R,  =  w{l-[-h)-Ri-R2 
Reaction  of  right  support 


(4) 


(5) 


(6) 


When  both  spans  are  equal  to  /,  the  reaction  of  each  end-support  is  %  wl,  and 
of  the  middle  support  %  wl;  hence  the  girder,  by  being  continuous,  reduces  the 
reactions  of  the  end-supports,  and  increases  that  of  the  middle  support  H,  or 
25%. 

Continuous  Girder  of  Three  Equal  Spans.  Concentrated  Load  of  P  Pounds  at 
the  Middle  of  Each  Span  (Fig.2). 

Reaction  of  either  abutment 

Ri  =  R4=  ^0  P  (7) 

Reaction  of  either  middle  support 


^2  =R3  =  2^^o  p 


(8) 


or  the  reactions  of  the  two  end-supports  are  ^io  less,  and  those  of  the 
two  middle  supports  •}^o 
greater  than  they  would 
have  been  had  three 
separate  girders  of  the 
same  cross-section  been 
used,  instead  of  one  con- 
tinuous girder. 

Continuous  Girder  of  Three  Equal  Spans.     Uniformly  Distributed  Load  Over 
Each  Span  (Fig.2).    The  load  per  unit  of  length  is  iv  lb. 

Reaction  of  either  end-support 


Fig.  2.     Continuous  Girder  of  Three  Spans 


Ri  =  Ri=  %  wl 
Reaction  of  either  middle  support 

R2=R^=  iVio  wl 


(9) 


do) 


Hence  the  reactions  of  the  end-supports  are  H  less,  and  of  the  middle  supports 
Ho  more,  than  if  the  girder  were  not  continuous. 


Bending  Moments  of  Continuous  Girders  673 

3.   Bending  Moments  of  Continuous  Girders 

Strength  of  Continuous  Girders.  The  strength  of  a  girder  depends  upon  its 
material  and  the  shape  of  its  cross-section,  and  also  upon  the  disposition  of  the 
external  loads  imposed  upon  it.  The  latter  give  rise  to  the  bending  moments, 
which  are  measures  of  the  tendencies  of  the  external  forces,  such  as  the  loads 
and  the  supporting  forces,  to  bend  or  to  break  the  girder.  It  is  the  difference 
in  the  numerical  values  of  these  bending  moments  which  causes  the  difference 
in  the  flexural  strength  of  continuous  and  non-continuous  girders  of  the 
same  cross-section. 

Continuous  Girders  of  Two  Spans.  When  a  beam  is  at  the  point  of  breaking 
by  flexure,  the  flexure-formula,  M  =  Sl/c,  is  frequently  used  to  calculate  a 
nominal  unit  stress  developed  in  the  beam;  and  when  the  beam  has  a  rec- 
tangular cross-section  the  formula  takes  the  form  (see  page  635) 

Maximum  bending       Modulus  of  rupture  *  X  breadth  X  square  of  depth  ,     . 

= — _   (11) 

moment  6 

In  order  that  the  beam  may  carry  its  load  with  perfect  safety,  the  breaking-load 
must  be  divided  by  a  proper  factor  of  safety.  Hence,  If  the  maximum 
bending  moment  of  a  beam  can  be  found  under  any  conditions,  the  required 
dimensions  of  the  beam  can  easily  be  determined  from  Formula  (11).  (See 
Table  I,  page  557,  for  the  safe  values  of  the  fiber-stresses.)  The  greatest 
bending  moment  for  a  continuous  girder  of  two  spans  is  almost  always  over  the 
middle  support,  and  is  a  minus  bending  moment,  if  the  plus  sign  is  given  to 
the  maximum  bending  moments  between  the  supports.  It  is  the  numerical 
VALUE  only,  however,  that  is  considered. 

Continuous  Girder  of  Two  Spans.  Distributed  Load  over  Each  Span.  The 
greatest  bending  moment  in  a  continuous  girder  of  two  spans,  /  and  U  (Fig.  1), 
loaded  with  a  uniformly  distributed  load  of  w  lb  per  unit  of  length  is  over  the 
middle  support  and  is 

wl^  -j-  wh^ 
Maximum  bending  moment  =  — — — — -  (12) 

o  (*  +  n) 

When  /  =  h,  or  both  spans  are  equal, 

Maximum  bending  moment  =  wl-fS  (12a) 

which  is  the  same  as  the  maximum  bending  moment  of  a  beam  supported  at 
both  ends  and  uniformly  loaded  over  its  whole  length.  Hence  a  continuous 
girder  of  two  spans  uniformly  loaded  is  no  stronger  as  far  as  flexure  is  concerned 
than  if  non-continuous. 

Continuous  Girder  of  Two  Equal  Spans.  Concentrated  Load  at  the  Middle 
of  Each  Span.  The  greatest  bending  moment  in  a  continuous  girder  of  two 
equal  spans,  each  of  length  /,  loaded  with  P  lb  at  the  middle  of  one  span,  and 
with  Pi  lb  at  the  middle  of  the  other,  is 

Maximum  bending  moment  =  %2 1  {P  +  Pi)  (13) 

•  The  modulus  of  rupture  is  equal  to  the  ultimate  flexural  unit  stress  developed  in  a 
beam  when  the  bending  moment  is  great  enough  to  cause  failure,  and  is  expressed  in 
pounds  per  square  inch.  It  usually  lies  between  the  ultimate  unit  compressive  strength 
and  the  ultimate  unit  tensile  strength  of  the  material.  (See,  also,  Chapter  XV,  page 
556.)  It  is  to  be  noted,  that  the  flexure-formula  M  =  SI /c  is  not  really  applicable'to 
beams  of  materials  for  which  the  stresses  are  not  proportional  to  the  deformation,  nor  to 
non-homogeneous  beams,  nor  to  beams  under  stresses  greater  than  the  elastic  limit  of 
the  material. 


674  Strength  and  Stiffness  of  Continuous  Girders       Chap.  19 

When  P  =  Pi,  or  the  two  loads  are  equal,  this  becomes 

Maximum  bending  moment  =  ^le  PI  {.130) 

or  34  less  than  its  value  when  the  beam  is  cut  at  the  middle  support.* 

Continuous  Girder  of  Three  Spans.  Uniformly  Distributed  Load  Over  Each 
Span.  The  greatest  bending  moment  in  a  continuous  girder  of  three  spans 
loaded  with  a  uniformly  distributed  load  of  w  lb  per  unit  of  length,  the  length 
of  each  end-span  being  h  and  of  the  middle  span  /,  is  at  either  of  the  middle  sup- 
ports, and  is  determined  by  the  formula 

Maximum  bending  moment  =  -- — 7—77  (^4) 

4  (3  ^  +  2  /i) 

When  the  three  spans  are  equal,  this  becomes 

Maximum  bending  moment  =  wl^/ 10  (i4<i) 

or  H  less  than  what  it  would  be  were  the  beam  not  continuous. 

Continuous  Girder  of  Three  Equal  Spans.  Concentrated  Load  of  P  Pounds  at 
the  Middle  of  Each  Span.  The  greatest  bending  moment  in  a  continuous 
girder  of  three  equal  spans,  each  of  a  length  /,  and  each  loaded  at  the  middle 
with  P  pounds,  is 

Maximum  bending  moment  =  Ho  PI  (15) 

or  y^  less  than  that  of  a  non-continuous  girder. 

4.   Deflection  of  Continuous  Girders 

Continuous  Girder  of  Two  Equal  Spans.  Uniformly  Distributed  Load  Over 
Each  Span.  The  greatest  deflection  of  a  continuous  girder  of  two  equal  spans 
loaded  with  a  uniformly  distributed  load  of  w  lb  per  unit  of  length  is 

Maximum  deflection  =  0.005416  wl^/EJ  (i6) 

in  which  E  is  the  modulus  of  elasticity  and  /  the  moment  of  inertia  of  the 
cross-section  of  the  beam.  The  greatest  deflection  of  a  similar  beam  supported 
at  both  ends  and  uniformly  loaded  is 

Maximum  deflection  =  o.oi2>020'wl^/EI 

Hence  the  deflection  of  the  continuous  girder  is  only  about  %  that  of  a  non- 
continuous  girder.  The  greatest  deflection  of  a  continuous  girder  of  two  spans 
is  not  at  the  middle  of  either  span,  but  between  the  middle  point  of  a  span  and 
one  of  the  abutments.  The  greatest  deflection  of  a  continuous  girder  of  two 
equal  spans,  loaded  at  the  middle  of  one  span  with  a  load  of  P  lb,  and  at  the 
middle  of  the  other  with  Pi  lb,  is,  for  the  span  with  the  load,  P 

(2sP-9Pi)/3 
Maximum  deflection  = -^—- 1  (17) 

for  the  span  with  load  Pi 

(23  P\  —  9  P)  P 

Maximum  deflection  =  • (iia) 

I  536  EI 

When  both  spans  have  the  same  load 

Maximum  deflection  =  J^es  Pl^/EI  {17b) 

*  In  this  continuous  beam  the  maximum  bending  moment  is  the  minus  bending  mo- 
ment over  the  middle  support  and  in  each  of  the  two  simple  beams  the  maximum  bend- 
ing moment  is  a  plus  bending  moment  and  is  between  two  supports. 


Notes  on  Reactions,  Strength  and  Stillness  of  Continuous  Girders      675 

The  greatest  deflection  of  a  simple  beam  supported  at  both  ends  and  loaded 
at  the  middle  with  P  lb  is 

Maximum  deflection  =  P/V48  EI 

or  the  deflection  of  the  continuous  girder  is  only  ^r,  that  of  a  non-continuous  one. 

Continuous  Girder  of  Three  Equal  Spans.  Uniformly  Distributed  Load  Over 
Each  Span. 

The  load  per  unit  of  length  is  w  lb. 

Greatest  deflection  at  the  middle  of  middle  span  =  0.00052  wl^/EI        (t8) 
Greatest  deflection  in  the  end-spans  =  0.006884  zf/^/£/      (19) 

Hence  the  maximum  deflection  of  the  continuous  girder  is  only  about  \^  that 
of  a  non-continuous  girder. 

Continuous  Girder  of  Three  Equal  Spans.  Concentrated  Load  P  at  the  Middle 
of  Each  Span. 

Greatest  deflection  at  the  middle  span  =  Hso  PPlEI  (20) 

Greatest  deflection  at  the  middle  of  end-spans  =  ^Heo  PP/EI  .  (21) 

Hence  the  maximum  deflection  of  the  continuous  girder  is  only  I'/^o  of  that  of 
the  non-continuous  girder. 

5.   Notes  on  Reactions,  Strength  and  Stiffness  of  Continuous  Girders 

Supports  and  Reactions  of  Continuous  and  Non-Continuous  Girders.  From 
the  foregoing,  some  conclusions  can  be  drawn  which  will  be  of  use  in  deciding 
whether  it  is  best  in  any  case  to  use  a  continuous  or  a  non-continuous 
GIRDER.  From  the  formulas  given  for  the  reactions  of  the  supporting  forces 
in  the  different  cases  of  continuous  girders  it  is  seen  that  the  end-supports  do 
not  bear  as  much  of  the  load  as  they  do  when  the  girders  are  non-continuous. 
The  difference  is  added  to  the  reactions  of  the  other  supports.  This  might  be 
of  advantage  in  a  building  in  which  the  girders  run  across  the  building,  and 
have  their  outside  ends  supported  by  the  side  walls  and  their  inside  ends  by 
piers  or  columns.  In  this  case,  by  using  continuous  girders,  part  of  the  load 
could  be  taken  from  the  walls  and  transferred  to  the  piers  or  columns.  But  in 
cases  of  this  kind,  the  vibration  may  have  to  be  considered.  .If  the  building 
is  a  miU  or  factory  in  which  the  girders  support  machines,  any  vibration  in  the 
middle  span  of  the  girder  is  carried  to  the  side  walls  if  the  girder  is  continuous; 
while  if  non-continuous  girders  are  used,  with  their  ends  an  inch  or  so  apart, 
little  or  no  vibration  is  carried  to  the  side  walls  from  the  middle  span.  In  all 
cases  of  important  construction  the  supporting  forces  should  be  carefully 
considered. 

Relative  Strength  of  Continuous  and  Non-Continuous  Girders.  As  the . 
RELATIVE  STRENGTH  of  contiuuous  and  non-continuous  girders  of  the  same 
cross-section,  material  and  spans,  and  loaded  in  the  same  way,  is  proportional 
to  their  maximum  bending  moments,  the  strength  of  a  continuous  girder  can 
be  calculated,  from  the  formula  for  its  maximum  bending  moment.  From  the 
values  given  for  these  bending  moments  for  the  various  cases  considered,  it  is 
seen  that  the  parts  of  the  girder  most  stressed  are  those  which  come  over  the 
middle  supports.  It  is  seen,  also,  that,  except  in  the  single  case  of  a  girder  of 
two  spans  uniformly  loaded,  the  strength  of  a  continuous  girder  is  greater 
than  that  of  a  non-continuous  girder.  But  the  gain  in  strength  in  some  in- 
stances is  not  very  great,  although  it  is  generally  enough  to  pay  for  making  the 
girder  continuous. 


676  Strength  and  Stiffness  of  Continuous  Girders       Chap.  19 

Relative  Stiffness  of  Continuous  and  Non-Continuous  Girders.  The  stiff- 
ness of  a  girder  varies  inversely  as  its  deflection;  that  is,  the  less  the  deflec- 
tion under  a  given  load  the  stiffer  the  girder.  From  the  values  given  for  the 
MAXIMUM  DEFLECTION  of  continuous  girders,  it  is  evident  that  the  stiffness  of 
a  girder  is  increased  by  making  it  continuous;  and  this  is  usually  the  principal 
advantage  in  the  use  of  continuous  girders.  It  sometimes  happens  in  building- 
construction  that  it  is  necessary  to  use  beams  and  girders  of  much  greater 
strength  than  is  required  to  carry  the  superimposed  load,  because  the  deflections 
of  smaller  beams  or  girders  would  be  too  great.  But  if  continuous  girders 
are  used  they  may  be  made  of  just  the  size  required  for  strength,  because  their 
deflections  are  less.  Where  great  stiffness  is  required,  therefore,  continuous 
beams  or  girders  should  be  used  if  possible,  as  in  the  case  of  grillage-girders. 
(See  Example  3,  page  679.) 

6.   Formulas  for  the  Strength  and  Stiffness  of  ContinuottS'  Gitders 

Girders  of  Rectangular  Cross-Section.  For  convenience,  the  proper  formulas 
for  Calculating  the  strength  and  stiffness  of  continuous  girders  of  rectangular 
cross-section  are  given.  The  formulas  for  strength  are  deduced  from  the  flexure- 
formula  M  =  67/ c,  modified  for  the  rectangular  section  of  breadth  b  and  depth  d. 

Bendmg  moment  =» (22) 

6 

in  which  S  is  the  safe  unit  fiber-stress.  This  is  eighteen  times  the  coefficient 
A*oi  Table  II,  page  628. 

Strength.  Continuous  Girder  of  Two  Equal  Spans.  Uniformly  Distributed 
Load  Over  Each  Span. 

Breaking-load  f  = -. (23) 

where  b  denotes  the  breadth  and  d  the  depth  of  the  girder  in  inches,  and  /  the 
length  of  one  span,  in  feet.  The  values  of  the  constant  A  are  three  times  the 
values  given  in  Table  II,  page  628.  For  long-leaf  yellow  pine,  201 ;  for  Douglas 
fir,  168;  chestnut,  132;  and  for  spruce  and  white  pine,  117  lb  per  sq  in,  are  rec- 
ommended for  the  values  of  A  in  these  formulas. 

Continuous  Girder  of  Two  Equal  Spans.  Concentrated  Load  at  the  Middle  of 
Each  Span. 

Breaking-load  =  %  X  ^-^^^i-^  (24) 

Continuous  Girder  of  Three  Equal  Spans.  Uniformly  Distributed  Load  Over 
Each  Span. 

Breaking-load  =  % X  ^^"^^'^^  (25) 

Continuous  Girder  of  Three  Equal  Spans.  Concentrated  Load  at  the  Middle 
of  Each  Span. 

Breakmg-load  =  %  x (26) 

*  See,  ilso.  Table  I,  page  557,  and  Tabie  XVI,  page  647,  for  safe  fiber-stresses, 
t  Breaking-load  in  pounds  in  all  cases. 


Formulas  for  the  Strength  and  Stiffness  of  Continuous  Girders    677 

Stiffness.  Continuous  Girder  of  Two  Equal  Spans.  Uniformly  Distributed 
Load  Over  Each  Span. 

The  following  formulas  give  the  loads  which  the  beams  will  support  without 
deflecting  more  than  one-thirtieth  of  an  inch  per  foot  of  span. 

r       .  bXd^Xei 

Load  on  one  span  = (27) 

^  0.26  X/2  ^  '^ 

Continuous  Girder  of  Two  Equal  Spans.  Concentrated  Load  at  the  Middle  of 
Each  Span. 

b  "X.  d^  X  €1 
Load  on  one  span  =  1%  x  -, (28) 

Continuous  Girder  of  Three  Equal  Spans.  Uniformly  Distributed  Load  Over 
Each  Span. 

Load  on  one  span  =  •  (20) 

0.33  Xl^  ^^^ 

Continuous  Girder  of  Three  Equal  Spans.  Concentrated  Load  at  the  Middle 
of  Each  Span. 

T      J  ,^,        bXd^Xei 

Load  on  one  span  =  2%i  x  (30) 

The  value  of  the  constant  ei  is  obtained  by  dividing  the  modulus  of  elas- 
ticity by  12  960;  and,  for  the  three  woods  most  commonly  used  as  beams,  the 
following  values  may  be  taken: 

Long-leaf  yellow  pine,  116;  white  pine,  77;  spruce,  92;  Douglas  fir,  116. 
(For  other  woods,  see  Table  I,  page  664.) 

For  Continuous  Steel  Beams  the  requisite  size  may  be  found  by  first  com- 
puting the  MAXIMUM  BENDING  MOMENT,  by  mcaus  of  Formulas  (12)  to  (15), 
and  then  selecting  a  beam  that  has  a 

3  X  maximum  bending  moment  in  ft-lb  ,     ^ 

section-modulus  =   ■ —  (31) 

4000 

Values  for  the  section-moduli  for  the  different  shapes  of  rolled  steel  used  as 
beams  are  given  in  the  tables  in  Chapter  X, 

Example  i.  What  steel  beam  should  be  used  to  support  two  loads  of  16  000 
lb  each,  concentrated  at  the  middle  of  two  spans  of  10  ft  each,  the  beam  being 
continuous? 

Solution.  Formula  (13(1)  gives  the  maximum  bending  moment  as  Me  PI,  or 
30000  ft-lb.  Therefore,  from  Equation  (31),  a  beam  having  a  section-modulus 
equal  to  3  X  30  000/4  000  or  22.5  should  be  used.  From  the  Table  IV,  page 
355,  it  is  found  that  a  9-in  30-lb  beam  has  a  section  modulus  of  22.6,  and  a 
lo-in  25-lb  beam  a  section  modulus  of  24.4.  Either  of  these  beams  will  there- 
fore answer,  the  lo-in  beam  being  the  cheaper,  however,  and  also  the  stiffer. 

Example  2.  A  steel  beam  continuous  over  three  spans  is  required  to  support 
a  uniformly  distributed  load  of  i  000  lb  per  lin  ft.  The  two  end-spans  are  12  ft 
each,  and  the  middle  span  10  ft.  What  should  be  the  size  and  the  weight  of  the 
beam  used? 

Solutio^,    The  maximum  bending  moment  is  found  by  Formula  (14),  and  is 
1000X1000-1-1000X1728 

' ; .  «  ;2  630 

4(30+24) 


678 


Strength  and  Stiffness  of  Continuous  Girders      Chap.  19 


The  section-modulus,  by  Equation  (31),  must  equal  3  X  12  630/4  000-  9.47, 
which  requires  a  7-in  15-lb  beam  (Table  IV,  page  355). 

If  the  beam  were  not  continuous  an  8-in  i8-lb  beam  would  be  required  for 
the  i2-ft  spans,  and  a  7-in  15-lb  beam  for  the  lo-ft  span. 

For  a  beam  of  two  equal  spans,  loaded  uniformly,  the  strength  is  the  same  as 
though  it  were  not  continuous. 

The  formulas  given  for  the  reactions  at  the  supports,  and  for  the  deflections 
of  continuous  girders  with  concentrated  loads,  were  verified  by  Mr.  Kidder  by 
means  of  careful  experiments  on  small  steel  bars.  The  remaining  formulas 
were  verified  by  comparing  them  with  the  formulas  of  other  authorities  where 
it  was  possible  to  do  so.  In  regard  to  some  of  the  cases  given  the  author  has 
never  seen  any  discussion  of  them  in  any  work  on  the  subject. 

7.    Continuous  Girders  in  Grillage-Foundations  ,„ 

GrlUage-Beams  Considered  as  Inverted  Continuous  Girders.  As  stated  in 
the  beginning  of  this  chapter,  continuous  girders,  as  such,  are  seldom  used  in 
building-construction,  although  their  employment  in  grillage-beam  footings  is  fre- 


^^^M\ 


R 


uiiiiiiiiiiiiiiiiiiiiiiiiiiniijl 

Fig.  3.     Continuous  Girder  in  Grillage-foundation 


Fig.  4.    Shear-diagram  and  Bending-moment  Diagram 

quent.  Fig.  3  represents  a  footing  consisting  of  two  layers  of  beams,  which  dis- 
tribute the  load  of  the  three  columns  above,  uniformly  over  the  foundation-bed. 
By  inverting  the  footing  the  three  columns  become  the  supports  or  reactions,  and 
the  upper  layer  of  beams,  a  continuous  girder,  loaded  with  a  uniformly  distrib- 
uted load  which  is  the  pressure  of  the  lower  layer.    As  in  practice  the  column- 


Continuous  Girders  in  Grillage-Foundations  679 

loads  are  never  equal,  and  the  distance  between  the  columns  seldom  equal,  it 
is  necessary  to  project  the  continuous  girder  beyond  the  most  heavily  loaded 
column  in  order  to  insure  a  uniform  pressure  upon  the  lower  layer.  Because 
of  these  limitations  none  of  the  formulas  previously  deduced  can  be  applied, 
although  the  principles  upon  which  they  are  based  hold  good. 

Maximum  Bending  Moment.  Since  the  reactions  in  this  case  are  the  given 
column-loads  it  is  required  first  to  find  the  maximum  bending  moment.  From 
what  has  already  been  said  about  continuous  girders,  it  is  evident  that  the 
point  of  maximum  bending  moment  may  be  under  columns  i  or  2,  or  between 
the  columns.  Since  the  maximum  bending  moments  are  the  points  of  no 
SHEAR,  construct  the  shear-diagram,  find  where  the  shear  passes  through 
zero,  and  calculate  the  bending  moments  at.  these  points.  The  maximum  bend- 
ing moment  is  determined,  as  in  examples  i  and  2,  in  order  to  determine  the 
section-modulus  of  the  girder. 

Example  3.  The  continuous  girder  under  columns  i,  2  and  3  (Fig.  3)  is 
S3  ft  long;  the  overhang,  to  the  left  of  column  i,  6.25  ft;  the  distance  between 
columns  i  and  2,  13.12  ft;  between  columns  2  and  3,  12.88  ft;  and  from  column 
3  to  the  right  edge  of  the  girder,  .75  ft.  The  column-loads  are  as  follows:  on 
column  I,  565  tons;   on  column  2,  600  tons;   and  on  column  3,  255  tons. 

The  column-loads  may  be  considered  uniformly  distributed  over  parts  of  the 
girder  by  the  bases,  which  are  3  ft  wide  under  columns  i  and  2  and  18  in  wide 
under  column  3.  The  unit  pressure  under  column  i,  therefore,  is  565/3  = 
188.3  tons;  under  column  2,  600/3  =  200  tons;  and  under  column  3,  255/1.5 
=  170  tons.  The  unit  pressure  under  the  continuous  girder  is 
(565  +  600 -[-  255)/33  =  43  tons     : ;  ,  , 

The  first  step  in  the  calculation  of  the  girder  is  the  determination  of  the 
POINTS  OF  no  shear  and  the  plotting  of  the  shear-diAgrAm  in  Fig.  4.  It  is 
obvious  from  the  shear-diagram  that  there  are  four  points  of  no  shear  and  con- 
sequently four  points  of  possible  maximum  bending  moment.  The  first  of 
these  is  under  column  i,  the  second  between  columns  i  and  2,  the  third  under 
column  3  and  the  fourth  between  columns  2  and  3.  The  bending-moment 
diagram  is  shown  by  the  solid  curved  line  in  Fig.  4.  The  points  of  contra- 
flexure  or  no  bending  moment  are  the  intersections  of  this  line  with  the  hori- 
zontal line  of  reference. 

The  shear-diagram,*  shown  by  the  broken  line  in  Fig.  4,  may  be  constructed 
as  follows: 

Fit  =  -h  43  tons  per  ft  X  (6.25  -  1.5  =  4.75  ft)  =  -f  204.25  tons 
F2   =  ( 4-  43  tons  per  ft  X  6.25  ft)  -  565/2  tons  =  -f  268.75  -  282.5 
=  -13.75  tons 

This  shows  that  xi,  the  point  of  no  shear,  lies  between  points  i  and  2.  To 
find  this  point  let  y  be  its  distance  beyond  or  to  the  right  of  point  i.  Then, 
the  equation  for  no  shear  is  43  tons  X  (4-75  ft  +  y  ft)  =  188.3  X  y,  or  204.25 
_^43-y=  188.33/,  from  whjch  145.33/=  204.25  and  y-  1.4  ft:  hence  xi,  the 
first  point  of  no  shear,  is  4.75  ft -I-  1.4  ft,  or  6.1  ft  from  the  left  end.| 

The  SECOND  POINT  OF  no  .shear,  Xi,  is  such  a  distance  from  the  left  end  that 
the  DOWNWARD  SHEARING-FORCE  of  565  tons  from  column  I  is  neutrahzed  by 

•  The  upward  forces  are  here  called  plus  or  positive  and  the  downward  forces  minus 
or  negative. 

•  t  Fi  is  taken  at  point  i,  the  left  edge  of  base  of  Column  i,  F2  at  point  2,  at  the  axis  of 
Column  2,  etc. 

X  The  following  computations  are  carried  oiit  to  one  decimal-place,  only,  the  nearest 
approximate  values  being  used. 


680  Strength  and  Stiffness  of  Continuous  Girders       Chap.  19 

an  equal  upward  shearing-force  of  43  tons  per  ft.  on  xt  ft.  Hence  xz  =  565/43 
=  13.1  ft. 

Fe  =  +  43  tons  per  ft  X  [(6.25  -f-  13.12  -  1.5)  =  17  9  ft]  -  565  tons 

=  7697  -  565  =  +204.7  tons 
^7  =  +43  tons  per  ft  X  (6.25  -f  13.12  =  19.4  ft)  -  (565  +  600/2  tons) 
=  +  834.2  —  865  tons  =  —  30.8  tons 

This  shows  that  the  third  point  of  no  shear,  xs,  lies  between  6  and  7.  Let 
y  be  its  distance  to  the  right  of  point  6.  The  equation  for  no  shear  at  this 
point  is  43  tonsX  (17.9  ft  + >>  ft)  =  565  tons-|-  (200  tonsXy  ft),  or  769.7  +  43  y 
—  565  +  200  y.  from  which  157  y  =  204.7  and  y  =  1.3  ft.  Hence  X3,  the  third 
point  of  no  shear,  is  17.9  ft+  1.3  ft  =  19.2  ft  from  the  left  end. 

The  FOURTH  POINT  OF  NO  SHEAR,  ^4,  is  such  distance  from  the  left  end  that 
the  DOWNWARD  SHEARING-FORCE  of  columns  I  and  2,  amounting  to  565  +  600 
or  1165  tons,  is  neutralized  by  an  equal  upward  shearing-force  of  43  tons 
per  ft  on  .^4  ft.     Hence  ^4=1  165/43  =  27.1  ft. 

Having  found  the  points  of  no  shear,  the  bending  moment  at  these  points 
may  now  be  determined. 
,  M  at  :¥i  =  43  tons  X  6.1  ft  X  6.1/2  ft  -  188.3  tons  X  1.4  ft  X  1.4/2  ft 
=  +  615.5  ft-tons 
M  2XXi  =  43  tons  X  13. 1  ft  X  13. 1/2  ft  —  565  tons  X  6.8  ft  =  —  152.4  ft-tons 
Af  at  :^3  =  43  tons  X  19.2  ft  X  19.2/2  ft  -  565   tons  X  12.9  ft- 200  Tx  1.3   ft 

X  1.3/2  =  +  467  ft-tons 
M  ditx\  =  43  tons  X  27.1  ft  X  27.1/2  ft  —  565  tons  X  20.8  ft  —  600  tons 
X  7.7  ft  =  ~  582.2  ft-tons 

The  maximum  bending  moment  therefore  is  at  xi  and  equals  615.5  ft-tons*  or 

I  231  000  ft-lb.     Substituting  in  Formula  (31),  the  section-modulus  is  found 

3X1  231  000 

to  be =  923.2.    The  following  beams  could  be  used,  as  far  as 

4000 

flexure  is  concerned.  For  investigations  of  the  resistance  of  the  girders  to  web- 
buckling  or  crippling,  see  Chapter  II,  pages  182  to  184,  and  Chapter  XV, 
pages  567  to  569. 

Four  standard  24-in  iio-lb  I  beams,  section-modulus  of  each,  240.3  (page  354) 
Three  Bethlehem  30-in  120-lb  I  beams,  section-modulus  of  each,  349.3  (page 

357) 
Three  Bethlehem  24-in  140-lb  girder-beams,  section-modulus  of  each,  350.1 

(page  358) 
Two  Bethlehem  28-in  i8o-lb  girder-beams,  section-modulus  of  each,  518.9 

(page  358)    . 
The  28-in  and  30-in  beams  are  stiff er  than  the  24-in  beams,  have  a  smaller 
total  amount  of  steel  and  cost  less  than  the  others  for  the  number  of  beams 
required. 

*  The  bending  moments  at  Xi  and  x^  have  very  nearly  the  same  numerical  values,  and 
in  the  computations  the  retaining  or  dropping  of  figures  in  the  second  decimal-place  ma.y 
change  the  result  and  make  the  value  at  x^  slightly  greater  than  at  Xi, 


General  Notes  on  Plate  and  Box  Girders 


681 


CHAPTER  XX 
RIVETED  STEEL  PLATE  AND  BOX  GIRDERS 

By 
CHARLES  P.  WARREN 

LATE   ASSISTANT   PROFESSOR   OF   ARCHITECTURE,    COLUMBIA   UNIVERSITY 

1.    General  Notes  on  Plate  and  Box  Girders 

Types  of  Riveted  Girders.  Girders  built  up  of  plates  and  angles,  as  shown 
in  section  in  Figs.  1  to  4,  are  extensively  used.  This  is  undoubtedly  owing  to 
the  simplicity  of  their  construction,  to  the  comparatively  low  cost  of  the  shapes 
of  which  they  are  fabricated  and  to  their  adaptability  to  any  arrangement  of 
loads  or  to  any  span  for  which  girders  are  usually  required.  Riveted  girders, 
however,  are  seldom  made  for  spans  greater  than  6o  ft  and  are  seldom  more 
than  6  ft  in  depth.  The  most  common  forms  of  these  girders  are  shown  in 
Figs.  2  and  4. 


-r 


JL. 


Fig.  1 


Fig.  2  Fig.  3 

Types  of  Riveted  Girders 


Fig.  4 


The  girders  with  a  single  vertical  plate  called  the  web  are  usually  called 
PLATE  GIRDERS,  and  thosc  with  double  or  triple  webs,  box  girders.  Plate 
girders  are  more  economical  than  box  girders,  and  more  accessible  for  painting 
and  inspection;  but  box  girders  are  stiff er  laterally  and  should  always  be  used 
where  great  length  of  span  requires  wide  flanges.  In  general,  it  may  be  said 
that  plate  girders  should  be  used  to  support  floor-beams  and  floor-arches  and 
walls  not  over  12  in  thick,  and  that  box  girders  should  be  used  where  a  flange- 
width  greater  than  12  in  is  required.  The  girder  shown  in  section  in  Fig.  1  has 
no  flange-plates  and  should  be  used  only  for  comparatively  light  loads  and  short 
spans,  and  never  to  support  masonry. 

Flange  and  Web.  The  term  flange,  as  applied  to  riveted  girders,  includes 
all  the  metal  in  the  top  or  bottom  parts  of  the  girder,  exclusive  of  the  web-plates.* 
The  DEPTH  of  a  riveted  girder  is  the  distance  between  the  centers  of  gravity  of 
the  flanges;  but  in  practice  this  is  usually  taken  as  the  depth  of  the  web- 
plate,  and  the  word  will  be  so  used  in  this  chapter.  The  top  and  bottom  of 
the  flange-angles  extend  H  in  beyond  the  top  and  bottom  of  the  web-plate. 
(See  the  figure  in  Table  IV,  page  706.)     Stiffeners  are  short  pieces  of  angles 

*  This  may  be  modified,  however,  as  some  engineers  include  one-sixth  of  the  web-area 
in  the  effective  flange-area.    See,  also,  Flange-Area  in  the  examples  of  this  chapter. 


682  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

riveted  to  the  web  at  intervals,  to  keep  it  from  buckling.  They  should  fit 
closely  against  the  horizontal  legs  of  the  llange-angles,  and  should  always 
be  used  at  the  supports  and  under  concentrated  loads. 

Economic  Depths  of  Girders.  The  depth  of  a  riveted  girder  may  vary 
from  one-tenth  to  one-fifteenth  or,  in  exceptional  cases,  one-sixteenth  the  span. 
The  greatest  economy  of  material  is  said  to  be  obtained  when  the  depth  is  one- 
twelfth  the  span.  Thus  for  a  36-ft  span  a  3-ft  girder  should  be  used  if  the 
conditions  will  permit;  but  the  least  depth  should  be  He  of  36,  or  about  2  ft 
5  in  or,  in  exceptional  cases,  He  of  36,  or  2  ft  3  in.  A  girder  is  said  to  have  its 
ECONOMIC  DEPTH  when  the  amount  of  material  in  the  flanges  is  equal  to  that 
in  the  web,  and  there  are  no  cover-plates.  The  rule  holds  approximately 
when  there  are  cover-plates. 

The  Width  of  the  Top  Flange  should  not  be  less  than  one-twentieth  the 
distance  between  lateral  supports;  or  if  there  are  no  lateral  supports,  then  not 
less  than  one-twentieth  the  span. 

Arches  Between  Girders,  or  floor-beams  riveted  to  the  sides  of  girders,  may 
be  considered  as  lateral  supports. 

2.   Details  of  Construction  of  Plate  and  Box  Girders* 

General  Requirements  for  Plate  and  Box  Girders.  The  following  re- 
quirements are  those  which  must  be  generally  satisfied  in  the  design  of  riveted 
girders. 

(i)  All  the  connections  and  details  of  the  several  parts  shall  be  of  such  strength 
that,  upon  testing,  rupture  shall  occur  in  the  body  of  the  members  rather  than 
in  any  of  their  details  or  connections. 

(2)  In  members  subject  to  tensile  stress  full  allowance  shall  be  made  for  the 
reduction  of  the  section  by  the  rivet-holes. 

(3)  The  webs  of  plate  girders,  when  they  cannot  be  obtained  in  one  length, 
must  be  spUced  at  all  joints  by  a  plate  on  each  side  of  the  web. 

(4)  Tees  must  not  be  used  for  splices. 

(5)  Stiff eners  shall  be  used  at  the  ends  of  all  girders,  wherever  there  are  con- 
centrated loads,  and  elsewhere  when  the  shearing-stress  is  greater  than  the 
resistance  to  buckling. 

(6)  The  pitch,  that  is,  the  distance  between  centers  of  rivets,  shall  not  ex- 
ceed 6  in,  nor  16  times  the  thickness  of  the  thinnest  outside  plate,  and  it  shall 
not  be  less  than  2H  in  for  H-in  rivets,  or  2^/i  in  for  Ji-in  rivets,  in  a  straight 
hne. 

(7)  The  rivets  used  should  be  H  in  in  diameter  for  plates  from  %  to  H-in 
thick,  and  %  in  in  diameter  for  plates  of  greater  thickness. 

(8)  The  distance  between  the  edge  of  any  piece  and  the  center  of  a  rivet- 
hole  must  never  be  less  than  iH  in. 

(9)  In  punching  plates  or  other  members,  the  diameter  of  the  die  shall  in  no 
case  exceed  the  diameter  of  the  punch  by  more  than  He  in. 

(10)  All  RIVET-HOLES  must  be  so  accurately  punched  that  when  the  several 
parts  forming  one  member  are  assembled,  a  rivet,  He  in  less  in  diameter  than 
the  hole,  can  be  inserted,  hot,  into  any  hole  without  reaming  or  stressing  the 
metal  by  the  use  of  drift-pins. 

(ti)  The  rivets  when  driven  must  completely  fill  the  holes. 

(12)  The  rivet-heads  must  be  hemispherical,  except  where  flush  surfaces 
are  required,  and  of  uniform  size  throughout  for  rivets  of  the  same  size.  They 
must  be  full  and  neatly  made,  and  be  concentric  with  the  rivet-holes. 

•  These  requirements  are  taken  largely  from  Biricmire's  "  Compound  Riveted  Girders.'* 


Design  of  Plate  and  Box  Girders  683 

(13)  Whenever  possible,  all  rivets  must  be  machine-driven, 

(14)  The  several  pieces  forming  one  built  member  must  fit  closely  together, 
and,  when  riveted,  must  be  free  from  twists,  bends  or  open  joints. 

(15)  Girders  60  ft  and  less  in  length  seldom  require  splicing,  as  the  plates  and 
angles  can  readily  be  obtained  in  such  lengths.  In  spUcing  the  top  flange, 
when  of  two  or  more  thicknesses,  no  additional  cover-plate  will  be  required 
over  the  joint,  but  the  ends  should  be  planed  true  and  butt  closely.  The  rivets 
should  be  spaced  closer  near  the  joint. 

(16)  The  plate  covering  the  bottom  flange  must  be  of  the  same  area  as  the 
plates  joined,  and  of  sufficient  length  to  take  a  number  of  rivets  equal  tOb  the' 
strength  of  the  cover-plate. 

3.   Design  of  Plate  and  Box  Girders 

The  Principal  Steps  in  the  Design  of  Riveted  Girders.     In  designing 
a  riveted  girder  to  sustain  safely  a  given  load,  the  following  steps  are  necessary: 
(i)  The  determination  of  the  required  flange-area. 

(2)  The  determination  of  the  thickness  of  the  web  to  resist 

(a)  Shearing. 

(b)  Buckling.     This  step  also  determines  if  stiffeners  are  necessary. 

(3)  The  determination  of  the  number  and  pitch  of  the  rivets. 

(4)  The  approximate  weight  of  the  girder. 

(5)  The  determination  of  the  length  of  the  flange-plates  when  more  than  one 
is  required  for  each  flange. 

(i)  The  Flange- Area.  In  determining  the  flange-area  of  riveted  girders, 
it  is  customary  to  assume  that  the  bending  moments  are  entirely  resisted  by  the 
upper  and  lower  flanges,  the  web  being  assumed  to  resist  the  shear  only.  Just 
what  should  be  included  in  the  flange-area  is  a  question  on  which  engineers  differ. 
Some  include  the  flange-plates  and  angles  and  one-sixth  of  the  web-area,  others 
the  flange-plates  and  angles  only,  while  others  include  the  flange-plates  and  only 
the  horizontal  legs  of  the  angles,  the  vertical  legs  being  considered  as  belonging 
to  the  web.  In  compression-flanges,  usually  the  upper  ones,  the  gross  section- 
area  may  be  taken,  provided  the  rivets  are  machine-driven  and  fill  completely 
the  holes;  but  in  tension-flanges,  usually  the  lower  ones,  the  net  area  is  taken, 
that  is,  the  gross  area  minus  the  area  of  the  greatest  number  of  rivet-holes  in 
any  cross-section,,  since  the  stresses  of  tension  are  not  transmitted  through  the 
rivets  as  are  those  of  compression. 

A  general  formula*  for  determining  the  flange-area,  which  applies  to 
all  conditions  of  loading  is 

Area  of  one  flange       __  maximum  bending  moment  in  foot-tons 

in  square  inches       depth  of  web  in  feet  X  safe  unit  fiber-stress  in  tons 
or 

A^Mm^^/dS  (l) 

*  This  may  be  derived  from  what  is  sometimes  called  the  p'tATE-GiRDER  formula, 
Afmax  =  SAd,  in  which  S  is  the  safe  unit  bending-stress  in  the  flange  at  the  section  of 
maximum  bending  moment,  A  is  the  area  of  the  cross-section  of  either  flange  and  d  is  ap- 
proximately the  depth  of  the  girder.  Of  course  the  units  must  be  the  same  in  both  mem- 
bers of  the  equation.  If  the  center  of  moments  is  taken  at  the  center  of  gravity  of  the 
cross-section  of  either  flange-area  and  if  the  area  of  metal  resisting  bending  is  considered 
to  be  concentrated  in  the  flanges,  the  depth  of  each  being  very  small  compared  to  that 
of  the  girder-depth,  then  5^1  is  the  total  horizontal  stress  in  either  flange,  d  its  lever- 
erm  and  SAd  the  resisting  moment  of  the  cross-section,  equal  to  Af  mai.  Hence  A  = 
Mmtix/dS.  Another  method  uses  the  section-modulus,  I/c  =  M/S,  in  determining  the 
flange-areas  and  proportioning  the  girder.     (See  pages  706  to  716.) 


684  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

Rules  for  finding  the  maximum  bending  moment  for  different  conditions  of 
loading  are  given  in  Chapter  IX. 

S,  the  SAFE  UNIT  FIBER-STRESS  FOR  FLANciE-BENDiNC,  was  formerly  taken  at 
from  13  000  to  16  000  lb  per  sq  in,  the  tallies  in  the  manufacturers'  handbooks 
giving  the  safe  loads,  etc.,  for  riveted  girders,  varying  in  regard  to  this  stress.* 

If  it  is  required  to  compute  the  safe  uniformly  distributed  load  for  a 
girder  already  constructed  or  designed,  the  following  formula  f  may  be  used. 
The  safe  load  in  pounds,  uniformly  distributed  is 

8  X  net  area  of  bottom  flange  X  depth  in  itxS 

W  = ■    f    ^ 

•  span  m  feet 

or 

W=^SAdS/l  (2) 

From  the  result  the  weight  of  the  girder  itself  should  be  subtracted. 

For  the  safe  concentrated  load  at  the  middle  of  the  span  take  one-half 
the  result  obtained  by  formula  (2)  and  subtract  the  weight  of  girder.  (See 
Case  IV,  page  326.) 

(2)  The  Thickness  of  the  Web.  The  thickness  of  the  web  is  determined 
by  its  resistance  to  vertical  shearing.  Whether  or  not  stiff eners  shall  be  used 
is  determined  by  the  resistance  of  the  web  to  buckling. 

(a)  Shearing.  To  resist  the  vertical  shear  the  net  sectional  area  of  the 
WEB  in  square  inches  must  be 

the  maximum  vertical  shear 


A  =  Fmax/5  (3) 

V  and  S  being  both  in  tons,  5  is  taken  at  10  000  J  lb  or  5  tons  per  sq  in.  (See 
Table  II,  page  703.) 

The  maximum  vertical  shear  in  any  beam  or  girder  is  at  the  greater  reaction 
and  is  equal  to  it. 

For  a  girder  supported  at  both  ends  and  uniformly  loaded  with  a  load  W, 
the  maximum  vertical  shear  is  ''^ 

F,nax=Tr/2 

For  a  girder  supported  at  both  ends  and  loaded  at  the  middle  with  a  load  P, 

Fmax  =  P/2 

For  a  girder  supported  at  both  ends  and  loaded  as  in  Fig.  7, 
Fmax  =  Pm/l  =  Ri 

For  a  girder  supported  at  both  ends  and  loaded  with  two  equal  concentrated 
loads  P,  P,  equally  distant  from  the  middle,  as  in  Fig.  8, 

Fmax  =  P  =  Ri  =  R2 

For  combinations  of  loads  the  maximum  vertical  shear  will  equal  the  greater 
reaction.  The  method  of  determining  the  reactions  at  the  supports  of  a  beam 
or  girder  is  given  in  Chapter  IX,  Subdivision  i.     The  vertical  sUearing- 

*  See  Chapter  XV,  paragraphs  relating  to  riveted  single  and  double-beam  girders  and 
foot-note  with  same,  pages  603  and  604;  also  page  704.  The  value  in  most  city  codes  is 
now  16  000  lb  per  sq  in. 

t  From  Formula  (i)  just  explained,  and  from  Case  V,  page  326,  If  max  =  SAd  and 
A/max  =  Wl/S.     Hence  Wl/S  =  SAd  and  TF  =  8  AdS/l. 

t  This  is  a  conservative  value.  The  Carnegie  Pocket  Companion  and  the  building 
laws  of  most  cities  permit  10  000  lb  per  sq  in  for  steel. 


Design  of  Plate  and  Box  Girders 


666 


FORCE  at  any  given  vertical  section  of  a  beam  or  girder  between  the  supports  is 
the  algebraic  sum  of  all  the  vertical  external  forces  acting  on  the  beam  to  the 


'IT 


a\      \ 


R 


Xi    Yx 


rig.5 


[R2  |r7 


_a 


.  Fig.6 


|R2 


ue — .n   >'< 


hUI 


-a. 


Fig.7 


T 


Ri 


Eig.8 


IR2 


■nL 

k=p 


50  80  100  60 


R|=140 


Figs.  5  to  9.    Diagrams  for  Vertical  Shears  for  Different  Loadings 

left  of  that  section,  forces  acting  upwards  being  considered  as  plus,  and  those 
acting  downwards  being  considered  as  minus. 

Thus,  in  the  case  of  the  beam  shown  in  Fig.  9,  the  reaction  Ri  will  be 
found,  by  the  method  explained  in  Example  2,  page  323,  and  by  Formulas  (2) 


686 


Riveted  Steel  Plate  and  Box  Girders 


Chap.  20 


and  (3),  page  323,  to  be  150  lb,  and  that  at  R2  to  be  140  lb.  The  shear  at  vari- 
ous sections  may  be  found  by  applying  the  foregoing  definition  of  vertical 
SHEAR,  thus: 

Shear  at  X  =  +  150  —  50  =  -f  100  lb 

Shear  at  F  =  +  150  —  50  —  80  =  +  20  lb 

Shear  at  Z  =  +  150  —  50  —  80  —  100  =  —  80  lb 

Shear  at  O  =  +  150  —  50  -  80  —  100  —  60  =  -  140  lb 
The  manner  in  which  the  vertical  shear  varies  between  the  supports,  under 
different  dispositions  of  the  loads,  is  shown  graphically  by  the  hatched  areas  in 
Figs.  5  to  9;  in  the  first  three  cases  W  and  F  are  assumed  to  have  the  same 
value. 

When  the  load  is  uniformly  distributed  the  vertical  shear  can  be  found 
graphically  by  laying  off  vertically  Ri  and  R2  to  a  scale  of  pounds,  and  drawing 
the  line  ab,  Fig.  5.  The  shear  at  X  will  then  be  represented  by  the  ordinate 
Xi  and  the  shear  at  Y  by  Fi,  and  they  can  readily  be  scaled. 

(b)  Buckling.*  The  safe  resistance  of  the  web  to  buckling,  in  pounds  per 
square  inch,  may  be  determined  by  the  formula 

10  000 
Sb  =  ■ 


i  +  - 


d^ 


(4) 

3  000/2 

in  which  Sb  is  the  safe  buckling  value  in  pounds  per  square  inch,  d  is  the  depth 
of  the  web  in  the  clear  between  flange-plates  in  inches  and  /  is  the  thickness  of 
the  web  in  inches.  When  this  resistance  is  less  than  the  unit  stress  for 
VERTICAL  shear  at  any  section,  stiffeners  must  be  used. 

Stiff eners.  These  should  be  made  of  angles,  not  less  than  sH  by  sH  by  % 
in  in  size.     They  should  always  be  tightly  fitted  between  the  flange-angles,  so 

as  to  support  the  horizontal  flanges.  In 
order  to  bring  the  stiffeners  in  contact  with 
the  web  and  the  vertical  leg  of  the  angles, 
fillers,  of  the  same  thickness  as  the 
flange-angles,  are  generally  used,  as  shown 
in  Fig.  10.  Where  there  are  several  girders 
exactly  alike,  something  may  be  saved  by 
omitting  the  flllers  and  bending  the  stif- 
feners, as  shown  in  Fig.  11.  This  bend- 
ing, however,  can  be  done  properly,  only 
by  the  use  of  special  dies,  and  costs  more 
than  the  fillers  unless  there  are  many 
stiffeners.  The  spacing  of  stiffeners  is 
more  a  matter  of  judgment  and  experience 
than  of  exact  calculation.  Shear-diagrams, 
shown  in  Figs.  5  to  9,  are  of  great  assistance  in  visualizing  shearing-stresses. 
The  general  rule  is  to  place  the  stiffeners  not  farther  apart  than  the  depth  of 
the  full  web-plate  on  girders  over  3  ft  in  depth,  with  a  maximum  spacing  of  5  ft. 
On  girders  under  3  ft  in  depth  they  are  placed  3  ft  apart.  Girders  2  ft  and  lesa 
in  depth  require  no  stiffeners.  On  girders  supporting  distributed  loads  they  are 
generally  placed  nearer  together  at  the  ends  than  towards  the  middle. 

*  See  Table  III,  page  705,  and  also  in  Chapter  XV,  the  paragraphs  and  foot-note, 
pages  567  to  569,  relating  to  the  web-buckling  of  beams  and  girders.  The  formula 
used  for  web-buckling  in  Table  III,  page  705,  is  the  formula  that  was  used  in  the  Pa.ssaic 
Steel  Company's  Manual,  and  as  the  values  computed  by  it  vary  but  little  from  those 
deduced  by  the  Cambria  formula  (see  page  568),  Table  III  is  retained|  ^  U  is« 


Fig.  10.     Stiffeners 
with  Fillers 


Design  of  Plate  and  Box  Girders  687 

Stiffeners  should  always  be  placed  at  the  ends  of  girders  and  directly  over  the 
edge  of  each  support,  as  shown  in  Fig.  18,  and  wherever  there  are  concentrated 
loads.  On  plate  girders  the  stiffeners  are  always  placed  on  each  side  of  the  web; 
on  box  girders  on  the  outside  only. 

The  Bearing  of  Girders.  This  depends  somewhat  upon  the  character  of  the 
loading,  but  a  safe  general  rule  is  to  make  the  bearing  of  the  girder  beyond  the 
edge  of  the  support  equal  to  one-half  the  depth  of  the  girder. 

(3)  The  Number  and  Pitch  of  the  Rivets,  (a)  Rivets  m  Web-Legs  of 
Angles.  It  will  readily  be  seen  that  when  a  plate  or  a  box  girder  is  loaded,  the 
tendency  of  the  bending  moments  is  to  cause  the  flange-plates  and  angles  to 
SLIDE  horizontally  past  the  web;  this  tendency  is  resisted  by  the  rivets 
which  connect  the  angles  with  the  web.  The  total  amount  of  this  tendency 
TO  slide,  called  the  horizontal  flange-stress,  between  any  section  of  the 
flange  and  the  nearer  end  of  the  girder,  is  equal  to  the  bending  moment  at 
that  point  divided  by  the  depth  oi  the  web.*  The  total  number  of  rivets 
between  that  section  and  the  nearer  end  must  be  such  that  their  combined 
resistance  to  shearing  or  bearing,  whichever  has  the  lower  value,  shall  equal 
this  horizontal  flange-stress  at  the  section;  or 

-    .  horizontal  flange-stress  ,  ^ 

number  of  rivets  =  :; ^ : ;^ —  (5) 

bearmg  or  shearing  of  one  rivet 

and  the  total  number  of  rivets  in  the  web-angle  from  end  to  end  is  twice  this,  or 

,  ,         r    .  2  X  maximum  bending  momentf  in  foot-pounds     ,  ^ 

total  number  of  nvets  =  ,       — ■; — : — ;: : ;: : —   (6) 

depth  of  web  in  feet  X  least  resistance  of  one  nvet 

If  the  number  or  rivets  determined  by  formula  (6)  is  such  that  they  would 
be  more  than  6  in  apart,  then  the  number  must  be  increased,  as  in  ho  case 
should  they  have  a  greater  pitch  than  6  in. 

(b)  Rivets  in  Flange-Legs  of  Angles.  With  a  single  cover-plate.  For 
girders  with  a  single  cover-plate,  it  is  customary  to  put  the  same  number  of 
rivets  in  the  flange-leg  as  in  the  web-leg  for  a  distance'of  3  ft  from  the  ends  of 
the  girder,  staggering  the  rivets  as  in  Fig.  15.  Beyond  that  point  to  the 
middle  of  the  girder  one-half  the  number  of  rivets  will  be  sufficient,  provided  this 
will  not  give  them  a  greater  pitch  than  6  in. 

With  two  or  more  cover-plates.  When  two  or  more  cover-plates  are 
used,  each  plate  must  have  sufficient  rivets  between  the  end  of  the  plate  and  the 
point  where  its  resistance  is  required,  that  is,  for  example,  between  a  and  b, 
Fig.  13,  to  transfer  to  the  angle  and  flange-plates  between,  an  amount  equal 
TO  the  safe  strength  of  the  plate.  From  this  point  to  the  middle  point  of 
the  girder,  the  rivets  can  be  spaced  according  to  the  rule  for  the  greatest  pitch. 

(c)  Rivets  in  Stiffeners.     The  spacing  of  rivets  in  the  stiffeners  is  generally 
determined  by  the  rules  given  for  the  pitch  of  rivets.     Further  explanation  of 
the  method  of  determining  the  spacing  of  rivets  will  be  found  in  the  following  • 
examples. 

'     (4)  The  Approximate  Weight  of  the  Girder.    In  determining  the  size  of 
a  riveted  girder  to  support  a  given  load,  it  is  desirable  to  be  able  to  add  to  the 

*  See  Formula  (i),  page  683,  and  foot-note  relating  to  it.  M  =  SAd,  and  hence 
SA  =  M/d,  SA  being  the  total  amount,  in  pounds,  of  the  tendency  to  slide,  and  5  being 
the  horizontal  unit,  flange,  fiber-stress  in  pounds  per  square  in,  due  to  flexure.  A  is  the 
area  in  square  inches  of  the  cross-section  of  the  flange  and  J"  is  the  approximate  depth  of 
the  girder. 

t  Because  the  maximum  horizontal  flange-stress  is  equal  to  the  maximum  bending 
moment  divided  by  the  girder -depth,  or  SuxazA  —  Mma.x/d. 


688  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

superimposed  load  the  weight  of  the  girder  itself,  as  this  often  forms  a  con- 
siderable part  of  the  load  to  be  supported.  The  following  empirical  rule*  is 
often  used  to  determine  the  approximate  weight  of  a  plate  or  box  girder: 

Weight  of  girder  between  supports,  in  tons  =  Wl/ ^oo  (7) 

in  which  W  equals  the  load  to  be  supported,  in  tons,  and  /  equals  the  span,  in 
feet.  The  constant  700  was  determined  for  girders  of  from  35  to  50  ft  long,  but 
may  be  used  without  much  excess  for  girders  of  shorter  spans. 

(5)  The  Determination  of  the  Lengths  of  the  Flange-Plates.  For  the 
methods  used  to  determine  these,  see  the  following  examples. 

4.   Explanation  of  Tables 

The  Calculations  for  the  Design  of  Riveted  Girders  may  be  greatly 
facilitated  by  the  use  of  Tables  I,  II,  III  and  IV  at  the  end  of  this  chapter. 

Table  I  gives  the  sectional  area  that  should  be  deducted  for  rivet-holes  in 
plates  of  different  thicknesses.  In  computing  this  table  %  in  was  added  to  the 
diameter  of  the  rivet  to  allow  for  the  injury  to  the  metal  caused  by  punching 
and  also  to  allow  for  the  expansion  of  the  heated  rivet. 

Table  II  gives  the  safe  shearing  value  for  web-plates  for  various  depths  and 
thicknesses,  and  the  deduction  to  be  made  for  each  %-in  or  J^-in  rivet. 

Table  III  gives  the  safe  resistance  to  buckling  per  square  inch  of  net  section, 
and  also  the  total  safe  resistance  in  pounds  for  the  more  common  sizes  of  web- 
plates,  with  two  rivet-holes  deducted.  It  is  very  seldom  that  any  vertical  sec- 
tion between  the  stiffeners  contains  more  than  two  rivet-holes.  Tables  giving 
the  dimensions  and  properties  of  angles  will  be  found  in  Tables  XI  and  XII, 
pages  362  to  367,  and  the  shearing  value  and  bearing  values  of  rivets  are  given 
in  Tables  II  and  III,  pages  418  and  419. 

Table  IV  gives  the  elements  of  riveted  plate  girders  of  various  depths,  from 
which  it  is  possible  to  select  economical  sections  for  almost  any  ordinary  condi- 
jjipn  of  loading. 

5.   Examples  of  Plate  and  Box  Girders 

Example  i.  It  is  required  to  support  the  floor  over  a  room  50  by  64  it,  by 
means  of  riveted  steel  plate  girders,  placed  across  the  room,  16  ft  on  centers. 
The  room  above  is  to  be  used  for  general  assembly  purposes.  The  floor-joists 
are  of  wood  and  there  is  a  plaster  ceiling  on  the  under  side  of  them.  The  design 
of  the  girder  is  required. 

First  Step.  The  Load.  The  first  step  is  to  determine  the  load  to  be  supported 
by  each  girder.  The  floor-area  supported  by  each  girder  is  50  by  16  ft,  or  Soo  sq 
ft.  The  weight  of  the  floor-construction  between  the  girders  will  not  be  over 
25  lb  per  sq  ft,  and  an  allowance  of  100  lb  per  sq  ft  for  the  live  load  will  be 
ample.  The  unit  load,  125  lb  X  800=  100  000  lb,  or  50  tons,  the  load  to  be 
carried  by  the  girder.  To  this  should  be  added  the  weight  of  the  girder  itself. 
Substituting  in  Formula  (7), 

the  approximate  weight  of  the  girder  =  -: —  =  3.57  tons,  or  about  7000  lb, 

700 

and  the  total  load,  in  round  numbers,  is  107  000  lb.  This,  of  course,  is  uni- 
formly distributed. 

•  From  "Compound  Riveted  Girders,"  by  W.  H.  Birkmirc. 


Examples  of  Plate  and  Box  Girders  689 

Second  Step.  The  Flange- Area.  The  next  step  is  to  determine  the  flange- 
area.  Before  this  can  be  done,  however,  the  width  and  depth  of  the  girder 
must  be  decided.  As  it  is  desirable  to  keep  the  girder  as  shallow  as  possible, 
consistent  with  good  engineering,  the  case  will  be  considered  an  exceptional 
one  and  the  depth  of  the  wcb-plate  will  be  made  36  in,  which  is  about  one- 
sixteenth  the  span  and   a  little  less  than  the  usual  hrait. 

As  the  girders  arc  braced  sidewise  by  the  floor-joists,  it  will  not  be  necessary 
to  make  the  width  of  the  flange-plates  one-twentieth  the  span  of  the  girder, 
and  it  may  be  made  12  in  width.  The  flange-area  may  be  determined  by 
Formula  (i),  page  683,  and  is 

A  =  Mru^^/dS 

a  /      .  X       maximum  bending  moment  (ft-tons) 

or  nange-area  (sq  m)  = — — 

depth  of  web  (ft)  X  ^  (tons  per  sq  in) 

The  maximum  bending  moment  for  a  uniformly  distributed  load  on  a  simple 
beam  is  Mm-Ax  =  Wl/S  (Case  V,  page  326),  or  in  this  particular  case,  53.57 
tons  X  50  ft/8  =  334-8  ft-tons. 

The  value  of  5  *  has  varied  in  the  handbooks  from  6  to  8  tons,  depending 
upon  varying  conditions  and  upon  the  judgment  of  engineers.  A  value  of  5 
of  8  tons  or  16  ooq  lb  per  sq  in  is  the  requirement  of  the  new  New  York  Building 
Code,  and  of  the  codes  of  most  cities.  In  this  example  14  cxx)  lb  per  sq  in  is 
assumed  for  S. 

Substituting  this  value  in  the  formula  gives  for  the  net  area  of  either  flange, 
334-8/(3  X7)  =  16  sq  in. 

The  upper  flange  may  now  be  designed.  For  a  girder  of  this  size  and  loaded 
in  this  way,  it  will  be  advisable  to  try  two  5  by  3H  by  Mo-in  angles,  with  the 
long  legs  horizontal. t  The  sectional  area  of  these  angles  (Table  XI,  page  363) 
is  7.06  sq  in  which  leaves  9  sq  in  for  the  area  of  the  flange-plates.  Dividing  this 
by  i2-in,  the  width  of  the  flange,  gives  %  in  for  the  total  thickness  of"  the  plates, 
which  may  be  made  up  of  two  %-m  thick  plates.  Of  course,  any  other  combina- 
tion of  plates  and  angles  having  an  area  of  cross-section  of  16  sq  in  will  fulfill 
the  conditions  of  the  problem,  the  selection  in  all  cases  depending  upon  the 
judgment  and  experience  of  the  designer.  Note,  also,  that  no  part  of  the  web 
has  been  included  in  the  flange-area  although  it  would  be  safe  to  include  one- 
sixth  of  it.     This  also  is  a  matter  of  individual  opinion. 

As  the  lower  flange  is  in  tension,  the  rivet-holes  should  be  deducted  in  order 
to  obtain  the  net  area.  Assuming  that  ^4-in  diameter  rivets  are  used,  it  will 
be  noted  that  the  greatest  loss  of  section  is  by  two  rivet-holes  opposite  each 
other,  connecting  the  angles  with  the  plates  of  the  bottom  flange.  From  Table  I, 
page  702,  the  area  of  two  %-in  rivets  in  a  %-in  plate  is  1.31  sq  in,  and  in  a 
Me-in  plate,  the  same  thickness  as  that  of  the  angles,  it  is  0.76  sq  in.  The  sum 
of  these  thicknesses  is  2.07  sq  in,  which  must  be  added  to  the  net  area  of  the 
upper  flange-plates,  16  sq  in,  making  18.07  sq  in  for  the  gross  area  of  the  lower 

*  See,  in  Chapter  XV,  paragraphs  and  foot-notes,  page  603,  relating  to  fiber-stresses 
for  bending  for  riveted  beam  girders,  etc. 

t  For  the  flange-angles  of  plate  girders  the  S  by  33'i-in  size  is  most  commonly  used, 
when  the  flange-plate  is  12  in  wide,  and  6  by  4-in  angles  when  the  flange-plate  is  over  12  in 
wide.  For  box  girders  5  by  4,  5  by  3^,  4^y  3V2  and  3H  by  3H-in  are  common  sizes;, 
while  for  very  heavily 'loaded  girders,  requiring  two  rows  of  rivets  in  the  web-leg,  6  by 
6-in  angles  are  often  used.  For  most  riveted  girders,  in  which  only  one  row  of  rivets  is 
required,  the  short  leg  is  riveted  to  the  web,  so  as  to  bring  most  of  the  material  as  far  from 
the  neutral  axis  of  the  girder  as  possible.  The  minimum  thickness  of  flangCrangles 
should  be  ^i  in,  and  the  maximum  thickness  for  ordinary  loads  is  H  in. 


690 


Riveted  Steel  Plate  and  Box  Girders 


Chap-  20 


flange-plates.     This  additional  area  may  be  obtained  by  increasing  the  thick- 
ness of  the  plates  to  H  in. 
The  flanges  will  then  be  made  up  as  follows: 

Upper  flange:  Two  angles,  5  by  3^  by  Me-in    =    7.06  sq  in,  gross  area 

Two  plates,  12  by  ^-in  =    9.00  sq  in.  gross  area 

Total  16.06  sq  in.  gross  area 

Lower  flange:  Two  angles,.  5  by  sVz  by  Me-in     =    7.06  sq  in,  gross  area 

Two  plates,  12  by  J^^-in  =  12.00  sq  in,  gross  area 

Total  =  19.06  sq  in,  gross  area 

Third    Step.    The   Length   of   the  Flange-Plates.     To  determine  this  it  is 
necessary  to  plot  the  bending-moment  diagram  shown  in  Fig.  12.    The  bending- 


Fig.  12.     Diagrams  for  Bending  Moments  and  Vertical  Shears. 


n[t^ment  diagram  for  a  girder  under  a  uniformly  distributed  load  is  bounded  by 
a  parabola  having  a  height  over  the  middle  of  the  girder  equal  to  the  maximum 
bending  moment.  From  the  middle  point  C,  of  a  horizontal  line  AB,  at  any 
convenient  scale,  lay  off  a  vertical  line  CD,  equal  to  the  maximum  bending 
moment,  334-8  ft-tons.  Construct  the  parabola  ADB  (see  page  79);  then  the 
bending  moment  at  any  other  point,  as  E,  is  equal  to  the  ordinate  EF  above 
that  point,  measured  to  the  same  scale. 


Examples  of  Plate  and  Box  Girders  691 

To  find  the  theoretical  length  of  the  flange-plates  of  the  lower  flange,  inclose 
the  bending-momen}  diagram  in  a  rectangle  and  from  any  convenient  point, 
such  as  C,  lay  off  any  line  CG,  equal  to  the  total  flange-area,  19  units  in  length, 
and  at  such  an  angle  that  the  upper  end  G  will  lie  on  a  horizontal  line  drawn 
through  D.  Divide  the  line  CG  into  three  parts.  CH  representing  the  sectional 
area  of  the  angles,  equal  to  7  units,  and  ///  and  IG  representing  the  sectional 
area  of  the  two  plates,  equal  to  6  units  each.  Draw  horizontal  lines  through 
//  and  /;  then  the  line  J  J  will  represent  the  theoretical  required  length  of  the 
second  or  upjx^r  flange-plate  and  the  line  KK  the  length  of  the  first  or  lower 
flange-plate.  In  practice,  however,  the  plates  are  usually  extended  beyond  the 
points  /  and  K  on  each  side  as  an  additional  factor  of  safety,  a  distance  suffi- 
cient to  take  enough  rivets  to  transmit  at  least  one-third  the  resistance  of  the 
plate.  It  is  also  customary  to  make  the  first  or  lower  flange-plate  the  full 
length  of  the  girder  as  it  greatly  stiffens  the  angles  and  adds  but  a  small 
amount  to  the  cost.  Theoretically  the  length  of  the  flange-plates  of  the  top 
flange  would  be  less  than  the  length  of  the  plates  of  the  lower  flange,  because 
the  flange-area  of  the  top  flange  is  less  than  that  of  the  lower  flange;  but  they 
are  usually  made  the  same  length. 

Fourth  Step.  The  Web.  Webs  are  proportioned  to  resist  the  shear.  The 
maximum  shearing-stress  in  a  girder  uniformly  loaded  is  equal  to  either  reaction, 
which  in  this  case  is  one-half  the  total  load,  or  53  500  lb.  As  the  girder  is  3  ft 
deep,  this  small  shear  would  require  a  very  thin  section,  thinner  than  the  min- 
imum thickness  for  webs,  which  is  %  in.  From  Table  II,  page  703,  it  is  seen 
that  the  shearing  resistance  of  a  -H  by  36-in  web-plate  is  135  000  lb,  which  is 
greatly  in  excess  of  the  actual  shear. 

Fifth  Step.  The  Stiflfeners.  As  before  explained,  stiffeners  will  be  required 
whenever  the  vertical  shear  exceeds  the  safe  resistance  of  the  web  to  buckling. 
The  vertical  shear  is  53  500  lb  and  the  resistance  to  buckling  may  be  found  from 
Table  III,  page  705.  This,  for  a  %  by  36-in  web  with  two  %-iu.  rivets  is  found 
to  be  31  560  lb;  hence  stiffeners  will  have  to  be  used.  As  stated  under  Buckling 
of  Web,  page  686,  the  spacing  of  stiffeners  is  more  a  matter  of  judgment  and 
experience  than  of  exact  calculation,  and  for  this  a  shear-diagram,  also  shown 
in  Fig.  12,  is  of  great  assistance.  It  may  be  constructed  as  follows:  On  a 
horizontal  line  LM,  lay  off  to  any  convenient  scale  vertical  lines  LN  and  MP, 
each  representing  53  500  lb.  Connect  the  points  N  and  P;  then  the  vertical 
shear  at  any  point  is  equal  to  the  ordinate  at  that  point,  measured  to  the  same 
scale.  Thus,  at  Xi,  3  ft  from  the  left  end,  the  shear  is  47  500  lb,  at  X2,  6  ft 
from  L,  it  is  40  500  lb,  at  X3,  9  ft  from  L,  it  is  34  000  lb  and  at  Xi,  12  it  from 
L,  it  is  27  500  lb.  As  the  vertical  shear  at  X3  is  greater  than  the  safe  resist- 
ance to  buckling  and  at  A"4  less,  it  might  be  safe  to  stop  the  stiffeners  at  X4; 
but  as  the  floor-joists  are  framed  flush,  or  nearly  so,  with  the  top  of  the  girder, 
and  rest  upon  angles  riveted  to  its  web,  it  will  be  advisable  to  put  about  3 
stiffeners  between  A'4  and  the  corresponding  point  on  the  right-hand  half  of 
the  girder.  Additional  stiffeners  should  be  placed  directly  over  each  support, 
making  15  stiffeners  on  each  side  of  the  girder.  These  will  be  made  of  4  by  4 
by  %-in  angles. 

Sixth  Step.  The  Number  and  Pitch  of  the  Rivets.  First,  the  number  of 
rivets  in  the  web  will  be  considered.  As  a  rivet  is  required  at  the  end  of  each 
stiffener,  it  will  be  necessary  to  determine  the  number  and  spacing  of  the  rivets 
between  each  pair  of  adjacent  stiffeners.  In  the  web,  the  rivets  are  in  double, 
shear.  In  Tables  II  and  III,  pages  418  and  419,  values  are  given  based  uponj 
unit  shearing  values  of  7  500  and  10  000  and  bearing  values  of  15000  and 
18  Qoo  lb  per  sq  in.     (See  foot-notes  with  these  tables.)     The  shearing  resistance 


692  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

of  a  %-in  rivet  at  lo  ooo*  lb  per  sq  in  is  4  420  X  2  =  S  840  lb  for  double  shear, 
and  the  bearing  value  of  the  same  rivet  in  a  ^^-in  plate,  at  20  000*  lb  per  sq  in, 
is  5  630  lb.  As  the  bearing  value  is  the  smaller,  it  will  determine  the  number 
of  rivets  required. 

The  number  of  rivets  from  either  end  of  the  girder  to  any  point  depends  upon 
the  horizontal  flange-stress  at  that  point,  and  it  has  been  shown  that  the  flange- 
stress  is  equal  to  the  bending  moment  divided  by  the  depth  of  the  web.  (See 
foot-notes  with  Equations  (5)  and  (6).)  Scaling  off  the  bending  moment  above 
the  point  Xi  gives  75  ft-tons;  hence  the  horizontal  flange-stress  is  equal  to  75/3  = 
25  tons  =  50  000  lb.  The  number  of  rivets  required  between  this  point  and  the 
left  reaction  is,  from  Formula  (5),  equal  to  50  000/5  630  =  10  rivets,  which  are 
to  be  spaced  in  a  distance  of  36  in,  making  the  spacing  3.6  in.  Above  X2  the 
bending  moment  scales  141.24  ft-tons,  the  flange-stress  is  141. 24/3  =  47.08  tons, 
or  94  160  lb,  and  the  number  of  rivets  required  between  X2  and  A  is  94  160/5  630 
=  17;  but  10  of  these  are  required  between  -Yi  and  A,  leaving  7  to  be  placed 
between  A'l  and  A'2  in  a  distance  of  36  in  making  the  spacing  5.1  in.  At  A's,  the 
bending  moment  scales  197.4  ft-tons,  and  the  flange-stress  is  197.4/3  =  65.3  tons, 
or  130  600  lb.  The  number  of  rivets  required  is  130  600/5  630=  24,  but  17  of 
these  are  required  between  X2  and  A,  leaving  7  to  be  placed  between  X2  and 
A3,  making  the  spacing  the  same  as  in  the  second  panel.  At  A'4  the  bending 
moment  scales  243.96  ft-tons,  and  the  flange-stress  is  243.96/3  =81.32  tons  or 
162  640  lb.  The  number  of  rivets  required  is  162  640/5  630=  30,  but  24  of 
these  are  required  between  A3  and  A ,  leaving  6  to  be  placed  between  A'3  and  A'4 
in  a  distance  of  36  in,  making  the  spacing  6  in.  As  this  is  the  maximum  spacing 
allowed,  it  will  be  used  from  Xa  to  the  corresponding  point  on  the  opposite 
right-hand  half  of  the  girder.  The  same  number  of  rivets  will  be  used  in  the 
flange-legs  of  the  angles  as  in  the  web-legs,  but  they  will  be  spaced  so  that 
they  will  come  between  those  in  the  web. 

The  outer  flange-plate  scales  28  ft  6  in  in  length  in  the  bending-moment  dia- 
gram, but  this  length,  as  before  stated,  should  be  increased  sufficiently  to  take 
enough  rivets  to  transmit  at  least  one-third  of  the  resistance.  The  area  of  the 
plate  is  y2  in  X  12  in  =  6  sq  in,  minus  the  area  of  two  %-in  rivet-holes,  0.87  sq 
in  (Table  I,  page  702),  leaving  a  net  area  of  5.13  sq  in.  The  resistance  of 
the  plate  is  therefore  equal  to  5.13  sq  in  X  14  000  lb  per  sq  in  =  71  820  lb.  One- 
third  of  this,  or  23  940  lb,  must  be  transferred  by  rivets  placed  beyond  the 
points  //.  As  the  rivets  in  the  flange  are  in  single  shear,  the  shearing  value 
of  one  rivet  in  single  shear,  4  420  lb,  will  govern.  The  number  of  rivets  re- 
quired, then,  is  23  940/4  420  =  6,  or  3  in  each  angle.  The  spacing  of  the  rivets 
in  this  panel  is  6  in.  The  plates  will  therefore  be  extended  18  in  on  either  side 
of//. 

*  The  shearing  value  of  rivets  is  taken  at  from  7  000  to  12  000  lb  per  sq  in  and  the 
bearing  value  at  from  12  000  to  24  000  lb  per  sq  in.  The  usual  values  are  10  000  lb  for 
shear  and  20000  or  24  000  lb  for  bearing.  Values  of  12  000  lb  for  shear  and  24  000  lb 
for  bearing  are  the  requirements  of  the  New  York  Building  Code  A  bearing  value 
other  than  those  of  Tables  11  and  III,  pages  418  and  419,  is  purposely  used  in  this  example, 
as  it  is  frequently  necessary  to  use  different  unit  stresses  than  those  from  which  some 
particular  table  has  been  computed.  If  no  other  table  is  at  hand  for  the  values  based  upon 
some  particular  rivet  bearing-stress.  Tables  II  and  III,  pages  418  and  419,  can 
be  used  and  the  new  value  found  by  proportion;  or  the  bearing-stress  can  be 
found  by  multiplying  the  product  of  the  diameter  of  the  rivet  and  the  thick - 
Bess  of  the  web  by  the  new  unit  stress.  In  this  example,  Table  III,  page  419, 
gives,  for  18000  unit  stress,  5060  lb  for  bearing;  ^%  of  this  gives  5622  lb 
for  a  20000  unit  stress.  Also,  H  in  by  ^  in  by  20000  lb  persqin  =5625 
lb. 


Examples  of  Plate  and  Box  Girders 


693 


splices.  As  the  total  length  of  the  girder  is  but  53  ft,  it  will  not  be  necessary 
to  splice  the  webs  or  the  flanges,  because  the  extreme  length  of  a  H  by  36-in 
plate  is  no  ft  and  of  a  12  by  H-in  plate,  90  ft.*  It  is  never  necessary  to  splice 
angles  as  they  are  rolled  in  lengths  up  to  90  ft.  In  very  long,  deep  girders, 
however,  it  is  sometimes  necessary  to  splice  the  web,  and  the  joint  is  sometimes 
made  at  the  middle,  as  theoretically  there  is  no  vertical  shearing-stress  in  the  web 


0,00.    00    0,0,     0,0     0,0     0.0,0     0,0 


b      '     '  '     '     '     L-   '     '     •  d 

Fig.  13.     Splicing  of  Inner  Plate  of  Bottom  Flange  of  Plate  Girder.    Example  i 

at  that  point  when  the  load  is  uniformly  distributed.  Gerterally,  however, 
the  web  is  spliced  in  two  places,  equidistant  from  the  middle  of  the  girder. 
The  splice  is  calculated  for  vertical  shear  only,  the  rule  being  to  divide  the  shear 
at  the  splice  by  the  safe  shearing  value  or  bearing  value  of  one  rivet.  This 
gives  the  number  of  rivets  required  on  each  side  of  the  splice-plate,  unless  the 
maximum  pitch  is  exceeded,  when  more  are  added. 


0 

oooooiooooo 

00        Ooo|00000 

0 

0 

00000          00000 
00     0      ooooo     00 

0 

Fig.  14.     Plan  of  Splice-plate.     Example  i 

Whenever  a  splice  is  required  in  a  flange-plate,  it  should  be,  if  possible,  at  a 
point  just  beyond  the  end  of  the  plate  above  it.  The  joint  must  be  made  by 
riveting  to  the  spliced  plate,  a  plate  of  the  same  thickness  and  of  sufficient  length 
to  receive  a  number  of  rivets  on  each  side  of  the  joint  equal  to  the  strength  of 
the  plate  that  is  spliced.  When  the  flange  is  made  up  of  two  plates  of  the  same 
thickness,  the  simplest  method  of  splicing  the  inner  plate  is  as  shown  in  Fig.  13. 

IB 


Fig.  15.     Elevation  of  Part  of  Plate  Girder.     Example  i 

Let  e  denote  the  theoretical  position  of  the  end  of  the  outer  plate,  as  determined 
by  the  bending-moment  diagram,  and  a  the  point  to  which  the  plate  must  be 
extended  to  receive  rivets  of  a  resistance  equal  to  one-third  the  strength  of 
the  plate.  Then  let  the  joint  in  the  inner  plate  be  just  over  a  and  extend  the 
outer  plate  to  b,  or  such  a  distance  that  it  can  receive  a  number  of  rivets  equal 
in  resistance  to  the  strength  of  one  plate. 

*  Tables  of  extreme  lengths  are  published  in  the  various  handbooks.  The  above 
dimensions,  for  example,  are  taken  from  the  table  en  page  iii  of  Carnegie's  Pocket  com- 
panion. 


694 


Riveted  Steel  Plate  and  Box  Girders 


Chap.  20 


Fig.  16  shows  one  end  of  the  girder,  drawn  according  to  the  foregoing  calcu- 
lations. 


The  Bill  of  Quantities  for  the  Girder. 
A  B  CD 


r 


/^^ 


K-5'3- 


f<3'0- 
Pi 


rr^ 


rt\ 


'6->|^104<-4: 

1?« 


r^ 


4'2'l(>H-4' 


Giitler 


r\ 


-  4'll"->i 


f?4 


-2410- 


Fig.    16.       Box 


Girder    Supporting 
Example  2 


Brick     Wall. 


The  following  is  a  bill  of  quantities 
^         for    the   construction    of  this 
girder. 

Load:  100  000  lb,  uniformly 
distributed.        Span     50     ft. 
Depth  3  ft 
Upper  flange: 
Two  angles,  5  by  3H  by 

Me  in,  53  ft  long 
One  plate  12  by  ^  in,  53 

ft  o  in  long 
One  plate,  12  by  H  in,  31 
ft  6  in  long 
Lower  flange: 

Two  angles,  5  by  3^^  by 

Ms  in,  53  ft  long 
One  plate,  12  by  H  in,  53 

ft  o  in  long 
One  plate,  12  by  H  in,  31 
ft  6  in  long 
Web: 

One  plate,  36  by  %  in,  53 

ft  o  in  long 
30  stiffeners,   4  by  4  by 
%-in  angles,  2  ft  11  in 
long 
30  filler-plates,  4  by  \^  in, 

29  in  long 
92  ft  8  in  of  4  by  4  by 
Vz-in    angles    for    sup- 
porting floor-joists 
Rivets: 

Yi  in  in  diameter 

Example  2.  The  wall  shown 
in  Fig.  16  is  to  be  supported  by 
a  riveted-steel  box  girder  at  the 
height  indicated.  It  is  re- 
quired to  design  the  girder. 


First  Step.  The  Load.  The  first  step  towards  designing  the  girder  is  the  de- 
termination of  the  load.  The  space  under  the  lower  windows  is  too  small  to  dis- 
tribute the  weight  from  the  piers  uniformly  over  the  girder,  so  that  the  only  safe 
assumption  is  that  the  weight  of  the  wall  between  the  lines  A  and  B  is  concen- 
trated at  Pi,  the  weight  of  wall  between  lines  B  and  C  at  P2  and  so  on.  The 
floor-joists  run  across  the  building,  so  that  only  the  weight  of  the  wall  will  be 
supported  by  the  girder.  Allowing  200  lb  per  square  foot  of  face  for  the  21-in 
wall,  and  165  lb  for  the  17-in  wall,  both  walls  being  plastered  on  the  inside: 
Load  at  Pi 


ils'  3"  X  10'  -  7'  X  2'  3'1  X  200  =    

Is'  3"  X  40'  -  (2'  3"  X  14'  +  3'  2"  X  7')1  X  165  =  . 


7350 

. . .  25  795 


I  =  33  145  lb 


Examples  of  Plate  and  Box  Girders 


695 


Load  at  P2 

[7'4"Xio'-4'6"X7'o"]X20o=    ^  366  (  _ 

[7'4"X  4o'-(4'6"X  14'+  4'  9"X  7')]  X  165  =   32  354  }  ~  4072om 

Load  at  Pz  =  that  at  Pa  = 40  720  lb 

Load  at  P4 

i"X  10'-  2'3"X7']X200  = ^  ^^^  I  =^0  27R  lb 

i"X4o'-  (2'3"X  i4'+3'2"X7')]X  165=  ....23595  )   ______ 

Total  load  on  girder  = 144  863  lb 

or  72.4  tons 
From  Equation  (7) 

approximate  weight  of  girder  = 


=  !' 


_  H4'  1 


Wxl      72.4X24)^ 

., ^ =  2.5  tons,  or  5  000  lb 

700  700 


About  one-third  of  this,  or  say  i  600  lb,  should  be  added  to  P2  and  Pz,  and  900  lb 
to  P\  and  P4.  This  will  give,  approximately,  the  following  loads,  applied  as  in 
Fig.  17: 

P\  =  34  000  lb        P2  =  42  300  lb 

Pz  =  42  300  lb        P4  =  31  200  lb 


P3 


m — ^'^''     T      ^''^' — ^ 


Li 

ML 


.--^y  /\  I 


Fig.  17.    Diagram  for  Bending  Moments.    Example  2 

Second  Step.  The  Determination  of  the  Maximum  Bending  Moment.  By 
means  of  the  formula  under  Case  VT,  page  327,  the  maximum  bending  moment 
in  foot-pounds  for  the  loads  are  found  to  be  as  follows: 

17      D     ir             34000X  i'6"X23'4"  o    ,,  ,, 

For  Pi,  Af max  =  T~~T, =  47  980  ft-lb 


For  P2,  Mmax 
For  P3,  ilf  max 
For  P4,  If  max 


24'  10" 
42  300X8^  11^^X15' 11'' 

24'  10" 
42  300  X  16^  3'' X  8^  7^^ 

24'  10" 
3i200Xi'4''X23'6^^ 

24'  10" 


=  242  000  ft-lb 
=  237  900  ft-lb 
=  39  420  ft-lb 


Plotting  these  moments  to  a  scale,  as  explained  for  Fig.  15,  page  329,  the 
bending-moment  diagram  shown  in  Fig.  17  *  is  obtained.     The  maximum  bend- 

*  The  bending  moments  in  this  diagram  are  drawn  to  a  scale  of  about  400  000  ft-lb 
to  one  inch. 


696  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

ing  moment  is  at  P2,  over  the  longest  ordinate  bb  and  where  the  vertical  shear 
is  zero,  and  is  equal  to  the  length  of  the  ordinate  bb,  which  scales  418  000  ft-lb, 
or  209  ft-tons. 

Third  Step.  The  Determination  of  the  Flange- Area  and  the  Length  of  the 
Cover-Plates.  Before  these  can  be  determined,  the  depth  of  the  web-plate 
must  be  decided.  As  there  is  nothing  to  limit  the  depth  of  the  girder,  it  will 
be  made  about  one-tenth  of  the  span,  or  30  in.  Then  by  Formula  (i),  page 
683,  A  =  Mma.\/dS,  and  using  14  000  lb  or  7  tons  per  sq  in  for  S, 

the  gross  area  of  upper  flange  =  209/2.5  X  7  =  12  sq  in 
As  the  thickness  of  the  wall  to  be  supported  is  21  in,  the  flange-plate  must  be 
at  least  20  in  wide  and  not  less  than  9i  in  thick.  The  sectional  area  of  a  % 
by  20-in  plate  is  7'/^  sq  in,  leaving  ^Vi  sq  in  to  be  made  up  by  the  angles. 
The  sectional  area  of  two  5  by  sH  by  Me-in  angles  is  7.06  sq  in  (Table  IX, 
page  363),  which  leaves  a  small  excess  for  the  lower  flange.  For  rivets  %  in 
in  diameter,  the  loss  in  area  due  to  two  rivet-holes  in  a  -^i-in  plate  is  (Table  I, 
page  702)  0.65  sq  in  and  in  a  Mo-in  plate,  the  thickness  of  each  angle,  0.76  sq'in, 
making  1.41  sq  in  in  all,  for  which  the  excess  in  the  angles  is  more  than  suffi- 
cient. The  width  of  the  flange  being  more  than  one-twentieth  the  span  makes 
lateral  support  unnecessary. 

Fourth  Step.  The  Webs  and  Stiffeners.  The  maximum  shear  is  equal  to  the 
maximum  reaction  which  in  this  case  is  obviously  equal  to  the  left  reaction. 
Taking  the  center  of  moments  at  the  right  reaction,  the  equation  of  moments  is, 
RiX  24.83'=  (17  tonsX  23.33') +  (21.15  tonsX  i5-9i')  +  (21.15  tonsX  8.58') 
+  (15.6  tons  X  1.33') 
whence  24.83  xRi=  935-3215  ft-tons  and  Ri  =  37-669  tons,  or  75  ssS  lb.  Note 
that  the  bads  have"  been  changed  from  pounds  to  tons,  for  convenience  in  mak- 
ing the  calculations.  As  this  box  girder  has  two  webs,  the  maximum  shear  in 
each  web  will  be  37  669  lb.  The  thinnest  web  permissible  is  ^i  in  thick.  From 
Table  IT,  page  703,  the  resistance  of  a  %  by  30-in  web-plate  to  shearing  is 
I T  2  500  lb,  so  that  the  webs  are  amply  safe  in  resisting  vertical  shear.  From 
Table  III,  page  705,  the  safe  resistance  to  buckling,  deducting  for  two  %-in 
rivets,  is  S3  830  lb.  As  this  is  less  than  the  maximum  shear,  stiffeners  will 
be  used,  placed  2  ft  4  in  from  each  support,  with  Ave  between  them,  making 
the  spacing  about  3  ft  4  in  on  centers.  Two  others  will  be  placed  over  each 
support.     4  by  4  by  ^-in  angles. will  be  sufficient  for  the  stiffeners. 

Note.  If  the  loads  were  really  concentrated  at  the  points  Pi,  Pi,  etc.,  as 
from  columns  or  girders,  it  would  be  necessary  to  place  stiffeners  at  each  one 
of  these  points  and  two  in  each  of  the  intermediate  spaces,  but  as  the  pier- 
loads  are  partly  distributed  it  will  be  better  to  space  them  as  first  planned. 

Fifth  Step.  The  Number  and  Pitch  of  the  Rivets.  The  rivets  in  the  web- 
legs  and  flange-legs  of  the  angles  are  in  single  shear.  From  Table  III,  page 
419,  the  shearing  value  of  a  %-'m  rivet  in  single  shear  at  10  000  lb  per  sq  in  is 
4  420  lb,  and  the  bearing  value  in  a  ^i-in  plate  at  18  000  lb  per  sq  in  is  5  060  lb. 
Hence  the  shearing  value  will  govern.  The  number  of  rivets  required  depends 
upon  the  flange-stress,  which  is  equal  to  the  maximum  bending  moment 
divided  by  the  depth  of  the  girder.  (See  Formula  (i),  page  683.)  The  bending 
moment  at  Pi,  found  by  moments  or  graphically  by  scaling  off  the  ordinate 
aa,  Fig  17.  is  56.5  ft-tons.*     This,  divided  by  the  depth  2.5  ft,  gives  22.6  tons, 

*  This  may  be  found,  also,  by  taking  Pi  as  the  center  of  moments  and  multiplying 
-^1  =  37-669  tons  by  the  lever-arm  1V2  ft.  The  result  is  56.5  ft-tons.  The  bending 
moments  at  the  other  loads  may  be  determined  by  taking,  in  each  case,  the  algebraic 
sum  of  the  moments  of  the  external  vertical  forces  on  either  side  of  each  point  considered. 


Examples  of  Plate  and  Box  Girders 


697 


or  45  200  lb,  for  the  flange-stress,  or  22  600  lb  for  each  web.  The  number  of 
rivets,  therefore  (Formula  (5),  page  687)  is  22600/4420=6.  The  distance 
from  Pi  to  the  left  reaction  is  18  in,  which  makes  the  spacing  3  in.  The 
flange-stress  at  P2  is  209.88  ft-tons/2.5  ft  =  83.95  tons,  or  167  900  lb,  and  oiTe- 
half  of  this  is  83  950  lb.  The  number  of  rivets  therefore  is  83  950/4  420  =  19. 
But  6  of  these  are  required  between  Pi  and  the  left  reaction,  leaving  13  to  go 
between  Pi  and  P2,  a  distance  of  89  in,  making  the  [)itch  about  6.9  in.  As 
this  exceeds  the  maximum  allowable  pitch,  the  rivets  will  be  spaced  6  in  on 
centers  between  Pi  and  Pi,  and  between  Pi  and  Ps.  The  spacing  on  the  right- 
hand  end  of  the  girder  will  be  made  the  same  as  that  on  the  left.  Some  details 
of  the  girder  are  shown  in  Fig.  18. 


0^ 

'o'^o^o^ol 

0 

t)^o'"o'"o"o'-o 

0 

["cT-Tr 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0000 

5_/a Q C\ 4 

^nOn°r.Or.O.^° 

0    0 

0^o|Po']opD' 
O  O 
o  C 
o  o 
o       o 

o  o    000 


Fig.  18.     Elevations  and  Section  of  Box  Girder.     Example  2 

The  Details  and  Bill  of  Quantities  for  the  Girder.  The  loads,  dimensioiw,  size, 
number  of  pieces,  etc.,  for  the  girder  are  given  in  the  following  summary: 

Loads:  34  000  lb,  i  ft  6  in  from  left  support.     Span:  24  ft  10  in 
42  300  lb,  8  ft  II  in  from  left  support.     Depth:  30  in 
42  300  lb,  8  ft  7  in  from  right  support 
31  200  lb,  I  ft  4  in  from  right  support 

Both  flanges:    Four  angles,  5  by  z\^  by  Yxa  in,  27  ft  6  in  long 
One  plate,  20  by  %  in,  27  ft  6  in  long 

Two  webs:  %  by  30  in,  27  ft  6  in  long 

Twenty-two  stiffeners:  4  by  4  by  %  in,  29H  in  long 

Twenty- two  filler-plates:  4  by  Me  in,  23  in  long 

Rivets:  %  in  in  diameter 

Example  3.  What  are  the  dimensions  of  a  box  girder,  40  ft  in  span,  required  to 
support  the  following  loads?  90  tons  from  a  column,  8  ft  from  the  left  support; 
75  tons  from  a  column,  12  ft  from  the  right  support;  and  a  masonry  pier,  10  ft 
in  length,  beginning  10  ft  from  the  left  support  and  weighing  4  tons  per  running 
ft.     (See  Fig.  19.) 

First  Step.  The  Determination  of  the  Reactions,  Shears  and  Bending  Mo- 
ments. To  find  either  reaction,  the  center  of  moments  is  taken  at  the  other 
reaction.  The  equation  of  moments  for  the  left  reaction  is,  therefore,  taking  the 
center  of  moments  at  the  right  reaction, 

40  Ri  =  (90  tons  X  32  ft)  -f-  (40  tons  X  25  ft*)  -\-  (75  tons  X  12  ft) 

from  which 

4o7?i  =  4  780  ft-tons  and  R\=  119.5  tons 

♦  In  considering  the  moments  of  forces,  distributed  loads  are  treated  as  if  they  were 
concentrated  at  their  centers  of  gravity. 


Riveted  Steel  Plate  and  Box  Girders 


Chap.  20 


In  like  manner,  the  equation  of  moments  for  the  right  reaction  is 

40  R2={75  tons  X  28  ft)  +  (40  tons  X  15  ft)  +  (90  tons  X  8  ft) 

from  which 

40  i?2  =  3  420  ft-tons,  and  Rz  =  85.5  tons 

The  greatest  vertical  shear   Vi  is  equal    to  the  greater  reaction,  which  is 
119.5  tons.    The  shear-diagram  (Fig.  19)  may  be  constructed  by  laying  off  at 


Fig.  19.    Elevation  of  Box  Girder  and  Diagrams  for  Bending  Moments  and  Vertical 
Shears.    Example  3 


any  convenient  scale  an  ordinate  equal  in  length  to  119.5  tons.  Immediately 
at  the  right  of  point  i,  under  the  left  column,  the  shear  is  equal  to  119.5  —  90  = 
29.5  tons.  It  is  the  same  at  point  2,  the  left  end  of  the  wall.  At  point  3,  the 
right  end  of  the  wall,  the  shear  is  1 19.5  -  90  -  40  =  - 10.5  tons,  showing  that  the 
shear  passes  through  zero  somewhere  between  2  and  3,  which  is  the  point  of 
maximum  bending  moment.  This  point,  X,  is  by  scaling  the  shear-diagram, 
17.4  ft  from  Ri.    It  is  over  the  point  of  intersection  of  the  slanting  line  ia 


Examples  of  Plate  and  Box  Girders  699 

the  shear-diagram,  with  the  horizontal  line  of  reference.  This  slanting  line 
is  drawn  from  the  top  of  the  shear-ordinate  for  point  2  to  the  bottom  of  the 
shcar-ordinate  for  point  3.  Just  at  the  right  of  point  4,  the  shear  is  119.5  — 
90—  40—  75  =  — 85.5  tons,  the  same  as  the  right  reaction.  The  point  X,  of  no 
shear  and  maximum  bending  moment,  may  be  found,  also,  as  follows:  At  the 
left  of  point  2  the  shear  is  29.5  tons.  One  foot  to  the  right  of  2  it  is  29.5 
tons— 4  tons=  25.5  tons.  Two  feet  to  the  right  of  2  it  is  29.5—  8  tons  = 
21.5  tons,  etc.  Therefore,  since  the  shear  decreases  at  the  rate  of  4  tons  per  . 
foot,  it  will  be  zero  at  29.5/4  or  7,4  ft  at  the  right  of  2,  or  17.4  ft  from  Ri. 

The  maximum  bending  moment  is  at  A^,  the  point  of  no  shear.  The  equation 
of  moments,  considering  the  forces  to  the  left  of  X,  is 

1/max  =  (119-5  tons  X  17-4  ft)  -  (90  tons  X  94  ft)  -  (4  tons  X  74  ft  X  74  ft/2) 
7.4  ft/2  is  the  distance  from  X  to  the  center  of  gravity  of  the  wall-load  to  the 
left  of  X,  and  is  the  lever-arm  of  that  load,  considered  as  a  vertical  downward 
force  concentrated  in  a  single  line  of  action.     Hence 

if  max  =  2  079.3  -  846  -  109.5  =  I  123.8  ft-tons 

The  bending-moment  diagram  may  be  constructed  by  laying  off  at  X,  at  any 
convenient  scale,  an  ordinate  XC  equal  to  i  123.8  ft-tons  in  length.     It  is  neces- 
sary to  find  the  bending  moment  at  other  points,  since  the  bending-moment 
diagram  cannot  be  plotted,,  as  in  the  previous  examples,  because  the  uniform 
load  is  not  distributed  over  the  entire  girder.     The  other  critical  points  are  i, 
2,  3  and  4. 
Ml  =  (119.5  tons  X  8  ft)  =  956  ft-tons 
3/2=  (119.5  tonsX  10  ft)  —  (90  tonsX  2  ft)  =  i  015  ft-tons 
Ms  =  (119.5  tons  X  20  ft)  —  (90  tons  X  12  ft)  —  (40  tons  X  5  ft)  =  i  no  ft-tons 
Mi  =  (119.5  tons  X  28  ft)  —  (90  tons  X  20  ft)  —  (40  tons  X  13  ft)  =  i  026  ft-tons 

By  laying  off  ordinates  at  these  points  equal  by  scale  to  the  respective  bending 
moments;  drawing  straight  lines  from  R  to  A,  the  extremity  of  the  ordinate 
through  I,  and  from  A  to  B;  drawing  curved  lines  from  B  through  the  points 
C  and  D;  and  connecting  D  and  E  and  E  and  R2  by  straight  lines;  the  bending- 
moment  diagram  R1ABCDER2  may  be  constructed. 

Second  Step.  The  Webs.  As  stated  on  page  683,  it  is  considered  safe  by 
many  engineers  to  include  one-sixth  of  the  web-area  in  the  flange-area,  and 
this  will  be  done  in  this  example.  The  web,  therefore,  must  be  designed  first. 
As  there  is  nothing  to  limit  the  depth  of  the  girder,  it  will  be  made  3  ft  deep, 
about  one-twelfth  the  span.  The  greatest  vertical  shear  is  equal  to  the  greater 
or  left  reaction,  119.5  tons.  Since  the  girder  carries  a  brick  wall,  it  must  be  of 
the  box  type,  and  hence  the  vertical  shear  on  each  web  is  59.75  tons.  A  ]r^  by 
36-in  web  will  be  tried  first.  Its  area  is  18  sq  in,  from  which  must  be  deducted 
the  loss  in  area  due  to  the  rivet-holes  for  the  rivets  through  the  stiff eners.  The 
rivets  will  be  placed  the  maximum  distance  on  centers,  making  six  in  each 
stiffener.  Because  of  the  concentrated  loads  near  the  reactions  more  rivets  will 
be  required,  and  in  order  to  avoid  a  close  spacing,  %-in  rivets  will  be  used. 
From  Table  I,  page  702,  the  sectional  area  to  be  deducted  for  a  ^^-in  rivet  in  a 
^^-in  plate  is  0.50  sq  in;  hence  the  net  area  of  the  web  is  18  —  (6  X  0.50)  =15 
sq  in,  and  its  shearing  resistance,  at  10  006  lb  or  5  tons  per  sq  in  (Table  II,  page 
703),  is  15  X  5  tons=  75  tons,  which  is  15.25  tons  in  excess  of  the  59.75  tons 
required. 

Third  Step.    The  Flange-Area.     From  Formula  (i),  page  683, 

the  flange  area,  A  =  Mmtix/dS  =•  ^-^  =  53.5  sq  in 

3X7 


700  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

As  the  girder  ha?  no  lateral  support,  the  flange-width  should  be  not  less  than  one- 
twentieth  the  span,  which  will  make  it  2  ft. 

The  upper  flange  may  be  proportioned  as  follows: 

One-sixth  of  net  section-area  of  two  webs  = 5 .  00  sq  in 

Two  5  by  5  by  ^ie-in  angles,*  with  section-area  = 10.62  sq  in 

Three  %&  by  24-in  plates,  with  section-area  of  13.50  sq 

in  each  = 40. 50  sq  in 

Total  section-area  of  upper  flange  = 56 . 1 2  sq  in 

To  proportion  the  lower  flange,  allowance  must  be  made  for 
the  loss  in  area  due  to  two  rivet-holes. 

From  Table  I,  page  702,  the  area  of  two  %-in  rivet-holes  in 

a  yia-in  plate  (thickness  of  angles)  = i .  12  sq  in 

Areat  of  two  rivet-holes  in  three  -^i-in  flange-plates  =. . .        3 .  75  sq  in 
Total  rivet-area  = 4 .  87  sq  in 

Hence  the  gross  section-area  of  the  lower  flange  must  be 
53.5  +  4-87=  58  sqin. 
This  may  be  made  up  of 

One-sixth  of  net  section-area  of  two  webs  = 5.0    sq  in 

Two  5  by  5  by  YiQ-in  angles,  with  section-area  = 10.62  sq  in 

Three  H  by  24-in  plates,  with  section-area  of  15  sq  in 

each  = 45 .  00  sq  in 

Total  section-area  of  lower  flange  J  = 60.62  sq  in 

The  length  of  the  flange-plates  is  determined  from  the  bending-moment 
diagram.  Draw  a  horizontal  line  through  C  (Fig.  19)  and  at  any  point,  as  3, 
lay  off  to  any  convenient  scale  and  angle,  a  line  3  //  =  60.62  units  in  length, 
with  its  upper  extremity  on  the  horizontal  line  FG  drawn  through  C.  Divide 
this  line  into  five  parts:  3  /,  containing  5  units  for  the  web-area;  //,  10.62  units 
for  the  angles;  and  JK,  KL  and  Z,//  of  15  units  each,  for  the  three  plates.  Draw 
horizontal  lines  through  the  points  7,  /,  K  and  L  as  shown.  The  horizontal 
intercepts  of  these  horizontals  in  the  bending-moment  diagram  will  give  the 
theoretical  lengths  of  the  flange-plates.  For  practical  considerations,  the  inner 
plate  is  always  carried  the  full  length  of  the  girder  and  the  other  plates  are  ex- 
tended beyond  the  intersection-points  on  either  side,  a  distance  sufficient  to 
take  enough  rivets  to  transmit  at  least  one-third  of  the  resistance  of  the  plate. 
The  resistance  yl 5,  of  the  outer  plate  is  15  sq  inXT4ooolb  per  sq  in  =2 10  000  lb. 
One-third  of  this,  or  70000  lb,  must  be  resisted  by  rivets  placed  beyond  the 
points  A  A.  From  Table  III,  page  419,  at  10  000  lb  per  sq  in,  the  shearing 
value  of  a  J^-in  steel  rivet  in  single  shear  is  6  010  lb  and  in  a  ^-in  plate  its  bearing 
value  at  18  000  lb  per  sq  in  is  9  820  lb.  Hence  the  number  of  rivets  required  is 
70  000/6  010  =  12,  or  6  on  each  side.  With  a  2-in  pitch  this  would  lengthen  the 
plate  12  in  at  each  end.  The'  outside  plates  in  this  particular  girder  would  be 
extended  far  enough  to  pass  beyond  the  bise  of  the  column  on  the  left  side  of 
the  girder. 

*  Angles  with  equal  legs  are  selected  because  the  same  number  of  rivets  will  be  re- 
quifecl  in  both  legs,  as  they  are  all  in  single  shear,  and  large  angles  are  selected  because 
the  rivets  will  have  to  be  staggered,  owing  to  the  concentrated  loads  being  placed  so  near 
the  ends  of  the  girder. 

t  Since  ^le-in  plates  are  selected  for  the  upper  flange,  it  is  reasonable  to  suppose  that 
^i-in  plates  will  be  necessary  for  the  lower  flange. 

X  Both  flange-areas  are  made  slightly  in  excess  of  the  requirements,  because  in  this 
example  one-sixth  of  the  web-area  is  included. 


Examples  of  Plate  and  Box  Girders  701 

Fourth  Step.  The  Stiffeners.  From  Table  III,  page  705,  the  safe  buckling 
value  of  a  ^^  by  36-in  plate  with  two  ^6-in  rivets  is  62  320  lb,  and  as  this  is 
much  less  than  the  shearing  value,  stiffeners  must  be  used.  The  stiffeners 
under  the  concentrated  loads  may  be  considered  as  short  struts  in  direct  com- 
pression. Assuming  that  4  by  4  by  H-in  angles  are  used  for  the  stiffeners,  the 
safe  load  from  Table  XV,  page  502,  is  over  20  tons.  The  greatest  concen- 
trated load  is  90  tons,  and  hence  four  stiffeners  will  be  placed  under  each 
column.  Four  more  will  be  placed  at  each  bearing,  as  shown  in  Fig.  19,  four 
on  each  side,  between  the  columns,  about  4  ft  on  centers;  and  two  on  each  side, 
between  the  columns  and  the  bearings,  making  15  on  each  side,  or  30  in  all. 

Fifth  Step.  The  Number  and  Pitch  of  the  Rivets.  In  a  box  girder,  the  rivets 
are  in  single  shear.  The  shearing  value  of  a  ^i-in  rivet  at  10  000  lb  per  sq  in 
is,  from  Table  III,  page  419,  6  010  lb,  and  its  bearing  value  at  18  000  lb  per 
sq  in,  in  a  Yie-in  plate,  the  thinnest  outside  plate,  is  6  880  lb;  hence  the  shearing 
value  will  govern. 

The  number  of  rivets  depends  upon  the  horizontal  flange-stress,  which  is 
equal  to  the  maximum  bending  moment  divided  by  the  depth  of  the  girder 
(Formula  (i),  page  683).  3/  at  i  =  956  ft-tons,  and  the  horizontal  flange-stress 
=  956/3  =  319  tons,  or  638  000  lb.  From  Formula  (5),  page  687,  the  number 
of  rivets  required  =  638  000/6  010  =  106,  or  53  on  each  side.  These  are  to  be 
spaced  in  a  distance  of  8  ft,  or  96  in,  which  makes  the  pitch  about  i  .8  in.  As 
this  is  less  than  the  minimum  pitch,  2^i  in,  or  three  diameters,  the  rivets  will 
have  to  be  staggered.  Hence  the  justification  for  selecting  large  angles  with, 
equal  legs  for  this  paricular  girder.  _  At  X  the  horizontal  flange-stress  =j 
I  123.8/3  =  374.6  tons,  or  749  200  lb,  and  the  number  of  rivets  is  749  200/6  oio; 
=  124,  or  62  on  each  side;  53  of  these,  however,  are  required  between  Ri  and  i, 
leaving  9  to  be  placed  between  i  and  X,  a  distance  of  about  9  ft.  As  the  re- 
sulting pitch  will  exceed  the  maximum  pitch,  they  will  be  placed  6  in  on  centers 
between  i  and  X.  At  4  the  horizontal  flange-stress  =  i  026/3  =  342  tons,  or 
684  000  lb.  The  number  of  rivets  is  684  000/6  010  =  112,  or  56  on  each  side, 
to  be  spaced  in  a  distance  of  12  ft,  or  144  in,  making  the  spacing  2.5  in.  Be- 
tween 4  and  X  the  maximum  pitch  will  be  determined  as  before. 

Sixth  Step.  The  Weight  of  the  Girder.  So  far,  no  account  has  been  taken 
of  the  weight  of  the  girder.  The  practice  is  to  neglect  this  weight  when  the  max- 
imum bending  moment  due  to  it  alone  is  less  than  10%  of  the  maximum  bend- 
ing moment  due  to  the  loads.  From  Formula  (7),  page  688,  the  weight  of  the 
girder  =  205  X  40/700  =12  tons.  From  Case  V,  page  326,  the  maximum  bend- 
ing moment  due  to  it  =  12  X  40/8  =  60  ft-tons.  As  this  is  much  less  than  10% 
of  I  123.8  ft-tons,  the  maximum  bending  moment  due  to  the  loads,  it  may  be 
neglected.  Had  it  been  otherwise,  the  weight  would  have  to  be  considered  as 
an  additional  uniformly  distributed  load  over  the  entire  girder  and  a  new  bend- 
ing-moment  diagram  drawn. 

Other  Data  on  Riveted  Girders.  By  applying  the  principles  illustrated  in 
the  preceding  examples  it  is  possible  to  compute  the  necessary  dimensions  and 
details  for  riveted  girders  under  any  conditions  of  loading.  If  further  examples 
are  desired,  the  reader  is  referred  to  "  Compound  Riveted  Girders,"  by  WilHam 
H.  Birkmire,  in  which  different  examples  of  loading  are  fully  worked  and  ex- 
plained, and  also  to  other  recent  treatises  on  this  subject. 

Detail  Drawings  and  Stress-Diagrams  of  one  of  the  earlier  heavy  plate 
girders  used  in  building-construction  are  published  in  the  Engijieering  Record 
of  Dec.  28,  1895.  This  girder  is  one  of  six  plate  girders  used  in  the  construc- 
tion of  Tremont  Temple,  Boston,  Mass.,  Blackall  &  Newton,  architects.  The 
girder  is  75  ft  long  between  centers  of  columns,  6  ft  i  in  deep,  with  flanges  28  in 


702 


Riveted  Steel  Plate  and  Box  Girders 


Chap.  20 


wide,  and  is  calculated  to  support  distributed  and  concentrated  loads  aggre- 
gating 497.5  tons.  The  single  web-plate  is  64%  in  deep,  and  "A  in  thick  at  the 
ends;  the  flanges  are  4y2  in  thick  at  the  middle  of  the  girder;  and  the  flange- 
angles  are  6  by  8  by  i  in.  Since  that  time  there  have  been  erected  for  many  of 
the  large  buildings  a  number  of  riveted  girders  of  very  great  size  and  strength, 
and  details  of  their  construction  may  be  found  in  the  engineering  and  architec- 
tural periodicals. 

6.   Tables  Used  in  the  Design  of  Plate  and  Box  Girders 

Tables  T,  II,  III  and  IV  contain  data  usually  reciuired  for  the  design  of  plate 
and  box  girders  to  satisfy  all  but  the  most  unusual  conditions. 

Table  I.*t     Sectional  Area  in  Square  Inches  to  be  Deducted  from  Plates  and 

Angles  for  Rivet-Holes 

Taken  %  inch  in  excess  of  diameter  of  rivet  J 


Number  of  rivets,  i  in 

Number  of  rivets,  li 

in 

Thickness 

diameter 

diameter 

of  plate, 
in 

I 

2 

3 

4 

1 

2 

3 

4 

I 

1. 12 

2.25 

3.37 

4.50 

1. 00 

2.00 

3.00 

4.00 

1^6 

1,05 

2.10 

3.16 

4.21 

0.94 

1.87 

2.81 

3.75 

% 

0.98 

1.97 

2.9s 

.3.93 

0.87 

I.7S 

2.62 

350 

m6 

0.91 

1.83 

2.74 

3.65 

0.81 

1.62 

2.44 

3.25 

H 

0.84 

1.69 

2.53 

3.37 

0.7s 

I.  SO 

2.25 

3.00 

•     iHe 

0.77 

1.55 

2.32 

3.09 

0.69 

1.37 

2.06 

2.75 

% 

0.70 

1. 41 

2. II 

2.81 

0.62 

1.25 

1.87 

2.50 

916 

0.63 

1.26 

1.90 

2.53 

0.56 

1. 12 

1.69 

2.25 

H 

0.56 

I. II 

1.69 

2.25 

0.50 

I. 00 

1.50 

2. CO 

Me 

0.49 

0.98 

1.47 

1.97 

0.44 

0.87 

1. 31 

I  75 

% 

0.42 

0.84 

1.26 

1.69 

0.37 

0.75 

1. 12 

1.50 

Ni 

mber  of  rivets,  ?l 

in 

Nur 

nber  of  rivets,  % 

in 

Thickness 

diameter 

diameter 

of  plate, 

in 

I 

2 

3 

4 

' 

2 

3 

4 

I 

0.87 

1.75 

2.62 

3. SO 

0.75 

1.50 

2.25 

3.00 

15/16 

0.82 

1.64 

2.46 

3.28 

0.70 

1.40 

2. II 

2.81 

% 

0.77 

I.  S3 

2.30 

3.06 

0.65 

1.31 

1.96 

2.62 

1^0 

0.71 

1.42 

2.13 

2.84 

0.61 

1.22 

1.83 

2.44 

H 

0.66 

1. 31 

1.96 

2.62 

o.s6 

1.12 

1.69 

2.25 

1M6 

0.60 

1.20 

1.80 

2.40 

0.51 

1.03 

1.54 

2.06 

H 

0.5s 

1.09 

1.64. 

2.19 

0.47 

0.94 

1. 41 

1.88 

Yie 

0.49 

0.98 

1.48 

1.96 

0.42 

0.84 

1.26 

1.69 

H 

0.43 

0.87 

1. 31 

I.7S 

0.37 

0.75 

1. 12 

1.50 

Me 

0.38 

0.76 

1. 15 

I. S3 

0.33 

0.66 

0.98 

1. 31 

% 

0.32 

0.6s 

0.98 

1. 31 

0.28 

0.56 

0.84 

1. 12 

Me 

0.27 

0.55 

0.82 

1.09 

0.23 

0.47 

0.70 

0.94 

K 

0.22 

0.44 

0.66 

0.87 

0.18 

0.37 

0.56 

0.75 

*  For  explanation  of  tables,  see  Subdivision  4,  page  688. 

t  This  table  is  taken  from  "Comiwund  Riveted  Girders,"  by  W.  H.  Birkmire. 

I  See  paragraph,  Punching  Rivet-Holes,  page  414,  and  Table  XI,  page  400. 


Tables  Used  in  the  Design  of  Plate  and  Box  Girders 


703 


Table  II.*     Safe  Shearing  Value  of  Web-Plates  in  Pounds 

Mild  steel.     Gross  area.     Safe  unit  stress,  lo  ooo  lb  per  sq  in 


Depth, 
in 

Thickness  in  inches 

% 

Me 

H 

ViO 

% 

H 

^ 

28 
30 
32 
36 

40 
42 
46 
48 

105  000 
112  500 
120000 
135000 
150000 
157500 
172500 
180  000 

122  500 
131  300 
140000 
157  500 
175000 
183800 
201  300 
210  000 

140  000 
150  000 
160000 
180  000 
200  000 
210  000 
230  000 
240  000 

157500 
168800 
180  000 
202  500 
225  000 
236  300 
258800 
270  000 

175000 
187500 
200  000 
225  000 
250000 
262  500 
287  500 
300  000 

210  ooo 

225  000 

240000 
270  000 
300  000 

315000 
345000 
360  000 

245000 

262  500 
280  000 

315000 

350  000 

367500 
402  500 
420  000 

Deductions  in  pounds  for 

one  %-in  rivet f 

3200 

3800 

4300 

4900 

5500 

6600 

7700 

Ded 

actions  in  ] 

X)unds  for 

one  }i-in  rivet  t 

3700 

4400 

5000 

5600 

6  200 

7500 

8700 

*  For  explanation  of  tables,  see  Subdivision  4,  page  688. 

t  The  area  of  the  hole  is  taken  ^i  in  in  excess  of  the  diameter  of  the  rivet  to  allow  for 
injury  of  the  metal  sustained  by  punching. 

Example  4.  What  is  the  safe  shearing  value  of  a  36  by  H-'m  wel>-piaie  with 
seven  H-in  rivets  in  the  stifleners? 

Solution.     The  gross  shearing  value  =  135  000  lb 

The  deduction  for  seven  rivets  =7X3  200  =    22  400  lb 
The  safe  shearing  value  =112  600  lb 

To  use  this  table  for  any  other  unit  stress,  divide  the  shearing  value  by  10  000 
and  multiply  by  the  given  unit  stress.  For  example,  what  is  the  safe  shearing- 
value  of  a  40  by  %-in  web-plate  at  12  000  lb  per  sq  in?  (250  ocx)/io)  X  12  = 
300  000  lb. 

Tables  of  Riveted  Steel  Plate  Girders.t  It  is  not  practicable  to  give 
TABLES  OF  SAFE  LOADS  for  riveted  steel  plate  girders  because  of  the  great  variety 
of  combinations  of  plates  and  angles  that  can  be  selected  for  any  given  condition 
of  loading.  Moreover,  any  variation  in  the  loading  would  make  the  tables  use- 
less. In  place  of  the  safe  loads,  therefore,  the  properties  or  elements  of 
RIVETED  STEEL  PLATE  GIRDERS  are  given  in  Table  IV,  pages  706  to  716,  which 
will  aid  in  determining  the  size  of  the  girder  and  the  approximate  thickness  of 
the  plates  and  angles  for  any  special  case.  To  determine  the  dimensions  and 
other  details  of  a  girder  suitable  to  carry  any  specified  loading,  determine  the 
MAXIMUM  END-REACTION  in  pounds  and  the  maximum  bending  moment  in  inch- 
pounds.  Select  from  Table  IV  the  different  parts  for  a  girder  of  the  required 
DEPTH,  a  THICKNESS  OF  WEB  as  determined  by  the  maximum  end-reaction  and 
a  suitable  section-modulus  as  determined  by  dividing  the  maximum  bending 

t  For  tables  of  riveted  single-beam  girders  and  double-beam  girders,  see  Tables  XIV 
and  XV,  pages  605  to  611. 


704  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

moment  by  the  permissible  unit  stress  for  flexure  in  pounds  per  square 
inch.  The  spacing  of  the  rivets,  the  number  and  position  of  the  stiffeners, 
the  LENGTH  OF  THE  FLANGE-PLATES,  if  more  than  one  are  needed,  and  the  loss 
IN  FLANGE-AREA  and  WEB-AREA  due  to  the  punching  of  the  rivet-holes,  must 
be  determined  in  each  case  by  the  rules  already  given.  The  weights  of  the 
rivets  and  stiffeners  are  not  included. 

As  an  illustration  of  the  use  of  these  elements  or  properties,  in  Example  (i) 
the  total  losui  on  the  girder  is  107  000  lb,  making  each  end-reaction  5,5  500  lb. 
The  maximum  bending  moment  is  334.8  ft-tons,  or  8  035  000  in-lb.  The  section- 
modulus  //c  =  MAS' =  8035000/14  000=  574.  The  depth  of  the  girder  is 
limited  to  36  in.  Looking  up  the  properties  of  36-in  girders  in  Table  IV,  page 
709,  it  is  seen  that  a  %-in  web  is  more  than  sufficient  to  resist  the  end- 
reaction.  The  nearest  section-modulus  to  574  is  567.2,  that  of  a  girder  com- 
posed of  a  36  by  Me-in  web,  5  by  sV^i  by  ^'2-in  angles,  and  12  by  H-in  flange- 
plates.  In  working  out  the  problem  in  detail  it  was  found  that  the  girder 
required  5  by  sV^  by  ^e-in  angles  and  two  12  by  yz-'m  flange-plates  to  com- 
pensate for  the  loss  of  area  due  to  the  punching  of  the  rivet-holes.  (See  pages 
219  and  710.) 

Table  IV  is  based  upon  an  extreme  fiber-stress  for  flexure  of  16  000  lb  per  sq  in, 
and  gross  sections  are  used  in  determining  the  values  given.  The  attention  of 
readers  is  called  to  the  two  methods  of  plate  and  box-girder  design:  (i)  the  oni^ 
using  the  plate-girder  formula  (page  683),  and  (2)  the  one  using  the  section- 
modulus  (pages  703  and  704,  and  706  to  716).  It  is  customary,  also,  to  take 
into  account  the  tendency  of  the  compressing-flange  of  the  girder,  if  long  between 
lateral  bracings,  to  buckle  or  fail  as  a  column;  and  the  permissible  reduced  flange- 
stregs  is  determined  by  column-formulas. 


Tables  Used  in  the  Design  of  Plate  and  Box  Girders         705 
Table  III.*     Safe  Buckling  Values  of  Web-Plates 

SAFE  UNIT   BUCKLING  VALUE  IN   POUNDS   PER  SQUARE  INCH 


Calculated  by  formula  f  Sb  =  ■ 


I  +- 


3000/2 


'    Sb  =  safe  buckling  resistance  in  pounds  per  square  inch;  d  =  depth  of  web 
between  flatige-plates  in  inches;  /  =  thickness  of  web  in  inches 

in  the  clear 

Depth, 
in 

Thickness  in  inches 

■K 

ha 

'A 

Vie 

% 

% 

H 

28 
30 
32 
36 
40 
42 
48 

3498 
3192 
2889 
2456 
2087 
1930 
1548 

4  228 
3896 
3624 
3069 
2696 
2  455 
1994 

4890 
4546 
4228 
3666 
3  191 
2983 
2543 

5476 
5  133 
4787 
4229 
3724 
3498 
2918 

5932 
5656 

5  339 
4748 
4  228 
3992 
3371 

6522 
6226 
5656 
5  133 
4889 
4228 

6  920 
6392 
5882 
5649 
4992 

TOTAL  SAFE   RESISTANCE  IN  POUNDS  FOR  PLATES  WITH  TWO   %-IN   RIVETS 

Depth, 
in 

Thickness  in  inches 

H 

Me 

K> 

80880 
81 560 
81 500 
79190 
75  920 

%    . 

% 

% 

28 
30 
36 

42 
48 

34  450 
33830 
31560 
29  140 
26860 

48  580 
48  150 
46  000 
43  230 
40360 

64  200 
64  230 
62800 
60  040 
58820 

97340 
99880 
loi  750 
100  440 
97450 

138  200 

145  300 
147  600 

146  670 

191  570 
198960 
202  000 

TOTAL  SAFE   RESISTANCE  IN  POUNDS  FOR  PLATES  WITH   TWO   ^^-IN   RIVETS 

Depth, 
in 

Thickness  in  inches 

Vs 

Vi6 

¥2 

9^6 

% 

% 

% 

28 
30 
36 
42 
48 

34  TOO 
33510 
31  310 
28  950 
26  700 

48  I  TO 
47720 
45660 
42960 
40  140 

(>3  570 
63  640 
62  320 
59660 
58490 

80  100 
80840 
80900 
78700 
75520 

96  390 
98980 
ICO  690 
99  800 
96910 

136960 

144  230 
146  690 

145  860 

190  170 
197  710 
200930 

*  For  explanation  of  tables,  see  Subdivision  4,  page  688. 

t  See  in  Chapter  XV  the  paragraphs  and  foot-notes,  pages  568  and  569,  relating  to 
the  web-buckling  of  I-beams.  The  formula  for  the  above  table  is  the  formula  that  was 
used  in  the  Passaic  Steel  Company's  Manual,  and  as  the  values  computed  by  it  vary  but 
little  from  those  deduced  by  the  Cambria  formula,  Table  III  is  retained  as  it  is. 

See,  also,  page  686.  paragraph  relating  to  Safe  Resistance  of  Web  to  Buckling. 


Riveted  Steel  Plate  and  'Box  Girders 


Table  IV.*    Elements  of  Riveted  Plate  Girders 


^ 


^ 


W 


"T" 


To  determine  the  details  of  construction  of  a  girder  suit- 
able to  carry  any  specified  loading,  determine  the  maxi- 
mum end-reactions  in  pounds  and  the  maximum  bending 
moment  in  inch-pounds 

Select  from  the  table  a  girder  having  the  desired  depth, 
St  thickness  of  web  as  determined  by  the  maximum  end- 
reaction  and  a  suitable  section-modulus,  determined  by 
dividing  the  maximum  bending  moment  by  the  permissi- 
ble unit  bending  fiber-stress  in  pounds  per  square  inch 

For  limiting  conditions,  see  the  pages  702  to  705  and 
the  first  three  subdivisions  of  this  chapter 

Weights  given  do  not  include  stiffeners,  rivet-heads,  or 
other  details 


Section- 
modulus, 
axis,  i-i, 
in3 


242.0 
270.9 
306.1 
343.6 
378. 5 
414. 1 

151. 5 
176.8 
186.6 
201.2 
219.6 
252 .  o 
260.7 

341  5 
354.4 
377.4 
386.1 
415.2 
435.1 
454-5 
479.3 
526.1 
569-9 
613.9 

200.4 
233.4 
233. 5 
265.8 
274-5 
314.8 


Web- 
plate, 


24X% 


26XM« 


26X5s 


26XIU 


Sizes 


Flange- 
angles, 


SX3>^XH 
5X3^X5^ 
5X31/^X1/2 

5X3K2XH 

4X3  XH 
5X31/^X^6 
4X3  XH 
6X4  X% 
5X3I/2XM2 
6X4  XV2 
SXsJ'^X^i 

6X4  XH 
6X4    X3/i 

5X3y2XH 

6X4  XH 
5X3i^iXV2 
6X4  XI/2 
5X3I/I2XH 
6X4  XK2 
6X4  XH 
6X4  XH 
6X4    XVi 

4X3  XV2 
4X3  XH 
5X3^/^X^2 
6X4  XH 
5X3HXH 
6X4    XH 


Flange- 
plates, 


12X3/8 

12XH 
12X/2 

12X58 
I2XH 


UXH 

i2XK> 
14  XH 
12XH 
14  XH 

I2XH 
uXH 

14XH 
I4XM 
I4XK 


Weight  per  foot 


Web- 
plate 
and 
flange- 
angles, 
lb 


97.8 
72.2 
72.2 
85.0 
85.0 
97.8 

61.6 
69.2 
72.0 
76.8 
82.0 
92.4 
94.8 

82.4 
127.6 
87.6 
82.4 
87.6 
98.0 
100.4 
98.0 
113. 2 
113. 2 
127.6 

83.1 
93.1 
93.1 
103.5 
105.9 
118. 7 


Flange- 
plates, 
lb 


30.6 
40.8 
40.8 
51.0 
51.0 


a5-7 

40.8 
47.6 
51.0 
47.6 
51.0 
59-5 
59-5 
71-4 
71.4 


Maximum 

end- 
reaction  in 
thousands 
of 
pounds 


60.8 
60.8 
60.8 
60.8 
60.8 
60.8 

56.3 
56.3 
563 
S6.3 
56.3 
56.3 
56.3 

67.5 
67.5 
67.5 
67.5 
67.5 
67. 5 
67.5 
67.5 
67.5 
67. 5 
67.5 

78.8 
78  8 
78.8 
78.8 
78.8 
78.8 


*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 
tional  values  are  given  in  the  Pocket  Companion. 


Tables  Used  in  the  Design  of  Plate  and  Box  Girders         707 
Table  IV  *t  (Continued).     Elements  of  Riveted  Plate  Gifders 


Sizes 

Weight 

per  foot 

Maximum 
end- 

Section- 

Web- 

modulus, 
axis  i-r, 

Web- 

Flange- 

Flange- 

plate 
and 
flange- 
angles, 

Flange- 

reaction  in 
thousands 

in3 

plate, 
in 

angles, 
in 

plates, 
in 

plates, 
lb 

of 
pounds 

lb 

361.3 

6X4    X% 

133. 1 

78.8 

384.0 

SXz^AXYz 

12XK2 

93.1 

40.8 

78.8 

421.8 

5X3K2XK2 

12  x% 

93.1. 

51.0 

78.8 

441.7 

6X4    XVi 

14XK2 

103.5 

47.6 

78.8 

461. 1 

26XM6 

SXzYzX^A 

12  X- 

■i 

105.9 

51.0 

78.8 

485.9 

6X4    XVi 

I4X^ 

■i 

103.5 

59.5 

78.8 

532.7 

6X4    X^^ 

I4X- 

^ 

118. 7 

59.5 

78.8 

576.5 

6X4    XH 

I4X-] 

i 

"118.7 

71.4 

78.8 

620.5 

6X4    X% 

14X5 

i 

133. 1 

71.4 

78.8 

185.6 

5X3HX% 

70.3 

56.3 

211. 0 

6X4    Xf^ 

77.9 

56.3 

1        230.3 

5X3^2X1'^ 

83.1 

56.3 

264.1 

27XM0 

6X4    XH 

93.5 

56.3 

273.2 

5X3^2X5/^ 

95.9 

S6.3 

304. 5 

5X3K2XH 

I2X?i 

70.3 

30.6 

56.3 

315.3 

6X4     X% 

108.7 

56.3 

344.2 

SXz\iX% 

12X3 

^ 

70.3 

40.8 

56.3 

337.7 

6X4    X^i 

115.7 

67.5 

366.7 

SX2,¥2X% 

12XK2 

77.3 

40.8 

67. 5 

i        372.8 

6X4     XH 

14XH 

84.9 

35.7 

67.5 

i        388.5 

6X4  xy\ 

130. 1 

67.5 

1        411. 7 

5X3'/^XH 

12X? 

'2 

90.1 

40.8 

67.5 

420.8 

6X4    x% 

14XJ 

12 

84.9 

47.6 

67.5 

1        437.0 

28X% 

6X4    X% 

144.5 

67. 5 

i        452.5 

5X3K2XK2 

I2Xv 

i 

90.1 

51.0 

67.5 

1         474.3 

6X4     XH 

14X3 

'2 

100.5 

47.6 

67.5 

1        49.5.3 

5X3^X^6 

12  X-^ 

i 

102.9 

51.0 

67.5 

1        521.9 

6X4    XH 

I4X^ 

i 

100.5 

595 

67.5 

I         573-1 

6X4    XM 

I4X^ 

4 

IIS. 7 

59.5 

67.S 

1         620.4 

6X4    X^)s 

14X2 

4 

115. 7 

71.4 

67.5 

i        668.6 

6X4    X% 

14X5 

4 

130. 1 

71.4 

67.5 

257.1 

SXzViXH 

96.1 

78.8 

i        292.4 

6X4    XH 

106.5 

78.8 

301.8 

5X3K'X5/^ 

108.9 

78.8 

'        345.8 

6X4    X% 

121. 7 

78.8 

!     396.5 

6X4    XVa. 

136. 1 

78.8 

1     419.5 

28X7l6 

5X3M2XI/2 

12X 

.^ 

96.1 

40.8 

78.8 

445.1 

6X4    Xli 

150.5 

78.8 

460.2 

5X3HXi/i 

12X 

Vs 

96.1 

51.0 

78.8 

1      482 . 0 

6X4    XK2 

14X 

Yt 

106.5 

47.6 

78.8 

503. 0 

5X3^2X5/^ 

12X 

H 

108.9 

51.0 

78.8 

529.6 

6X4    XVi. 

14X 

54 

106. 5 

59. 5 

78.8 

580.8 

6X4    XH 

14X 

% 

121. 7 

59-5 

78.8 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 
t  For  explanation  of  table,  see  page  706. 


708  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

Table  IV  *t  (Continued).    Elements  of  Riveted  Plate  Girders 


Sizes 

Weight  1 

3er  foot 

Maximum 
end- 

Section- 

■ 
Web- 

modulus, 

plate 
and 
flange- 
angles. 

reaction  in 

axis  I- 1, 

Web- 

Flange*- 

Flange- 

Flange- 

thousands 

in3 

plate, 
in 

angles, 
in 

plates, 
in 

plates, 
lb 

of 

pounds 

lb 

628.0 

28X^6 

6X4    XH 

14X^4 

121. 7 

71.4 

78.8 

676.2 

6X4    X^4 

14X^1 

136. 1 

71.4 

78.8 

221.8 

5X3^2X5^ 

79  9 

74.3 

250.5 

6X4     X3/6 

87.5 

74-3 

272.1 

5X3l"2X»/2 

92.7 

74.3 

310.3 

6X4     XVz 

103. 1 

74.3 

320.5 

5X3'/iXH 

105.5 

74.3 

353.8 

5X3HX->6 

I2X?8 

79  9 

30.6 

74-3 

366.2 

5X3'/''X3/i 

117. 5 

74.3 

368.1 

6X4     X^A 

118. 3 

74.3 

397.8 

5X3HXH 

12XH 

799 

40.8 

74.3 

404.7 

6X4     X% 

I4XH 

87.5 

35.7 

74.3 

423.1 

30XH 

6X4     XH 

132.7 

74.3 

446.6 

SXsViXH 

12XH 

92.7 

40.8 

74.3 

456.1 

6X4     X% 

14XH 

87. 5 

47.6 

74.3 

475.8 

6X4    Xli 

147. 1 

74.3 

490.3 

5X3V2Xyz 

I2X% 

92.7 

51.0 

74.3 

514.0 

6X4     XH 

I4XH 

103. 1 

47.6 

74.3 

536.7 

5X3HX->i 

I2XH 

105. 5 

510 

74.3 

565.1 

6X4    XH 

14X5/^ 

103. 1 

59  5 

74.3 

620.6 

6X4     X'>i 

I4X:H 

118. 3 

59  5 

74.3 

671.3 

6X4     X% 

14X94 

118. 3 

71.4 

74.3 

723.8 

6X4    XH 

14X94 

132.7 

71.4 

74.3 

281.4 

5X3HXH 

99-0 

86.6 

319  5 

6X4    XK> 

109.4 

86.6 

329.7 

sX3HX-5^ 

III. 8 

86.6 

375.5 

5X3HX^/4 

123.8 

86.6 

377.3 

6X4    X% 

124.6 

86.6 

432.3 

6X4     X% 

139  0 

86.6 

455.5 

5X3'AXVz 

12XH 

99  0 

40.8 

86.6 

485.0 

30X^10 

6X4    x% 

I. S3. 4 

86.6 

499  2 

5X3HXV2 

12X% 

99-0 

51.0 

86.6 

523  0 

6X4     XH 

I4XH 

109.4 

47.6 

86.6 

545.6 

SXsViXH 

I2XH 

III. 8 

51. 0 

86.6 

574.0 

6X4     XH 

I4XH 

109.4 

59  5 

86.6 

629. 5 

6X4     XH 

14x9^ 

124.6 

59-5 

86.6 

680.1 

6X4    XH 

I4XK 

124.6 

71.4 

86.6 

732.6 

6X4    XH 

14x94 

139.0 

71.4 

86.6 

290.6 

5X3HXH 

105-4 

99-0 

328.8 

6X4     XH 

IIS. 8 

99.0 

338.9 

30XH 

5X3HX5^ 

118. 2 

99-0 

384.7 

5X3HXH 

130.2 

99.0 

386.5 

6X4     X5^ 

131. 0 

99-0 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 
t  For  explanation  of  table,  see  page  706. 


Tables  Used  in  the  Design  of  Plate  and  Box  Girders        709 
Table  IV *t  (Continued).    Elements  of  Riveted  Plate  Girders 


Sizes 

Weight 

per  foot 

Maximum 
end- 

Section- 

Web- 

modulus, 
axis  i-i. 

Web- 

Flange- 

Flange- 

plate 
and 
flange- 
angles. 

Flange- 

reaction  in 
thousands 

in3 

plate, 
in 

angles, 
in 

plates, 
in 

plates, 
lb 

of 
pounds 

lb 

441.5 

145.4 

99.0 

6X4    X% 

464.4 

5X3^/^X1/^ 

I2X^^ 

105.4 

40.8 

99.0 

494.2 

6X4    X% 

159.8 

99.0 

508.0 

5X3^/^XJ^ 

12X5^ 

105.4 

51.0 

99.0 

531.9 

2PX\^ 

6X4    XK2 

14X1/2 

115. 8 

47.6 

99.0 

554. 5 

SXzyiX% 

12XH 

118. 2 

51.0 

99.0 

582.8 

6X4   xy2 

I4X^^ 

115. 8 

59.5 

99.0 

638.3 

6X4    X^^ 

14XH 

131. 0 

59.5 

99.0 

688.9 

6X4    X% 

14  X% 

131. 0 

71.4 

99.0 

741.3 

6X4    X% 

14X3/1 

145.4 

71.4 

990 

351.7 

5X3^2X3/^ 

83.7 

81.0 

283.7 

6X4     X?6 

91.3 

81.0 

307.7 

33X^% 

5X3i/2X'/^ 

96.5 

81.0 

308.4 

6X6    XH 

101.7 

121. 5 

350.3 

6X4    X\i 

106.9 

81.0 

430.3 

6X6    X\^ 

124.3 

135.0 

460.0 

5X3'/2X?4 

125. 1 

87.8 

462.4 

6X4    X% 

125.9 

87.8 

503.3 

6X4     X^^ 

14X5^ 

95.1 

35.7 

87.8 

510.5 

6X6    XH 

142.7 

135.0 

530.2 

6X4    X% 

140.3 

87.8 

531.6 

6X6    X% 

I4X^^ 

105. 5 

35.7 

135.0 

554.3 

5X3K2XK2 

12X1/^ 

100.3 

40.8 

87.8 

565.1 

6X4    X% 

14  XH 

95.1 

47.6 

87.8 

593.2 

6X6    X?4 

I4X^^ 

105. 5 

47.6 

135.0 

595.3 

6X4    X% 

154.7 

87.8 

606.8 

36X3/8 

5X3HXK2 

I2X5i 

100.3 

51.0 

87.8 

636.5 

6X4    XK2 

14X/2 

no. 7 

47.6 

87.8 

654.9 

6X6    X% 

I4X-H 

105.5 

59.5 

135.0 

664.2 

5X3HX-5i 

12XH 

113. 1 

51.0 

87.8 

674.4 

6X6    XV^ 

14X/2 

124.3 

47'.  6 

135.0 

698.0 

6X4     XK' 

14X^4 

110.7 

59.5 

87.8 

735.5 

6X6    XH 

i4X^/i 

124.3 

59.5 

135.0 

766.6 

6X4     XH 

iaX% 

125.9 

59-5 

87.8 

796.8 

6X6    XI/2 

i4xyi 

124.3 

71.4 

135.0 

813. 1 

6X6    XM 

I4XH 

142.7 

59. 5 

135.0 

827.6 

6X4     XH 

14X3/ 

125.9 

71.4 

87.8 

873.8 

6X6    XYi 

14x54 

142.7 

71.4 

135.0 

892.8 

6X4    XYi 

i4X^i 

140.3 

71.4 

87.8 

357.7 

5X3'/2XH 

108.0 

102.4 

404.7 

36X^6 

6X4    XH 

118. 4 

102.4 

417.0 

sxmx% 

120.8 

102.4 

443.6 

6X6    X\^ 

132.0 

157.5 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 
t  For  explauation  of  table,  see  page  706, 


710  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

*"  Table  IV *t  (Continued).    Elements  of  Riveted  Plate  Girders 


Sizes 

Weight 

per  foot 

Maximum 
end- 

Section- 

Web- 

modulus, 

plate 

reaction  in 

axis  i-i. 

Web- 

Flange- 

Flange- 

Flange- 

thousands 

in3 

plate, 

angles, 

plates, 

flange- 

plates, 

of 

in 

in 

in 

angles, 
lb 

lb 

pounds 

473. 3 

5X3HXM 

132.8 

102.4 

475-7 

6X4     XVs 

133.6 

102.4 

523.8 

6X6     XH 

150.4 

157.5 

543.5 

6X4    XH 

148.0 

102. 4 

567.2 

5X3yixy2 

12XK2 

108.0 

40.8 

102.4 

608.6 

6X4    x% 

162.4 

102.4 

619.7 

5X3HXH 

12X54 

108.0 

51-0 

102.4 

649  5 

6X4    XH 

I4XK^ 

118.4 

47.6 

102.4 

677.1 

36X^6 

5X3HXH 

12XH 

120.8 

51.0 

102. 4 

687.3 

6X6    XH 

14XH 

132.0 

47.6 

157-5 

710.8 

6X4     XH 

uXH 

118. 4 

59.5 

102.4 

748.4 

6X6     XH 

uXH 

132.0 

59.5 

157.5 

779  5 

6X4    X^^ 

14XH 

133.6 

59-5 

102.4 

809.5 

6X6    X]^ 

I4X% 

132.0 

71.4 

157.5 

825.9 

6X6    XH 

14X5^ 

150.4 

59.5 

157-5 

840.4 

6X4    XH 

14X34 

133.6 

71.4 

102.4 

886.6 

6X6    XH 

UXH 

150.4 

71.4 

157-5 

905.5 

6X4    XH 

14XH 

148.0 

71.4 

102.4 

418.0 

6X4    XH 

126.0 

117.0 

456.9 

6X6    XH 

139.6 

180.0 

489.0 

6X4    X% 

141.2 

117. 0 

537.1 

6X6    XH 

158.0 

180.0 

556.9 

6X4    XU 

• 

155.6 

117.0 

614.5 

6X6    XH 

176.© 

180.0 

621.9 

6X4    Xli 

170.0 

117. 0 

662.5 

6X4    XH 

14XH 

126.0 

47-6 

117.0 

689.2 

6X6    Xli 

193.6 

180.0 

700.3 

6X6    XH 

I4X^ 

139.6 

47.6 

180.0 

723.7 

36X}'^ 

6X4    XH 

14  X -^'6 

126.0 

59-5 

117.0 

761.3 

6X6    XH 

I4XH 

139-6 

59-5 

180.0 

792.3 

6X4    X^^ 

14X5/^ 

141.2 

59-5 

117.0 

822.3 

6X6    XH 

UXH 

139.6 

71.4 

180.0 

838.8 

6X6    XH 

uXH 

158.0 

59-5 

180.0 

853.2 

6X4    XH 

14x34 

141. 2 

71.4 

117. 0 

899.4 

6X6    XH 

14X^4 

158.0 

71.4 

i8o.o 

918.3 

6X4    XH 

14X3/4 

155.6 

71.4 

117.0 

973.7 

6X6    XM 

uXH 

176.0 

71.4 

180.0 

I  039.4 

6X4    XH 

14X1 

155.6 

95.2 

117. 0. 

I  094.1 

6X6    X3/4 

14X1 

176.0 

95.2 

180.0 

I  lOI.I 

6X4    X^ 

14X1 

170.0 

95.2 

117. 0 

I  164.9 

6X6    Xli 

14X1 

193.6 

95.2 

180.0 

444.7 

36XH 

6X4    Xi/i 

141. 3 

146.3 

483.5 

6X6    XH 

154.9 

225.0 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 
t  For  explanation  of  table,  .see  page  706- 


Tables  Used  in  the  Design  of  Plate  and  Box  Girders        711 
Table  IV *t  (Continued).    Elements  of  Riveted  Plate  Girders 


Sizes 

Weight 

per  foot 

Maximum 
end- 

Section- 

Web- 

modulus, 

plate 
and 
flange- 
angles. 

reaction  in 

axis  i-i, 

Web- 

Flange- 

Flange- 

Flange- 

thousands 

in3 

plate, 

angles, 

plates, 

plates, 

of 

in 

in 

in 

lb 

pounds 

lb 

SIS. 7 

6X4XH 

156. 5 

146.3 

S63.7 

6X6X5/^ 

173.3 

225.0 

S83.S 

ex4XH 

170.9 

146.3 

641.2 

6X6XH 

191.3 

225.0 

648.  s 

6X4XH 

18S.3 

146.3 

688.4 

6X4XH 

14XH 

141. 3 

47.6 

146.3 

715.8 

6X6X^^ 

208.9 

225.0 

726.2 

6X6XH 

I4X>^ 

154.9 

47.6 

749-4 

6X4X1/^ 

I4XH 

141. 3 

59-5 

146.3 

787.0 

6X6XK2 

14  XH 

154-9 

59  5 

225.0 

818. 1 

36X^8 

6X4X5^ 

14XH 

156.5 

59-5 

146.3 

847.9 

6X6XK2 

14X% 

154.9 

71.4 

225.0 

864.6 

6X6X5/^ 

14X% 

173.3 

59-5 

225.0 

878.8 

6X4X5/^ 

14XM 

156.5 

71.4 

146.3 

924.9 

6X6X5/^ 

14X^4 

173.3 

71.4 

225.0 

943.9 

6X4X% 

I4X% 

170.9 

71-4 

146.3 

999-3 

6X6X% 

I4X% 

191-3 

71.4 

225.0 

1045.9 

6X6XH 

i4Xi 

173.3 

95.2 

225.0 

1064.7 

6X4XM 

14X1 

170.9 

95.2 

146.3 

I  119. 3 

6X6X3/4 

I4XI 

191. 3 

95.2 

225.0 

I  126.3 

6X4X^ 

14X1 

185.3 

95.2 

146.3 

I  190. 1 

6X6XT^ 

14X1 

208.9 

95.2 

225.0 

390.2 

^X4X3/^ 

102.8 

101.3 

427. 5 

6X6X34 

113. 2 

157.5 

477.2 

6X4XH 

118. 4 

IOI.3 

527.2 

6X6XH 

132.0 

157. 5 

561.4 

6X4X^/6 

133.6 

101.3 

606.6 

.    6X4X% 

14X34 

102.8 

35.7 

101.3 

623.5 

6X6X5i 

ISO.  4 

157  5 

638.3 

6X4X5^ 

i6X^i 

102.8 

40.8 

101.3 

642.1 

6X4XM 

148.0 

101.3 

643.2 

6X6X34 

14X34 

113. 2 

35.7 

157. 5 

675.1 

42XH 

6X6X3/i 

i6X% 

113. 2 

40.8 

157. 5 

678.6 

6X4X'^^ 

14XK2 

102.8 

47.6 

101.3 

715.2 

6X6XH 

14X^4 

113. 2 

47.6 

157.5 

716.5 

6X6X94 

168.4 

157.5 

719.5 

6X4X% 

162.4 

101.3 

757.7 

6X6X% 

i6X^^ 

113.2 

54.4 

157.5 

763.7 

6X4X^4 

I4XV^ 

118. 4 

47.6 

101.3 

787.2 

6X6XH 

14X^4 

113. 2 

59-5 

157.5 

806.2 

6X4X5'^ 

16XH 

118. 4 

54.4 

101.3 

806.4 

6X6X^^ 

186.0 

157.5 

812.7 

6X6XK2 

UXH 

132.0 

47.6 

157.5 

*  From  Pocket  Companion,  Carnegie  Steel  Company  Pittsburgh,  Pa. 
t  For  explanation  of  table,  see  page  706. 


Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

Table  IV *t  (Continued).    Elements  of  Riveted  Plate  Girders 


Sizes 

Weight 

E)er  foot 

Maximum 
end- 

Section- 

Web- 

modulus, 

plate 
and 
flange- 
angles, 

reaction  in 

axis  i-i. 

Web- 

Flange- 

Flange- 

Flange- 

thousands 

in' 

plate, 
in 

angles, 
in 

plates, 
in 

plates, 
lb 

of 

pounds 

lb 

835. 5 

6X4X'/^ 

14X9^ 

118. 4 

59-5 

101.3 

855.2 

6X6XK2 

16XK2 

132.0 

54.4 

157.5 

884.2 

6X6X1^^2 

14X9^ 

132.0 

59-5 

157.5 

917.3 

6X4X)i 

14X9^ 

133.6 

59-5 

101.3 

937.3 

6X6XK2 

i6X9i 

132.0 

68.0 

157.5 

955.7 

6X6XH 

14X94 

132.0 

71-4 

157.5 

970.4 

6X4XH 

i6X9i 

133.6 

68.0 

101.3 

977.6 

exexH 

i4X9i 

150.4 

59.5 

157.5 

988.7 

6X4X^A 

14X94 

133.6 

71-4 

101.3 

I  030.8 

42X^4 

6X6XH 

16X9^ 

150.4 

68.0 

157.5 

1048.6 

6X6X'}i 

14X94 

150.4 

71.4 

157.5 

1066.6 

6X4X^4 

14X94 

148.0 

71.4 

101.3 

I  112. 4 

6X6X5^ 

16X94 

150.4 

81.6 

157.5 

I  130.4 

6X4X94 

16X94 

148.0 

81.6 

101.3 

1138.S 

6X6X% 

14X94 

168.4 

71-4 

157.5 

I  194. I 

6X6XH 

i6X7/^ 

150.4 

95.2 

157.5 

I  202.3 

6X6X94 

16X94 

168.4 

81.6 

157.5 

I  283.5 

6X6X)4 

16X74 

168.4 

95.2 

157-5 

I  286.4 

6X4Xli 

i6X^i 

162.4 

95.2 

101.3 

1369.9 

6X6XH 

i6X^i 

186.0 

95.2 

157.5 

495.3 

6X4XH 

127.3 

118. 1 

545.4 

6X6XK2 

140.9 

183.8 

579.5 

6X4X9^ 

142.^ 

118. 1 

641.6 

6X6XH 

159.3 

183.8 

660.2 

6X4X94 

156.9 

118. 1 

734.7 

6X6X)4 

*77.3 

183.8 

737.6 

6X4X^^ 

171. 3 

1x8. 1 

781.5 

6X4XK2 

14XK' 

127.3 

47.6 

118. 1 

824.0 

6X4XK2 

i6X3'2 

127.3 

54 

4 

118. 1 

824.6 

6X6X^s 

194.9 

183.8 

830.4 

6X6XK2 

14X^2 

140.9 

47 

6 

183.8 

853.1 

42XM6 

6X4X1/2 

i4X9i 

127.3 

59 

5 

118. 1 

872.9 

6X6XK2 

16XK2 

140.9 

54 

4 

183.8 

901.8 

6X6X1/^ 

i4X9i 

140.9 

59 

S 

183.8 

934.9 

6X4X9i 

14X96 

142.5 

59 

5 

118. 1 

954.9 

6X6X1/^ 

16X98 

140.9 

G3 

0 

183.8 

973.2 

6X6X1/^ 

14X94 

140.9 

71 

4 

183.8 

988.1 

6X4XH 

16X96 

142.5 

68 

0 

118. 1 

995.3 

6X6XH 

14X98 

159-3 

59 

5 

183.8 

I  006.2 

6X4X9^ 

14X94 

142.5 

71 

4 

118. 1 

I  048.4 

6X6XH 

16X96 

159-3 

68 

0 

183.8 

1066.2 

6X6X9i 

14X94 

159-3 

71 

4 

183.8 

I  084.1 

6X4X94 

14X94 

156.9 

71  4 

118.1 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 
t  For  explanation  of  table,  see  pago  706. 


Tables  Used  in  the  Design  of  Plate  and  Box  Girders         713 
Table  IV *t  (Continued).     Elements  of  Riveted  Plate  Girders 


Sizes 

Weight 

per  foot 

Maximum 
end- 

Section- 

Web- 

modulus, 

plate 
and 
flange- 
angles, 

reaction  in 

axis  i-i. 

Web- 

Flange- 

Flange- 

Flange- 

thousands 

in3 

plate, 

angles, 

plates, 

plates, 

of 

in 

in 

in 

lb 

pounds 

i6X% 

lb 

I  129.9 

6X6XH 

159-3 

81.6 

183.8 

I  147.9 

6X4X>4 

16X^/4 

156.9 

81.6 

118. 1 

I  156.0 

6X6XM 

I4X% 

177.3 

71-4 

183.8 

I  211. 6 

42X7/6 

6X6XH 

16X7/6 

159-3 

95-2 

183-8 

I  219.8 

6X6X)4 

i6X% 

177.3 

81.6 

183.8 

1300.9 

6X6X% 

i6X% 

177-3 

95-2 

183.8 

1387.3 

6X6Xj^6 

i6Xi^6 

194.9 

95.2 

183-8 

513  5 

6X4XH 

136.2 

135.0 

563.5 

6X6XK2 

149-8 

210.0 

597.7 

6X4X-H 

151. 4 

135-0 

659.8 

6X6XH 

168.2 

210.0 

678.4 

6X4X=^4 

165.8 

135  0 

752.8 

6X6X% 

186.2 

210.0 

755.8 

6X4X^i 

180.2 

I3S-0 

799.2 

6X4X5^^ 

14X1/^2 

136.2 

47-6 

135.0 

841.7 

6X4XK2 

16XM2 

136.2 

54-4 

135.0 

842.7 

6X6X7/i 

203.8 

210.0 

848.1 

6X6X'/2 

14XK2 

149-8 

47-6 

210.0 

870.8 

6X4XH 

14XH 

136.2 

59-5 

135.0 

890.6 

6X6XH 

16XH 

149-8 

54-4 

210.0 

919-4 

6X6X3'^    , 

14X^6 

149-8 

59-5 

210.0 

952.6 

6X4X^/6 

14XH 

151-4 

59-5 

135.0 

972.6 

42XK2 

6X6XH 

16XH 

149-8 

68.0 

210.0 

990.8 

6X6X3^^ 

I4X% 

149-8 

71-4 

2I0,0 

1005.7 

6X4XH 

16X^/6 

151. 4 

68.0 

135.0 

I  012.9 

'6X6X)6 

14XH 

168.2 

59-5 

210.0 

1023.7 

6X4X>i 

14XM 

151-4 

71.4 

135. 0 

I  066.0 

6X6XH 

16X-H 

168.2 

68.0 

210.0 

1083.7 

6X6XH 

14X3/4 

168.2 

71.4 

2IO.O 

I  101.7 

6X4XM 

I4X'% 

165.8 

71.4 

135.0 

I  147.5 

6X6XH 

16XM 

168.2 

81.6 

210.0 

I  165.4 

6X4X=H 

i6X% 

165.8 

81.6 

135.0 

I  173.6 

6X6X% 

i4X% 

186.2 

71.4 

210.0 

I  229.0 

6X6X)i 

16X^6 

168.2 

95-2 

210.0 

I  237.4 

6X6X-)4 

i6X% 

186.2 

81.6 

210.0 

I  318.4 

6X6  XK 

16X7/6 

186.2 

95.2 

210.0 

I  321.2 

6X4X^6 

16X3^6 

180.2 

95.2 

135.0 

I  4047 

6X6X^i 

16X^6 

203.8 

95.2 

210.0 

466.9 

6X4X3/i 

no. 4 

121. 5 

512.7 

6X6X3/6 

120.8 

180.0 

567.4 

4^X% 

6X4X^^ 

126.0 

121. 5 

628.9 

6X6XH 

139-6 

180.0 

664.9 

6X4XH 

141. 2 

121. 5 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 
t  For  explanation  of  table,  see  page  706. 


714  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

Table  IV  *t  (Continued).     Elements  of  Riveted  Plate  Girders 


Sizes 

Weight 

per  foot 

Maximum 
end- 

Section- 

Web- 

modulus, 

plate 
and 
flange- 
angles. 

reaction  in 

axis  i-i, 

Web- 

Flange- 

Flange- 

Flange- 

thousands 

in3 

plate, 
in 

angles, 
in 

plates, 
in 

plates, 
lb 

of 
pounds 

lb 

714.4 

6X4XK 

I4X?^ 

no. 4' 

35.7 

121. 5 

741-3 

6X6X5^ 

158.0 

180.0 

750.8 

cxaxh 

i6X3/^ 

no. 4 

40.8 

121. 5 

758. 5 

6XAXH 

155-6 

121. 5 

759-5 

6X6X% 

UXH 

120.8 

35.7 

180.0 

795-9 

6X6XH 

i6X% 

120.8 

40.8 

180.0 

797.0 

6X4XH 

14XM2 

no. 4 

47.6 

121. 5 

841.9 

6X6X% 

14XK2 

120.8 

47.6 

180.0 

848.3 

6X4X% 

170.0 

121. 5 

850.1 

6X6X% 

176.0 

180.0 

890.4 

6X6XH 

i6XJ/^ 

120.8 

54.4 

180.0 

895.5 

ex^xH 

UXH 

126.0 

47-6 

121. 5 

924.3 

0X6XH 

14XH 

120.8 

59-5 

180.0 

944-0 

6XaX^ 

16X1/2 

126.0 

54-4 

121.5 

955-2 

6xex% 

193-6 

180.0 

955 -8 

6X6X3'^ 

14X1/^ 

139-6 

47-6 

180.0 

977.7 

6X4X1/^ 

UX% 

126.0 

59-5 

121.5 

1004.3 

48X-K 

6X6XV2 

lexvz 

139-6 

54-4 

180.0 

1037-6 

6X6XV2 

ux% 

139.6 

59.5 

180.0 

1072.7 

6X4XH 

14XH 

141.2 

59.5 

121. 5 

1098.2 

6X6XH 

16XH 

139.6 

68.0 

180.0 

I  119-5 

6X6X1^ 

UXH 

139.6 

71.4 

180.0 

I  133-3 

6X4X^i 

lexH 

141.2 

68.0 

121. 5 

I  147- I 

6X6XH 

uX^A 

158.0 

59.5 

180.0 

I  154.4 

6X4XH 

14XM 

141. 2 

71.4 

121. 5 

I  207.8 

6X6X5;^ 

16XH 

158.0 

68.0 

180.0 

I  228.4 

6X6XH 

I4X% 

158.0 

71.4 

180.0 

I  245.2 

6X4X% 

14X3/4 

155. 6 

71.4 

121.5 

I  301.2 

6X6XH 

i6X% 

158.0 

81.6 

180.0 

I  317.9 

6X4X% 

i6XH 

155.6 

81.6 

121. 5 

1334.0 

6X6X% 

14X^1 

176.0 

71.4 

180.0 

1394.7 

6X6XH 

i6X^i 

158.0 

95.2 

180.0 

I  406.7 

6X6X% 

16XM 

176.0 

81.6 

180.0 

1498.1 

6X4X^6 

i6X7/i 

170.0 

95-2 

121.5 

1499-7 

6X6X3/i 

16X^6 

176.0 

95-2 

180.0 

I  601.3 

6X6X^6 

i6X^i 

193.6 

95-2 

180.0 

591 -2 

6X4XH 

136.2 

141. 8 

652.7 

6X6X1/^ 

149 -8 

210.0 

688.7 

6X4XH 

151. 4 

141.8 

765 -0 

48XM6 

6X6X5/^ 

168.2 

210.0 

782.3 

6X4X3/1 

165.8 

141. 8 

872.1 

6X4X7/6 

180.2 

141.8 

873-8 

6X6X% 

186.2 

210.0 

•  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 
t  For  explanation  of  table,  see  page  706. 


Tables  Used  in  the  Design  of  Plate  and  Box  Girders         715 
Table  IV  *t  (Continued).     Elements  of  Riveted  Plate  Girders 


Sizes 

Weight 

per  foot 

Maximum 

Section- 

Web- 

end- 

modulus, 

plate 
and 
flange- 
angles. 

reaction  in 

axis  I -I, 

Web- 

Flange- 

Flange- 

Flange- 

thousands 

in3 

plate, 

angles, 

plates, 

plates, 

of 

in 

in 

in 

lb 

pounds 

lb 

918.8 

6X4X^2 

14  X'/ 

136.2 

47-6 

141. 8 

967.3 

6X4X^/^ 

16XH 

136.2 

54-4 

141. 8 

979.0 

6X6X^4 

203.8 

210.0 

979 -o 

6X6XK2 

14X/2 

149.8 

47.6 

210.0 

I  000.8 

6X4X1/2 

i4X)6 

136.2 

59. 5 

141. 8 

I  027  ■  6 

6X6XK2 

16X1/ 

149.8 

54.4 

210.0 

1060.8 

6X6X'/2 

I4X-H 

149-8 

59.5 

210.0 

1095.8 

6X4XH 

14XH 

151. 4 

59.5 

141 -8 

I  121. 4 

6X6X^^ 

16X5/6 

149-8 

68.0 

210.0 

I  142.5 

6X6XH 

14X^4 

149-8 

71.4 

210.0 

I  156.5 

6X4XS/i 

16X5/6 

15I-4 

68.0 

141. 8 

I  170.3 

48XM6 

6X6XH 

14XH 

168.2 

59.5 

210.0 

I  177.4 

6X4XH 

14XM 

151-4 

71.4 

141 -8 

I  230.9 

6X6X% 

i6X-)6 

168.2 

68.0 

210.0 

1251.5 

6X6XM 

14XK 

168.2 

71.4 

210.0 

1268.2 

6X4XU 

i4X)4 

165.8 

71.4 

141. 8 

1324  3 

6X6XH 

i6X-)4 

168.2 

81.6 

210.0 

I  341.0 

6X4X% 

i6X% 

165.8 

81.6 

141. 8 

1357.0 

6X6X-M 

I4X-M 

186.2 

71.4 

210.0 

I  417.7 

6X6X5/6 

16X7/ 

168.2 

95.2 

210.0 

I  429.8 

6X6XM 

16XM 

186.2 

81.6 

210.0 

I  521.0 

6X4X7/6 

16X7/ 

180.2 

95.2 

141. 8 

1522.7 

6X6X3/4 

16X7/6 

186.2 

95.2 

210.0 

I  624 . 2 

6X6X3^6 

16X7/ 

203.8 

95-2 

210.0 

615.0 

6X4XH 

146.4 

162.0 

676.4 

6X6XK2 

160.0 

240.0 

712.4 

6X4X% 

161. 6 

162.0 

788.8 

6X6X^6 

178.4 

240.0 

806.0 

6X4X% 

176.0 

162.0 

■    895.8 

6X4X7/6 

190.4 

162.0 

897.6 

6X6X% 

196.4 

240.0 

942.1 

6X4XK2 

14X1/ 

146.4 

47-6 

162.0 

990.6 

6X4X1/2 

16XH 

146.4 

54.4 

162.0 

I  002.3 

48X'/2 

6X6X/2 

14X1/2 

160.0 

47.6 

240.0 

I  002.7 

6X6X7/6 

214.0 

240.0 

I  024.0 

6X4X/2 

14X5/6 

146.4 

59-5 

162.0 

I  050 . 8 

6X6XH 

16x1/2 

160.0 

54-4 

240.0 

1083.9 

6X6X1/ 

14X5/6 

160.0 

59-5 

240.0 

I  119. 0 

6X4X% 

14XH 

161. 6 

59.5 

162.0 

I  144.5 

6X6X/2 

16X5/ 

.     160.0 

68.0 

240.0 

I  165.6 

6X6X1/ 

14X3/4 

160.0 

71.4 

240.0 

I  179.6 

6X4X5/6 

16X5/6 

161. 6 

68.0 

162.0 

I  193.4 

6X6X5/ 

UXH 

178.4 

59.5 

240.0 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa. 
t  For  explanation  of  table,  see  page  706. 


716  Riveted  Steel  Plate  and  Box  Girders  Chap.  20 

Table  IV *t  (Continued).     Elements  of  Riveted  Plate  Girders 


Sizes 

Weight 

per  foot 

Maximum 
end- 

Section- 

Web- 

modulus, 

plate 
and 
flange- 
angles. 

reaction  in 

axis  i-i. 

Web- 

Flange- 

Flange- 

Flange- 

thousands 

ins 

plate, 
in 

angles, 
in 

plates, 
in 

plates, 
lb 

of 
pounds 

lb 

I  200.5 

• 

161. 6 

71.4 

162.0 

6X4X-H 

14XK 

1254. 1 

6X6XH 

16XH 

178.4 

68.0 

240.0 

I  274.5 

6X6XH 

14  XK 

178.4 

71^4 

240.0 

I  291 . 2 

6X4X->4 

14XK 

176.0 

71.4 

162.0 

I  347.3 

6X6XH 

i6X>4 

178.4 

81.6 

240.0 

1  364.0 

48XI/2 

6X4  X}4 

16X3/1 

176.0 

81.6 

162.0 

I  380.0 

6X6X% 

14X^/4 

196.4 

71.4 

240.0 

I  440.6 

6X6XH 

i6X^/i 

178.4 

95.2 

240.0 

1452.8 

6X6X^1 

i6X)i 

196.4 

81.6 

240.0 

1543.9 

6X4Xj^^ 

i6Xli 

190.4 

95.2 

162.0 

I  545.6 

6X6X% 

i6X% 

196.4 

95.2 

240.0 

I  647.1 

6X6X^4 

i6X% 

214.0 

95.2 

240.0 

*  From  Pocket  Companion,  Carnegie  Steel  Company,  Pittsburgh,  Pa, 
t  For  explanation  of  table,  see  page  706. 


Layout  of  Floor-Framing  717 


CHAPTER  XXI 

STRENGTH  AND   STIFFNESS  OF  WOODEN  FLOORS 

By 
THOMAS  NOLAN 

PROFESSOR  OF  ARCHITECTURAL  CONSTRUCTION,  UNIVERSITY  OF  PENNSYLVANIA 

The  Problems  Stated.  The  problems  which  are  presented  in  this  part  of 
building-construction  are,  in  general,  (i)  the  designing  of  the  joists  and  girders 
forming  the  framework  of  the  floor  to  safely  support  the  greatest  load  likely  to 
come  upon  it,  and  (2)  the  determination  of  the  maximum  safe  load  for  a  floor 
already  built.  The  first  of  these  problems  is  the  one  with  which  architects 
and  builders  more  commonly  have  to  deal,  and  is,  therefore,  considered  first. 

Layout  of  the  Floor-Framing.  Before  any  calculations  can  be  made  for 
the  sizes  of  the  timbers  it  is  necessary  to  know  the  spans  of  the  joists,  and,  if 
there  are  openings  in  the  floor,  or  the  floor-joists  have  to  support  longitudinal 
partitions,  a  framing-plan  should  be  made,  showing  the  floor-area  that  will 
be  supported  by  each  joist,  and  also  the  position  of  partitions  or  special  loads. 
If  the  floor  is  to  be  supported  by  posts  and  girders  the  position  of  these  should 
also  be  accurately  indicated  on  the  framing-plan.  Where  the  joists  are  sup- 
ported entirely  by  walls  or  partitions,  the  spans  of  the  joists  will  of  course  be 
fixed  by  the  plan  of  the  building.  When  the  distance  between  a  wall  and  a 
partition  is  too  great  for  a  single  span,  there  may  be  a  question  as  to  the  best 
locations  for  the  posts  and  girders.  When  planning  a  building  in  which  wooden 
joists  are  to  be  used,  it  is  important  to  keep  in  mind  the  general  scheme  of  the 
floor-framing  and  particularly  the  spans.  Whenever  practicable  the  spans  of 
wooden  joists  should  not  exceed  24  ft.  When  the  distance  between  the  sup- 
porting waUs  exceeds  30  ft,  girders  should  be  placed  so  that  the  maximum  span 
of  the  joists  will  not  exceed  24  ft  for  light  buildings  nor  from  16  to  18  ft  for 
warehouses. 

In  School  Buildings  it  is  desirable  to  have  the  rooms  at  least  27  ft  wide,  and 
hence  in  this  class  of  buildings  the  joists  usuaUy  have  spans  of  from  27  to  30  ft. 
For  a  span  of  30  ft,  however,  16- in  joists  should  be  used,  and  as  these  are  expen^ 
sive,  and  often  diflicult  to  obtain,  it  is  much  better  and  more  economical  to 
make  the  schoolrooms  27  by  32  or  34  ft,  than  to  make  them  30  ft  square.  A 
schoolroom  27  ft  wide  by  from  32  to  34  ft  long,  with  windows  on  the  long  side, 
only,  is  economical  and  satisfactory,  as  it  permits  of  using  3  by  14-in  joists, 
28  ft  long,  and  also  results  in  the  most  satisfactory  lighting. 

Continuous  Joists.  When  joists  are  supported  by  a  girder  placed  so  that  a 
24-ft  or  26-ft  joist  extends  over  the  two  spans,  it  is  always  better  to  have  the 
joists  continuous  over  the  girder,  as  by  that  construction  they  make  a  much 
stiffer  floor.     (See  Chapter  XIX.) 

Floor-Loads.  Having  decided  on  the  arrangement  of  the  joists,  and  drawn 
a  framing-plan  showing  the  spaa  and  the  locations  of  all  special  timbers,  the 


718 


Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 


next  step  involves  the  determination  of  the  loads  for  which  the  joists  and  girders 
are  to  be  proportioned.  Floor-loads  are  made  up  of  two  parts,  the  weight  of 
materials  composing  the  floor  itself,  and  the  ceiling  below,  if  there  is  one;  and 
the  load  liable  to  be  put  on  the  floor.  The  first  is  called  the  dead  load,  and 
the  second  the  live  load.  When  the  safe  load  for  a  floor  is  spoken  of  the 
^live  load  is  generally  meant. 

Weight  of  "Wooden  Floor-Construction.  Wooden  floors  usually  consist  of 
(i)  beams,  commonly  called  joists,*  or  floor- joists,  (2)  one  or  two  thcknesses 
of  flooring-boards,  and,  in  a  finished  building,  (3)  a  ceiling  underneath  the 
joists.  In  figuring  the  weight  of  %-in  flooring-boards  it  will  be  sufliciently 
accurate  to  estimate  the  weight  of  a  single  thickness  at  3  lb  per  sq  ft.  The 
joists  may  also  be  figured  at  3  lb  per  ft,  board-measure,  with  the  exception  of 
hard-pine  and  oak  joists,  which  should  be  figured  at  4  lb  per  ft,  board-measure. 
The  weight  of  the  joists  must  also  be  reduced  to  their  equivalent  weight  per 
square  foot  of  floor.  Thus,  the  weight  of  a  2  by  12-in  joist  is  about  6  lb  per  lin 
ft.  If  the  joists  are  spaced  12  in  on  centers,  this  will  be  equal  to  6  lb  per  sq  ft; 
but  if  the  joists  are  16  in  on  centers  there  will  be  but  one  lineal  foot  of  joist 
to  every  iH  sq  ft,  which  will  be  equivalent  to  4li  lb  per  sq  ft;  and  if  they  are 
20  in  on  centers,  the  weight  will  be  equal  to  3H  lb  per  sq  ft;  spaced  24  in  on 
centers,  the  weight  wiU  be  3  lb  per  sq  ft.  The  weight  of  a  lath-and-plaster 
ceiling  should  be  taken  at  10  lb  per  sq  ft,  and  of  a  ^4 -in  wooden  ceiling  at  2I/2  lb 
per  sq  ft.  A  corrugated-iron  ceiling  weighs  about  i  lb  per  sq  ft.  For  stamped- 
steel  ceilings,  2  lb  per  sq  ft  will  cover  the  weight  of  the  metal  and  furring.  The 
following  table,  giving  the  weight  of  joists,  wiU  be  found  convenient  in  figuring 
the  weight  of  floors: 


Table  I.    Weight  of  Floor- Joists  per  Square  Foot  of  Floor 


Sizes  of  joists 


Spruce,  hemlock, 
white  pine 


Spacing  in  inches, 
center  to  center 


Hard  pine  or  oak 


Spacing  in  inches, 
center  to  center 


16 


2X  6. 
2X  8. 
3X  8. 
2X10. 
3X10. 
2X12. 
3X12. 
2X14. 
3X14. 


lb 


lb 


3 

4 

6 

5 

7H 

6 

9 

7 


2H 
3 

4H 
3H 

sH 

6H 


4 


6% 


m 
14 


3 
4 

6 

S 

7H 

6 

9 

7 

lOl/^ 


Weight  of  Crowds.    I    J.  Johnson  reports  f  results  of  some  tests  to  ascer- 
tain the  weight  of  crowds  ot  men,  in  which  he  obtained  weights  of  154.2,  143.9, 

*  Some  building  laws  use  the  term  floor -beam;  in.ste?Ld[  of  the  word  joist. 
\  See  Engineering  News,  April  14,  1904. 


Loads  on  Floors 


719 


148.1  and  156.9  lb  per  sq  ft.  The  last-mentioned  weight  was  obtained  by  pack- 
ing 67  men  in  a  room  about  6  by  11  ft  in  size.  Professor  Johnson  also  found 
that  with  50  men  in  the  room,  making  a  load  of  122  lb  per  sq  ft,  the  crowd  was 
compacted  "so  that  a  man  could  elbow  his  way  through  it  only  with  persever- 
ance and  determined  effort." 

Superimposed  Loads.  There  is  much  difference  of  opinion  as  to  what. 
allowance  should  be  made  for  the  live  load.  Table  II  shows  the  minimum 
allowance  for  live  loads  for  different  classes  of  buildings,  as  fixed  by  the  build- 
ing laws  of  the  cities  mentioned.     (See,  also,  page  149.) 


Table  11.     Minimum  Safe  Superimposed  Loads  for  Floors,  Required  by 
Various  Building  Laws 


Classes  of  buildings 


Dwellings 

Hotels,  tenements  and  lodg- 
ing-houses  

Office-buildings 

Buildings  for  public  assembly 

Stores,  warehouses  and  mfg. 
bldgs 


Minimum  live  load  per  square  foot  of  floor 


Buffalo,  Boston, 
1905         191S 


70 
70 
100 

I20t 


SO 
80 
100 

I25t 


lOOj 


Phila- 
delphia, 
914 


70 
100 
120 

I20t 


New 

York, 

1917 


40 

60 
60* 
100 

I20t 


St. 

Louis, 
1910 


60 

60 

70* 

loot 

isot 


■*  First  floor,  150  lb.  f  Also  sch6olhouses.  J  And  upwards. 

It  was  the  opinion  of  Mr.  Kidder  that  the  following  allowances  for  floor-loads, 
taken  in  connection  with  the  values  given  for  the  safe  strength  of  joists  or  beams, 
provide  absolute  safety  with  proper  allowance  for  economy. 

Lb  per 
sq  ft 

For  dwellings,  sleeping-rooms  and  lodging-rooms 40 

For  schoolrooms 50 

For  office-buildings,  upper  stories 60 

For  office-buildings,  first  story 80 

For  stables  and  carriage-houses 65 

For  banking-rooms,  churches  and  theaters 80 

For  assembly-halls,  dancing-halls  and  the  corridors  of  all  public 

buildings,  including  hotels 120 

For  drill-rooms 150 

Live  Loads  for  Stores  and  Buildings  for  Light  Manufacturing.  Floors  for 
ordinary  stores,  light  manufacturing  and  light  storage  should  be  computed  for 
not  less  than  120  lb  per  sq  ft,  and  for  a  concentrated  load  at  any  point  of 
4  000  lb. 

Live  Loads  for  Dwellings,  etc.  Floors  of  dwellings,  tenements,  lodging-houses 
and  rooms  in  hotels,  are  seldom  loaded  with  more  than  20  lb  per  sq  ft  for  the 
entire  area,  and  a  minimum  load  of  40  lb  per  sq  ft  should  provide  for  all 
possible  contingencies. 


720  Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 

Live  Loads  for  Office-BuUdings.  The  floors  of  offices  are,  as  a  rule,  not  more 
heavily  loaded  than  the  floors  of  dwellings,  but  the  possibilities  for  increased 
loads  from  safes  and  heavy  furniture,  and  possibly  from  a  more  compact  crowd 
of  people,  are  greater,  so  that  the  minimum  floor-load  for  offices  should  be  some- 
what increased.  Some  years  ago  the  firm  of  Blackall  &  Everett,  in  Boston, 
found  that  the  average  live  load  in  210  offices,  in  three  prominent  office-buildings 
in  that  city,  was  between  16  and  17  lb  per  sq  ft,  while  the  average  load  for  the  10 
heaviest  office-buildings  was  33.3  lb  per  sq  ft.  As  such  loads,  however,  are  as 
a  rule  unevenly  distributed,  some  portions  of  the  floor  being  generally  much 
more  heavily  loaded  than  others,  it  would  not  appear  to  be  safe  to  use  this 
average  to  determine  the  strength  of  floor-beams  and  floor-arches,  although  it 
would  probably  answer  for  the  columns.  There  seems  to  be  a  considerable  differ- 
ence of  opinion  among  the  leading  architects  and  structural  engineers  as  to  just 
what  allowance  should  be  made  for  office-floors.  Among  some  of  the  earlier 
fire-proof  office-buildings,  for  example,  may  be  mentioned  the  former  Mills 
Building  in  San  Francisco  in  which  the  five  loads  were  assumed  at  40  lb  per  sq 
ft  for  all  floors  above  the  first.  In  the  Venetian  Building,  Chicago,  the  second, 
third  and  fourth  floors  were  calculated  for  60,  and  the  upper  floors  for  35  lb  per 
sq  ft  of  live  load,  while  in  the  Old  Colony  and  Fort  Dearborn  Buildings  in 
Chicago,  the  five  loads  on  the  floor-beams  were  assumed  at  70'  lb  per  sq  ft. 
At  the  present  time  (1915),  50,  60,  70,  75,  100  and  150  lb  per  sq  ft  are  the 
minimum  live  loads  for  the  design  of  floors  of  office-buildings  required  by  the 
building  laws  of  six  different  cities.  C.  C.  Schneider  recommends*  for  the 
design  of  floors  of  office-buildings  above  the  first  floor,  for  the  uniform  load 
of  the  floor-area,  50;  for  concentrated  loads  applied  at  any  point  of  the  floor, 
5  000;  and  for  the  uniform  load  for  girders,  i  000;  the  50  being  in  pounds  per 
sq  ft,  the  5  000  in  pounds  and  the  i  000  in  pounds  per  linear  foot. 

Live  Loads  for  Churches,  Theaters  and  School-Houses.  ''An  allowance  of 
120  lb  per  sq  ft  for  the  live  load  in  churches,  theaters  and  school-houses  is  much 
greater  than  the  actual  conditions  reciuire.  The  average  size  of  a  schoolroom 
is  about  28  by  32  ft,  and  such  a  room  usually  contains  seats  for  fifty-six  scholars 
and  the  teacher.  Assuming  the  average  weight  of  each  scholar  at  120  lb,  the 
average  live  load,  including  ten  visiting  adults  and  the  desks  and  furniture,  is 
13  lb  per  sq  ft.  Even  supposing  that  the  scholars  of  two  rooms  were  united 
for  some  special  occasion,  there  would  be  only  22  lb  per  sq  ft;  and  this  is  as 
great  a  load  as  it  is  possible  to  imagine  in  such  a  room,  as  the  fixed  desks  prevent 
the  crowding  together  of  the  scholars  except  at  the  sides  of  the  room.  From 
this  reasoning,  therefore,  50  lb  per  sq  ft  would  appear  ample  for  schoolrooms. 
As  a  matter  of  fact,  3  by  14-in  long-leaf  yellow-pine  joists,  16  in  on  centers 
and  with  a  28-ft  span,  have  been  used  for  school-room  floors  for  years;  but 
such  beams,  if  calculated  by  the  formula  for  stiffness,  would  support  a  live 
load  of  only  43  lb  per  sq  ft.  (Table  XII,  page  643  and  Table  I,  page  718.) 
The  minimum  floor-space  allotted  to  a  single  seat  in  theaters  is  4  sq  ft,  while 
the  average  is  about  5  sq  ft.  Assuming  the  weight  of  an  opera-chair  at  35  lb 
and  of  the  average  adult  at  140  lb,  a  liberal  allowance,  there  results  an  average 
of  44  lb  per  sq  ft  of  floor.  A  minimum  of  80  lb  per  sq  ft  would  therefore  seem 
to  provide  for  any  possible  crowding  during  a  panic,  except  in  corridors.  On 
the  other  hand,  it  has  been  shown  (see  Weight  of  Crowds,  page  718)  that  a 
crowd  of  able-bodied  men  may  result  in  a  load  of  about  120  lb  per  sq  ft,  and 
this  should  be  the  minimum  for  assembly-halls  without  fixed  desks  and  also  for 
the  corridors  of  all  public  buildings.  For  armories,  the  minimum  load  should 
be  increased  on  account  of  the  vibration. "  f 

*  "General  Specifications  for  Structural  Work  of  Buildings,"  19 10,  page  57. 
t  F.  E.  Kidder. 


Weights  of  Merchandise 


721 


The  Average  Floor-Loads  for  Stores  has  also  been  greatly  over-estimated. 
W.  L.  B.  Jenney  found  that  the  average  load  on  the  floors  of  the  wholesale  ware- 
house of  Marshall  Field  &  Company,  in  Chicago,  was  but  50  lb  per  sq  ft,  and 
very  few  retail  stores  will  average  over  80  lb  per  sq  ft.  An  allowance  of  1 20  lb 
per  sq  ft  is  suflicient  for  ordinary  retail  stores,  with  the  possible  exception  of 
hardware  stores. 

Live  Loads  for  Warehouses.  Warehouses,  on  the  other  hand,  may  be  very 
heavily  loaded,  and  the  floors  in  buildings  intended  for  the  storage  of  merchan- 
dise should  be  prorx)rtioned  to  the  especial  class  of  goods  which  they  are  de- 
signed to  support.  Table  III,  originally  compiled  by  C.  J.  H.  Woodbury,* 
and  to  which  some  additions  have  been  made  by  the  Insurance  Engineering 
Experiment  Station  and  by  Mr.  Kidder,  will  be  found  of  assistance  in  deciding 
upon  the  live  load  to  be  assumed  for  warehouse-floors.  The  weights  per  square 
foot  are  for  single  packages.  If  the  goods  are  piled  two  or  more  cases  high, 
the  weight  per  square  foot  of  floor  will  of  course  be  increased  accordingly.  In 
fact,  the  height  to  which  the  goods  are  liable  to  be  piled  is  a  very  important  con- 
sideration in  fixing  upon  the  floor-load.  In  Table  III  "the  measurements  were 
always  taken  to  the  outside  of  case  or  package,  and  gross  weights  of  such  pack- 
ages are  given. " 

Methods  of  Determining  the  Sizes  of  Joists,  Beams  or  Girders  Re- 
quired for  Any  Building.  As  already  explained,  the  first  step  is  the  making 
of  a  framing-plan  of  the  floors  or  enough  of  it  to  show  any  special  framing 
and  also  the  span  and  floor-area  supported  by  the  different  joists,  beams 
or  girders. 


Table  III.    Weights  of  Merchandise 


Materials 


Measurements 


Floor- 
space, 
sq  ft 


Con- 
tents, 
cu  ft 


Weights 


Total, 
lb 


Per 

sq  ft 


Per 

cuft 


Wool 


Bale,  East  India 

Bale,  Australia 

Bale,  South  America. . 

Bale,  Oregon 

Bale,  California 

Bag,  wool 

Stack  of  scoured  wool . 


30 
5.8 
7.0 
6.9 

7.5 
5.0 


12.0 
26.0 
340 
33  o 
330 
30.0 


340 
385 
I  000 
482 
550 
200 


113 
66 
143 

70 
73 
40 


IS 
29 
15 
17 
7 
5 


Woollen  Goods 


Case,  flannels 

Case,  flannels,  heavy., 

Case,  dress  goods 

Case,  cashmeres 

Case,  underwear 

Case,  blankets 

Case,  horse-blankets.  . 


S-S 

12.7 

220 

40 
46 

71 

IS. 2 

330 

5.5 

22.0 

460 

84 

10.5 

28.0 

5S0 

52 

7-3 

21.0 

350 

48 

10.3 

3S..0 

450 

44 

4.0 

14.0 

250 

63 

16 
13 
18 


'  The  Fire  Protection  of  Mills,  page  118. 


722  Strength  and  Stiffness  of  Wooden  Floors  Chap.  21 

Table  III  (Continued).     Weights  of  Merchandise 


Materials 


Measurements 


Floor- 
space, 
sq  ft 


Con- 
tents, 
cuft 


Weights 


Total, 
lb 


Per 

sqft 


Cotton,  Etc 


Bale 

Bale,  compressed 

Bale,  American  Cotton  Co 

Bale,  Planters'  Compressed  Co, 

Bale,  jute 

Bale,  jute  lashings 

Bale,  manila 

Bale,  hemp 

Bale,  sisal 


8.1 

44.2 

515 

64 

41 

21.6 

550 

134 

4.0 

II. 0 

263 

66 

2.3 

7.2 

254 

no 

2.4 

9-9 

300 

1 25 

2.6 

I0.5 

450 

172 

3-2 

10.9 

280 

88 

8.7 

34.7 

700 

81 

53 

17.0 

400 

75 

Cotton  Goods 


Bale,  unbleached  jeans. . . 

Piece  duck 

Bale,  brown  sheetings. . . . 
Case,  bleached  sheetings . 

Case,  quilts 

Bale,  print  cloth 

Case,  prints 

Bale,  tickings 

Skeins,  cotton  yarn 

Burlaps 

Jute  bagging 


3.6 
4.8 
7.2 
4.0 
4.5 
3.3 


300 
75 
235 
330 
295 
175 
420 
325 

130 

100 


72 
68 
65 
69 
41 
44 
93 
99 


Rags  in  Bales 


White  linen .... 
White  cotton . . . 
Brown  cotton .  . 
Paper  shavings. 

Sacking 

Woollen 

Jute  butts 


8.5 

39-5 

910 

107 

9-2 

40.0 

715 

78 

7.6 

30.0 

442 

59 

7-5 

340 

507 

68 

16.0 

65.0 

450 

28 

7.5 

30.0 

600 

80 

2.8 

II. I 

40c 

143 

Paper 


Calendered  book 

Supercalendered  book . 

Newspaper 

Strawboard . . . 

Leather-board.  .^ 

Writing 

Wrapping 

Manila 


Weights  of  Merchandise 
Table  III  (Continued).     Weights  of  Merchandise 


Materials 


Measurements 


Floor- 
space, 

sq  ft 


Con- 
tents, 
cu  ft 


Weights 


Total, 
lb 


Per 

sq  ft 


Grain  ' 


Wheat,  in  bags 

Wheat,  in  bulk 

Wheat,  in  bulk 

Wheat,  in  bulk mean 

Barrels,  flour,  on  side 

Barrels,  flour,  on  end 

Corn,  in  bags 

Cornmeal,  in  barrels 

Oats,  in  bags 

Bale  of  hay 

Hay,  Dederick,  compressed 

Straw,  Dederick,  compressed. . . . 

Tow,  Dederick,  compressed 

Excelsior,  Dederick,  compressed. 
Hay,  loo.se 


4.1 
3.1 
3.6 
3-7 
3-3 
5.0 
1.75 
1-75 
1.75 
1,75 


5.4 
7-1 
3.6 
5.9 
3.6 

20.0 

5.25 
5.25 
5.25 
5.25 


2i8 
2i8 

112 
2l8 

96 
284 
125 
100 
150 
100 


39 


53 

70 
31 
59 
29 
57 
72 
57 
86 
57 


Dyestuffs,  Etc 


Hogshead,  bleaching  powder. 

Hogshead,  soda-ash 

Box,  indigo 

Box,  cutch 

Box,  sumac 

Caustic  soda  in  iron  drum 

Barrel,  starch 

Barrel,  pearl-alum 

Box,  extract  logwood 

Barrel,  lime 

Barrel,  cement,  American. . .  . 

Barrel,  cement,  English 

Barrel,  plaster 

Barrel,  rosin 

Barrel,  lard-oil , 

Rope 


11.8 

39-2 

I  200 

102 

10.8 

29.2 

T^T 

128 

3.0 

9.0 

385 

4.0 

3.3 

150 

38 

1.6 

4-1 

160 

100 

4.3 

6.8 

600 

140 

3.0 
3.0 

10.5 

250 

83 

10.5 

350 

117 

1.06 

0.8 

55 

52 

3.6 

4-5 

225 

63 

3.8 

5.5 

325 

86 

3.8 

5.5 

400 

105 

3.7 

6.1 

325 

88 

3-0 

9.0 

430 

143 

4-3 

12.3 

422 

98 

MlSCELL.^NEOUS 


Box,  tin 

Box,  glass 

Crate,  crockery 

Cask,  crockery 

Bale,  leather 

Bale,  goatskins 

Bale,  raw  hides 

Bale,  raw  hides,  compressed. 

Bale,  sole-leather 

Pile,  sole-leather 

Barrel,  granulated  sugar 

Barrel,  brown  sugar 

Cheese 


2.7 


9-9 
13-4 

7-3 
II. 2 

6.0 
6.0 
12.6 


3.0 
3-0 


0 

5 

39 

6 

42 

5 

12 

2 

16 

7 

30 

0 

30 

0 

8 

9 

7 

5 

7 

5 

139 

99 

I  600 

162" 

600 

52 

190 

26 

300 

27 

400 

67 

700 

117 

200 

22 

317 

106 

340 

113 

*  For  pressure  of  grain  in  deep  bins,  see  Engineering  News,  March  10,  1904,  pages  224 
and  336,  and  Dec.  15.,  1904. 


724  Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 

The  second  step  is  to  determine  approximately  the  weight  of  the  floor  and  ceil- 
ing, and  decide  what  superimposed  load  per  square  foot  the  floor  is  to  be  designed 
to  carry.  Having  done  this,  the  next  step  is  the  computing  of  the  required 
dimensions  of  the  common  floor-joists.  For  most  buildings  the  size  of  floor- 
joists  required  can  be  readily  determined  by  reference  to  Tables  XIII  to  XVII, 
inclusive,  and  XXII  to  XX \T,  inclusive,  of  this  chapter.  For  other  floor-loads 
the  sizes  of  the  common  joists  may  be  determined  by  computing  the' load  to 
be  supported  by  a  single  joist  and  then,  l^y  the  formulas  or  tables  in  Chapter 
XVI  or  the  formulas  in  Chapter  XVIII,  determining  the  dimensions  of  tHe  joists 
to  support  that  load.  (See  Example  i.)  P'or  the  floors  of  all  buildings  except 
stores  and  warehouses  it  is  recommended  that  the  sizes  of  the  common  joists 
be  determined  by  the  formulas  for  stiffness  in  Chapter  XVIII  or  the  stiffness- 
values  in  the  tables  in  Chapter  XVI,  unless  one  value,  only,  is  given  in  tables 
for  safe  loads,  in  which  case  that  value  may  be  used.  For  stores  and  ware- 
houses the  sizes  of  the  joists  may  be  proportioned  by  the  formulas  or  strength- 
values  of  the  tables  in  Chapter  XVI. 

The  Dimensions  of  Special  Beams,  such  as  headers,  trimmers  and  beams  sup- 
porting partitions,  and  also  of  the  girders,  should  be  determined  in  the  same 

way,  that  is,  by  comput- 
W;^      ing   the  maximimi   load 
___^p      the  beam  may  have  to 
Wm      support,    and   then    the 
^^--^^      dimensions    of    a    beam 
ym/-       that    will    support    that 
^p      load    with   safety.     The 
Zm       manner  of    making   the 
^p       computations  is  ex- 
^p       plained  in  the  following 
~^^M.      examples. 
:==:^P  Example  i.     The  sim- 

.-^^.  plest  type  of  floor-fram- 
^^  ing  is  that  shown  in  Fig. 
1,  in  which  all  of  the 
joists  are  of  the  same 
span  and  support  equal  floor-areas.  In  such  a  floor,  the  floor-area  sup- 
ported by  each  joist  is  equal  to  the  span,  L,  multiplied  by  the  spacing,  5,  in 
feet.  The  load  on  each  joist  is  equal  to  the  floor-area  multiplied  by  the 
sum  of  the  dead-loads  and  superimposed  or  live  loads.  To  show  the  applica- 
tion of  the  above-mentioned  formulas  and  tables  we  will  assume  that  Fig.  I 
represents  the  framing  of  a  floor  in  a  dwelling-house  or  lodging-house,  that 
L  =  i8  ft,  5  =  1 6  in  or  I H  ft,  and  that  the  timber  is  common  white  pine.  The 
joists  are  to  support  a  plastered  ceiling  and  a  double  floor  of  ^i-in  boards. 
What  should  be  the  size  of  the  joists;   average  quality,  conditions  not  ideal? 

Solution.  The  floor-area  supported  by  each  joist  is  iH  by  i8,  or  24  sq  ft. 
From  Table  XIII  or  XXII,  pages  737  and  742,  for  a  span  of  18  ft,  the  joists 
will  probably  have  to  be  at  least  2  by  12  in,  and  their  weight  will  be  about  \Vi.  lb 
per  sq  ft  (see  Table  I,  page  718).  The  plastered  ceiling  weighs  about  10  lb  and 
the  flooring  6  lb  per  sq  ft,  making  the  total  weight  of  the  floor  20V2  lb  per  sq  ft. 
For  the  superimposed  load  we  should  allow  at  least  40  lb  per  sq  ft  (see  page 
719).  This  might  be  greater,  if  exacted  by  any  particular  building  law.  The 
load  on  a  single  joist  will,  therefore,  be,  with  these  assumed  unit  loads,  ^oVi  lb 
by  24  sq  ft,  or  i  452  lb. 

From  Table  VIII,  page  639,  we  find  that  the  maximum  load  for  a  i  by 


* 


^ 


Fig.  1.     Plan  of  Floor-joists 


Computations  for  Wooden  Beams  and  Girders 


725 


i2-in  white-pine  joist  of  i8  ft  span  is  623  lb;  hence  to  support  i  452  lb  will 
require  a  breadth  equal  to  1452/623  =  2^''^  in.  Therefore,  to  comply  with  the 
requirements  for  both  strength  and  stiffness,  the  joists  should  be  2H  by  12  in. 
This  is  not  a  stock  size.  Joists  2  by  12  in,  12  in  on  centers,  may  next  be 
tried.  Each  joist  must  support  i  116  lb,  requiring,  by  Table  VIII,  page 
639,  a  1.8  by  i2-in  joist,  determined  by  the  quotient  i  116/623.  So  that,  in 
this  example,  white-pine  joists  of  a  nominal  size  of  2  by  12  in  and  spaced  12  in 
on  centers  might  be  used,  although  they  are  slightly  under  the  required  depth, 
as  the  dressed  size  is  about  1%  by  113-^  in.  From  Table  VI,  page  637,  the 
conversion-factor  is  1.61,  and  623  lb  X  1.61  =  i  003  lb  which  is  less  than  i  116  lb, 
the  load  to  be  supported.  From  Tables  XIII  and  XXII,  pages  737  and  742, 
the  maximum  spans  for  2  by  12  in  white-pine  joists,  12  in  on  centers,  are  19  ft 
and  18  ft  8  in  respectively,  according  to  the  assumed  value  of  the  modulus  of 
elasticity  for  white  pine.  For  3  by  12-in  joists,  16  in  on  centers,  the  load  is 
I  506  lb,  and  i  506/623  =  2%  in.  The  dressed  size  is  almost  2^4  by  iiH  in, 
the  conversion-factor,  2.53,  and  623  X  2.53  ==  i  576  lb,  an  amount  greater  than 
I  506  lb.  Tables  XIII 
and  XXII,  again,  give 

19  ft  8  in  and  19  ft 
4  in  for  the  maximum 
spans.  Joists  3  by  12, 
16  in  on  centers,  are 
stronger  than  neces- 
sary. If,  in  this  ex- 
ample, the  span  is  made 

20  ft,  by  Table  VIII, 
page  639,  for  12-in 
joists  two  values  for  the 
safe  loads  are  found, 
and  the  smaller,  stiff- 
ness-value, should  be 
used,  unless  the  deflec- 
tion need  not  be  con- 
sidered. 

Example  2.  Fig.  2 
shows  a  partial  section 
of  a  dwelling,  in  which 
the  second-floor  joists 
support  a  plastered 
partition  which  also 
supports  the  attic  joists. 
What  should  be  the 
size  of  the  second-floor 
joists  to  meet  the  re- 
quirements of  STRENGTH,  the  timber  being  fair-quality  Eastern  spruce  with  a 
safe  fiber-stress  assumed  to  be  700  lb  per  sq  in  for  flexure?  As  the  effect  of  a 
concentrated  load,  compared  with  a  distributed  load,  in  producing  deflection,  is 
not  as  great  as  the  comparative  effect  in  producing  rupture,  whenever  a  beam 
has  a  considerable  concentrated  load  it  may  be  calculated  by  the  formula  or 
tables  FOR  strength  only.    The  timber  is  assumed  to  be  poorly  seasoned. 

Solution.  The  first  step  will  be  to  determine  the  load  on  a  single  floor-joist. 
We  will  assume,  as  a  trial,  that  the  joists  are  to  be  2  by  10  in,  12  in  on  centers, 
that  both  the  first-story  and  second-story  ceiUngs  are  to  be  plastered,  and  that 


Section  Through  Floors  and  Partitions 


72G  Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 

only  single  flooring  will  be  used  in  the  second  story  and  attic.  We  will  assume 
that  the  attic-joists  are  to  be  2  by  8  in,  16  in  on  centers,  and  that  the  width  of 
floor  supported  by  the  partition  is  10  ft. 

The  second-floor  area  supix)rted  by  a  single  joist  is  12  in  by  15  ft,  or  15  sq  ft. 
The  weight  of  the  floor- joists  per  sq  ft  is  5  lb,  of  the  plastered  ceiling  10  lb  and 
of  the  flooring  3  lb,  making  the  dead  load  per  sq  ft  18  lb.  For  the  live  or  super- 
imposed load  we  should  allow  40  lb  and  hence  the  load  per  square  foot  on  each 
second-floor  joist  due  to  the  second  floor  and  its  load  is  58  lb.  As  the  floor- 
area  for  a  single  joist  is  15  sq  ft  the  load  from  tiue  second  floor  is  15  sq  ft  by 
58  lb  per  sq  ft  or  870  lb  on  each  joist.  We  must  now  find  what  will  be  the 
load  from  the  partition  and  attic-floor.  The  attic-floor  and  ceiling  weigh  about 
16  lb  per  sq  ft,  and  24  lb  is  a  sufiicient  allowance  for  the  live  load.  The  weight 
per  linear  foot  on  the  partition  will  therefore  be  400  lb.  A  partition  of  2  by 
4-in  studs,  lathed  and  plastered  on  both  sides,  weighs  about  20  lb  per  sq  ft  of 
face;  hence  tlie  partition  itself  weighs  iSo  lb  per  lin  ft.  The  partition  and 
attic-floor,  therefore,  bring  a  load  of  580  lb  on  each  second-floor  joist,  con- 
centrated at  a  point  one-fourth  of  the  span  from  the  inner  end  of  the  joist. 
To  combine  this  concentrated  load  with  the  load  from  the  second  floor,  we 
must  multiply  the  concentrated  load  by  1.5  (Table  IV,  page  632),  which  gives 
an  equivalent  distributed  load  of  870  lb.  Adding  this  to  the  second-floor  load 
we  have  i  740  lb  as  the  total  load  for  which  each  joist  should  be  proportioned. 
From  Table  VIII,  page  639,  we  find  that  the  safe  load  for  a  i  by  lo-in  spruce 
joist  of  15-ft  span  is  5r8  lb;  hence  the  breadth  of  each  joist  should  be  equal  to 
I  740/518=  3.36  or  about  33^  in.  Deeper  joists,  therefore,  must  be  used.  If 
we  try  2  by  12-in  joists,  12  in  on  centers,  the  safe  load  for  a  i  by  lo-in  spruce 
joist  of  15-ft  span  is  747  lb.  Hence  the  breadth  is  i  755/747  =  2.35  or  about 
2\i  in,  indicating  2H  by  12-in  joists,  12  in  on  centers.  If  the  fiber-stress  is 
assumed  at  800  lb  per  sq  in,  the  values  of  Table  X,  page  641,  may  be  used. 
This  will  give,  for  2  by  12-in  joists,  12  in  on  centers  and  15-ft  span,  850  lb  for 
the  safe  load  for  a  i  by  12-in  joist;  and  i  755/850  =  about  2  in.  The  load  per 
sq  ft  on  each  of  these  joists  is  i  755/15  =  117  lb;  and  Tables  XVI  and  XXV, 
pages  739  and  744,  give  16  ft  6  in  and  16  ft  i  in  for  the  maximum  safe 
spans. 

Example  3.  It  is  required  to  determine  the  sizes  of  the  girders  and  joists  in 
the  floor  shown  in  Fig.  3,  all  of  the  timbers  being  of  long-leaf  yellow  pine,  and 
the  floor  above  being  supported  by  posts  and  girders  in  the  same  way.  The 
building  is  intended  for  lodging  purposes,  and  the  height  of  the  story  is  10  ft. 
There  is  to  be  a  double  floor  and  the  ceilings  and  partitions  are  to  be  plastered. 
The  floor-joists  are  to  be  spaced  16  in  on  centers.  Average  timber,  poorly  seasoned. 

Solution.  We  will  first  determine  the  size  of  the  common  joists  at  A ,  calling 
the  span  24  ft.  The  floor-area  supported  by  a  single  joist  is  24  by  iH  ft,  or 
32  sq  ft. 

From  Table  XIII  or  XXII,  pages  737  and  742,  for  a  24-ft  span,  2H  by  14-in 
joists  are  probably  required.  We  will  allow  8%  lb  per  sq  ft  for  the  weight  of 
joists  and  bridging  (Table  I,  page  718),  10  for  the  ceiling  and  6  for  the  flooring, 
making  24%  lb  per  sq  ft  for  the  dead  load.  For  the  live  load  we  will  allow  40 
lb  per  sq  ft.  The  load  for  which  the  joists  should  be  proportioned  is,  there- 
fore, 32  by  64^4  or  2  072  lb.  We  may  use  Table  XII,  page  643,  to  find  the 
maximum  load  for  a  i  by  14-in  joist  of  24-ft  span.  The  deflection-load  given  in 
the  table  is  882  lb;  hence  the  thickness  of  the  joists  must  equal  2  072/882  == 
2.35  or  about  2H  in.  Therefore  2H  by  14-in  long-leaf  yellow-pine  joists,  16  in 
on  centers,  may  be  used,  but  they  should  run  -full  2I/I2  iji  thick.  The  joists 
at  B  (Fig.  3)  have  to  support  a  partition,  but  as  the  span  is  much  less,  and  the 


Computations  for  Wooden  Beams  and  Girders 


727 


partition  is  quite  near  the  end  of  the  joists,  it  will  be  safe  to  make  them  of  the 
same  size  as  at  ^ . 

The  joists  at  C  (Fig.  3)  have  the  same  floor-load  to  support  as  at  ^,  and  in 
addition  the  weight  of  the  partition,  which  is  concentrated  at  one-third  of  the 
span  from  one  support.  As  the  partition  is  lo  ft  high,  13 H  sq  ft  of  partition  will 
be  supported  by  each  joist,  the  joists  being  i6  in  on  centers.     Assuming  20  lb 


Fig.  3.     Plan  of  Floor-framing  Showing  Partitions  Above 


per  sq  ft  of  face  as  the  weight  of  the  partition,  we  have  267  lb  as  the  weight 
from  the  partition  to  be  borne  by  each  joist.  To  reduce  this  to  an  equivalent 
distributed  load,  we  should  multiply  by  1.78  (Table  IV,  page  632),  which  gives 
468  lb.  The  joists  at  C,  therefore,  should  be  proportioned  to  a  uniformly 
distributed  load  of  2  o72-f  468=  2  540  lb,  which  requires  14-in  joists,  2,88  in 
thick,  or,  say,  3  .by  14-in  joists. 


728  Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 

The  Header.  We  will  next  determine  the  required  breadth  for  the  header, 
H  (Fig.  3),  the  depth  being  necessarily  14  in,  the  same  as  for  the  joists. 

The  header  is  14  ft  long  and  must  support  the  floor  half-way  to  the  wall,  or 
a  floor-area  of  14  by  9  ft,  or  126  sq  ft.  Multiplying  this  area  by  64%  lb,  the 
weight  per  square  foot,  we  have  8  159  lb,  the  total  floor-lead  to  be  supported, 
to  which  must  be  added  a  certain  percentage  of  the  partition.  The  portion  of 
the  partition  supported  by  the  header  is  (14  f t  —  i  ft  4  in)  =  12  ft  8  in  long  and 
10  ft  high,  and  v/ill  weigh  about  20  lb  per  sq  ft  of  face,  or  a  total  of  2  532  lb. 
As  the  partition  is  one-ninth  of  the  span  from  the  header,  eight-ninths  of  its 
weight  will  be  supported  by  the  header  and  on-^-ninth  by  the  wall.  Eight-ninths 
of  2  532  is  2  251  lb,  which,  added  to  the  floor-load,  makes  a  total  load  for 
the  header  of  10  410  lb.  From  Table  XII,  page  643,  we  find  that  the  safe 
load  for  a  i  by  14-in  beam  of  long-leaf  yellow  pine,  14-ft  span,  is  i  867  lb;  hence 
it  will  require  a  breadth  of  10  410/1  867  =  5.58  in.  If  the  tail-beams  are  framed 
into  the  header,  it  should  be  thicker  to  allow  for  the  weakening  effects  of  the 
framing;  so  that,  in  this  case,  the  header  should  be  at  least  6  by  14  in  in  actual 
cross-section,  before  any  framing  is  done. 

The  Trimmers.  We  will  next  consider  the  trimmer,  T  (Fig.  3).  This 
beam  has  four  loads:  (i)  a  distributed  floor-load;  (2)  a  distributed  load  from 
the  partition  above;  (3)  one-half  the  load  on  the  header  //;  (4)  and  a  small 
direct  load  from  the  longitudinal  partition. 

(i)  The  strip  of  floor  supported  by  the  trimmer  will  be  about  12  in  wide  and 
24  ft  long,  and  wiU  weigh  64%  lb  per  sq  ft  X  24  sq  ft  =  i  554  lb. 

(2)  The  partition  above  wiU  weigh  10  X  24  ft  X  20  lb  per  sq  f t  =  4  800  lb. 

(3)  One-half  of  the  load  on  //  is  10  410/2  =  5  205  lb.  As  this  is  concentrated 
at  one-fourth  the  span  from  the  support,  we  must  multiply  it  by  1.5  (Table  IV, 
page  632)  to  obtain  the  equivalent  distributed  load,  which  then  becomes 
5  205  X  1.5  =  7  808  lb. 

(4)  About  8  in  of  the  longitudinal  partition  must  be  supported  by  the  trimmer, 
and  this  will  weigh  10  x  ^^  ft  x  20  lb  per  sq  ft  =  133  lb.  As  it  is  concentrated 
at  one-third  the  span  from  the  support,  we  must  multiply  by  1.78  (Table  IV, 
page  632)  to  obtain  the  equivalent  distributed  load,  which  then  becomes 
133  X  1.78=  237  lb. 

The  total  load  for  which  the  trimmer  must  be  computed  will  be,  therefore: 

;     (i)  From  the  floor i  554  ih 

(2)  From  the  partition  above 4  800  lb 

(3)  From  the  header 7  808  lb 

(4)  From  the  longitudinal  partition 237  lb 

Total : 14  399  ih 

The  trimmer  should  be  of  the  same  depth  as  the  joists,  14  in.  From  Table 
XII,  page  643,  we  find  that  a  i  by  14-in  long-leaf  yellow-pine  beam  of  24-ft 
span  will  safely  support  882  lb  and  not  cause  a  deflection  of  more  than  Heo  of 
the  span.  Hence,  the  breadth  of  the  trimmer  would  be  14  399/882  =  16.34  in, 
which  is  greater  than  the  depth.  This  would  suggest  the  substitution  of  a  steel 
I  beam  of  proper  size  or  the  use  of  a  deeper  wooden  beam,  such  as  an  11  by  16  or 
a  12  by  i6-in  beam.  If  the.  deflection  of  the  wooden  beam  is  not  taken  into 
account,  the  strength-value,  i  090  lb  of  Table  XII,  page  643,  may  be  used, 
giving  14  399/1  090=  13.21  in  as  the  width  of  the  beam.  This  would  agree 
with  the  former  New  York  Code  for  strength.  If  the  flexure  fiber-stress  is 
taken  at  i  300  lb  per  sq  in,  permitted  by  the  Chicago  code,  Table  XIII,  page 
644,  may  be  used,  giving  14  399/1  179  =  12.21  in  for  the  widttj  of  the  trimmer. 


Computations  for  Wooden  Beams  and  Girders  729 

If  I  800  lb  per  sq  in  is  taken  for  S,  Table  XV,  page  646,  is  used,  giving  14  399/. 
I  63.3  =  8.81  in  for  the  width.  Hence,  the  architect  will  be  governed  by  laws 
in  cities,  or  by  engineering  judgment  or  experience  elsewhere,  and  this  applies 
to  the  joists  as  well  as  to  the  girders.  If  wooden  trimmers  are  used,  they  should 
be  hung  in  beam-hangers  (see  last  part  of  this  chapter).  The  load  on  the  trim- 
mer, R,  will  be  the  same  as  on  the  trimmer,  T,  except  for  the  cross-partition. 
Deducting  the  weight  of  this  partition,  we  have  14  399  —  4  8cx3  =  9  599  lb  for 
the  equivalent  distributed  load  on  R,  wkich,  from  Table  XII,  page  643,  gives,  for 
the  required  breadth  10.88  in  or  8.8  in,  depending  upon  whether  the  deflection 
is  or  is  not  considered.  Other  variations  in  the  required  width  of  a  14-ia 
wooden  girder  will  result  from  the  use  of  other  fiber-stresses. 

The  Girders.  The  floor-area  supported  by  the  girder,  G  (Fig.  3),  is  equal  to 
12  by  24  ft,  or  288  sq  ft.  As  a  general  rule,  it  will  be  safe  in  estimating  the  live 
load  on  girders  to  take  only  85%  of  the  load  assumed  for  the  floor-beams,  be- 
cause there  will  always  be  some  portion  of  the  floor  supported  by  the  girder  that 
is  not  loaded,  and  pro])ably  other  portions  that  will  not  be  loaded  up  to  the 
assumed  load.  Hence,  the  live  load  would  be  85%  of  40  lb,  or  34  lb.  The 
dead  load  of  the  floor  and  ceiling  will  be  about  25  lb,  and  the  girder  itself  will 
weigh  between  i  and  2  lb  per  sq  ft,  say*  2  lb  per  sq  ft  of  floor,  more,  so  that  we 
will  use  61  lb  per  sq  ft  for  the  total  floor-load  on  this  girder.  As  girder  G  sup- 
ports 288  sq  ft,  this  will  be  equivalent  to  17  568  lb.  The  girder  supports,  also, 
a  partition,  9  ft  high,  above,  which  will  weigh  12x9x20  =  2  160  lb.  The  total 
load  for  which  the  girder  should  be  proportioned  is,  therefore,  19  728  lb.  As- 
suming 14  in  for  the  depth  of  the  girder,  we  find  from  Table  XII,  page  643, 
that  the  safe  load  for  a  i  by  14-in  long-leaf  yellow-pine  beam  of  12-ft  span  is 
I  867  lb;  hence  the  breadth  of  girder,  G,  should  be  19  728/1  867  =  10.56  in  and 
an  II  by  14-in  girder  could  be  used. 

The  girder,  G'  (Fig.  3),  supports  a  floor-area  at  the  left  of  12  x  12  =  144  sq  ft, 
which  represents  a  distributed  load  of  8  784  lb.  On  the  right  side  of  the  girder, 
there  is  a  strip  of  floor  40  in  wide  by  12  ft  long  (8  in  of  the  floor  being  included 
in  the  load  on T)  which  will  weigh  2  440  lb.  This  may  be  considered  as  a  con- 
centrated load  applied  20  in,  or  one-seventh  the  span,  from  the  end  of  the 
girder,  in  which  case  the  effect  of  the  load  is  practically  the  same  as  if  the  load 
were  distributed.  The  load  coming  upon  girder  G'  from  T  will  equal  one-half 
the  actual  distributed  load  on  T,  plus  three-eighths  (H  of  %)  of  the  load  on  //. 
The  load  on  //  we  found  to  be  104101b,  and  three-eighths  of  this  is  about 
3900  lb.  The  actual  distributed  load  on  T  we  found  to  be  i  5544-4800  = 
6354  ib,  and  one-half  of  this  is  3  177  lb.  Hence  the  trimmer,  T,  transmits  a 
load  of  3  900  -1-  3  177  =  7  077  lb  to  the  girder,  which  must  be  considered  as  a 
concentrated  load  applied  at  one  third  the  span  from  the  support,  and  hence  we 
must  multiply  it  by  1.78  (Table  IV,  page  632)  to  obtain  the  equivalent  dis- 
tributed load,  which  gives  12  597  lb. 

The  load  for  which  the  girder,  G'  (Fig.  3),  should  be  computed  will  be 

From  the  floor  at  the  left 8  784  lb 

From  the  floor  at  the  right 2  440  lb 

From  the  trimmer,  T .* 12  597  lb 

From  the  partition  above. 2  160  lb 


'$ 


^.,.1 ,  Total 25  981  lb 

From  Table  XIT,  page  643,  we  find  that  this  load  will  require  a  (13.9  by 
14-in)  14  by  14-in  girder.  For  this  floor,  therefore,  the  requirements,  if 
long-leaf  yellow  pine  is  used,  and  if  the  maximum  flexure  fiber-stress,  S,  is 


730  Strength  and  Stiffness  of  Wooden  Floors  Chap.  21 

taken  at  i  200  lb  per  sq  in  (a  conservative  vaUie  for  non-ideal  conditions, 
for  example)  and  the  modulus  of  elasticity,  E,  at  i  500  000  lb  per  sq  in,  are  as 
follows:  an  II  by  14-in  girder  at  G;  a  14  by  14-in  girder  at  G' ;  an  11  by  16,  or  12 
by  i6-in  wooden  beam  or  a  steel  I  beam  for  the  trimmer,  J";  an  11  by  14-in 
beam  for  the  trimmer,  R;  a  6  by  14-in  beam  for  the  header,  //;  23^  by  14-in 
joists  at  A  and  B;  and  3  by  14-in  joists  at  C.  For  these  stress-requirements 
the  architect  might  decide  to  use  steel  I  beams  for  girders  G,  G',  etc.,  and  for 
the  trimmers,  T  and  R.  For  5,  1300,  Q'able  XIII,  page  644,  may  be  used  for 
long-leaf  yellow  pine;  for  S,  1500  lb  per  sq  in.  Table  XIV,  page  645;  for  a  fiber- 
stress,  S,  of  1800  lb  per  sq  in,  Table  XV,  page  646;  and  for  S  equal  to  1600  lb 
per  sq  in.  Table  XII,  page  643,  with  the  strength-values  increased  one-third. 
Of  course,  the  sizes  of  the  timbers  are  diminished  as  the  assumed  safe  fiber- 
stre.sses  are  increased. 

This  example  illustrates  nearly  all  of  the  computations  that  are  required  to 
determine  the  sizes  of  the  joists  and  special  beams  or  girders  in  any  ordinary 
floor-construction.  The  method  of  computation  is  the  same  for  any  floor- 
load,  the  only  difference  being  that  the  greater  the  live  load  assumed  the  greater 
will  be  the  loads  for  which  the  beams  must  be  proportioned.  As  will  be  seen, 
the  most  laborious  computations  are  those  for  beams  which  receive  loads  from 
different  sources,  and  it  will  generally  be  found  that  the  weakest  portions  of 
any  particular  floor  arc  the  headers,  trimmers  and  girders,  and  the  beams  which 
support  partitions. 

The  Strength  of  Mill-Floors.  The  beams  and  girders  for  mill-floors 
should  be  computed  by  the  same  general  method  illustrated  in  the  foregoing 
examples,  involving,  (i)  the  determination  of  the  loads  on  the  beams  and 
girders  and,  (2)  the  sizes  of  the  beams  and  girders  required  to  support  such 
loads. 

Required  Thickness  of  Plank  Flooring.  The  thickness  of  the  plank  floor- 
•ing  in  mill  construction  may  be  determined  by  formulas  (i)  and  (2): 


k  in  in )       4  /weig 
nigth    )  "  V 


Thickness  of  plank  in  in )       4  /weight  per  sq  ft  x  l"^ 


required  for  strength    )        »  24  x  .4 


Thickness  of  plank  in  in  )       *  /weight  per  sq  ft  x  l^ 


required  for  stiffness  )        V  19.2  X  <^i 


(i) 
(2) 


In  these  formulas,  /  is  the  span  in  feet,  from  center  to  center  of  beams,  A  the 
constants  for  strength  (page  628),  and  ei  the  constant  for  stiffness  (page  664), 

When  the  planks  are  connected  by  ^4-in  splines,  and  extend  over  two  spans. 
Formula  (i)  may  be  used.  If  the  planks  arc  in  single  lengths  from  beam  to  beam, 
or  are  not  splined,  then  Formula  (2)  should  be  used. 

Tables  IV  to  XI,*  inclusive,  show  the  safe  loads  for  plank  flooring  of  different 
woods,  thicknesses  and  spans,  derived  from  the  formulas  for  strength  and  stiffness, 
the  values  in  the  first  horizontal  line  in  the  case  of  each  thickness  of  plank 

*  Tables  VIII  to  XI,  inclusive,  were  calculated  by  Mr.  F.  E.  Kidder  and  are  retained 
from  the  preceding  edition  of  the  Pocket-Book.  Tables  IV  to  VII,  inclusive,  are  added 
to  conform  to  the  most  conservative  fiber-stresses  of  the  building  codes  and  of  the  other 
chapters  of  the  new  edition.  In  the  judgment  of  many  constructors  the  higher  values  of 
Tables  VIII  to  XI  are  safe  when  more  favorable  conditions  of  quality  and  dryness  of 
materials  prevail.  In  using  any  of  the  tables,  care  must  be  taken  to  notice  whether 
or  not  the  safe  loads  given  include  the  weight  of  the  flooring  itself.  In  the  revision  of 
this  chapter  the  author  is  indebted  to  Professor  F.  H.  Safford,  of  the  University  of  Penn- 
sylvania, for  the  computations  required  for  the  new  Tables  IV  to  VII  and  for  the  checking 
9f  Tables  VII!  to  XI. 


•    Explanation  of  Tables  731 

denoting  the  loads  given  by  the  formula  for  strength  and  the  figures  iri  the 
second  line  those  given  by  the  formula  for  stiffness.  The  span  is  supposed  to  be 
measured  from  center  to  center  of  beams.  The  values  given  by  the  formula  for 
strength  should  be  considered  safe  only  for  spHned  floors  and  where  the  planks 
are  continuous  over  at  least  two  spans.  If  the  thickness  of  the  planks  falls 
short  H  or  even  H  in  from  the  dimensions  given,  the  safe  loads  must  be  mate- 
rially reduced. 

In  Table  IV,  the  modulus  of  elasticity,  E,  on  which  ci  in  the  stiffness-formula 
depends,  is  i  500  000  lb  per  sq  in,  and  the  safe  fiber-stress,  S,  on  which  the 
constant  for  strength.  A,  depends,  is  i  200  lb  per  sq  in,  A  being  67.  The  safe 
loads  given  are  within  the  requirements  of  all  cities  for  strength  and  stiffness  foi; 
long-leaf  yellow  pine,  and  of  all  cities  for  Douglas  fir. 

In  Table  V,  £  is  i  200  000  lb  per  sq  in,  S,  i  000  lb  per  sq  in,  and  A  is  56, 
The  loads  given  satisfy  the  requirements  of  Chicago  and  of  most  other  citie^ 
for  strength  for  short-leaf  yellow  pine.  The  values  given  for  stiffness,  also,  are 
recommended  for  this  wood.  ! 

In  Table  \T,  E  is  i  200  000  lb  per  sq  in,  S,  800  lb  per  sq  in,  and  A  is  44^ 
The  loads  given  satisfy  the  requirements  of  all  cities  for  strength,  for  spruce,' 
Norway  pine  and  white  pine,  and  the  values  given  for  stiffness,  also,  are 
recommended  for  spruce.  For  Norway  pine,  E  =  i  100  ocx)  lb  per  sq  in  may 
be  used. 

In  Table  VII,  E  is  i  000  000  lb  per  sq  in,  S,  'joo  lb  per  sq  in,  and  A  is  39. 
The  loads  given  for  strength  can  be  used  for  any  woods  of  that  safe  fiber- 
stress,  and  the  loads  for  stiffness  are  recommended  for  white  pine. 

In  Tables  VIII,  IX,  X  and  XI,  the  safe  loads  are  calculated  from  still  other 
values  oi  S,  A,  E  and  ei,  indicated  with  each  table,  and  may  be  used  by  those 
who  wish  to  assume  larger  safe  values  for  the  strength  and  stiffness-factors 
in  cases  where  there  are  no  restrictions  from  building  laws.  For  any  other  values 
of  A  or  ei  required,  such  values  must  be  inserted  in  Formula  (i)  or  (2)  and  the 
thicknesses  of  the  planks  determined  or  the  safe  load  determined  for  any  given 
thickness  of  planks. 

Note.  It  is  to  be  noted  that  for  ideal  conditions  and  commercially  dry  lum- 
ber, protected  from  moisture,  and  when  there  is  no  impact,  the  given  fiber-stresses 
for  flexure  may  be  increased  from  30  to  40%.  (See,  also,  important  notes  on 
pages  628,  637  and  647  regarding  stresses  in  and  loads  on  wooden  beams.) 


732 


Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 


Table  IV.    Safe  Live  Loads*  in  Pounds  per  Square  Foot  for  Plank  Flooring 

See  explanation  on  pages  730-1  •    The  loads  are  based  on  the  following  values. 
Strength:  S=  1  200  lb  per  sq  in,  A=  67;  stiffness:  £=  i  500  000  lb  per  sq  in,  ei=  116 

LONG-LEAF  YELLOW  PINE  AND  DOUGLAS  FIR  f 


Thickness 

of  planks, 

in 

Distance  between  centers  of  floor-beams,  in  feet 

4 

5 

6 

7 

8 

9 

10 

II 

12 

iH 

353 
229 

226 

117 

157 

68 

115 
43 

88 
29 

70 
20 



2H 

567 
466 

363 
239 

252 
138 

185 
87 

142 
58 

112 

41 

91 
30 

75 
22 

63 
17 

2% 

760 
724 

486 
371 

338 
214 

248 
135 

190 
90 

150 
64 

122 

46 

100 
35 

84 
27 

3H 

788 
764 

547 

442 

402 
278 

308 
187 

243 
131 

197 
95 

163 

72 

137 
55 

4 

715 

660 

525 
416 

402 
278 

318 
196 

257 
143 

213 

107 

179 
82 

5 

820 
812 

628 
544 

496 
382 

402 
278 

332 
209 

279 
161 

6 

904 

940 

715 
660 

579 
481 

478 
361 

402 
278 

*  Weight  of  ceiling,  if  any,  and  also  of  the  flooring  itself  is  to  be  deducted  from  these  values, 
t  If  S  for  Douglas  fir  is  taken  at  1000  lb  per  sq  in,  use  Table  V. 

Table  V.     Safe  Live  Loads  "i"  in  Pounds  per  Square  Foot  for  Plank  Flooring 

See  explanation  on  pages  730-1.     The  loads  are  based  on  the  following  values. 

Strength:  S  =  1  000  lb  per  sq  in,  ^  =  56;  stiffness:  E  =  1  200  000  lb  per  sq  in,  Cx  =  92 

SHORT-LEAF  YELLOW  PINE 


Thickness 

of  planks, 

in 

Distance  between  centers  of  floor-beams,  in  feet 

4 

5 

6 

7 

8 

9 

10 

II 

1 

12 

.li 

295 
182 

189 
93 

131 

54 

96 
34 

74 
23 

2% 

474 
370 

303 
189 

211 
no 

155 

69 

118 
46 

94 
32 

76 
24 

23/4 

635 

574 

406 
294 

282 
170 

207 
107 

159 
72 

125 

50 

102 
37 

84 
28 

71 
21 

3V2 

I  029 

659 
606 

457 
351 

336 
221 

257 
148 

203 
104 

165 
76 

136 

57 

114 

44 

4 

860 

597 
523 

439 
330 

336 
221 

26s 
155 

215 
113 

178 
85 

149 
65 

S 

933 

686 
644 

525 
431 

415 
303 

336 
221 

278 
166 

233 
128 

6 

987 

756 

745 

597 
523 

484 
382 

400 
.87 

336 
221 

♦  Weight  of  ceiling,  if  any,  an4  also  of  the  flooring  itself  is  to  be  deducte4  from  these 
values. 


Tables  of  Safe  Loads  for  I*lank  Flooring 


733 


Table  Vt.     Safe  Live  Loads*  in  Pounds  per  Square  Foot  for  Plank  Flooring 

See  explanation  on  pages  730-1  •     The  loads  are  based  on  the  following  values. 

Strength:  S=  800  lb  per  sq  in,  A  =  44;  stiffness:  £=  i  200  000  lb  per  sq  in,  Ci=  92 

SPRUCE,    NORWAY   PINE    AND    WHITE    PINE 


Thickness 

of  planks, 

in 

Distance  between  centers  of  floor-beams,  in  feet 

4 

5 

6 

7 

8 

9 

ID 

n 

12 

1% 

232 

182 

148 
93 

103 
54 

76 
34 

58 
23 



2% 

372 

370 

238 
189 

i6s 
no 

122 
69 

93 

46 

74 
32 

60 
24 

2% 

499 

319 
294 

222 

170 

163 
107 

125 

72 

99 
50 

80 
37 

66 
28 

zV^ 

809 

517 

359 
351 

264 
221 

202 
148 

160 
104 

129 
76 

107 
57 

89 

44 

4 

676 

469 

345 
330 

264 
^221 

209 
155 

169 
113 

140 
85 

117 
65 

S 

733 

539 

412 

326 
303 

264 
221 

218 
166 

183 
128 

6 

776 

594 

469 

380 

314 

287 

264 
221 

*  Weight  of  ceiling,  if  any,  and  also  of  the  flooring  itself  is  to  be  deducted  from  these 
values. 


Table  VII.     Safe  Live  Loads*  in  Pounds  per  Square  Foot  for  Plank  Flooring 

See  explanation  on  pages  730-1  •     The  Iq^ds  are  based  on  the  following  values. 

Strength:  S  =  700  lb  per  sq  in,  A  =  39;  stiffness:  £  =  i  000  000  lb  per  sq  in,  Ci  =  77 

FOR   HEMLOCK    AND    WOODS    OF    SIMILAR    STRENGTH   AND    STIFFNESS 


Thickness 

of  planks, 

in 

1 

Distance  between  centers  of  floor-beams,  in  feet 

4 

206 
152 

8 

9 

10 

II 

12 

5 

6 

7 

l7/^ 

132 
78 

91 

45 

67 
28 

2% 

330 
309 

212 
158 

147 
92 

lOJi 

58 

82 
39 

65 
27 

.,... 

2% 

442 
480 

283 
246 

197 
142 

146 
90 

III 
60 

87 
42 

71 
31 

zVi 

717 

459 

319 
293 

234 
185 

179 
124 

142 
87. 

115 
63 

95 
48 

80 
37 

4 

936 

599 

416 

306 
276 

234 
185 

185 
130 

ISO 
95 

124 
71 

104 
55 

5 

936 

650 

478 

366 
361 

289 
253 

234 

185 

193 
139 

163 

107 

6 

936 

688 

526 

416 

337 
319 

278 
240 

234 
18S 

*  Weight  of  ceiling,  if  any,  and  also  of  the  flooring  itself  is  to  be  deducted  from  these 
valu«s. 


734 


Strength  and  Stiffness  of  Wooden  Floors        Chap,  21 


Table  VIII.    Safe  Live  Loads*  in  Pounds  per  Square  Foot  for  Plank  Flooring 

See  explanation  on  pages  730-1.    The  loads  are  based  on  the  following  values. 

Strength:  -5**  i  800  lb  per  sq  in,  A  =  100;  stiffness:  E=«  1 780 000  lb  per  sq  in,  Ci«  137 

Recommended  by  Mr.  Kidder  for 

LONG-LEAF   YELLOW  PINE 


Thickness 

of  planks, 

in 

Distance  between  centers  of  floor-beams,  in  feet 

4 

5 

6 

7 

8 

9 

10 

11 

12 

iH 

515 
258 

325 
126 

222 
68 

160 
38 

120 
21 

92 
II 

72 
5 

2H 

831 
536 

527 
268 

362 
149 

262 
88 

197 
.  54 

153 
34 

121 
24 

97 
12 

80 
6 

2U 

1 118 
838 

710 
421 

488 
237 

354 
144 

267 
91 

208 
59 

165 
38 

134 

25 

no 
15 

zYi 

1 158 
884 

798 
504 

582 
310 

442 
202 

345 
136 

276 
94 

225 
67 

186 

47 

4 

1046 
759 

763 

470 

580 
308 

454 
210 

364 
148 

296 
106 

246 

77 

5 

1200 
934 

913 
618 

716 

427 

576 
304 

471 
223 

392 
166 

6 

1322 
I  081 

1038 
751 

836 

540 

686 
398 

572 
300 

*  Weight  of  ceiling,  if  any,  to  be  deducted.    The  weight  of  the  flooring  has  been  deducted 
from  values  derived  from  formulas.     Deduction  about  72  lb  per  cu  ft  floor-material. 

Table  IX.     Safe  Live  Loads  *  in  Pounds  per  Square  Foot  for  Plank  Flooring 

See  explanation  on  pages  730-1.     The  loads  are  based  on  the  following  values. 

Strength:  5  =  i  620  lb  per  sq  in,  A  =  90;  stiffness:  E=  1  425  000  lb  per  sq  in,  fi=  110 

Recommended  by  Mr.  Kidder  for 

DOUGLAS   FIR  AND    SHORT-LEAF   YELLOW   PINE 


1 

1  Thickness 
:  of  planks, 

■     in 

Distance  center  to  center  of  floor-beams,  in  feet 

4 

5 

6 

7 

8 

9 

10 

II 

12 

1% 

462 

205 

291 
99 

199 
52 

143 

28 

106 
15 

81 
7 

64 

2% 

747 
428 

473 
212 

324 
117 

234 
68 

176 
41 

136 

25 

107 
14 

■    2% 

1005 
670 

637 
335 

438 
187 

317 
112 

239 
69 

185 
44 

147 

23 

119 
17 

.  97 
9 

'       zVi 

I  040 
7c6 

717 

401 

522 
246 

395 
159 

308 
106 

246 

72 

200 
50 

165 
34 

4 

1362 
I  061 

940 
606 

685 
374 

520 

244 

406 
165 

325 
115 

265 
81 

220 
58 

•    5 

1476 
1 198 

1078 

745 

819 
491 

642 
338 

516 

240 

.  422 
174 

351 

128 

6 

1560 
1302 

1 187 
863 

932 
597 

749 
428 

614 
314 

512 

236 

*  Weight  of  ceiling,  rf  any,  to  be  deducted.    The  weight  of  the  flooring  has  been  deducted 
from  values  derived  from  formulas.    Deduction  about  72  lb  per  cu  ft  floor-material. 


Tables  of  Safe  Loads  for  Plank  Flooring 


73S 


fable  X.    Safe  Live  Loads  *  in  Pounds  per  Square  Foot  for  Plank  Flooring 

See  explanation  on  pages  730-1  •    The  loads  are  based  on  the  following  values. 

Strength:  5=  1  260  lb  per  sq  in,  A  =»  70;  stiffness:  £=  i  294  000  lb  per  sq  in,  ej  «  100. 

Recommended  by  Mr.  Kidder  for 

SPRUCE 


Thickness 

of  planks, 

in 

Distance  between  centers  of  floor-beams,  in  feet 

4 

5 

6 

7 

8 

9 

10 

II 

12 

1% 

360 
188 

227 

92 

155 

49 

III 
28 

83 
15 

64 
8 

50 

2% 

581 
391 

368 
194 

252 
108 

182 
64 

137 
39 

105 

24 

83 
15 

67 

54 

23/4 

782 
612 

496 
307 

341 
173 

247 
104 

186 
66 

144 
42 

115 

28 

-  93 
18 

76 

2>yi 

1228 
1274 

781 
644 

548 
367 

391 
225 

296 
146 

231 

98 

184 
68 

150 
47 

124 
33 

4 

1060 
968 

731 
554 

533 
343 

405 
225 

317 
153 

253 
108 

207 
77 

171 
56 

5 

1 148 
1093 

839 
682 

638 
450 

500 
311 

402 
212 

329 
162 

273 
120 

6 

I  213 

I  188 

924 
789 

725 

548 

583 
394 

478 
290 

400 
220 

*  Weight  of  ceiling,  if  any,  to  be  deducted.    The  weight  of  the  flooring  has  been  deducted 
from  values  derived  from  formulas.     Deduction  about  72  lb  per  cu  ft  floor-material. 

Table  XI.     Safe  Live  Loads  *  in  Pounds  per  Square  Foot  for  Plank  Flooring 

See  explanation  on  pages  730-1.     The  loads  are  based  on  the  following  values. 

Strength:  S  =  x  080  lb  per  sq  in,  A  =  60;  stiffness:  E=  1  073  000  lb  per  sq  in,  ei  =  83 

Recommended  by  Mr.  Kidder  for 

WHITE   PINE 


Thickness 

of  planks, 

in 

Distance  between  centers  of  floor-beams,  in  feet 

4 

5 

6 

7 

8 

9 

10 

II 

12 

iH 

307 
•153 

193 
74 

131 
39 

94 
21 

70 
II 

53 

5 

41 

2% 

496 
318 

314 
157 

214 
85 

154 

50 

116 

40 

89 
18 

70 
10 

56 



2% 

668 
499 

424 
249 

290 
139 

210 
83 

158 
52 

122 
33 

97 
20 

78 
12 

63 

z\^ 

1088 
I  041 

691 
526 

476 
298 

346 
183 

261 
119 

203 
78 

162 
53 

131 
36 

108 
25 

4 

906 
791 

625 
451 

455 
278 

345 
181 

269 
123 

215 
85 

175 
60 

145 
43 

5 

982 
893 

716 
555 

544 
366 

426 
251 

342 
178 

281 
129 

232 
95 

6 

I  419 
1553 

1037 
970 

789 
643 

619 
445 

497 
319 

407 
234 

339 
175 

*  Weight  of  ceiling,  if  any,  to  be  deducted.    The  weight  of  the  flooring  has  been  deducted 
from  values  derived  from  formulas.     Deduction  about  72  lb  per  cu  ft  floor- material. 


736  Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 

Tables  for  the  Maximum  Span  of  Floor- Joists.  As  the  timbers  commonly 
used  for  floor-joists  are  sawed  to  regular  sizes  and  are  usually  spaced  either  1 2 
or  16  in  on  centers,  it  is  practicable  to  show  by  means  of  tables  the  sizes  of  joists 
required  to  support  given  loads  with  given  spans  and  spacings.  Tables  giving 
the  MAXIMUM  SAFE  SPANS  are  the  most  convenient  for  general  use,  and  the  follow- 
ing tables  have  accordingly  been  prepared.  They  show  at  a  glance  the  max- 
imum spans  for  which  different  sizes  of  floor-joists  and  ceihng-joists  should  be 
used  for  different  loads  and  spacings,  and  it  is  believed  that  they  will  be  found 
applicable  to  most  buildings  in  which  wooden  floor-joists  are  used.  By  knowing 
the  size  of  a  room  and  the  purpose  for  which  it  is  to  be  used,  the  sizes  of  the 
floor-joists  required  can  be  determined  at  a  glance.  Incidentally  the  tables 
show,  also,  the  kind  of  wood  most  economical  to  use.  If,  owing  to  the  room 
being  irregular  in  shape,  the  joists  must  be  of  different  lengths,  the  spacing  or 
thickness  of  the  joists  may  be  varied,  so  that  the  same  depth  may  be  used 
throughout. 

Precautions  Required  in  Using  Tables.  The  precautions  necessary  in  using 
these  tables  are  in  regard  to  the  superimposed  loads  and  the  actual  sizi:s  of 
the  timbers.  The  total  loads  for  which  the  maximum  spans  have  been  com- 
puted are  given  at  the  head  of  each  table.  The  actual  weight  of  the  floor 
(joists,  flooring,  plastering  and  deafening,  if  any)  subtracted  from  the  total  load 
will  give  the  superimposed  load,  that  is,  the  load  which  the  floor  is  expected  to 
carry.  If  the  actual  sizes  of  the  joists  are  less  than  the  nominal  dimensions, 
the  spans  or  spacings  must  be  reduced  from  those  given  in  the  tables,  and  as 
the  stock  sizes  of  joists  generafly  run  from  li  in  to  %  in  scant  of  the  nominal 
dimensions,  this  fact  should  always  be  taken  into  account  when  determining 
upon  the  sizes  of  joists.  In  this  connection  it  will  be  convenient  to  remember 
that  2-in  joists,  spaced  16  in  on  centers,  have  the  same  strength  as  I'/ii-in  joists, 
12  in  on  centers.  A  reduction  should  also  be  made  for  any  cutting  of  the 
JOISTS  that  may  be  required.  No  allowance  has  been  made  for  partitions,  and 
when  they  are  to  be  supported  by  the  floor-joists,  additional  joists  should  be 
used  or  the  span  reduced  according  to  the  relative  direction  or  position  of  the 
partitions  and  joists.  ,  ■        I 

Tables  XH  to  XX.  Tables  XII  to  XVI,  inclusive,  were  computed  by  the 
formula  for  stiffness  (Chapter  XVI,  page  636  and  Chapter  XVIII,  page  665), 
on  the  assumption  that  the  deflection  should  not  exceed  Ho  in  per  foot  of  span. 
They  are  based  on  the  values  of  E  (the  modulus  of  elasticity)  recommended  by 
F.  E.  Kidder.  Tables  XVII  to  XX,  inclusive,  were  computed  by  the  formula 
for  strength  (Chapter  XVI,  page  635),  and  values  for  S  (the  safe  fiber-stress) 
recommended  by  Mr.  Kidder.  The  spans  given  in  Tables  Xlt  to  XX;  inclu- 
sive, come  within  the  requirements  of  the  Buffalo  and  Denver  building  laws, 
and  Tables  XII,  XIV,  XV,  XVI  and  XVII  comply  with  the  Chicago  law  and 
very  nearly  with  the  New  York  law;  but  to  comply  with  the  Boston  law  a 
reduction  of  about  one-sixth  must  be  made  from  th«  spans  given  (1914).* 

Tables  XXI  to  XXIX  f  inclusive,  were  computed  for  reduced  values  of  E  (the 
modulus  of  elasticity,)  S  (the  flber-stress  for  flexure)  and  A  (the  constant  for 
flexural  strength)  in  the  formulas  used,  these  values  agreeing  generally  with  the 
stresses  throughout  the  revised  handbook.  Of  these  neW~-tables,  also,  Tables 
XXI  to  XXV,  inclusive,  were  computed  by  the  fo"rmula  for  stiffness,  and 
Tables  XXVI  to  XXIX,  inclusive,  by  the  formula  for  strength. 

*  Building  Codes  arc  frequently  revised  and  must  be  consulted. 

t  In  the  revision  of  this  chapter  the  author  is  indebted  to  Mr.  A.  T.  North.  M.  Am.  Soc. 
C.  E.,  for  valuable  assistance  in  the  computations  required  for  the  new  Tables  XXI  to 
XXIX.  "^ 


Tables  for  Maximum  Span  of  Ceiling  and  Floor-Joists        737 


Table  XII.     Maximum  Span  for  Ceiling- Joists 

See  explanatory  notes  on  page  736 




d,  20  pounds 

1 

^    .    Total loa 

per  square  foot 

Sizes 
of 

Distance 
on 

Hemlock, 
*E  = 

White  pine, 
£  =  I  073  000 

Norwav 
pine  or 
spruce. 

Douglas 

fir  or 

Texas  pine, 

Long-|eaf 
yellow 
pine. 

joists 

centers 

I  045  000 

R  =  i  294000 

E  =  i  425000 

£  =  i  780000 

in 

in 

ft         in 

ft         in 

ft         in 

ft         in 

ft         in 

2X4 

12 

9          3 

9          5 

10          I 

10          5 

II          2 

2X4 

16 

8          5 

8          6 

9          I 

9          5 

10          I 

2X6 

12 

14          0 

14          I 

15          I 

15          7 

16          8 

2X6 

16 

12          8 

.12        10 

13          8 

14  '      2 

15          2 

2X8 

12 

18          8 

18        10 

20          I 

20         9 

22          4 

2X8 

16 

17          0 

17          2 

18          4 

18        II 

20          5 

2X8 

20 

15          9 

IS        10 

17          0 

17         6 

18        10 

'     Total  load,  24  pounds  per  square  foot                                           | 

2X10 

12 

22          0 

22          2 

23          8 

24          5 

26          4 

2X10 

16 

20          0 

20          2 

21          7 

22          3 

23        10 

2X10 

20 

18         6 

18          8 

20          0 

20          7 

22          2 

2X1 V 

12 

26         s 

26          8 

28          5 

29          4 

31          7 

2X12 

16 

24         0 

24          2 

25        10 

26         8 

28          8 

2X12 

20 

22          3 

22          5 

24          0 

24         8 

26          8 

*  E  is  the  modulus  of  elasticity  and  is  in  pounds  per  square  inch. 

Table 

XIII.     Maximum  Span  for  Floor- Joists  for  Dwellings,  Tenements 

ar 

id  Grammar 

-School  Roo 

ms  with  Fix 

ed  Desks 

See  explanatory  notes  on  page  736 


Total  load,  60  pounds 

per  square  foot 

Sizes 
of 

Distance 

Hemlock, 

White  pine, 

Norway 
pine  or 

Douglas 
firot 

Long-leaf 
yellow 

R  =  i  073000 

spruce. 

Texas  pine. 

pine. 

joists 

centers 

I  045  000 

E  =  I  294  000 

E  =  i  425  000 

E  =  i  780000, 

in      ^ 

in 

ft         in 

ft         in 

ft         in 

ft         in 

ft         in 

2X6 

12 

9         9 

9        10 

10          5 

10        10 

II          7 

2X6 

16 

8         9 

8        10 

9         6 

9        10 

10          6 

3X6 

12 

II          I 

II          2 

12          0 

12          5 

13          4 

3X6 

16 

10          I 

10          2 

10        10 

II          2 

12          I 

2X8 

12 

12        II 

13          I 

13        II 

14        S 

IS          6 

2X8 

16 

II         9 

II        10 

12          8 

13          I 

14          I 

3X8 

12 

14         9 

14        II 

16          0 

16          6 

17          8 

3X8 

16 

13         6 

13          7 

14          6 

IS          0 

16          2 

2X10 

12 

16         2 

16          4 

17          5 

18          0 

19           4 

2X10 

16 

14         9 

14        10 

15         9 

16          4- 

17          7 

Total  loa 

d,  66  pounds 

per  square  fc 

)Ot 

3     Xio 

12 

18         0 

18          I 

19          3 

20         0 

21          6 

3     Xio 

16 

16         3 

16          5 

17          7 

18          2 

19          6 

2     X12 

12 

18        10 

19          0 

20          3 

20        10 

22    *      6 

2     X12 

16 

17          2 

17           3 

18          4 

19         0 

20         6 

3     X12 

12 

21          6 

21            8 

23          2 

24         0 

2S          9 

3     X12 

16 

19         7 

19          8 

21          I 

21          9 

23          5 

2     X14 

12 

22         0 

22          2 

23          8 

24          4 

26          3 

2     X14 

16 

20         ■• 

20          I 

21          6 

22          2 

23        10 

2^/^2X14 

12 

23          8 

23        10 

25          6 

26          3 

28          3 

2' 2X14 

16 

21          6 

21          8 

23         2 

23        10 

25          8 

3     X14 

12 

25          4 

25          4 

27          I 

28          0 

30          I 

3     X14 

16 

23          0 

23          0 

24          7 

2S          4 

27          4 

E  is  the  modulus  of  elasticity  and  is  in  pounds  per  square  inch. 


738 


Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 


Table  XIV.     Maximum  Span  for  Floor- Joists  for  Office-Buildings 

See  explanatory  notes  on  page  736 


Total  load,  93  pounds  per  square  foot 

Sizes 

Distance 

White  pine, 
*  E  =  i  073000 

Norway  pine 

Douglas  fir 

Long-leaf 

of 

on 

or  spruce, 

or  Texas  pine, 

yellow  pine, 

joists 

centers 

E  =  i  294  000 

E  =  i  425  000 

£  =  i  780000 

in 

in 

ft         in 

ft           in 

ft           in 

ft          in 

3X8 

12 

12        10 

13           9 

14           2 

15            4 

3X8 

16 

II          8 

12           6 

12          10 

13          10 

2X10 

12 

14          I 

IS           I 

15           6 

16            7 

2X10 

16 

12          9 

13            8 

14           I 

15               2 

3X10 

12 

16          I 

17            3 

17           9 

19               2 

3X10 

16 

14          8 

15            8 

16           2 

17            5 

2X12 

12 

16        10 

18            I 

18           8 

20               I 

2X12 

16 

15          4 

16            5 

17           0 

18            3 

Total  load,  96  pounds  per  square  foot 

3     X12 

12 

19          ? 

20           6 

21            2 

22            9 

3     X12 

16 

17        S 

18           7 

19            3 

20            8 

2     X14 

12 

19          6 

20          10 

21            7 

23            2 

2     X14 

16 

17          9 

19           0 

19            7 

21            2 

2^2X14 

12 

21          I 

22           6 

23               2 

25            0 

2i/^Xi4 

16 

19          2 

20           4 

21                2 

22            8 

3     X14 

12 

22          4 

23          10 

24            8 

27            7 

3     X14 

16 

20          4 

21            8 

22               S 

24            I 

E  is  the  modulus  of  elasticity  and  is  in  pounds  per  square  inch. 


Table  XV.     Maximum  Span  for  Floor- Joists  for  Churches  and  Theaters 
with  Fixed  Seats 

See  explanatory  notes  on  page  736 


Total  load,  102  pounds  per  square  foot 

Sizes 

Distance 

White  pine, 
*  E  =  i  073000 

Norway  pine 

■  Douglas  fir 

Long-leaf 

of 
joists 

on 
centers 

or  spruce, 
£  =  I  294  000 

or  Texas  pine, 
E  =  i  42s  000 

yellow  pine, 
E  =  i  780000 

in 

in 

ft         in 

ft          in 

ft          in 

ft           in 

3X8 

12 

12          6 

13            4 

13           9 

14          10 

3X8 

16 

II          4 

12            2 

12           6 

13           6 

2X10 

12 

13          7 

14           7 

IS           I 

16           a 

2X10 

16 

12          4 

13            3 

13           8 

14           9 

3X10 

12 

15          8 

16            9 

17            3 

18           7 

3X10 

16 

14          2 

IS            2 

IS            8 

16          10 

2X12 

12 

16          5 

17            7 

18            I 

19           6 

2X12 

16 

14        10 

IS          II 

16            5 

17           8 

Total  load,  ic 

)5  pounds  per  sq 

uare  foot 

3     X12 

12 

18          7 

19         II 

20           6 

22           I 

3     X12 

16 

16        10 

18           I 

18           7 

20           I 

2     X14 

12 

19         0 

20           3 

20         10 

22           6 

2     X14 

16 

17          3 

18          s 

-  19           0 

20           6 

2K2X 14 

12 

20          4 

21           9 

22           6 

24            3 

21^^X14 

16 

18          7 

19          10 

20           6 

22            I 

3     X14 

12 

21          8 

23           2 

23          10 

2S            9 

3     X14 

16 

19          8 

21           I 

21           9 

23            4 

■  E  is  the  modulus  of  elasticity  and  is  in  pounds  per  square  ioQh. 


Tables  for  Maximum  Span  of  Floor-Joists 


739 


Table  XVI.     Maximum  Span  for  Floor- Joists  for  Assembly-Halls  and 
Corridors 

See  explanatory  notes  on  page  736 


Total  load,  123  pounds  per  square  foot 


Sizes 

of 
joists 

in 


3X8 

3X8 

2X10 

2X10 

3X10 

3X10 

2X12 

2X12 


Distance 

on 

centers 

in 


16 
12 
16 


Whit 

s  pine, 

E  =  i 

073  000 

ft 

in 

II 

7 

10 

8 

12 

10 

II 

7 

14 

8 

13 

4 

IS 

4 

14 

0 

Norway  pine 
or  spruce, 

£  =  I  294  000 
ft  in 


IS 
14 
16 
15 


Douglas  fir 

or  Texas  pine, 

E  =  i  425  000 

ft  in 


13 


16 
14 
17 
15 


Long-leaf 
yellow  pine, 
£  =  I  780  000 

ft  in 


14 
12 
15 
13 
17 
15 
18 
16 


8 


Total  load,  126  pounds  per  square  foot 


3  X12 
3  X12 
2     X14 

2  X14 
2K2X14 
2HX14 

3  X14 
3     X14 


17 
IS 
17 
16 
19 
17 


18 
17 
19 

17 


19 
17 
19 
17 


19 


*  E  is  the  modulus  of  elasticitv  and  is  in  nounds  ner  snuare  inch. 

Table  XVII. 

Maximum  Span  for  Floor- Joists  for  Retail  Stores 

See  explanatory  notes  on  page  736 

Total  load,  174  pounds  per  square  foot 

White  pine, 
5  =  1080 

lb  per  sq  in 
*  A=6o 

Norway  pine 

Douglas  fir 

Long-leaf 

Sizes 
of 

Distance 
on 

or  spruce, 
5  =  1  260 

or  Texas  pine, 
5  =  1620 

yellow 
5=1 

pine, 
800 

joists 

centers 

lb  per  sq  in 
A  =70 

lb  per  sq  in 
A=go 

lb  per  sq  in 
A=ioo 

in 

m 

ft         in 

ft           in 

ft          in 

ft 

in 

3X8 

12 

II          6 

12            5 

14           I 

14 

9 

3X8 

16 

9        II 

10            2 

12           2 

12 

9 

2X10 

12 

II          8 

12           8 

14         S 

15 

I 

2X10 

16 

10          2 

10          II 

12           5 

13 

I 

3X10 

12 

14          4 

IS           6 

17           7 

18 

7 

3X10 

16 

12          5 

13            5 

IS           2 

16 

0 

2X12 

12 

14          I 

IS           2 

17           2 

18 

2 

2X12 

16 

12          2 

13           I 

14          II 

IS 

8 

Total  load,  177  pounds  per  square  foot                                           | 

3     X12 

12 

17          2 

18            5 

20          II 

22 

I 

3     X12 

16 

14        10 
16          3 

16  0 

17  7 

18  2 

19  n 

19 
21 

I 

I 

2     X14 

16 

14          2 

IS            2 

17             3 

18 

2 

2i/^Xi4 

12 

18          2 

19            7 

22               3 

23 

6 

23.2X14 

16 

IS          9 

17            0 

19             3 

20 

4 

3     X14 

12 

19        II 

21           6 

24            S 

2S 

8 

3     X14 

16 

17           3 

18            7 

•21            2 

22 

3 

*  A  in  the  tables  is 
assumed  flexural  fiber 


the  coefficient  in  formulas  for  beams  and  is  one-eighteenth  of  the 
stress,  S. 


T40 


Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 


Table  XVIII.*     Maximum  Span  for  Rafters.     Shingled  Roofs  not  Plastered 

See  explanatory  notes  on  page  736 


Total  load,  48  pounds 

per  square  foot 

Norway 

Douglas 

Long-leaf 

Hemlock, 

White  pine» 

pine  or 

fir  or 

Sizes 
of 

Distance 

5=990 

5  =  1080 

spruce. 

Texas  pine, 

yellow  pine, 
5=1800 

on 

lb  per  sq  in 

lb  per  sq  in 

5=1  260 

5  =  1620 

joists 

centers 

t^=55 

A=6q 

lb  per  sq  in 
A  =  7o 

lb  per  sq  in 
A=9o 

lb  per  sq  in 

A  =  100 

in 

in 

ft         in 

h     in 

ft         in 

ft         in 

ft         in 

2X4 

16 

7          4 

7          9 

8          4 

9         6 

10        10 

2X4 

20 

6          7 

6        10 

7          6 

8         6 

8        10 

2X6 

16 

II          I 

II          7 

12          6 

14          2 

15          0 

2X6 

20 

9        II 

ID            4 

II          2 

12          8 

13          4 

3X6 

16 

13          7 

14          2 

15           3 

17          5 

18          3 

3X6 

20 

12          2 

12          8 

13          8 

15          7 

16          4 

2X8 

16 

14          9 

15          6 

16          8 

18        II 

20          0 

2X8 

20 

13          3 

13        10 

14        II 

16        II 

17         10 

2X8 

24 

12          I 

12  .       7 

13          7 

15          6 

16           3 

2X10 

16 

18          6 

19          3 

20        10 

23          8 

25           0 

2X10 

20 

16          7 

17          3 

18          8 

21          2 

22             3 

2X10 

24 

IS          I 

15          9 

17          0 

19          3 

20             4 

Table  XIX.*     Maximum  Span  for  Rafters.     Slate  Roofs  not  Plastered, 
or  Shingle  Roofs  Plastered 

See  explanatory  notes  on  page  736 


Total  load,  57  pounds 

per  square  foot 

Norway 

Douglas 

Long-leaf 
ellow  pine, 
5  =  1800 

Sizes 
of 

Distance 
on 

Hemlock, 

White  pine, 

5  =  1  080 
lb  per  sq  in 

pine  or 
spruce, 
5=1260 

fir  or 
Texas  pine, 
5  =  1620      J 

5=990 
lb  per  sq  in 

joists 

centers 

tA-SS 

A  =60 

lb  per  sq  in 
A=yo 

lb  per  sq  in 
A  =90 

b  per  sq  in 
A  =  100 

in 

in 

ft         in 

ft         in 

ft         in 

ft         in 

ft         in 

2X4 

16 

6          9 

7          I 

7          7 

8          8 

9          2 

2X4 

20 

6         0 

6          4 

6         9 

7          9 

8          2 

2X6 

16 

10         2 

10          7 

II          6 

13          0 

13          8 

2X6 

20 

9          I 

9         6 

10          2 

II          7 

12          3 

3X6 

16 

12          6 

13         0 

14          I 

IS        II 

16          9 

3X6 

20 

II          I 

II          8 

12          7 

14          3 

IS          0 

2X8 

16 

13          7 

14          2 

IS          3 

17          4 

18          3 

2X8 

20 

12          2 

12          8 

13          8 

IS         6 

16          4 

2X8 

24 

II          I 

II          7 

12          6 

14         2 

14        II 

3X8 

16 

16          7 

17          4 

18          9 

21          3 

22          5 

3X8 
3X8 

20 
24 

14           ID 

15          6 

16          9 

19         0 

20          I 

13          7 

14          2 

15          3 

17          4 

18          4 

2X10 

16 

17          0 

17          8 

19          2 

21          7 

22        10 

2X10 

20 

15          2 

15        10 

17          I 

19          4 

20         6 

2X10 

24 

13        10 

14         6 

IS          7 

17          8 

18          8 

♦Tables 

XVIII,  XIX  and  XX  are  intended  fr 

r  climates  where  a  2-ft  snow- 

fall  may  be 

(expected. 

In  the  Southern  States,  where  there 

is  very  little  snow,  the  spa 

IS  in  Table 

XVIII  will 

be  safe  for  slate  or  gravel  roofs  if  th 

2  joists  arc  sawed  to  the  full 

dimensions. 

Variations 

in  "  Safe  spans"  in  different  tables,  1 

or  the  same  kind  of  wood,  d 

spend  upon 

the  assume 

d  safe  flex 

ural  fiber-stre 

3S  or  moduhis 

of  elasticity 

or  both. 

t  A  in  the  tables  is  the  coefhcient  in  formulas  for  beams  and  is  one-eighteenth  of  the 
assumed  flexural  fiber-stress,  S. 


Table  for  Maximum  Span  of  Rafters 


741 


Table  XX.*     Maximum  Span  for  Rafters.     Slate  Roofs  Plastered,  or 
Gravel  Roofs  not  Plastered 

See  explanatory  notes  on  page  736 


Total  load,  66  pounds 

per  square  foot 

Sizes 

of 
joists 

Distance 

on 
centers 

Hemlock, 

5  =  990 
lb  per  sq  in 

White  pine, 

5  =  1  080 

lb. per  sq  in 

A  =60 

Norway 
pine  or 
spruce, 
5=1260 
lb  per  sq  in 
A  =70 

Douglas 

fir  or 

Texas  pine, 

5  =  1620 

lb  per  sq  in 

A  =90 

Long-leaf 
yellow  pine, 

5=1800 

lb  per  sq  in 

A  =  100 

in 

in 

ft         in 

ft         in 

ft         in 

ft         in 

ft         in 

2X6 

16 

9          5 

9        10 

10          8 

12          I 

12          9 

2X6 

20 

8          6 

8        10 

9         6 

10         9 

II          5 

3X6 

16 

II          7 

12          I 

13          I 

14        10 

15          7 

3X6 

20 

10          4 

10        10 

II          8 

13          3 

14         0 

2X8 

16 

12          7 

13          2 

14          2 

16          2 

17          0 

2X8 

20 

II           3 

II          9 

12          9 

14         5 

IS          2 

2X8 

24 

10          3 

10          9 

II          7 

13         2 

13        10 

3X8 

16 

15          5 

16          I 

17          5 

19         9 

20        10 

3X8 

20 

13          9 

14          5 

IS          3 

17          8 

18          8 

3X8 

24 

12          7 

13          2 

14          2 

16          2 

17          0 

2X10 

16 

15          9 

16          6 

17          9 

20          2 

21          3 

2X10 

20 

14          I 

14          8 

15        II 

18          0 

19          0 

2X10 

24 

12        10 

13          5 

14         6 

16         6 

17          5 

2X12 

16 

18        10 

19         9 

21          4 

24         2 

2S          6 

2X12 
2X12 

20 

16        10 

17          8 

19         I 

21          8 

22        10 

24 

15         5 

16          I 

17          5 

19          9 

20        10 

*  Tables  XVIII,  XIX  and  XX  are  intended  for  climates  where  a  2-ft  snow-fall  may  be 
expected.  In  the  Southern  States,  where  there  is  very  little  snow,  the  spans  in  Table 
XVIII  will  be  safe  for  slate  or  gravel  roofs  if  the  joists  are  sawed  to  the  full  dimensions. 
Variations  in  "Safe  spans"  in  different  tables,  for  the  same  kind  of  wood,  depend  upon 
the  assumed  safe  flexural  fiber-stress  or  modulus  of  elasticity  or  both. 

t  A  in  the  tables  is  the  coefficient  in  formulas  for  beams  and  is  one-eighteenth  of  the 
assumed  flexural  fiber-stress,  5. 


742  Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 

Table  XXI.     Maximum  Span  for  Ceiling- Joists 

See  explanatory  notes  on  page  736 


Total  load,  20  pounds  per  square  foot 

Sizes 

of 
joists 

Distance 

Hemlock, 

White  pine, 

Norway 

Short-leaf 
yellow  pine 

Long-leaf 
yellow  pine, 

centers 

*  £  =  900  000 

E  =  i  000  000 

pine, 
£  =  i  100  000 

spruce, 

Douglas  fir, 

£  =  I  200  ooc 

£  =  i  sooooo 

in 

in 

ft         in 

ft         in 

ft         in 

ft         in 

ft         in 

2X4 

12 

8        II 

9          3 

9          6 

9        10 

10          7 

2X4 

16 

8          I 

8          5 

8          8 

8        II 

9         7 

2X6 

12 

13          5 

13        10 

14          4 

14          9 

IS        10 

2X6 

16 

12          2 

12          7 

13          0 

13  -      5 

14         s 

2X8 

12 

17        10 

18          6 

19          I 

19          8 

21             2 

2X8 

16 

16          3 

16        10 

17           4 

17        10 

19          3 

2X8 

20 

15           I 

IS          7 

16           I 

16          7 

17         10 

Total  load,  24  pounds  per  square  foot                                            | 

2X10 

12 

21             0 

21          9 

22             5 

23          I 

24       II 

2X10 

16 

19             I 

19          8 

20             5 

21          0 

22             2 

2X10 

20 

17          8 

18          4 

18     II 

19         6 

21             0 

2X12 

12 

25             2 

26          0 

26       II 

27          9 

29           II 

2X12 

i6 

22          II 

23         9 

24          6 

2S          2 

27             2 

2X12 

20 

21             3 

22         0 

22          9 

23          S 

25             2 

*  £  is  the  modulus  of  elasticity  and  is  in  pounds  per  square  inch. 

Table 

XXn.     Maximum  Span  for  Floor- Joists  for  Dwellings,  Tenements 

an 

d  Grammar-School  Rooms  with  Fixed  Desks 
See  explanatory  notes  on  page  736 

Total  load,  60  pounds  per  square  foot                                          j 

Sizes 

of 
joists 

Distance 

Hemlock, 

White  pine, 

Norway 

Short-leaf 
yellow  pine. 

Long-leaf 
yellow  pine. 

on 
centers 

*£:=9ooooo 

£  =  i  000000 

pine, 
£  =  i  100  000 

spruce, 
£  =  i  200  000 

Douglas  fir, 
£  =  I  500  000 

in 

in 

ft        in 

ft        in 

ft        in 

ft         in 

ft         in 

2X  6 

12 

9         3 

9         7 

9        II 

10         3 

II          0 

2X  6 

16 

8         5 

8         9 

9         0 

9         3 

10          0 

3X  6 

12 

10          8 

II          0 

II          4 

II          8 

12          7 

3X  6 

16 

9         8 

10         0 

10          4 

10          8 

II          S 

2X  8 

12 

12          4 

12        10 

12          3 

13         8 

14          8 

2X  8 

16 

II          3 

II          8 

12          0 

12          4 

13          4 

3X  8 

12 

14          2 

14          8 

IS          2 

IS          7 

16         10 

3X  8 

16 

12        II 

13          4 

13          9 

14          2 

15          3 

2X10 

12 

IS          6 

16          0 

16          7 

17          0 

18          3 

2X10 

16 

14          I 

14          7 

IS          0 

15          6 

16          8 

Total  load,  66  pounds  per  square  foot                                         [ 

3    Xio 

12 

17          2 

17          9 

18          4 

18        II 

20          4 

3    Xio 

16 

IS          7 

16          2 

16          8 

17         2 

18         6 

2     X12 

12 

18          0 

18          8 

19          3 

19          8 

21          4 

2     X12 

16 

16          4 

16        II 

17          8 

18          0 

19        S 

3     X12 

12 

20          7 

21          4 

22          0 

22          8 

24          S 

3     X12 

16 

18          8 

19          4 

20          0 

20          7 

22          2 

2     X14 

12 

21          0 

21         II 

22          5 

23          I 

24        10 

2     X14 

16 

19          I 

19          9 

20          5 

21          0 

22          7 

2HX14 

12 

22          7 

23          S 

24          2 

24        II 

26        10 

2M2X14 

16 

20         6 

21          3 

21        II 

22          7 

24           4 

3     X14 

12 

24         0 

24        10 

2S          8 

26          5 

28          6 

3     X14 

16 

21        10 

22          7 

23           4 

24          0 

2S         10 

'  E  is  the  modulus  of  elasticity  and  is  in  pounds  per  square  inch. 


Tables  for  Maximum  Span  of  Floor- Joists 


743 


Table  XXUI 

.     Maximum  Span  for  Floor- Joists 

for  Office-Buildings 

See  explanatory  notes  on  page  736 

Total  load,  93  pounds  per  square  foot                                         j 

Sizes 

of 
joists 

Distance 

Hemlock, 

White  pine, 

Norway 

Short-leaf 
yellow  pine, 

Long-leaf 
yellow  pine, 

centers 

*  £  =  900  000 

E  —  i  000  000 

£  =  I  100  000 

spruce, 
E  =  i  200  000 

Douglas  fir, 
E  =  i  500  000 

m 

m 

ft         in 

ft         in 

ft         in 

ft         in 

ft        in 

3X  8 

12 

12          3 

12          8 

13          I 

13          6 

14         6 

3X  8 

16  ■ 

II          I 

II          6 

II        II 

12          3 

,13         2 

2X10 

12 

13          4 

13        10 

14          3 

14         8 

IS        10 

2X10 

16 

12          2 

12          7 

13          0 

13          4 

14         5 

3X10 

12 

15          4 

IS        10 

16          4 

16        10 

18           2     ; 

3X10 

16 

13        II 

14         5 

14         10 

IS          4 

16           7     ' 

2X12 

12 

16          0 

16          7 

17          2 

17          8 

19           0 

2X12 

;« 

14          7 

15          I 

15          7 

16          0 

17          3 

Total  load,  96  pounds  per  square  fo 

•ot 

3     X12 

12 

18          2 

18        10 

19          5 

20         0 

21            6 

3     X12 

16 

16         6 

17          I 

17          8 

18         2 

19          7 

2     X14 

12 

18         6 

19         2 

19        10 

20         s 

21          II 

2     X14 

16 

16        10 

17          5 

18          0 

18         6 

19          II 

2I/2X14 

12 

19        II 

20         8 

21          4 

22         0 

23         8 

2 1/2X14 

16 

18         2 

18          9 

19          5 

19        II 

21         6 

3     X14 

12 

21          2 

21        11 

22          8 

23          4 

25         a 

3     X14 

16 

19          3 

19        II 

20          7 

21            3 

22        10 

*  £  is  the  modulus  of  elasticity  and  is  in  pounds  per  square  .inch.  ,. 

Table  XXIV.    Maximum  Span  for  Floor- Joists  for  Churches  and  Theaters 
with  Fixed  Seats 

See  explanatory  notes  on  page  736 


Total  load,  102  pounds 

per  square  foot 

Sizes 
of 

joists 

Distance 

Hemlock, 

White  pine. 

Norway 

pine, 

£  =  i  100  000 

Short-leaf 
yellow  pine, 

Long-leaf 
yellow  pine, 

on 
centers 

♦£=900000 

£  =  i  000000 

spruce, 
£  =  i  200000 

Douglas  fir, 
£  =  i  500000 

in 

in 

ft        in 

ft        in 

ft        in 

ft        in 

ft        in 

3X  8 

12 

II        10 

12         3 

12 

8 

13         I 

14         I 

3X  8 

16 

10         9 

II         2 

II 

6 

II        II 

12         9    ' 

2X10 

12 

12        II 

13         5 

13 

10 

14          3 

15          4 

2X10 

16 

II          9 

12          2 

12 

7 

13          0 

13        II    , 

3X10 

12 

14        10 

IS          4 

IS 

10 

16          4 

17          7    '■■ 

3X10 

16 

13         6 

13        II 

14 

S 

14        10 

16         0 

2X12 

12 

IS          7 

16          I 

16         8 

17          I 

18         5 

2X12 

16 

14          2 

14         8 

IS          I 

IS          7 

16         9 

Total  loa 

i,  105  pounds 

per  square  f 

30t 

3     X12 

12 

17         8 

i8         3 

18        10 

19        S 

20        II 

3     X12 

16 

16         0 

16         7 

17         I 

17          8 

19          0 

2     X14 

12 

18         0 

18         7 

19         3 

19          8 

21          4 

2     X14 

16 

16         4 

16        II 

17          5 

18          0 

19          4 

2I/2X14 

12 

19          4 

20         I 

20         8 

21          4 

23          0 

2I/2X14 

16 

17          7 

18         3 

18        10 

19          4 

20          11 

3     X14 

12 

20          7 

21         4 

22          0 

22          8 

24          5 

3     X14 

16 

18          8 

19           4 

20         0 

26           7 

22          2 

E  is  the  modulus  of  elasticity  and  is  in  pounds  per  square  inch. 


744 


Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 


Table  XXY.     Maximum  Span  for  Floor- Joists  for  Assembly-Halls  and  Corridors 

See  explanatory  notes  on  page  736 


Total  load 

,  12a  pounds 

per  square  foot 

Sizes       D 

of 
joists      c 

istance 

Hemlock, 

White  pine. 

Norway 

Short-leaf 
yellow  pine. 

Long-leaf 
yellow  pine. 

enters 

*  £=900  000 

E  =  i  000000 

R  =  i  100  000 

spruce, 
£  =  I  200  000 

Douglas  fir, 
£  =  I  500  000 

in 

in 

ft         in 

ft         in 

ft         in 

ft         in 

ft         in 

3X  8 

12 

II          2 

II          7 

II        II 

12         3 

13          3 

3X  8 

16 

II          0 

10         6 

10        10 

II          2 

12            0 

2X10 

12 

12          2 

12         7 

13         0 

13       S 

14         5 

2X10 

16 

II          I 

II          S 

II        10 

12          2 

13       I 

3X10 

12 

13        II 

14         5 

14        II 

15          4 

16         6 

3X10 

16 

12         8 

13          I 

13         7 

13        II 

IS         0 

2X12 

12 

14         7 

IS          2 

IS         8 

16          I 

17         4 

2X12 

16 

13         3 

13         9 

14         2 

14         8 

IS         9 

Total  loac 

[,126  pounds 

per  square  foot 

3     X12 

12 

16         7 

17         2 

17          9 

18         3 

19         8 

3     X12 

16 

IS          I 

IS         7 

16          I 

16          7 

17        10 

2     X14 

12 

16        II 

17         6 

18          I 

18          7 

20          I 

2     X14 

16 

IS          4 

15        II 

16        s 

16        II 

18         3 

21^^X14 

12 

18          2 

18        10 

19         6 

20          I 

21          7 

2i/iXi4 

16 

16         8 

17          3 

17        10 

18          4 

19         9 

3     X14 

12 

19         4 

20          I 

20         8 

21          4 

22       II 

3     X14 

16 

17          7 

18          3 

18        10 

19          4 

20       10 

•  £  is  the  modulus  of  elasticity  and  is  in  pounds  per  square  inch. 

Table  XXVI.     Maximum  Span  for  Floor- Joists  for  Retail  Stores 

See  explanatory  notes  on  page  736 


Total  load,  174  pounds 

per  square  foot 

Sizes 
of 

Distance 

Hemlock, 
5  =  600  lb 

White  pine, 

spruce, 

5=700  lb 

Norway 
pine, 

5=800  lb 

Douglas  fir 

short-leaf 

yellow  pine 

5  =  1  000  lb 

Southern 

long-leaf 

yellow  pine, 

5  =  1  200  lb 

on 

per  sq  in 
*A=33H 

joists 

centers 

per  sq  in 
A  =38.88 

per  sq  in 

per  sq  in 

per  sq  in 

A  =44.44 

A=5S.SS 

A  =66^^ 

in 

in 

ft         in 

ft         in 

ft         in 

ft         in 

ft         in 

3X  8 

12 

8         7 

9         3 

9        II 

II          I 

12         2 

3X  8 

16 

7          S 

8         0 

8         7 

9         7 

10         6 

2X10 

12 

8         9 

9         S 

10          I 

II          4 

12         5 

2X10 

16 

7         7 

8         2 

8         9 

9        10 

10         9 

3X10 

12 

10         9 

II          7 

12        s 

13        10 

IS         2 

3X10 

16 

9         3 

10         0 

10         9 

12          0 

13         2 

2X12 

12 

10         6 

II          4 

12         2 

13         7 

14        10 

2X12 

16 

9         I 

9        10 

10         6 

II          9 

12        10 

Total  loac 

[,  177  pounds 

per  square  fc 

X)t 

3    X12 

12 

12         6 

13         6 

14         6 

16          2 

17         9 

3     X12 

16 

10        10 

II          9 

12         6 

14         0 

IS          4 

2     X14 

12 

12          2 

13          I 

14         0 

15          8 

17          2 

2     X14 

16 

10         6 

II          4 

12          2 

13          7 

14        II 

2\iXi4 

12 

13         7 

14          8 

IS         8 

17          6 

19          2 

2HX14 

16 

II          9 

12         8 

13          7 

15          2 

16          8 

3     X14 

12 

16          8 

18         0 

19          3 

21          6 

23          7 

3     X14 

16 

14          5 

l^          7 

16          8 

18          8 

20          5 

♦  A  in  the  tables  is  the  coefficient  in  formulas 
allowable  flexural  fiber-stress  S.  For  values  of 
62S. 


for  beams  and  is  one-eighteenth  of  the 
A  for  other  woods,  see  Table  II,  page 


Tables  for  Maximum  Span  of  Rafters 


746, 


Table  XXVII.'<'     Maximum  Span  for  Rafters.     Shingled  Roofs,  not  Plastered 

See  explanatory  notes  on  page  736 


Total  load,  48  pounds 

per  square  foot 

Sizes 
of 

Distance 
on 

Hemlock, 
5=600  lb 
per  sq  in 
tA=33H 

White  pine, 

spruce, 
5  =  700  lb 

Norway 

pine. 
5=800  lb  ' 

Douglas  fir, 

short-leaf 

yellow  pine, 

5  =  1  000  lb 

Southern 

long-leaf 

yellow  pine, 

5=1  200  lb 

joists 

centers 

per  sq  in 
yl  =38.88 

per  sq  in 
A  =44-44 

per  sq  in 
A  =55.55 

per  sq  in 
A=66% 

in 

in 

ft         in 

ft         in 

ft         in 

ft         in 

ft         in 

2X  4 

16 

5          9 

6         3 

6         8 

7          5 

8         2 

2X  4 

20 

5          2 

S          7 

5        II 

6         8 

7         4 

2X  6 

16 

8          8 

9         4 

10         0 

II          2 

12         3 

2X  6 

20 

7         9 

8          4 

8        11 

10         0 

10        II 

3X  6 

16 

10         7 

II          S 

12          3 

13         8 

IS          0 

3X  6 

20 

9         6 

10         3 

10        II 

12          3 

13       S 

2X  8 

16 

11          6 

12         6 

13          4 

14        II 

16         4 

2X  8 

20 

10         4 

II          2 

II         II 

13          4 

14         7 

2X  8 

24 

9         5 

10         2 

10        II 

12             2 

13          4 

2X10 

16 

14         5 

15          7 

16          8 

18          8 

20          5 

2X10 

20 

12        II 

13        II 

14         II 

16          8 

18          3 

2X10 

24 

II          9 

12          9 

13          7 

15          2 

16         8 

Table  X 

xvin.* 

Maximum  Span  for  Rai 

ters.     Slate  Roofs,    not  Plastered, 

or  Shingled  Roofs 

,  Plastered 

J 

See  explanatory  note 

3  on  page  736 

IXS 

Total  load,  57  pounds 

per  square  foot 

-■■'. 

Sizes 
of 

Distance 

Hemlock, 
5=600  lb 

White  pine, 

spruce, 

5=700  lb 

Norway 
pine, 

Douglas  fir, 

short  leaf 

yellow  pine. 

Southern 

long-leaf 

yellow  pine. 

on 

per  sq  in 

5=800  lb 

5=1  000  lb 

5=1  200  lb 

joists 

centers 

tA=33H 

per  sq  in 
A  =38.88 

per  vsq  in 

per  sq  in 

per  sq  in 

A  =44.44 

A  =55.55 

A=66H 

in 

in 

ft         in 

ft         in 

ft         in 

ft         in 

ft        in 

2X  4 

16 

5          3 

5         9 

6          I 

6        10 

7         6 

2X  4 

20 

4         9 

5          I 

5         6 

6          I 

6         8 

2X  6 

16 

7        II 

8         7 

9         2 

10         3 

II         3 

2X  6 

20 

7          I 

7          8 

8         2 

9          2 

10         I 

3X  6 

16 

9         9 

10         6 

II          3 

12          7 

13         9 

3X  6 

20 

8         8 

9         5 

10         I 

II          3 

13           4 

2X  8 

16 

10         7 

II          5 

12          3 

13          8 

IS         0 

2X  8 

20 

9         6 

10         3 

10        II 

12          3 

13         5 

2X  8 

24 

8         8 

9         4 

10         0 

II          2 

12         3 

3X  8 

16 

13         0 

14         0 

IS          0 

16          9 

18         4 

3X  8 

20 

II          7 

12         6 

13          5 

15          0 

16         4 

3X  8 

24 

10         7 

II          5 

12          3 

13          8 

IS         0 

2X10 

16 

13          3 

14          4 

15          3 

17          I 

18         9 

2X10 

20 

II         10 

12          9 

13          8 

IS          3 

16         9 

2X10 

24 

10        10 

II          8 

12          6 

13        II 

IS          3 

*  Tables  XXVII,  XXVIII  and  XXIX  are  intended  for  climates  where  a  2-ft  snow-fall 
may  be  expected.  In  the  Southern  States,  where  there  is  very  little  snow,  the  spans  in 
Table  XXVII  will  be  safe  for  slate  or  gravel  roofs  if  the  joists  are  sawed  to  the  full  dimen- 
sions.  Variations  in  "Safe  spans"  in  different  tables,  for  the  same  kind  of  wood,  depend 
upon  the  assumed  safe  fliexural  fiber-stress  or  modulus  of  elasticity  or  both. 

t  See  foot-note  with  Table  XXVI. 


746 


Strength  and  Stiitness  of  Wooden  Floors  Chap.  21 


Table  XXIX.'*'     Maximum  Span  for  Rafters.     Slate  Roofs,  Plastered,  or 
Gravel  Roofs,  not  Plastered 

See  explanatory  notes  on  page  736 


Total  load,  66  pounds 

per  square  foot 

Sizes 
of 

joists 

Distance 

on 
centers 

Hemlock, 
6' =600  lb 
per  sq  in 
tA=33H 

White  pine, 

spruce, 
5=700  lb 
per  sq  in 
yl  =38.88 

Norway 

pine, 
5=800  lb 
per  sq  in 
^=44.44 

Douglas  fir, 

short-leaf 

yellow  pine, 

5  =  1  000  lb 

per  sq  in 

/I  =55-55 

Southern 
long-leaf 
yellow  pine, 
5  =  1  200  lb 
per  sq  in 
A=66^yi 

in 

in. 

ft        in 

ft        in 

ft         in 

ft        in 

ft         in 

2X  6 

16 

7         S 

8         0 

8         6 

9         6 

10         5 

2X  6 

20 

6         7 

7          2 

7          7 

8         6 

9         4 

3X  6 

16 

9         0 

9         9 

10          5 

II          8 

12        10 

3X  6 

20 

8         I 

8         9 

9         4 

10 

5 

II          5 

2X  8 

16 

9        10 

10         8 

II          4 

12 

8 

13        11 

2X  8 

20 

8        10 

9         6 

10          2 

II 

4 

12          5 

2X  8 

24 

8         0 

8          8 

9         3 

10 

5 

II          4 

3X  8 

16 

12          I 

13          0 

13        II 

IS 

7 

17          I 

3X  8 

20 

10         9 

n          8 

12          5 

13 

II 

IS          3 

3X  8 
2X10 

24 
16 

9        10 

10         8 

II          4 

12 

8 

13        II 
17          5 

12          4 

13         3 

14          2 

IS        ii 

2X10 

20 

II          0 

II        II 

12          9 

14             2 

IS          7 

2X10 

24 

10         I 

10       tb  i 

II        10 

13             0 

14         a 

2X12 

16 

14         9 

ti       If 

17          I 

19             I 

20       II 

2X12 

20 

13         2 

14          3 

15          3 

17             I 

18         8 

2X12 

24 

12         I 

13          0 

13        II 

IS          7 

17       '1 

•  Tables  XXVII,  XXVIII  and  XXIX  are  intended  for  climates  where  a  2-ft  snow-fall 
may  be  expected.  In  the  Southern  States,  where  there  is  very  little  snow,  the  spans  in 
Table  XXVII  will  be  safe  for  slate  or  gravel  roofs  if  the  joists  are  sawed  to  the  full  dimen- 
sions. Variations  in  "Safe  spans"  in  different  tables,  for  the  same  kind  of  wood,  depend 
upon  the  assumed  safe  flexural  fiber-stress  or  modulus  of  elasticity  or  both. 

t  See  foot-note  with  Table  XXVI. 

To  Determine  the  Strength  of  an  Existing  Floor.  When  a  building 
i$  leased  for  mercantile  or  manufacturing  purix)ses  the  tenant  will  generally 
desire  to  know  the  greatest  load  w!\ich  it  will  be  safe  to  put  upon  the  floors, 
and  some  building  laws  require  that  the  safe  load  for  the  floors  in  certain  classes 
of  buildings  shall  be  computed  and  posted  in  a  conspicuous  place  in  each  story. 
It  is  therefore  important  that  every  architect  should  know  how  to  compute  the; 
safe  strength  of  any  existing  floor.  The  problem  is  practically  the  reverse  of' 
that  of  proportioning  a  floor  to  a  given  load.  In  speaking  of  the  strength  of  a 
floor  a  distinction  should  be  made  between  the  safe  strength  and  the  safe  load. 
The  SAFE  STRENGTH  should  mean  the  maximum  safe  load  for  the  beams,  includ- 
ing the  weight  of  the  construction,  flooring  and  ceiling,  while  the  safe  load 
refers  to  the  maximum  load  which  may  safely  be  placed  uix)n  the  floor.  The 
safe  load  is  found  by  first  computing  the  safe  strength  and  then  subtracting 
the  weight  of  tl\e  materials  forming  the  floor,  including  the  ceiling  below,  if  there 
is  one.  The  most  convenient  measurement  for  either  the  safe  strength  or 
the  SAFE  LOAD  of  a  floor  is  in  pounds  per  square  foot.  The  following  examples 
will  serve  to  show  the  method  of  determining  the  safe  load  for  an  ordinary  ware- 
house-floor. 

Example  4.  It  is  required  to  determine  the  safe  load  per  square  foot  for  a 
floor  framed  as  shown  in  Fig.  4,  the  building  being  in  a  city  the  laws  of  which 


Determination  of  Strength  of  an  Existing  Floor 


747 


allow  I  200  lb  per  sq  in  for  the  safe  flexure  fiber-stress  for  the  wood  of  which 
the  joists  and  girders  are  made.  The  joists  are  covered  with  two  thicknesses 
of  %-in  flooring  and  the  ceihng  below  is  corrugated  iron. 

Solution.  The  first  step  will  be  to  find  the  s'afe  strength  of  the  22-ft  joists. 
As  this  is  a  warehouse-floor  we  will  use  the  tables  for  strength  throughout. 
From  Table  XII,  page  643,  for  S  =  1  200  lb  i)er  sq  in,  we  find  the  safe 
strength  of  a  i  by  14-in  joist  of  22-ft  span  to  be  i  188  lb;  hence  the  strength 
of  a  2Vz  by  14-in  joist  will  be  i  188  x  2^^  =  2  970  lb.  As  the  joists  are 
16  in  on  centers,  each  joist  supports  a  floor-area  of  V/ix  22  ft=  29!^  sq  ft. 
The  SAPE  STRENGTH  PER  SQUARE  TOOT  of  this  portion  of  the  floor  will  therefore 


Load  from  Staii- 
1800  Ibg. 


Stin-up 
Fig.  4.     Plan  of  a  War^lipuse-floor 


be  2  970/29.3  =  loi  lb.-  Suppose  the  estimated  weight  of  the  floor  per  square 
foot  is  8  lb  for  the  joists,  6  lb  for  the  flooring  and  i  lb  for  the  corrugated-iron 
ceiling,  or,  say,  15  lb  in  all.  Then  the  SAtE  load  per  square  rooT  for  the  22-ft 
joists  will  be  loi  —  15  =^  86  lb. 

The  Headers.  We  will  next  find  the  safe  load  for  the  4  by  14-in  headers  at 
each  side  of  the  stair-well.  As  the  tail-beams  are  framed  into  the  headers, 
we  should  deduct  one  inch  from  the  thickness  of  each  header  for  the  loss  of 
strength  in  framing,  leaving  3  by  14  in  for  the  effective  dimension  of  each. 
From  Table.  XII,  page  643,  we  find  the  safe  strength  of  a  i  by  14-in  beam 
of  i2-ft  span  to  l>e  i  867  lb.  Hence  the  strength  of  the  3  by  14  will  be  i  867  x  3 
=  5  601  lb.  The  floor-area  supported  by  each  header  is  4H  x  12  ft  =  54  sq  ft; 
hence  the  safe  strength  of  the  header  per  square  foot  of  floor  is  5  601/54  == 
104  lb.  Deducting  the  weight  of  the  floor  per  square  foot,  we  have  104  ■-  15  = 
89  lb  for  the  safe  load.  i  -'■  ■ 

Trimmer  A.  Trimmer  A  (Fig.  4)  supports  about  the  same  amount  of  floor- 
ing as  one  of  the  common  joists,  and  supports,  also,  the  ends  of  the  headers. 
Deducting  2H  in,  the  thickness  of  the  common  joists,  we  have  a  5  by  14-in  beam 


748  Strength  and  Sti^ness  of  Wooden  Floors  Chap.  21 

left  to  support  the  headers.  As  the  headers  are  supported  in  iron  stirrups,  or 
beam- hangers,  no  deduction  in  strength  need  be  made  for  framing.  To  find  the 
safe  strength  of  a  beam  loaded  with  two  concentrated  loads,  equidistant  from 
the  supports,  we  must  use  Formula  (14),  Fig.  11,  page  631.  In  tliis  case  m  = 
8  ft  10  in,  or  8%  ft  and  A  =  1  200/18  =  66.7  (Table  XII,  page  643). 

Applying  the  formula,  the  safe  load  at  each  joint  =  5  X  14  X  14  X  66.7/4  X 
8-^6  =  I  848  lb. 

The  floor-area  supported  by  one  stirrup  is  equal  to  one-half  of  the  area  sup- 
ported by  the  header,  or  27  sq  ft;  hence  the  safe  strength  per  square  foot  of 
the  5  by  14-in  header  is  i  848/27  =  68  lb,  and  deducting  15  lb  per  sq  ft  for 
the  weight  of  the  floor,  we  have  53  lb  per  sq  ft  as  the  safe  load  that  the  trimmer 
will  support  on  the  floor  at  each  side  of  the  stairs.  Considering,  as  found 
above,  that  the  safe  load  for  the  2^/^  in,  which  we  deducted  to  take  the  place  of  a 
common  joist,  is  86  lb  per  sq  ft,  we  might  consider  the  safe  load  for  the  trimmer 
as  the  average  of  86  and  53,  or  about  70  lb  per  sq  ft. 

Trimmer  B.  This  10  by  14-in  timber  (Fig.  4)  has  to  support  the  same  floor- 
loads  as  trirtimer  A,  and  also  the  lower  end  of  a  flight  of  stairs  for  which  an  allow- 
ance of  at  least  i  800  lb  should  be  made.  This  stair-load  being  practically 
concentrated  at  the  middle  of  the  trimmer  is  equivalent  to  a  distributed  load  of 
3  600  lb.  As  the  safe  load  for  a  i  by  14-in  joist  of  22-ft  span  is  i  188  lb  (Table 
XII,  page  643),  it  win  require  a  thickness  of  3  600/1  188=  3  in  to  support 
the  stairs,  leaving  7  in  to  support  the  floor-loads.  As  this  is  I'i  in  less  than  the 
thickness  of  trimmer  A,  it  is  evident  that  the  strength  of  the  floor  at  B  will  be 
a  little  less  than  at  A ;  but  as  it  is  improbable  that  the  entire  floor-space  will  be 
loaded  at  any  given*  time,  it  would  be  safe  to  rate  the  strength  of  the  floor  at 
each  side  of  the  stairway  at  70  lb  per  sq  ft,  live  load,  and  beyond  the  stair- 
way at  86  lb. 

Partitions.  When  the  floor  supports  partitions,  the  weight  of  the  latter  and 
any  load  resting  upon  them  must  be  taken  into  account  in  determining  the 
safe  load  for  the  floor.  If  a  partition  runs  the  same  way  as  the  joists,  then  only 
the  joist  directly  under  the  partition,  and  the  joists  at  each  side  will  be  affected; 
but  if  a  partition  runs  across  the  joists,  then  it  affects  the  safe  load  of  the  entire 
floor. 

Example  5.  Suppose  that  the  22-ft  joists  in  the  floor  shown  in  Fig.  4  have  to 
support  a  plastered  partition  12  ft  high,  running  across  the  joists  half-way  be- 
tween the  walls.    What  will  be  the  safe  load  for  the  floor? 

Solution.  A  plastered  partition  with  2  by  4  or  2  by  6-in  studs,  set  16  in  on 
centers,  weighs  about  20  lb  per  sq  ft  of  partition-face;  hence  a  partition  12  ft 
high  will  weigh  240  lb  per  lin  ft  of  partition.  As  the  joists  are  16  in  on  cen- 
ters, each  joist  supports  iH  hn  ft  of  partition,  weighing  320  lb.  As  this  load  is 
concentrated  at  the  middle  span  of  the  joists  it  is  equivalent  to  a  distributed 
load  of  640  lb.  In  Example  4,  we  found  the  safe  distributed  load  for  the  2y2  by 
14-in  joists  of  22-ft  span  to  be  2  970  lb.  Subtracting  640  lb  from  this  we  have 
2  330  lb,  which  may  be  used  for  the  floor.  As  the  floor-area  supported  by  one 
joist  is  29H  sq  ft,  the  safe  strength  of  the  floor  per  square  foot  is  2  330/29 H  =  79 
lb,  and  the  safe  load  is  79  —  15  =  64  lb  per  sq  ft.  Hence  the  partition  decreases 
the  safe  load  by  86  —  64  =  22  lb  per  sq  ft.  Whenever  the  ui:)per-floor  joists 
are  supported  b}''  a  partition  carried  by  a  floor  below,  the  effect  of  the  partition 
and  its  load  upon  the  strength  of  the  lower  floor  should  be  very  carefully  com- 
puted. 

Bridging  of  Floor- Joists.  By  BRrociNrG  is  meant  a  system  of  bracing  for 
floor- joists,  either  by  means  of  small  struts,  as  in  Fig.  5,  or  by  means  of  single 


Bridging  and  Framing  of  Wooden  Floors 


749 


Fig.  5.     Floor-joists  with  Bridging 


pieces  of  boards  set  at  right-angles  to  the  joists  and  fitting  in  between  them. 
The  effect  of  this  bracing  is  of  decided  advantage  in  sustaining  any  concen- 
trated LOAD  upon  a  tloor;   but  it  does  not  materially  strengthen  a  floor  to  resist 

a     UNIFORMLY     DISTRIBUTED     LOAD.      The 

bridging  also  stiffens  the  joists,  and  pre- 
vents them  from  turning  sidewise.  It  is 
customary  to  insert  rows  of  cross-bridging 
from  5  to  8  ft  apart;  and  to  be  effective 
the  rows  of  bridging  should  be  in  straight 
lines  along  the  floor,  so  that  each  bridging- 
strut  may  abut  directly  opposite  those 
adjacent  to  it.  The  method  of  bridging 
shown  in  Fig.  5,  and  known  as  cross- 
bridging,  is  considered  to  be  by  far  the 
best,  as  it  allows  the  thrust  to  act 
parallel  to  the  axis  of  the  strut,  and  not 
across  the  grain,  as  must  be  the  case 
where  single  pieces  of  boards  are  used. 
The  bridging  should  be  of  iH  by  3-in 
stock,  for  2  by  lo-in  and  smafler  joists, 
and  of  2  by  3-in  stock  for  12-  and  14-in 
joists. 

Framing  of  Wooden  Floor-Beams. 
In  dwellings,  tenements  and  lodging- 
houses  it  is  frequently  necessary  to  frame  the  timbers  so-  that  they  are  fluslf 
with  one  another.  The  old  methods  of  framing  the  tail-beams  and  headers  or 
headers  and  trimmers  by  mortise-and-tenon  joints  are  now  generally  superseded 
by  hanging  the  timbers  in  stirrups  or  malleable-iron  joist -hangers.  In  this  con- 
struction the  entire  strength 
of  the  timbers  is  retained,  whib 
the  cost  of  the  hangers  is  often 
less  than  the  labor-cost  in  pre- 
paring the  mortise-and-tenoi\ 
joints.  All  headers  6  ft  oi 
more  in  length  should  be 
carried  in  joist-hangers  ot 
stirrups  and  this  is  usually 
required  in  the  building  codes, 
of  the  large  cities.  In  ware^ 
houses  and  all  first-class  build-' 
ings  the  •  framing  should  be 
done  by  means  of  joist-hangers. 
For  light  floors,  with  moderate 
spans,  it  is  generally  safe  to 
frame  the  tail-beams  into  a 
header,  provided  the  latter  is 
strong  enough  to  carry  the 
load  and  allow  i  in  in  thickness 
for  the  mortising.  Headers, 
also,  carrying  not  more  than  two  tail-beams  are  often  framed  into  the  trimmers. 
In  case  the  old  methods  of  framing  are  used  instead  of  the  superior  methods 
with  joist-hangers,  the  best  shape  and  proportions  for  the  tenons  and  ends  of 
the  tail-beams  or  headers  are  those  shown  in  Fig.  6.    This  form  of  framing 


Fig.  6.     Framing  of  Joists  into  Header 


750 


Strength  and  Stiffness  of  Wooden  Floors         Chap.  21 


probably  offers  as  large  a  proportion  of  the  strength  of  the  timbers  as  it  is 
possible  to  utilize,  although  for  tail-beams  it  was  the  opinion  of  Mr.  Kidder 
that  a  single  tenon  like  that  shown  in  Fig.  7  is  fully  as  strong,  especially  when 
the  header  is  built  up  of  2-in  planks  spiked  together.     In  either  case,  if  the  floor 


Fig.  7.    Alternate  Method  of 
Framing  Joists  into  Header 


Fig.  8.     Framed  Joist  Split  by  Load 


is  loaded  to  its  full  strength,  the  tail-beam  will  split  at  the  bottom  of  the 
tenon,  as  shown  in  Fig.  8,  which  illustrates  the  weakening  effect  of  the 
mortise-and-tenon  framing. 

Stirrups  and  Joist-Hangers.  The  first  device  used  for  framing  headers  to 
trimmers  without  mortising  was  the  wrought-iron  stirrup  shown  in  Fig.  9. 
These  are  made  either  single  or  double,  depending  upon  whether  one  or  two 
beams  are  to  be  supported.    To  prevent  the  floor  from  spreading  and  thus  per- 


DOUBLE  STIRRUP 


Fig.  9.    Framing  with  Wrought-iron  Stirrups 


mitting  the  header  to  slip  out  of  the  stirrup,  a  joint-bolt  may  be  inserted,  as 
shown  in  the  two  right-hand  illustrations  of  Fig.  9.  To  determine  the  strength 
of  a  stirrup,  multiply  the  sectional  area  of  the  iron,  in  square  inches,  by  12  000 
lb  per  sq  in.     (Table  i,  page  376.) 

The  following  sizes  of  iroa  should,  in  general,  be  used  for  the  different  sizes 
of  joists  to  be  supported: 


Joist  and  Beam-Hangers  751 

Sizes  of  joists  or  timbers  to  be  Sections  of  stirrup- 

supported,  in  inches  •  iron  in  inches 

2  by    8  to  3  by  lo H  by  2H 

4  by  10  to  4  by  12 ^6  by  2}^^ 

6  by  1 2  to  3  by  14 %hy  s 

8  by  12  to  4  by  14 H  by  3H 

6  by  14 H  by  4 

8  by  14  to  10  by  14 H  by  4 

Joist-Hangers.  Aside  from  the  matter  of  strength  there  are  objections  to 
the  use  of  stirrups.  If  the  timber  on  which  they  rest  is  not  perfectly  dry,  the 
stirrups  will  settle  by  an  amount  equal  to  the  shrinkage  of  the  beam  on  which  they 
rest,  and  let  down  the  header  with  them,  and  the  projection  of  the  iron  above 
the  top  of  the  timbers  will  necessitate  cutting  out  the  flooring.  If  the  stirrups 
are  exposed  in  this  way  their  appearance  is  objectionable.  While  they  may 
be  designed  to  resist  any  tensional  stress  the  resistance  of  steel  to  bending 
is  comparatively  small,  and  the  resulting  crushing  of  the  timber  where  they 
go  over  the  edge  is  the  chief  objection  to  the  use  of  stirrups  of  this  type 
for  heavily  loaded   floors.    The  small  bearing  of  a  timber  on  a  stirrup  is 


y///){///////j\ 

Cracka  Developed  >^ 

^^^ 

X —               / 

^'' rj^^^^z^ 

i*    / 

'"'/^^^m 

5-  / 

%|%gw 

Iv  1 

^M^m^ 

p" 

-,_,,.  Timber  Crushed 

Cracka  Developed 

Fig.  10.    Failure  of  Steel  Stirrup  Wall-hanger 


not  sufficient  to  distribute  the  load  on  the  wood  over  the  required  area.  This 
increases  the  bearing  per  square  inch,  allows  the  hanger  to  crush  into  the  edge 
and  tends  to  straighten  out  the  stirrup  as  shown  in  Fig.  29,  page  757.  The 
same  serious  objection  applies  to  the  use  of  steel  stirrup-hangers  in  brick  walls 
to  carry  beams  free  of  the  walls.  As  previously  explained,  all  the  load  is 
brought  to  the  extreme  edge,  causing  a  much  greater  load  per  square  inch  on 
the  masonry  than  is  allowable.  Fig.  10  *  shows  the  effect  of  crushing,  in  a 
warehouse-building  in  Minneapolis,  Minn.  Wall-hangers  made  of  steel 
stirrups  should  not  be  used.  Patented  steel  hangers  riveted  to  bearing-plates 
are  likewise  very  undesirable  as  the  crushing  effect  is  greatest  at  the  outer 
edge,  due  to  the  straightening-out  tendency  of  the  hanger  at  this  point. 

Figs.  11  and  12  illustrate  the  Duplex  and  Goetz  joist-hangers,  which  are 
patented  and  are  claimed  to  be  superior  to  the  old-style  stirrups.  The  Duplex 
hanger  is  used  not  only  for  ordinary  building-construction,  but  for  the  most 
heavily  loaded  mill-construction  in  factories  and  warehouses.  As  these  hangers 
are  made  of  malleable  iron  they  will  not  straighten  out  when  heated,  in  case  of 
fire,  and  drop  the  beams.     That  is  what  happens  to  wrought-steel  stirrups 

*  Taken  from  a  paper  on  "Joist  and  Wall-Hangers,"  read  by  Mr.  F.  E.  Kidder  at  a 
meeting  of  the  Colorado  Chapter  of  the  American  Institute  of  Architects,  February  27, 

X903. 


752 


Strength  and  Stiffness  of  Wooden  Floors         Chap.  2 


when  the  twist  becomes  heated.  This  hanger  has  proven  perfectly  satisf actor 
and  is  extensively  used.  Both  are  made  in  sizes  to  fit  all  regular  sizes  of  joist 
oi  girders,  and  have  ample  strength  for  the  purpose  for  which  they  are  intended 


Fig.  11.     Duplex  J»ist-hanger 


Fig.  12.     Goetz  Joist-hanger 


As  shown  by  the  illustrations,  they  are  made  to  be  inserted  in  round  holes  bore( 
in  the  side  of  the  carrying  timbers,  at  or  a  little  above  the  center  line.  Witl 
these  hangers  the  effect  of  shrinkage  is  reduced  one-half,  and  the  other  two  ob 


Fig.  14.     Duplex  I-beam  Shelf-hanger.     Joists  Raised  Less  than  Four  Inches 


jections   to  the  stirrup,   previously  mentioned,   are  overcome.     The  Duple: 
hanger  has  ridges  on  the  inside  of  the  side  brackets  to  hold  the  beam. 
For  timbers  of  larger  size  and  for  the  heaviest  construction,  the  Duplex  hangers 


Joist  and  Beam-Hangers 


753 
By  this 


shown  in  Fig.  32,  page  789,  ate  used  and  are  bolted  to  the  beams, 
construction  the  entire  building  is  tied  together  laterally. 

Fig.  13  shows  the  Duplex  I-beam  hanger  for  framing  floor-joists  to  I  beams' 
This  hanger  is  made  to  exactly  lit  into  the  flange  of  the  I  beam.     It  has  a  rib 


15.     Duplex    I-beam    Box    Hanger.     Joists 
Raised  More  than  Four  Inches 


Fig.  16.    Duplex  Wall-hanger  for 
Joists 


on  the  bottom,  Ys  in  high,  which  serves  as  a  tie  when  the  joist  is  placed  in  the 
hanger,  and  it  provides  a  bearing  of  at  least  4'/2  in  for  the  joist.  It  is  made 
to  carry  any  joist  of  regular  size,  and  offers  one  of  the  best  devices  for  framing 
wooden  joists  to  I  beams  of  the  same 
depth.  The  hangers  arc  looked  to  the 
web  of  the  I  beam.  Fig.  14  shows  the 
Duplex  I-beam  shelf-hanger  which  is  used 
when  the  construction  requires  the  joists 
to  be  raised  above  the  lower  flange  of  the 
I  beam  less  than  4  in.  Fig.  15  illustrates 
the  Duplex  I-beam  box-hanger  and  is 
recommended  where  the  joists  are  raised 
more  than  4  in  above  the  lower  flange 
of  the  I  beam.  In  both  these  construc- 
tions the  hangers  arc  bolted  singly  or 
opposite,  as  required,  on  the  I  beam  and 

the  loads  are  carried  on  the  lower  flanges  of  the  beams.  Fig.  16  shows  a 
similar  hanger  made  to  support  the  wall-end  of  a  floor- joist.  This  form  of 
construction  is  considered    much   superior   to    the   method   of   building    the 


Fig.  17. 


Duplex  Steel  Wall-hanger  for 
Large  Beams 


Fig.  18.     Duplex  Extra-heavy  Wall-hanger  for  Mill-construction 

joists  into  a  wall,  as  it  absolutely  prevents  dry-rot,  and  permits  the  joists  to 
fall,  in  case  of  fire,  without  throwing  the  wall.  It  also  gives  the  load  a  good 
bearing  on  the  wall.  Fig.  17  illustrates  the  Duplex  steel  wall-hanger  for  larger 
timbers,  and  Fig.  18  shows  the  Duplex  extra-heavy  wall-hanger  for  the  heaviest 


754 


Strength  and  Stifitness  of  Wooden  Floors  Chap.  21 


mill-constmction.  These  hangers  bear  the  label  of  approval  of  the  National 
Board  of  Fire  Underwriters  and  are  generally  considered  the  best-designed  wall- 
hangers  now  on  the  market.  This  hanger  gives  an  extra  bearing  on  the  masonry* 
and  is  so  constructed  that  it  reacts  as  a  unit  and  distribute >  the  load  equally  over 
the  entire  surface  of  the  masonry.     There  is  no  tendency  for  a  hanger  of  this 


Fig.  19.     Duplex  Wall-hanger 
for  Concrete  Blocks 


Fig.  20.     "Ideal"  Wrouglit-steel  Beam-hanger 


type  to  crush  in  at  the  edge  of  the  masonry  and  straighten  out,  as  is  the  case 
with  some  other  types  of  wall-hangers.  Fig.  19  shows  the  Duplex  wall-hanger 
used  in  connection  with  walls  constructed  of  concrete  blocks.  These  hangers  are 
often  used  in  repair-work  in  party  walls,  as  they  avoid  the  cutting  of  large  holes 
in  the  walls,  and  also  provide  an  easy  and  simple  method  of  carrying  the  joists 
clear  of  the  walls.    The  Ideal  hanger  illustrated  in  Fig.  20  is  made  of  wrought 


Fig.    21.     "Ideal"    Wrought- 
steel  Beam-hanger 


Fig.  22.     "Ideal"  Wrought-steel  Wall-hanger 


steel  and  corrugated  at  the  points  where  it  is  beiit  over.  This  reinforces  it  and 
tends  to  prevent  bending  at  these  points.  Fig.  21  illustrates  another  form  of 
the  Ideal  hanger  with  holes  for  spiking  to  a  timber.  This  hanger,  also,  is 
corrugated.  In  these  hangers  the  full  strength  of  the  steel  is  retained  as  the 
6bers  of  the  metal  are  not  cut  in  forming  them.  They  are  made  of  wrought- 
steel  bars  folded  to  the  required  shape.    Fig.  22  shows  the  Ideal  hanger  riveted 


Joist  and  Beam-Hangers 


755 


to  a  steel  plate  and  in  position  to  be  built  into  a  brick  wall.  Other  illustrations 
of  wall-hangers  are  given  in  Chapter  XXII.  The  Van  Dorn  hanger,  illustrated 
in  Fig.  23,  is  essentially  a  stirrup  forged  from  high-grade  steel.  The  few  tests 
that  have  been  made  would  seem  to  indicate  that  it  developes  a  greater  re- 
sistance to  bending  than  the  ordinary  stirrup,  while  it  gives  a  wider  bearing 


Fig.  23.     Van  Dorn  Beam-hanger 


Fig.  24.     Van  Dorn  Wall-hanger 


for  the  joist  and  presents  a  much  neater  appearance.  Fig.  24  shows  the  same 
hanger  riveted  to  a  bent  iron  plate,  to  build  into  brick  walls.  When  the  hanger 
is  to  be  used  over  a  steel  beam  the  upper  ends  are  bent  to  fit  over  the  flange  of 
the  beam,  as  in  Fig.  25.  "Although  I  know  of  no  test  of  the  strength  of  a  Van 
Dorn  I-beam  hanger,  it  would  seem  as  though  it  must  be  much  stronger  than 


Fig.  25.    Van  Dorn  I-beam  Hanger 


Fig.  26.    National  Joist  or  Beam-hangCT 


the  pattern  made  for  wooden  beams,  on  account  of  the  clinch  over  the  flange  of 
the  I  beam.  The  Van  Dorn  hangers  have  been  used  in  many  important  build- 
ings. "  * 

Figs.  26  and  27  show  the  general  form  of  two  other  patented  joist-hangers,, 
v^hich  are  forged  from  plate  steel.    Both  of  these  hangers,  also,  are  made  to  be 

*F.  E.  Kidaer. 


756 


Strength  and  Stiffness  of  Wooden  Floors        Chap.  21 


built  into  brick  walls  and  to  go  over  steel  beams.  The  National  hanger  (Fig.  26) 
has  a  flange  on  top,  which  helps  materially  in  distributing  the  load  over  the  top 
of  the  beam  as  shown  in  figure.     The  larger  hangers  of  this  style  have  holes  in 

the  top  for  large  spikes.  This 
hanger  and  the  Lane  hanger 
(Fig.  27)  have  been  much  used. 
Comparative  Strengths  of 
Different  Types  of  Joist- 
Hangers.  Although  the  tests 
that  have  been  made  to  deter- 
mine the  strength  of  different 
hangers  are  few  in  number,  a 
sufficient  nmnber  have  been 
made  to  show  that  any  one  of 
the  hangers  described,  including 
the  common  stirrup,  is  abun- 
dantly strong  for  any  single 
rLOOR-BEAM  not  exceeding  4  by 

Fig.  27.    Lane  Joist  or  Beam-hanger  ^4    in    in    cross-section      It    is 

only  m  the  case  of  a  header  or 
trimmer  which  supports  a  load  over  a  considerable  floor-area  that  the  strength 
need  be  considered  at  all.  From  tests  made  at  various  times  on  joist-hangers 
and  on  girder-hangers,  it  would  appear  that,  under  extreme  loads,  two-part 
hangers  usually  develop  great  strength.  A  two-part  hanger,  carrying  a  le 
by  i47in  girder,  sustained  a  load  of  38  000  lb  without  injury  to  the  hanger 
itself.  A  similar  hanger  held  until 
loaded  up  to  39  550  lb,  when  one 
side  broke  off  short  under  the 
nipple  projecting  into  the  timber, 
the  condition  of  the  hanger  after 
failure  being  shown  in  Fig.  28.  A 
common  stirrup  made  from  %  by 
2V2-in  wrought  iron  failed  under  a 
load  of  13  750  lb  by  bending  and 
pulling  over  the  header,  as  shown 
in  Fig.  29.  A  6  by  12-in  steel 
hanger  "  began  to  straighten  out 
under  a  load  of  13  300  lb,  and  failed 
to  hold  under  a  load  of  18  750 
lb."*  Single  hangers  of  the 
stirrup-type  do  not  break,  but  fail 
by  the  bending  up  of  the  parts 
which  lie  over  the  top  of  the  header 
as  shown  in  Fig.  29.  They  also  appear  to  crush  the  wood  under  them  par- 
ticularly at  the  edges,  to  a  very  much  greater  extent  than  does  the  spool  of 
the  Duplex  hanger.  With  a  double  stirrup  the  ultimate  strength  is  measured 
by  the  strength  of  the  iron.  Thus,  a  double  stirrup,  made  of  %  by  2]4-\n  wrought 
iron,  was  loaded  up  to  57  650  lb  (28  825  lb  on  each  side),  when  it  broke  at  one 
of  the  lower  corners.  A  single  stirrup  would  of  course  be  just  as  strong  if  it 
could  be  kept  from  bending.  In  actual  construction  the  flooring  over  the  beams 
to  some  extent  prevents  the  top  of  a  stirrup  from  springing  up.     The  tests  that 

*  From   data  compiled   by  Mr.   K-idcJer   from  a  series  of  tests  on  beam-hangers 
au4  joist-hangers, 


Fig.  28. 


Result  of  Test  of  a  Two-part 
Beam-hanger 


Comparative  Strengths  of  Joist-Hangers 


757 


have  been  made  of  two-part  hangers  show  conclusively  that  where  only  a 
single  hanger  is  used  the  holes 
which  are  bored  in  the  header  do 
not  seriously  affect  its  strength 
when  the  load  is  within  the  safe 
limit,  and  a  test  made  at  Balti- 
more, Md.,  August  24,  1904,  with 
2  by  i2-in  joists,  spaced  12  in  on 
centers  and  suspended  by  these 
hangers  let  into  a  header  formed 
of  three  3  by  12-in  joists,  spiked 
together,  would  seem  to  prove 
that  even  when  the  holes  are  1 2  in 
apart  they  do  not  seriously  weaken 
it.  ''  The  only  record  of  the  fail- 
ure of  any  form  of  hanger  when 
in  actual  use  in  a  building,  of 
which  I  am  aware,  is  that  of  a 
failure  in  Minneapohs,  where  a 
portion  of  six  floors  of  a  ware- 
house fell,  on  Nov.  7,  1902,  through 
the  failure  of  a  wall-hanger  made 
from  a  4  by  2  by  %.-in  structural- 
steel  angle,  which  was  sheared  and  bent,  and  riveted  to  an  8  by  16  by  %-in 
bearing-plate.  The  failure  was  due  to  the  crushing  of  the  outer  edge  of  the 
brickwork  under  the  hanger,  and  the  consequent  bending  up  of  the  top  portioc-. 
The  actual  load  on  the  hanger  was  about  15  000  lb."  * 

*F   E.  Kidder.    See,  also,  Engineering  News,  Nov.  20,  1.902. 


Fig.  29. 


Result  of  Test  of  Wrought-iron  Stirrup- 
hanger 


758^  Wooden  Mill  and  Warehouse-Construction        Chap.  22 

CHAPTER  XXII 

WOODEN  MILL  AND  WABEHOUSE-CONSTEUCTION 

By 
A.  P.  STRADLING 

SUPERINTENDENT  OF   SURVEYS,    PHIL.^DELPHIA  FIRE   UNDERWRITERS* 
ASSOCIATION 

1.   Mill-Construction 

Definition.  The  term  mill-construction  is  commonly  used  to  designate  a 
method  of  construction  brought  about  largely  through  the  influence  of  the 
Boston  Manufacturers'  Mutual  Fire  Insurance  Company  of  Boston,  Mass.,  and 
especially  through  the  efforts  of  Mr.  Wm.  B.  Whiting,  whose  judgment  in 
mechanical  matters,  and  experience  and  skill  as  a  manufacturer  were  for  many 
years  devoted  to  the  interests  of  insurance  companies,  and  to  the  improvement 
of  factories  of  all  kinds.  The  extended  use  of  this  system  and  the  improvements 
that  have  been  made  in  it  during  recent  years  are  probably  due  more  to  the 
influence  of  Mr.  Edward  Atkinson,  President  of  the  Boston  Manufacturers' 
Mutual  Insurance  Company  and  Director  of  the  Insurance  Engineering  Experi- 
ment Station  at  Boston,  than  to  that  of  any  other  individual. 

Cost.  The  purpose  of  mill-construction  is  to  reduce  the  fire-risk  to  its  low- 
est point  without  going  to  the  expense  of  fire-proof  construction.  The  increasing 
cost  of  heavy  timber,  however,  and  in  fact  of  all  lumber,  together  with  the 
lessened  cost  of  the  erection  of  the  so-called  fire-proof  types,  constructed 
entirely  of  reinforced  concrete,  or  built  with  protected  steel  frames  and  incom- 
bustible floors,  and  the  recognition,  also,  of  the  obvious  advantages  of  more 
fire-resisting  CONSTRUCTION,  especially  in  the  congested  sections  of  cities,  are 
bringing  these  types  into  more  general  use.  The  cost  of  these  latter  types  of 
construction  is,  in  many  instances,  no  more  than  the  cost  of  various  types  of 
mill-construction. 

The  Slow-burning  or  Mill-Construction  Type.  The  experience  of  years 
has  entirely  justified  the  use  of  this  type.  It  renders  possible  a  somewhat  less 
costly,  and  at  the  same  time,  what  is  of  great  importance,  a  more  effective  system 
of  fire-protection  than  can  be  installed  in  buildings  of  light  construction,  with 
the  so-called  joisted  floors  and  with  the  roofs  made  of  boards  supported  on 
2-in,  3-in,  or  4-in  joists.  The  entire  subject  of  slow-burning  or  mill-con- 
struction as  applied  to  factories  is  most  admirably  described  and  illustrated 
in  Report  No.  5  of  the  Insurance  Engineering  Station  of  the  Boston  Manu- 
facturers' Insurance  Company,  No.  31  Milk  Street,  Boston,  Mass.,  from  which 
the  author  has,  by  permission,  taken  and  adapted  many  of  the  following  illus- 
trations and  descriptions. 

2.   What  Mill-Construction  Is* 

(i)  Heavy  Timbers.  Mill-construction  consists  in  so  disposing  the 
timbers  and  planks  in  heavy,  solid  masses  as  to  expose  the  least  number  of 
corners  or  ignitable  projections  to  fire;  and  to  the  end,  also,  that  when  fire 
occurs  it  may  be  most  readily  reached  by  water  from  sprinklers  or  hose. 

'  *  From  Report  No.  5  of  the  Insurance  Engineering  Station  of  the  Boston  Manufac 
tmers'  Insurance  Company,  No.  31  Milk  Street,  Boston,  Mass. 


What  Mill-Construction  is  Not  769 

(2)  Flr6-Stops.  It  consists  in  sepai'ating  every  floor  from  every  other 
floor  by  incombustible  stops,  by  installing  automatically  closing  hatchways 
and  by  encasing  stairways  either  in  brick  or  other  incombustible  partitions,  so 
that  a  fire  will  be  retarded  in  passing  from  floor  to  floor  to  the  utmost  consistent 
with  the  use  of  wood  or  any  material  not  absolutely  fire-proof. 

(3)  Fire*Retardatits.  It  consists  in  guarding  the  ceilings  over  all  specially 
hazardous  stock  or  processes  with  fire-retardant  materials,  such  as  plaster- 
ing laid  over  wire  lath  or  expanded  metal,  or  over  wooden  dovetailed  lath, 
following  the  lines  of  the  ceilings  and  of  the  timbers  and  leaving  no  interspaces 
between  the  plastering  and  the  wood;  or  else  in  protecting  the  ceilings  over 
hazardous  places  with  asbestos,  air-cell  boards,  sheet  metal,  Sackett  Plaster 
Board,  or  other  fire-retardant. 

(4)  Fire-Safeguards.  It  consists  not  only  in  so  constructing  the  mill,  work- 
shop, or  warehouse  that  fire  will  pass  as  slowly  as  possible  from  one  part  of  the 
building  to  another,  but  also  in  providing  all  suitable  safeguards  against  fire. 

3.   What  Mill-Construction  Is  Not 

(i)  Concealed  Spaces.  Mill-construction  does  not  consist  in  so  disposing  a 
given  quantity  of  materials  that  the  whole  interior  of  a  building  becomes  a  series 
OF  WOODEN  cells,  or  concealed  spaces,  connected  with  each  other  directly  or 
by  cracks  through  which  fire  may  freely  pass  where  it  cannot  be  reached  by 
water.  ^' 

(2)  Size  of  Timbers,  Fire-Stops,  etc.  It  does  not  consist  of  an  open-timber 
construction  of  floors  and  roofs  which  resembles  mill-construction,  but  which 
is  built  with  light  timber  of  insufficient  size  and  with  thin  planks,  without  fire- 
stops  or  fire-guards  from  floor  to  floor. 

(3)  Stairways.  It  does  not  consist  in  connecting  floor  with  floor  by  com- 
bustible wooden  stairways  encased  in  wood  less  than  two  inches  thick. 

(4)  Partitions.  It  does  not  consist  in  putting  in  very  numerous  light, 
wooden  divisions  or  partitions. 

(5)  Sheathing  and  Furring.  It  does  not  consist  in  sheathing  brick  walls 
with  wood,  especially  when  the  wood  is  set  off  from  the  walls  by  furring,  and 
even  if  there  are  stops  behind  the  furring. 

(6)  Varnish.  It  does  not  consist  in  permitting  the  use  of  varnish  on  wood- 
work over  which  a  fire  will  pass  rapidly. 

(7)  Glass,  Fire-Shutters  and  Wire-Glass.  It  does  not  consist  in  leaving 
windows  exposed  to  adjacent  buildings  and  unguarded  by  fire-shutters  or 
wire-glass. 

(8)  Painting  and  Dry-Rot.  It  does  not  consist  in  painting,  varnishing, 
filling  or  encasing  heavy  timbers  and  thick  planks,  as  they  are  customarily 
delivered,  and  thus  making  possible  what  is  called  dry-rot,  caused  by  a  lack 
of  ventilation  or  opportunity  to  season. 

(9)  Sprinklers,  Pumps,  Pipes,  Hydrants,  etc.  It  does  not  consist  in 
leaving  even  the  best-constructed  building  in  which  dangerous  occupations  are 
followed  without  automatic  sprinklers,  and  without  a  complete  and  adequate 
equipment  of  pumps,  pipes  and  hydrants. 

(10)  Finishing  in  Wood  and  Other  Materials.  It  does  not  consist  in 
using  more  wood  in  finishing  a  building  after  the  floors  and  roof  are  laid  than 
is  absolutely  necessary,  since  there  are  now  many  safe  methods  available  at  low 
cost  for  fi^nishing  walls  and  constructing  partitions  with  slow-burning  or  in- 


760  Wooden  Mill  and  Warehouse-Construction         Chap.  22 

combustible  materials.  Accordingly  if  plaster  is  to  be  put  on  a  ceiling  and  is 
to  follow  the  line  of  the  underside  of  the  flooring  and  the  flooring-timbers,  it 
should  be  plain  lime-mortar  plaster,  which  is  suflSciently  porous  to  permit 
seasoning.  The  addition  of  a  skim-coat  of  lime-putty  is  hazardous,  especially 
if  the  overflooring  is  laid  over  rosin-sized  or  asphalt  paper.  This  rule  applies 
to  almost  all  timber  as  now  delivered.  Examples  of  all  of  the  faulty  methods 
of  construction  above  mentioned  have  been  found  in  various  buildings  pur- 
porting to  be  of  mill-construction,  and  they  all  form  parts  of  what  has  some- 
times been  called  combustible  construction. 

4.    Standard  Mill-Construction 

Example  of  Standard  Mill-Construction.  Fig.  1  shows  a  cross-section 
through  a  mill  of  the  customary  or  standard  type  recommended  by  the  Boston 
Manufacturers'  Mutual  Insurance  Company,  the  details  of  construction  being 
revised  to  May,  1908. 

"Walls.  If  additional  stories  are  required,  the  walls  may  be  increased  in 
thickness  according  to  the  number  of  stories  added,  after  a  computation  has 
been  made  of  the  loads  which  a  standard  factory  may  be  called  upon  to  sus- 
tain. Walls  should  be  of  brick  and  at  least  13  in  thick  in  the  upper  story,  and 
their  thickness  should  be  increased  in  the  lower  stories  to  support  additional 
loads.  Plastered  walls  are  often  to  be  preferred  to  unplastered  walls.  Window- 
arches  and  door-arches  should  be  of  brick,  and  window-sills,  outside  door-sills  and 
under-pinning  of  granite  or  concrete. 

Roofs  and  Floors.  The  roofs  should  be  of  3-in  pine  planks  spiked  directly 
to  the  heavy  roof-timbers,  and  covered  with  five-ply  tar-and-gravel  roofing. 
Roofs  should  incline  from  V2  to  %  in  per  ft,  and  incombustible  cornices  are 
recommended  when  there  is  exposure  from  neighboring  buildings.  Floors 
should  be  of  spruce  planks,  4  in  or  more  in  thickness  according  to  the  floor- 
loads,  spiked  directly  to  the  floor-timbers,  and  kept  at  least  V2  in  away  from  the 
face  of  the  brick  walls.  In  order  to  obviate  the  danger  of  cracking  the  walls, 
which  sometimes  results  from  the  swelling  of  planks  laid  close  against  them, 
these  spaces  left  between  walls  and  floor-planks  must  be  covered  by  strips  or 
battens  both  above  and  below.  In  floors  and  roofs,  the  bays  should  be  from 
8  to  loVu  ft  wide,  and  all  planks  two  bays  in  length  should  be  laid  to  break 
joints  every  4  ft,  and  grooved  -for  hard-wood  splines.  Usually  an  overfloor  of 
birch  or  maple  is  laid  at  right-angles  to  the  planking,  but  the  best  mills  have  a 
double  overfloor,  a  lower  one  of  soft  wood,  laid  diagonally  upon  the  planks  and 
an  upper  on^e  laid  lengthwise.  This  latter  method  allows  boards  in  alleys  or 
passageways  to  be  easily  replaced  when  worn,  while  the  diagonal  boards  brace 
the  floors,  reduce  the  vibration,  and  distribute  the  floor-loads  more  uniformly 
than  the  former  method.  Between  the  planking  and  the  overfloor  should  be 
two  or  three  layers  of  heavy,  hard  paper,  laid  to  break  joints,  and  each  mopped 
with  hot  tar  or  similar  material  to  make  a  reasonably  water-tight  as  well  as 
dust-tight  floor.  The  usually  rapid  decay  of  the  basement  or  lower  floors  of 
mills  makes  it  desirable,  whenever  wood  is  not  absolutely  necessary,  to  make 
such  floors  of  cement.  If  wooden  floors  are  required,  crushed  stone,  cinders, 
or  furnace  slag  should  be  spread  evenly  over  the  surface,  and  covered  with  a 
thick  layer  of  hot-tar  concrete.  On  this  tarred  felt  is  often  laid,  well  mopped 
with  hot-tar  asphalt,  and  over  it  a  flooring  of  2-in  seasoned  planks,  well  pressed 
down  and  nailed  on  edge  without  perforating  the  water-proofing  under  it.  The 
hard- wood  boards  of  the  overfloor  are  then  nailed  across  the  planks.  Cement 
concretes  promote  decay  of  wood  in  contact  with  them.  If  extra  supports  are 
required  for  heavy  machinery,  independent  foundations  of  masonry  should  be 


Standard  Mill-Construction 


762 


Wooden  Mill  and  Warehouse-Construction         Chap.  22 


provided.  In  view  of  the  difficulties  frequently  met  with  in  preserving  base- 
ment floors  of  the  ordinary  timber  construction,  because  of  the  lack  of  suitable 
ventilation  underneath,  and  also  in  view  of  the  rapid  decay  of  timber  and  plank 
floors  in  bleacheries,  dye-works,  print-works,  and  the  like,  in  which  the  floors 
quickly  become  saturated  with  moisture,  artificial-stone  floors  are  being  laid 
in  many  of  the  modern  plants. 

Sizes  and  Kinds  of  Timbers.  All  woodwork,  not  standard  construc- 
tion, in  order  to  be  slow-burning,  must  be  in  large  masses  which  present  the 
least  surface  possible  to  a  fire.  No  pieces  less  than  6  in  in  width  should  be  used 
for  the  lightest  roofs,  and  for  substantial  roofs  and  floors  much  wider  ones  are 
needed.  Timbers  should  be  of  sound,  long-leaf,  yellow  pine,  and  for  sizes  up 
to  14  by  16  in,  single  pieces  are  preferred;  or,  timbers  7  to  8  by  16  in,  are  often 
used  in  pairs  bolted  together,  without  air-spaces  between.  They  should  not 
be  painted,  varnished  or  filled  for  three  years  because  of  the  danger  of  dry  rot, 
and  for  the  same  reason,  an  air-space  should  be  left  in  the  masonry  around  the 
ends. 

Beam-Boxes,  Column-Caps,  etc.  Timbers  should  rest  on  cast-iron 
PLATES  or  beam-boxes  in  the  walls  and  on  cast-iron  caps  on  the  columns.  Beam- 
boxes  are  of  value  as  they  strengthen  the  walls  when  the  floor  loads  are  heavy 
and  the  distance  between  windows  small;  they  facilitate  the  laying  of  the 
bricks  and  the  handling  of  the  beams;  and  there  is  less  danger  of  breaking  the 
bricks  in  putting  the  beams  in  place.    They  also  insure  proper  air-spaces  around 


Flashing 


Rooflngv 


Fig.  2.    Floor-timber  on  Wall-plate 


Fig.  3.    Roof -timber  on  Wall-plate 


the  ends  of  the  beams.  Fig.  2  shows  a  floor-timber  resting  on  a  cast-iron  wall- 
plate  with  a  lug  for  anchoring  the  timber  to  the  wall.  Fig.  3  shows  a  roof- 
timber  resting  on  a  cast-iron  wall-plate,  an  overhanging,  open,  wooden 
cornice  and  a  wrought-iron  joist-anchor.  Fig.  4  shows  a  cast-iron  cap  and 
PINTLE  for  columns,  and  dogs  for  holding  the  floor-timbers  together.  Fig.  5 
shows  a  roof-timber  resting  on  a  column-cap  cast  to  fit  the  slope  of  the  roof; 
the  timbers  are  held  together  by  i-in  wrought-iron  dogs.  These  diagrams  are 
Intended  only  as  general  illustrations  of  slow-burning  or  mill-construction. 
The  details  should  always  be  adapted  to  the  special  conditions  of  the  site  and 
to  the  purposes  for  which  the  buildings  are  used. 

Columns  of  yellow  pine  should  be  bored  through  the  axis,  making  a  i^^-in- 
diameter  hole,  and  should  have  y2-in  lateral  vent-holes  near  the  top  and  bottom. 
The  ends  should  be  carefully  squared.    To  prevent  dry-rot,  wooden  columns 


Standard  Mill-Construction 


763 


should  not  be  painted  until  they  are  thoroughly  seasoned.  They  should  be  set 
on  PINTLES  which  may  be  cast  in  one  piece  with  the  cap,  or  separately.  Cast- 
iron  COLUMNS  are  preferred  by  some  engineers,  and  when  a  building  is  equipped 
with  automatic  sprinklers,  such  columns  have  proved  satisfactory;    but  they 

ToplFioorinff 
Tarred  Paper 


Roof  Planking, 


Fig.  4. 


Post-cap  and  Pintle  for  Floor-timber  and 
Columns 


Roof, 
Timber 


Fig.  5.    Roof -timbers  on  Column- 
cap 


are  not  as  fire-resisting  as  wooden  columns.     Wrougiit-iron  or  steel  columns 
should  not  be  used  unless  encased  with  at  least  3  in  of  fireproofing. 

Windows  should  be  placed  as  high  and  made  as  wide  as  possible  to  obtain  the 
greatest  amount  of  light,  and  the  use  of  ribbed  glass  is  recommended  for  the 
upper  sashes. 

Weight,  Deflection  and  Vibration.  In  computing  the  size  of  the  timbers 
as  a  ratio  to  the  working-load,  consideration  must  be  given  not  only  to  the  weights 
which  are  to  be  carried,  but  also  to  the  character  of  the  machinery  which  is 
to  be  operated  on  the  floors.  Beams  of  sufficient  strength  to  support  the  weights 
may  vibrate  or  deflect  under  the  weight  and  action  of  the  machinery;  and  there 
are,  therefore,  three  factors,  weight,  deflection  and  vibration,  which  must 
be  considered  in  determining  the  width  and  depth  of  the  beams  that  are  to 
be  used  in  the  structure. 

Objectionable  Types  of  Construction.  "We  do  not  approve  what  has 
been  sometimes  miscalled  mill-construction,  that  is,  longitudinal  girders 
resting  upon  posts  and  supporting  floor-beams  spaced  4  ft,  more  or  less,  on 
centers.  This  mode  of  construction  not  only  adds  to  the  quantity  of  wood 
used,  but  the  disposal  of  the  timbers  obstructs  the  action  of  the  sprinklers,  pre- 
vents the  sweeping  of  a  hose-stream  from  one  side  of  the  mill  to  the  other,  and 
the  girders  also  obstruct  the  most  important  light,  that  from  the  top  of  the 
windows." 

Timber,  Ventilation,  Painting,  etc.  Timbers,  unless  known  to  be  thor- 
oughly seasoned,  should  not  be  encased  in  any  kind  of  air-proof  plastering  nor 
painted  with  oil-paints;  white-wash,  calcimine  and  water-paints  may  be  used, 
as  they  are  porous.  As  a  rule,  timbers  should  be  left  unprotected,  since  a 
fire  which  will  seriously  impair  and  destroy  heavy  timbers  will  already  have 
done  its  work  upon  other  parts  of  the  structure. 

Single  and  Compound  Beams.  While,  in  general,  single  beams  should  be 
used,  in  some  instances  it  may  be  desirable  to  substitute  compound  beams, 
made  by  fastening  two  or  more  beams  or  thick  planks  side  by  side.  It  is  often 
easier  to  obtain  well -seasoned  lumber  in  small  dimensions.  Such  compound 
beams  should  be  tightly  bolted  together  without  air-spaces,  and  owing  to  the 
danger  of  dry-rot,  should  not  be  painted  or  varnished  for  three  years. 


764 


Wooden  Mill  and  Warehouse-Construction        Chap.  22 


Steam-Pipes.  If  a  mill  is  to  be  heated  by  conveying  steam  through  pipes, 
such  pipes  should  be  hung  overhead. 

Cornices.  Wherever  buildings  are  exposed  or  are  liable  fo  be  exposed  to 
fire  in  the  near  future,  the  cornices  should  be  of  non-combustible  construction  or, 
preferably,  the  walls  should  extend  above  the  roof-timbers. 

Glass,  Frames  and  Shutters.  All  openings  in  walls  should  be  protected 
either  by  approved  wire-glass  in  approved,  metal  frames  or  by  standard  fire- 
shutters.  . 

5.   Belts,  Stairways  and  Elevator-Towers 

Continuous  Floors.  One  of  the  most  important  features  of  slow-burning 
<;:0NSTRUCTi0N  is  to  make  each  and  every  floor  continuous  from  wall  to  wall, 


1  s 

3    "    ■ 

J 

1 

1 

i               ' 

1               ' 

e 

i 

J.-' 

-t^: 

pq 


avoiding,  as  far  as  possible,  holes  for  belts,  stairways,  or  elevators  so  that  a 
fire  may  be  confined  to  the  story  in  which  it  starts.  No  well-informed  mill- 
owner,  engineer  or  builder  will,  therefore,  fail  to  locate  elevators,  stairs,  and 
main  belts,  in  brick  towers  or  in  sections  of  the  building  cut  off  from  all  rooms 


Standard  Storehouse-Construction 


765 


by  incombustible  walls.  All  openings  in  these  walls  should  be  protected  by 
STANDARD  FIRE-DOORS,  preferably  self-closing.  In  modern  practice  all  belts 
and  ropes  which  may  be  used  for  the  transmission  of  power  to  the  various  rooms, 
are  placed  in  incombustible  vertical  belt-chambers,  from  which  the  power 
is  transmitted  by  shafts  through  the  walls  into  the  several  rooms  of  the  factory. 
There  should  be  no  unprotected  openings  in  the  inner  walls  of  this  belt- 
chamber. 

Shafts  above  Roof.  Skylights.  All  shafts  for  stairs,  elevators, 
BELTS,  etc.,  should  extend  at  least  36  in  above  the  roof,  and  all  such  shafts 
should  be,  if  possible,  on  the  outside  of  the  building.  Elevator  and  belt-shafts 
should  be  covered  with  thin  glass  skylights  in  metal  frames,  protected  under- 
neath with  wire  netting.  Figs.  6  and  7  illustrate  a  section  and  plan  of  a  cotton- 
mill,  showing  elevator,  stair  and  belt-shafts  arranged  on  the  above  principle. 
Closets  should  be  in  a  separate  tower  rather  than  in  manufacturing  rooms. 

The  Boiler-Plant  should  be  in  a  separate  building  cut  off  from  the  engine- 
room  by  a  brick  wall,  and  the  openings  in  this  wall  should  bp  protected  by  auto- 
matic, sliding,  standard  fire-doors. 


6.    Standard  Storehouse-Construction 

Example  of  Storehouse-Construction.  Fig.  8  shows  a  cross-section  through 
the  fire-tower  and  Fig.  9  the  first-story  plan,  including  the  elevator  and  stair- 
tower  of  a  four-story 
storehouse. 

Area.  Buildings 
for  this  purpose 
should  not,  in  gen- 
eral, exceed  5  000  sq 
ft  in  AREA.  When 
used,  however,  for 
storage  of  non-haz- 
ardous goods,  the 
area  may  be  in- 
creased to  10  000  sq 
ft. 

Height  of  Stories. 
In  storehouses,  the 
stories  should  be  made  low  enough  (Fig.  10)  to  prevent  overloading,  and  when 
designed  for  case-goods,  the  height  of  stories  should  be  sufficient  to  take  two 
cases,  with  a  12-in,  clear  space  under  the  beams  to  allow  for  the  distribution  of 
water  from  the  sprinklers. 

Fire-Walls.  For  convenience,  as  well  as  to  separate  the  different  hazards  of 
raw  materials  and  finished  goods,  the  building  should  be  divided  into  sections 
by  fire-walls  extending  at  least  36  in  above  the  roof. 

One-Story  Storehouses.  A  one-story  storehouse  is  recommended  in 
preference  to  the  design  just  described,  whenever  there  is  a  sufficient  quantity 
of  level  land  at  disposal  for  this  purpose.  The  one-story  building  is  cheaper, 
more  convenient,  and,  when  separated  into  small  divisions  by  fire- walls,  repre- 
sents the  safest  method  of  storehouse-construction. 

Timbers  and  Framing.  The  floor-timbers  and  roof-timbers  should  be 
of  long-leaf  yellow  pine,  in  single  pieces,  if  possible.  If  necessary  to  use  double 
beams,  they  should  be  bolted  together  without  air-spaces  between  them.    Tim- 


CR0S5  SECTION  THROUGH  TOWER 


Fig.  8.     Four-story  Storehouse.     Section  through  Fire-tower 


766 


Wooden  Mill  and  Warehouse-Construction        Chap.  22 


bers  should  rest  on  cast-iron  plates  or  beam-boxes  in  the  walls,  and  on  cast-iron 
caps  on  the  columns.  At  least  V2-in  air-spaces  should  be  left  around  all  beams 
built  into  the  masonry,  allowing  free  ventilation  and  preventing  dry  rot.    Col- 


Fig.  9.    Four-story  Storehouse.    First-story  Plan 

UMNS  of  yellow  pine  should  have  their  end-surfaces  cut  square  with  the  column- 
axis.  . . 

Floors.    The  floors  of  such  buildings  should  be  continuous,  without  open- 
ings, and  of  the  standard  slow-burning  construction,  described  under  Standard 


Isometric  view 
Fig.  10.     Four-story  Storehouse.     Isometric  View 


MiLL-CoNSTRUCTiON.  The  flooring  should  be  constructed  as  called  for  under 
Standard  Mill-Construction.  In  order  that  the  floors  may  be  as  nearly 
water-proof  as  possible,  tarred  paper,  mopped  with  tar,  should  be  applied,  as 
previously  suggested.  The  floors  in  each  story  of  the  tower  should  be  at  least 
I  in  lower  than  the  floor  in  the  adjoining  compartment,  and  the  sills  of  the  door- 
openings  to  the  tower  should  be  inclined  to  make  up  the  difference  in  levels. 
The  sill,  also,  of  the^  outside  door  of  the  tower  should  be  lower  than  the  tower- 
floor. 


Standard  Storehouse-Construction 


76? 


Scuppers.  Water  on  the  floors  of  the  tower  will  ordinarily  flow  down  the 
tower-stairs,  and  the  arrangement  of  the  floor-levels  indicated  above  will  ordi- 
narily prevent  water  from  an  upper  story  from  flowing  into  one  of  the  lower 
compartments,  if  it  is  escaping  through  the  tower.  Cast-iron  scuppers  are 
advised,  and  they  should  be  set  in  the  brickwork  at  frequent  intervals,  and  so 
designed  that  they  will  carry  away  rapidly  a  maximum  quantity  of  water  from 
the  floors  of  each  compartment.  To  further  the  drainage  of  water,  the  floors 
should  be  inclined  from  the  middle  of  the  compartments  to  the  scuppers.  Fig. 
11  shows  the  wind-shield  scupper*  which  embodies  the  latest  improvements. 


^xVERTICAL  SECTION 


FRONT  ELEVATION 


Fig.  11.    Detail  of  Wind-shield  Scupper 

In  the  old-style  scupper  only  one  flap  is  provided  on  the  outside  of  the  building. 
During  winter  and  windy  weather,  this  flap  blows  open  and  sometimes  freezes 
open.  This  results  in  a  continuous  draft  through  the  scupper  and  over  the 
working  floor  of  the  factory  or  warehouse  and  necessitates  an  increase  in  the 
amount  of  heat  furnished.  The  scupper  shown  in  Fig.  11  corrects  this  condi- 
tion by  providing  the  light  wind-shield  on  the  floor-level  of  the  scupper.  When 
the  outer  flap  blows  open  the  wind-shield  shuts  off  the  draft  from  the  outside. 
This  scupper,  in  addition,  acts  as  a  fire-retardant  when  an  adjoining  building 
is  burning,  and  when  there  is  a  tendency  for  the  flames  to  communicate  through 
an  open  scupper  and  ignite  merchandise  on  the  floor.  The  wind-shield,  by 
shutting  off  the  drafts  and  fire,  acts  as  a  retardant  or  shield  to  keep  out  the 
llames. 

*  Manufactured  by  the  Wind-Shield  Scupper  Company,  i  Madison  Avenue,  New 
York  City. 


768 


Wooden  Mill  and  Warehouse-Construction        Chap.  ^2 


Tower  for  Stairways,  Elevators,  etc.  Access  to  the  various  stories  is 
obtained  by  means  of  a  brick  tower  outside  the  main  building,  extending  36  in 
above  the  roof,  and  containing  stairways,  elevators,  etc.,  .access  to  which  is 


Storage  oLRaw  Material      Y///////^////////////// 

i 


storage  of  Goods 


Fig.  12.    Stairway-tower  and  Galleries  at  Side  of  Storehouse 

obtained  by  open  galleries  at  each  floor-level.  (See  Fig.  12.)  A  doorway 
from  the  upper  story  of  the  tower  affords  a  ready  means  of  reaching  the  roof. 
Automatic  hatches  are  not  necessary  for  the  elevator,  as  guard-gates  serve 
every  purpose.  If  it  is  necessary  to  construct  the  tower  for  the  elevator  and 
stairs  inside  of  the  building,  access  to  it  should  be  as  shown  in  Fig.  13.    This 


Fig.  13.    Stairway-tower  Inside  of  Storehouse  ' 


construction    serves,  also,  as  a  fire-tower,  part  of    the  outside  wall   being 
omitted. 

Roof  Walls  and  Parapets.  The  walls  should  extend  36  in  above  the  roof 
and  the  parapet  should  be  laid  in  cement,  because  the  moisture  readily  ab- 
sorbed by  the  bricks  would  otherwise  pass  downward  and  make  the  walls  of  the 
top  story  damp.  In  some  instances  a  course  of  bricks  dipped  in  coal-tar  is 
laid  above  the  roof-level. 

Sprinklers,  Standpipes  and  Hose.  Mills  and  storehouses  should  ibe  pro- 
tected throughout  by  automatic  sprinklers  and  by  inside  standpipe  and 
hose-equipments.  Dry-pipe  sprinklers  should  never  be  used  unless  it  is  im- 
practicable to  heat  the  building.  These  systems  should  be  planned  and  super- 
vised by  a  thoroughly  reliable  fire-protection  engineer.  (See,  also,  Chapter 
XXIII,  pages  903  to  905.)  .^ 


Example  of  One-Story  Work-Shop  769 

7.   Example  of  One-Story  Work-Shop 

Economy.  For  work-shops  on  cheap,  level  land,  and  especially  for  buildings 
in  which  the  stock  is  heavy,  one-story  buildings  have  proved  to  be  more 
economical  than  higher  buildings,  in  cost  of  floor-area,  supervision,  moving 
stock  in  process  of  manufacture  and  repairs  to  machinery,  much  of  which 
can  be  run  at  greater  speeds  than  when  it  is  in  high  buildings. 

Warming  and  Ventilating.  Window-Area.  Such  buildings  are  readily 
warmed  and  ventilated,  and  heavy-plank  roofs  are  free  from  condensation  in 
cold  weather.  Window-areas  should  be  as  large  as  practicable,  as  a  large  window- 
area  reduces  the  hours  of  artificial  illumination.  If  the  building  is  exposed  to 
fire  from  another  building  or  buildings  of  hazardous  occupancy,  the  windows 
should  be  of  the  Fenestra,  Lupton  or  other  equally  good,  steel  construction, 
glazed  with  wire-glass.  The  forced  circulation  of  heated  air  is  a  very  desirable 
method  of  heating  mills,  and  should  be  used  in  connection  with  overhead  steam- 
pipes. 

Floors.  As  wooden  floors  are  subject  to  rot,  the  general  floor-construction, 
if  possible,  should  be  of  concrete  or  earth  or  some  other  non-combustible  mate- 
rial. But  as  the  dust  rising  from  floors  of  such  materials  injures  machinery, 
and  as  the  dripping  of  oils  weakens  such  floors  and  seems  to  make  a  wooden 
flooring-surface  necessary,  the  following  construction  is  recommended. 
Broken  slag  or  stone,  several  inches  in  thickness  and  thoroughly  rolled,  is  first 
put  down,  and  over  this  a  4-in  layer  of  tar-concrete.  On  this  is  laid  a  i-in 
thickness  of  asphalt,  evenly  rolled.  Over  this,  2  or  3-in  hemlock  planks,  bedded 
in  hot  pitch,  are  laid  and  over  them  a  %  or  iVs-in  maple  floor,  at  right-angles 
to  the  planks. 

Column  and  Beam-Construction.  Figs.  14  and  15  show  clearly  the  mode 
of  column  and  beam-construction.  No  beams  or  other  structural  timbers 
should  be  painted  or  varnished  until  thoroughly  seasoned. 

The  Roofs  should  be  as  called  for  under  Standard  Mill-Construction. 
Trusses  in  roofs  are  ordinarily  from  8  to  20  ft  on  centers,  the  3-in  planks  span- 
ning the  distance  between  the  trusses  as  shown  in  Fig.  14,  or  resting  on  purlins 
not  less  than  8  ft  on  centers,  and  running  longitudinally,  as  in  Fig.  15. 

Cornices  and  Gutters.  In  Fig.  14,  the  overhanging  open  cornice  is 
shown,  with  a  drip  to  the  outside  and  without  gutters.  Roofs  sloping  back  to 
inside  gutters,  as  shown  in  Fig.  15,  are  preferable.  Projecting  brick  cornices, 
which  protect  the  woodwork  from  outside  fires,  are  shown  in  Fig.  15.  If  the 
building  is  exposed  to  other  buildings  of  hazardous  construction  and  occupancy, 
parapetted  brick  walls  and  cornices  are  needed. 

Roof-Construction.  The  roof-planks  should  be  at  least  two  bays  in  length, 
breaking  joints  every  3  ft;  or,  if  purlins  are  used,  the  planks  should  cover  at 
least  two  spaces  between  the  purlins,  and  break  joints  as  above.  Roof-timbers 
should  be  well  anchored  to  walls  in  a  safe  and  suitable  manner.  While  the 
saw-tooth  form  of  roof  may  be  used  with  this  type  of  building,  it  may 
not  be  always  necessary  or  advisable;  and  the  types  shown  in  Figs.  14  and 
15  are  types  common  for  machine-shops,  foundries,  and  similar  buildings,  in 
which  increased  head-room  is  required  for  traveling  cranes.  The  middle  sec- 
tion over  the  crane  is  often  provided  with  saw-tooth  skylights  with  excellent 
results,  and  the  side  bays  and  others  are  made  higher  for  galleries. 

Steel  Structural  Members.  In  ordinary  one-story  machine-shops,  or  in 
buildings  of  similar  nature,  where  wide  spans  or  trusses  are  necessary,  the 
use  of  steel  structural  members  is  not  objectionable. 


770 


Wooden  Mill  and  Warehouse-Construction         Chap.  22 


^ 

b 


S 

^ 


Example  of  One-Story  Work-Shop 


m 


Lp^H 


772  Wooden  Mill  and  Warehouse-Construction        Chap. 

8.   Saw-Tooth  Roof-Construction* 

The  Great  Advantages  and  the  increasing  use  of  saw-tooth  roof-construc- 
tion, and  the  lack  of  familiarity  with  it  at  many  factories,  make  it  desirable  to 
outUne  important  features. 

Two  Typical  Designs  are  illustrated,  Fig.  16,  a  textile  weave-shed  with 
a  good  basement  for  the  shafting  for  driving  the  looms  on  the  main  floor  above, 
thus  dispensing  with  the  overhead  shafting  and  belting  in  the  weave-room; 
and  Fig.  17,  a  design  for  a  light  machine-shop  or  foundry.  Other  designs, 
using  light  wooden  trusses  or  reinforced-concrete  walls,  are  applicable. 

Roof-Types.  It  may  be  well  to  state  here  that  while  light  roofs  with  2-in 
and  3-in  joists  and  with  light  boards  should  never  be  used,  and  while  the  prin- 
ciples of  SLOW-BURNING  or  MILL-CONSTRUCTION,  with  its  heavy  timbers,  are 
preferred,  the  increasing  difficulty  of  promptly  obtaining  yellow-pine  lumber  of 
good  dimensions,  and  its  increasing  cost,  often  necessitate  the  use  of  trusses 
and  rather  light  timbers;  but  in  no  case  should  these  timbers  be  less  than  6  in 
in  width  nor  of  insufficient  depth  to  carry  the  load.  This,  also,  is  in  order 
that  they  may  be  slow-burning.  The  roofs  in  all  cases  should  be  constructed 
of  planks  and  have  wide  bays. 

Steel  Roof-Trusses.  The  adaptability  of  the  light  forms  of  steel  for 
FRAMING  TRUSSES,  especially  when  wide  spans  are  needed,  often  compels  their 
use;  and  in  plants  having  a  safe  occupancy,  such  as  that  of  metal-workers,  steel 
trusses  are  not  objectionable,  providing  adequate  sprinkler-protection  with  a 
good  water-supply  is  available  to  prevent  quick  failure  of  the  steel  work,  due 
to  heat  from  the  combustion  of  the  contents  of  the  building  or  from  the  burning 
of  the  roof.  Similar  protection  is,  of  course,  needed  in  shops  with  wooden 
TRUSSES,  if  disastrous  fires  are  to  be  prevented;  but  experience  has  shown  that 
the  STEEL-TRUSSEu  ROOF  will  fail  much  more  rapidly  than  one  of  wood  under 
similar  conditions. 

Wooden  versus  Steel  Columns.  Wooden  posts  are  nearly  always  avail- 
able and  should  be  given  preference;  but  if  light  steel  columns  are  necessary 
they  should  be  well  protected  by  insulating  materials  if  they  are  in  roorns  con- 
taining combustibles,  as  the  column  is  the  vital  part  of  the  roof-support. 

Advantages  of  Saw-Tooth  Roofs  may  be  outlined  as  follows: 

(i)  Uniform  Diffusion  of  Light  throughout  the  room,  thus  making  all 
space  in  it  available.  With  all  interior  surfaces  painted  white  and  with  ribbed 
glass  in  the  sashes,  the  diffusion  of  light  is  almost  perfect. 

(2)  Better  and  Cheaper  Lighting.  Greater  adaptability  for  lighting 
large  floor-areas  in  wide  buildings  with  low  head-room  when  compared  with 
what  is  necessary  in  wide  buildings  with  the  ordinary  form  of  monitor-skylights. 
Saw-tooth  roofs  furnish  the  true  solution  of  the  problem  of  excluding  the  direct . 
riys  of  the  sun  and  obtaining  the  very  desirable  north  light.  They  result  in 
greater  econOxMY  in  lighting,  as  they  lower  the  fixed  charges  due  to  the  smaller 
number  of  hours  per  day  during  which  artificial  light  is  necessary. 

(3)  Better  Working-Conditions,  especially  in  textile-mills,  thereby  increas- 
ing production  and  encouraging  permanency  of  employees. 

(4)  Special  Adaptability  to  many  Industries.  The  saw-tooth  form  is 
especially  adapted  to  weaving  and  similar  processes  in  textile-factories,  to  ma- 
chine-shops, foimdries  doing  hght  work,  and  similar  processes,  such  as  assem- 

*  Taken  and  adapted  by  permission  from  the  Boston  Manufacturers'  Mutual  Insur- 
ance Company's  specifications  for  the  construction  of  saw-tooth  roofs. 


Saw-Tooth  Roof-Construction 


773 


774 


Wooden  Mill  and  Warehouse-Construction        Chap.  22 


Saw-Tooth  Roof-Construction  776 

bling  and  drafting,  and  to  some  dye-houses  where  careful  matching  of  colors  is 

necessary. 

Disadvantages  of  Saw-Tooth  Roofs.  While  the  testimony  of  those  who 
have  had  experience  with  saw-tooth  roofs  is  almost  uniformly  favorable, 
some  difficulties  have  been  experienced,  practically  all  of  which  may  be  summed 
up  as  due  to  either  faulty  design  or  poor  workmanship.  The  difficulties  ia 
general  are  caused  by 

(i)  Leaks,  due  to  severe  conditions  during  winter  in  our  northern  cUmates. 

(2)  Poor  Ventilation. 

(3)  Excessive  Heat  when  roofs  are  thin. 

(4)  Excessive  Condensation  on  the  underside  of  roof  and  glass  when  the 
temperature  outside  is  low  and  there  is  considerable  moisture  in  the  rooms. 

Approved  Methods  of  Construction.  The  following  suggestions  show  how 
the  difficulties  mentioned  may  be  obviated  if  the  approved  methods  are  applied 
to  special  cases  by  competent  engineers  or  architects.  What  is  good  engineer- 
ing from  the  view-point  of  the  manufacturer  can  also  be  good  fire-protection 
ENGINEERING,  and  any  design  should  be  adapted  to  both  if  the  best  interests 
of  the  manufacturer  are  to  be  served: 

(i)  Diffused  Indirect  Sunlight.  As  it  is  desirable  to  avoid  direct  sun- 
light and  at  the  same  time  obtain  an  abundance  of  light,  perfectly  diffused, 
the  saw-teeth  should  face  approximately  north  and  the  glass  should  be  inclined 
to  the  vertical  to  take  advantage  of  the  brighter  light  in  the  upper  sky  and  to 
prevent  cutting  off  the  light  by  the  saw-tooth  immediately  in  front;  and,  above 
all,  to  assure  the  diffusion  of  the  light  over  the  floor  rather  than  on  the  under 
side  of  the  roof-planking. 

(2)  Angle  of  Glass.  For  the  glass  an  angle  of  from  20°  to  25**  from  the 
vertical  and  an  angle  of  approximately  90°  at  the  top  of  the  saw-tooth  will  be 
about  right,  the  variations  depending  upon  the  amount  of  light  required  and  the 
latitude.  A  sharper  angle  at  the  top  is  not  needed,  as  it  increases  the  cost,  and 
makes  more  roof  to  be  covered  and  larger  spans;  more  glass,  also,  is  required 
in  proportion,  and  the  light  is  not  as  good,  as  more  light  from  the  sky  is  lost 
and  too  much  light  is  thrown  on  the  under  side  of  the  roof. 

(3)  Glazing-Details.  Double  glazing  with  a  space  left  between  the 
lights  of  glass  is  preferred  on  account  of  its  conducting  qualities;  but  it  is  not 
always  necessary,  except  in  the  more  northerly  countries.  The  inside  glazing 
should  be  done  with  factory-ribbed  glass,  set  with  the  ribs  vertical  and  facing 
in.     Shadows  cast  by  trusses  are  then  almost  unnoticeable. 

(4)  Gutters  and  Conductors.  Condensation-gutters  are  needed  inside, 
at  the  bottom  of  the  sashes,  and  they  should  be  drained  through  inside  con- 
ductors and  not  to  the  outside  under  the  bottom  of  the  sashes,  as  these  latter 
admit  cold  air  and  are  liable  to  freeze. 

(5)  Valleys  between  the  saw-teeth  should  be  flat,  from  14  in  to  2  ft  in  width 
and  pitched  V2  in  per  ft  towards  the  conductors,  which  should  be  of  ample  size, 
and  not  much  over  50  ft  apart,  and  prefciably  less.  The  necessary  pitch  may 
be  obtained  by  cross-pieces  of  varying  heights  set  on  top  of  the  trusses,  and  thus 
avoiding  hollow  spaces. 

(6)  Prevention  of  Leaks.  Leaks,  which  are  common  faults,  may  ordi- 
narily be  prevented  by  a  careful  design  of  the  gutters,  valleys  and  sashes,  and  by 
insisting  on  good  workmanship  and  materials.  The  roof-covering  of  asphalt 
or  pitch  should  be  continuous  through  the  valleys  and  extend  up  to  the  glas^ 


776 


Wooden  Mill  and  Warehouse-Construction         Chap.  22 


^Galv.  Iron  Plashing 
,5  Ply  Roofing:  plus  extra  layer  of  Felt 
'^No24  Gal  V.Iron 
Asbestos 

-Summit 


One  form  of  construction  understood  to  have  been  very  satisfactory  is  shbwn  in 
Fig.  18  and  in  connection  with  it,  reference  should  be  made  to  the  papers  and 
discussion  on  Saw-Tooth  Roofs  in  Trans.  Am.  Soc.  M.  E.,  1907,  vol.  2S,  which 
contain  much  of  value. 

(7)  Warming  and  Ventilation.  Experience,  has  demonstrated  the  advan- 
tage of  a  combination  of  direct  radiation  with  a  fan  sufficient  only  for  ven- 
tilation and  TEMPERING  the  heat  of  the  room.  Heating-pipes,  should  usually 
be  placed  overhead  and  directly  under  the  front  of  the  saw-teeth,  and  run  the 

entire  length,  and  in 
this  position  assist  in 
preventing  condensa- 
tion. Where  there  is 
no  moving  shafting, 
some  forced  circula- 
tion is  necessary,  and 
it  is  best  obtained  by 
a  fan,  which  drives 
the  air  from  either  a 
dry  basement  or  from 
outside  as  may  be 
required,  and  dis- 
charges it  over  heat- 
ing-coils to  the  story 
above.  In  weaving 
and  similar  rooms 
this  is  especially 
necessary  and  advan- 
tageous in  promoting 
the  health  and  com- 
fort of  the  employees, 
and  in  making  their 
w  o  r  k  i  n  g-efficiency 
greater.  Ventilation  and  cooling  of  these  large  areas  with  comparatively  low 
stories  must  not  be  neglected.  Ample  vents  are  needed  at  the  top  in  the 
form  of  large  metal  ventilators  with  double  walls  and  tight  dampers.  They 
are  recommended  in  place  of  pivoted  or  swinging  sash,  which  are  apt  to  leak 
in  driving  storms,  and  when  open,  allow  dirt  to  blow  in  from  the  roof. 
Good  windows  are  advised  in  side  walls  and  experience  has  shown  their  value. 

(8)  Details  of  Framing  and  Construction.  The  framing  of  the  saw- 
teeth may  be  of  timber,  steel  or  reinforced  concrete.  The  design  should  be 
such  as  will  obstruct  the  light  as  little  as  possible,  strong  enough  to  hold  wet 
snow  without  sagging,  and  stiff  enough  to  carry  shafting  motors,  etc.,  when 
they  are  to  be  overhead.  When  wood  or  steel  is  used  the  roof-planking 
should  be  3  in  or  more  in  thickness  spanning  bays  from  8  to  10  ft  in  width. 
Hollow  spaces  in  roofs  should  not  be  permitted.  They  are  very  undesir- 
able from  a  fire-standix)int,  and  any  condensation  which  may  take  place  in 
them  during  cold  weather  soon  rots  both  planks  and  sheathing.  Sheathing, 
even  without  spaces  behind  it,  is  a  more  or  less  objectionable  feature,  as  it  is 
readily  combustible;  but  if  it  is  used  it  should  be  applied  directly  to  the  under 
side  of  the  roof-planks,  with  only  a  layer  of  some  insulating  material  between,  so 
that  there  will  be  no  concealed  spaces.  If  3-in  planks  are  sufficient  for  a  flat 
roof,  they  should  be,  also,  for  a  saw-tooth  roof;  and  with  a  good  circulation 
of  air  there  should  be  no  trouble,  except  in  wet  rooms.    In  such  rooms  there  i3 


Fig.  18.     Detail  of  Valley  of  Saw-tooth  Roof 


Mill-Construction  as  Applied  to  Warehouses  777 

bound  to  be  tondcnsalion,  whether  they  are  under  a  roof  or  under  the  floor 
of  a  room  above,  unless  large  quantities  of  dry  air  are  discharged  into  them. 

(9)  Cost.  Saw-tooth  roofs  necessarily  cost  more  than  flat  roofs,  as 
there  is  practically  the  same  amount  of  roofing  as  in  flat  roofs  and,  in  addition, 
the  cost  of  windows,  glazing,  flashing,  conductors,  condensation-gutters  for 
skylights,  and  a  somewhat  larger  cost  for  heating.  The  additional  cost  of  these 
items  does  not,  however,  fairly  represent  the  comparative  cost,  as  there  should 
be  considered  the  total  cost  of  the  building  compared  with  that  of  an  ordinary 
one  with  sufficiently  high  stories  and  with  a  width  narrow  enough  to  give  the 
required  light.  When  this  is  done  the  slight  additional  cost  is  far  outweighed 
by  the  advantages  gained  for  work  requiring  very  good  light. 

9.   Mill-Construction  as  Applied  to  Warehouses 

Cost.  Owing  to  the  increasing  cost  of  heavy  timbers  for  wooden  construc- 
tion, to  the  lower  cost  of  the  so-called  fire-proof  construction,  and  also  to  the 
better  fire-resisting  qualities  of  the  latter,  owners,  architects  and  builders 
should  carefully  compare  the  cost  of  construction,  and  also  the  cost  of  insur- 
ance of  the  two  types,  before  deciding  on  the  one  to  be  used.  The  difference  in 
the  cost  of  construction  between  these  two  types  is  so  small,  that  in  many  local- 
ities the  lower  cost  will  be  in  favor  of  the  reinforced  concrete  or  other  type 
of  FIRE-PROOF  construction.  The  cost  of  construction  is  al3o  in  favor  of  the 
fire-proof  type,  where  both  long  spans  and  strength  are  required. 

Timber-Spacing  for  Sprinklers.  Warehouses  of  mill-construction 
should  be  built  so  as  to  allow  the  best  possible  distribution  of  water  from  auto- 
matic SPRINKLERS,  with  the  least  possible  obstructions,  and  floor-timbers, 
therefore,  should  be  as  few  as  the  floor-loads  will  allow.  There  should  be  no 
concealed  spaces  of  any  kind  in  the  building.  To  insure  the  greatest  efficiency 
for  sprinkler-systems,  it  is  better  to  adapt  the  timber-spacing  to  suit  the  sprink^ 
lers,  rather  than  to  arrange  the  sprinklers  to  suit  the  timber-spacing. 

Mill-Construction  Adapted  to  Warehouses.  The  features  of  bad  con-r 
struction  mentioned  under  What  Mill-Construction  is  Not  are  as  objec- 
tionable in  warehouses  as  in  factories,  while  the  construction  advocated  fot 
mills  may  be  used  with  almost  equal  advantage  in  the  erection  of  warehouses. 
But  as  the  latter  are  usually  erected  in  the  more  thickly  settled  portions  of  a 
city,  they  are  more  subject  to  the  dangers  of  a  conflagration;  and  it  should  be 
understood  that  even  the  best  slow-burning  construction  will  stand  but  a 
short  time  after  a  Are  has  obtained  a  good  headway,  the  main  object  of  mill- 
construction  being  to  retard  the  spreading  of  fire  by  the  use  of  heavy  timbers 
and  the  absence  of  concealed  spaces.  In  applying  the  principles  of  mill- 
construction  to  warehouses,  therefore,  the  general  principle  of  using  large 
timbers  placed  as  far  apart  as  the  loads  will  permit,  and  of  avoiding  aU  concealed 
spaces,  should  be  constantly  kept  in  mind. 

Warehouse-Floors,  however,  are  generally  required  to  sustain  heavier  loads 
than  are  found  in  woolen  and  cotton-mills,  and  hence  require  heavier  con- 
struction. While  WAREHOUSE -FLOORS  are  quite  often  built  with  transverse 
girders,  8  orio  ft  apart,  the  spaces  being  spanned  by  flooring  from  4  to  6  in  thick, 
the  more  common  method  of  construction  is  to  use  one  or  more  lines  of  longitu- 
dinal girders  supporting  floor-beams  spaced  as  far  apart  as  possible,  preferably 
not  less  than  8  ft  on  centers. 

Area  and  Height.  The  area  of  buildings  of  this  type  should  be,  preferably, 
not  over  7  500  sq  ft,  and  in  no  case  should  it  exceed  15  000  sq  ft  between  fire-walls. 
If  buildings  of  large  area  are  required,  it  is  advisable  to  divide  them  into 


778 


Wooden  Mill  and  Warehouse-Construction         Chap.  22 


separate  sections  by  fire-walls,  thus  reducing  the  liability  to  one  fire,  and  afford- 
ing an  opportunity  of  storing  hazardous  goods  in  one  or  more  sections,  and 
non-hazardous  or  less  hazardous  goods  in  the  remaining  sections.  Where 
ground  is  available,  it  is  better  to  have  a  building  of  large  area  and  lower 
HEIGHT  divided  into  fire-sections,  than  to  have  a  building  of  lesser  area  and 
greater  height,  as  the  former  construction  affords  a  more  economical  handling 
of  goods,  and  less  concentration  of  values.  Buildings  of  this  type  should  be 
limited  to  65  ft  in  height,  and  to  six  stories,  thus  discouraging  the  overloading 
of  floors.  Piled  goods  should  be  kept  at  least  18  in  away  from  beams,  thus 
allowing  for  the  distribution  of  water  from  the  sprinklers. 

Walls  should  be  of  brick,  and  not  less  than  13  in  thick  in  the  upper  story, 
and  they  should  be  increased  in  thickness  on  the  lower  floors  to  take  care  of 
additional  loads.  Party  walls  should  be  increased  at  least  4  in  in  thickness, 
and  all  walls  should  be  laid  in  cement  mortar,  should  extend  above  the  roof 
at  least  36  in  and  be  coped  with  stone,  salt-glazed  terra-eotta,  or  similar  non- 
combustible  materials.  Openings  in  division  walls  should  be  limited  to  as 
few  as  possible,  not  over  three  in  each  story,  they  should  not  exceed  80  sq  ft 
each  in  area,  and  should  be  protected  by  double,  automatic,  sliding  fire-doors, 
as  specified  elsewhere.     (See  Chapter  XXIII,  page  907.) 


ELEVATION 


Balcony  Floor-supports 
and  rails  Fire-proof. 


Note:  Walls  of  brick  or  other  approved  material,  built  solidly 
from  foundations  to  at  least  36  inches  above  I'oof. 
Stair-treads,  etc.,  of  fire-proof  material. 

Fig.  19.     Tower  Fire-escape.     Outside-balcony  Entrance 


Openings  in  "Walls.  As  a  protection  against  fires  from  surrounding  prop- 
erties, openings  in  outer  walls  should  be  small,  limited  to  as  few  as  possible, 
and  protected  by  standard  fire-shutters  and  doors,  or  standard  wire-glass 
windows.  If  the  surrounding  buildings  are  of  hazardous  occupancy  or  inferior 
construction,  and  the  distance  between  the  warehouse  and  the  latter  but  a  few 
feet,  shutters  are  preferable,  as  wire-glass  windows  are  recommended  only 
where  the  exposures  are  moderate.     Even  though  the  building  is  not  exposed 


Mill- Construction  as  Applied  to  Warehouses 


779 


to  fire  from  other  buildings,  the  protection  of  window-openings  may  prevent 
the  spread  of  fire  from  story  to  story  through  the  windows. 

Girders  and  Beams  which  support  the  floors  and  roof  should  be  single 
PIECES,  not  less  than  6  in  in  least  dimension,  and  with  a  sectional  area  of  not 
less  than  72  sq  in;  while  columns  should  be  not  less  than  8  by  8  in  in  cross- 
section  in  the  upper  story,  and  should  be  increased  in  size  in  the  other  stories 
to  take  care  of  any  additional  loads.  The  beams  and  girders  should  be  self- 
releasing  (Fig.  2),  and  the  floors  should  be  built  as  outlined  under  standard 
mill-construction,  page  760,  inclined  at  least  i  in  in  20  ft,  made  as  nearly 
water-proof  as  possible,  and  scuppered  to  the  outside  of  the  building.  These 
scuppers  should  be  set  in  brick-work  at  frequent  intervals,  of  sufficient  size  to 
carry  off  the  maximum  amount  of  water  from  each  floor,  and  so  constructed 
that  they  will  prevent  the  admission  of  cold  air  to  the  building.     (See  Fig.  11.) 

Towers.  The  floors  should  be  continuous  from  wall  to  wall,  avoiding  holes 
for  belts,  stairways,  elevators,  etc.  All  such  openings  should  be  enclosed  in  a 
brick  tower  or  in  towers  extending  not  less  than  36  in  above  the  roof,  coped 
as  above,  and  accessible  from  each  story  by  means  of  an  outside  balcony  (Fig.  19). 


Openings  in  face-wall  extend 
from  floor  to  ceiling,  Vestibule-floor 
of  fire-proof  construction.  Railing  at 
opening. 

Fig.  20.    Tower  Fire-escape  for  Adjoining  Buildings 

Where  it  is  impossible,  owing  to  the  location  or  otherwise,  to  have  these  open- 
ings on  the  outside,  they  should  be  placed  in  brick  towers  constructed  inside 
the  building  and  connecting  with  an  entrance  to  a  fire-proof  vestibule,  open  to 
the  weather.  There  should  be  openings  from  each  story  to  the  vestibule,  each 
protected  by  standard  fire-doors  (Fig.  20). 

Gravity-Tanks  for  Automatic  Sprinklers  are  usually  placed  on  extension^ 
of  such  towers,  and  they  should  be  built  to  carry  the  additional  load  iniposed. 
Easy  access  to  the  roof  of  the  building  may  be  had  from  a  window  or  windows 
placed  in  the  tower,  and  such  opening  or  openings  should  be  protected  by  fire- 
shutters,  especially  where  the  tower  is  elevated  a  sufficient  distance  to  allow 
the  tank  to  be  placed  inside  of  the  tower,  thus  preventing  flames  from  gaining 
access  to  the  tower  and  destroying  the  tank  and  tank-supports.  ^ 


780 


Wooden  Mill  and  Warehouse-GortstrUctioil        Chap.  22 


Boilers  should  be,  preferablyy  in  a  separate  building,  cut  off  by  standard 
fire-doors  from  the  warehouse;  or,  if  in  the  main  building,  should  be  located  in 
a  room  of  fire-proof  construction,  access  to  which  should  be  from  outside 
the  building  only. 

Structural  Steel  Members  should  never  be  used  in  this  type  o^  coiistriiction, 
as  they  will  not  resist  even  a  moderate  fire.  If  used,  they  should  be  protected 
with  fire-proof  material.  The  lintels  should  be  brick  arches  and  not  sleel 
sections. 


10.   Steel  and  Iron  Structural  Members  in  Warehouse-Construction 

Metal  versus  Wooden  Standard  Members.  Owing  to  the  fact  that  a 
beam  or  column  of  steel  or  wrought  iron  when  heated  will  fail  by  buckling 
or  bending  very  much  sooner  than  an  equivalent  beam  or  post  of  wood,  it  is 
important  that  such  members  be  of  wood,  provided  that  the  wooden  beams 
have  a  sectional  area  of  at  least  72  sq  in,  and  are  not  less  than  6  in  in  least  dimen- 
sion, and  that  wooden  columns  have  a  sectional  area  of  not  less  than  8  by  8  in. 
Cast-iron  columns,  also,  will  generally  fail  in  fire  and  water  sooner  than 
wooden  columns. 

Fireproofing  Steel  Beams  and  Girders.  When  steel  beams  and  col- 
umns are  used,  fireproofing  is  necessary  to  make  them  as  fire-resisting  as 

____^____^__^ __^      the  floors.     Such  beams 

'         ^—p  (  and  girders  may  be  fire- 

-i •B$«.r— ^^ ----v:^        ^  PROOFED  as  shown  in  Fig. 

21.  Metal- wire  mesh 
should  be  placed  as 
shown,  and  tied  to  the 
beams  and  girders  with 
metal  clips;  and  to 
insure  rigidity  during  the 
pouring  of  the  concrete 
and  to  keep  the  mesh  in 
alignment,  forms  should 
be  used.  The  concrete 
should  be  poured  before 
the  floors  are  laid,  and 
after  the  wooden  beams 
are  in  position.  After 
completion,  the  insulation  should  be  at  least  i  in  at  the  edges  of  the 
flanges,  2  in  under  the  lower  flange  of  the  beam  and  3  in  under  the  lower  flange 
of  the  girder.  The  webs  should  be  filled  solid.  Where  there  is  little  storage 
of  a  combustible  nature  in  the  building,  the  beams  may  be  protected  as  shown 
in  Fig.  22.     (See,  also,  pages  863  to  866.) 

Fireproofing  Metal  Columns.  Columns,  either  steel,  wrought-iron, 
or  cast-iron,  should  be  protected  even  to  a  greater  extent  than  girders  and  beams, 
and  should  have  at  least  3  in  of  concrete  at  the  flanges,  at  least  iVu  in  at  the 
edges,  and  be  filled  solidly  against  the  webs.  Fig.  23  shows  two  columns  protected 
by  concrete  held  by  wire  mesh  on  %-in  rods,  and  all  securely  held  to  the  column 
by  metal  clips.  Forms  should  be  used  and  the  concrete  should  be  poured  as 
the  girders  and  beams  are  protected.  Steel  beams,  girders  and  columns  are 
difficult  to  protect,  especially  at  the  intersections  of  steel  and  wood,  and  this 
insulating  material  can  best  be  applied  before  the  floors  are  laid.  The  fire- 
proofing of  these  members  wUJ  bgjptit^e^avail,  unless  the  materials  are  good. 


^Mesh 
-Clip 


Fig.  21.    Fireproofing  of  Steel  Beam  with  Concrete  and 
Plaster 


Steel  and  Iron  Structural  Members  in  Warehouse-Construction   781 

well  tied  to  the  metal  members,  and  applied  by  workmen  who  understand  such 
work. 


Alternate  Metliod 
Rods  if  used  may  bo 
Bharpeued  and  driven  and 
fastened  with  heavy  staple. 

At  least  %  in  of  plaster 
outside  of  lath, 2  coat  work. 


Between  rods  or  cJiannels 
wrap  lower  flange  with  piece 
of  metal  latli  to  provide  ample 
thiclgjess  of  plaster  over  flange. 


Channel  punchecl^ 
for  2  in  wire  nails. 

Metal  lath  to  be  well 
stapled  on  to  the  wood, 

H  in.  rod  or  H  in 
channel  spaced  every" 
18  in.  where  beam  la 
more  than  10  in  deep. 

Metal  lath  to  be  wired 
to  channel  or  rod.. 

Can  be  cut  away  for 
hauyers  and  pointed  up 
after  hangers  are  in  place. 

Fig.  22.     Fireproofing  of  Steel  Beam  with  Metal-lath  and  Plaster 


^"Rods  - 


Pat.  Clamp 


"^Wire  Mesl/ 
l"Plaster''^ 

Fig.  23.     Fireproofing  of  Steel  Columns  with  Concrete  and  Plaster 


Fig.  24  illustrates  the  protection  of  a  round  column  by  reinforced  concrete. 
Here  the  concrete  is  held  in  position 
by  wire  mesh  on  metal  furring,  held 
in  position  by  metal  clips  or  ties. 
The  fireproofing  should  be  at  least  4 
in  thick,  and  forms  should  be  used  in 
surrounding  the  columns.  In  addition 
to  the  above  reinforcements  for  these 
columns,  lateral  reinforcement  should 
be  added  by  means  of  iron  rods  wound 
spirally  around  mesh,  and  placed  12  in 
on  centers.  After  the  forms  are  re- 
moved, and  the  wooden  floors  are  laid, 
the  columns  and  girders  should  be 
finished  with  a  i-in  thickness  of  hard 
plaster,  filUng  all  interstices  between  the  woodwork  and  the  insulation. 


1  riastei 


3  Concrete 


Fig.  24. 


Fireproofing  of  Cast-iron  Column 
with  Concrete  and  Plaster 


Tile, 


782 


Wooden  Mill  and  Warehouse-Construction        Chap.  22 


owing  to  the  difficulty  of  properly  bonding  it,  is  not  as  effective  as  concrete; 
but  if  securely  bonded  by  means  of  metal,  it  is  quite  satisfactory.  Fig.  25 
illustrates  the  protection  of  a  girder  and  a  column  by  means  of  tile.  There 
are  other  equally  efficient  methods  of  beam  and  column-protection,  described 
in  Chapter  XXIII.     In  buildings  of  warehouse-construction,  heavy  goods  are 


7jWf;?f/^/f/f/fw?wmfjfjff/)f//f///>f//nf;/////N/f/f/fnf^ 


ttttl 


IflffW 


'M% 


'Hnllow  Til 


Ywu(u<{({<UMU(({^ua(rmuuaai 


% 


WSZZZZk 
'Hollow  Tile  ^master  

Terra-cotta 
Fig.  25.    Fireproofing  of  Steel  Columns  and  Beam  with  Tile 


handled,  and  it  may  be  advisable  to  protect  the  base  of  each  column  with  sheet 
metal  to  a  height  of  36  in  above  the  floor,  to  prevent  any  weakening  of  the  fire- 
proofing.     (See,  also,  pages  822  to  827,  Figs.  1  to  13.) 

Pipes  for  Gas,  "Water,  etc.,  should  not  be  enclosed  in  column  or  girder- 
insulation.     (See,  also,  page  827.) 


11.   Structural  Details  of  Mill- Construction  as  Applied  to 
Factories  and  Warehouses 

Column,  Girder  and  Joist-Framing.  Fig.  26  illustrates  the  method  of 
carrying  the  girders  from  the  walls,  posts,  etc.,  the  bottom  post  resting  on  a  steel 
POST-BASE.  The  first  floor  above  the  basement  is  shown  with  longitudinal 
girders  only,  and  heavy  mill-flooring  set  on  them.  The  girders  are  framed  at 
the  post  in  a  steel  post-cap,  and  are  hung  clear  of  the  wall  in  an  approved 
steel  WALL-HANGER.  The  next  floor  above  shows  the  construction  in  which  the 
joists  are  framed  into  the  girders  by  means  of  joist-hangers.  The  framing 
at  the  post,  also,  is  done  by  means  of  a  Duplex  four-way  post-cap,  while  the 
girder  is  built  into  the  wall  in  a  Duplex  wall-box.  The  joist-hangers  are 
used  singly  or  opposite  each  other  as  required  and  are  bolted  to  the  girder, 
thus  tying  the  building  laterally.  The  upper  floor  shows  the  joists  resting  on 
the  girder.  This  construction,  however,  does  not  conform  to  strict  mill- 
construction,  as  it  exposes  a  larger  amount  of  timber-surface.  The  girder 
is  shown  built  into  the  wall  and  resting  on  a  wall-plate.  This  distributes  the 
load  over  the  ma;>onry  but  is  not  as  elTectlve  in  preventing  dry-rot  as  the  wall- 
box  or  wall-hanger. 

Steel  and  Malleable-Iron  Post-Caps  and  Bases.  Fig.  27  illustrates  other 
details  of  construction  which  may  be  used.  The  bottom  post  rests  on  a  steel 
POST-BASE.    The  post-cap  shown  on  the  bottom  post  is  a  Duplex  four-way 


Structural  Details  of  Mill-Construction 


783 


STEEL  POST-CAP,  while  the  POST-CAP  above  it  is  one  of  the  malleable-iron  type, 
approved  by  the  National  Board  of  Fire  Underwriters.  The  post-cap  shown 
at  the  top,  also,  is  of  malleable  iron  and  intended  for  lighter  construction  or 
for  girders  which  run  across  the  post  as  shown.  The  girders  in  every  case  are 
carried  clear  of  the  wall  by  means  of  approved  wall-hangers  and  the  beams 
are  carried  by  the  girders  in  malleable-iron  joist-hangers. 


Fig.  26.     Mill-construction.     Column,  Girder  and  Joist-framing 


Cast-iron  Post-Caps  and  Bases.  Fig.  28  illustrates  other  details  of  con^ 
struction.  The  lowest  post  rests  on  a  heavy,  cast-iron,  ribbed  post-base. 
The  first-story  floor-girders  are  carried  at  the  post  by  means  of  heavy,  cast-iron 
post-caps  and  are  built  into  the  wall  in  cast-iron  wall-boxes.  When  cast 
iron  is  used  for  post-caps  it  is  essential  that  it  be  made  extra-heavy,  as  cast 
iron  is  very  uncertain  on  account  of  the  uneven  shrinkage  when  cooling,  which 
often  causes  internal  stresses  and  weakens  the  caps.    Flaws,  also,  may  develop 


784 


Wooden  Mill  and  Warehouse-Construction        Chap.  22 


during  the  manufacuure  which  weaken  the  caps  and  greatly  impair  the  safety 
of  the  building.  An  objection  to  cast  iron  is  its  tendency  to  crack  and  break 
during  a  lire  when  cold  water  is  thrown  on  it.  The  post-caps  shown  in  Fig.  28 
are  of  cast  iron  for  the  first  and  second  floors,  Duplex  steel  for  the  third  floor, 
and  malleable  iron  on  the  top  post. 


'/r/AV/Z/A-'/^ 


Fig.  27.    Mill-construction.     Malleable-iron  Post-caps  and  Bases 

Duplex,  Combination  Post-Cap.  Fig.  29  illustrates  the  use  of  the  Duplex 
COMBINATION  POST-CAP  on  the  bottom  post.  This  cap  is  made  with  a  malleable- 
iron  lower  part  and  a  steel  upper  part.  The  post-cap  shown  on  the  second 
post  is  called  the  Ideal  post-cap  and  consists  of  a  steel  upper  part  with  steel 
angles  riveted  underneath  to  fit  the  post.    The  cap  shown  on  the  top  post 


Structural  Details  of  Mill-Construction 


785 


is  the  old-style,   cast-iron  cap.     The  wall-hanger,   wall-box,   wall-plate 
and  JOTST-HANGER  shown  are  used  in  standard  construction. 


Fig.  28.     Mill-construction.     Cast-iron  Post-caps  and  Bases 


Steel  Post-Caps.  Fig.  30  illustrates  various  forms  of  steel  post-caps. 
The  Ideal  post-cap  is  shown  on  the  bottom  post  and  the  Van  Dorn  post-cap  on 
the  post  next  above.  On  the  top  post  the  Star  post-c.ai'  is  shown.  This  hrva 
a  fin  for  wliich  the  top  of  the  post  must  be  slotted  to  receive  it.     Steel  joist- 


786 


Wooden  Mill  and  Warehouse-Construction         Chap.  22 


HANGERS  aic  shown  for  the  two  lower  floors.  The  Ideal  joist-hanger  is 
illustrated  in  the  lower  floor.  Tt  is  spiked  to  the  sides  and  top  of  the  girder. 
The  Van  Dorn  joist-hanger  is  shown  in  the  second  floor,  while  the  old-style 
STIRRUP  is  shown  in  the  top  floor.  The  wall-hangers  illustrated  are  of  the 
approved  type. 


Fig.  29.     Mill-construction.     Combination  Post-caps,  etc. 


Framing  Steel  Beams  and  Girders.  Fig.  31  iUustrates  the  use  of  I-beam 
girders  in  place  of  wooden  girders  and  their  connections  with  wooden  beams. 
In  this  kind  of  construction  it  is  necessary  to  fireproof  the  steel  beams,  as  they 
are  more  readily  afi"ected  by  heat  in  case  of  fire  than  large  wooden  timbers. 
Intense  heat  often  causes  them  to  collapse  and  ruin  a  building.    The  hanger 


Structural  Details  of  Mill-Construction 


787 


shown  in  the  first  floor  is  used  where  the  I  beams  and  wooden  beams  are  of  the 
same  height.  This  hanger  provides  an  extra  bearing  for  the  timber  and  has 
proved  very  satisfactory.  The  hanger  shown  in  the  second  floor  is  used  when 
it  is  necessary  to  raise  the  wooden  beam  above  the  lower  flange  of  the  ^teel 
beam.     This  hanger  brings  all  the  load  on  the  lower  flange  of  the  I  beam  and 


Fig.  30,     Mill-construction.     Steel  Post-caps,  etc. 


provides  an  anchorage  for  the  wooden  beam.  It  is  used  singly  or  in  pairs  on 
the  I  beam  as  required,  and  is  bolted  through  the  web  of  the  I  beam.  This  has 
been  found  to  be  a  very  economical  and  efficient  construction.  In  the  third 
floor  the  wooden  beam  is  shown  framed  to  the  I  beam  by  means  of  a  shelf- 


ANGLE.     With   this  form  of   construction  it  is  necessary  to  rivet  the  shelf- 


788 


Wooden  Mill  and  Warehouse-Construction        Chap.  22 


'■////////x  y////////////////////////y/////////////////7^ 


Fig.  31.     Mill-construction.     Framing  Steel  Beams  and  Girders 


ANGLE  to  the  web  of  the  I  beam.  The  upper  detail  shows  the  old-fashioned 
STIRRUP  passing  over  the  top  flange  of  the  I  beam  and  carrying  the  wooden 
beam.  The  post-caps  shown  are  the  Duplex  steel  post-caps  which  are 
approved  by  the  National  Board  of  Fire  Underwriters. 


Connections  of  Floor-Beams  and  Girders 


789 


12.   Connections  of  Floor-Beams  and  Girders 

Girder-Hangers  and  Joist-Hangers.  To  render  the  construction,  and 
particularly  the  girders,  slow-burning,  it  is  important  to  have  no  hollow  spaces 
between  the  top  of  the  girders  and  the  flooring,  that  is,  to  have  the  top  surface 

of  the  floor-beams  flush 
with  that  of  the  girders. 
This,  of  course,  neces- 
sitates framing  the 
floor-beams  into  the 
girders.  For  heavy 
CONSTRUCTION  the  only 
kind  of  framing  that 
is  permissible  is  one  in 


Fig.  32.     Duplex  Hanger  for  Heavy  Floor-beams 


Fig.  33.  Framing  I  Beam 
and  Wooden  Beam  of 
Same  Depth 


which    some    kind    of    joist-hanger   is     used.    The 

various  kinds   of  joist-hangers   now   in    the    market 

have  been  illustrated  and  commented  on  in  the  last  part  of  Chapter  XXI^ 

When  the  floor-beams  are  6  by  12  in  or  larger  in  cross-section,  and  the  girders! 

are  of  wood,  the   author  would  give  the  preference  to  the  Duplex  hanger' 

shown  in  Fig.  32.     (See,  also,  pages  752  and  753.) 

If  steel-beam  girders  are  used  in  place  of  wooden  girders,  there  are 
several  methods  in  use  for 
framing  the  wooden  beams. 
Fig.  33  shows  a  steel  I  beam, 
and  a  wooden  beam  of  the 
same  depth  framed  into  it 
and  resting  on  its  lower  flange. 
In  most  cases,  however,  this 
does  not  afford  a  sufficient 
bearing  for  the  wooden  beam. 
Fig.  34  shows  a  shelf-angle 
riveted  to  the  web  of  the  I 
beam.  Whenever  this  method 
of  supporting  the  beams  is 
used,  enough  bolts  or  rivets 
should  be  used  to  support  the 
load  carried  by  the  shelf- 
angles.  Each  %-m  bolt  may 
be  considered  to  support  3  000  Fig.  34.  Wooden  Beam  Framed  to  I  Beam  with 
lb  on  each  side  of  the  girder,  Shelf-angle 

and  each  %-in  bolt,  4  000  lb. 

The  methods  shown  in  Figs.  35  and  36  are  sometimes  used,  but  are  open  to 
objection  on  account  of  the  weakening  of  the  wooden  beams  when  loaded. 
Fig.   37    shows  a  stirrup-type  of   hanger.    This  construction  permits   the 


790  Wooden  Mill  and  Warehouse-Construction        Chap.  22 


Fig.  35.     Wooden  Beam  Framed  to  I  Fig. : 

Beam  with  Wooden  Cleat 


Wooden  Beam  Framed  to  I  Beam 
with  Shelf-angle 


Fig.  37.     Wooden  Beam  Framed  to  I  Fig.  38.     Wooden  Beam  Framed  to  I  Beam 

Beam  with  Stirrup-hanger  with  Duplex  Hanger 


Fig.  39.    Wooden  Beam  Framed  to  I  Beam 
with  Duplex  Shelf-hanger 


L=ri] 


Fig.  40.     Wooden  Beam  Framed  to  I  Beam  with  Duplex  Box-hanger 


Connections  ot  Floor-Beams  and  Girders  791 

framing  of  the  wooden  beam  at  any  desired  height,  and  has  proved  satisfactory. 
These  hangers  can  be  used  with  any  depth  of  beam  or  girder,  and  are  furnished 
by  all  manufacturers  of  steel  joist-hangers  of  the  various  types,  as  well  as  by 
blacksmiths  who  can  make  wrought-iron  stirrups.  Fig.  38  shows  the  Du- 
plex-type OF  HANGER  for  framing  a  wooden  beam  flush  with  the  lower  flange 
of  the  I  beam.    This  hanger  is  attached  by  means  of  bolts.     Fig.  39  shows 


Fig.  41.    Floor-framing  with  Van  Dorn  Hangers  and  Post-caps 

the  same  design  of  hanger,  with  the  shelf-construction  used  to  carry 
the  wooden  beams  up  to  4  in  above  the  lower  flange  of  the  I  beam.  Fig. 
40  shows  a  hanger  for  carrying  the  wooden  beams  4  in  or  more  above  the 
lower  flange  of  the  I  beam. 

The  hangers  described  in  Figs.  38,  39  and  40  are  all  of  the  Duplex  type, 
and  arc  so  constructed  that  all  the  load  is  carried  on  the  lower  flange  of  the 


Fig.  42.     Floor-framing  with  Duplex  Hangers  and  Post-caps 

I  beam,  which  is  a  very  satisfactory  and  ideal  construction  whenever  it  is 
necessary  to  frame  wooden  beams  into  and  not  rest  them  on  the  I  beams.  The 
design  is  a  very  economical  one  for  framing  wooden  beams  to  I  beams,  as  the 
holes  for  attaching  these  hangers  can  be  punched  while  thS  steel  is  being  fabri- 


792 


Wooden  Mill  and  Warehouse-Construction        Chap.  2^ 


cated,  and  the  hangers  are  attached  to  the  steel  beams  by  means  of  boUs  when 
the  wooden  beams  are  put  in  place.  These  hangers  are  provided  with  lugs 
or  lag-screws  for  anchoring  the  wooden  beams  securely  to  the  steel  girder. 
Fig.  41  shows  a  floor-framing  with  the  Van  Dorm  steel  hangers.  Fig.  42 
shows  the  floor  framed  with  the  Duplex  type  of  hanger  and  post-cap.  The 
same  principle  of  construction  is  applicable  to  larger  wooden  beams  spaced 
farther  apart. 

13.   Wall-Supports  and  Anchors  for  Joists  and  Girders 

Box  Anchors,  Wall-Hangers,  etc.  Anchoring.     In  a  warehouse  intended 
to  be  constructed  on  the  slow-burning  principle,  the  floor-beams  and  girders 

should  be  anchored  to, 
and  supported  by  the 
walls  in  such  a  way  that 
in  case  the  beams  are 
burned  through,  the  ends 
may  fall  without  injuring 
the  walls;  and  where 
large  timbers  are  used, 
provision  should  be  made 
against  the  possibility  of 
drv  rot. 

Box  Anchors.  The 
method  of  supporting  the 
beams  in  mill-construc- 
tion as  originally  de- 
veloped in  the  New  Eng- 
land mills  is  shown  in 
Fig.  43.     Early  Form  of  Beam-support  in  Mill-construction    Fig.    43.     This    fulfilled 

the   requirements  above 
mentioned,  but  it  weakened  the  walls  to  some  extent.     The  Goetz  cast-iron 


Fig.  44.     Goetz  Box  Anchor  for  Wooden  Beams 


Fig.  4.5.     Goetz  Box  An- 
chor for  Wooden  Beams 


BOX  anchors  shown  in  Figs.  44,  45  and  46  and  the  Duplex  wall-box  shown 
in  Fig.  47  are  decided  improvements  on  the  anchor  shown  in  Fig.  43,  as  they 


Wall-Supports  and  Anchors  for  Joists  and  Girders 


793 


Fig.  46.     Goetz  Box  Anchor  for  Wooden  Girders 


afford  all  the  advantages  of  the  latter  without  weakening  the  walls,  unless  the 

floor-beams  are  very  wide.     The   wall-box   as   shown  in   Fig.  47  is  rnade 

with  a  malleable-iron   bottom  plate  and   a  steel   box  above.     It  has  a  rib 

on  the  plate  at  the  back,  which  extends  up  and  down,  and  acts  as  a  secure 

anchorage    in    the    brickwork.     These    wall-boxes   are   made    wedge-shape, 

and    it    is    therefore 

impossible     to     pull 

them  out  of  the  wall. 

The     more     weight 

there  is  on  the  beam, 

the  stronger  will  be 

the  bond  that  holds 

the  beam  to  the  box 

and  the  box  to  the 

wall. 

In  case  of  fire  or 
accident,  the  joists 
can  burn  through  or 
break;  and  in  falling 
they  can  free  them- 
selves from  the  an- 
chorage and  leave 
the  wall  standing. 
The  wall  is  not  even  weakened  by  the  space  left  in  it,  because  the  box 
remains,  and  the  crushing  strength  of  this  cast-iron  box  is  much  greater  than 
that  of  the  wall.  No  break  or  breach  is  made  in  the  wall,  and  the  box  that 
remains,  securely  held,  forms  a  space  for  the  easy  replacement  of  the  wooden 
beam.  The  box  provides  a  perfect  and  secure  foundation  for  each  beam. 
Fire  from  a  defective  flue  cannot  ignite  a  beam-end,  because  it  is  protected  by 

a  ventilated,  CASx-moN  box.  The 
WALL-BOXES  have  air-spaces,  also,  in 
the  sides,  Yj  in  wide,  which  permit  a 
circulation  of  air  around  the  ends  of 
the  beams,  effectually  preventing  dry  , 
rot.  If  timber  is  wet  or  unseasoned 
these  wall-boxes  allow  it  to  dry  out 
after  it  is  put  in  the  building.  The 
average  weight  of  a  box  like  that 
shown  in  Fig.  45,  for  2  by  12-in 
joists,  is  10  lb. 

Wall-Hangers.     Another    device 

[y^  for  obtaining  the   same  results  in  a 

different   way   is   the   wall-hanger. 

Figs.  48  and  49  show  Duplex  wall- 
hangers  for  large  timbers.  The  hanger  shown  in  Fig.  49  is  made  of  open-hearth 
steel  and  is  extra-heavy.  Each  of  these  hangers  is  provided  with  a  plate  which  has 
an  8-in  bearing  on  the  wall,  and  the  bearing  of  the  timbers  on  the  hanger  is  also 
8  in.  For  beams  not  exceeding  10  in  in  breadth  there  is  probably  little  choice 
between  the  box  anchor,  Fig.  46,  and  the  wall-hangers,  Figs.  48  and  49, 
except  perhaps  in  the  price  and  appearance.  When  the  wall-hanger  is  used, 
no  hole  is  left  in  the  wall,  and  a  saving  of  6  in  in  the  length  of  the  beams  is 
effected,  which  in  some  cases  would  be  a  consideration.  For  girders  12  by  14  in 
9,^4  upw£|.rds  in  cross-section,  the  author  believes  that  the  hanger  shown  itt 


Fig.  47.     Duplex  Wall-box  with  Ribbed  Plate 


794 


Wooden  Mill  and  Warehouse-Construction         Chap.  22 


Fig.  49  is  preferable  to  the  box  anchor.    Wall-hangers  made  from  stirrups 
should  not  be  used  for  heavy  beams.    The  use  of  any  one  of  the  hangers  or 


Fig.  48.     Duplex  Wall-hanger  for  Large 
Wooden  Girder 


Fig.  49.     Duplex   Extra-heavy   Wall- 
hanger  for  Large  Wooden  Girder 


boxes  is  obviously  greatly  superior  to  the  ordinary  method  of  anchoring  beams 
or  girders  to  walls,  and  the  use  of  such  hangers  will  undoubtedly  save  much  loss 
which  would  be  caused  by  the  falling  of  the  walls.    These  are  almost  invariably 


Fig.  50.    Application  of  Wall-hanger  to  Brick  Wall 

pulled  down  by  the  ordinary  iron  anchors  when  the  beams  fall.    Fig.  50 
shows  the  application  of  a  wall-hanger. 

14.   W.eakness  of  Wrought-Iron  Stirrups  when  Exposed  to  Fire 

Stirrups  and  Fire-Tests.  Referring  to  this  subject,  Professor  J.  B.  Johnson, 
of  Washington  University,  said:  "  The  recent  fire-tests  of  steel  stirrups  and 
brick  walls  which  were  made  under  my  supervision  in  this  city  (St.  Louis), 
show  very  conclusively  that  unprotected  stirrups  are  extremely  dangerous. 
These  stirrups  become  red-hot  in  a  few  minutes  and  then  rapidly  char  and 
burn  away  the  ends  of  the  beams;  and  they  also  bend  down,  so  that  in  from 
twenty  to  thirty  minutes  after  the  fire  reaches  the  stirrups,  the  beam  is  dropped 
right  out  of  the  twisted  steel  by  the  straightening  out  of  this  bend  or  twist." 

The  Duplex  Hangers  possess  an  advantage  over  steel  stirrups  because, 
being  of  malleable  iron,  they  are  not  as  quickly  afifected  by  heat,  there  are 
no  twists  or  bends  to  straighten,  and  the  bearing  in  the  trimmer  or  header  is  to 
a  great  degree  protected  by  the  form  of  construction.  During  the  severe  fire 
at  Paterson,  N.  J.,  February  9,  1902,  some  Duplex  wall-hangers  were  sub- 
jected to  a  most  severe  test  without  apparent  injury.  It  is  undoubtedly  desir- 
able that  all  structural  iron  should  be  protected  from  fire,  but  it  is  almost  im- 
practicable to. effectively  protect  the  stirrups  used  in  connection  with  woodtn 
beams  without  going  to  a  greater  expense  than  the  character  of  the  construction 
Varrants. 


Form  and  Materical  of  Post-Caps  795 

15.   Post  and  Girder-Connections 

Iron  Cap-Plates,  Wooden  Bolsters,  etc.  Whenever  a  building  is  con- 
structed with  wooden  posts  extending  through  several  stories,  each  upper  post 
should  rest  on  an  iron  cap-plate,  fitted  over  the  post  below,  and  never  on  a 
girder  or  even  on  a  wooden  bolster.  A  bolster  would  not  be  objectionable 
were  it  not  for  the  fact  that  the  pressure  under  the  post  is  generally  sufficient  to 
crush  the  fibers  of  any  kind  of  wood.  Then,  too,  there  is  always  some  settle- 
raent  due  from  shrinkage.  As  posts  are  used  expressly  for  the  support  of  beams 
or  girders,  the  iron  caps  must,  of  course,  extend  sufficiently  beyond  the  upper 
post  to  afford  ample  bearing  for  the  end  of  the  girder.  This  bearing  in  square 
inches  should  be  equal  to  at  least  one-half  the  load  on  the  girder  divided  bj^  the 
safe  resistance  of  the  wood  to  crushing  across  the  grain,  as  given  in  Table  IV, 
page  454. 

Example.  A  i^  by  14-in  yellow  pine  girder  is  designated  to  support  a  possible 
load  of  38  000  lb.     What  bearing  should  it  have*  at  the  ends.^ 

Solution.  The  safe  resistance  given  for  long-leaf  yellow  pine  to  crushing  across 
the  grain,  is  350  lb  per  sq.  in.  One-half  the  load  on  the  girder  is  19000  lb, 
and  hence  the  bearing  area  should  be  19  000  divided  by  350  or  about  54  sq  in. 
As  the  breadth  of  the  beam  is  12  in  this  would  require  a  bearing  lengthwise 
of  the  girder  of  4V2  in.  In  no  case  should  the  bearing  be  less  than  that  required 
by  the  above  rule. 

16.   Form  and  Material  of  Post-Caps 

Cast-iron  versus  Steel  Post-Caps.  Formerly  cast-iron  post-caps  were 
used  for  the  framing  of  the  girders  at  the  columns  and  posts.  But  the  uncer- 
tainty attached  to  the  use  of  cast  iron,  and  the  necessity  of  extremely  heavy 
caps  to  assure  safe  construction  have  led  most  engineers  to  specify  steel  post- 
caps,  as  they  are  unquestionably  the  strongest  form  of  construction  for  fram- 
ing posts  and  girders.  The  use  of  steel  post-caps  is  to  be  recommended,  there 
being  no  uncertainty  regarding  the  strength  of  steel  as  there  is  concerning  the 
strength  of  cast  iron  used  for  post-cap  construction.  Internal  stresses  due  to 
uneven  cooling  may  seriously  affect  the  strength  of  a  cast-iron  cap,  while  a 
honeycombed  casting  may  be  used,  undetected,  and  affect  the  safe  carrying 
capacity;  so  that  failure  of  the  cap  may  occur  even  from  the  vibration  due  to 
the  machinery  in  the  building. 

Cast-iron  Post-Caps  are  still  used  in  some  localities  and  a  few  of  the  com- 
mon forms  as  well  as  those  of  steel  post-caps  are  shown.  Fig.  51  shows  a 
form  which  is  frequently  used  for  light  construction.  Fig.  52  shows  a  similar 
cap  for  a  cylindrical  post.  These  caps  permit  the  use  of  girders  wider  than  the 
post.  When  the  girders  and  floor-beams  are  in  place,  and  especially  when  the 
building  is  occupied,  there  is  no  danger  of  the  girders  or  posts  slipping  on 
the  plate;  in  fact  it  would  require  a  greater  force  to  move  them.  The  girders 
should  be  tied  together  longitudinally  by  iron  straps  spiked  to  their  sides. 
Many  persons,  however,  consider  it  important  in  a  building  of  slow-burning 
construction,  to  have  the  posts  tied  together  in  vertical  lines,  and  the  girders 
secured  in  such  a  way  that  they  will  be  self-releasing  without  pulling  dowii 
the  posts.  Figs.  5.3  and  54  show  two  post-caps  which  fulfill  these  requirements. 
With  these  caps  the  ends  of  the  girders  are  not  fastened  by  bolts  or  spikes,  but 
are  held  in  place  and  tied  longitudinally  by  means  of  the  lug  L  on  the  Goetz 
cap,  and  by  pins  on  the  Duvinage  cap;  so  that  in  case  the  girder  is  burned  to 
the  breaking  point,  it  can  fall  without  pulling  on  the  post.  Provision  is  also 
made  for  bolting  the  cap  to  the  upper  post.    The  author  doubts  very  much. 


796 


Wooden  Mill  and  Warehouse-Construction         Chap.  22 


Fig.  51.    Cast-iron  Post-cap  for        Fig.  52.     Cast-iron  Post-cap  for  Cylindrical  Wooden 
Square-section  Wooden  Post      ,  Post 


Fig.  53.     Cast-iron  Duvinage  Post-cap  with  Beam-pins 


Fig.  54.     Cast-iron  Goetz  Post-cap  with  Beam-lugs      Fig.  55.     Cast-iron  Post-cap  with 

High  Sides 


Form  and  Material  of  Post-Caps 


797 


however,  if  posts  bolted  together  in  this  way  will  stand  after  the  girders  have 
fallen,  as  the  planking  will  be  likely  to  pull  the  posts  over,  even  if  they*  do  not 
burn  as  quickly  as  the  beams.  Fig.  55  shows  another  form  of  cast  cap  with 
high  sides,  allowing  lag-screws  to  be  driven  in  the  holes  to  tie  the  girders. 


Fig.  57.    Steel  Post-caps  for  Posts  Varying  in  Section.     Second  Figure  Shows  Four- 
way  Beam-construction 

A  Steel  Post-Cap,  v/hich  is  approved  by  the  National  Board  of  Fire*  Under- 
writers and  bears  their  label,  is  shown  in  Fig.  56.  This  post-cap  is  made  up  of 
steel  side-plates  and  heavy  steel  brackets,  all  held  rigidly  together  by  means 
of  four  heavy  bolts.    The  posts  and  girders  are  fastened  to  the  cap  by  means  of 


798  Wooden  Mill  and  Warehouse-Construction        Chap.  22 


Fig.  58.    Steel  Post-cap.     One-way  Beam-construe-       Fig.  59.     Malleable-iron  Post- 
tion  caps 


Fig.  60.    Steel  Post-cap  for  Continuous  Post        Fig.  61.     Malleable-iron  Post-cap  with 

Steel  Top-plate 


Z^ 


IT     # 


""^^ ."iri%^ 


Fig.  62.     Steel  Post-cap  for  Cylindrical  Wooden  Post.     Perspective 


Form  and  Material  of  Post-Caps 


790 


lag-screws,  permitting  the  girders  to.  release  themselves  in  case  of  fire.  By 
this  method  the  entire  construction  is  tied  together  vertically  and  longitudinally. 
This  cap,  on  account  of  its  simple  design,  lends  itself  readily  to  every  form  of 
construction  desired. 

Various  Types  of  Post-Caps.     Fig.  57  illustrates  one  post-cap  in  which 
the  width  of  the  girder  is  less  than  that  of  the  post  below,  and  also  another  post- 


o 

o 

o 

U)             o 

1                  t 

1 1, 

5       l) 

SIDE 


(  ) 


•    ,x'==-->^ 

— 1'     l-^ 

— 

^^^^^.r^'" 

PLAN 
Fig.  63.     Steel  Post-cap  for  Cylindrical  Wooden  Post.     Elevations  and  Plan 

CAP  in  which  the  width  of  the  girder  is  greater  than  that  of  the  post  below.     In 
the  latter  four-way  brackets  are  riveted  to  the  side-plates  to  provide  for  the 

FOUR- WAY  CONSTRUCTION.      Fig.  58  sllOWS  a  ONE-WAY  CONSTRUCTION.      Fig.  60 

shows  a  POST-CAP  which  is  used  when  it  is  required  to  run  a  post  through  two 
stories.  This  is  what  is  known  as  a  con- 
tinuous POST-CAP.  The  bracket  instead 
of  being  made  clear  across  l^e  cap  is  made 
short  on  both  sides  and  fitted  into 
shoulders  notched  into  the  post,  so  as 
to  make  a  more  rigid  construction.  Fig. 
59  shows  two  POST-CAPS  made  of  malleable 
iron  which  are  preferable  to  cast-iron  caps 
as  they  will  not  break  off  in  case  of  a  fire 
when  cold  water  comes  in  contact  with 
them.  This  danger  is  present  when  cast- 
iron  POST-CAPS  are  used.  The  cap  shown 
is  made  in  two  parts  so  that  it  will  fit 
posts  and  girders  of  different  sizes.  This 
cap,  also,  is  approved  by  the  Board  of 
Fire  Underwriters.  Fig.  61  shows  a  com- 
bination POST-CAP,  the  upper  part  of  which  is  made  of  steel  plate,  and  the 
lower  part  of  malleable  iron.  Figs.  62  and  63  show  steel  post-caps  for 
round  posts.  They  are  also  frequently  used  for  pipe-columns  and  concrete- 
filled  columns.  (See,  also,  Steel-Pipe  Columns,  page  469  and  Lally  Columns, 
pages  474  and  477.)     F,ig.  64  shows  a  steel  post-cap  intended  for  lighter 


Fig.  64.    Steel  Post-cap  for  Light  Con- 
struction 


800 


Wooden  Mill  and  Warehouse-Construction        Chap.  22 


construction.  Fig.  65  shows  Van  Dorn  post-caps.  Fig.  66  illustrates  the 
Star  post-cap  which  is  made  of  a  bent  steel  plate  with  a  fin  projecting  below 
into  a  slot  in  the  post.     Both  are  approved  by  the  Underwriters.     It  is  necessary 


I 


J 


Fig.  65.     Van  Dorn  Steel  Post-caps 


to  slot  out  the  post  in  order  to  insert  this  fin.  Post-caps  which  completely 
encircle  the  top  of  the  post  in  a  socket,  to  a  great  measure  tend  to  pre- 
vent the  twisting  effect  of  the  post,  which  is  so  noticeable  when  the  posts 

are  of  wood.  There  is  an  objection 
to  the  use  of  the  four-way  post-cap 
when  the  girders  are  of  wood,  because 
the  floor-beams  that  are  hung  from  a 
girder  drop  a  distance  equal  to  the 
shrinkage  in  the  girder,  if  the  beams 
are  hung  in  stirrups,  or  by  one-half 
this  amount  if  they  arc  hung  in 
Duplex  hangers.  The  beams  sup- 
ported on  the  post-cap  cannot  drop 
at  all,  and  consequently  the  floor  will 
be  higher  over  the  beam  supported 
by  the  posts,  than  over  the  inter- 
mediate beams.  In  one  building 
where  deep  beams  were  used,  the 
unevenness  in  the  floor  amounted  to 
nearly  an  inch  and  was  very  notice- 
able. Wherever  wooden  girders  are 
used  it  is,  therefore,  a  much  better  construction  to  support  all  of  the  floor- 
beams  from  the  girders,  in  which  case  the  shrinkage  will  be  uniform.  With 
steel  girders  there  is  no  shrinkage,  and  a  beam  may  be  placed  opposite  the 
posts  with  advantage. 

17.   Roofing-Materials 

Warehouse-Roofs  are  almost  always  flat  and,  like  floors,  should  be  continu- 
ous from  wall  to  wall,  without  openings.  The  occupancy  of  such  buildings 
calls  for  little  light,  and  hence  skylights  and  other  roof-structures  are  not  re- 
quired. 

Dampness  and  Leaks.  Stored  goods  may  l)e  very  easily  damaged  by  water, 
and  roofs,  therefore,  should  be  of  such  construction  that  they  will  prevent  damp- 
ness, either  through  leakage  or  condensation.  While  roofs  are  usually  built  as 
flat  as  possible,  the  incline  should  be  sufficient  to  dr;^in  readily,  and  the  out- 


Fig.  66.     Star  Steel  Post-cap  with  Fin 


Fire-Protection  801 

lets  should  be  of  sufficient  capacity  to  quickly  drain  the  roof  of  a  maximum 
amount  of  water. 

Slag  or  Tin  are  almost  exclusively  used  on  buildings  of  this  type,  although 
asphalt  or  other  mastics  are  sometimes  used  with  good  results. 

Slag  Roofs  should  be  constructed  generally  as  described  on  pages  1595 
to  1599  and  should  be  not  less  than  S-ply,  with  the  maximum  amount  of  coating. 
The  flashings  and  counterflashings  should  be  of  copper  or  heavily-coated  best 
terne- plates. 

Tin  Roofs  should  be  laid  with  the  best  open-hearth,  palm-oil-process  terne- 
plates,  laid  on  felt  or  other  suitable  material  which  will  avoid  condensation  and 
act  as  a  fire-retardant. 

Canvas  Roofing  will  stand  hard  usage,  as  is  shown  by  its  continued  use  on 
decks  of  vessels  and  steamers;  but  it  is  not  adapted  to  large  buildings. 

Provisions  for  Flooding  Roofs.  When  warehouses  are  located  in  congested 
districts,  surrounded  by  higher  buildings,  or  by  buildings  of  light  construction 
or  hazardous  occupancy,  their  roofs  should  be  so  constructed  that  they  may  be 
flooded  during  severe  fires  in  such  surrounding  buildings.  '  This  can  be  accom- 
plished by  using  good  roofing-materials,  making  high  flashings,  waterproofing 
the  walls  above  the  roof-line,  and  providing  roof-outlets  of  types  that  will  allow 
the  placing  of  stoppers  at  the  scuppers.     (See  Fig.  11.) 

18.   Partitions 

Non-bearing  Partitions.  This  refers  only  to  those  light  walls  or  enclosures 
which  separate  rooms,  etc.,  and  not  to  those  walls  which  divide  the  building  into 
sections.  Partitions,  as  here  defined,  bear  no  floor-loads.  Buildings  of  the 
SLOW-EURNING  TYPE,  for  occupancies  described  above,  need  but  few  partitions, 
and  these  should  be  built  of  non-inflammable  materials,  preferably  metal  lath 
and  plaster  on  light,  metal  studding.  All  cupboards,  closets,  lockers,  etc.,  in 
a  building  of  this  type  should  be  of  metal,  or  other  equally  non-inflammable 
material. 

19.   Doors  and  Shutters 

Fire-Underwriters'  Specifications.  Doors  and  shutters  should  be  built  as 
outlined  in  the  Rules  and  Requirements  of  the  National  Board  of  Fire  Under- 
writers for  the  construction  and  installation  of  fire-doors  and  fire-shutters,  as 
these  specifications  are  accepted  by  architects  and  builders  as  the  standard. 

Door-Openings  should  be  limited  to  80  sq  ft,  or  less,  each,  and  all  communica- 
tions between  buildings  or  sections  of  a  building  protected  with  double,  auto- 
matic, sliding  doors. 

20.    Fire-Protection 

Automatic  Sprinklers,  supplied  with  an  ample  quantity  of  water  at  a  good 
pressure,  are  needed  in  mills,  storehouses,  factories,  warehouses,  etc.,  where 
combustible  goods  are  made  or  stored,  or  where  large  values  are  at  stake.  They 
may,  in  fact,  be  installed  in  buildings  of  any  type  of  construction  and  occupancy, 
but  are  most  effective  in  buildings  of  fire-proof  or  mill-construction. 

Inside  Standpipes,  with  outlets  in  each  story,  in  the  basement  and  on  the 
roof,  should  be  installed  at  points  readily  accessible  in  case  of  fire,  and  should 
have  a  sufficient  quantity  of  good  hose  attached  at  each  outlet. 

Roof  Nozzles.  If  a  building  is  badly  exposed  to  other  buildings  of  inferior 
construction  or  hazardous  occupancy,  a  Monitor-nozzle  of  large  size,  located 
on  the  roof,  is  advisable. 


802  Wooden  Mill  and  Warehouse-Construction        Chap.  22 

Public  Water-Supplies.  If  these  are  not  available,  a  private  fire-service 
may  be  advisable. 

Competent  Supervision.  All  of  the  above  fire-protection  equipments 
should  be  installed  by  men  familiar  with  their  operation,  and  supervised  by 
competent  fire-protection  engineers,  under  plans  approved  by  underwriters 
having  jurisdiction. 

21.     Cost*  of  Mills  and  Factories  Built  on  the  Slow-Burning  Principle 

Difficulty  of  Estimating  Costs  from  Tables.  The  cost  of  a  building  of 
this  type  of  construction  depends  upon  the  cost  of  material  plus  the  cost  of 
labor,  and  as  the  cost  of  either  varies  greatly  in  different  localities  the  cost  of 
similarly  constructed  buildings  must  also  vary.  Even  if  the  cost  of  labor  and 
materials  does  not  vary,  the  cost  of  buildings  of  the  same  area  will  depend  much 
upon  the  height,  floor-loads,  distance  between  bearing-points,  design,  etc.,  and 
it  is  dilhcult  to  deduce  a  table  accurate  enough  for  use  in  computing  even  the 
approximate  cost  of  buildings  per  square  foot  of  floor-areas.  One  firm  of 
architects  t  states:  ''Experience  has  taught  us  that  estimating  the  cost  of 
a  building  either  by  the  square-foot  'method  or  the  cubic-foot  method 
has  proved  dangerous  and  misleading,  and  it  was  al^andoned  by  us  many 
years  ago  except  to  obtain  a  general  idea  of  the  cost  of  a  building.  We 
have  found  that  the  only  relia1)le  way  to  approximate  the  cost  of  a  building 
is  to  block  it  out  and  to  figure  the  approximate  quantities,  which  at  the  market 
prices  prevailing  at  the  time  the  building  is  to  be  erected,  will  give  the  approxi- 
mate cost  of  said  building."  Owing  to  the  high  cost  of  lumber,  a  fire-proof 
building  will  cost  but  little,  if  any,  more  than  a  building  of  mill-constriktion; 
and  owing  to  this  fact  it  is  always  advisable  to  determine  the  cost  of  buildings 
of  both  types  before  deciding  upon  the  t3^pe  to  be  used.  Buildings  of  mill- 
construction  are  becoming  obsolete  in  some  .localities,  and  owing  to  the  lower 
rate  of  insurance  on  buildings  of  fire-proof  construction,  those  of  the  latter 
type  are  much  preferred,  as  in  the  end  they  cost  less.  It  is  not  always  safe  to 
compare  the  total  cost  of  labor  with  the  cost  of  the  labor  per  diem,  as 
the  cheaper  labor  is  often  the  more  expensive  in  the  end,  this  depending  largely 
upon  the  locality  and  the  conditions  imposed.  Tables  showing  the  approximate 
cost  of  buildings  of  the  mill-construction  type  are  computed  from  the  cost 
of  mill-buildings  of  light  construction  (cotton-mills  with  lateral  beams  only) 
and  are  not  adapted  to  computing  the  cost  of  heavy  warehouses  or  similar 
factory-construction.  The  figuring  of  the  cost  of  such  buildings  from  the  COST 
PER  square  foot  gives,  at  the  very  best,  only  approximate  results;  and  as  a 
discrepancy  of  but  i  ct  per  sq  ft  will  sometimes  amount  to  thousands  of  dollars, 
the  method  is  hardly  accurate  enough  to  estimate  even  the  approximate  cost. 

The  Cost  of  Buildings  of  Mill-Construction  in  New  England.  The 
following  eight  buildings  were  designed  by  Lockwood,  Greene  and  Company 
of  Boston,  Mass.,  who  submit  data  and  descriptions  of  ])uildings  of  mill-con- 
struction with  their  cost  per  square  foot.  These  buildings  are,  with  a  single 
exception,  situated  within  a  limited  area  where  cost  of  labor  and  materials 
vary  but  little.  The  floor-loads  vary  from  75  to  150  lb  per  sq  ft,  and  the  cost 
runs  from  $0,715  to  $1.56  per  sq  ft.  Considering  the  textile-mills  only,  the 
average  cost  is  $1,038  per  sq  ft,  while  the  average  cost  of  all  these  buildings  is 
$1,113  per  sq  ft. 

*  These  are  pre-war  prices,  but  the  data  are  retained  for  purposes  of  comparison  of  rela- 
tive costs  of  different  types  of  buildings,  or  of  buildings  in  different  sections  of  the  country. 
For  the  cost  of  reinforced-concrete  mills,  warehouses,  etc.,  see  pages  1613  and  1618, 

t  Farrot  &  Livaudais,  Ltd..  New  Orleans.  La. 


Cost  of  Mills  and  Factories  Built  on  the  Slow-Burning  Principle      803 

A  Cotton  Spinning-Mill.  This  mill  has  an  attached  picker-house,  office 
and  dye-house  wings,  and  was  built  in  Rhode  Island  in  191 1.  The  following 
are  the  details  of  construction:  main  mill,  four  stories;  size,  263.17  by  131.67  ft; 
two-story  picker-house,  42,67  by  131.67  ft;  one-story  dye-house  55  by  85.67 
ft;  brick  stair- tank,  and  other  towers;  walls  of  hard  brick;  plank  and  wearing- 
lloors  on  transverse  I-beam  framing,  supported  by  cast-iron  columns,  except 
in  five  bays,  where  both  transverse  and  longitudinal  framing  is  used;  slag  roof- 
ing on  plank  on  wooden  transverse  rafters;  floors  Ijuilt  for  a  live-load  of  75  lb 
per  sq  ft.     The  cost  of  the  buildings  was  $0,965  per  sq  ft. 

A  Four-Story  Cotton-Mill.  This  mill  is  without  basement.  It  was  built, 
together  with  the  fan-room  and  repair-shop  additions  in  Georgia,  in  19 10.  The 
following  are  the  details  of  construction:  mill,  four  stories;  size,  272  by  128  ft; 
office  and  repair-shop,  one  story  in  height  and  122.67  by  36  ft  in  plan;  regular 
mill-construction,  that  is,  brick  walls,  hard-pine  transverse  floor-framing,  wooden 
columns  and  plank  floors,  except  for  six  bays  of  the  fourth  floor  which  .have 
steel  I-beam  longitudinals  in  addition  to  the  hard-pine  transverse  timbers,  and 
for  sixteen  bays  of  the  roof-framing  which  have  both  longitudinal  and  transverse 
hard-pine  timbers,  these  having  been  found  necessary  in  both  cases  because  of 
the  omission  of  the  alternate  columns.  These  buildings  have  extensive  monitors, 
saw-tooth  skylights,  stair-towers,  etc.  The  floors  are  designed  to  carry  a  live 
load  of  75  lb  per  sq  ft.     The  cost  of  the  building  was  $0,715  per  sq  ft. 

A  Cotton-Mill  of  Irregular  Shape.  This  mill  is  considerably  wider  at 
one  end  than  at  the  other  and  has  a  basement  at  one  end.  It  was  built  in 
Massachusetts  in  191 1.  The  following  are  the  details  of  its  construction:  mill, 
five  stories;  length,  311.67  ft  and  average  width,  75.42  ft;  five-story  wing, 
65.26  by  40.01  ft,  with  extensive  pent-houses;  stair  and  elevator-towers  and 
skylights;  brick  walls,  transverse  wooden  floor-framing,  supported  by  cast-iron 
columns  and  brick  walls;  conditions  at  site  demanded  extensive  foundations; 
windows  in  fourth  and  fifth  stories  of  one  wall  protected  by  wire-glass  in  metal 
frames;  and  floors  built  for  a  live  load  of  75  lb  per  sq  ft.  The  cost  of  the  buildings 
was  $1,172  per  sq  ft. 

A  One-Story  Machine-Shop.  This  was  built  near  Boston,  Mass.,  in  19 10. 
The  main  building  is  200  by  136.375  ft  with  a  connecting  wing,  50  by  39.33  ft. 
It  has  brick  walls;  longitudinal,  steel,  I-beam  framing;  transverse,  steel,  saw- 
tooth skylight  framing;  plank  roof  covered  with  tar  and  gravel;  20-ft  longitu- 
dinal and  i6-ft  transverse  bays;  steel  I-beam  columns;  4¥2-'m  cement  floors 
except  for  three  bays  which  have  a  i-in  maple  overflooring,  a  i-in  North  Caro- 
lina pine,  intermediate  layer,  a  3-in  kyanized  spruce-plank  layer,  and  4V2  in  of 
tar-concrete;  and  extensive  saw-tooth  sky  fights.  The  cost  of  the  buildings 
was  $1,288  per  sq  ft. 

A  Building  for  Manufacturing  Automobiles.  This  building  has  forge- 
shop  extensions  and  was  built  in  Connecticut  in  19 10.  The  main  building 
has  four  stories  and  a  basement  and  is  54  by  151  ft  in  plan  with  a  one-story 
extension,  50  by  149  ft,  with  extensive  pent-houses  and  monitors.  The  factory- 
building  has  brick  walls,  transverse  yellow-pine  framing  on  heavy  wooden  col- 
umns and  on  walls,  floors  of  i-in  maple  overflooring  over  4-in  yellow-pine  planks, 
a  roof  of  3-in  yellow-pine  planks  covered  with  tar  and  gravel,  and  a  4^^-in 
cement,  basement-floor.  The  extension  has  brick  walls;  a  brick-on-edge  floor 
laid  on  a  4-in  course  of  cement  concrete  on  earth;  steel  roof-trusses,  of  47-ft, 
4-in  span  placed  10  ft  on  centers;  tar-and-gravel  roof;  and  extensive  monitors. 
The  floors  are  built  to  carry  a  five  load  of  125  lb  per  sq  ft.  The  cost  of  the 
building  was  $1,075  P^r  sq  ft. 


804  Wooden  Mill  and  Warehouse-Construction         Chap.  22 

A  Two-Story  Wooden  Box-Factory.  This  factory  has  no  basement.  It 
was  built  near  Boston,  Mass.,  in  1909.  In  plan  it  is  155  by  305  ft  and  its  aver- 
age height  is  32.5  ft.  It  has  brick  shafts;  transverse  wooden  framing  for  the 
first  floor;  transverse  beams  supported  by  longitudinals  for  the  second  floor 
and  roof;  wooden  columns  and  plank  floors;  and  wooden  monitors.  The  floors 
are  designed  to  carry  a  live  load  of  150  lb  per  sq  ft.  The  cost  of  this  building 
was  $0.84  per  sq  ft. 

A  One-Story-and-Basement  Weave-Shed.  This  was  built  near  Boston 
Mass.,  in  1909.  It  is  213  by  244.17  ft  in  plan,  with  extensive  entrances,  towers 
and  saw-tooth  skylights.  It  has  brick  waUs;  longitudinal  I-beam  girders  sup- 
porting transverse  I-beam  girders  in  the  first  story,  resting  on  brick  piers; 
transverse  hard-pine  girders  supporting  longitudinal  girders  for  the  saw-tooth 
skylight-framing;  heavy,  wooden  floors  and  roof;  wooden  columns;  an  earth 
basement-floor;  and  foundations  on  concrete  piles.  The  floors  are  designed 
to  carry  a  five  load  of  100  lb  per  sq  ft.  The  cost  of  the  buildings,  on  the  one- 
story  basisj  was  $1.56  per  sq  ft. 

A  Two-and-One-half  Story  Picker-House.  There  is,  also,  a  two-story 
house  and  a  one-story  connecting  passage  between  the  two  buildings  mentioned 
above  for  the  cotton  mill  of  irregular  shape,  which  were  built  in  Massachusetts 
in  191 1.  The  picker-house  is  64  by  95  ft  in  plan;  the  waste-house  21  by  49  ft; 
the  covered  bridge  10  by  40  ft;  and  the  average  height  of  the  building  42.58  ft. 
The  wafls  are  of  brick.  The  picker-house  has  transverse  wooden  framing  sup- 
ported by  wooden  columns  and  has  plank  floors.  The  waste-house  wing  has 
transverse,  steel  I-beam  framing  and  no  columns,  and  concrete-slab  floors. 
The  floors  are  designed  to  carry  a  live  load  of  75  lb  per  sq  ft.  The  cost  of  the 
building,  including  plumbing,  was  $1.29  per  sq  ft. 

The  Cost  of  Buildings  of  Mill-Construction  in  Philadelphia,  Pa.,  and 
Vicinity.  The  following  five  buildings  were  designed  by  Stearns  &  Castor, 
Philadelphia,  Pa.,  who  submit  data  and  descriptions,  with  the  cost  per  square 
FOOT.  These  buildings  are  within  a  very  limited  area,  being  in  or  within  a  few 
miles  of  l^hiladelphia,  and  are  of  somewhat  heavier  construction  than  those 
described  above,  the  floor-loads  varying  from  120  to  150  lb  per  sq  ft  and  the 
cost  ranging  from  $0.86  to  $1.23  per  sq  ft.  The  average  floor-load  is  132  lb  and 
the  average  cost  $1.02  per  sq  ft.  The  two  spinnirig-mifls  mentioned  are  de- 
signed for  avera,ge  floor- loads  of  120  lb  and  their  average  cost  was  $1.00 
per  sq  ft. 

A  Chocolate-Factory.  This  was  built  in  Philadelphia,  Pa.,  on  open  ground. 
It  has  an  ornamental  exterior;  walls  of  Sayer  and  Fisher  brick  with  terra-cotta 
trimmings,  and  a  main  building,  83  by  303  ft  in  plan  and  two  stories  in  height. 
One  section  of  the  building,  60  ft  in  length,  is  three  stories  high.  The  story- 
heights  are  14  ft  from  top  to  top  of  floors.  The  floors  are  designed  to  carry 
a  Hve  load  of  150  lb  per  sq  ft.  It  has  foundations  of  concrete;  heavy  mill- 
floors  on  heavy  timber-framing;  a  slag  roof;  all  stairways  and  elevators  in 
brick  towers;  and  openings  in  division  walls  equipped  with  fire-doors.  The 
cost  of  the  building,  excluding  plumbing,  heating,  electric  work,  elevators,  fire- 
protection  and  mechimical  equipment,  was  $0.86. 

A  Four-Story-and-Basement  Chocolate-Factory.  This  building  was 
erected  in  Philadelphia,  Pa.  It  is  44  by  130  ft  in  plan,  with  average  story- 
heights  of  13  ft.  It  was  built  in  a  congested  part  of  the  city,  between  other  build- 
ings. The  cost  of  underpinning  and  shoring  the  adjacent  buildings  is  included 
in  the  cost  given.  It  has  plain  brick  walls;  slow-burning  floor-construction  on 
heavy,  wooden  timbers,  with  finished  flooring  of  maple;  stairways  and  elevators 


Cost  of  Mills  and  Factories  Built  on  the  Slow-Burning  Principle     805 

in  brick  enclosures;  and  a  slag  roof.  The  floors  are  designed  to  carry  a  live 
load  of  150  lb  per  sq  ft.  The  cost  of  the  buildings  including  plumbing,  but 
excluding  heating,  electric  work,  elevators,  fire-protection  and  mechanical 
equipment,  was  $1.23  per  sq  ft. 

A  Spinning-Mill.  This  building  was  erected  in  Philadelphia,  Pa.,  on  ground 
open  and  easy  of  access.  Its  exterior  is  of  brick,  without  ornamentation.  It 
is  64  by  268  ft  in  plan,  three  stories  in  height,  the  stories  throughout  being  15  ft 
6  in  from  top  to  top  of  floors.  The  floors  throughout  are  calculated  to  carry  a 
live  load  of  120  lb  per  sq  ft.  It  has  walls  of  brick;  a  slow-burning  floor-con- 
struction with  finished  flooring  of  maple;  a  slag  roof;  and  stairways  and  ele- 
vators in  brick  enclosures.  The  cost  of  the  building,  excluding  plumbing, 
heating,  electric  work,  elevators,  fire-protection  and  mechanical  equipment 
was  $0.93  per  sq  ft. 

A  Spinning-Mill.  This  building  was  erected  in  Philadelphia,  Pa.,  on  ground 
open  and  easy  of  access.  Its  exterior  is  a  plain  brick  design.  It  is  69  by  269  ft 
in  plan  and  three  stories  in  height,  the  story-heights  throughout  being  15  ft' 
6  in  from  top  to  top  of  floors.  The  floors  throughout  are  calculated  for  a  live 
load  of  120  lb  per  sq  ft.  It  has  brick  walls  with  concrete  foundations;  a  slow- 
burning  floor-construction  with  a  finished  flooring  of  maple; '  a  slag  roof;  all 
stairways  and  elevators  in  brick  enclosures;  and  aU  openings  in  division  walls 
equipped  with  fire-doors.  The  cost  of  the  building  excluding  the  plumbing, 
heating,  electrical  work,  elevators,  fire-protection  and  mechanical  equipment, 
was  $1.07;  and  the  cost  of  the  building  including  the  plumbing,  heating,  elec- 
trical work,  elevators  and  fire-protection,  but  excluding  the  mechanical  equip- 
ment, was  I1.34. 

A  Clothing-Factory.  This  building  was  erected  in  Woodbine,  N.  J.,  on 
ground  open  and  easy  of  access.  Its  exterior  is  of  brick,  without  ornamentation. 
It  is  45  by  179  ft  in  plan  and  three  stories  in  height.  The  basement  is  10  ft  in 
height,  and  the  other  stories  12  ft  in  height  from  top  to  top  of  floors.  The 
floors  are  calculated  throughout  for  a  live  load  of  1 20  lb  per  sq  ft.  It  has  walls 
of  brick;  slow-burning  floors  with  yellow-pine  finished  flooring;  a  slag  roof;  and 
aU  stairways  and  elevators  in  brick  towers.  The  cost  of  the  building,  exclud- 
iilfe  heating,  electrical  work,  fire-protection  and  mechanical  equipment,  but  in- 
cluding freight-elevators  and  plumbing,  was  $1.01  per  sq  ft. 

The  Cost   of  Buildings   of  Mill-Construction  in  the   Middle   West. 

The  following  six  buildings  were  designed  by  F.  C}.  Mueller,  Hamilton,  Ohio, 
who  submits  data  and  descriptions  with  the  costs  of  buildings  of  heavier  con- 
struction. The  floor-loads  vary  from  200  to  300  lb  and  the  cost  from  $0.62 
to  $0.96  per  sq  ft.  The  paper-mill  at  Taylorsville,  III.,  is  partly  of  concrete 
construction,  and  was  built  at  a  cost  of  $1.30  per  sq  ft.  Exclusive  of  the  last- 
named  building,  the  average  floor-load  is  230  lb  and  the  average  cost  $0,805 
per  sq  ft. 

An  Addition  to  a  Paper-Mill.     This  was  built  in  Dayton,  Ohio..    It  is  a 

two-story  brick  building,  116  by  79  ft  in  plan.  The  first  story  is  used  for  paper- 
storage  and  the  second  story  as  a  finishing-room.  The  first  floor  is  of  cement 
on  a  Qnder  fill;  and  the  second  floor  of  2%-in  yellow- pine  planks  with  an  over- 
flooring  of  %-in  maple,  supported  by  8  by  14-in  beams,  14  by  ifi-in  girders  and 
10  by  lo-in  wooden  posts.  The  floors  are  figured  for  a  live  load  of  200  lb  per 
sq  ft.  The  roof  is  supported  by  six  steel  trusses  and  4  by  lo-in  wooden  purlins, 
and  covered  with  i%-in  sheathing  and  composition  roofing.  The  foundations 
are  of  concrete.  The  cost  of  the  building,  exclusive  of  the  plumbing  and  heat* 
ing,  was  $0.75  per  sq  ft. 


806  Wooden  Mill  and  Warehouse-Construction        Chap.  22 

An  Addition  to  a  Foundry.  This  one-stor>',  brick,  foundry-building  was 
erected  in  Hamilton,  Ohio,  is  432  by  63  ft  in  plan,  and  has  a  one-story  wing, 
86  by  46  ft  in  plan,  and  a  one-story  cupola-house,  28y2  by  26y2  ft  in  plan.  It 
has  a  wooden  floor  in  the  wing  only  and  dirt  floors  elsewhere.  It  has  concrete 
foundations;  a  composition  roof  on  2V4-in  sheathing,  supported  by  12  by  14-in 
girders,  6  by  12-in  beams  and  6-in  cast-iron  columns;  an  elevator  in  the  cupola- 
house;  and  all  doors  of  tin-clad  construction.  The  cost  of  the  building  was 
$0,836  per  sq  ft. 

A  Paper-Mill.  This  was  built  in  Monroe,  Mich.,  and  is  a  one-story-and- 
basement  brick  building,  185  by  87  ft  in  plan,  with  an  end-wing  234  by  35  ft. 
It  has  heavy  beam  and  girder  floor-construction,  designed  to  carry  a  live  load 
of  300  lb  per  sq  ft;  concrete  foundations  and  a  basement- part,  130  by  87  ft. 
It  is  designed  for  one  paper-making  machine  and  four  beaters,  has  a  composition 
roofing  and  one  skylight  over  the  boiler-room.    The  cost  was  $0.88  per  sq  ft. 

A  Paper-Mill.  This  is  an  irregular-shaped  brick  building  erected  in  Kennil- 
worth.  La.,  and  is  356  by  168  ft  in  plan.  About  one-third  of  it  is  two  stories 
and  the  remainder  one  story  in  height.  It  has  a  heavy  wooden,  beam,  girder 
and  post-construction;  a  stone  foundation  on  cypress-grillage  footings;  and 
floors  designed  to  carry  heavy  paper-making  machinery  with  a  live  load  of 
250  lb  per  sq  ft.     The  cost  of  the  building  was  $0.96  per  sq  ft. 

A  Warehouse.  This  is  a  one-story-and-basement  brick  building,  erected  in 
Hamilton,  Ohio,  and  is  38  by  50  ft  and  designed  for  a  live  load  of  200  lb  per  sq 
ft.  It  has  a  cement  floor  in  the  basement;  10  by  14-in  girders,  8  by  12-in  beams 
and  ID  by  lo-in  posts  supporting  3%-in  flooring;  10  by  14-in  girders  and  lo-in 
round,  wooden  posts  carrying  2H-in  sheathing  and  composition  roofing.  The 
cost  of  the  building  was  $0.62  per  sq  ft. 

A  Paper-Mill.  This  was  built  in  Taylorsville,  111.,  and  has  a  main  building, 
two  stories  in  height  and  49  by  130  ft  in  plan;  a  one-story  part,  138  by  81  ft 
in  plan;  and  a  one-story  wing,  42  by  144  ft  in  plan.  There  is  a  basement  under 
almost  the  entire  building.  The  foundations  are  of  concrete  and  there  are  . 
cement  floors  in  the  basement.  The  first  floor  is  of  reinforced-beam,  girder 
and  slab-construction,  designed  for  a  live  load  of  250  lb  per  sq  ft;  the  second 
floor  of  mill-construction,  supported  by  cast-iron  columns,  14  by  i8-in  wooden 
girders  and  12  bj^  i6-in  wooden  beams;  and  most  of  the  roof  is  supported  by 
steel  trusses  and  wooden  purlins.  The  second  floor  was  designed  for  a  live  load 
of  150  lb  per  sq  ft.  There  arc  extensive  skylights,  pent-houses,  etc.  The  cost 
of  the  building  was  $1.30  per  sq  ft. 

The  Cost  of  Buildings  of  Mill-Construction  in  Toronto^  Canada. 
The  building  described  in  the  following  paragraph  was  designed  by  Sproatt  & 
Rolph,  of  Toronto,  Canada,  who  submit  data  of  a  warehouse-building  with  all 
floor-openings  and  windows  and  other  outer  wall-openings  protected  in  an 
approved  manner,  and  erected  at  a  cost  of  $1.12  per  sq  ft. 

A  Five-Story-and-Basement  Seed-Warehouse.  This  was  built  in 
Toronto,  Canada,  and  is  1 11  by  14c  ft  3^2  in  in  plan.  The  floor-heights  are  13 
ft  1  in,  and  the  total  height  is  66  ft.  The  floors  are  built  of  2  by  6-in  pieces  of 
pine  on  edge  and  the  bays  measure  1 2  ft  5  in  by  13  ft.  The  beams  are  of  loijg-leaf 
yellow  pine,  14  by  18  in  in  section;  the  posts  of  similar  material,  varying  from 
8  by  8  in  to  16  by  16  in;  the  walls  are  of  hard,  red  brick  with  gray  stone  fac- 
ings; and  the  sashes  and  frames  are  of  steel  throughout.  The  building  has  three 
elevators  in  a  brick-enclosed  shaft  and  one  staircase  in  a  separate  brick  shaft. 
The  floors  are  designed  to  carry  a  live  load  of  250  lb  per  sq  ft.  The  cost  o! 
the  building,  exclusive  of  the  heating  and  lighting,  was  $1.12  per  sq  ft. 


Cost  of  Mills  and  Factories  Built  on  the  Slow-Burning  Principle     807 

The  Cost  of  Buildings  of  Mill-Construction  in  Northwestern  Canada. 

The  following  four  buildings  were  designed  by  J.  H.  G.  Russell,  Winnipeg, 
Canada,  and  are '  warehouses  of  very  superior,  heavy  construction,  widely 
separated  in  location,  yet  varying  little  in  cost.  The  floor-loads  used  vary 
from  300  to  350  lb,  hve  load,  per  sq  ft  and  the  cost  varied  from  $1.41  to  $1.54 
per  sq  ft.     The  average  cost  was  $1.46  per  sq  ft. 

A  Seven-Story-and-Basement  Warehouse.  This  was  built  in  Winnipeg, 
Canada,  and  is  50  ft  6  in  by  1 19  ft  9  hi  in  plan.  The  floors  are  of  6-in  spruce  with 
%-in  maple  overflooring.  All  floors  are  on  heavy  girders  and  columns;  the 
elevators  are  in  brick  shafts;  and  the  walls  are  of  brick,  except  the  first  story 
front  wall,  which  is  of  cut  stone.  The  floors  are  designed  to  carry  300  lb  per 
sq  ft,  live  load.  The  cost  of  the  building,  exclusive  of  the  heating,  elevators, 
etc.,  was  $1.46  per  sq  ft. 

A  Three-Story-and-Basement  Warehouse.  This  was  built  in  Winnipeg, 
Canada,  and  is  62  ft  6  in  by  86  ft  6  in  in  plan.  Heavy  fir  timbers  were  used  for 
framing.  It  has  a  6-in  fir-plank  solid  floor  with  Vn-in  maple  overflooring; 
stairs  and  elevators  in  brick  towers;  brick  walls  with  the  openings  in  the  rear 
and  sides  of  the  building  protected.  The  floors  were  designed  to  carry  a  live 
load  of  350  lb  per  sq  ft,  and  the  cost  of  the  building,  excluding  the  heating,  etc., 
was  $1.41  per  sqft. 

A  Warehouse.  This  is  a  six-story-and-basement  building,  erected  in  Saska- 
toon, Canada,  and  is  50  by  112  ft  in  plan.  The  floors  are  of  6-in  fir,  with%-in 
maple  overflooring,  and  are  supported  by  heavy  fir  timbers.  The  building  has 
brick  walls  with  a  front  of  pressed  brick  and  cut-stone  trimmings;  some  of  the 
openings  are  protected  by  wire-glass  windows;  and  the  stairs  and  elevators  are  in 
brick  shafts.  The  floors  were  built  to  carry  35^  lb  yier  sq  ft,  Hve  load,  and  the 
building  cost,  exclusive  of  the  heating,  elevators,  etc.,  $1.44  per  sq  ft. 

A  Five-Story-and-Basement  Warehouse.  This  was  built  in  Edmonton, 
Canada,  and  is  50  by  137  ft  in  plan.  The  floors  are  of  6-in  fir  with  %-in  maple 
overflooring.  The  building  has  brick  walls  and  the  front  and  one  side  wall 
are  faced  with  pressed  bricks  with  stone  trimmin/^s.  It  has  the  openings  in 
the  rear  wall  protected  and  the  stairs  and  elevators  are  in  brick  shafts.  The 
walls  are  strong  enough  for  two  additional  stories  and  the  floors  are  designed 
to  carry  350  lb,  live  load,  per  sq  ft.  The  cost  of  the  building,  exclusive  of 
heating,  elevators,  etc.  was  $1.54  per  sq  ft. 

The  Cost  of  Buildings  of  Mill-Construction  in  Vancouver,  Canada. 
The  building  described  in  the  following  paragraph  was  designed  by  Dalton  & 
Eveleigh,  Vancouver,  Canada,  who  give  data  of  a  warehouse  with  floors  designed 
to  carry  an  average  load  of  500  lb  per  sq  ft  and  costing  $1.09  per  sq  ft.  Although 
the  heaviest  timbers  and  the  heaviest  wall-hangers  and  beam-hangers  were 
used,  and  the  floors  built  of  the  maximum  thickness,  the  cost  was  extremely 
low.  This  no  doubt  was  partly  due  to  the  proximity  of  the  timber  and  the 
facilities  for  transporting  it  by  water. 

A  Warehouse  for  the  Storage  of  Heavy  Hardware.  This  was  erected 
in  Vancouver,  Canada.  The  main  building  has  four  stories  and  a  basement, 
and  is  85  ft  6  in  by  115  ft  6  in  in  plan.  The  oflace-wing  has  four  stories  and  a 
basement  and  is  60  by  40  ft.  There  is,  also,  a  four-story  and  half-length-base- 
ment building,  38  by  120  ft,  connecting  with  the  two  upper  stories  of  the  main 
building  by  means  of  a  steel  bridge  40  ft  long.  The  walls  above  the  basement 
are  of  hard-burned  brick  and  the  concrete  basement  walls  and  floors  are  treated 
with  hydrolite.  The  main  girders  are  set  23  ft  on  centers  and  vary  in  section 
from  12  by  16  in  to  18  by  24  in  and  are  all  one-piece  sticks.    The  posts,  set  11  ft 


808  Wooden  Mill  and  Warehouse-Construction        Chap.  22 

lo  in  on  centers,  vary  from  12  by  12  in  in  one  piece,  to  20  by  38  in,  in  three 
pieces.  The  joists,  set  4  ft  on  centers,  vary  from  8  by  16  in  to  16  by  24  in  in  one 
piece.  The  floors  are  made  of  4  by  6-in  and  4  by  4-in  pieces,  laid  soUd,  with 
top  flooring  made  of  2  by  6-in,  edge-grain,  tongued  and  grooved  pieces,  with 
two  layers  of  asbestos  between,  weighing  lo^^-i  ounces  per  sq  ft.  All  the  tim- 
bers are  of  fir.  There  are  three  brick-enclosed  elevators  with  fire-doors,  and 
one  elevator  in  a  wooden  shaft,  built  ''solid"  of  3 -in  thick  pieces.  The  office- 
front  is  of  pressed  brick,  and  has  plate  glass,  marble  steps  and  copper  trim. 
The  windows  are  glazed  with  wire-glass  in  metal  frames,  and  there  are  fire- 
doors  on  the  outer  door-openings.  The  roof  is  made  of  a  6-ply  composition  with 
a  gravel  coating.  The  live  load  used  for  the  floors  varied  from  i  000  lb  per 
sq  ft  on  the  ground  floor  to  250  lb  on  the  top  floor,  the  average  five  load  being 
500  lb  per  sq  ft.  The  walls  and  posts  were  designed  to  carry  two  additional 
stories,  with  a  five  load  of  225  lb  per  sq  ft.  The  cost  of  the  building,  exclusive 
of  the  heating  and  office  and  warehouse-fixtures,  was  $1.09  per  sq  ft. 


22.   Cost*  of  Brick  Mill-Buildings  of  Slow-Burning  Construction 

Approximate  Cost  of  Brick  Mill-Buildings.  Mr.  C.  T.  Mainf  has  made  a 
series  of  diagrams  showing  the  cost  in  New  England,  in  19 10,  per  square  foot 
OF  FLOOR  SPACE,  of  BRICK  MILL-BUILDINGS  of  different  sizes,  from  one  to  six 
stories  in  height,  and  of  the  type  known  as  slow-burning.  The  calculations 
are  made  for  total  floor-loads  of  about  75  lb  per  sq  ft.  The  figures  taken  from 
the  diagrams  are  given  on  the  following  page.  The  costs  include  ordinary 
foundations  and  plumbing,  but  no  heating,  sprinklers  or  lighting. 

Modifications  of  the  Costs  given  in  Table  I:  (i)  If  the  soil  is  poor  or  the 
conditions  of  the  site  are  such  as  to  require  more  than  ordinary  foundations, 
the  cost  win  be  increased. 

(2)  If  the  building  is  to  be  used  for  ordinary  storage-purposes  with  low  stories 
and  no  overflooring,  the  cost  will  be  decreased  from  about  10%  for  large, 
low  buildings  to  25%  for  small,  high  ones,  about  20%  being  usuaUy  a  fair 
allowance. 

(3)  If  the  building  is  to  be  used  for  manufacturing  and  is  substantially  built 
of  wood,  the  cost  will  be  decreased  from  about  6%  for  large,  one-story  building^ 
to  33%  for  ^mall,  high  buildings;    15%  would  usually  be  a  fair  allowance. 

(4)  If  the  building  is  to  be  used  for  storage  and  built  with  low  stories  and  sub- 
stantially of  wood,  the  cost  wiU  be  decreased  from  13%  for  large,  one-story 
buildings  to  50%  for  small,  high  buildings;  30%  would  usually  be  a  fair  allow- 
ance. 

(5)  If  the  total  floor-loads  are  more  than  75  lb  per  sq  ft  the  cost  is 
increased. 

(6)  For  oflSce-buildings,  the  cost  must  be  increased  to  cover  the  exterior 
architectural  treatment  and  the  interior  finish. 

(7)  Reinforced-concrete  buildings,  designed  to  carry  floor-loads  of  100  lb  or 
less  per  sq  ft  will  cost  about  25%  more  than  those  of  the  slow-burning  type 
of  mill-construction. 

*  These  are  pre-war  prices,  but  the  data  are  retained  for  purposes  of  comparison  of 
relative  costs  in  the  analysis  made.    For  the  cost  of  reinforced-concrete  mills,  warehouses, 
etc.,  see  pages  4613  and  1618, 
I  f  Engineering  News,  January  27,  1910. 


Cost  of  Brick  Mill-Buildings  of  Slow-Burning  Construction     809 
Table  I.     Cost  of  Brick  Mill-BuUdings  per  Square  Foot  of  Floor-Area 


Length  in  ft 

50 

100 

150 

200 

250 

300 

350 

400 

500 

Width  in  ft 

One  story 

25 

$1.90 

$1.66 

$1.58 

$1.54 

$1.51 

$1.49 

$1.48 

$1.47 

$1.46 

50 

1.52 

1.29 

1. 21 

1. 18 

1. 16 

1. 15 

1. 14 

1. 13 

1.13 

75 

1. 41 

1. 21 

1. 12 

1.08 

1.06 

1.04 

1.03 

1.02 

1.02 

125 

1.32 

1.09 

1.02 

0.98 

0.90 

0.94 

0.94 

0.93 

C.92 

Two  stories 

25 

2.00 

1.62 

1.52 

1.47 

1.44 

1. 41 

1.39 

1.38 

1.36 

50 

1.50 

1.21 

1. 13 

1.09 

1.06 

1.05 

1.04 

1.03 

1.02 

75 

1.34 

1.08 

1. 01 

0.97 

0.94 

0.92 

0.92 

0.91 

0.90 

125 

1.22 

0.97 

0.90 

0.86 

0.84 

0.82 

0.81 

0.80 

0.86 

Three  stories                                                           | 

25 

1.98 

1.57 

1.47 

1.42 

1.39 

1.38 

1.36 

1.35 

1.34 

50 

1.47 

1. 17 

1.07 

1.03 

1. 01 

1. 00 

0.98 

0.98 

0.98 

75 

1.30 

1.05 

0.98 

0.94 

0.91 

0.89 

0.88 

0.87 

0.86 

125 

1. 18 

0.93 

0.86 

0.82 

0.80 

0.78 

0.77 

0.76 

0.76 

Four  stories                                                             | 

25  - 

2.00 

1. 61 

1.50 

1.45 

1.42 

,    1.40 

1.38 

1.37 

1.36 

50 

1.38 

1. 17 

1. 10 

1.05 

1.02 

1. 00 

1. 00 

0.99 

0.98 

75 

1.32 

1.08 

0.97 

0.93 

0.90 

0.88 

0.88 

0.87 

0.87 

125 

1.20 

0.93 

0.85 

0.81 

0.78 

0.77 

0.76 

0.75 

0.74 

Six  stories                                                                    | 

25 

2.10 

1.72 

1.57 

1.51 

1.48 

1.46 

1.44 

1.43 

1.42 

50 

I. S3 

1. 21 

1. 12 

1.08 

1.05 

M.04 

1.03 

1.02 

1.02 

75 

1.35 

1.08 

0.98 

0.94 

0.92 

0.90 

0.89 

0.88 

0.86 

125 

1.22 

0.96 

0.86 

0.82 

0.79 

0.78 

0.77 

0.76 

0.76 

The  COST  PER  SQUARE  FOOT  of  a  building  100  ft  wide  is  about  midway  between  that 
of  one  75  ft  wide  and  one  125  ft  wide;  and  the  cost  of  a  five-story  building  about  mid- 
way between  the  costs  of  a  four-story  and  a  six-story  building. 

Additional  Data  for  estimating  costs  of  foundation-walls  and  other  walls 
are  given  in  the  following  table: 

Table  11.     Cost  of  Walls  in  Brick  Mill-Buildings  of  Slow-Burning  Construction 


Number  of  stories 

I 

2 

3 

4 

5 

6 

Foundations,  including  excavations 
Cost  per  lin  ft: 
Outside  walls 

$2. 00 
1.75 

0.40 
0.40 

$2.90 
2.25 

0.44 
0.40 

$3.80 
2.80 

0.47 
0.40 

$4.70 
3.40 

0.50 
0.43 

$5.60 
3.90 

0.53 
0.45 

$6.50 
4.50 

0.57 
0.47 

Inside  walls                

Brick  walls 

Cost  per  sq  ft  of  surface: 
Outside  walls 

Inside  walls                           

810  Wooden  Mill  and  Warehouse-Construction        Chap.  22 

Columns,  including  piers  and  castings,  cost  about  $15  each. 

Assumed  Height  of  Stories:  From  ground  to  first  floor,  3  ft.  Buildings 
25  ft  wide,  stories  13  ft  high;  50  ft  wide,  14  ft  high;  75  ft  wide,  15  ft  high; 
100  ft  and  125  ft  wide,  16  ft  high. 

Cost  of  Floors:  32  cts  per  sq  ft  of  gross  floor-space,  not  including  columns; 
38  cts,  including  columns. 

Cost  of  Roof:  25  cts  per  sq  ft,  not  including  columns;  30  cts,  including 
columns.     Roof  to  project  18  in  on  all  sides  of  buildings. 

Stairways,  including  partitions,  $100  each  flight.  Include  two  stairways  and 
one  elevator-tower  for  buildings  up  to  150  ft  long;  two  stairways  and  two  eleva- 
tor-towers for  buildings  up  to  300  ft  long.  In  buildings  over  two  stories  in 
height,  three  stairways  and  three  elevator-towers  for  buildings  over  300  ft  long. 

Plumbing  Fixtures.  In  buildings  of  more  than  two  stories  figure  $75  for 
each  fixture,  including  the  piping  and  partitions.  Allow  for  two  fixtures  on 
each  floor  up  to  5  poo  sq  ft  of  floor-space,  and  one  fixture  for  each  additional 
5  000  sq  ft,  or  fraction  thereof,  of  floor-space. 


Definitions  SIX 


CHAPTER  XXIII 

FIREPROOFING  OF  BUILDINGS 

By 
RUDOLPH  P.  MILLER 

SUPERINTENDENT   OF   BUILDINGS,   NEW   YORK  CITY 

1.  Definitions,  Areas,  Heights,  and  Costs 

Definitions.  The  term  fire-proof,  while  now  quite  well  understood  by 
architects,  is  still  used  in  a  very  broad  sense  by  the  public.  To  be  strictly 
fire-proof,  a  building  must  be  constructed  and  finished  entirely  with  incom- 
bustible materials,  and  any  of  these  materials,  such  as  steel  or  iron,  which  are 
injuriously  affected  by  heat  or  streams  of  water  must  be  efficiently  protected 
by  other  materials  which  are  not  so  affected.  This  precludes  the  use  of  wood, 
whether  exposed  or  not  exposed,  also  all  exposed  steel  or  iron,  common  glass^ 
and  most  building  stones.  It  is  safe  to  say  that  there  are  very  few  buildings 
in  this  country  that  are  absolutely  riRii-PROOF.  There  are  many,  however, 
that  could  not  be  destroyed  by  fire,  and  in  which  the  salvage  would  probably 
amount  to  from  60  to  80%;  and  it  is  the  latter  class  which  is  generally  meant 
when  the  term  fire-proof  is  used.  Incombustible  buildings,  and  buildings  of 
wooden  construction  protected  to  a  greater  or  less  degree  from  the  flames,  are 
sometimes  advertised  as  fire-proof;  but  such  buildings  should  be  considered 
merely  as  slow-burning.  It  is  undoubtedly  the  duty  of  every  architect  to  be 
well  informed  concerning  the  fire-proof  qualities  of  all  materials  that  enter 
into  the  construction  and  finishing  of  buildings,  and  to  know  how  to  use  these 
materials  to  the  best  advantage.  His  choice  and  use  of  materials  is  then  limited 
only  by  the  character  of  the  building  and  the  interests  of  his  clients.  It  is 
intended  to  furnish  this  information  in  a  concise  manner  in  this  chapter.  The 
National  Fire  Protection  Association  recommends  the  discontinuance  of  the 
term  fire-proof,  and  the  use  of  the  term  fire -resistive  in  its  stead.  The 
former  term  is  the  one  used  in  the  building  laws  of  all  the  larger  cities. 

Municipal  Definitions,  Municipal  definitions  as  to  what  constitutes  fire- 
proof construction  have  a  great  bearing  on  the  construction  of  buildings 
within  their  jurisdiction.  None  is  entirely  comprehensive  and  the  detailed 
requirements  must  be  consulted  in  each  case.  The  Chicago  definition  is 
typical  of  most  of  them. 

Chicago  Definition.*  "The  term  fire-proof  construction  shall  apply  to 
all  buildings  in  which  all  parts  that  carry  weights  or  resist  strains,!  a-nd  also  all 
exterior  walls  and  all  interior  walls  and  all  interior  partitions  and  all  stairways 
and  all  elevator  enclosures  are  made  entirely  of  incombustible  materials,  and  in 
which  all  metallic  structural  members  are  protected  against  the  effects  of  fire 
by  coverings  of  a  material  which  shall  be  entirely  incombustible,  and  a  slow  heat 
conductor,  and  hereinafter  termed  fire-proof  material.     Reinforced  concrete 

*  Quoted  matter  is  left  in  its  original  form.     The  editor-in-chief  is  not  responsible  for 
its  syntax,  punctuation,  etc. 
t  Stresses  are  meant. 


812  Fireproofing  of  Buildings  Chap.  23 

as  defined  in  this  ordinance  shall  be  considered  fire-proof  construction,  when 
built  as  required  by  Section  550." 

When  Fire-proof  Construction  Should  be  Employed.  A  building  should 
be  designed,  built,  and  finished  to  conform  to  the  purpose  for  which  it  is  to  be 
used.  A  building  containing  but  Uttle  inflammable  material,  and  that  not  of 
great  value,  need  not  be  as  thoroughly  fire-proof  as  one  designed  for  the  storage 
of  valuable  goods,  or  for  the  protection  of  life  in  case  of  fire.  The  height  of  a 
building  is  an  important  factor  in  determining  whether  it  should  be  fire-proof 
or  not.  The  rate  of  increase  in  the  difficulty  of  coping  with  fire  in  a  building 
is  greater  than  that  of  the  increase  in  the  height.  The  area  covered  by  a 
building,  also,  is  important,  although  in  most  instances  interior  division-walls 
may  be  provided  which  practically  cut  up  a  building  into  a  series  of  smaller 
buildings.  Some  of  the  limitations  placed  upon  non-fire-proof  buildings  by 
various  municipal  laws  will  be  found  in  the  following  classification  and  in  Table  I, 
page  813. 

Limiting  Areas  for  Non-Fire-proof  Buildings. 
New  York  City,      7  500  sq  ft  on  an  interior  lot. 

12  000  sq  ft  on  a  corner. 

15  000  sq  ft  when  facing  three  streets. 
Chicago,  111.,  9  000  sq  ft  if  of  ordinary  joisted  construction. 

1 2  000  sq  ft  if  of  slow-burning  construction. 
St.  Louis,  Mo.,         7  500  sq  ft. 
Boston,  Mass.,       10  000  sq  ft. 
Cleveland,  Ohio,    Mill-Construction: 

20  000  sq  ft  when  facing  streets  on  four  sides. 

15  000  sq  ft  when  facing  streets  on  three  sides. 

12  000  sq  ft  when  facing  streets  on  two  sides. 
9  000  sq  ft  when  facing  streets  on  one  side. 
5  000  sq  ft  on  any  lot  when  of  hazardous  occupancy. 
Cleveland,  Ohio,  Ordinary  Construction: 

1 2  500  sq  ft  when  facing  streets  on  four  sides. 

10  000  sq  ft  when  facing  streets  on  three  sides. 
7  500  sq  ft  when  facing  streets  on  two  sides. 
5  000  sq  ft  when  facing  streets  on  one  side. 
2  000  sq  ft  on  any  lot  when  of  hazardous  occupancy. 

Cost  of  Fire-proof  Construction.  F.  VV.  Fitzpatrick,  found,  previous  to 
1903,  that  fire-proof  construction  for  office-buildings,  hotels,  etc.,  adds  from 
9  to  13%  to  the  cost  of  ordinary  construction  with  wooden  joists.  For  stores 
and  warehouses  the  difference  will  often  be  less  than  5%.*  Walter  F.  Ballinger 
stated  (1909)  that  reinforced-concrete  construction  cost  from  10  to  15%  more 
per  square  foot  of  floor-surface  than  mill-construction  and  about  25%  less  than 
steel-frame  and  terra-cotta  fire-proof  construction,  f  Figures  given  by  J.  P.  H. 
Perry  (191 1)  indicated  that  reinforced-concrete  construction  added  from  2  to  20% 
to  the  cost  of  mill-construction  for  commercial  buildings,  with  an  average  of 
6.7%  for  various  localities  and  all  classes  of  buildings  in  the  United  States. 
The  increase  in  cost  of  structural-steel  fire-proof  construction  over  reinforced- 
concrete  construction  averaged  6.4%  for  fourteen  buildings  of  all  classes  in 
various  localities,  t  More  recent  comparisons  are  not  available,  but  it  can 
be  safely  asserted  that  the  increased  cost  of  fire-proof  construction  over  mill- 

*  Fireproof,  for  Marcii,  June,  and  July,  1903. 
t  Proc.  Nat.  Fire  Prot.  Asso.,  1909. 
tProc.  Nat.  Asso.  Cement  Users,  191 1. 


Heights  for  Non-Fire-proof  Buildings 


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fel4  Fireproofing  of  Buildings  Chap.  22 

construction  and  ordinary  joisted  construction  is  less  than  indicated  by  thes( 
figures. 

Divisions  of  the  Subject.  In  constructing  fire-proof  buildings  it  is  neces 
sary  to  consider: 

(i)  Materials  to  be  used. 

(2)  Form  of  construction. 

(3)  Protecting  devices. 

(4)  Extinguishing  appliances. 

This  general  order  is  followed  in  the  discussion  of  the  subject  in  this  chapter. 

2.  Fire-Resistance  of  Materials 

Effect  of  Heat  on  Building  Materials.  All  materials  of  construction  an 
more  or  less  injuriously  afifected  by  high  temperatures.  Furthermore,  an  incom 
BUSTIBLE  material  is  not  necessarily  fire-resisting,  as,  for  instance,  steel 
The  value  of  various  materials  in  fire-proof  construction  is  indicated  in  th( 
following  paragraphs. 

Brickwork.  Common  brickwork,  when  of  a  good  quality,  will  stand  exposun 
to  severe  fire  for  a  considerable  length  of  time.  Experience  has  shown  thai 
thick  walls  are  less  afi"ected  by  heat  than  thin  walls,  and  that  hard-burnec 
bricks  stand'  better  than  soft  or  underburned  bricks.  In  the  Baltimore  anc 
San  Francisco  fires,  it  was  demonstrated  that  for  outside  v/alls  brick  is  superioi 
as  a  fire-proof  material  to  any  other  material  used  in  wall-construction. 

Stone  in  General.  Very  few  stones  successfully  stand  the  action  of  seven 
heat,  and  consequently  stone  in  general  should  l)e  used  very  sparingly  in  fire 
proof  buildings,  and  certain  kinds  of  stone  not  at  all. 

Granite  will  explode  and  fly  to  pieces  or  disintegrate  into  sand  when  exposec 
to  flames. 

Limestone  and  Marble  are  usually  ruined  if  not  totally  destroyed  by  ar 
ordinary  fire.  They  are  the  least  desirable  of  all  stones  for  use  in  a  fire-prooi 
building,  and  the  granites  come  next. 

Sandstone  when  fine-grained  and  compact  sometimes  stands  fire  without 
serious  injury,  but  in  the  case  of  a  severe  conflagration  it  is  generally  so  badly 
affected  that  it  has  to  be  replaced. 

Terra-Cotta  is  made  from  clay  by  mixing  it  with  water  into  a  plastic  mass, 
shaping  the  same  into  the  form  desired  and  baking  it  at  a  high  temperature  in 
kilns.  For  the  usual  structural  form  the  shaping  is  generally  done  by  forcing 
the  plastic  mass  through  a  special  die  by  means  of  machinery.  Ornamental 
terra-cotta  must  generally  be  shaped  by  hand. 

Ornamental  Terra-Cotta.  This  material,  and  especially  that  which  has  a 
glazed  surface,  is  well  adapted  for  the  trimmings  of  a  building  that  is  intended 
to  be  fire-proof.  It  should,  however,  be  made  heavy  enough  to  carry  both  its 
own  weight  and  its  share  of  the  wall-load.* 

Structural  Terra-Cotta.  Terra-cotta,  as  used  for  floor-arches,  column  and 
girder-protection,  and  for  building  light,  hollow  walls,  is  made  of  three  differ- 
ent compositions,  the  material  being  known  as  Dense,  Porous,  and  Semi- 
porous,  according  to  the  method  of  manufacture. 

Dense  Tiling  is  made  from  a  variety  of  clays.  Some  manufacturers  use 
•  Fire  Prevention  and  Fire  Protection,  J.  K.  Freitag. 


Fire-Resistance  of  Materials 


815 


more  or  less  fire-clay,  and  combine  it  with  potter's  clay,  plastic  clays,  or  tough 
brick-clay.  It  is  very  dense  and  possesses  high  crushing  strength.  In  outer 
walls  exposed  to  the  weather  and  required  to  be  light,  it  is  very  desirable.  Some 
manufacturers  furnish  it  with  a  semiglazed  surface  for  the  outer  walls  of  build- 
ings. For  such  use  it  has  great  durability,  and  effottually  stops  moisture.  In 
using  dense  tilHng  for  fireproof  filling,  care  should  be  taken  that  the  tiles  are: 
free  from  cracks,  sound,  and  hard-burned. 

Porous  and  Semiporous  Terra-Cotta  is  made  by  mixing  sawdust  with  the 
clay,  the  sawdust  being  destroyed  by  the  action  of  the  heat,  leaving  the  material 
light  and  porous.  A  small  proportion  of  fire-clay  mixed  with  the  plastic  clay 
is  desirable  but  not  essential.  The  proportion  of  sawdust  should  be  from" 
25  to  35%,  according  to  the  toughness  of  the  clay  used.  Care  is  required  in 
the  process  of  manufacture  to  have  the  work  of  mixing,  drying,  and  burning 
thoroughly  done.  The  burning  should  be  done  in  down-draught  kilns,  by  a 
quick  process.  The  product  should  be  compact,  tough,  and  hard,  and  should 
ring  when  struck  with  metal.  Poorly-mixed,  pressed,  or  burned  tiles,  or  tiles 
from  short  or  sandy  clays,  present  a  ragged,  soft,  and  crumbly  appearance,  and 
are  not  desirable.  When  properly  made,  porous  terra-cotta  will  not  crack  or 
break  from  unequal  heating,  or  from  being  suddenly  cooled  with  water  when  in 
a  heated  condition.  It  can  be  cut  with  a  saw  or  edge-tools,  and  nails  or  screws 
can  be  easily  driven  into  it  to  secure  interior  finish,  slates,  tiles,  etc.  As  a 
successful  heat-resistant  and  non-conductor  for  the  protection  of  other  materials, 
it  must  be  ranked  very  high. 

Semiporous  Tiling.  This  material  was  introduced  by  those  factories  which 
use  pure  fire-clay  in  the  manufacture  of  tile,  to  enable  them  to  compete  with 
the  standard  porous  material.  During  the  process  of  grinding  the  clay,  about 
2o%  of  ground  coal  is  mixed  with  it.  This  coal  aids  in  the  burning  of  the 
material  and  also  makes  it  lighter  and  more  or  less  porous.  Tiling  made  by 
this  process  is  admitted  to  be  a  much  better  fire-resistant  than  the  solid  or. 
dense  material.  E.  V.  Johnson  says:  "personally,  I  believe  that  good  semi- 
porous fire-clay  tile  is  fully  as  efficient  as  a  fire-resisting  material  as  the  standard 
makes  of  porous  terra-cotta." 

Strength  of  Terra-Cotta.  (Sec,  also,  page  276.)  In  tests  made  at  Columbia 
University  for  the  building  authorities  of  New  York  City  on  terra-cotta  blocks 
taken  from  material  delivered  in  the  open  market,  the  following  crushing 
STRENGTH  was  developed: 


Table  II.     Crushing  Strength  of  Terra-Cotta 


Description  of  material 

Position  of  cells 
in  test 

Compressive  strength, 
lb  per  sq  in 

Gross  area 

Net  area 

Dense  tile 

(     Vertical 
1      Horizontal 

I     Vertical 
(      Horizontal 

1864 
S8S 

I  027 
257 

4721 
2613 

2168 

I  008 

Semiporous  tile 

The  inequality  in  strength  of  the  two  materials  can  be  overcome  by  using 
thicker  webs  and  shells  for  the  semiporous  or  porous  material.     In  the  matter 


816  Fireproofing  of  Buildings  Chap.  23 

of  WEIGHT,  porous  and  semiporous  terra-cotta  have  the  advantage  over  dense 
tile.  Dense  tiling,  when  heated  and  cooled  by  water,  is  liable  to  crack  from 
the  sudden  contraction;  "blocks  with  two  or  more  air-spaces  are  very  liable 
to  have  the  outer  webs  destroyed  under  this  action.  .  Even  if  not  cooled  with 
water,  other  fires  have  shown  that  hard-burned  terra-cotta  will  crack  and  fall 
to  pieces  under  severe  heat  alone."  *  The  experience  of  the  recent  conflagra- 
tions in  Baltimore  and  San  Francisco  fully  bears  out  this  statement.  The 
collapse  of  the  floors  of  one  of  the  buildings  in  Baltimore  was  largely  due  to 
the  weakening  of  the  terra-cotta  arches  by  reason  of  the  breaking  off  of  the 
outer  shells.  Porous  terra-cotta  is  non-heat-conducting  in  itself,  and  the  best 
qualities  will  usually  resist  fire  and  water  successfully;  but  if  the  product  "is 
not  burned  at  a  sufficiently  high  temperature  to  consume  all  of  the  sawdust,  the 
throwing  of  cold  water  upon  the  heated  surfaces  will  cause  an  expansion  or 
disintegration  due  to  the  absorption  of  the  water  and  its  conversion  into  steam." 
Porous  terra-cotta  absorbs  water  freely,  and  if  allowed  to  freeze  when  wet  is 
more  or  less  injured.  If  the  process  is  permitted  to  continue,  the  blocks  become 
so  weakened  that  they  are  unsafe  for  use. 

Concrete  Blocks  and  Concrete  Tiles. f  Numerous  forms  of  building  blocks 
and  tiles  are  manufactured  of  I^ortl.md-cement  mortar  or  concrete  for  use  as 
substitutes  for  brick,  stone,  and  terra-cotta.  Concrete  blocks  are  made  by 
the  DRY  PROCESS  I)y  tamping  a  dry-concrete  mix  into  shape  in  forms,  or  by  the 
WET  PROCESS  which  consists  of  pouring  a  semiliquid  or  slusii-mix  into  molds 
and  curing  the  product  by  air  or  steam.  A  third  method,  known  as  the 
PRESSURE-PROCESS,  is  similar  to  the  first,  mechanical  or  hydraulic  pressure 
being  substituted  for  the  tamping.  Concrete  hollow  tile  is  being  made  for 
the  same  uses  as  terra-cotta  tiling,  for  partitions  and  floors  in  general,  and 
for  enclosure-walls  as  well  as  for  partitions  in  residences.  For  wall-bearing 
purposes,  the  tiles  are  usually  filled  solid  for  a  layer  or  two  where  the  beams 
rest  upon  them.  In  hollow-block  construction,  distinction  should  always  be 
made  between  the  strength  -of  the  jjbcks  when  laid  with  the  core-holes  vertical 
and  when  laid  with  the  core-holes  horizontal,  as  the  strength,  in  the  latter 
position,  approximates  only  one  half  ot  what  it  is  in  the  former.  The  specifica- 
tions of  the  American  Concrete  Institute,  1917,  are  generally  accepted  as  the 
best  practice  in  the  manufacture  of  concrete  blocks.  (See,  also,  Chapter  III, 
page  233.) 

Concrete  Tile.  Concrete  building  tiles  have  been  used  for  residences  in 
Chicago,  III.,  Rochester,  N.  Y.,  and  the  suburbs  of  New  York  City.  The 
shape  and  size  of  the  blocks  vary  with  the  make  of  the  product.  In  size  and 
shape  they  resemble  terra-cotta  tile,  though  the  walls  and  webs  are  thicker. 
A  WET-PROCESS  tile  was  tested  by  the  Bureau  of  Buildings,  New  York  City, 
in  191 1,  and  showed  a  compressive  strength  in  pounds  per  square  in  as 
shown  in  Table  III,  page  817. 

The  Trout  Concrete  Tile  Corporation  of  Flushing,  N..Y.,  has  developed  a 
method  of  making  hollow  tile  whereby  lightness  is  combined  with  strength. 
The  Trout  tile  is  made  in  a  hydraulic  machine,  with  a  pressure  of  1200  lb  to 
each  sq  in  of  net  area  of  the  tile.  While  this  pressure  is  being  applied,  the 
particles  of  concrete  are  automatically  moved  about  until  the  voids  are  filled, 
find  the  result  is  a  dense,  hard  product  of  even  quality.  This  process  permits 
the  making  of  tile  with  thm  walls,  thereby  reducing  the  weight  to  a  minimum, 
A  tile  8  in  high,  8  in  wide,  and  15M  in  long,  with  two  cells,  and  with  walls 

•  Fife  Prevention  and  Fire  Protection,  J.  K.  Freitag. 

t  The  subject  is  fully  treated  in  Concrete  Engineers'  Handbook,  by  Hool  and  Johnson, 


Fire-Resistance  of  Materials 
Table  III.     Compressive  Strength  of  Concrete  Tile 


817 


Dimensions  and  use 

Cells  vertical 

Cells  horizontal 

Height, 
in 

Kind  of  tile 

Number 
of    cells 

Gross 
area, lb 
per  sq  in 

Net 
area, lb 
per  sq  in 

Gross 
area, lb 
per  sq  in 

Net 
area, lb 
per  sq  in 

8 

ID 

lo 

12 

8 

Wall-tile 
Wall-tile 
Corner-tile 
Wall-tile 
Wall-tile 
(Trout^O 

2 
2 
2 

4 

2 

528* 

633 

5IO 

I  oi6 

I  510 

I  580 

1  050 

2  588 

320 
351 

■360' 

746 
I  228 

I  066 

-              *r 

rrout  Tile  tes 

ted  by  Bare 

au  of  Buildi 

ngs,  New  York,  in  1914 

and  webs  i  in  thick,  weighed  91.7  lb.  Its  compressive  strength  is  given  in 
the  last  line  of  Table  III. 

Concrete.  Stone  concrete,  under  the  action  of  heat,  is  affected  much  the 
same  way  as  brickwork  The  heated  surface  expands,  and  as  the  concrete  is 
a  very  poor  conductor,  the  other  surface  remains  cool  and  either  cracks  or 
causes  warping.  The  heat  also  affects  the  strength  and  texture  of  the  concrete, 
causing  a  disintegration  of  the  concrete  to  a  depth  of  about  i  in.  Often  the 
surface  spalls  off  with  a  report.  If  water  is  applied  after  the  heat,  the  surface 
is  washed  away  to  the  depth  of  the  affected  part.  These  effects  vary  somewhat 
with  the  stone  used  in  the  aggregate.  SiUceous  gravel  has  been  found  by  tests 
and  in  actual  fires  to  be  very  destructive  to  concrete.  Granite,  on  account  of 
the  difference  between  its  coefficient  of  expansion  and  that  of  the  concrete,  is 
likely  to  spall.  Limestone  calcines  under  the  action  of  heat  and  is  liable  to 
destruction  for  some  depth  by  the  water.  Trap-rock  is  a  satisfactory  material 
to  use,  from  the  standpoint  of  fire-resistance  as  well  as  that  of  strength.  If 
there  is  no  application  of  water  after  the  fire  and  the  surface  is  allowed  to  cool 
off  gradually,  the  concrete  may  set  again  and  become  hard.  It  is  not  well 
however,  to  rely  on  this.  (See,  also,  Chapter  III,  page  245,  for  the  effect 
of  heat  on  concrete  fireproofing.) 

Slag  Concrete.  Blast-furnace  slag  has  been  used  as  the  aggregate  in  con- 
crete, with  satisfactory  results  as  to  both  fire-resistance  and  strength.*  Care 
must  be  exercised  in  the  selection  of  the  slag.  R.  L.  Humphrey  says  that 
only  acid  slag  should  be  used  and  that  it  must  be  "dense,  tough,  and  free 
from  sulphur."  Sanford  Thompson  states  that  the  slag  must  be  "air-cooled, 
crushed,  screened  from  dust,  and  free  from  foreign  material,"  and  that  "excep- 
tional care  must  be  used  in  proportioning,  mixing,  and  placing."  f 

Cinder  Concrete.  Cinder  concrete,  because  of  its  porous  character  and  the 
nature  of  its  aggregate,  makes  an  excellent  fireproofing  material.  Tests  and 
the  experience  of  conflagrations  would  indicate  that  it  is  the  best.  Care  must, 
however,  be  taken  in  the  selection  of  the  cinders.  They  must  be  clean  furnace- 
cinders,  free  from  unburnt  coal.     When  properly  selected  and  proportioned, 

*  For  a  series  of  tests  and  description  of  materials,  see  pamphlet  issued  by  the  Camegi* 
Steel  Company,  1911,  Furnace  Slags  in  Concrete.     See,  also,  Proc.  Am.  Soc.  for  Test. 
Mat.,  1914.     A  full  discussion  of  slag  concrete  is  published  in  the  Iron  and  Coal  Trade 
Review  (London),  for  Nov.  22  and  29,  1918. 
,  .  t  Engineering  Record,  March,  1917. 


818  Fircproofing  of  Buildings  Chap.  23 

cinders  produce  good  concrete,  but  generally  a  very  non-homog6neous  material 
is  obtained,  so  that  its  strength  is  variable  and  doubtful.  If  ground  by 
machinery  before  mixing,  a  better  and  more  reliable  concrete  is  produced. 
In  using  cinder  concrete  in  floor-construction  the  working  loads  are  generally 
determined  from  load-tests  and  a  high  factor  of  safety  is  used.  The  former 
practice  in  New  York  City  was  to  take  oue  tenth  of  the  breaking-load  as 
the  WORKING  LOAD.  The  building  code  now  prescribes  a  formula  for  com- 
puting the  strength  of  cinder-concrete  floors,  within  certain  Umitations. 

Corrosive  Action  of  Cinders.  When  cinder  concrete  is  used  to  encase 
steel,  either  as  a  protective  covering  or  as  a  part  of  a  concrete  construction,  the 
corrosive  effect  of  cinders  must  be  guarded  against.  A.  discussion  of  thi? 
subject  will  be  found  in  Chapter  XXIV,  pages  960  and  961. 

Mortars,  Plasters,  and  Plaster  of  Paris.  Mortar  and  plaster  must  neces- 
sarily enter  into  the  composition  of  all  masonry  buildings,  whether  built  of 
brick,  stone,  or  terra-cotta.  That  ordinary  lime  mortar,  when  weU  made,  v^ill 
endure  for  unlimited  periods  of  time,  in  dry  situations,  has  been  proved  by 
actual  use.  Hydraulic-cement  mortars  are  equally  durable  in  wet  or  damp 
places.  For  laying  brickwork  or  tile  work  in  first-class  buildings,  cement-and- 
sand  mortar  is  preferable  to  any  other;  and  cement  mixed  with  lime  mortar 
gives  greater  strength  than  lime  and  sand  alone.  Regarding  the  fire-proof 
qualities  of  mortars  and  plaster  compositions  there  has  been  much  controversy; 
the  truth  of  the  matter  seems  to  be  that  all  such  compositions  will  withstand 
the  action  of  heat  up  to  a  certain  degree,  when  they  are  affected  in  one  way 
or  another,  depending  not  only  upon  the  composition  but  in  large  measure  upon 
their  body,  and  upon  the  way  in  which  they  are  used.  Lime  mortar  for  walls 
was  formerly  considered  as  the  most  satisfactory,  so  far  as  fire-resistance  is 
concerned;  but  since  the  improvements  in  cement-manufacture,  cement  mortar 
is  generally  preferred.  Lime  plaster,  applied  on  wire  lath,  will  withstand  a  high 
degree  of  heat  without  injury,  but  is  liable  to  be  washed  away  in  places  by 
streams  of  water.  Gypsum  plasters,  usually  termed  hard  wall-plasters,  or 
patent  plasters,  when  applied  to  brickwork  or  metal  lath,  are  superior  in  heat- 
resistance  to  common  lime,  and  the  patent  plasters  will  stand  the  combined 
effects  of  fire  and  water  longer  than  the  common  mortars. 

Plaster  of  Paris.  Compositions  of  plaster  of  Paris  (gypsum)  and  broken 
bricks,  wood  chips,  or  sawdust  are  non-conductors  of  heat  and  possess  fire- 
resisting  properties  of  considerable  importance;  and  on  account  of  their  light- 
ness and  cheapness,  are  often  used  in  fire-proof  or  semi-fire-proof  buildings. 
In  France  such  compositions  have  been  used  for  generations  to  form  ceilings 
between  beams,  and  their  durability  and  fircproofing  qualities  are  unquestioned 
in  that  country.  Plaster  of  Paris  compositions  when  subjected  to  severe  heat 
are  softened  on  the  surface,  and  when  water  is  thrown  upon  them  they  wash 
away  to  some  extent. 

Asbestic  Plaster.  A  plaster  made  by  mixing  Asbestic  with  freshly  slacked 
lime-putty  has  been  used  to  some  extent  in  New  York  City.  Asbestic  is  made 
from  a  serpentine  rock,  mined  near  Montreal,  Canada,  and  contains  a  large 
proportion  of  asbestos.  "Claims  of  great  fire-resisting  properties  are  made  for 
this  material,  as  well  as  resistance  to  the  effects  of  water  during  fire;  cracking 
and  discoloration  due  to  the  percolation  of  water  or  acids  are  also  claimed  to  be 
avoided.  The  plaster  is  tough  and  elastic,  and  it  will  receive  Aails  without 
chipping  or  cracking.  The  weight  is  siiid  to  about  half  that,  of  ordinary 
cement  mortar."  Asbestic  was  subjected  to  a  severe  fire-and- water  test  in 
the  presence  of  the  oflicials  of  the  Supervising  Architect's  office  at  Washington, 
D.  C,  "and  the  plaster  did  not  crack  or  drop,  but  remained  intact.    All  of 


Fire-Resistance  of  Materials  819 

the  walls,  ceilings,  and  columns  of  the  appraiser's  warehouse  in  New  York 
City  were  covered  with  a  coat  of  Ashestic,  from  J^  to  ^  in  thick,  applied  on 
the  concrete  or  terra-cotta  surfaces.  The  great  objection  to  the  use  of  this 
materi;il  lies  in  its  slow  drying,  the  time  required  for  a  thorough  drying  out 
being  usually  very  long."  * 

Asbestos-Products.  Asbestos  fiber  combined  with  cement  is  manufactured 
in  the  form  of  steam-packings,  corrugated  sheathings,  roof-coatings  and  shingles, 
wall-boards  and  building-lumber,  insulating  sheathing  and  blocks,  asbestos 
theater-curtains,  various  forms  of  preservative  and  fire-resisting  compounds, 
and  substitutes  for  v/all-plaster  and  stucco.  The  value  of  these  products  lies 
in  their  low  heat-conductivity  and  incombustibility. 

Asbestos  Building  Lumber  is  made  in  standard  sheets,  42  by  48,  and  42 
by  96  in  in  size,  and  varying  in  thickness  from  %  i«  (about  iH  lb  per  sq  ft  in 
weight)  to  I  in  (about  10%  lb  per  sq  ft  in  weight).  When  seasoned  it  is 
harder  than  ordinary  wood,  stakes  nails  and  screws,  and  it  can  be  manipulated 
with  heavy  tools  and  machinery  such  as  are  used  for  working  iron.  It  is  too  hard 
for  ordinary  wood- working  tools.  It  is  sufficiently  elastic  to  withstand  ordinary 
vibration,  expansion,  and  contraction  of  surrounding  parts,  wind-pressure,  and 
blows;   and  in  large  pieces,  it  can  be  bent  around  slight  curves  without  splitting. 

Asbestos  Corrugated  Sheathing  is  corrugated  asbestos  building-lumber, 
reinforced  with  sheet  steel  of  from  No.  24  to  No.  27  United  States  gauge,  or  with 
woven-wire  netting.  It  is  applied  in  the  same  way  that  corrugated  iron  is 
applied,  either  nailed  to  wooden  strips  bolted  to  the  purlins,  or  clipped  directly 
to  the  purlins  by  clips  of  hoop-iron  or  wire.  It  comes  in  standard  sheets,  27H  in 
wide  and  in  lengths  of  4,  5,  6,  7,  8,  and  10  ft. 

Asbestos  Roofing-Shingles,  suitable  for  wooden-roof  construction,  possess 
fire-resisting  qualities  far  superior  to  wooden  shingles.  The  ad\'antages  claimed 
are  their  fire-proof  qualities,  toughness,  elasticity,  and  hghtness  in  weight;  ease 
of  manipidation,  cutting,  sawing,  and  shaping  to  fit  dormer  windows,  chimneys, 
etc.;  and  their  immunity  from  the  corrosive  action  of  salt  air.  The  principal 
companies  manufacturing  asbestos  building-products  are  the  Johns-Manville 
Company,  New  York  City;  the  Keasljcy  &  Mattison  Company,  Ambler,  Pa.; 
and  the  Asbestos  Manufacturing  Company,  Lachine,  Canada. 

Asbestos-protected  Metal  consists  of  steel  sheets  of  from  No.  28  to  No.  20 
United  States  gauge,  coated  on  both  sides  with  asphaltum-compoimds  contain- 
ing heavy  natural  oils,  and  covered  with  layers  of  asbestos-felt  put  together 
under  great  pressure.  The  sheets  are  made  flat,  corrugated,  or  beaded.  It 
forms  an  incombustible  roofing,  siding,  sheathing,  and  interior-finish  material. 
The  manufacture  of  this  product  is  controlled  by  the  Aspromet  Company,  ot 
ritt.sburgh,  Pa. 

Steel  and  Wrought  Iron.  Wrouglit  iron  and  steel  will  expand,  bend,  and 
twist  under  a  moderate  degree  of  heat.  Inasmuch  as  a  temperature  of  i  700"  F. 
is  not  unusual  in  fires,  these  materials  should  not  be  used  in  fire-proof  con- 
struction without  proper  protection.  Fire  tests  at  the  Continental  Iron  Works 
in  1896  showed  that  unprotected  steel  columns  under  load  began  to  fail  when 
the  temperature  reached  about  i  100°  F.f  In  the  Baltimore  and  San  Francisco 
fires  there  were  many  instances  of  failure  in  steel  columns  due  to  lack  of  or  to 
insulRcient  protection. 

Cast  Iron.  "As  the  result  of  tests  and  actual  experience  in  conflagrations 
it  may  be  stated  that  unprotected  cast  iron  can  stand  practically  unharmed  up 

*  Freitap;. 

t  See  Engineecring  News,  Aug.  6,  1896. 


820  Fireproofing  of  Buildings  Chap.  23 

to  temperatures  of  1 3cx>  or  i  500°  F.  while  carrying  very  heavy  loads,  even  with 
frequent  applications  of  cold  water  while  the  metal  is  at  a  red  heat."*  In  the 
tests  at  the  Continental  Iron  Works,  referred  to  in  the  preceding  paragraph,  a 
temperature  of  nearly  1 300°  F.  was  reached  before  the  cast-iron  columns  began  to 
fail.  The  contents  of  most  mercantile  buildings,  when  burning  freely,  would 
probably  generate  a  heat  exceeding  at  times  2000°  F.  Consequently,  cast-iron 
columns,  when  unprotected,  are  almost  sure  to  fail  in  such  a  fire  either  bj''  bend- 
ing or  breaking.  No  building  in  which  unprotected  iron  or  steel  columns  are 
used  can  be  considered  fire-proof;  but  in  many  classes  of  buildings  unprotected 
cast-iron  columns  might  safely  withstand  any  heat  to  which  they  would  probably 
be  exposed.  From  a  fire-resisting  point  of  view,  when  there  is  no  protective 
covering,  cast-iron  columns  are  unquestionably  preferable  to  steel  columns. 

Fire-proof  Wood.  To  meet  the  requirements  of  certain  provisions  of  the 
New  York  City  Building  Code,  an  attempt  has  been  made  to  produce  fire-proof 
wood.  The  processes  for  rendering  wood  fire-proof,  in  general,  consist  in  im- 
pregnating its  fibers  with  certain  chemicals.  After  the  fireproofing-process, 
the  lumber  should  be  thoroughly  kiln-dried  before  it  is  used.  The  softwoods 
are  more  easily  thoroughly  treated  than  the  hardwoods,  the  resinous  woods 
bdng  particularly  difficult  to  handle. 

"The  treatment  of  the  wood  to  render  it  fire-proof  slightly  raises  the  igniting- 
point  of  the  wood.  The  treated  wood  is  harder  to  light  than  the  untreated 
wood,  taking  two  to  three  times  as  long  to  ignite.  The  amount  of  wood  destroyed 
when  exposed  to  the  action  of  a  flame  is  from  5  to  12  per  cent  greater  in  the 
case  of  an  untreated  wood  than  in  the  case  of  a  treated  wood.  The  untreated 
wood  furnished  more  flame  than  the  treated  wood.  The  untreated  wood  will 
sustain  flame  longer  than  the  treated  wood  after  the  source  of  heat  has 
been  removed.  From  this  it  can  be  seen  that  the  fire-proofed  wood  is  less 
Hkely  to  ignite  and  less  likely  to  cause  the  spread  of  fire  than  the  imtreated 
wood."t 

Among  the  disadvantages  of  fire-proof  wood  should  be  mentioned  an  increased 
difficulty  in  working  the  wood,  and  a  tendency  to  dull  woodworking-tools  more 
rapidly  than  with  untreated  wood.  Hence  an  increased  cost  in  the  use  of  fire- 
proof wood.  The  salts  used  in  the  process  of  fireproofing  being  hygroscopic, 
tend  to  keep  the  woodwork  damp.  Hardware  or  other  metalwork  in  contact 
with  fire-proofed  wood  is  liable  to  corrode.  The  strength  of  the  wood  is  often 
affected,  and  in  some  cases  the  wood  becomes  quite  brittle.  These  two  last- 
mentioned  faults  can  be  largely  overcome  by  neutralizing  the  fireproofing- 
solution  by  a  proper  mixture  of  acid  and  alkaline  salts. 

The  test,  known  as  the  timber- test,  applied  to  fire-proof  wood  in  New  York 
City,  consists  in  placing  a  stick  of  the  treated  wood,  %  by  1 1^  in  in  cross-section 
and  8  in  in  length,  for  two  minutes  over  a  crucible  gas-furnace  in  which  a  con- 
stant temperature  of  1 700°  F.  is  maintained;  then  removing  the  test-piece, 
noting  the  time  it  continues  to  flame  and  glow;  and  then  scraping  away  the 
charred  wood  and  determining  the  percentage  of  unburned  wood.  The  con- 
ditions of  acceptance  are  that,  "the  flame  and  glow  should  disappear  within 
ten  to  twenty  seconds  after  the  removal  of  the  test-piece  from  the  furnace,  and 
the  unburned  and  uncharred  section  at  the  center  of  the  specimen  should  be 
not  less  than  50  to  70  per  cent  of  the  original  cross-section,  depending  on  the 
variety  of  wood  under  test."  If  the  wood  has  been  thoroughly  treated,  a 
splinter  of  it  after  having  been  exposed  to  flame  and  withdrawn,  wiU  show 

*  Freitag. 

t  See  Insurance  Engineering,  Vol.  IV,  page  551;  also  Professor  Norton's  Report 
No.  I  to  t\\";  Boston  Manufacturers'  Mutual  Fire  Insurance  Company. 


Fire-Resistance  of  Materials  821 

no  glow  or  flame.     Other  tests  have  been  suggested  and  used  but  need  not 
be  described  here. 

Wire-Glass.  The  introduction  of  this  material  has  made  it  possible  to 
secure  fire-protection  in  many  cases,  without  the  necessity  of  disfigurement  due 
to  fire-shutters.  Wire-glass  is  either  ribbed,  rough,  maze,  cobweb,  or  polished 
PLATE,  with  wire  embedded  in  its  center  during  the  process  of  manufacture. 
\  "The  temperature  at  which  the  wire  is  embedded  in  the  glass  insures  ad- 
hesion between  the  metalhc  netting  and  the  glass,  and  the  two  materials  become 
one  and  inseparable,  so  that  if  the  glass  is  broken  by  shock,  by  intense  heat,  or 
from  other  cause,  it  remains  intact."  It  is  this  property  of  remaining  intact 
that  gives  it  its  fire-retarding  qualities.  Although  fire  and  water  may  cause 
cracks  to  spread  throughout  the  glass,  the  wire  holds  the  pieces  so  firmly  that 
flames  cannot  pass  through  it.  Many  severe  tests  during  actual  fires  have 
positively  demonstrated  the  truth  of  the  above  claim.  For  warehouses  and 
factories  the  ribbed  or  maze  glass  is  generally  preferable;  but  for  oflices,  or 
wherever  clear  transparent  glass  is  desired,  the  polished  plate  is  nearly  if 
not  quite  as  acceptable  as  the  same  glass  without  the  wire,  the  effect  being  the 
same  as  that  obtained  by  looking  through  a  window  with  a  screen  on  the  out- 
side. Where  fire -resistance  is  the  desired  feature,  the  following  requirements 
should  be  satisfied.  The  thickness  of  the  plate  at  the  thinnest  part  should 
be  not  less  than  }i  in,  and  the  plane  of  the  wire  mesh  should  be  midway  between 
the  two  surfaces  of  the  glass.  No  wire  should  be  smaller  than  No.  24  Brown 
&  Sharpe  gauge.  The  unsupported  surface  of  the  glass  should  not  exceed 
720  sq  in  in  any  case  and  should  be  contained  in  a  metal  frame  not  larger  than 
5  by  9  ft  between  supports.  The  chief  manufacturers  of  wire-glass  in  this  coun- 
try are  the  Pennsylvania  Wire  Glass  Company,  Philadelphia,  Pa;  the  Mis- 
sissippi Wire  Glass  Company,  New  York;  the  Western  Glass  Company,  Streator, 
111.;  and  the  Highland  Glass  Company,  W^ashington,  Pa.  As  now  manufactured 
by  the  continuous  process,  it  is  rolled  in  lengths  up  to  about  10  ft  and  in  thick- 
nesses up  to  Yi  in. 

Prism  Glass.  Prisms  installed  for  the  purposes  of  increased* light  are  usu- 
ally not  contained  in  frames  which  are  designed  to  withstand  severe  heat. 
The  dimensions  of  the  unsupported  electro-glazed  panel  should  not  exceed 
50  in  in  either  direction.  The  polished  plate  in  prism-glass  units  should  not 
exceed  4  in  in  either  direction,  with  a  minimum  thickness  of  Me  in.  In  Report 
No.  II  of  the  Insurance  Engineering  Experiment  Station,  C.  L.  Norton  describes 
a  scries  of  comparative  fire-tests  on  electro-glazed  Luxfer  prisms,  0.35  in  thick 
and  4  in  square;  electro-glazed  plate,  }4  in  thick  and  4  in  square;  and  J^-in  wire- 
glass.  The  results  of  these  tests  indicate  that  the  three  materials,  in  sheets  up 
to  24  by  30  in,  are  of  equal  value  in  fire-resistant  properties  and  remain 
in  effective  operation  up  to  the  time  when  the  temperature  of  melting  glass  is 
reached.     (See,  also,  page  1578.) 

Fire-proof  Paint.  Numerous  so-called  fire-proof  paints  have  been  in- 
troduced in  recent  years.  When  applied  to  woodwork  they  provide  a  more  or 
less  effective  protection  against  fire  and  may,  for  this  reason,  prevent  the 
spread  of  fire.  The  following  regulations  regarding  fire-proof  paint  were 
given  in  the  annual  report  of  the  Manhattan  Bureau  of  Buildings,  New  York, 
for  1904. 

"(i)  The  term  fire -proof  paint  shall  be  understood  to  mean  any  prepara- 
tion used  to  cover  the  surfaces  of  wood  or  other  materials  for  the  purpose  of 
protecting  the  same  against  ignition. 

"  (2)  No  fire-proof  paint  will  be  considered  satisfactory  unless  it  so  protects 
the  wood  or  other  material  to  which  it  is  apphed  that  the  same  will  not  flame 


822 


Fireproofing  of  Buildings 


Chap.  23 


or  glow  after  having  been  subjected  to  the  flame  of  a  gasoHne  torch  for  two 
minutes. 

"  (3)  Before  applying  fire-proof  paint  to  any  material  the  surfaces  must  be 
cleaned. 

"  (4)  Application  of  fireproof  paint  must  be  repeated  whenever  it  is  found 
that  the  material  to  which  it  is  applied  is  no  longer  protected  to  fulfill  Specifi- 
cation No.  2." 


3.  Column -Protection 

Girder  and  Column-Protection.  As  the  columns  and  girders  of  a  building 
form  the  back-bonf-  of  the  structure,  it  is  of  vital  importance  that  they  he  very 
thoroughly  protected  from  heat.  As  a  rule,  the  manner  of  protecting  these 
structural  elements  depends  quite  largely  upon  the  floor-system  adopted. 
Where  concrete  is  used  for  the  floor-construction  it  is  generally  also  employed 
for  incasing  the  columns  and  girders;  where  hollow  tile  is  used  in  the  floors,  the 
same  material  is  almost  invariably  employed  for  protecting  the  steel  frame. 
The  methods  used  for  protecting  girde.s  are  described  in  Subdivision  4  of  this 
chapter.     (.See,  alsj,  piges  780  to  782.) 

Necessity  for  Column-Protection.  It  is  now  gcnerafly  recognized  that  iron 
and  steel  columns  should  he  incased  with  some  material  that  will  thoroughly  pro- 
tect the  metal  against  fire.  In  1896  a  committee  of  the  American  Society  of 
Mechanical  Engineers,  in  conjunction  with  representatives  from  other  organiza- 
tions, made  a  scries  of  fire-tests  on  full-sized  unprotected  cast-iron  columns  and 
steel  columns,  loaded  to  their  figured  safe  capacities.  These  tests  showed  that 
the  steel  columns  failed  at  an  average  temperature  of  i  150°  F.,  and  the  cast- 
iron  columns  at  an  average  temperature  of  i  300°  F.,  the  failure  setting  in  after 
an  exposure  to  the  fire  of  from  23  minutes  to  i  hour  and  20  minutes,  or  an 
average  duration  of  about  50  minutes.  In  order  to  determine  the  vdlue  of 
several  materials  as  satisfactory  protective  coverings,  the  Bureau  of  Buildings 

Table  IV.     Tests  of  Protective  Coverings 


Materials  under  test 

Temp, 
on  face 
of  pro- 
tective 
material, 
degrees 
Fahr. 

Temperature  of  plate  at 

back  of  protective  material, 

degrees  Fahr. 

Before 
heating 

After 
heating 
for  2  hr 

Heat- 
trans- 
mission 

Terra-cotta:  dense,  hollow,  2  in  thick.. 

Terra-cotta:     semiporous,  solid,  2  in 

thick 

1700 

I  700 

I  700 
I  700 

I  700 

I  700 
I  700 
I  700 

75 

73 

69 
70 

72 

73 

66 

76 

223 

244 

159 
163 

167 

363 

248 

296 

148 
171 

90 
93 

95 

290 

182 

218 

Piaster  of  Paris  and  shavings,  2  in 
thick .-. 

Plaster  of  Paris  and  asbestos,  2  in  thick . 

Plaster  of  Paris,  wood  fibers,  and  in- 
fusorial earth,  2  in  thick 

Concrete  of  ground  cinders,   iMo   in 
thick 

Cinder  concrete,  on  metal  lath,  2  in 
thick 

Metal  lath  and  patent  plaster,  about 
^2  in  thick  over  i  in  air-space 

Column-Protection 


mz 


of  New  York  City  made  a  series  of  tests  on  the  iiEAT-coNinTCTrvrTY  of  these 
materials.  A  cast-iron  plate  covered  with  tlie  material  under  test  was  subjected 
to  a  temperature  of  i  700°  F.  for  two  hours  over  a  crucible  furnace,  and  the 
heat  of  the  plate  noted  at  regular  intervals  of  time.  The  results  of  the  tests  are 
shown  in  Table  I.V  on  page  822. 


Fig.  2.     Hollow-tile  Protection. 
Cylindrical  Column 


Blocks  set  in  cement  mortar,  occasionally, 
in  addition,  bound  witli  copper  wire  at  inter- 
vals of  I'o" 

Fig.  1.     Hollow-tile  Protection.     Plate-and-anglc 
Column 


Fig.  3.     Ribbed-tile  Protection. 
Cylindrical  Column 


Terra-Cotta  Column-Protection.  Fig.  1  shows  the  manner  in  which  built- 
up  columns  are  protected  in  the  best  class  of  fire-proof  buildings  when  tile  fire- 
proofing  is  used.  Figs.  2,  3,  and  4  show  common  methods  of  protecting  cylin- 
drical columns,  and  Figs,  o  and  6  columns  of  rectangular  cross-section.  The 
steel  guard,  shown  in  Fig.  1,  is  often  employed  in  mercantile  and  manufacturing 
buildings,  and  put  on  to  a  height  of  4  or  5  ft  above  the  floor.  The  efficiency  of 
this  construction  is  greatly  increased  by  wrapping  the  columns  with  wire  lat\> 
before  plastering,  although  it  is  not  a  common  practice.  To  insure  the  protec- 
tion of  the  metal  under  the  most  trying  conditions,  it  is  imperative  that  the 


Fig.  4.  Solid-tile  Pro- 
tection. Cylindrical 
Column 


Fig.  5.     Hollow-tile  Protec- 
tion. Built-up  Box  Column 


Fig.  C.  Hollow-tile  Pro- 
tection. Square  Column 
section 


824 


Fireproofing  of  Buildings 


Chap.  23 


protective  coverirtg  shall  not  be  detached  by  the  streams  from  the  firemen's 
hose,  and  thus  expose  the  steel.  This  can  be  positively  guarded  against  only 
by  using  two  layers  of  tiling  or  concrete  and  wrapping  the  inner  layer  with 
metal  lathing.  Fig.  7  shows  a  column  protected  in  this  way,  the  construction 
being  essentially  that  adopted  in  the  Fair  Building  in  Chicago,  111.  The 
inner  layer  of  tiles  is  wrapped  with  wire  lath  embedded  in  the  mortar,  and  all 

spaces  between  the  tiles 
and  metal  are  filled 
solid  with  cement  mor- 
tar. 

Concrete  Column- 
Protection.  Where 
concrete  is  to  be  used 
for  column-protection, 
the  way  to  obtain  the 
most  efficient  construc- 
tion is  undoubtedly  to 
surround  the  metal  with 
cinder  concrete,  poured 
inside  of  a  plank  form 
set  around  the  column, 
a  coat  of  liquid  cement 
being  first  applied  with 
a  brush  to  the  metal. 
The  plank  form  should 
be  set  at  least  2  in  out- 
ade  of  the  metal.  It  is  generally  conceded  that  this  forms  one  of  the  most 
efficient  fire-casings  for  columns,  and,  in  addition,  lends  added  stiffness  to  the  steel 
members  embedded  in  it.     It  is  advisable  to  reinforce  the  concrete  or  anchor  it  by 


Fig.  7.    Double-tile  and  Metal-lath  Column-protection 


i:rz: 


#10  Galv.  Steel  Wire  Loops 


B,^ 


Wood  Form,  Full  Column 


Fig.  8.     Concrete  Column-protection 
and  Wooden  Form 


yH    Bolt 


-^ 


SS^SSS^^^^^" 


J^fBoIt'' 


Fig.    9.      Concrete    Column-protection    and 
Wooden  Form 


Column-Protection 


825 


means  of  metal  lath  to  the  steel  column.  There  are  two  general  methods  in 
use  in  applying  the  concrete.  Fig.  8  illustrates  a  column  which  is  first  wrapped 
spirally  with  No.  lo  gauge  galvanized  wire,  12  in  on  centers,  to  afford  a  key 
for  the  concrete.  The  wood  forms  are  placed  the  full  length  of  the  column, 
and  the  concrete  poured  from  a  hole  in  the  ceiling  above.  A  slush -mixture  of 
either  cinder  or  stone  concrete  of  i  :  2  :  5  mix  may  be  used.  Fig.  9  shows  a  form 
of  rough  boards,  made  in-  sections  from  4  to  6  ft  in  length  and  provided  with 
yokes  at  each  end.  The  concrete  may  be  thoroughly  tamped  about  the  column 
as  each  section  is  placed  and  filled.  Fig.  10  shows  a  method  of  furring  the 
column  with  stiffened  wire  lath,  which  serves  as  a  substitute  for  the  wooden 
forms  and   at   the  same  time  anchors  the  concrete  to  the  steel.     A  similar 


^Plas':;er  ^"  thick 


Space 


Steel  rurring 
Strips 


Fig.  10.     Concrete  Column-protection. 
Wire-lath  Furring 


Fig.  11.     Metal-lath  and  Plaster  Column-pr<^ 
tection 


method  may  be  employed  to  obtain  an  air-space  by  placing  immediately 
around  the  column  an  envelope  of  metal  lath  with  a  2-in  layer  of  concrete. 
In  many  buildings  with  reinforced  concrete  floors,  the  columns  are  protected 
simply  by  plaster  on  metal  lath.  When  only  a  single  covering  is  provided, 
the  protection  cannot  properly  be  considered  fire-proof;  but  when  two  cover- 
ings are  provided,  as  in  Fig.  11,  they  are  probably  all  that  is  necessary  for  cast- 
iron  columns.  The  greatest  defect  in  lath  and  plaster  for  fireproofing  is  that 
the  plaster  is  hable  to  be  dislodged  by  the  force  of  the  water  from  the  firemen's 
hose.  When  there  are  two  coverings,  however,  thfs  danger  is  reduced  to  a  mini- 
mum.    (See,  also,  Chapter  XXII,  Figs.  23,  24,  and  25.) 

Plaster  Column-Covering.  Plaster-blocks  have  been  used  in  buildings  as 
a  column-covering,  but  their  use  is  not  to  be  recommended.  While  it  is  true 
that  their  non-conductivity  is  in  their  favor,  it  is  difficult  to  secure  them 
firmly.  Tlicy  are  easily  washed  away  by  hose-streams  and  subject  to  greater 
damage  than  other  materials.  In  unimportant  work  their  cheapness  may,  at 
times,  justify  their  use. 

Protection  of  Connections  between  Columns  and  Girders.  The  most 
defective  parts  of  the  coverings  of  columns,  whatever  the  materials  used,  are 
probably  those  about  the  connections  with  the  beams  and  girders.  Concrete 
undoubtedly  is  better  adapted  for  covering  these  parts  of  the  column  than  any 
other  material,  because,  being  elastic,  it  can  be  made  to  fit  into  any  space  and 
around  any  form  of  connection. 


826 


Fircproofing  of  Buildings 


Chap.  23 


The  Cement-Gun.  During  recent  years,  a  new  method  of  protecting 
structural  steel  by  means  of  the  cement-gun  has  been  introduced.  This  gun 
consists  essentially  of  two  superimposed  tanks,  forming  two  compartments, 
from  the  bottom  of  which  a  dry  mixture  of  sand  and  cement  is  ejected  by  com- 
pressed air  through  a  hose-hne  with  a  nozzle  at  the  end.  To  this  nozzle  a  smaller 
hose  delivers  a  supply. of  water  under  pressure,  which  is  applied  to  the  dry  con- 
stituents just  before  they  emerge  from  the  nozzle.  The  mortar  issuing  in  the 
form  of  a  spray  shoots  out  from  the  nozzle  with  considerable  force  and  im- 
pinges on  the  surface  of  the  steelwork.  The  columns  of  the  fifty-five-story 
Woolworth  Building  in  New  York  City  are  provided  with  a  ij^-in  coating  of 
cement  mortar  applied  in  this  way,  and  coated  on  the  outside  with  a  2-in 
thickness  of  terra-cotta.  The  steelwork,  also,  of  the  new  Grand  Central  Ter- 
minal Buildings  in  New  York  City  are  protected  with  a  2-in  coat  of  cement 
mortar  or  Gunnite.  By  this  means,  inaccessible  corners  are  readily  protected 
without  the  use  of  forms.  Tests  have  shown  that  Gunnite  is  superior  in  tensile 
and  compressive  strength,  permeability,  absorption,  porosity,  and  adhesion  to 
good  hand-made  products  of  the  same  kind.* 

Recesses  for  Pipes.  "As  a  matter  of  economy,  both  in  original  cost  and 
in  the  matter  of  space,  it  has  been  the  common  practice  to  rim  water-pipes, 
waste-pipes,  and  vent-pipes  immediately  alongside  the  steel  columns  and  inside 
the  fire-resisting  covering." f    This  is  undoubtedly  "bad  construction,  as  Freitag 

1 


Space  for  Pipes  and  Wires«^ 
Concretev 


Pipe-space 


Fig.  12.    Tile  Column-protection  with  Pipe- 
space 


Fig. 


13.     Concrete   Column-protec- 
tion with  Pipe-space 


illustrates  by  explaining  its  disastrous  results  in  recent  conflagrations;  and  in 
the  better  types  of  fire-proof  "buildings,  the  pipe-space  is  now  separated  from  the 
columns  by  the  fircproofing.  Fig.  12  shows  a  method  of  running  the  pipes 
in  some  fire-proof  buildings,  and  it  is  probably  as  satisfactory  as  any  arrange- 
ment in  which  the  pipes  are  to  be  run  beside  the  columns.  Fig.  13  shows  a 
somewhat  similar  method  in  which  concrete,  metal  lath,  and  plaster  are  em- 
ployed for  the  fircproofing. 


4.    Fire-proof  Floor-Construction 

Fire-proof  Floors.  In  the  study  of  fireproofing-materials  by  far  the  great- 
est attention  has  been  given  to  floor-construction;  and  of  the  very  large 
number  of  types  which  have  been  developed,  the  characteristic  and  leading 
ones  are  here. considered. 


*  Engineering  News,  191 2,  Vol.  67,  page  26;  and  Vol.  68,  page  1086. 
t  Fire  Prevention  and  Fire  Protection.  J.  K.  Freitag,  page  374' 


I 


Fire-proof  Floor-Construction  827 

Requirements  for  a  Fire-proof  Floor.  It  goes  without  saying  that  a  fire- 
proof floor  must  l)e  made  of  incombustible  materials.  It  seems  unnecessary, 
also,  to  mention  that  it  must  resist  as  much  as  possible  the  transmission  of 
heat,  so  as  to  afford  thorough  protection  to  the  metal  incased  by  it  or  forming 
an  essential  part  of  it.  The  materials  used  should  not  disintegrate  or  otherwise 
fail  when  exposed  to  heat  or  flame.  They  should  also  resist  the  action  of  water 
that  may  be  used  to  extinguish  a  fire.  The  lloor-construction  should  be  essen- 
tially water-tight,  so  as  to  prevent  damage  by  water  in  stories  below.  It  should 
be  designed  to  safely  carry  its  load  at  all  times.  The  New  York  City  Building 
Code  describes  certain  acceptable  forms  of  fire-proof  floors,  but  also  provides  for 
the  acceptance  of  other  forms  which  successfully  meet  the  prescribed  fire  and 
strength  tests.  Fully  eighty  tests  have  been  made  under  the  auspices  of  the  New 
York  City  authorities  and  these,  together  with  a  few  made  by  the  authorities  of 
other  cities,  comprise  practically  all  that  have  been  made  in  this  country.  The 
British  Fire-Prevention  Committee  of  London  has  also  made  a  number  of  such 
tests.* 

Fire  Tests  for  Floors.  The  standard  fire  test  of  the  American  Society 
for  Testing  Materials!  is  essentially  the  same  as  that  required  by  the  New 
York  City  Building  Code  and  as  the  one  used  by  the  British  Fire  Prevention 
Committee.  Briefly,  the  New  York  test  consists  in  subjecting  the  floor  in  ques- 
tion, carrying  a  load  of  150  lb  per  sq  ft,  to  a  fire  maintained  at  1 700°  F.  for  four 
hours;  and  then  in  applying  a  stream  of  water,  at  60-lb  nozzle-pressure,  for  ten 
minutes,  the  floor  being  considered  satisfactory  if  there  has  been  no  appreciable 
deterioration  due  to  the  test  and  if  it  has  resisted  the  passage  of  flames  during 
the  test. 

Types  of  Floor-Constructions.  In  considering  the  several  systems  of  floor- 
construction,  they  are  for  convenience  divided  into  the  following  types  or 
groups: 

(i)  Brick  arches, 

(2)  Terra-cotta  or  tile  floors: 

a.  Segmental, 

b.  Flat  side-construction, 

c.  Flat  end-construction, 

d.  Reinforced-tile  arches, 

e.  Guastavino, 

(3)  Concrete  floors: 

a.  Segmental, 

b.  Flat  reinforced  floors, 

c.  Sectional  systems, 

(4)  Gypsum  floors, 

(5)  Metal-lumber-construction. 

Brick  Floor-Arches.  The  first  attempt  at  fire-proof  floor-construction 
between  wrought-iron  beams  was  made  by  using  brick  arches  sprung  between 
the  beams  and  resting  on  the  bottom  flanges,  as  iUustrated  by  Fig.  14.  When 
this  form  of  construction  is  used  the  bricks  should  be  hard,  well-burned  bricks, 
or  hoflow  bricks  of  jgood  shape,  laid  to  a  line  on  centers  without  mortar,  with 
their  lower  edges  touching;  and  all  the  joints  should  be  filled  in  with  cement 
grout.  The  bricks  of  one  line  should  break  joints  with  those  of  the  next  adjoining, 
and  in  case  there  is  more  than  one  row,  the  joints  of  one  row  should  also  break 

*  For  a  list  of  these  tests  made  in  the  United  States  and  in  London,  see  Proc.  Am 
Soc.  for  Test.  Mats.,  Vol.  VI,  page  128. 
t  See  Year  Book,  Am.  Soc.  Test.  Mats. 


828 


Fireproofing  of  Buildings 


Chap.  23 


joints  with  those  of  the  row  above  or  below.  The  arches  need  not  be  over  4  in 
thick  for  spans  between  6  and  8  ft,  provided  the  haunches  are  filled  with  a  good 
cement  and  gravel  concrete,  put  in  rather  wet.  The  rise  of  the  arch  should 
be  about  one-eighth  the  span,  or  i^  in  to  the  foot;  and  the  most  desirable  span 


Fig.  14.     Brick  Floor-arch 


is  between  4  and  6  ft.  The  building  laws  of  many  cities  provide  that  when  the 
spans  exceed  5  ft  the  arches  must  be  increased  in  thickness,  generally  to  8  in. 
The  HAUNCHES  should  be  filled  with  concrete,  level  with  the  top  of  the  arch. 
In  first-class  fire-proof  construction  the  bottom  flanges  of  the  beams  should  be 
protected  by  terra-cotta  skewbacks,  as  in  Fig.  15  which  shows  the  construction 


Finished  Floor^ 


Fig.  15.     Brick  Floor-arch.     Government  Printing  Office,  Washington,  D.  C. 

used  for  the  floors  of  the  principal  stories  of  the  Government  Printing  Office  at 
Washington,  D.  C*  A  4-in  brick  arch  of  6-ft  span,  well  grouted  and  leveled  off 
with  Portlant-cement  concrete,  should  safely  carry  300  or  400  lb  to  the  square 
foot.  Experiments  have  shown  that  brick  arches  will  stand  very  severe  pound- 
ing and  a  great  amount  of  deflection  without  failure.  The  weight  of  a  floor, 
such  as  is  shown  in  Fig.  14,  is  about  40  lb  per  sq  ft,  without  the  concrete  fill  or 
finish.  Tie -RODS,  as  described  on  page  865,  should  always  be  provided.  The 
brick  arch  is  the  strongest  type  of  arch  for  the  span  it  occupies,  with  the  excep- 
tion, perhaps,  of  the  stone-concrete  arch.  It  is  perhaps,  also,  the  most  expensive. 
Its  weight  necessitates  a  heavier  framework  than  is  required  for  other  types; 
and,  on  account  of  its  appearance,  it  is  adapted  only  to  buildings  of  the  warehouse 
type. 

Terra-Cotta  or  Tile  Floor-Arches.  Terra-cotta  or  tile  as  a  fire-proof 
material,  and  the  relative  merit  of  dense,  porous,  and  scmip(3rous  tile  have  been 
discussed  on  page  815.  For  floor-construction  the  scmiporous  tile  is  probably 
the  best  as  it  is  a  compromise  between  the  advantages  and  disadvantages  of  the 
dense  and  porous  tile,  particularly  as  to  strength  and  fire-resisfance.    As  indi- 

*  A  description  of  the  structural  features  of  this  building  may  be  found  in  the  Engineer- 
ing Record  for  Dec.  6,  1902, 


Fire-proof  Floor-Construction  829 

cated  on  page  827,  five  different  types  of  terra-cotta  floor-construction,  including 
a  larger  number  of  systems,  will  be  discussed.  For  these  a  great  variety  of 
shapes  and  sizes  of  blocks,  of  the  dense,  porous,  and  semiporous  material,  are 
manufactured  in  this  country.  The  largest  company  devoted  to  the  manu- 
facture and  erection  of  hollow-tile  fireproofing-material  is  the  National  Fire 
Proofing  Company,  New  York  and  Chicago.  Another  large  company  is  Henry 
Maurer  &  Son,  New  York.  Any  one  of  the  large  companies  can  make  any 
form  of  blocks  desired,  except  such  as  are  covered  by  letters-patent,  and,  as  a 
rule,  they  can  make  them  in  dense,  porous,  and  semiporous  material. 

Advantages  of  Tile  Floor-Arches.  Many  architects  prefer  the  use  of 
TERRA-COTTA  ARCHES  in  buildings  because  the  setting  of  them  causes  less  dis- 
turbance to  the  mechanics  of  other  branches  of  the  construction.  During  the 
placing  of  concrete  arches  the  continual  dripping  of  water  and  bits  of  con- 
crete interferes  seriously  with  other  work.  The  work  of  installing  tile  arches 
is  generally  more  rapid  than  for  other  types  and  it  is  not  necessary  to  wait  for 
them  to  dry  out.  The  quality  of  terra-cotta  can  be  readily  judged  from  its 
appearance,  not  only  before  it  is  put  in  place  but  also  after  it  is  set.  Thus  it  does 
not  require  the  constant  supervision  necessary  for  materials  that  are  mixed 
as  they  are  put  in  place. 

Disadvantages  of  Tile  Floor-Arches.  The  principal  disadvantage  of 
TILE  ARCHES  for  floor-construction  is  the  difficulty  of  adapting  any  system  to 
the  filling  of  irregular-shaped  spaces.  The  arches  must  be  set  between  I  beams 
or  channels,  and  to  get  the  best  effect  the  supporting  beams  must  be  parallel  or 
nearly  so.  Tile  arches,  especially  of  the  end-constructions,  are  weakened 
more  by  holes  for  pipes  than  are  the  monolithic  floors.  As  there  is  no  bond 
between  the  rows  of  tiles  in  the  end-construction  arch,  if  a  single  tile  in  a  row 
is  cut  out  or  omitted,  there  is  nothing  to  hold  up  the  remaining  tiles  in  the  row 
except  the  adhesion  of  the  mortar  in  the  side  joints.  In  this  respect  side- 
method  arches  have  an  advantage  over  the  end-construction.  Where  it  is 
necessary  to  use  considerable  concrete  filling  over  the  arch  the  weight  of  the 
floor-construction  will  usually  greatly  exceed  that  of  the  concrete  systems,  and 
this  additional  weight  means,  also,  additional  expense.  The  floor-blocks  are 
liable  to  breakage  and  chipped  blocks  in  the  floor  are  not  unusual. 

Inspection  of  Floor- Arches.  Flat  arches  of  hollow  tile  require  close  inspec- 
tion during  erection  to  see  that  broken  or  imperfect  tiles  are  not  used;  that 
the  ribs  in  end-construction  tiles  abut  opposite  each  other;  that  all  joints 
are  properly  mortared  and  that  all  of  the  steelwork  is  properly  protected.  Much 
poor  workmanship  has  been  allowed  to  pass  in  order  to  avoid  delay,  and  also 
because  it  cannot  be  discovered  until  the  centering  is  removed.  A  tile  arch 
generally  looks  better  on  the  top  surface  than  it  does  on  the  bottom.* 

Setting  of  Tile  Floor-Arches.  Tile  arches  are  always  set  on  wooden 
centers  suspended  by  1)olts  hooked  over  the  tops  of  the  I  beams.  For  all  spans 
of  5  ft  and  over,  the  centers  should  be  sHghtly  cambered.  Before  any  floor- 
arches  are  set,  all  girders  projecting  below  floor-beams  should  be  completely 
covered  on  the  bottom  and  sides,  independently  of  the  floor-construction.  To 
protect  the  steel  from  rust  it  should  have  a  good  coat  of  Portland-cement  mortar 
before  the  tiles  are  applied.  After  the  centers  are  in  place  the  beam-tiles  should 
be  placed  under  the  bottom  of  the  beams  and  mortar  slushed  on  the  sides.  The 
entire  sides  of  the  skew  backs  which  rest  against  the  floor-beams  should  then 
be  covered  with  just  enough  mortar  to  give  them  a  perfect  bearing,  and  shoved 

*  The  careless  workmanship  possibk^  in  the  setting  of  tile  arches  was  clearly  set  forth 
in  an  article  in  Engineering  News,  April  14,  1898. 


830 


Fireproofing  of  Buildings 


Chap.  23 


up  against  the  beams.  After  this,  the  intermediate  blocks,  with  their  ribg 
on  one  end  and  one  side  covered  with  a  full  bed  of  mortar,  should  be  shoved 
into  place.  The  keys  should  have  mortar  on  both  sides  and  one  end,  if  side- 
method  KEYS  are  used,  and  they  should  tit  snugly,  but  not  tight.  "  Under  no  con- 
ditions should  a  key  be  rammed  in  place.  It  is  better  to  use  a  smaller  key  and  fill 
out  the  space  left  with  either  a  solid  slab  of  tile,  or,  if  the  opening  is  too  small, 
with  a  piece  of  slate."*  "In  setting  tile  arches  it  is  very  common  to  build  the 
arches  in  string-courses,  first  fitting  all  the  skews,  then  all  the  intermediates, 
and  finally  all  the  keys.  This  is  bad  practice,  as  it  loads  the  center,  both  planks 
and  stringers,  to  excess,  causing  too  great  a  deflection.  In  the  end-construc- 
tion the  arches  should  be  built  one  by  one,  each  being  complete  before  the 
next  is  started.  In  side-construction,  where  joints  are  broken  longitudi- 
nally, the  arches  should  be  keyed  up  or  completed  at  the  first  point  wheie  the 
intermediates  meet  the  hues  of  the  key,  thus  completing  the  successive  arches 
as  rapidly  as  possible."!  All  joints  in  the  arches  should  be  filled  with  mortar, 
especially  at  the  top. 

Wetting  the  Floor- Tiles.  In  warm  weather  all  hollow  tiles,  whether  dense 
or  porous,  should  be  well  wet  or  water-soaked  before  laying.  In  freezing  weather 
they  must  be  kept  dry. 

Mortar  for  Setting  Floor-Tiles.  "Mortar  for  setting  porous  hollow  tile 
should  never  be  made  of  cement  and  sand  alone,  as  such  mortar  is  too  short, 
rolls  off  the  tile,  and  does  not  insure  a  full  joint."*  A  good  mortar  is  made 
by  mixing  the  cement  and  sand  in  the  proportion  of  1:3,  and  adding  cold 
lime  putty  or  hydrated  lim.e  to  the  extent  of  10%  of  the  cement-content.  The 
mortar  should  be  thoroughly  worked.  Hot  lime  mortar  should  never  be  used. 
In  dry  weather  the  centers  can  be  removed  in  36  hours  after  the  tiles  are  in  place, 
but  it  is  much  better  to  allow  48  hours  and  even  longer  in  cold  or  wet  weather. 

Filling  above  Tile  Floor-Arches.  The  strength  of  all  tile  arches  is  greatly 
increased  by  wetting  their  top  surface  and  covering  it  with  a  rich  cinder  con- 
crete, mixed  with  Portland  cement,  well  tamped  and  brought  level  with  the 
t  jps  of  the  steel  beams.  If  the  floors  are  to  be  finished  in  wood,  nailing-strips 
are  required  to  secure  the  flooring.  These  naihng-strips  are  usually  dovetail- 
shape  in  cross-section,  about  2K'  in  wide  at  the  top,  sH  in  at  the  bottom  and 
from  1%  to  2  in  thick.  It  is  preferable  to  lay  them  at  right-angles  to  the  steel 
beams,  so  that  they  may  be  secured  to  the  top  flanges  by  metal  chps,  as  in  Fig.  16. 


/""[TZ-^y'y^ 


Fig.  16.     Segmental  Tile  Floor-arch 

Before  the  nailing-strips  are  laid,  all  piping  and  wiring  which  must  go  above 
or  through  the  tile  arches  should  be  put  in  place.  After  the  nailing-strips  are 
in  place  the  tops  of  the  steel  beams  should  be  covered  with  a  thin  coat  of  Port- 


*  E.  A.  Hoeppner. 


t  I'rcitiig 


Fire-proof  Floor-Construction 


831 


land-cement-and-sand  grout,  applied  with  a  brush.  The  spaces  between  the 
nailing-strips  should  be  filled  with  a  i  :  8  or  i  :  lo  cinder  concrete,  finished 
about  yi  in  below  the  tops  of  the  strips.  Some  architects  claim  better  results 
with  strips  of  rectangular  section,  with  nails  driven  horizontally  into  the  ver- 
tical sides  to  form  the  grip  in  the  concrete.  This  method  avoids  the  loosening 
of  the  strips  and  flooring  from  any  shrinkage  of  the  strips. 

Tile  Filling-Blocks.  In  cases  where  the  tops  of  the  tile  arches  are  2  in  or 
more  below  the  tops  of  the  steel  beams,  hollow  tile  blocks  are  sometimes  used 
for  fiUing  to  the  top  of  the  beams,  as  in  Fig.  23.  These  blocks  are  lighter  than 
good  concrete,  but  they  do  not  strengthen  the  arches. 

Cement  Floors.  If  the  floors  are  to  be  finished  with  cement,  the  cement  and 
concrete  should  be  at  least  2V2  in  and  preferably  3  in  thick  above  the  steel  beams, 
and  should  be  blocked  out  in  sections  of  not  over  6  ft  square,  with  joints  extend- 
ing through  the  concrete.  When  practicable  the  joints  in  one  direction  should 
be  over  the  beams. 

Weather-Protection.  Terra-cotta  arches  should  always  be  protected  against 
rain  or  snow,  especially  in  freezing  weather,  as  both  the  blocks  and  the  mortar 
in  the  joints  are  injured  by  freezing.  Porous  terra-cotta,  especially,  may  be 
utterly  ruined  by  freezing  when  soaked  with  water. 

Protection  of  Ceilings  from  Stains.  "If  plastered  ceilings  are  to  be  used, 
the  terra-cotta  work  should  be  protected  against  the  smoke  or  soot  from  the 
hoisting-engines.  Stains  are  also  quite  hable  to  occur  from  the  effects  of  iron 
in  the  clay,  or  from  the  cinders  in  the  concrete  over  the  arches,  if  the  floor  is 
allowed  to  become  wet."*  To  prevent  these  stains  several  kinds  of  hydraulic 
paints  have  been  used,  some  of  which  have  proved  very  effective. 

Segmental  Tile  Floor- Arches.  "This  form  of  arch  is  the  strongest  and 
cheapest.  It  is  particularly  adapted  to  warehouses,  lofts,  factories,  sidewalks, 
or  wherever  great  strength  is  required  and  a  flat  ceiling  is  not  necessary.  When 
a  light,  strong  arch  is  required  in  deep  beams  and  a  flat  ceiHng  is  also  demanded, 
this  result  can  be  obtained  by  using  a  metal-lath  ceiHng  suspended  below  the 
beams."  f  These  arches  are  usually  formed  by  either  6  or  8-in  hollow  tiles, 
set  on  the  side-coNstruction  principle  and  bonded  endwise  like  a  brick  vault. 


^oUcLBeam  TUe 


Fig.  17.     Segmental  Tile  Floor-arch.     Deep  Skew 


They  can  be  used  for  spans  up  to  20  ft,  but  it  is  better  to  limit  the  span  to 
about  16  ft.  "End-construction  blocks  may  be  used,  but  they  are  unsatisfac- 
tory, unless  the  arches  are  of  uniform  span  and  rise  throughout.  The  rise  of 
the  side-construction  arch  can  be  varied  by  increasing  the  thickness  of  the 
upper  or  lower  part  of  the  mortar  joint,  but  this  cannot  be  done  with  the  end- 
construction  method."  t 


*  P>eitag. 

t  Bevicr,  National  Fire  Proofinj;  Company,  New  York  City. 


832 


Fireproofing  of  Buildings 


Chap.  23 


Figs.  17  and   18  show  typical  forms  of  segmental  arches.     The  weighi 
of  the   arch-tiles  will   run  about  26  lb  per  sq  ft  for  6-in  tile  and  32  lb  for  8-in 


Span,  c.  to  c  of  beams,  19  1}4 


Fig.  18.     Segmental  Tile  Floor-arch.     Deep  Beam.    Dropped  Skew 

tile.  To  these  weights  should  be  added  the  weight  of  concrete  filling,  flooring, 
plaster,  etc. 

Thickness  of  Webs.  "For  general  use  the  webs  of  segment-tile  should  be 
^  in  thick  for  semiporous  tile  and  H  in  for  porous  tile.  The  skewback  should 
be  at  least  H  in  thick  for  the  first-named  material  and  i  in  for  the  second.  For 
printing-establishments  or  any  other  building  where  a  large  amount  of  vibra- 
tion occurs  the  webs  of  all  tiles  must  be  designed  in  proportionate  thickness  to 
the  load  they  are  required  to  carry."*  These  thicknesses  apply  to  Chicago 
practice  more  particularly,  where  a  stronger  tile  is  produced  than  in  the  East.  In 
New  York  City  webs  are  generally  %  in  thick  for  semiporous  and  i  in  for  porous 
tiles. 

Rise  of  Segmental  Floor-Arches.  The  rise  of  the  soffit  of  the  arch  above 
the  springing-line  should  be  from  one  tenth  to  one  eighth  the  span.  The  greater 
the  rise  the  less  will  be  the  thrust  of  the  arch.  No  single-cell  tiles  should 
ever  be  used  in  any  form  of  terra-cotta  arch-construction. 

Filling  the  Haunches.  The  haunches  of  segmental  arches  should  be 
filled  with  good  cement  concrete-leveled  up  to  a  point  not  less  than  i  in  above 
the  CROWN  of  the  arch.  For  short  spans  cinder-concrete  filling  may  be  used, 
but  for  wide  spans  it  is  better  to  use  gravel  concrete,  as  the  concrete  filling 
contributes  to  the  strength  of  the  arch  at  the  haunches. 

Tie-Rods.  The  thrust  of  segmental  arches  is  very  considerable,  so  that  it 
is  important  to  provide  tie-rods  between  the  beams.  A  formula  for  determin- 
ing the  stress  in  the  tie-rods  and  their  diameter  is  given  on  page  865.  To  be 
most  eft'cctive  the  tie-rods  should  be  placed  at  the  center  of  the  skew.  Placing 
the  tie-rods  in  this  manner,  however,  may  cause  them  to  project  below  the 
soffit  of  the  arch,  giving  an  unsightly  appearance  to  the  ceiling.  It  is  also 
more  difficult  to  protect  them  when  in  this  position. 

Strength  of  the  Segmental  Semiporous- Tile  Floor-Arches.  The  safe 
.LOADS  per  square  foot  on  6  and  S-in  segmental  arches,  with  side-construction, 
scmiparous  tile,  a  rise  of  one-eighth  the  sp m,  webs  and  shells  %  in  thick,  and 
with  a  factor  of  safety  of  7,  as  obtained  from  the  tables  of  the  National  Fire 
Proofmg  Company  are  given  in  Table  V. 

Side-Construction  Tile  Floor-Arches.  By  this  term  is  understood  the 
llat-tile  arches  in  which  the  voids  in  the  blocks  run  parallel  with  the  beams,  as 
shown  in    Fig.  19.     One   advantage   of   this  arch  over  the  end-construction  is 

*  E.  A.  Hocppner. 


Fire-proof  Floor-Construction  833 

Table  V.     Safe  Loads  for  Segmental  Semiporous-Tile  Floor-Arches 


Span, 

6-inch  arch, 

8-inch  arch, 

Span, 

6-inch  arch, 

8-inch  arch, 

ft 

lb 

lb- 

ft 

lb 

lb 

4 

I  103 

I  318 

II 

402 

480 

5 

878 

1049 

12 

370 

442 

6 

735 

883 

13 

340 

407 

7 

630 

735 

14 

317 

379 

8 

554 

662 

15 

296 

353 

9 

490 

585 

16 

278 

331 

10 

443 

529 

These  loads  include  the  weight  of  construction;    so  that  to  get  the  safe  live  load,  all 
the  dead  load  of  arch-blocks,  concrete  fill,  plastering,  flooring,  etc.,  must  be  deducted. 

the  BREAKING  OF  JOINTS  that  is  effected  in  the  setting  of  the  blocks,  by  means 
of  which  the  failure  of  a  single  block  does  not  impair  the  strength  of  the  arch 
beyond  that  block.  The  webs  should  not  be  less  than  ^  in  thick.  "Radial 
JOINTS  are  sometimes  specified  but  should  be  avoided,  as  they  incur  needless 
expense  in  manufacture  and  endless  confusion  and  delay  in  setting,  without  any 


Fig.  19.    Flat  Tile  Floor-arch. .  Side-construction 

compensating  advantage. "  *  In  the  skew^acks  a  web  should  always  be  pro- 
vided across  the  block  at  the  lower  flange  of  the  beam,  as  at  this  point  comes 
the  greatest  pressure  in  this  block.  Arches  have  collapsed  because  of  failure 
to  provide  this  web.  The  depth  of  the  arch  must  be  proportioned  to  the  span 
between  the  beams  and  to  the  load  to  be  carried.  For  ordinary  loads,  a  safe 
rule  is  to  make  the  depth  of  the  block  iH  in  for  each  foot  of  span,  plus  the 
amount  necessary  for  protection  below  the  beams.  Safe  loads  for  semiporous- 
tile  arches,  side-construction,  with  webs  %  in  thick  and  a  factor  of  safety  of  7, 
as  given  by  the  National  Fire  Proofing  Company,  are  shown  in  Table  VI. 

End-Constniction  Flat  Floor-Arches.  In  this  construction  the  sides  and 
voids  of  the  individual  blocks  run  at  right-angles  to  the  beams,  so  that  the  pres- 
sure on  the  blocks  is  endwise  of  the  tile.  It  has  been  conclusively  demonstrated 
that  hollow  tiles  are  much  stronger  in  end-compression  than  transversely. 
"The  objection  urged  against  this  construction  is  that  it  is  wasteful  of  mortar 
and  difficult  to  get  the  edges  of  the  blocks  properly  bedded.  They  do  require 
slightly  more  mortar,  but  the  second  objection  is  not  serious,  for,  if  the  blocks 
are  cut  to  a  proper  bevel,  the  tighter  they  are  set  the  stronger  the  arch."*  The 
individual  blocks  in  the  end-construction  are  commonly  made  rectangular 
in  shape,  advancing  by  i  in  from  6  to  15  in  in  depth.  The  length  and  width, 
also,  of  the  blocks  may  be  varied,  but  the  standard  size  is  12  in  for  both  dimen- 
sions.    The  number  of  partitions  or  webs  in  the  blocks  varies  with  the  size  of 

*  Bevier,  National  Fire  Proofing  Company,  New  York  City. 


831 


Fireproofing  of  Buildings 


Chap.  : 


Table  VI.     Safe  Loads  for  Semiporous,  Side-Construction,  Tile  Floor-Arches 


Depth  of  arch 

6  in 

7  in 

Sin 

9  in 

ID  in 

12  in 

Weight  of  arch 
per  sq  ft 

24  lb 

261b 

27  lb 

29  lb 

34  lb 

37  lb 

Span  of  arch, 
ft    in 

Strength  of  arch  in  pounds  per  square  foot 

4    0 

4  6 

5  0 

5  6 

6  0 

6  6 

7  0 

197 
156 

230 
182 
148 

263 

208 
168 

296 
233 
189 
156 
131 

438 
346 
281 
232 
195 
166 

525 
415 
336 
278 
234 
199 
172 

These  loads  represent  the  gross  loads;  so  that  for  the  safe  live  loads  the  weight 

of  the  construction,  including  the  arch-blocks,  fill,  flooring,  plastering,  etc.,  must  be 

deducted.     For  blocks  with  thicker  webs  the  loads  may  be  increased  proportionately. 

Where  no  loads  are  given  in  the  table,  the  spans  are  considered  excessive  for  the 

depth  of  block  specified.    The  weights  of  arch  given  in  the  table  are  for  the  lightest 

blocks.     If  thicker  webs  are  used,  the  weight  of  block  must  be  taken  proportionately 

greater. 

'» 

the  blocks  and  also  with  the  strength  desired.  The  6-in,  7-in,  and  8-in  blocks 
usually  have  two  vertical  partitions  and  one  horizontal  partition,  or  one  vertical 
and  one  horizontal,  for  blocks  8  in  wide.  The  lo-in  and  12-in  arches  may  have 
either  one  or  two  horizontal  partitions.  Arch-blocks  over  12  in  deep  should 
always  have  at  least  two  horizontal  partitions.  In  the  strongest  blocks  the 
voids  are  about  3  in  square.  "The  arch-blocks  must  be  set  end  to  end  in  straight 
courses  from  beam  to  beam,  and  cannot  be  set  breaking  joints,  as  in  the  side- 
construction  method."* 

Thickness  of  Web.  This  should  be  at  least  %  in  for  porous  and  ^  in  for 
semiporous  tiling.  The  thicker  the  webs  the  greater  will  be  the  strength  and 
fire- resistance  of  the  arch.  The  end-joints  are  always  beveled,  as  in  Fig.  20, 
the  ends  being  parallel;  thus  all  the  intermediate  blocks  are  made  with  the  same 
die. 

Form  of  Skewback.  An  end-construction  arch  may  have  skewbacks 
formed  of  the  same  blocks,  with  notches  in  the  ends  of  the  blocks  to  fit  over  the 


Fig.  20.     Flat  Tile  Floor-arch.     End-construction 


bottom  flanges  ol"  the  beams,  as  in  -Fig.  20.     It  is  generally  considered  that  the 
end-construction  skewback  is  much  stronger  than  the  side-construction  skew- 


Fire-proof  Floor-Construction 


835 


back  but  on  account  of  the  large  amount  of  mortar  lost  in  the  voids  and  the 
difficulty  of  obtaining  an  even  bearing  with  end-construction  skewbacks, 
and,  also,  because  of  the  greater  facility  with  which  the  side-construction  skew- 
backs  can  be  used,  contractors  generally  prefer  to  use  the  latter;  and  this  has 
given  rise  to  the  form  of  arch  shown  in  Fig.  21.  But  a  more  important  reason  for 
using  side-construction  skewbacks  with  end-construction  arches  is  the  better 
protection  against  fire  that  they  afford  to  the  beam  or  girder.  To  develop  the 
necessary  strength,  side-construction  skewbacks  should  have  a  large  sectional 
area  and  a  suffi(  ient  number  of  partitions,  following,  approximately,  the  lines  of 
thrust.  With  any  form  of  skewback  the  recess  for  the  beam-flange  should  be  of 
ample  width,  so  that  when  the  tiles  are  set  the  protecting  flanges  on  the  skew- 
backs  will  not  touch  the  bottom  of  the  beams,  but  will  be  at  least  34  in  below 
them.  Many  varieties  of  side-construction  skewbacks  are  made  to  meet  all 
possible  conditions. 

Keys.     Both  end-construction  and  side-construction  keys  are  used  with 
end-construction  arches,  the  choice  of  the  key  depending  principally  upon  its 


Fig.  21.     Flat  Tile  Floor-arch.     Combination  End-construction  and  Side-construction 


length.  If  the  span  of  the  arch  is  such  that  the  standard  intermediate  blocks 
require  a  key  6  in  or  more  in  width,  the  end-method  key  is  used,  as  in  Fig.  20; 
but  if  the  space  for  the  key  is  small,  a  side-method  key,  such  as  shown  in  Fig. 
21,  is  used.  As  the  key  is  almost  entirely  in  compression,  a  side-construction  key 
6  in  or  less  in  width  will  usually  give  all  the  strength  required,  provided  that  the 
horizontal  webs  are  in  the  same  line  with  those  in  the  intermediate  blocks.  E.  V. 
Johnson,  western  manager  of  the  National  Fire  Proofing  Company,  says:  "We 
prefer  the  use  of  an  end-construction  key  in  all  cases  where  possible.  Our  cus- 
tom is  to  use  side-construction  keys  for  spaces  of  6  in  and  under,  and  end- 
construction  keys  for  larger  spaces.  When  using  the  latter  keys  we  inserts 
J^-in  fire-clay  slab  between  the  ends  of  the  tile."  \ 

Raised  Skewbacks.  Where  flat  arches  are  sprung  between  i8-in,  20-in,  or\ 
24-in  beams  it  is  necessary  either  to  use  a  raised  skewback  or  else  to  have  a  largf 
space  above  the  top  of  the  tile  arches  which  must  be  filled  in  some  way.  Rdv'o^ 
skewbacks  are  preferable  to  a  hollow  space  above  the  tiles  and  cheaper  thai 
concrete  filling.  They  are  often  used  for  roof-arches,  because  for  that  pur- 
pose it  is  seldom  necessary  to  make  the  arches  as  deep  as  the  beams,  while  the 
top  must  be  about  on  a  level  with  the  beams.  Raised  skewbacks  are  almost 
always  made  on  the  side-construction  principle.  Fig.  22  shows  a  typical  form 
of  raised  skewback  for  end-construction  arches. 

Flat  Versus  Paneled  Ceilings.  In  connection  with  the  raising  of  the 
arches  above  the  bottom  of  the  beams  or  girders,  J.  K.  Freitag  calls  attention 
to  the  advantages  of  flat  ceilings,  as  follows:  "Flat,  unbroken  ceilings  are 
always  to  be  preferred  to  any  type  of  terra-cotta  arch  which  may  require  a 
paneled  efi:ect  due  to  the  projection  of  the  girders  or  beams  below  the  main 


836 


Fircproofing  of  Buildings 


Chap.  23 ■ 


ceiling-line."  A  perfectly  flat  ceiling  reflects  more  li^ht,  makes  a  better-lighted 
room,  and  deflects  the  heat.  Paneling  forms  pockets  for  the  retention  of  heat 
and  flame  and  greatly  increases  the  exposed  area. 


Fig.  22.     Raised  Skews  for  End-constmction  Arches 


Floor-Arches  and  Beams  of  the  Same  Depth.  A  deep  block  makes  a  much 
stronger  floor  than  a  shallower  one,  and  for  tho  same  depth  of  beams  a  lighter 
and  cheaper  floor.  A  12-in  arch  weighs  less  per  sciuare  foot  than  a  10-in  arch 
with  2  in  of  concrete  flUing;  and  it  costs  less. 

Depth,  Span,  and  Weight.  The  maximi^m  spans  for  different  depths  and 
the  AVERAGE  WEIGHTS  per  square  foot  of  this  type  of  arch,  set  in  place,  are  as 
follows: 


Table    VII. 


Maximum  Spans  for  Flat  Tile  Floor-Arches  of  Different  Depths 
and  Weights 


Depth  of  arch , 

Maximum  span, 

Weight  per  sq  ft, 

m 

ft     in 

lb 

6 

4     6 

29 

8 

5      6 

31 

9 

6     0 

32 

10 

6     6 

33 

12 

8     0 

39 

IS 

9     0 

46 

16 

10     0 

50 

The  weights  per  square  foot,  as  given  by  different  manufacturers  vary  greatly, 
V  no  doubt,  to  the  character  of  the  material  used   and  to  the  thickness  of 
the  we"bs. 

The  DEPTH  OF  ARCH  most  frequently  used  i?  10  in,  the  girders  being  spaced 
to  use  lo-in  I  beams  for  joists  spaced  from  5  to  6  ft  apart.  As  a  rule  the  depth 
of  the  arch  should  be  about  equal  to  the  depth  of  the  beam,  as  it  is  just  about  as 
cheap  and  much  better  construction  to  use  deeper  tiles  and  less  concrete  filling. 

Safe  Loads  for  End-Construction  Tile  Floor-Arches.  The  strength: 
of  flat  arches  of  hollow  tile  depends  upon  the  crushing  resistance  of  the  mate- 
rial, the  sectional  area  per  linear  foot  of  arch,  the  depth,  and  the  span.  For  these 
reasons  it  is  impossible  to  give  a  table  for  strength  which  applies  to  all  arches. 
The  values  given  in  Table  VIII  for  end -construction  arches  are  based  upon 
arch-blocks  of  the  cross-sectional  areas,  per  foot,  given  in  the  second  horizontal. 


Fire-proof  Floor-Construction 


837 


line  of  the  table,  and  arc  intended  to  have  a  factor  of  safety  of  7,  with  the 
weight  of  the  tile  only,  deducted.  Mr.  Hinton  says:  "The  safe  loads  a,s  they 
stand  in  the  table  afford  a  safe  general  statement  of  safe  loads  for  all  section  i 
since  they  represent  specifically  a  Ught  section  in  the  case  of  each  arch." 

Table  VIII.     Safe  Loads  for  End-Construction  Tile  Floor-Arches  * 

Semiporous  material  of  sectional  area  per  linear  foot,  as  given  in  the  second  line 
The  loads  are  in  pounds  per  square  foot  of  floor 


Depth  of  arch  in 
inches 

6 

' 

8 

9 

10 

12 

15 

Areas,  sq  in 

310 

340 

370 

400 

430 

490 

580 

Spans, 
ft  in 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

4  6 

5  0 

5  6 

6  0 

6  6 

7  0 

7  6 

8  0 

196 
155 

254 
202 
1^)3 

319 
254 
206 
170 
141 

391 
312 
254 
209 
175 
147 

470 
376 
306 
253 
212 
179 
153 

648 
519 
424 
352 
29s 
251 
215 
185 

968 
777 
636 
529 
446 
380 
326 
282 

*  This  table  is  condensed  from  two  tables  prepared  by  H.  L.  Hinton. 

Patented  End-Construction  Tile  Floor-Arches.     Figs.  23   and  24  show 
two  variations  of  a  type  of  arch  invented  and  patented  Ijy  E.  V.  Johnson  when 


Fig.  23.     Excelsior  End -construction  Tile  Floor-arch.     Side-skew 


manager  of  the  Pioneer  Company,  Chicago,  III.  The  right  to  manufacture  and 
use  this  arch,  in  certain  territory,  has  been  granted  to  the  National  Fire  Proofing 
Company,  and  to  Henry  Maurer  &  Son,  New  York  City.  The  original  shape  of  the 
arch-tile  is  illustrated  in  Fig.  24.  Henry  Maurer  &  Son  have  modified  the  shape 
to  that  shown  in  Fig.  23,  as  they  consider  that  this  shape  gives  a  stronger  and 
slightly  heavier  atch  than  one  of  the  original  shape.  The  advantages  of  this 
arch  are  the  reduction  in  weight  for  an  equal  strength,  and  the  clear  space  of  5 
in  between  the  tiles,  which  avoids  the  cutting  of  the  blocks  for  the  tie-rods. 
This  arch  can  be  adapted  to  any  span  up  to  lo  ft  by  using  blocks  of  suitable  depth 


838 


Fireproofing  of  Buildings 


Chap.  23 


Fig.  24.     Johnson  End-construction  Tile  Floor-arch.     Original  Form 


The  LIMIT  OF  SPAN,  WEIGHT  PER  SQUARE  FOOT,  and  SAFE  LOAD  of  the  ExcelsiOF' 

arch  (Fig.  23)  is  given  by  Maurer  &  Son  as  follows: 

Table  IX.     Maximum  Spans  for  Excelsior  Tile  Floor-Arches 

Depth  of  arch, 
in 

Limit  of  span, 
ft 

Weight  per  sq  ft, 
lb 

Safe  load  per  sq  ft, 
lb 

8 
9 

ID 
12 

Sto^ 

6  to  7 

7  to  8 

8  to  9 

27 
29 

33 

38 

300 
350 
300 
350 

The  National  Fire  Proofing  Company  has  made  arch-blocks  as  deep  as  20  in 
and  as  h^avy  as  56  lb  per  sq  ft.  This  company  and  Henry  Maurer  &  Son  use 
semiporous  material  for  the  arch-blocks.  It  should  be  noticed  that  the  arch 
made  by  the  former  has  an  end-construction  skewback,  while  the  latter  uses  a 
SIDE-CONSTRUCTION  SKEWBACK.  The  National  Fire  Proofing  Company  for- 
merly used  the  side-construction  skewback,  but  found  that  when  arches  of  this 
tyi)e  were  tested  to  destruction  the  skewbacks  were  almost  invariably  the  parts 
which  failed;  hence  their  adoption  of  the  end-construction  skewback.  Henry 
Maurer  &  Son,  however,  have  tested,  without  failure.  Excelsior  arches  of  8  ft  and 
lo-ft  spans,  and  with  skewbacks  as  shown  by  them,  with  loads  of  over  i  000  lb 
per  sq  ft.  These  arches  have  been  extensively  used  in  l)oth  eastern  and  western 
cities 

Reinforced-Tile  Floor-Arches.  In  order  to  obtain  a  wide-span  flat  arch  or 
to  obtain  a  reduced  depth  of  arch-block  for  the  shorter  spans,  the  manufacturers 
of  terra-cotta  have  applied  to  their  floor-construction  the  principle  of  rein- 
forcement WITH  METAL,  wliich  is  the  basis  of  reinfori  ed-concrcte  construction. 
Compared  with  reinforced  concrete,  even  when  cinders  nre  used  for  the  aggre- 
gate, the  greater  depth  and  hollow  construction  of  these  reinforced-tile 
ARCHES  secure  for  them  greater  strength  per  square  foot  for  the  same  weight 
of  construction.  On  the  other  hand,  however,  they  are  undoubtedly  more  ex- 
pensive than  cinder-concrete  floor-construction,  because  of  the  material  used 
and  the  increased  height  of  the  building  due  to  thicker  floors. 

The  Herculean  Arch.*  These  floor-arches  are  built  of  semiporous  terra- 
cotta blocks,  12  by  12  in  on  top  and  var^^ing  from  6  to  12  in  in  depth,  according 
*  Patented  and  manufactured  by  Henry  Muurer  &;  Son,  1898  and  1900. 


Fire-proof  Floor-Construction 


839 


to  the  span  and  load.  In  the  sides  of  the  blocks  are  grooves  to  receive  iH  by 
iH  by  yiG-'m  T  bars.  The  blocks  are  laid  end  to  end  the  entire  length  of  the 
span,  with  a  bearing  of  from  4  to  6  in  on  the  walls  or  girders,  presenting  two 
continuous  grooves,  which  are  filled  with  cement  mortar,  and  into  which  the 
T  bars  are  then  inserted.  The  T  bars  must,  of  course,  extend  the  full  length  of 
the  span.  The  grooves  in  the  next  course  are  then  filled  with  cement  mortar 
and  the  blocks  pushed  into  place,  thus  thoroughly  covering  the  steel  with  mortar. 
All  joints  between  the  blocks  are  filled  with  cement  mortar  and  the  blocks  are 
laid  to  break  joint  endwise,  as  in  Fig.  25.    This  iloor  has  been  used  for  spans 


Fig.  25.     Herculean  Reinforced,  Tile  Floor-arch 

varying  from  19  to  23  ft.  The  weight  per  square  foot  given  for  the  terra- 
cotta blocks  and  steel  T  bars  is  26  lb  for  blocks  6  in  deep,  33  lb  for  8-in  blocks, 
42  lb  for  lo-in  blocks  and  51  lb  for  12-in  blocks.  The  manufacturers  estimate 
the  s^\rE  LOADS  for  this  construction  as  follows: 

For  a  i2-in  arch  with  a  20-ft  span,  400  lb  per  sq  ft. 
For  a  lo-in  arch  with  a  i6-ft  span,  400  lb  per  sq  ft. 
For  a    8-in  arch  with  a  12-ft  span,  150  lb  per  sq  ft. 

The  CHIEF  ADVANTAGE  of  this  Construction  is  said  to  be  its  low  cost  as  com- 
pared with  the  cost  of  systems  equally  fire-proof  and  requiring  steel  beams 
every  6  or  8  ft.  It  is  particularly  well  adapted  to  buildings  with  masonry  walls 
and  partitions,  as  in  such  buildings  little  or  no  structural  steel  is  required.  The 
floor-construction  affords,  also,  an  unusually  smooth  undersurface,  thereby 
reducing  the  cost  of  plastering.     No  tie-rods  are  required  for  this  floor. 

The  Johnson  Long-Span  Flat  Floor-Construction.  This  reinforced- 
TiLE  FLOOR  was  iuvcntcd  by  E.  V.  Johnson,  and  is  now  controlled  and  erected 
by  the  National  Fire  Proofing  Company.  Its  general  construction  is  as  follows: 
A  temporary  flat  centering  is  first  erected,  and  over  this  is  spread  a  layer  of 
rich  Portland-cement  mortar  about  %  in  thick.  On  top  of  this  mortar  is  laid 
a  woven  fabric  containing  steel  rods  varying  from  ^  to  H  in  in  diameter, 
according  to  the  span,  and  spaced  from  2  to  8  in,  center  to  center.  Another 
layer  of  the  same  mortar  is  then  spread  on  top  and  hollow  tiles,  from  3  to  1 2  in  in 
depth,  according  to  the  span,  are  then  set  in  the  mortar  and  laid  so  as  to  break 


310 


Fireproofing  of  Buildings 


Chap.  23 


JOINT  and  to  form  continuous  rows  from  one  support  to  the  ofher.     A  layer 
of  concrete,  also,  about  2  in  thick,  is  usually  spread  on  top  of  the  tiles.   Fig.  26 


Fig.  26.    Johnson  Reinforced,  Tile  Floor-arch 

shows  the  general  method  of  construction  of  this  system,  but  without  the  rods, 
which  are  inserted  in  place  as  the  fabric  is  used.  For  short  spans  the  fabric 
can  be  used  without  the  rods.  This  system  differs  from  the  flat  concrete  system- 
only  in  the  substitution  of  hollow  tiles  for  the  concrete  in  the  upper  portion  of 
the  slabs,  the  strength  of  the  floor  depending  upon  the  reinforcement  and 
the  ADHESION  of  the  cement  mortar  to  the  steel  and  tiles.  As  the  tiles  are 
covered  both  on  the  bottom  and  top  with  concrete,  the  fireproofing  prop- 
erty, also,  is  measured  by  the  resistance  of  the  concrete  and  not  by  that  of  the 
tiles.  Tests  have  shown  that  the  adhesion  of  the  mortar  is  perfect  and  that  it 
will  stand  a  high  temperature  without  injury.  This  construction  can  be  used 
for  any  span  up  to  25  ft,  the  most  advantageous  span  being  about  16  ft.  The 
WEIGHT  per  square  foot,  including  the  fabric  and  the  cement  on  the  bottom  and 
in  the  joints,  but  not  on  top  of  the  tile,  is  as  follows: 

Depth  of  tile,  inches 12     10      9       8      7       6       5       4 

Weight  per  square  foot,  in  pounds     60     55     45     42     37     34     26     24 

Tha  concrete  above  the  tile  should  l:>e  figured  at  12  lb  per  sq  ft  for  each  inch 
in  thickness.  The  strength  of  the  floor,  with  i  in  of  1:3  Portland-cement 
mortar  on  top  of  the  tiles,  is  given  in  Table  X. 

The  New  York  Reinforced-Tile  Floor-Arch.  This  arch  (Fig.  27)  was 
designed  by  P.  H.  Bevier,  of  the  New  York  City  branch  of  tlie  Nation^il  Fire 
Proofing  Company,  for  use  ''when  a  Hght  and  cheap  but  strong  floor  construc- 
tion with  a  flat  ceiling  is  required,  and  is  particularly  adapted  to  wide  spans 
in  shallow  beams.  When  light  flcKjr-const ruction  with  deep  !>eams  is  necessary 
it  can  be  secured  by  setting  the  blocks  level  with  the  tops  of  the  beams  and  using 
a  flat  metal  lath  ceiling,  or  by  omitting  the  ceiling  a  panel  effect  is  obtained. 
When  shallow  beams  arc  used  the  blocks  are  set  level  and  1  in  below  the  bottom 
of  the  beams.  Light  cinder  concrete  or  dry  cinders  are  used  to  level  up  to  the 
top  of  the  beams.  A  wire-truss  reinporckmp.nt,  similar  to  that  shown  in  Fig. 
28,  used  in  this  system,  is  shipped  to  the  building  in  reels,  and  is  cut  to  proper 


Fire-proof  Floor-Construction  841 

Table  X.     Ultimate  Strength  of  the  Johnson  Floor-Construction 


Span  in 
feet 

Thicknes 

3  of  tiles 

in  inches 

12 

10 

9 

8 

7 

6 

s 

4 

3 

Ultimate  strength 

n  poun 

Is  per  square  foot 

10 

3  375 

2  5f^o 

2  140 

I  8,^0 

I  525 

T  265 

I  000 

775 

560 

II 

2  8oo 

2  340 

1  780 

I  53'i 

1  264 

I  0-^2 

832 

640 

464 

12 

2  350 

I  <Soo 

I  4  So 

I  23o 

I  ot)4 

880 

700 

540 

390 

IJ 

2  OOO 

I  540 

I  265 

I  10  J 

910 

752 

595 

460 

334 

1\ 

I  730 

I  325 

I  100 

950 

7S0 

650 

Sio 

400 

290 

15 

1  500 

I  i6o 

950 

830 

63o 

590 

450 

348 

250 

i() 

I  320 

1  010 

8;o 

7JO 

God 

500 

395 

305 

220 

17 

I  180 

(JOO 

710 

bp 

578 

440 

350 

270 

194 

l8 

I  020 

79^ 

o;)4 

570 

473 

392 

310 

242 

174 

20 

84.} 

645 

535 

A()2 

381 

314 

250 

194 

22 

700 

530 

445 

3'H 

316 

263 

208 

24 

58/ 

450 

370 

320 

2<M) 

220 

lengths  on  the  job  as  required.     It  is  embedded  in  Portland-cement  mortar  be- 
tween the  blocks,  so  that  it  is  protected  both  against  rust  and  fire.     The  open- 


Soffit-Skew  Plain-Skew 

Fig.  27.     New  York  Reinforced,  Tile  Floor-arcn 

work  construction  of  the  wire  truss  enables  the  mortar  to  flow  freely  all  about 
it,  and  the  joint  can  be  thoroughly  filled  between  the  blocks,  and  the  wire  perfectly 


Fig.  28.     Wire  Reinforcement  for  New  York  Floor-arch 

embedded.  The  floor  has  successfully  passed  the  fire  and  load  tests  of  the 
Bureau  of  Buildings,  of  New  York,  and  as  a  result  has  been  used  in  a  number  of 
large  buildings  in  New  York.  Load  tests  were  made  to  determine  the  ultimate 
STRENGTH  of  the  6-in  arch  on  a  6-ft  span,  and  it  was  found  to  be  i  600  lb  per  sq  ft." 
The  Guastavino  Tile-Arch  System.  This  is  a  method,  devised  by  R. 
Guastavino  of  New  York  and  Boston,  of  constructing  floors,  partitions,  stair- 


842  Fireproofmg  of  Buildings  Chap.  23 

cases,  etc.,  by  means  of  thin  tiles,  i  in  thick,  about  6  in  wide,  and  from  12  to 
24  in  long,  all  bonded  together  in  Portland-cement  mortar  so  as  to  make  one 
solid  mass.  The  floors  are  built  by  spanning  the  spaces  between  the  girders 
with  single  arches,  vaults,  or  domes,  constructed  of  two,  three,  or  more  thick- 
nesses of  I -in  tiles,  the  number  of  thicknesses  depending  upon  the  dimensions 
of  the  arches  or  vaults.  In  its  best  application,  steel  is  used  in  tension  only  in 
tie-members;  and  in  place  of  steel  girders,  tile  girders  are  constructed  of  the 
same  material.  Wherever  steel  is  used  it  is  embedded  in  the  masonry  construc- 
tion. One  of  the  earhest  notable  buildings  in  which  this  system  was  used  is  the 
Boston  Public  Library  Building,  completed  in  1895.  Some  of  the  later  important 
constructions  are  the  Cathedral  of  St.  John  the  Divine,  New  York  City;  the 
Minnesota  State  Capitol  Building,  St.  Paul,  Minn.;  the  Girard  Trust  Company's 
Building,  Philadelphia;  the  Chicago  and  Northwestern  Railway  terminal 
station,  Chicago;  the  Pennsylvania  and  the  New  York  Central  Railroad  ter- 
minal stations,  New  York  City;  and  the  Hall  of  Fame,  University  of  New  York, 
New  York  City. 

An  illustration  of  the  wide  spans  that  can  be  safely  used  with  this  system  of 
construction  is  seen  in  the  Cathedral  of  St.  John  the  Divine  in  New  York  City. 
The  floor  above  the  crypt,  measuring  56  by  60  ft,  with  no  interior  supports, 
and  designed  to  carry  a  safe  load  of  400  lb  per  sq  ft,  was  constructed  on  this 
principle.  Wherever  a  vaulted  ceiling  is  desired  this  form  of  construction 
seems  to  be  well  adapted  for  use.  Floors  l:)iiilt  in  this  way  have  been  tested 
under  the  supervision  of  the  New  York  City  Building  Department  up  to  3  700  lb 
per  sq  ft,  on  spans  of  10  ft.  When  used  between  I  beams  the  only  steel  beams 
required  are  those  spanning  from  column  to  column.  Architects  contemplating 
the  use  of  this  system  of  construction  are  advised  to  consult  the  R.  Guastavino 
Company  before  letting  any  contracts.  Wherever  vaulted  ceilings  are  required 
this  construction  should  he  at  least  as  cheap  as  any  other  form  of  equally  fire- 
proof construction,  and  it  is  often  cheaper.  One  particular  advantage  of  the 
system  is  that  frequently  the  soffit-course  of  tile  is  of  pressed  or  glazed  mate- 
rial, making  a  most  effective  and  permanent  finish,  as  in  the  case  of  the  City 
Hall  station  of  the  New  York  City  subway.  This  station  was  constructed  for 
very  heavy  loads  and  without  the  use  of  steel. 

Incidentally,  attention  may  be  called  to  the  Rumford  tile  developed  in  con- 
nection with  this  construction,  to  be  used  as  the  first  course  of  tile,  that  is,  on 
exposed  surfaces  on  the  interior  of  auditoriums,  on  account  of  its  sound-absorbing 
character.  Professor  Sabine  of  Harvard  University  concluded  from  his  in- 
vestigations that  this  tile  "has  over  sixfold  the  absorbing  ix>wer  of  any  existing 
masonry  construction,  and  one  third  the  absorbing  power  of  the  best-known 
felt."* 

Concrete  Floors.  Concrete  used  in  fire-proof  floors  may  be  either  plain  or 
reinforced.  Without  reinforcement  its  use  is  generally  practicable  for  very 
short  spans  only,  on  account  of  its  weight.  In  this  chapter  it  is  considered  only 
as  a  floor-filling  between  steel  beams.  Chapter  XXIV  is  devoted  to  a  dis- 
cussion of  the  principles  governing  the  design  and  use  of  reinforced  concrete. 

Advantages  of  Reinforced  Concrete  for  Floor-Construction.  Although 
many  advantages  are  claimed  for  reinforced  concrete  over  the  tile  systems 
the  principal  advantage  is  that  of  economy,  taking  into  account  the  cost  of 
both  the  steel  framework  and  the  filling  between.  The  other  important  ad- 
vantages are  less  weight  per  square  foot  of  floor  (usually  but  not  always  the 
case),  adaptabihty  to  irregular  framing,  and  rapidity  of  construction.  Except 
in  the  immediate  locality  of  the  tile-factories,  fire-proof  floors  of  concrete  can 
*  The  Brickbuilder,  January,  1914. 


Fire-proof  Floor- Construction  843 

usually  be  placed  at  less  expense  than  is  incurred  in  setting  floors  of  hollow  tile; 
and  when  the  spans  permit  the  use  of  cinder  concrete,  the  concrete  floors  are 
lighter  than  those  of  the  tile,  when  both  floors  have  the  same  strength.  Some 
of  the  long-span  tile-systems,  on  the  other  hand,  are  much  lighter  than  many 
of  the  concrete  floors  that  are  now  being  built.  The  materials  entering  into  the 
construction  of  reinforced-concrete  floors  are  readily  obtained  in  almost  any 
locality,  no  specially  prepared  material  is  required,  except  perhaps  in  a  few 
special  forms  of  reinforcement,  and  the  work  can  be  done  almost  entirely  by 
unskilled  labor.  Less  capital  is  required  for  concrete  work  than  for  the  tile- 
constnictions,  and  no  material  need  be  carried  in  stock  during  an  idle  period, 
except  tools,  mixing-machines,  old  centering,  etc.  That  the  above  advantages 
are  real  is  sufliciently  proved  by  the  immense  amount  of  reinforced  concrete 
now  under  construction  throughout  the  world.  Wherever  a  floor  is  to  have  a 
finished,  cement  surface,  reinforced-concrete  constructions  are  considerably 
cheaper  than  any  tile  system,  because  in  the  former,  the  entire  concrete  is  used 
to  give  strength,  while  with  the  flat-tile  arches  it  merely  increases  the  dead  weight. 

Disdavantages  of  Reinforced  Concrete  for  Floor-Construction.  One 
decided  disadvantage  connected  with  concrete  floor-construction  is  the  inter- 
ference in  a  large  measure  with  the  progress  of  other  parts  of  the  work.  During 
its  installation,  there  is  a  constant  dripping  from  the 'floor,  making  it  some- 
times impossible  to  continue  other  lines  of  work.  After  the  completion  of  the 
floors  a  long  time  is  required,  depending  upon  the  weather,  for  the  drying  out, 
before  interior  fmishing  can  proceed. 

Composition  of  the  Concrete.  The  materials  used  for  concrete  are  dis- 
cussed on  pages  240  to  241  and  on  page  817.  Portland  cement,  only,  should 
be  used  in  any  floor-construction.  For  most  reinforced-concrete  floors,  having 
a  span  between  the  steel  beams  of  8  ft  or  less,  cinder  concrete  is  generally 
used  for  the  reason  that  concrete  mixed  with  cinders  is  much  lighter  than  that 
mixed  with  broken  stone  or  gravel.  The  usual  proportions  of  cinder  con- 
crete are  one  of  cement,  to  two  of  sand,  and  five  or  six  of  cinders.  For  a  first- 
class  concrete  the  cinders  must  be  screened  through  a  mesh  not  larger  than 
^/i  in,  and  only  hard-coal  cinders  should  be  used.  Good  cinders  may  some- 
times be  obtained  from  power-plants  using  soft  coal,  but  they  must  be  well 
screened  and  free  from*  ash.  Concrete  mixed  with  common  ashes,  a  mixture  oc- 
casionally used,  has  little  strength  and  is  totally  unrehable.  For  all  spans  ex- 
ceeding 8  ft,  either  gravel  or  broken  rock  should  be  used,  and  these  should 
be  mixed  with  one  part  cement,  to  two  of  clean  sharp  sand,  and  four  of  stone 
or  gravel.  The  weight  of  cinder  concrete  will  vary  from  80  to  no  lb  per 
sq  ft,  depending  upon  the  coarseness  of  the  material,  the  quantity  of  sand,  and 
the  amount  of  tamping.  For  ordinary  purposes  a  1:2:5  cinder  concrete 
should  be  used,  weighing  96  lb  per  cu  ft,  or  8  lb  per  sq  ft  per  inch  of  thickness. 

Forms  of  Reinforcement.  While  steel  in  small  sections  is  used  almost 
entirely  for  the  reinforcement,  there  is  a  great  variety  in  the  shape  and  char- 
acter of  the  rnetal  employed.  Different  forms  of  reinforcement  are  described 
and  discussed  in  Chapter  XXIV.  AH  of  them  may  be  used,  and  most  of  them 
are  now  being  used  in  floor-construction.  In  addition  to  those  forms  discussed 
there,  others  that  are  not  readily  adapted  to  beam-construction  are  used  in 
floor-construction.  Such  are  the  mi<:tal  fabrics  described  farther  on  under 
the  different  types  of  construction.  The  proper  position  for  the  reinforcement 
in  a  floor-construction  is  that  in  which  it  wiH  take  the  tensionai,  stresses, 
that  is,  in  floor-slabs,  near  the  lower  surface.  The  most  logical  form  is  that  of 
a  rod  or  bar.  a  greater  number  of  smafl  rods  or  bars  is  preferable  to  a  smaller 
number  of  larger  ones,  because  the  proportion  of  the  area  of  adhesion  between 


844  Fireproofing  of  Buildings  Chap.  23 

steel  and  concrete  to  the  sectional  area  of  steel  is  greater  in  the  former  case. 
This  result  is  apparently  attained  in  systems  in  which  wire  fabrics  are  used. 
But  the  disadvantage  in  the  use  of  the  smaller  reinforcement  is  the  greater  pos- 
sibility of  CORROSION  and  consequent  failure  of  the  construction.  There  is  a 
further  disadvantage  in  the  use  of  wire  fabrics;  they  are  easily  displaced  in 
the  process  of  placing  of  concrete,  either  getting  too  low  and  becoming  exposed 
to  fire  or  corrosion,  or  getting  too  high  with  a  corresponding  weakening  of  the 
floor.  Another  detail  that  must  be  remembered  when  using  metal  fabric  is 
that  the  mesh  must  be  large  enough  to  allow  a  good  bond  to  be  formed  between 
the  concrete  above  and  below  it.  Reinforcements  in  the  form  of  bars  set  ver- 
tically in  the  concrete  have  a  tendency  to  shear  through  slabs  which  are  under 
heavy  loads.  The  best  and  most  logical  reinforcement  for  fire-proof  floors 
consists  of  from  ^  to  ;>i-in  round  or  square  rods,  either  plain  or  deformed, 
spaced  at  varying  distances  to  suit  the  spans  and  loads. 

Necessity  for  Cross-Bars.  Where  wire  strands  or  bars  are  used  for  rein- 
forcement it  is  essential  to  have  cross-bars  as  well  as  transverse  tension- 
bars,  because,  when  the  loads  are  heavy  and  concentrated,  or  when  a  heavy 
body  falls  upon  a  slab  the  concrete  will  crack  between  the  carrying  bars.  This 
can  be  readily  demonstrated  by  testing  with  a  drop-test  a  floor-slab  that  has  no 
cross-bars.  When  the  load  is  uniformly  distributed  the  cross-bars  are  not 
brought  into  play;  floor-loads,  however,  are  more  often  concentrated  than 
uniformly  distributed 

Segmental  Concrete  Floor-Arches.  For  heavy  warehouse-floors  the 
ARCH  systems  are  preferable  to  the  flat  systems,  because  in  the  former  the 
concrete  is  used  in  its  strongest  form,  and  less  reinforcement  is  required.  In 
warehouses,  also,  a  ceihng  formed  of  a  series  of  arches  is  not  objectionable. 
For  spans  between  floor-beams  of  5  ft  or  less,  a  i  :  6  gravel-concrete  arch,  3  in 
thick  at  crown  and  without  any  reinforcement,  should  sustain,  without  crack- 
ing, a  distributed  load  of  i  500  lb  per  sq  ft.  For  spans  exceeding  5  ft,  the  cele- 
brated Austrian  experiments  (i 891-189 2)  see"m  to  show  that  the  reinforcing  of 
concrete  with  small  I  beams  adds  greatly  to  the  strength  of  the  arch;  but  that 
small  rods  or  netting  are  not  of  sufiicient  advantage  to  warrant  the  additional 
expense.*     Tests  made  on  arches  of  8-ft  span  gave  the  foUowing  results: 

A  concrete  arch,  s%  in  thick,  91^  in  rise,  broke  at  1 130  lb  per  sq  ft.  A  Monier 
arch  (wire  netting),  ii^o  in  thick,  101.4  in  rise,  or  about  one  half  the  thickness 
of  the  concrete  arch,  failed  at  i  217  lb  per  sq  ft.  A  brick  arch,  51,^  in  thick, 
9.85  in  rise,  failed  at  885  lb  per  sq  ft.  A  hoUow-brick  arch,  s^Yie  in  thick,  51^6 
in  rise,  failed  at  401  lb  per  sq  ft.  A  concrete  arch,  13-ft  span,  31^6  in  thick,  15^ 
in  rise,  failed  at  812  lb  per  sq  ft.  A  Melan  arch,  3^  in  thick,  11.4  in  rise,  broke 
at  3360  lb  per  sq  ft.  The  Melan  arch  had  I  beams  s],i  in  deep,  spaced  40  in 
apart.     The  structure  was  one  year  old  when  tested. 

The  concrete  arch,  considered  as  a  monolithic  construction,  if  built  of  stone 
concrete,  is  superior  to  the  brick  arch.  The  cinder-concrete  arch  is  inferior 
only  in  point  of  strength.  Such  an  arch  should  be  at  least  4  in  deep  at  the 
crown,  and  the  rise  should  be  not  less  than  one  eighth  the  span.  '  Cinder  con- 
crete should  not  be  used  for  spans  exceeding  8  ft.  The  strength  of  such  an  arch 
for  ordinary  cinder  concrete  is  about  the  same  as  that  of  a  6-in  segmental-tile 
arch  of  the  same  span,  a  s  gi  ven  in  Table  V.  All  arch  systems,  whether  of  concrete 
or  tile,  require  tie-rods  between  the  beams  to  take  up  the  thrust  of  the  arches. 
(See  page  865.) 

Weight  of  Segmental  Concrete  Arches.     The  weight  of  soHd  segmental 

Q-y,  *  See  Architecture  and  Building,  Jan.  4,  1896. 


Fire-proof  Floor-Construction 


845 


arches  may  be  found  by  the  following  formula  which  gives  results  approximately 
correct  when  the  rise  of  the  arch  is  not  more  than  one  sixth  of  the  span: 

W=(w/i2){c+4S/p) 
in  which 

W  =weight  of  arch,  in  pounds  per  square  foot; 
w  =  weight  of  material,  in  pounds  per  cubic  foot; 
c  =  thickness  of  arch  at  crown,  ^n  inches; 
5  =span  of  arch,  in  feet; 
p  =  ratio  of  span  to  rise  of  arch. 

Table  XI  gives  the  weight  per  square  foot  of  arches  having  a  thickness  of  4  in 
at  the  crown  and  constructed  of  stone  or  gravel  concrete,  taken  at  144  pounds  per 
cubic  foot,  for  various  spans  and  ratios  of  span*  to  rise.  For  greater  thicknesses 
at  the  crown  these  weights  should  be  increased  by  1 2  lb  for  each  inch  of  additional 
thickness.  For  other  materials  the  weights  are  directly  proportional  to  the 
weights  of  the  materials.  Thus,  if  cinder  concrete  weighing  102  lb  per  cu  ft  is 
used,  the  weight  of  the  arch  for  any  particular  span  and  ratio  of  span  to  rise 
is  102/144,  or  17/24,  of  the  weight  given  in  the  table  for  the  same  span,  ratio, 
and  thickness  at  the  crown.  Cinder  concrete  of  good  quality  weighs,  according 
to  density,  from  96  to  108  lb  per  cu  ft. 


Table  XI. 


Weight  per  Square  Foot  of  Segmental  Concrete  Arches 
Concrete  taken  at  144  lb  per  cu  ft 


Ratio  of 

span  to 

rise 

Thickness  of 

arch  at  crown, 

in 

Span  in  feet 

5 

6 

7 

8 

9 

ID 

6 

7 

7  V' 

8  ." 

4 
4 
4 
4 
4 

88 
85 
82 
80 
78 

96 
93 

89 
86 
84 

104 

100 

96 

93 

90 

112 

107 

102 

99 

96 

120 
114 
109 
106 
102 

128 
122 
116 
112 
108 

Flat  Reinforced  Floors.  These  floors  consist  of  slabs  of  concrete,  varying 
in  thickness  according  to  the  span  and  load,  constructed  between  the  steel 
floor-beams  and  reinforced  near  the  lower  surface  with  steel  in  one  of  the  shapes 
referred  to  on  page  843,  and  further  described  under  their  respective  names.  For 
ordinary  loads  the  thickness  of  the  slab  should  be  at  least  5^8  in  for  each  foot  of 
span,  with  a  minimum  thickness  of  sH  in.  Thinner  slabs  have  been  used,  but 
the  thickness  should  be  carefully  considered  for  each  particular  case.  The  floor- 
slabs  are  not  usually  of  the  same  depth  as  the  beams  supporting  them.  The 
position  of  the  slabs,  therefore,  determines  the  character  of  the  ceiling.  When 
the  bottom  of  the  slabs  is  placed  at  or  below  the  lower  flanges,  a  flat  ceiling  results, 
and  the  space  over  the  slabs  must  be  flUed  to  the  underside  of  the  flooring  with 
some  incombustible  material,  thus  often  increasing  the  weight.  When  the  slabs 
are  set  at  the  top  flanges,  there  is  a  paneled  ceiling,  unless  a  hung  ceiling  is  pro- 
vided. 

Strength  of  Flat  Floor-Construction.  The  following  empirical  formula, 
representing  the  practise  established  by  the  New  York  Building  Code,  is  based  on 
an  investigation  of  cinder  concrete  floor-construction  made  by  Harold  Perrine 


846 


Fircproofing  of  Buildings 


Chap.  23 


and  Oeor^e  E.  Strehan,*  undc.T  the  joint  auspices  of  Columbia  University  and 
the  Bureau  of  Buildings,  Manhattan,  New  York. 

w  =  Kda/S'^ 
in  wlii(  li 

w  =safe  load,  in  pounds  pf:r  sfjuare  foot,  including  the  weight  of  slab; 

d  =  distance,  in  inches,  from  toj)  of  slab  to  center  of  reinforcement; 

a  =  cross-sectional  area,  in  square /inches,  of  the  reinforcement,  for  each 
foot  of  width  of  slab; 

S  =span,  in  feet,  of  slab; 

K  =a  coefficient  with  values  as  follows:  when  cinder  concrete  is  used, 
26000  if  the  reinforcement  consists  of  steel  fabric  continuous  over 
supports;  18000  if  the  reinforcement  consists  of  steel  rods  or  other 
shapes  securely  hooked  over  or  attached  to  the  supports;  and  14  000 
if  the  reinforcement  is  not  continuous  over  the  supports;  and  when 
stone  or  gravel  concrete  is  used,  30000,  20000,  and  16000,  respect- 
ively, for  the  corresponding  conditions. 

The  material  contemplated  by  this  formula  is  a  concrete  consisting  of  one  part 
of  J'ortland  cement,  and  not  more  than  two  [)arts  of  sand,  and  five  parts  of  stone, 
gravel,  or  cinders.  The  reinforcement  consists  either  of  steel  rods  or  other 
suitable  shaixis,  or  steel  fabric.  In  case  cold-drawn  steel  fabric  is  used,  the  ten- 
sional  reinforcement  should  not  be  less  than  ^Moo%,  and  in  case  other  forms  of 
reinforcement  are  us(;d,  not  l(;ss  than  2>^oo%,  the  percentage  being  based  on  the 
sectional  area  of  the  slal)  al)ove  the  center  of  the  reinforcement.  For  proper 
Iprotection  against  fire  and  corrosion  the  center  of  the  rciiifoncment  should  be  at 
least  I  in  al)ove  the  lK)ttom  of  the  slab,  l)Ut  there  should  always  be  at  least  %  in 
of  concrete  outside  of  any  part  of  the  reinforcement.  The  formula  should  not  be 
applied  to  spans  exceeding  8  ft.  Cinder-concrete  floors  should  be  limit(;d  to 
that  span  in  any  case. 

Expanded  Metal.  This  mat(;rial  is  now  so  well  known  that  it  requires  only 
a  brief  descrii)tion.     The  diamond  mesh  shown  in  Fig.  29  is  used  in  floor-con- 


FiG.  29.     Expanded  Metal,  Diamond  Mesh 

struction.  For  this  purpose;  the  3-in  juesh  is  used,  the  size  of  the  mesh  being 
designated  by  the  width  of  the  diamond  shaped  spaces.  It  comes  in  sheets 
8,  10,  12,  and  j6  ft  long,  and  from  3  to  8  ft  wide,  according  to  the  width  of  the 
mesh.  It  is  made  from  a  soft,  tough  .steel  of  fine  texture,  varying  in  thickness 
from  No.  13  to  No.  r,  Stubbs  gauge.     The  standard  sizes  offered  by  the  Cq 


•  Trans.  Am.  Soc.  C.  E.,  Vol.  LXXIX,  191S.  pagc  .-523. 


the  Uoiia, 

J 


Fire-proof  Floor-Construction 


847 


soHdated  Expanded  Metal  Companies  and  the  Northwestern  Expanded  Metal 
Company  are  in  accordance  with  a  decimal  variation  in  cross-section,  thus: 
0.25,  0.30,  0.35,  0.40,  etc.,  sq  in  per  ft  of  width.  The  designations  of  the  sizes 
indicate  the  cross-sectional  areas  per  foot  of  width,  thus:  3-9-20  denotes  a  3-in 
mesh,  No.  9-gauge  plate,  and  a  cross-sectional  area  of  0.20  sq  in  per  ft  of  width. 
The  Youngstown  Iron  &  Steel  Company  and  the  General  Fire  Proofing  Company 
offer  from  eight  to  ten  sizes  of  expanded  metal  with  a  range  sufficient  to  take 
care  of  the  needs  of  concrete-floor  designs. 

Concrete  and  Expanded-Metal  Floor-Construction.  Of  the  numerous 
styles  of  floor-construction  possible  with  expanded-metal  reinforcement,  the 
type  shown  in  Fig.  30  is  generally  used  and  recommended.     At  the  right  hand 


Fig.  30.     Concrete  Flodr-construction.     Expanded-metal  Reinforcement 

of  the  figure  is  shown  the  construction  when  there  are  steel  beams,  and  at  the 
left  hand  when  there  are  reinforced-concrete  beams.  The  advantages  claimed 
for  expanded  metal  as  a  reinforcement  are  La  better  arrangement  in  the  con- 
crete than  is  possible  with  an  equal  amount  of  material  in  any  other  form;  great 
efficiency  in  the  carrying  of  concentrated  loads,  due  to  the  obliquity  of  the 
strands;  a  uniform  distribution  of  small  sections  at  frequent  intervals,  pref- 
erable to  larger  sections  at  greater  intervals;  an  increased  ultimate  strength 
and  high  elastic  limit,  due  to  the  method  of  manufacture,  thus  combining 
the  advantages  of  a  low-carbon  steel  with  a  high  ultimate  strength;  and  a 
mechanical  bond  with  the  surrounding  concrete.  When  used  between  I  beams, 
without  other  reinforcement,  the  spans  usually  vary  from  6  to  8  ft,  although 
panels  12  ft  wide  between  beams  have  been  constiucted.  In  placing  expanded 
metal  in  the  concrete,  it  is  necessary  to  lap  the  sheets  on  the  ends  up  to  and 
including  3-9-20,  one  diamond  (8  in);  from  3-9-25  to  3-6-60,  one  and  a  half 
diamonds  (12  in);  and  heavier  than  3-6-60,  two  diamonds  (16  in). 


Table  XII. 

Properties  of  Rib-Metal 

Size- 

Width  of 
sheet, 

Area  of  metal 
per  foot  of 

number 

width, 

sq  m 

2 

I") 

0.540 

3 

24 

0.360 

4 

32 

0.270 

5 

40 

0.216 

6 

48 

0. 180 

7 

56 

O.IS4 

8 

64 

0.13s 

Rib-Metal.  The  Trussed  Concrete  Steel  Company  of  Detroit,  Mich.,  is 
manufacturing  a  steel  reinforcement  for  concrete  floors  consisting  of  a  series 
of  straight  ribs  or  main  tension-members  rigidly  connected  by  light  cross-ties 
expanded  from  the  same  sheet  of  metal  in  the  form  of  a  mesh  (Fig.  31).  It 
is  manufactured  from  medium  open-hearth  steel  in  seven  sizes  of  mesh,  2,  3,  4, 


848 


Fireproofing  of  Buildings 


Chap.  23 


5,  6,  7,  and  8  in,  and  in  lengths  up  to  i8  ft.     It  is  supplied  in  either  flat  or  curved 
sheets,  and  longer  lengths  and  special  sizes  of  mesh  can  be  provided.     The  width 


Area  of  rib  0.09  sq  in 

Ribs  spaced  2,  3,  4,  5,  6,  7,  and  8  in 

Fig.  31.     Rib-metal  Reinforcement  for  Concrete  Floors 


of  sheet  is  governed  by  the  size  of  mesh, 
there  being  nine  bars  or  ribs  in  each  sheet. 
Welded-Metal  Fabric.  The  CHnton 
Wire  Cloth  Company  manufactures  a  welded 
fabric  or  mesh  which  has  been  extensively 
used  in  the  United  States  as  a  reinforce- 
ment for  concrete  construction  of  all  kinds. 
Fig.  32  shows  the  general  style  of  the  fabric, 
the  meshes  and  wires  of  which  can  be  varied 
indefmitely,  upwards  from  a  i-in  mesh. 
The  advantage  claimed  for  this  fabric  as  a 
reinforcement  for  slab-construction  is  that 
the  carrying  wires  may  be  varied,  both  in 
size  and  spacing,  to  give  the  necessary  area 
for  any  given  weight  and  span,  and  the 
distriliuting  or  cross-wires,  also,  may  be 
varied  in  the  same  way.  The  direction  of 
the  wires  coincides  with  the  line  of  stress, 
so  that  there  is  no  tendency  to  distort  the 
rectangle  of  the  mesh.  The  cross- wires, 
being  welded  to  the  carrying  wires,  are 
rigidly  held  in  place  and  prevent  the  latter 
from  shpping  in  the  concrete.  The  claim 
is  made  that  the  elongation  that  takes  place 
in  the  carrying  wire  under  the  stress  of  heavy 
loading,  is  divided  along  the  carrying  wire 
as  often  as  the  cross-wires  occur,  instead  of 
being  concentrated  at  one  point  as  is  the 
case  with  loose  rods  or  wires.  In  the  meshes 


Fig.  32.   Welded-metal  Fabric.    Clii 
•  ton  Wire  Cloth 


Fire-proof  Floor-Construction 


849 


Commonly  used  the  carrying  wires  vary  from  No.  lo  to  No.  3  in  size  (Washburn 
&  Moen  gauge),  and  are  spaced  from  1  lo  4  in  on  center?;  while  the  distribut- 
ing wires  vary  from  No.  11  to  No.  6  in  size,  and  are  spaced  from  3  to  12  in  on 
centers.  Welded  metal  is  manufactured  in  long  rolls,  and  l>y  its  use  all  joints 
and  laps  are  avoided.  A  floor  can  be  made  with  a  continuous  metallic  bond  from 
wall  to  wall,  that  is,  when  the  mesh  is  laid  over  the  tops  of  the  steel  beams.  The 
width  of  the  rolls  varies  from  48  to  86  in. 

Lock-woven  Steel  Fabric.  This  fabric*  is  made  up  in  a  rectangular  mesh, 
the  usual  spacing  of  the  longitudinal  wires  being  3  in  on  centers  and  that  of  the 
•transverse  wires  12  in  on  centers.     These  spacings  can  be  easily  varied  to  meet 


Longitudinal  Wire 


Transverse  Wire 


DETAIL  OF  LOCK 
Fig.  33.     Lock-woven  Fabric 

special  conditions.  The  fabric  is  usually  made  54  in  wide  and  comes  in  rolls 
containing  from  150  to  600  hn  ft,  the  150-ft  length  being  commonly  used.  While 
the  usual  width  of  the  fabric  is  54  in,  it  can  be  varied  in  multiples  of  i3^  in  from 
18  in  up  to  a  maximum  of  54  in.  The  longitudinals  or  carrying  wires  of  the 
fabric  are  held  in  place  by  the  transverse  wires  as  shown  in  Fig.  33.    The  longi- 


Stonc  or  Cinder  Concrete. 


^  Lock-voven  Steel  Fabric. \^^- 


wm^$i^ 


Beam  Wrap/ 
Fig.  34.     Concrete  Ceiling-slab  Reinforced  with  Lock-woven  Fabric 

tudinal  wires  can  be  furnished  in  sizes  \-arying  from  No.  14  to  No.  7  gauge,  the 
sectional  area  of  the  fabric  ranging  from  0.0201  sq  in  to  0.1968  sq  in  per  ft  of 
width.  Heavier  fabric  can  be  furnished  to  meet  special  conditions.  The  trans- 
verse wires  are  usually  No.  14  or  No.  12.  The  longitudinal  wires  are  made  by  a 
special  process  which  gives  them  an  ultimate  tensii-e  strength  of  from  150  000 
to  180  000  lb  per  sq  in,  with  a  correspondingly  high  elastic  limit.  The  fabric 
can  be  furnished  either  black  or  galvanized.  This  fabric  has  the  general  advan- 
tages common  to  any  continuous,  rectangular-mesh  material,  as  it  provides  a 
continuous  bond  from  end  to  end  of  a  structure,  and  the  wires  are  so  placed  that 
they  lie  parallel  to  the  lines  of  stresses  which  they  are  called  upon  to  carry.  The 
standard  type  of  construction  for  floor-slabs  and  roof-slabs  is  similar  to  that 
shown  in  Fig.  30  for  expanded  metal.  Where  a  flat  ceihng  is  desired  the  type 
of  construction  shown  in  Fig.  34  is  very  useful.  Both  of  these  types  have  been 
tested  by  the  Bureau  of  Buildings  of  the  City  of  New  York  on  spans  up  to  ana 
*  Controlled  by  W.  N.  Wight  &  Company,  New  York  City. 


850  Fireprooling  of  Buildings  Chap.  23 

including  6  ft,  for  live  loads  running  from  130  to  3,30  lb  per  sq  ft;  and  on  spans  of 
7  ft,  approvals  have  been  given  up  to  175  lb  per  sq  ft,  and  on  spans  of  8  ft,  up  to 
150  lb  per  sq  ft.  The  arches  were  constructed  of  cinder  concrete  and  the  figures 
given  are  based  on  a  factor  of  safety  of  10.  In  addition  to  its  use  for  the  con- 
struction, of  floor-slabs  and  roof-slabs,  the  fabric  is  suitable  for  use  in  panel- walls, 
sewers,  penstocks,  and  tanks,  and  in  all  other  places  where  a  sheet-reinforcement 
can  be  used  to  advantage. 

Triangle-Mesh  Wire-Fabric  Reinforcement.  Under  this  name  the  Ameri- 
can Steel  and  Wire  Company  is  manufacturing  a  wire  fabric  of  cold-drawn  steel 
wire  for  the  reinforcement  of  fire-proof  floors.  A  detail  of  the  standard  material 
is  shown  in  Fig.  35.  The  triangular  mesh  is  built  up  of  either  single  or  stranded 
longitudinals  with  the  cross-wires  or  bond-wires  running  diagonally  across  the 
width  of^  the  fabric.  It  is  claimed  that  the  triangular  mesh  affords  an  even 
distribution  of  the  steel,  reinforcing  in  every  possible  direction,  and  that  the 


Fig.  35.     Wire-fabric  Reinforcement,  Triangular  Mesh 

Strength  is  increased  by  reason  of  the  truss-construction.  For  floor-reinforce- 
ment, this  fabric  is  used  the  same  way  that  any  of  the  other  fabrics  previously 
described  are  used,  and  as  indicated  in  Figs.  26,  30,  and  34.  The  longitudinal 
wires  in  Triangle  Mesh  are  invariably  spaced  4  in  on  centers,  but  the  diagonal 
wires  may  be  spaced  either  4  or  8  in  apart.  The  manufacturers  can  furnish 
different  styles,  giving  variations  in  the  cross-sectional  area  from  about  0.032  sq 
in  to  about  0.395  sq  in  per  ft  in  width  of  the  fabric,  or  a  variation  in  weight  per 
square  foot  of  from  0.2  to  1.6  lb.  The  material  is  furnished  either  galvanized 
or  plain.  The  longitudinal  wires  are  made  of  either  a  single  wire  or  of  two  or 
three  wires  stranded.  The  cross-wires  or  bond-wires  are  of  either  No.  14  or 
No.  i2>^  gauge.  Special  sizes  of  additional  area  can  be  furnished  upon  applica- 
tion>to  the  company.  This  fabric  is  said  to  have  an  ultimate  strength  of  not  less 
than  85  000  lb  per  sq  in. 

Dovetailed  Corrugated  Sheets.  Ferroinclave.  Sheets  of  thin  steel  corru- 
gated so  as  to  form  dovetailed  grooves  have  been  used  as  a  reinforcement  and  cen- 
tering for  concrete-steel,  the  dovetailing  serving  to  unite  the  sheets  to  the  con- 
crete.    The  Brown  Hoisting  Machinery  Company  of  Cleveland,   Ohio,   has 


Fire-proof  Floor-Construction  851 

patented,  under  the  name  Ferroinclave,  a  tapered  corrugation  which  is  small 
enough  to  hold  hard  mortar,  and  hence  can  ])e  plastered  on  the  under  side.  Fig. 
36  shows  a  partial  section  of  the  Ferroinclave  corrugated  sheets,  the  depth  of  the 
corrugations  being  3^  in,  the  distance  from  center  to  center  of  corrugations  2  in, 
and  the  corrugations,  with  the  opening  between  the  edges,  K  in.  The  tapering  of 
the  corrugations  is  of  especial  advantage  for  roofs,  as  it  allows  the  sheets  io  be 
lapped  at  the  end-joints,  making  a  roof  absolutely  tight,  even  if  water  should 
penetrate  the  cement  coating.  The  principal  advantage  in  the  use  of  corru- 
gated sheets  for  floor-construction  is  that  they  sustain  the  concrete,  when  the 
spans  are  of  moderate  width,  before  it  has  set,  thus  saving  the  cost  of  centering 
and  the  time  required  to  put  it  in  place.  This  advantage,  however,  appears  to 
be  offset  by  the  high  cost  of  the  sheets  when  they  have  to  be  shipped.  For  roofs, 
however,  this  construction  is  light  and  relatively  cheap,  as  the  total  thickness 
need  not  exceed  iK  in  for  spans  of  4  ft  10  in.  To  make  the  roof  water-tight 
some  water-proof  covering  is  required.  With  a  good  coat  of  hard  plaster  or 
gauged  mortar  on  the  under-side,  the  iron  will  not  be  affected  by  heat  in  case  of 
fire  until  a  considerable  time  has  elapsed;  and  even  if  the  mortar  on  the  under- 
side should  be  more  or  less  dislodged  by  the  streams  of  water,  it  can  be  replaced, 

Fig.  36.     Ferroinclave  Reinforcement  for  Concrete  Floors 

at  a  very  slight  expense.  Another  advantage  in  the  use  of  Ferroinclave  for  roofs 
is  that  a  building  can  be  covered  and  made  water-tight  in  the  mo.st  severe  winter 
weather  and  the  cement  appHed  during  the  following  spring. 

Ferroinclave  is  made  in  sheets  20  in  wide  and  up  to  10  ft  long,  and  it  is  usu- 
ally of  No.  24  gauge.  For  roofs  it  is  attached  to  purlins  in  the  same  way  that 
iron  roofmg  is  attached,  the  most  economical  spacing  of  the  purlins  being  4  ft  loj^^ 
in  center  to  center,  which  accommodates  sheets  10  ft  long  and  leaves  an  end- 
lap  of  3  in.  For  the  cement  top  coat  on  roofs,  a  mixture  of  one  part  Portland 
cement  to  two  parts  sand,  applied  to  a  thickness  of  %  in  above  the  top  of  the 
sheets,  is  sufficient.  For  floors  a  rich  gravel  or  crushed-stone  concrete  should  be 
used,  the  thickness  being  governed  by  the  span  and  the  loads  to  be  supported. 

The  following  table  shows  the  ultimate  strength  of  No.  24  Ferroinclave  with 
different  thicknesses  of  concrete,  as  determined  by  actual  tests  with  sheets  20  in 
wide  over  a  4-ft  10 ^-in  span: 

Thickness  in  inches  of  i  :  2  mortar  above 

the  metal ii^       2        21,^         3         31.^         4 

Ultimate  strength  in  lb  per  sq  ft  for  a  span 

4  ft  loH  in 615     915     1220    1560     i860    2120 

A  factor  of  safety  of  6  should  be  ample  for  ordinary  loads. 

Ferroinclave  is  especially  adapted  for  the  roofs  and  floors  of  large  manufac- 
turing plants,  and  may  be  used  to  advantage  for  partitions,  stair-treads,  vats, 
water-closet  partitions,  and  fire-proof  doors. 


852 


Fireproofing  of  Buildings 


Chap.  23 


Berger's  Multiplex  Steel  Plate.  Fig.  37  shows  a  section  of  a  corrugated 
steel  plate  manufactured  by  the  Berger  Manufacturing  Company,  Canton, 
Ohio,  for  floor  and  roof -construction,  the  plate  being  an  invention  of  G.  Fugman. 
As  shown  in  the  illustration,  it  consists  of  a  series  of  vertical  corrugations  of 
sheet  steel,  painted  or  galvanized,  ending  at  the  top  and  bottom  in  three  half- 
circle  arches,  separating  the  vertical  sides  of  the  corrugations  from  each  other 
and  giving  stiffness  to  the  top  and  bottom  of  the  plate.  The  plate  is  made  with 
depths,  D,  of  2,  23.4,  3,  31.^,  and  4  in,  and  in  corresponding  widths  of  131,^,  14, 
14H,  and  15  in.  The  maximum  length  of  plate  is  10  ft.  It  can  be  made  of  any 
gauge  of  steel,  from  No.  24  to  No.  16,  but  No.  18  is  as  heavy  a  weight  as  is 
generally  required.  For  floors  and  roofs,  the  corrugated  plate  is  laid  on  top  of 
the  beams  and  the  top  portion  filled  with  concrete  and  leveled  off  about  i  in 
above  the  plate.  For  wooden  floors  the  nailing-strips  may  be  embedded  in 
the  concrete  and  the  bottom  of  the  strips  raised  only  about  yi  in  above  the 
top  of  the  plate.  The  construction  is  very  hght  and  strong  and  requires  no 
centering.    It  cannot  be  plastered,  however,  on  the  under  side,  and  where  a 


Fig.  37.     Berger's  Multiplex  Steel  Plate 


plaster  ceiUng  is  required  it  must  be  constructed  independently  of  the  plate  by 
means  of  furring-strips  and  metal  lath.  The  weight  of  the  4-in  plate,  with  a 
1:2:5  furnace-slag  concrete  leveled  i  in  above  the  top  of  the  plate,  is  about 
40  lb  per  sq  ft,  and  the  safe  load  for  a  io-ft  span  is  given  at  270  lb  per  sq  ft. 
While  this  floor  has  several  practical  advantages,  it  cannot  be  considered 
thoroughly  lire-proof,  because  the  metal  is  exposed  on  the  bottom.  But  with 
a  plastered  cdiling  on  the  under  side,  the  iron  would  probably  not  be  affected 
by  any  ordinary  fire  before  the  latter  could  be  controlled. 

Permanent  Centering.  Numerous  forms  of  sheet-metal  fabrics  have  been 
developed  in  recent  years  for  use  as  floor-reinforcements.  They  consist,  gen- 
erally, of  steel  plates  pressed  into  series  of  solid  ribs,  variously  spaced,  between 
which  the  metal  is  stamped  or  perforated,  or  deployed  into  an  open  mesh- work. 
The  characteristic  form  is  shown  in  Fig.  3S.  The  mesh  is  kept  small  enough 
to  prevent  ordinary  concrete  from  passing  through.  For  use  as  a  reinforcement 
the  sheets  are  furnished  either  in  flat  or  segmental  form.  A  i  :  21,-2  :  5  stone  or 
cinder  concrete  may  be  used,  the  thickness  depending  upon  the  span  and  the  load 
to  be  provided  for.  For  spans  exceeding  from  3  to  5  ft,  according  to  the  gauge  of 
metal,  the  sheets  must  be  temporarily  supported  until  the  concrete  has  set.  The 
difficulty  of  providing  efficient  fire-protection  on  the  underside  of  reinforce- 
ments of  this  type,  and  around  the  lower  flanges  of  the  supporting  steel  beams, 
is  a  serious  disadvantage.  Besides,  the  bond  between  the  metal  and  the  floor- 
concrete  is  on  one  side  of  the  sheet  only.     Some  of  the  forms  now  on  the  market. 


Fire-proof  Floor-Construction  853 

with  their  special  characteristics,  are  briefly  described  in  the  following  para- 
graphs. 


Fig.  38.     Permanent  Centering.     Characteristic  Form 

Rib-Truss.  These  plates,  manufactured  by  the  Berger  Manufacturing  Com- 
pany, Canton,  Ohio,  are  designed  with  five  longitudinal  ribs,  6  in  on  centers, 
and  1/2,  %,  I,  and  ly,  in  high.  The  metal  between  the  ribs  is  slit  into  truss- 
loops  which  are  further  reinforced  with  beads  at  right-angles  to  the  main  ribs. 
The  standard  sheets  are  24  in  in  width  and  are  carried  in  stock  in  lengths  up  to 
12  ft,  and  made  of  No.  24,  26,  27,  and  28-gauge  metal. 

Self-Sentering.  In  this  form,  manufactured  by  the  General  Fireproofing 
Company,  Youngstown,  Ohio,  the  ribs  are  lyie  in  in  height,  3%  in  on  centers, 
and  connected  by  expanded  metal.  The  sheets  are  29  in  in  width  and  come  in 
lengths  from  4  to  12  ft,  varying  by  units  of  i  ft.  Self-Sentering  is  made  of  Nos. 
24,  26,  and  28-gauge  metal.     (Sec,  also,  page  885.) 

Hy-Rib.  Ily-rib,  controlled  by  the  Trussed  Concrete  Steel  Company 
Detroit,  Mich.,  is  made  in  sheets  measuring  10^/2  in  from  center  to  center  of 
outside  ribs  and  having  four  ribs  i>i6  in  in  height;  and  also  in  sheets  14  in  in 
width  having  three  ribs.  There  is  also  a  type  known  as  the  Deep  Rib.  The 
lengths  are  6,  8,  10,  and  12  ft.  The  sheets  are  of  No.  24,  26,  or  28  United  States 
gauge,  and  are  furnished  either  flat  or  in  various  types  of  curves.  (See,  also, 
page  886.) 

Corr-Mesh.  Corr-Mesh  is  manufactured  by  the  Corrugated  Bar  Company, 
Inc.,  Buffalo,  N.  Y.,  which  supplies,  also,  special  clips  for  splicing  and  fastening 
the  mesh  to  the  supporting  members.  It  is  made  in  two  types.  One  has  ribs 
%  in  high,  spaced  3%  in  on  centers;  the  other  type  has  ribs  Yiq  in  high,  spaced 
3  in  on  centers.  For  the  ^.i-in-rib  Corr-Mesh  the  sheets  are  13  in  wide,  and  for 
the  -^ie-in-rib  Corr-Mesh  they  are  18  in  wide.  The  mesh  is  furnished  in  United 
States  standard  gauges,  Nos.  24,  26,  and  28.  Standard  sheets  are  6,  8,  10,  and 
12  ft  in  length.  No  allowance  need  be  made  for  side  laps,  but  at  least  2  in  should 
be  allowed  for  end-laps. 

Duplex  Self-Centering.  The  Youngstown  Iron  Steel  Company,  Youngs- 
town, Ohio,  manufactures  the  Duplex  Self-Centering  It  is  23  in  in  width,  is 
furnished  in  lengths  of  from  4  to  12  ft,  and  in  Nos.  24,  26,  and  28  metal,  United 
States  gauge.  It  weighs  1.37  lb  per  sq  ft  for  the  No.  24  gauge,  1.03  lb  for  the 
No.  26  gauge,  and  0.86  lb  for  the  No*.  28  gauge;  and  it  has  a  corresponding  cross 
sectional  area  per  foot  of  width,  of  0.411,  0.308,  and  0.257  sq  in. 

Sectional  Systems.  During  recent  j'ears,  the  unit  system  or  separately 
MOLDED  SYSTEM,  cousisting  of  sliop-madc  reinforced-concretc  members,  such  as 


854 


Fireproofing  of  Buildings 


Chap.  23 


girders,  lintels,  floor-slabs,  and  wall-panels,  made  at  a  factory  and  shipped  to  the 
sites  of  building  operations,  has  been^ receiving  considerable  attention  in  this 
country.  This  system  is  more  completely  discussed  in  Chapter  XXiV,  page 
953,  under  the  title  Separately  Molded  Construction.  Separately  molded 
members  have  been  used  between  the  steel  beams  of  fire-proof  floor-construction 
as  a  substitute  floor-filling  for  the  usual  terra-cotta  or  concrete  floor-arches. 
The  advantages  of  such  systems,  where  they  are  practicable,  are  obvious.  Such 
members  are  usually  made  as  large  as  can  be  conveniently  handled  and  of  com- 
paratively long  span. 

Disadvantages  of  Sectional  Systems.  The  reason  that  the  sectional 
SYSTEMS  have  not  found  favor  is  because  they  necessitate  a  fairly  uniform  spacing 
of  beams  throughout  a  structure,  and  this  is  generally  impracticable.  The 
casting  of  the  parts  has  hitherto  not  been  commercially  successful,  as  the  forms, 
although  used  repeatedly,  have  been  more  expensive  than  the  usual  centering 
at  the  building;  and  it  is  also  generally  necessary  to  use  a  concrete  that  is  richer 
and  more  carefully  prepared  in  order  that  it  may  stand  the  additional  handling. 
Even  with  all  possible  care,  the  breakages  in  transportation  are  considerable. 
As  the  methods  of  manufacture  of  factory-made  members  are  constantly  being 
perfected,  chiefly  in  mechanical  contrivances  for  cheapening  the  forms  and  reduc- 
ing the  handling  during  the  process  of  manufacture,  the  economy  of  this  system 
is  being  substantiated,  and  particularly  when  it  is  used  in  combination  with  a 
light  structural-steel  fire-proofed  frame. 

Waite's  Concrete  Beam.  In  Fig.  39  is  shown  a  type  of  sectional  floor- 
CONSTKUCTION  that  has  been  used  in  a  number  of  buildings  by  the  Standard 


Jlod  Relnforceownt 
Cliaanel  Reinforcement 


Fig.  39.     Waite's  Concrete  I  Beams 


Concrete  Steel  Company  of  New  York  City.  The  floor-construction  consists  of  a 
series  of  concrete  I  beams  lo  or  12  in  in  depth,  supported  on  the  lower  flanges  of 
the  steel  beams,  which  are  spaced  from  5  to  7  ft  apart.  The  concrete  beams  are 
set  about  18  in  apart  and  the  spaces  between  the  lower  flanges  are  filled  in  with 
a  cinder  concrete  of  the  same  composition  as  the  I  beams.  On  the  tops  of  the 
concrete  beams  is  placed  a  metal  fabric  of  small  mesh  on  which  a  lean-concrete 
slab  is  laid.  This  makes  a  comparatively  light  floor-construction,  because  of 
the  large  spaces  between  the  concrete  beams.  The  concrete  I  beams  are  cast 
at  the  shop  and  allowed  to  harden  before  they  are  sent  to  the  building.  In 
the  lower  flange  is  inserted,  as  shown,  a  steel  reinforcement,  of  small  circular 
or  other  cross-section,  to  furnish  the  necessary  tensile  strength.  The  beams 
are  cast  with  the  proper  lengths,  in  accordance  with  the  drawings;  and  any 
slight  variations  at  the  building  are  made  up  by  filling  the  spaces  between  the 
ends  of  the  concrete  beams  and  the  webs  of  the  steel  beams,  and  covering  the 
webs  of  the  latter  with  concrete.     A  similar  construction,  consisting  of  a  series 


Fire-proof  Floor-Construction 


855 


of  T  beams,  with  lower  flanges  11,^2  i"  thick  and  12  in  wide  and  stems  2  In  thick 
and  12  in  deep,  of  i  :  4  cinder  concrete,  reinforced  with  Mo-in  rods  near  the 
flanges,  and  without  floor-finish  of  any  kind,  successfufly  withstood  the  fire, 
water,  and  load  tests  of  the  New  York  City  Bureau  of  Buiklings  after  having 
been  constructed  28  days.  This  system  has  proved  to  he  practical  in  cases  in 
which  a  flat  or  level  ceiling  is  required  and  the  steel  floor-beams  are  10  in  or 
more  in  depth.  The  cost  of  construction  compares  favorably  with  that  of 
other  flush-ceiling  types. 

The  Siegwart  Floor  System.     This  system  (Fig.  40),  designed  by  Hans 
Siegwart,  of  Lucerne,  Switzerland,  is  in  extensive  use  in  that  country.     The 


^  1  X  2^4  wood  sleepers 


2  •  yi°  rods  at  supports 


iiir-  r    i^i^iiiiirii  III  .r  r.  iiiiii-iiiiiiii-iri 

-  2  -  3C  °  rodb  at  supports 
TYPICAL  FLOOR  BLOCK 

6^0  Vide  IsVlonu.  Total  Weight  48G7^or  G2.3^ sq.ft. 
llein  f orcement  1  -f ^"x  %'  Havemeycr  Bar  in  eacti  Web 
Mixture(l  -2»4-3i4)top  inch  1-5  Mortar 

Fig.  40.     Siegwart  Reinforced-concrete  Floor-construction 


sectional  units  are  usually  made  10  in  in  width,  the  height  and  reinforcement 
varying  with  the  span  and  load.  In  a  test  on  a  beam  of  this  type,  designed  to 
carry  a  Uve  load  of  150  lb  per  superficial  ft  over  a  i6-ft  span,  the  construction 
withstood  a  satisfactory  four-hour  fire  test  with  a  load  of  150  lb  per  sq  ft,  followed 
after  the  fire  by  a  test  with  a  load  of  600  llj  per  sq  ft.  It  is  claimed  for  this 
system,  that  using  the  same  working  units  for  the  strength  of  the  material,  the 
dead  weight  of  the  construction  is  only  one  half  that  of  a  monolithic  reinforced- 
concrete  floor  designed  to  carry  the  same  load  with  the  same  percentage  of 
reinforcement.  "The  Siegwart  Company  claim  their  method  to  be  much 
cheaper  than  monolithic  floors.  From  quotations  furnished  by  their  Canadian 
Company,  the  price  in  Montreal  is  quite  a  little  less  than  the  author's  expe- 
rience for  monolithic  floors  in  the  same  city,  ranging  from  17  to  26  cts  per  sq  ft, 
erected  for  various  spans  and  loads."*  A  modification  of  the  Siegwart  system 
has  been  developed  by  Gros\'enor  Atterbury,  and  has  been  employed  in  two-story 
and  three-story  residence-buildings  for  the  Sage  Foundation  Homes  Company 
at  Forest  HiUs  (Long  Island),  N.  Y. 


SECTION 
Fig.  41.  ^^  Climax  Reinforced-concrete  Floor-construction 


The  Climax  Floor  System.     This  system  (Fig.  41)  was  designed  by  S.  M. 
Randolph.     The  design  is  similar  to  that  of  the  Siegwart  floor  system. 

*  Chas.  D.  Watson,  Concrete  Construction  with  Separately  Moulded  Members  and 
Costs,     Proc.  Nat.  Asso.  Cement  Users,  Vol.  VI,  1910. 


856 


Fireproofing  of  Buildings 


Chap.  23 


The  Vaughan  Floor  System.  The  Vaughan  Company  of  Detroit,  Mich., 
is  manufacturing  a  shop-made  unit  which  is  employed  considerably  throughout 
the  Middle  West.  The  general  form  of  this  unit  is  like  that  of  Waite's  concrete 
beam,  shown  in  Pig.  39. 

The  Watson  Floor  System.  Two  typ^s  of  sectional  floor  systems  foi  fire- 
proof floor-fillings  between  steel  beams  are  shown  in  Figs.  42  and  43.     Foi  long 


Factory  made  Unit 
Concrete  Floor  Beam 


TYPE  A 

Suspended  Ceiling? 
Fig.  42.     Watson  Reinforced-concrete  Floor-construction.     Without  Slabs 


spans  and  heavy  loads,  the  T  sections  are  used,  laid  side  by  side;  and  for  spans 
less  than  20  ft  and  loads  of  200  lb  per  sq  ft  or  less,  the  beams  are  spaced  5  ft 
on  centers  with  flat  slabs  between.  This  system  is  controlled  and  installed  by 
the  Unit  Construction  Company  of  St.  Louis,  Mo.     Beams  and  girders  are 


Field  Concrete]['«V 
Fireproofing 


Fig.  43.     Watson  Reinforced-concrete  Floor-construction.     With  Skibs 


cast  with  unit  frames  in  horizontal  molds,  and  slabs  are  made  on  edge  in  steel 
forms.  In  the  American  School  Board  Journal  for  August,  1912,  Theodore  II. 
Skinner  describes  the  construction  and  erection  of  a  story-and-basement  school- 
house  with  a  structural-steel  frame  and  shop-made  reinfc5tced-concrete  joists, 
with  unit-ril)lK'd  reinforced-concrete  slabs. 

Gypsum  Floors.     Gypsum  has  been  extensively  used  for  floors  and  roofs  in 
fire-proof  buildings.     It  furnishes  a  light  construction  which,  with  the  additional 


Fire-proof  Floor-Construction 


857 


advantage  of  the  rapidity  with  which  it  can  be  put  in  place,  is  economical  not 
only  with  respect  to  the  floor  itself  but  also  on  account  of  a  saving  in  the  amount 
of  the  structural  steel  supporting  it.  Another  favorable  feature  is  the  great 
heat-insulating  property  of  gypsum,  resulting  in  absence  of  condensation  and  a 
reduction  in  the  cost  of  heating  the  building. 

The  Metropolitan  System.  This  construction  consists  of  a  series  of  steel 
cables  suspended  from  the  supporting  steel  beams  and  encased  in  a  slab  of  pure 
calcined  gypsum  containing  about  15%  of  wooden  chips.  The  cables  are  generally 
composed  of  two  No.  12  galvanized-steel  wires,  twisted.  They  are  made  contin- 
uous over  the  supports,  being  securely  fastened  over  the  flanges  of  the  end-beams 
or  channels  by  heavy  S  hooks  or  other  suital)le  means.  The  cables  are  spaced  from 
I  to  3  in  apart,  depending  on  the  carrying  capacity  desired.  They  are  held  taut 
by  a  ^i-m  round  steel  rod,  laid  at  the  middle  of  the  span  at  right-angles  to  their 
direction.  The  mixture  of  gypsum  and  chips  is  sent  to  the  work  in  bags  and 
placed  on  wooden  centers,  as  in  the  case  of  concrete  floors,  wet,  and  allowed  to 
set.  The  sides  and  flanges  of  the  supporting  steel  beams  are^'ncased  in  the  same 
material,  all  as  shown  in  Fig.  44.     The  minimum  thickness  of  floor-slabs  is  4  in; 


Cables  Composed  of  Two  No.  12     ,^ 
Galvanised -Steel  Wires   Twisted 


,X' 


F4=^ 


'  Metropolitan  Com.po6ition 


/  ^^"Steel  DeflecU. 


Under  Steel 
Deflection  -  Hod 


FiG.  44.     MetropoHtan  Fire-proof  Floor 


the  usual  thicknesses  for  roofs  are  3  and  3H  in.  The  finished  slabs  weigh  about 
4  lb  per  sq  ft  per  in  in  thickness.  Spans  of  from  6  ft  6  in  to  7  ft  are  said  to  make 
the  most  economical  arrangement,  all  things  considered.  Spans  should  not 
exceed  10  ft.  The  safe  gross  strength  of  the  construction  may  be  determined 
by  the  formula, 

24.Td 


in  which 

w  =the  safe  gross  load  per  sq  ft  of  floor  or  roof-surface,  in  pounds; 

r=the  safe  tensile  strength  of  the  twisted  cables,  in  pounds,  which  for  the 

ordinary  case  of  two  No.  12  cold-drawn  steel  wires,  may  be  taken  at 

365  lb; 
d  =the  deflection  of  the  cable,  in  inches,  and  equals  the  slab-thickness  less  the 

sum  of  the  protection  of  the  cables  at  the  center  of  the  slab  and  over  the 

supports,  that  is,  ordinarily,  the  slab-thickness  less  i  in; 
h  =the  spacing  of  the  cables,  in  inches; 
L  =the  span,  or  distance,  between  centers  of  supports  of  the  slab,  in  feet. 

No  tie-rods  are  necessary  in  this  floor-construction;  but  in  the  end-bays,  when 
the  lateral  stiffness  of  the  beams  together  with  the  compressive  strength  of  the 
floor-slab  is  not  sufficient,  struts  must  be  provided  of  such  size  and  spacing  as 
are  necessary  to  resist  the  pull  of  the  cables.  This  floor-construction  is  con- 
trolled and  installed  by  the  Keystone  Gypsum  Fireproofing  Corporation,  New 
York. 


858 


Fireproofing  of  Buildings 


Chap.  23 


Metal  Lumber.  A  system  of  prcssed-steel  I  joists,  channel- joists,  corner- 
joists,  wall- ribbons,  etc.,  has  been  developed  as  a  substitute  for  ordinary  wooden 
framing  in  the  construction  of  walls,  floors,  roofs,  and  partitions.  In  the  floor- 
construction,  the  I  joists  and  channel-joists,  of  from  No.  i6  to  12  United  States 
gauge  sheet  metal,  are  braced  by  metal  bridging,  to  give  additional  rigidity..  A 
typical  floor-construction  is  shown  in  Fig.  45.  The  steel  floor-joists  are  covered 
above  with  a  concrete  slab  reinforced  with  expanded-metal  lath,  and  the  lower 
flanges  are  protected  by  a  ceiling  of  metal  lath  and  cement  plaster  attached  to 
the  joists  by  means  of  the  prongs.  The  metal-lumber  joists  frame  into  ordinary 
steel  girders,  resting  on  a  shelf-angle  as  shown  in  the  drawing.  The  joists  are 
cut  to  length  at  the  factory,  properly  marked  and  tagged  and,  with  the  erection- 
diagrams,  are  shipped  to  the  site.  All  joints  and  splices  are  riveted  in  the  fleld. 
The  steel  girders  should  be  properly  incased  in  some  flre-proof  covering.     The 


Fig.  45.     Berber's  Metal  Lumber  and  Concrete  Floor-construction 


materials  for  this  floor-construction  are  manufactured  l)y  the  Berger  Manufac- 
turing Company,  Canton,  Ohio;  the  General  Fireproofing  Company,  Youngs- 
town,  Ohio;  the  Truscon  Steel  Company,  Youngstown,  Ohio;  and  the  National* 
Pressed  Steel  Company,  Massiflon,  Ohio.  They  publish  safe-load  tables  for 
ipetal-lumber  I  joists  and  channel-studs  for  spans  of  from  4  to  20  ft.  This  sys- 
tem, contemplating  the  use  of  steel  joists  and  girders,  not  thoroughly  incased 
with  fire-proof  materials,  cannot  ordinarily  be  considered  thoroughly  fire- 
resistant,  although  a  specially  constructed  floor  with  all  the  steel  covered  and' 
protected  with  fire-proofing-material  has  passed  the  fire  test  prescribed  by  the 
New  York  Building  Code.  (See  page  S27.)  It  has  been  extensively  used  to 
replace  combustible  building-construction,  especiaUy  in  residence-buildings. 

Protection  of  Girders  and  Beams.  No  form  of  floor-construction  can  he 
considered  thoroughly  fire-proof  unless  it  includes  a  protection  of  the  lower 
flanges  of  all  steel  beams  and  girders,  or  provides  for  the  protection  of  all  steel 
used  in  its  construction  or  support.  The  material  used  for  the  protective  cover- 
ing is  generally  the  same  as  that  used  in  the  floor-construction  itself.     The 


Fire-proof  Floor- Construction 


859 


principal  materials  are  tile,  either  dense,  porous,  or  semiporous;  gypsum;  and 
concrete,  either  of  cinders,  stone,  or  slag.  Beam-protection,  where  the  floor- 
construction  incases  the  side  of  the  beams,  as  in  Fig?.  17,  19,  or  34,  should 
never  he  less  than  i  in  thick.  Where  paneled  ceihngs  are  used,  that  is,  where 
the  lower  part  of  the  beams  is  below  the  lower  side  of  the  floor-construction, 
as  in  Figs.  18  or  30,  the  protection  should  be  increased  to  at  least  iy2  in  at  all 
points. 

Tile  Beam-Protection.     When  tile  is  used,  there  are  two  types  of  protec- 
tion.    In  one  case  the  blocks  incasing  the  bottom  flanges  of  the  steel  beams  meet 


Fig.  46.     Tile  Protection  for  Box  Girder 

at  the  middle  of  the  lower  side  of  the  flanges;  in  the  other,  they  simply  turn 
under  the  edges  of  the  bottom  flanges  and  hold   flat  tiles  with   beveled  edges 


Fig.  47.    Tile  Protection  for  Single-beam  Girder 

against  the  lower  side  of  those  flanges.     The  latter  is  considered  the  better 
method,  although  in  this  method  the  danger  of  breakage  of  the  part  extending 


860  Fireproofing  of  Buildings  Chap.  23 

under  the  flange  is  supplemented  by  the  possibility  of  an  omission  of  the  flat 
protection-tiles.  The  blocks  incasing  the  lower  flanges  may  be  the  skewbacks 
of  the  arch,  or  they  may  be  separate  blocks.  Different  forms  and  conditions  are 
illustrated  in  Figs.  15  to  24.  Fig.  26  shows  the  entire  beam  protected  by  blocks 
on  both  sides.  Girders,  which  often  project  below  the  ceiHng-line,  are  much 
more  exposed  to  the  effects  of  fire  and  water  than  the  floor-beams,  and  they 
should  have,  therefore,  the  most  eflacient  protection.  As  a  rule,  such  girders 
should  be  provided  with  not  less  than  4  in  of  terra-cotta  protection  at  the  sides, 
and  iy2  in  of  solid  tile  on  the  lower  side,  with  a  space  of  H  in  between  the  terra- 
cotta tiles  and  the  girder.  Fig.  46  is  a  typical  method  of  protecting  girders  by 
means  of  hollow  tiles.  The  bottoms  of  the  skewbacks  are  prevented  from 
spreading  by  wire  ties  placed  in  the  end-joints  between  the  soffit-tiles  and  hooked 
into  the  round  holes  in  the  skewbacks.  Single-beam  girders  are  usually  pro- 
tected as  shown  in  Figs.  22  and  47,  the  latter  figure  showing  more  particularly 
the  protection  of  a  beam  at  the  side  of  an  opening  in  the  floor. 

Concrete  Beam-Protection.  A  more  thorough  incasing  of  the  webs  and 
lower  flanges  of  beams  and  girders  can  be  accomphshed  by  the  use  of  concrete. 
The  superior  fire-proof  character  of  cinder  concrete  makes  it  the  best  material 
for  this  purpose.  If  of  sufficient  thickness  and  properly  applied,  it  will  hold 
securely,  without  reinforcement,  around  the  flanges  of  beams  and  girders. 
But  where  it  is  less  than  2  in  thick,  wire  or  metal  lath,  wrapped  around  the 
flanges,  should  be  embedded  in  it.  A  common  form  of  concrete-protection  is 
shown  on  right  hand  side  of  Fig.  30.  Sometimes  the  soffit  of  the  beam  is  pro- 
tected by  a  concrete  slab  with  an  insulating  air-space.  This  method  is  one  that 
may  be  advantageously  used  for  the  protection  of  girders.  A  fire  test  of  this 
form  of  girder-protection  made  in  the  Butterick  Building,  New  York  City, 
thoroughly  estabhshed  its  efficiency.  Hung  ceilings  are  sometimes  used  as  the 
protection  for  the  steel  beams.  This  is  very  bad  practice,  as  these  ceilings 
are  more  than  likely  to  collapse  in  a  severe  fire.  The  experience  in  the  Bal- 
timore fire  confirms  this  belief.     (See,  also,  pages  780  to  782.) 

The  Fireproofing  of  Trusses.  When  steel  trusses  are  used  to  support  the 
roof  or  several  stories  of  a  building  it  is  very  important  that  they  be  protected, 
not  only  from  heat  sufficient  to  warp  them,  but  also  from  expansion  sufficient 
to  affect  the  vertical  position  of  the  columns  on  which  they  are  supported.  The 
following  description  of  the  covering  of  the  trusses  in  the  Tremont  Temple, 
Boston,  Mass.,  furnishes  a  good  illustration  of  the  way  in  which  this  should  be 
accomphshed:  "The  steel  girders  were  first  placed  in  terra-cotta  blocks  on  all 
sides  and  below,  these  blocks  being  then  strapped  with  iron  all  around  the 
girders,  and  upon  this  was  stretched  expanded-metal  lathing,  covered  with  a 
heavy  coating  of  Windsor  cement;  over  this  comes  iron  furring,  which  receives 
a  second  layer  of  expanded-metal  lath,  the  latter,  in  turn,  receiving  the  finished 
plaster.  There  is,  consequently,  in  this  arrangement  for  fire-protection,  first, 
a  dead-air  space,  then  a  layer  of  terra-cotta,  a  Windsor  cement  covering,  another 
dead-air  space,  and  finally,  the  external  Windsor  cement."  Numerous  shapes 
of  terra-cotta  tiles  are  made  for  incasing  the  structural  shapes  commonly  used 
in  steel  trusses.  Some  of  these  are  shown  in  Fig.  48.  The  tiles  should  always 
be  secured  in  place  by  metal  clamps  passing  entirely  around  the  envelope,  or 
better  stiff,  by  wrapping  with  wire  lath.  The  tiling  should  then  be  plastered 
with  hard  wall-plaster.  Trusses,  also,  may  be  fire-proofed  by  completely  in- 
casing the  several  members  in  cinder  concrete,  either  with  or  without  metal 
reinforcement.  The  method  of  incasing  steel  columns  by  means  of  the  cement- 
gun  (page  826)  is  also  applicable  t9  the  protection  of  steel  trusses,  and  if  of  suf- 
ficient thickness  would  probably  serve  as  a  suitable  fire-protection;  but  no 


Fire-proof  Floor-Construction 


861 


definite  data  on  this  latter  point  are  as  yet  available.  When  trusses  are  to  be 
fireproofed,  the  additional  weight  must  be  provided  for  in  the  strength  of  the 
trusses  themselves. 


SECTION  OF  BRACING 
SECTION  OF  STRUT 

Fig.  48.     Tile  Protection  for  Members  of  Steel  Trusses 

Steel  Framing  for  Fire-proof  Floors.  Before  the  framing-plans  of  a  build- 
ing can  be  made,  it  is  necessary  to  decide,  in  a  general  way,  upon  the  system 
OF  FLOOR-CONSTRUCTION  or  fireproofing  that  will  be  employed  Thus,  if  any  one 
of  the  LONG-SPAN  SYSTEMS,  such  as  the  Herculean,  Johnson,  and  many  of  the 
concrete  systems,  is  to  be  adopted,  the  girders  should  be  spaced  so  that  the 
floor-construction  will  span  between  them,  without  floor-beams,  as  shown 
in  Fig.  49,  while  if  an  ordinary  flat-tile  arch  is  to  be  used,  floor-beams  will 


Jj^r^l^ 


V 


fr 


Fig.  49.    Steel  Floor-framing  for  Long-span  Construction 


862 


Fireproofing  o{  Buildings 


Chap.  23 


be  required,  spaced  from  5H  to  9  ft  apart,  and  these  beams  must  be  supported 
by  girders,  as  indicated  in  Fig.  50.  When  there  are  no  floor-beams,  a  strut- 
beam  should  be  riveted  between  the  columns,  as  in  Fig.  49,  to  hold  the  latter 
in  place  during  erection  and  to  stiffen  the  building.  It  should  be  remembered 
that  with  floor-beams  spaced  not  more  than  7  ft  on  centers,  almost  any  system 


■iDf^^^o^^"^^ 


/^ 


^ 


H 


XL 


»E1 


h  6  C  - 


CI 


rl- 


4- 


66  — - 


3^ 


□ q 

Fig.  50.    Steel  Floor-framing  for  Short-span  Construction 


^ 


of  floor-construction  may  be  employed;  while  if  the  floor-beams  are  omitted, 
there  are  few  systems  to  select  from.  With  any  form  of  filling  between  beams 
or  girders,  less  steel  is  required  for  moderate  than  for  excessive  spans  of  beams 
or  girders. 

Computations  for  the  Steel  Framing.  The  computations  for  the  steel 
beams  and  girders  of  a  fire-proof  floor  are  very  much  the  same  as  for  a  wooden 
floor.  The  load  or  loads  which  any  given  beam  is  required  to  support  are  first 
estimated  and  then  the  beam  of  the  necessary  size  to  support  the  load  is  selected.. 
The  DEAD  LOAD  for  any  fire-proof  floor  may  be  estimated  with  sufficient  accuracy 
by  means  of  the  data  given  in  this  chapter  in  connection  with  the  different 
systems  of  floor-construction.  The  dead  load  should  include  the  weight  of  the 
beams,  the  fireproofing,  including  all  concrete  filling,  the  plastering,  furring, 
lathing,  nailing-strips,  and  flooring.  The  live  loads  may  be  estimated  by 
means  of  the  data  given  in  Chapter  XXI,  pages  718  to  721. 

Example.  The  best  arrangement  for  the  columns  in  a  retail  store  is  to  set 
them  18  ft  on  centers  in  one  direction  and  19  ft  6  in  in  the  other.  It  is  decided 
to  run  the  girders  as  shown  by  Fig.  50,  and  to  put  a  beam  opposite  each  column 


Fire-proof  Floor-Construction  863 

and  two  beams  between  the  columns.  It  Is  required  to  determine  the  proper 
sizes  of  the  beams  and  girders,  using  an  ordinary  end-arch  construction  between 
the  beams 

Solution.  From  Table  VII,  page  836,  we  find  that  the  least  depth  of  arch 
which  it  is  advisable  to  use  is  10  in,  but  as  we  will  probably  have  to  use  12-in 
beams  it  will  be  better  to  figure  on  a  12-in  arch,  as  this  will  give  less  filling 
on  top.  The  weight  of  the  12-in  arch  will  be  about  39  lb  per  sq  ft.  We  shall 
probably  require  2  in  of  concrete  filling  on  top,  which  will  weigh  16  lb,  and 
I H  in  of  hght  fiUing  between  naiUng- strips,  weighing,  say,  9  lb  per  sq  ft.  The 
flooring  and  nailing-strips  will  weigh  about  4  lb,  the  plastering  on  the  ceiling 
5  lb,  and  we  must  allow  at  least  6  lb  per  sq  ft  for  the  weight  of  the  beams  them- 
selves. These  make  a  total  dead  weight  of  79  lb  per  sq  ft.  The  live  load  for 
a  retail  store  should  be  taken  at  150  lb  per  sq  ft,  making  a  total  load  per  square 
foot  on  the  beams  of  229  lb.  The  total  load  that  each  beam  must  be  capable  of 
supporting  will  be  6H  ft  by  18  ft  by  229  lb,  or  26  793  lb,  or  134  tons,  which  is 
assumed  to  be  uniformly  distributed.  From  Table  IV,  page  580,  we  find  that 
this  load,  with  a  span  of  i^  ft,  will  require  either  a  12-in,  4S-lb  beam,  or  a  is-in, 
42-lb  beam.  The  latter  will  be  both  stronger  and  cheaper,  but  will  increase  the 
thickness  of  the  floor  by  3  in  and  require  additional  filling. 

The  girder  must  support  two  concentrated  loads  of  26  793  lb  or  13.4  tons  each. 
On  page  566  it  is  stated  that  when  a  beam  supports  two  equal  loads  applied 
at  points  one  third  the  length  of  the  span  from  each  end,  the  equivalent  uni- 
formly distributed  load  may  be  found  by  multiplying  one  load  by  2^.  Multi- 
plying 26  793  lb  by  2%  we  have  71  448  lb  as  the  equivalent  distributed  load  on 
the  girder,  to  which  should  be  added  the  weight  of  the  girder.  This  requires 
a  standard  24-in  80-lb  beam  (Table  IV,  page  577). 

If  instead  of  using  tile  arches  between  beams  6J4  ft  apart,  we  conclude  to 
use  the  Herculean  or  Johnson  construction  spanning  from  girder  to  girder,  we 
should  frame  our  floor  as  in  Fig.  49.  For  this  span  we  should  require  lo-in  tiles, 
weighing  55  lb  per  sq.  ft.  Allowing  8  lb  for  i  /n  of  concrete,  9  lb  for  filling,  4  lb 
for  flooring  and  strips,  and  5  lb  for  pkstering,  we  have  81  lb  as  the  dead  load  per 
square  foot.  We  have  added  nothing  for  the  weight  of  the  girder,  as  this  will 
be  fully  offset  by  the  portions  of  the  floor  not  loaded.  The  live  load  per  square 
foot  will  be  150  lb  as  before,  and  the  total  load  to  be  supported  by  the  girder, 
18  ft  by  19  ft  6  in  by  231  lb,  or  81  081  lb,  or  40.54  tons,  which  will  require  a 
24-in  80-lb  beam  (Table  IV,  page  577).  Hence  by  this  arrangement  we  save 
the  weight  of  the  floor-beams;  but  a  6-in  strut-beam  should  be  pierced  between 
the  columns,  as  in  Fig.  49.  The  calculations  for  any  other  floor-construction 
are  similar  to  the  calculations  for  this  example,  the  only  variations  being  in 
the  figuring  of  the  dead  weights  of  the  construction. 

Tables  for  Floor-Beams.  It  is  a  difficult  matter  to  prepare  tables  that  may 
be  generally  used,  showing  the  size  of  steel  beams  required  for  fire-proof  floors, 
because  such  beams  are  often  irregularly  spaced,  and  there  is  a  wide  variation 
in  the  dead  loads.  The  following  tables,  however,  may  be  used  in  making  approx- 
imate estimates  and  in  checking  the  computations  for  any  particular  floor.  The 
sizes  of  I  beams  given  may  be  safely  used  where  the  total  live  and  dead  loads 
do  not  exceed  the  values  given  in  the  headings.  The  total  loads  should  include 
sufficient  allowance  for  the  weights  of  any  partitions  that  the  floor-beams  may 
be  called  upon  to  support. 

Table  XIII  gives  the  sizes  and  weights  of  I  beams  for  floors  of  offices, 
hotels,  and  apartment  houses;  Table  XIV,  for  floors  of  retail  stores  and  as- 
sembly-rooms; and  Table  XV,  for  floors  of  warehouses.  The  total  loads  used 
in  the  computations  are,  respectively,  120,  200,  and  270  lb  per  sq  ft. 


864 


Fireproofmg  of  Buildings 


Chap.  23 


Table   XIII.     Sizes   and  Weights  of  I  Beams   for   Floors   of    Ofl&ces,   Hotels, 
and  Apartment-Houses 

Total  load,  120  pounds  per  square  foot 


Span  of 

Distance  between  centers  of  beams  in  feet            ' 

' 

beams 

4 

^/^ 

5 

S'A 

6 

7 

in  feet 

in 

lb 

in  lb 

in  lb 

in  lb 

in 

lb 

10 

6 

121/4 

6  12I.I 

6   12^ 

6  12H 

7 

IS 

II 

6 

12M 

6  12M 

7  IS 

7  IS 

7 

IS 

12 

6 

12  M 

7  IS 

7  IS 

7  IS 

8 

18 

13 

7 

15 

7  IS 

7  IS 

8  18 

8 

18 

14 

7 

IS 

8  18 

8  18 

8  18 

9 

21 

15 

8 

18 

8  18 

8  18 

'  9  21 

9 

21 

16 

8 

18 

9  21 

9  21 

9  21 

10 

25 

17 

9 

21 

9  21 

9  21 

10  25 

10 

25 

18 

9 

21 

9  21 

10  25 

10  25 

12 

31  ^'i 

19 

9 

21 

10  25 

10  25 

10  25 

12 

Zi\^ 

20 

10 

25 

10  25 

12  31 H 

12  31 H 

12 

3l¥i 

21 

10 

25 

12  31 H 

12  31 H 

12  31H 

12 

Zi\^ 

22 

10 

25 

12  31 H 

12  31 H 

12  31 H 

15 

42 

23 

12 

31 5^^ 

12  31H 

12  31 H 

12  31 V^ 

15 

42 

24 

12 

31^/^ 

12  31^/^ 

12  zi\i 

IS  42 

15 

42 

25 

12 

31^/^ 

12  31^/^ 

IS  42 

IS  42 

15 

42 

Table  XIV.    Sizes  and  Weights  of  I  Beams  for  Floors  of  Retail  Stores 
and  Assembly-Rooms 


Total  load,  200  pounds  per  square  foot 

Span  of 

Distance  between  centers  of  beams  in  feet 

beams 

.  4)'^ 

5 

5K2 

6 

7 

in  feet 

in  lb 

in  lb 

in  lb 

in  lb 

in 

lb 

10 

7  IS 

7  IS 

7  IS 

8  18 

8 

18 

II 

7  15 

8  18 

8  18 

8  18 

9 

21 

12 

8  18 

8  18 

9  21 

9  21 

9 

21 

13 

8  18 

9  21 

9  21 

10  25 

10 

25 

14 

9  21 

9  21 

10  25 

10  25 

12 

31 1/^ 

IS 

9  21 

10  25 

10  25 

12  31 H 

12 

31 H 

16 

10  25 

10  25 

12  311/^ 

12    31 H 

.12 

31 H 

17 

10  25 

12  z^Vi 

12  31^/^ 

12  ziYi 

12 

40 

18 

12  31 H 

12  J1M2 

12  313-^ 

12  40 

12 

40 

19 

12  31 H 

12  31 3'^ 

12  40 

12  40 

15 

42 

20 

I?  31 H 

12  40 

12   40 

IS  42 

15 

42 

Fire-proof  Floor-Construction 


865 


Table  XV.     Sizes  and  Weights  of  I  Beams  for  Floors  of  Warehouses 

Total  load,  270  pounds  per  square  foot 


Distance  between  centers  of  beams  in  feet 

Span  of 

beams 

4K2 

5 

s'A       ■ 

6 

6V2 

•"  (ppf 

in  lb 

in  lb 

in  lb 

in  lb 

in  lb 

10 

8  18 

8  18 

8  18 

9  21 

9  21 

II 

8  18 

9  21 

9  21 

9  21 

10  25 

12 

9  21 

9  21 

10  25 

10  25 

10  25 

13 

10  25 

10  25 

10  25 

12  31 3-^ 

12  31 H 

14 

10  25 

12  31 H 

12  31 V^ 

12  s^Vz 

12  3iV^ 

15 

12  31^2 

12  31 H 

12   31^2 

12  31 Vi 

12  40 

16 

12  31 H 

12  31 3^^ 

12  31 3'^ 

12  40 

12  40 

17 

12  31 '/i 

12   40 

12  40 

12  40 

15  42 

18 

12  40 

12   40 

IS  42 

IS  42 

15  42 

19 

12  40 

IS  42 

IS  42 

IS  42 

15  42 

20 

IS  42 

IS  42 

IS  42 

IS  45 

IS  55 

Tie-Rods.  In  all  segmental  arches  and  other  types  in  which  a  thrust  is 
exerted  against  the  beams,  tie -rods  must  be  provided  to  prevent  the  beams 
from  being  pushed  apart,  and  especially  to  prevent  the  outer  bays  from  spread- 
ing. They  should  run  from  beam  to  beam  from  one  end  of  the  floor  to  the 
other.  If  the  outer  arches  spring  from  an  angle,  as  in  Fig.  14,  the  tie-rods  in 
this  bay  should  be  anchored  into  the  walls  with  large  plate-washers.  The 
tie-rods  should  be  located  in  the  lines  of  thrust  of  the  arches,  which  are 
ordinarily  below  the  half -depth  of  the  beams,  and  in  some  cases  near  the  bottom 
flanges.  If  their  appearance  is  objectionable,  they  should  be  hidden  by  a  hung 
ceiUng.  For  constructional  purposes  they  are  desirable  in  all  types  of  floor- 
construction,  even  though  the  floors  do  not  exert  a  thrust  on  the  beams. 
As  a  rule  tie-rods  are  proportioned  and  spaced  according  to  some  rule  of 
THUMB  rather  than  by  actual  calculations  of  the  thrust.  For  the  interior  arches 
this  practice  is  probably  safe  enough,  but  for  outside  spans,  and  particularly 
for  segmental  arches,  the  thrusts  of  the  arches  should  be  computed  and  the 
rods  proportioned  accordingly.  The  spacing  of  the  rods  is  generally  eight 
times  the  depth  of  the  supporting  beams,  but  never  more  than  8  ft.  For  interior 
flat-tile  arches,  the  following  rule  can  usually  be  safely  followed:  for  spans  of 
6  ft  or  less,  use  %-in  rods  spaced  about  5  ft  apart;  for  7 -ft  spans,  ^-in  rods, 
5  ft  apart;  and  for  g-ft  spans,  K-in  rods,  4  ft  apart. 

The  horizontal  thrust  of  an  arch  may  be  found  by  the  following  formula: 


r  = 


in  which 


T  =  pressure  or  thrust  in  pounds  per  linear  foot  of  arch; 

w  =  load  on  arch  in  pounds  per  square  foot,  uniformly  distributed; 

L  =  span  of  arch,  in  feet; 

K  =  rise  of  segmental  arch,  or  effective  rise  of  flat  arch,  in  inches. 


866  Fireproofing  of  Buildings  Chap.  23 

The  RISE  of  a  segmental  arch  is  measured  from  the  springing-line  to  the  soffit 
of  the  arch  at  the  middle.  For  flat  hollow-tile  arches,  the  effective  rise  may  be 
figured  from  the  top  of  the  beam-flange  to  the  top  of  the  tiles.  As  the  tiles 
usually  project  from  i\^  to  2  in  below  the  bottom  of  the  beams,  the  effective 
rise  will  be  from  2  to  2]^i  in  less  than  the  thickness  of  the  arch.  For  the  interior 
arches  of  a  floor,  w  may  be  taken  for  the  live  load  only,  but  for  the  exterior 
arches,  w  should  include  both  the  full  dead  and  live  loads.  Having  found  the 
thrust  of  the  arch,  the  spacing  of  the  rods  of  any  particular  size  may  be 
readily  determined  by  dividing  the  safe  load  given  for  that  size  of  rod  in  the 
table  on  page  388,  allowing  16  000  lb  unit  stress,  by  the  thrust.  The  result 
•will  be  the  spacing  in  feet. 

Example.  What  size  of  tie-rods  and  what  spacing  should  be  used  for  the 
floor-construction  described  on  page  863,  in  the  preceding  example? 

Solution.  The  depth  of  a  tile  arch  is  12  in,  the  dead  load  79  lb  and  the 
assumed  live  load  150  lb.  The  span  between  the  beams  is  6\i  ft.  Then,  for 
the  interior  arches,  w  =  150  lb,  R  =  12  —  2}'i  ==  g\i  in,  L  =  6H  ft  and  T  = 
(3  X  150  X  42.25)7(2  X  9H)  =  I  000  lb.  The  tensile  strength  of  a  M-in  rod,  not 
upset,  at  16  000  lb  per  sq  in,  is,  from  Table  II,  page  388,  4  832  lb.  Divid- 
ing this  by  I  000  we  have  a  little  less  than  4  ft  10  in  as  the  spacing.  The 
tensile  strength  of  a  %-in  rod  is  given  as  6  720  lb,  which  would  admit  of  a  spac- 
ing of  a  little  more  than  6  ft  8  in.  For  the  outer  spans,  w  should  be  taken  at 
150+79=229  lb.  Then  7"=  (3  X  229  X  42.2S)/(2  X  9^^)  =  i  526  lb..  For 
this  thrust  we  should  use  %-m  rods  spaced  about  4  ft  5  in  apart. 

Load-Tests.  It  may  be  desirable  at  times  to  test  fire-proof  floors  after  they 
have  been  installed.  The  same  precautions  should  be  taken  as  for  tests  on  rein- 
forced-concrete  construction,  described  on  page  967.  If  it  is  desired  to  determine 
from  such  tests  the  ultimate  strength,  a  section  of  the  floor  of  a  width  equal 
to  the  span  should  be  cut  loose  from  the  rest  and  loaded  to  destruction,  the 
supporting  steel  beams  being  shored  up  during  the  test.  The  safe  working 
load  is  found  by  dividing  the  breaking-load  by  the  proper  factor  of  safety. 

5.  Fire-proof  Roof-Construction 

Flat  Roofs.  Flat  roofs  are  constructed  in  the  same  way  as  the  floors,  except 
that  the  beams  and  girders  are  set  so  as  to  give  a  slight  pitch  to  the  roof  to 
drain  the  water.  As  the  roof-loads  are  usually  less  than  the  floor-loads  and 
as  there  are  no  partitions  to  be  supported,  the  arches  or  roof-panels  are  usually 
considerably  lighter  than  the  floor-panels,  but  the  general  construction  is  prac- 
tically the  same  for  both.  When  the  roof  is  formed  of  reinforced  concrete, 
the  beams  may  be  set  so  that  the  concrete  will  give  the  desired  inclination 
to  the  roof  and  will  have  a  nearly  uniform  thickness,  as  this  reduces  the  amount 
of  concrete  required,  and  also  the  weight.  In  cases  where  level  ceilings  are  de- 
sired, however,  it  would  be  cheaper  to  set  the  roof-beams  level  and  to  grade 
the  roof  with  dry  cinders,  as  the  cost  of  the  hung  ceiling  would  more  than  offset 
the  cost  of  the  extra  construction  necessary  to  take  the  added  weight  of  cinder 
fill.  Jf  the  roof  is  to  be  covered  with  tin  or  copper,  nailing-strips  should  be  em- 
bedded in  the  concrete,  as  for  wooden  floors,  and  the  entire  roof  sheathed,  as  it 
is  claimed  that  tin  or  copper  laid  over  terra-cotta  or  concrete  will  rust  out  in  a 
few  years.*  Gravel  or  tile  roofs  may  be  built  without  woodwork  of  any  kind. 
Whether  terra-cotta,  gypsum  tile,  or  concrete  is  used  for  the  roof-panels,  the 
sides  and  bottoms  of  the  steel  beams  and  girders  should  be  efficiently  protected, 

♦  Freitag. 


Firc-proof  Roof-Construction 


867 


as  well  as  all  columns  and  all  other  structural  metal  in  the  roof-space.  In 
an  ordinary  building,  in  which  there  are  stair-wells  or  elevator-wells,  the  roof 
and  upper  ceiling  are  likely  to  be  more  severely  tested  by  heat,  in  case  of  fire, 
than  any  of  the  floors  below,  and  experience  has  shown  that  this  part  of  the  build- 
ing often  has  the  poorest  protection. 

Pitched  Roofs.  Pitched  roofs  may  be  constructed  in  various  ways,  accord- 
ing to  the  material  that  is  to  be  used  and  the  kind  of  roofing  that  is  to  be  em- 
ployed. When  terra-cotta  or  gypsum  tile  is  to  be  used  for  the  fireproofing,  the 
most  common  method  of  construction  is  that  which  involves  the  framing  of  the 
roof  with  I-beam  rafters  and  T-iron  purhns,  set  horizontally  and  spaced  i  in 
farther  apart  than  the  lengths  of  the  tile.  Between  the  tees,  book  tiles,  or  roofing- 
tiles  are  placed  as  in  Fig.  51,  and  the  roofing  is  appUed  directly  to  the  surface  of 


Fig.  51.    Tile  Fireproofing  for  Roof -construction 


the  tiles.  If  the  roofing  is  to  be  of  slate  or  of  clay  tiles,  solid,  porous  terra-cotta 
blocks  should  be  used  between  the  tees,  as  nails  are  held  better  by  solid  blocks 
than  by  hollow  tiles;  gypsum  roof  tile  is  also  suitable  for  this  purpose.  The 
same  construction  may  be  used  for  flat  roofs;  but  on  account  of  the  expense  of 
the  tees  it  will  usually  be  more  expensive  than  the  construction  above  described, 
and  not  as  strong  or  desirable.  With  the  construction  shown  in  Fig.  51,  it  is 
impossible,  by  any  economical  method,  to  efliciently  protect  the  bottom  of  the 
T  irons  from  the  efi"ects  of  heat.  Rcinforced-ciruier  concrete,  or  reinforced 
porous  terra-cotta  tile,  Johnson  System,  affords  an  excellent  and  also  an 
economical  construction  for  fire-proof  pitched  roofs.  Either  of  these  construc- 
tions may  be  filled  between  or  on  top  of  the  rafters  without  the  use  of  purlins, 
except  about  once  in  from  6  to  lo  ft,  to  prevent  sliding  and  to  stiffen  the  roof. 
"Three-inch  plates  of  concrete,  with  expanded  metal  embedded,  have  been 
successfully  used  in  spans  of  from  6  to  7  ft  and  in  some  cases  even  in  8-ft  spans. 
The  concrete  is  deposited  on  wooden  centerings,  as  in  the  floor-construction, 
and  the  upper  side  is  smoothed  off  during  the  setting  and  floated  smooth  and 
straight  to  receive  the  roof-covering."*     The   roof-covering,   usually   slate,  or 

*  Freitag. 


868 


Fireproofing  of  Buildings 


Chap.  23 


clay  tiles,  may  be  nailed  directly  to  the  concrete,  as  nails  are  held  nearly  as 
well  by  cinder  concrete  as  by  wood.  This  applies  only  to  cinder  concrete,  as  it 
is  quite  impossible  to  nail  into  rock  concrete  or  gravel  concrete.  In  concrete 
roofs  the   rafters,  also,  should  be  surrounded  with  concrete  held  in  place  by 


BOOK  TILE  GOVE:RNMENr  ROOFING  THE 

Fig.  52.     Hollow  Book  Tile  and  Solid  Tile  for  Roofs 

metal  lath.  With  tcrra-cotta  roofs,  the  beams  should  be  incased  with  terra- 
cotta blocks.  Fig.  52  shows  the  standard  shapes  of  book  tiles  and  solid  roofing- 
tiles.  These  are  made  2,  21,4,  and  3  in  thick,  and  from  16  to  24  in  long.  Three- 
inch  book  tiles  weigh  about  13  lb  per  sq  ft,  and  21,^-in  solid  tiles  about  16  lb 


Fig.  53.     Bonanza  Reinforced-cement  Tiles  for  Pitched  Roofs 


per  sq  ft.     Tiles  of  both  of  these  shapes  are  also  used  for  ceilings  and  where  a 
light,  fire-proof  filHng  is  required. 

Reinforced-Cement  Tiles.  Cement  tiles  of  interlocking  types,  made  in  the 
factory  and  reinforced  with  metal  fabric  or  mesh,  may  be  laid  without  sheathing 
directly  on  steel  purlins.  This  type  of  construction,  however,  is  suitable  only 
as  a  semi  fire-resisting  roof -covering,  as  it  is  usually  made  with  plates  of  insuffi- 
cient thickness  and  does  not  contemplate  the  thorough  incasing  of  the  steel 
understructure  with  concrete  or  other  fire-resisting  materials.  Bonanza  Cement 
Tile  roofing  is  a  type  of  this  shop-made  tile  and  is  manufactured  and  controlled 
by  the  American  Cement  Tile  Manufacturing  Company,  Pittsburgh,  Pa. 
Two  types  of  tiles  are  made,  one  for  pitched-roof  and  the  other  for  flat-roof 
construction  (Figs.  53  and  54).  The  properties  of  the  tiles  are  given  in  the  fol- 
lowing tabulation: 


Fire-proof  Roof- Construction 

Standard,  Pitched-Roof  Tiles 

Thickness  of  tiles about  i  in 

Over-all  dimensions  of  tiles 26  by  52  in 

Tile-surface  exposed  to  weather 24  by  48  in 

Number  of  tiles  per  100  sq  ft  of  roof i2j.^ 

Weight  of  tiles  per  100  sq  ft  of  roof 1450  lb 

Standard,  Flat-Roof  Tiles 

Width  of  tiles 24  in 

Length  of  tiles 60  in  or  less 

Thickness  of  tiles iy2  In 

Weight  of  tile-construction 16  lb  per  sq  ft 


869 


Fig,  54.     Bonanza  Reinforced-cement  Tiles  for  Flat  Roofs 

The  flat-roof  tiles  are  designed  for  and  have  been  used  in  connection  with 
buildings  for  manufacturing-plants  on  spans  of  5  ft  between  purlins.  On 
these  spans  they  have  l^een  tested  up  to  an  ultimate  live  load  of  250  lb  per  sq  ft. 
The  top  surfaces  of  these  tiles  are  finished  in  a  weather-proof  and  water-proof 
material  of  a  dark,  terra-cotta-red  color. 


.  Steel  Fabric 


r=f; 


"^  Eeinf  orcjlng  -  Steel 


THROUGH  TYPE 


Reinforcing  -  Steel 


Reinforcing  -  Steel 
"H"  TYPE 


Fig.  55.     Structolite  Roof-tile 


870 


Fireproofing  of  Buildings 


Chap.  23 


Structolite  Roof-Tile.  Shop-made  roof-tiles  made  of  a  dense  quick-setting 
gypsum  cement,  called  structolite  by  the  manufacturers,  are  put  on  the  market 
by  the  United  States  Gypsum  Company  of  Chicago,  III.  The  material  used  is 
said  to  have  an  average  ultimate  crushing  strength  of  2  000  lb  per  sq  in.  As  the 
material  weighs  only  77  lb  per  cu  ft,  a  very  light  roof-construction  results.  The 
tiles  are  reinforced  with  steel  in  much  the  same  manner  as  reinforced  concrete, 
and  their  strengths  are  figured  by  the  same  formulas,  using  working  stresses 
appropriate  to  the  materials.  For  spans  from  4  to  6  ft,  a  trough-like  tile  is  used, 
as  shown  in  Fig.  55.  For  greater  spans,  up  to  10  ft,  the  T  type  and  H  type  of 
tile  are  used,  the  latter  when  a  continuous  flat  ceiling  is  desired.  The  tiles  are 
placed  directly  on  channel  or  I-beam  purlins,  but  when  the  flanges  of  the  purlins 
are  less  than  21,^  in  wide,  bearing-plates  should  be  inserted  between  the  tiles  and 
purlins.  The  weights  of  the  roof-tiles  in  lb  per  sq  ft  are  as  follows,  the  tiles 
themselves  being  generally  designed  for  safe  superimposed  loads  of  50  lb  per 
sq  ft. 


Span, 
ft 

Depth, 
in 

Trough  type, 
lb 

T  type, 
lb 

H  type, 
lb 

4 
5 
6 
7 
8 
9 
10 

5 
5 
5 
6 
6 

7 

14 
14 
IS 

13!/^ 

•  14H 
16 
16 

21 
21 
22 
22 

Robertson  Process.  Under  the  name  of  Robertson  Process  Floor, 
the  H.  H.  Robertson  Company,  Pittsburgh,  Pa.,  make  and  install  gypsum  floor- 
construction  of  the  same  general  character  and  design  as  the  Metropolitan  Floors 
(page  857).  They  also  manufacture  pre-cast  roof- tiles  designed  on  the  same 
suspension-principle.  The  cables  protrude  about  2  in  at  the  ends  of  the  slabs, 
near  the  top  surface.  When  set  in  place  on  the  roof-purlins  with  their  ends 
abutting,  the  projecting  ends  of  the  cables  of  adjoining  slabs  are  tied  together 
by  a  device  that  draws  them  taut,  thus  effecting  continuity.  The  tiles  are  rab- 
betted  at  the  ends  where  the  cables  emerge,  and  these  rabbets  are  filled  with 
gypsum,  covering  over  and  protecting  the  cable-connections.  The  following  are 
the  standard  sizes  of  roof -tiles: 

3  in  thick,  24  in  wide,  varying  in  length  by  3  in,  from  4  ft  o  in  to  6  ft  o  in 
3  in  thick,  21  in  wide,  varying  in  length  by  3  in,  from  6  ft  o  in  to  6  ft  9  in 
3  in  thick,  18  in  wide,  varying  in  length  by  3  in,  from  6  ft  9  in  to  7  ft  o  in 
3^  in  thick,  15  in  wide,  varying  in  length  by  3  in,  from  7  ft  o  in  to  8  ft  o  in 
sy2  in  thick,  12  in  wide,  varying  in  length  by  3  in,  from  8  ft  o  in  to  8  ft  6  in 

The  weight  per  sq  ft  is  14  lb  for  the  3-in  tiles  and  16  lb  for  the  s^^-in  tiles. 

Mansard  Roofs  are  usually  framed  with  rafters,  riveted  or  bolted  to  wall- 
plates.  The  space  between  the  rafters  may  be  filled  with  cinder  concrete,  hollow 
partition-tiles,  or  blocks  extending  from  rafter  to  rafter,  as  in  Fig.  56.  Slates 
or  tiles  may  be  nailed  directly  to  cinder  concrete  or  to  porous  terra-cotta.  Prob- 
vibly  the  best  way  to  attach  slates  or  tiles  is  to  nail  11,4  by  2-in  wooden  strips  to 
\he  outer  face  of  the  concrete  or  terra-cotta,  set  them  at  the  proper  distances 
Hpart  to  receive  the  slates  or  tiles,  and  then  plaster  between  the  strips  with 


Fire-proof  Roof-Construction 


871 


icement  mortar.     This  gives  a  better  nailing  for  the  roofing,  and  the  wooden 
L Strips  are  not  affected  by  fire  until  the  slate  is  practically  destroyed. 

Roof-Coverings.  The  materials  ordi- 
narily used  for  the  roof -covering  of  fire- 
pro©?  buildings  are:   (i)  tar  and  gravel; 

(2)  asphalt  and  gravel  or  sand;  (3)  vitrified 

tiies,  bricks,  or  slate  tiles  over  tarred  felt. 

Tar   and   gravel,   or   asphalt  felting  and 

gravel    or   sand,  offer  the  cheapest    roof 

suitable    for    a    fire-proof    building;   and 

when  a  good  quality  of  felt  and  distilled 

pitch  or  the  best  grades  of   asphalt  are 

used,  make  a  very  satisfactory  covering. 

Such  roofs,  however,  require  to  be  renewed 

about  every  ten  years.     The  roofing  is  put 

on  in  the  same  manner  as  over  wooden 

construction,  the  felt  being  laid  directly  on. 

the  concrete.     Probably  the  best  flat  roof 

that  can  be  put  on  a  building  is  one  of 

vitrified  or  slate  tiles,  laid  over  five  plys  of 

tarred  felt.     The  felt  is  laid  and  mopped 

as    for  a  gravel  roof,   and  the  tiles  are 

bedded  on  the  felt  in  cement  mortar.     Vitrified  tiles,  about  8  in  square  and 

1 3^  in  thick,  are  made  for  this  purpose,  and  slate  tiles,  1 2  in  square  by  i  in 

ithick,  have  been  used.     Flat,  vitrified-brick  tiles,  also,  are  used.     Gravel  roofing 

,'should  not  be  used  on  roofs  which  have  an  indination  exceeding  f4  in  in  i  ft. 

For  pitched  or    inclined  roofs,  slates,  clay  tiles,  or  metal  tiles  may  be  used. 

Clay  tiles  are  superior  to  slate  when  exposed  to  fire  and  are  generally  to  be 

preferred  to  slate;  this  is  especially  true  of  some  of  the  patent  interlocking  tiles. 

v(See,  also,  pages  1582  to  1587,  and  1595  to  1599.) 

Suspended  Ceilings.    Office-buildings,  apartment-houses,  etc.,  having  flat 

roofs,  require  ceilings  below  the  roofs  in  order  to  make  a  proper  finish  in  the 


Fig.  56.    Tiles  for  Mansard  Roof 


IH  X  5fa  Haflgera, 


Geiliag  Constmction 


HZ3 


(i]^  "channel  Bars    ^Metal  Lath :  Laced  to  Channel  Bars 

Tig,  57.    Suspended-ceiling  Construdioil 

rooms,  and  also  for  heat-in»ulation.  In  office-buildings  the  ceilings  of  the  top 
story  are  often  framed  and  constructed  like  the  floors,  but  with  a  lighter  con- 
struction. More  often  the  ceilings  are  suspended  from  the  roof;  as  this  requires 
much  less  steel  and  is  consequently  much  cheaper.  It  answers  the  purpose 
fully  as  well,  that  is,  if  the  roof-b6ams  are  efficiently  protected:     Fig.  57  shows 


872 


Fireproofing  of  Buildings 


Chap.  23 


a  common  construction  for  such  ceiUngs.  Wrought-iron  hangers,  about  1 16  by 
YiQ  in  or  I  by  i<^  in,  split  at  one  end  to  hook  over  the  lower  flanges  of  the 
roof-beams,  are  used  to  support  Me  by  %-in  flat  steel  bars,  spaced  about  4  ft  on 
centers;  and  to  the  under-side  of  these  are  laced  %-in,  ^-in,  or  11,4 -in  channels, 

12  or  16  in  on  centers,  to 
receive  the  metal  lathing. 
The  bottom  of  each  hanger 
is  bent  at  right-angles  to 
form  a  seat  for  the  bar, 
and  the  bar  is  laced  to  the 
hangers.  No  bolting  or 
riveting  is  required,  all  con- 
nections being  made  by 
lacing  wire,  or  by  bending 
the  iron.  Where  stiffened 
wire  lath  is  used,  the  chan- 
nels may  be  spaced  16  in 
on  centers;  but  if  the  or- 
Fig.  58.    Suspended  Ceiling.    Details  of  Two-bar  System  dinary  expanded  laths  are 

used,  it  is  better  to  place 
the  channels  12  in  on  centers.  If  ordinary  lime  mortar  is  used  for  plastering  a 
1 2-in  spacing  is  really  necessary.  Another  system  is  one  which  uses  only 
one  set  of  horizontal  bars,  which  are  spaced  close  enough  to  receive  the 
lathing,  and  Which  are 
supported  by  hangers. 
With  stiffened  wire  lath- 
ing, roof-beams  spaced 
not  over  5  ft  apart,  and 
short  hangerp,  this  may 
be  the  cheaper  system; 
but  without  the  stiffened 
lathing,  there  is  no  stiff- 
ness to  the  ceiling  at 
right-angles  to  the  bars. 
Where  the  hangers  are 
3,  4,  or  5  ft  long,  and  the 
spans  between  the  beams 


Roof  beams  5  0  ets. 


J— -12^=-^ 


Fig.  59.    Suspended  Ceiling    Details  of  Two-bar  System 

wider  than  5  ft,  the  two-bar  system,  shown  in  Fig.  57,  requires  less  steel,  for 
the  reason  that  the  channels,  having  spans  of  only  4  ft,  may  be  made  very 
light,  and  only  one  third  or  one  fourth  the  number  of  hangers  are  required.  In 
place  of  the  small  channels,  small  T  bars  or  flat  bars  may  be  used,  but  when  the 
bars  are  held  by  lacing,  channels  are  preferable. 

iMgs.  58*  and  59*  show  very  satisfactory  details  for  the  construction  of  the 
two-bar  system.  Instead  of  the  hook  shown  in  Fig.  58,  the  hanger  may  be 
spHt  at  the  top,  one  half  bending  around  one  side  of  the  beam-flange  and  the 
other  half  around  the  other  side.  Where  the  ceiling  is  suspended  below  terra- 
cotta arches,  toggle-bolts  are  used  for  the  support  of  the  hangers.  The  ends 
of  the  small  bars  supporting  the  lathing  are  usually  spliced  by  means  of  sheet- 
iron  clamps,  about  6  in  long,  wrapped  closely  around  the  bars  and  hammered 
tight.  For  suspended  ceilings  under  segmental  or  paneled  floor-construction, 
the  same  methods  are  employed,  except  that  the  hangers  are  replaced  by  clips 
holding  the  ceiUng-bars  close  to  the  soffits  of  the  beams. 


"  From  Fire  Prevention  and  Fire  Protection,  J.  K.  Freitag,  pages  687  and  688. 


Partitions  and  Wall-Coverings  873 

6.  Partitions  and  Wall-Coverings 

Requirement  of  Fire-proof  Partitions.  As  a  rule  the  partitions  in  fire- 
proof buildings  are  not  required  to  support  any  weight,  but  merely  to  serve  the 
purpose  of  dividing  the  spaces  into  rooms,  and  to  confine  a  fire  to  the  compart- 
ment in  which  it  originates.  No  greater  strength,  therefore,  is  required  in  a 
partition  than  is  necessary  to  carry  its  own  weight.  Rigidity,  however,  is  re- 
quired, and  a  rigidity  in  proportion  to  its  height  and  unsupported  length.  When 
partitions  separate  apartments  or  sections  of  a  story,  that  is,  when  they  are 
practically  without  window-openings  or  door-openings,  they  should  be  rigid 
enough  to  prevent  the  passage  of  water  from  a  hose-stream  as  well  as  the  pass- 
age of  flame.  In  other  cases  this  may  be  unnecessary;  in  fact,  at  times  it  may 
seem  desirable  to  construct  partitions  which  can  be  easily  removed  to  get  at 
a  fire  spreading  through  doors  or  windows.  The  materials  of  partitions  should 
be  incombustible.  They  should  be  poor  conductors  of  heat.  It  is  desirable, 
also,  to  have  them  unaffected  by  water.  Lightness  is  a  good  property,  as  any 
increase  in  the  dead  weight  of  the  construction  adds  to  the  cost  of  the  structure. 
Partitions  should  be  as  sound-proof  as  possible.  Window-openings  should  be 
avoided,  when  possible,  in  fire-proof  partitions,  and  even  door-openings  should 
be  reduced  in  number  to  a  minimum.  In  many  buildings,  however,  in  which 
halls  have  no  openings  into  streets  or  courts,  such  windows  are  necessary  for 
lighting  the  halls.  When  this  is  the  case  the  frames  should  be  made  fire-proof, 
wire-glass  should  be  used,  and,  if  possible,  the  sash  made  stationary. 

Fire  Tests  on  Partitions.  In  New  York  City  no  materials  or  types  of  con- 
struction are  permitted  for  interior  permanent  partitions  in  fire-proof  buildings 
that  have  not  met  the  required  fire  tests.  The  standard  test  of  the  American 
Society  for  Testing  Materials  is  based  on  the  New  York  test.*  Briefly,  these 
tests  require  that  the  partition  shall  resist  for  one  hour  the  destructive  action  of  a 
wood  fire,  the  heat  of  which  has  been  gradually  increased  to  1 700°  F.  during 
the  first  half-hour  and  maintained  at  that  temperature  for  the  balance  of  the 
time;  and  that  it  shall  resist,  also,  for  two  and  a  half  minutes  at  the  conclusion  of 
the  fire  test,  the  application  of  a  hose-stream  at  30  lb  pressure. 

Types  of  Partitions.  Fire-proof  partitions  that  are  in  common  use  may 
be  grouped,  according  to  the  materials  or  the  method  of  construction  used,  as 
follows: 

(i)  Brick; 

(2)  Hollow  tile  or  terra-cotta; 

(3)  Concrete  (stone  or  cinder) ; 

(4)  Gypsum  block; 

(5)  Plaster  or  concrete,  with  metal. 

The  choice  of  the  materials  and  the  type  of  construction  are  largely  influenced 
by  the  character  of  the  building  and  the  purposes  for  which  it  is  used. 

Partition- Walls.  For  bearing-partitions,  that  is,  those  which  support  floor- 
beams,  there  are  probably  no  materials  more  satisfactory  than  brick  and  con- 
crete. The  latter  may  be  used  either  in  the  form  of  blocks,  or  may  be  poured 
into  forms.  Dense  tile,  also,  is  being  used  with  satisfactory  results  for  bearing- 
walls.     Tests  show  a  crushing  strength,  on  net  sections,  equal  to  that  of  brick. 

Hollow-Tile  or  Terra-Cotta  Partitions.  These  are  usually  built  of  blocks, 
either  square  or  brick-shaped,  according  to  the  particular  product  used.  The 
square  blocks  are  usually  12  by  12  in  on  the  face,  and  the  brick-shaped  blocks 
are  usually  12  in  long  iDut  vary  in  height.     Both  shapes  are  made  in  thick- 

*  See  latest  Year  Book,  Am.  Soc.  for  Test.  Mats. 


874 


Fircprooiing  of  Buildings 


Chap.  23 


nesscs  varying  from  2  to  12  in.  The  3-in,  4-in,  and  6-in  blocks  are  commonly 
used,  the  4-in  blocks  being  the  most  popular  for  ordinary  work.  For  the 
more  important  partitions,  such  as  stair  and  elevator-enclosures,  nothing 
narrower  than  the  6-in  blocks  with  the  double  row  of  cells  should  be  used. 
The  blocks  are  commonly  set  with  the  voids  vertical.     Fig.  60  shows  typical 


Fig.  60.     Hollow-tile  or  Terra-cotta  Partition-blocks 

shapes  of  both  the  square  and  brick-shaped  blocks.  Fig.  61  shows  round- 
cornered  and  angle-cornered  partition-blocks,  which  must  be  set  vertically. 
"Terra-cotta  partitions  of  a  2-in  thickness  have  been  placed  on  the  market, 
but  have  not  been  extensively  used.  A  2-in  terra-cotta  partition  of  any  strength 
or  efficiency  is  quite  impracticable,  and  where  floor-area  is  so  valuable  that 
more  space  cannot  be  occupied,  terra-cotta  is  not  the  material  to  be  employed."* 

•  Freitag. 


Partitions  and  Wall- Coverings 


875 


Through  the  addition,  however,  of  band-iron  laid  between  the  courses  and 
patented  under  the  name  Phoenix,*  the  strength  of  a  2-in  tile  partition  is  greatly- 
increased.  The  New  York  partition,  Bevier  Patent,  consists  of  2-in  tiles,  rein- . 
forced  with  truss-metal,  such  as  is  used  in  the  New  York  floor-arch.  (See  Fig.  28.) 


Fig.  61.    Hollow-tile  Round-comer  and  Angle  Partition-blocks 

Porous  Versus  Dense  Materials.  For  inside  partitions  the  porous  mate- 
rials are  preferable  to  the  dense,  while  for  outside  walls  the  dense  materials 
should  be  used.  With  dense  tiling  it  is  necessary  to  insert  either  wooden 
nailing-strips,  which  are  very  objectionable,  or  blocks  of  porous  tile  to  take 
their  place.  It  is  becoming  daily  more  difficult  to  get  the  sawdust  necessary  to 
make  the  porous  material. 

Mortar.  Tile  partition-blocks  should  be  set  in  mortar  made  of  one  part 
lime-putty,  two  parts  cement,  and  from  two  to  three  parts  sand.  The  blocks 
should  be  well  wet  before  setting  and  the  partition  wet  down  before  the  plaster- 
ing is  appHed. 

Heights  and  Lengths  of  Terra-Cotta  Partitions.  "The  safe  height 
of  terra-cotta  partitions  in  inches  may  be  approximated  by  multiplying  the 
thickness  in  inches  by  40.  Common  practice  allows  a  safe  height  of  12  ft  for 
3-in,  16  ft  for  4-in,  and  20  ft  for  6-in  partitions.  For  partitions  without  side- 
Supports  the  LENGTH  should  not  materially  exceed  the  safe  height.  Doors  and  . 
high  windows  may  be  considered  as  side  supports,  provided  the  studs  run  from 
floor  to  ceiHng."t 

Weights.  The  weights  of  either  porous  or  dense  terra-cotta  partitions 
should  not  be  taken  at  less  than  the  following,  adopted  by  the  Hollow  Building 
Tile  Association,  as  proper  average  weights: 

2-in  partition,  14  lb  per  sq  ft; 
3-in  partition,  16  lb  per  sq  ft; 
4-in  partition,  18  lb  per  sq  ft; 
5-in  partition,  20  lb  per  sq  ft; 

*  Made  by  Henry  Maurer  &  Son,  New  York, 
t  Freitag. 


876 


FIreproofing  of  Buildings 


Chap.  23 


6-in  partition,  22  lb  per  sq  ft  for  one-cell  blocks; 
6-in  partition,  24  lb  per  sq  ft  for  two-cell  blocks; 
8-in  partition,  30  lb  per  sq  ft; 

not  including  plastering,  which  adds  about  10  lb  per  sq  ft  for  both  sides. 

Concrete  Partitions.  Partitions  of  stone  concrete  are  seldom  used  because 
of  the  forms  necessary  for  their  erection,  which  make  them  comparatively 
expensive.  Unless  reinforced  they  take  up  too  much  room.  Furthermore 
they  are  the  heaviest  of  all  partitions.  Even  in  buildings  that  are  entirely  of 
reinforced  concrete  they  are  not  always  used.  Cinder-concrete  partitions  are 
somewhat  lighter  and  considerably  cheaper  than  those  of  stone  concrete.  Yet 
even  these  are  too  heavy  and  too  troublesome  to  construct  to  be  satisfactory. 
Among  the  partitions  tested  and  approved  by  the  New  York  City  Building 
Bureau  is  one  that  consists  of  cinder-concrete  blocks,  2 1.4  and  3  in  thick,  the 
thicker  ones  being  hollow,  12  in  high,  and  18  in  long.  They  have  their  edges 
cast  with  tongues  and  grooves  that  furnish  more  or  less  of  a  bond  between  the 
blocks  when  they  are  set.  Hollow,  concrete  building-blocks  make  fairly  good 
partitions,  but  are  objectionable  on  account  of  their  thickness  and  weight. 

Gypsum-Blocks.  The  term  gypsum-blocks  is  now -more  generally  em- 
ployed than  the  term  plaster-blocks,  as  it  is  more  accurately  descriptive.     The 

principal  makes  on  the  market 
are  the  acme,  made  by  the 
Acme  Cement  Plaster  Com- 
pany, St.  Louis,  Mo.;  the 
ANCHOR,  made  by  the  Ameri- 
can Gypsum  Company,  Port 
Clinton,  O.;  the  pyrobar, 
made  by  the  United  States 
Gypsum  Company,  Chicago, 
111.;  the  BELL,  made  by  the 
Rock  Plaster  Manufacturing 
Company;  the  blocks  of  the 
Niagara  Gypsum  Company 
and  the  M.  A.  Reeb  Corpora- 
tion, both  of  Buffalo,  N.  Y.; 
and  the  blocks  of  the  Plymouth 
Gypsum  Company,  Fort 
Dodge,  Iowa.  The  usual  size 
of  these  blocks  is  12  in  by  30 
in,  although  some  are  made 
ISH  in  by  32  in.  The  thickness  is  generally  2,  3,  4,  5,  6,  and  8  in,  for  the  hol- 
low blocks,  and  2  and  3  in  for  the  solid  blocks. 

Gypsum-Block  Partitions.  Blocks  made  of  gypsum  (plaster  of  Paris) 
combined  with  various  substances,  such  as  cinders,  wood  chips,  cocoanut  fiber, 
asbestos,  etc.,  have  been  largely  used  for  partitions  in  fire-proof  buildings.  The 
principal  advantages  claimed  for  these  partitions  are  their  great  lightness  and 
reduced  cost  compared  with  other  forms  of  partitions.  Gypsum  blocks  can  be 
readily  cut  with  a  saw,  and  have  a  considerable  holding  power  for  nails.  In  the 
fire  tests,  made  for  the  Bureau  of  Buildings,  New  York  City,  they  have  generally 
shown  considerable  resistance  to  the  flame  and  have  transmitted  less  heat  than 
partitions  of  any  other  form.  They  did  not,  however,  always  stand  the  hose- 
stream,  some  of  them  being  easily  pierced,  and  all  of  them  being  more  or  less 
washed  away  by  the  water.    An  objectionable  characteristic  of  these  blocks  is 


^G.  62.    Plaster-blocks.    Doweled  Construction. 


Partitions  and  Wall-Coverings 


877 


their  tendency  to  absorb  moisture  while  being  stored  and  to  draw  water  from  the 
plastering  when  it  is  applied.  This  moisture  works  down  to  the  bottom 
of  the  partition  where  it  is  hkely  to  injure  the  wooden  base.  These  par- 
titions are  made  in  thicknesses  varying  from  2  to  4  in,  those  less  than  3  in 
in  thickness  generally  being  solid;  and  their  height  should  not  exceed  from  50 
to  60  times  the  thickness  of  the  blocks,  unplastered.  Hollow  blocks  should 
always  be  set  with  the  ceils  horizontal.  The  edges  of  the  blocks  are  generally 
grooved  or  otherwise  arranged  so  that  the  mortar  joint  forms  a  key  between 
them.  In  some  forms  of  these  partitions  the  blocks  are  bonded  together  by 
means  of  metal  dowels,*  running  across  the  horizontal  and  vertical  joints  from 
one  block  into  the  adjoining  one,  as  shown  in  Fig.  62.  The  cut  illustrates  the 
use  of  the  block  in  the  construction  of  dumb-waiter  shafts  and  shows  how  the 
blocks  are  anchored  at  the  corners  by  iron  dowel-angles.  Gypsum  plaster  is 
used  in  laying  plaster-blocks,  and  occasionally  fibered-gypsum  plaster,  tempered 
with  Fand,  may  be  employed.  All  of  the  partitions  in  the  newer  portions  of  the 
Monadnock  Block,  Chicago,  and  in  many  other  prominent  buildings  of  Chicago 
and  New  York  City,  are  of  Gypsum  blocks.  Gypsum  blocks  make  the  lightest 
practical  partition  known.  The  weight  of  these  partitions  per  square  foot  may 
be  taken  as  follows; 

Thicknessof  block,  inches. .     23  4  5  6         8 

Weight  in  lb  per  sq  ft 10       121,^        141,^        171,^       19       26 

About  8  lb  per  sq  ft  should  be  added  to  obtain  the  weight  of  the  partition 
when  plastered  on  both  sides. 

Mackolite.  A  plaster-block  extensively  used  is  the  Mackolite  Hollow  Block, 
made  by  the  A.  B.  Fireproofmg  Company,  Chicago,  III.  Mackolite  partition  tiles 
are  generally  made  in  the  form 
shown  in  Fig.  63.  The  3-in,  31,4-in, 
and  4-in  tiles  are  made  48  and  the 
others  30  in  long,  all  the  tiles  being 
12  in  high.  The  blocks  are  laid  in 
regular  courses,  breaking  joint  as 
in  cut-stone  work.  Lime  mortar 
is  used  for  setting.  In  fitting 
around  openings  or  at  angle?  the 
blocks  are  cut  with  a  saw,  and  this 
effects  a  material  saving  in  time 
and  material.  It  is  claimed  that 
the  blocks  make  very  strong  par- 
titions. The  composition  of  the 
blocks  is  plaster  of  Paris  mixed 
with  certain  chemicals,  reeds,  and 
fiber.     Reeds  of  the  same  length 

as  the  blocks  are  placed  in  the  molds  and  the  plaster  of  Paris  and  fiber  are  then 
mixed  with  water,  to  which  the  chemical  has  been  added,  and  poured  around  the 
reeds  so  that  they  are  nowhere  exposed.  The  reeds  give  longitudinal  strength  to 
the  blocks  while  the  fiber  makes  them  tough  and  elastic.  The  material  sets  in 
about  half  an  hour,  after  which  the  blocks  are  kiln-dried  for  four  days. 

Gypsinite  Partitions.  The  main  feature  of  these  partitions  is  the  gypsinite 
STUD  which  is  handled  and  erected  in  the  same  manner  as  a  wooden  stud  in  the 
ordinary  non-fire-proof  partitions.  The  stud  is  composed  of  wooden  naihng- 
strips  completely  protected  and  embedded  in  a  plaster-composition  known  as 

*  Patented  by  the  Sanitary  Fircproofing  and  Contracting  Co.,  New  York  City. 


Fig.  63.     Mackolite  Partition-blocks 


878 


Fireproofing  of  Buildings 


Chap.  23 


GYPSiNiTE  CONCRETE.  The  studs  arc  carefully  made  and  are  plumb  and  true. 
Metal  lath  or  plaster-boards  are  secured  to  the  studs  and  plastered,  completing 
the  partition,  which  is  about  4I/S  in  thick.  (Fig.  64.)  This  partition  is  slightly 
heavier  than  the  ordinary  partition  of  wooden  construction.  It  is  quite 
as  stiff  and  as  strong  as  a  good  tile  or  other  partition,  and  the  nailing-strip 
feature  of  the  studding  facilitates  the  application  of  a  wooden  trim.  It 
is  said  to  be  particularly  sound-proof,  and  the  spaces  between  the  studs 
afford  an  opportunity  to  conceal  pipes,  wires,  etc.  Gypsinite  studs  are  3  by  3 
by  12  in,  and  weigh  3  lb  to  the  foot.    They  can  be  made  any  size  required. 


Fig.  64.     Gypsinite  Studs,  Metal  Lath,  and  Plaster 


in  the  partitions  the  studs  are  usually  placed  16  in  on  centers  and  bridged  as 
iriay  be  required.  They  are  fastened  to  the  floor  or  ceihng  by  the  use  of  sills 
and  plates  of  the  same  material,  or  by  light  channel-irons,  which  are  spiked  to 
the  fireproofing.  The  manufacturers  believe  that  in  large  quantities  these  studs 
can  be  furnished  as  cheaply  as  wooden  studs  and  that  the  partitions  can  be 
erected  as  cheaply  as  ordinary  lath-and-plaster  partitions.  Gypsinite  studs  are 
manufactured  by  the  United  States  Gypsum  Company,  Chicago,  111. 

Solid,  Plaster-and-Metal  Partitions.  Thin  partitions  of  plaster  appHed 
to  metal  lath  and  metal  studs,  made  solid,  and  finished  about  2  in  thick,  have 
been  extensively  used  in  fire-proof  buildings.  They  are  remarkably  stiff,  owing 
to  the  adhesion  of  the  plaster  to  the  steel,  and  they  are  lighter  and  occupy  less 
^pace  than  any  other  practical  fire-proof  partition  of  equal  strength.  In  the 
^re  tests  these  partitions  act  very  much  like  the  plaster-block  partitions,  resist- 
ing thoroughly  the  passage  of  the  flames.  But  the  plaster  always  washes  off 
Vhen  the  hose  is  applied  and  the  lath  becomes  exposedr    The  rigidity  of  the 


Partitions  and  Wall-Coverings 


879 


metal  fabric  on  the  metal  studding  has  been  considered  by  firemen  a  disad- 
vantage, as  it  is  very  difficult  to  cut  through  it  when  necessary  to  get  at  a  fire. 
The  construction  of  these  partitions  is  practically  the  same  for  the  different 
fabrics  used,  which  are  described  on  pages  846  to  850.  This  lath  or  fabric  ap- 
pears to  be  subject  to  the  corrosive  effects  of  the  plaster.  In  the  demolition 
of  the  Pabst  Building,  Ne^  York  City,  the  metal  lath  used  throughout  in  the 
partitions  was  found  to  be  considerably  corroded,  after  about  four  years,  even 
though  the  lath  had  been  painted.     On  the  other  hand  other  cases  are  cited  by 


%'  Nailing 
/  Strip 


Fig.  65.    Two-inch  Solid  Plaster  Partition.     Elevation 


the  manufacturers,  such  as  the  Chess  residence  at  Pittsburgh,  Pa.,  the  Sturtevant 
residence  at  Springfield,  Mass.,  and  the  West  End  Trust  Building  at  Philadelphia, 
Pa.,  in  which  after  twenty  years  no  corrosion  of  the  metal  lath  in  plaster  par- 
titions was  observed.  The  investigations  of  the  United  States  Bureau  of 
Standards  of  various  forms  of  stucco-construction  seem  to  bear  out  the  manu- 
facturers' contention.  The  lath  should  in  all  cases  be  protected  against  initial 
or  incipient  corrosion  by  painting  or  galvanizing  before  being  embedded  in  the 
cementitious  material. 

Weights  of  Plaster-and- Metal  Partitions.     The  weight  of  a  2-in  solid 
partition,  when  dry,  is  about  20  lb  per  sq  ft.     The  weight  of  partitions  of  greater 


Fireproofing  of  Buildings 


Chap.  23 


thickness  may  be  estimated  on  a  basis  of  1 20  lb  per  cu  ft  for  plaster,  and  96  lb 
for  cinder  concrete,  slightly  tamped. 

Construction  of  Solid  Two-Inch  Partitions.     Figs.  65  and  66  show  the 
usual  method  of  constructing  2-in  partitions.     The  studs,  usually  J^-in  or  i-in 


%*  Channel- 
Furring  for  Base' 


3^  Steel  Rod- 


FlG.  ( 


R'juLrli  Frame 


Staple/ 
No.  18  Gai.  Wire  Lacing.^ 

Two-inch  Solid  Plaster  Partition.     Horizontal  Section 


channels,  are  bent  and  punched  at  the  ends,  and  at  the  bottom  are  nailed  to 
wooden  strips,  which  are  first  secured  to  the  floor-panels,  or  to  the  top  of  the 
steel  beams  where  the  partitions  come  over  them.  These  wooden  strips  have 
been  found  necessary  as  a  sort  of  cushion  to  allow  the  studding  to  expand  in 
case  of  fire.  At  the  top,  the  studs  are  nailed  to  the  underside  of  the  floor-panels, 
or,  if  there  is  a  suspended  ceiling,  they  are  wired  to  the  bars  supporting  the 
ceiHng.  At  the  openings,  i  by  i  by  sig-in  angles  are  used,  and  these  are  bored 
every  16  in  for  No.  12  screws,  used  in  attaching  the  rough  wooden  frames  to 
the  angles.  After  the  studding  is  in  position,  the  metal  lathing  is  laced  to  one 
side  of  it  with  No.  18  galvanized  wire.  After  the  lathing  is  in  place  the  car- 
penter should  attach  wooden  grounds  to  secure  the  base,  and  pegs  or  spot-grounds 
for  chair-rail,  picture-molding,  etc.  These  grounds  are  secured  by  staples, 
and  when  the  partition  is  plastered,  become  very  rigid.  In  plastering  these 
partitions,  five  coats  of  plaster  are  required  to  make  a  good  job;  a  scratch -coat 
on  one  side,  a  brown  coat  on  each  side,  and  the  usual  white  coat  on  each  side  for 
finishing.  It  is  essential  for  all  thin  partitions  that  a  hard-setting  mortar  be 
used,  such  as  Acme  Cement,  King's  Windsor  Cement,  Adamant,  or  Rock  Wall 
Plaster.*  The  partitions  acquire  their  stiffness  largely  from  the  solidity  of  the 
plastering,  hence  the  firmer  and  harder  the  plastering  the  more  substantial  the 
walls. 

Double  Partitions.     Electric  wires  and  yAn  gas-pipes  can  be  run  in  the  2-in 
SOLED  partitions;  but  if  it  is  desired  to  run  larger  pipes,  double  partitions, 


X  Steel  Rod' 


IS^Y  ':^'Concret^;:>,^-.o. 


^1,^ Rough  Frame 


^o..l8  Gal.  Wire  Lacing  ''  ^2  "x  2"^  >^"  L 

Fig.  67.    Four-inch  Solid  Plaster  and  Concrete  Partition.    Horizontal  Section 


that  is,  partitions  with  lathing  on  each  side  of  the  studding,  must  be  used.  For 
these  partitions,  2-in,  3-in,  or  4-in  channels,  or  fiat  bars  set  edgewise,  may  be  used, 
sheet-steel  channels  being  probably  the  most  economical.  When  the  space 
between  the  studs  is  not  filled  with  mortar  or  concrete,  the  double  partition 

*  Made  respectively  by  the  Acme  Cement  Plaster  Company,  St.  Louis,  Mo.; 
T.  B  King  &  Company,  New  York;  the  United  States  Gypsum  Company,  Chicago,  111.; 
ftnd  the  Rock  Plaster  Manufacturing  Company,  New  York. 


Partitions  and  Wall-Coverings 


881 


i 


1 


i 


t 


i 


L 


will  not  stand  fire  and  water  as  well  as  the  solid  partition,  while  it  is  much  more 
expensive. 

Construction  of  Solid  Four-Inch  Partitions.  Fig.  67  shows  a  partial  sec- 
tion through  a  solid  partition  finishing  4  in  thick  when  plastered.  It  has  great 
strength  and  resistance  to  fire  and  water,  and  afi'ords 
convenient  spaces  for  pipes  and  thicker  jambs  for 
door-frames.  These  partitions  have  cores  of  cinder 
concrete,  with  metal  lath  on  both  sides,  and  are  plas- 
tered in  the  usual  way.  As  the  concrete  will  receive 
nails,  no  wooden  furring  is  required  to  fasten  the  base- 
boards, chair-rails,  and  picture-moldings  in  place. 

Berger's  Economy  Studding  and  Furring.  Fig. 
68  illustrates  a  patent  stud  manufactured  by  the 
Berger  Manufacturing  Company,  Canton,  Ohio.  It 
is  made  of  No.  18  or  No.  20  sheet  steel,  and  in  five 
sizes,  varying  from  %  to  11,4  in.  The  peculiar  ad- 
vantage of  this  stud  is  the  provision  for  attaching  the 
lath.  For  this  purpose  prongs  are  punched  from 
both  sides  of  the  flange,  which  are  left  standing  at 
right-angles  to  the  face  of  the  flange.  The  lath  is 
placed  against  the  stud,  the  prongs  pressed  through 
the  meshes  and  then  turned  up  over  the  lath  with  a 
hammer.  This  fastens  the  lath  more  firmly  and 
securely  than  by  any  other  method.  The  ends  of  the 
studs  are  secured  by  sockets  which  are  fastened  to  the 
floor  and  ceiling,  a  clear  space  being  left  above  the 
top  of  the  studs  for  expansion.  Where  partitions 
intersect  or  where  there  are  angles,  angle-irons  with 
prongs  are  used  in  place  of  the  T  irons.  By  using 
these  studs  and  expanded-metal  lathing,  a  saving  in 
cost  can  be  effected  over  the  construction  shown  in 
Fig.  66.  These  T's  are  used,  also,  for  supporting 
suspended  ceilings  under  I  beams,  the  T's  being 
secured  to  the  flanges  of  the  beams  by  specially  de- 
signed clips.  Furring-strips  and  channels,  also,  are 
made  on  the  same  principle. 

Spacing  of  Studs  in  Two-Inch  Solid  Partitions. 
For  2-in  solid  partitions  with  ys-in  roUed  channels  or 
I -in  Economy  Studs,  the   studs  should  be  placed  12 

in  on  centers  when  the  height  of  the  story  exceeds  10  ft.  When  the  height  of 
the  story  is  less  than  10  ft,  a  spacing  of  16  in  will  answer.  For  hollow  partitions 
with  2-in  studs,  the -studs  can  be  spaced  16  in  on  centers  for  story-heights  of  61 
ft  and  less.     For  greater  heights  they  should  be  placed  1 2  in  on  centers. 

Rib  Stud.  In  Fig.  69  is  shown  the  Rib  Stud  made  by  the  Truscon  Steel 
Company,  Detroit,  Mich.  It  is  made  in  widths  of  214,  sH,  4\i,  63,4,  and 
814  in;  and  in  lengths  up  to  18  ft.  The  studs  are  made  of  open-hearth  steel, 
the  two-rib  studs  weighing  0.55  lb  per  ft  and  the  three-rib  studs,  0.85  lb  per  ft. 
P'or  2-in  solid  partitions  with  %  or  i-in  channels  or  studs,  the  studs  should 
be  spaced  from  12  to  16  in  on  centers,  depending  upon  the  stiffness  and  rigidity 
of  the  lath.  A  1 2-in  spacing  should  never  be  exceeded  when  the  height  of  story 
is  more  than  12  ft.  For  hollow  partitions  with  2-in  studs,  the  studs  can 
be  spaced  16  in  on  centers  for  story-heights  of  16  ft  or  less,  when  No,  24  (United 
States  gauge)  expanded  metal  or  No.  18  (United  States  gauge)  wire  lath,  2},^  by 


i 


Fig.  68.  Berger  Studding 
or  Furring  and  Stud- 
sockets 


882 


Fireproofmg  of  Buildings 


Chap.  23 


2}i  mesh,  are  employed.  For  greater  heights  the  spacing  should  never  exceed 
12  in.  No.  2  2  (United  States  gauge)  expanded  metal,  weighing  at  least  4^4  lb 
per  yard,  and  No.  20-gauge  V-stiffened  wire  lath  or  wire  lath  with  rods  or  stifl- 
eners  spaced  7i,<>  to  8  in  on  centers,  give  satisfactory  rigidity  for  both  partitions 


"  jf  J  ff  jr  f  f  f  f  f  jr  /' 


2J4  Inches  and  3%  Indies  Wide. 


k 

u 

r* 

jd 

y 

y 

9 

4M  Inches  Wide. 


» el &? &! Bf! a? b! a . 


6^  Inches  and  8J4  Inches  Wide. 
Fig.  69.     Rib  Stud  for  Plaster  Partitions 


and  ceilfngs  when  the  studs  or  furring-strips  are  set  16  in  on  centers.  Lath 
should  be  wired  to  the  metal  studding  with  No.  i8-gauge  annealed  galvanized 
wire. 

Metal  Lath.     Numerous  styles  of  metal  lath  have  been  put  on  the  market 
in  recent  years  to  provide  for  a  cheap,  light,  and  thin  partition-construction. 

For  fire-proof  buildings  metal 
STUDDING  should  always  be 
used.  Metal  lath  is  supplied 
either  plain,  painted,  or  gal- 
vanized. It  is  recommended 
that  metal  lath  be  always  at 
least  painted,  to  prevent  initial 
corrosion  until  the  lath  can  be 
covered  by  the  mortar.  Gal- 
vanizing is  necessary  where 
there  is  danger  of  moisture 
reaching  the  lath  while  it  is 
without  a  protective  coat  of 
lime  or  cement.  Where  a  par- 
ticular type  of  lath  is  not 
mentioned  in  a  specification,  it  should  be  generally  described  as  follows: 
"  Painted  or  galvanized  No.  24-gauge  expanded-metal  lath,  weighing  not  less 
than   3H  lb  per  sq  yd,  or  painted  or  galvanized  woven- wire  cloth.  No.  19 


Fig.  70. 


Expanded-metal    Lath   with   Diamond- 
shaped  Mesh 


Partitions  and  Wall-Coverings  883 

gauge,  2i/^  meshes  to  the  inch,  with  stiffeners  placed  8  in  on  centers  and  weigh- 
ing not  less  than  s}i  lb  per  sq  yd."  Metal  lath  should  be  so  made  that  it  will 
take  plaster  freely,  key  it  thoroughly,  and  wholly  embed  itself  in  it.  These  are 
characteristics  of  expanded-metal  and  woven-wire  laths  which  make  them 
superior  to  sheet  lath.  Sheet  laths  are  economical  in  the  use  of  mortar,  which 
merely  covers  one  side  of  the  lath  and  latches  through  the  perforations  without 
thoroughly  embedding  the  metal.  The  difficulty  of  stretching  plain  wire  lath 
tight  enough  to  make  a  firm  foundation  for  plaster  and  the  resulting  necessity 
for  a  close  spacing  of  the  studs  to  secure  the  required  bearing,  has  led  to  the 
introduction  of  stiffened  wire  cloth  and  ribbed  or  corrugated  expanded  metal 
in  order  to  obtain  the  necessary  rigidity.  To  overcome  the  necessity  for  separate 
bearing-studs,  expanded-metal  and  sheet-metal  laths  are  manufactured  also  in  a 
one-piece  steel  lath-and-stud. 

Expanded  metals  differ  in  the  process  of  manufacture.  One  type  is  made 
by  simply  slitting  the  sheet  and  deploying  it  into  the  diamond  shape;  the^ther 
type  is  made  from  thin 
strips  of  soft,  tough 
steel,  by  a  mechanical 
process  which  pushes 
out  and  expands  the 
metal  into  the  mesh 
and  at  the  same  time 
reverses  the  direction 
of  the  edge,  so  that  the 
flat  surface  of  the  cut 
strand  is  nearly  at 
right-angles  to  the 
.general  surface  of  the 
sheet.  It  is  claimed  Fig.  71.  Expanded-metal  Lath  with  Rectangular  Mesh 
that  the  cold  work- 
ing of  this  low-carbon  steel  increases  the  elastic  limit  and  ultimate 
STRENGTH.  In  Specifying  expanded  metal,  it  is  necessary  to  give  the  weight  of 
the  finished  product  per  square  yard  as  well  as  the  gauge  of  metal,  as  the  strands 
may  be  of  various  widths.  Expanded  metal  is  made  either  with  diamond-  shaped 
(Fig.  70)  or  rectangular  (Fig.  71)  meshes.  When  laid  with  the  long  strands  per- 
pendicular to  the  studs,  the  lath  with  the  rectangular  mesh  is  the  stronger  of  the 
two.  Rigidity  is  also  obtained  by  corrugating  and  expanding  the  metal  in  various 
forms,  which  make  the  so-called  ribbed,  corrugated,  and  integral  laths.  Wire 
cloth  is  stiffened  by  clipping  corrugated-steel  furring-strips  to  the  lath  or  by 
weaving  or  welding  rods  or  V-shaped  stiffeners  at  regular  intervals. 

Types  of  Metat  Lath.    Metal  lath  may  be  classified  as  follows: 

(i)  Expanded-metal  lath; 

(a)  Diamond  and  rectangular  mesh, 

(b)  Ribbed  or  corrugated, 

(c)  Integral,  combining  functions  of  both  lath  and  studding, 

(2)  Sheet  lath; 

(a)  Flat  perforated, 

(b)  Integral,  combining  functions  of  both  lath  and  studding, 

(3)  Woven-wire  lath; 

(a)  Plain, 

(b)  Stiffened. 

Some  of  the  laths  and  their  characteristics  are  given  in  the  following  para- 
graphs. 


884  Fireproofing  of  Buildings  Chap.  23 

(1)  Expanded-Metal  Lath 

Rotary  Diamond-Mesh  Lath.  This  lath  is  made  by  the  Berger  Manu- 
facturing Company,  Canton,  Ohio.  It  is  furnished  in  sheets  i8  by  96  in,  of 
Nos.  27,  26,  25,  and  24  gauge,  weighing  respectively  2^  lb,  2i,<>  lb,  3  lb,  and  3.4 
lb  per  sq  yd.  It  is  made  of  Toncan  Metal,  for  which  greater  homogeneity  is 
claimed  than  for  charcoal-iron  and  steel,  and  less  liability   to   corrosion  or 

PITTING. 

Bostwick  Lath.  Bostwick  lath  is  made  by  the  Bostwick  Steel  Lath  Com- 
pany, Niles,  Ohio.  It  is  furnished  in  sheets  14  by  96  in,  approximately  i  sq  yd, 
and  is  made  in  Nos.  24  and  27  gauge. 

Steelcrete  Lath.  This  material  is  manufactured  by  the  Consolidated 
Expanded  Metal  Companies,  Braddock,  Pa.,  and  is  furnished  in  two  styles, 
known  as  steelcrete  A  lath  and  steelcrete  B  lath,  for  exterior  stucco-work; 
and  in  the  standard-form  diamond  lath,  extensively  used  for  exterior  and  in-- 
terior  plastering- work.  Steelcrete  diamond  lath  is  divided  into  three  desig- 
nations, P  lath,  F  lath,  and  H  lath.  The  P  lath  meets  the  specifications  of 
the  United  States  Post  Office  Department,  weighs  4.37  lb  per  sq  yd,  and  is  manu- 
factured from  22-gauge  material  in  sheets  24  by  97  in.  The  F  lath  is  manufac- 
tured in  sheets  24  by  97  in  from  the  gauges  24,  25,  26,  and  27,  respectively 
weighing  3.40,  3.00,  2.55,  and  2.33  lb  per  sq  yd.  The  H  lath  has  a  size  of  sheet 
28  by  97  in  and  is  manufactured  from  the  gauges  24  and  26,  weighing  respect- 
ively 2.90  and  2.20  lb  per  sq  yd.  Steelcrete  lath  can  be  obtained  manufac- 
tured from  open-hearth  black  sheets  or  galvanized  sheets,  or  in  copper-bearing 
sheets  (acid-resisting) . 

A  Diamond-Mesh  Lath  is  made  by  the  Penn  Metal  Company,  Boston, 
Mass.,  in  sheets  24  by  96  in  in  size  and  of  the  following  gauges:  No.  22,  weighing 
4  lb  per  sq  yd;  No.  24,  weighing  3.4  and  3  lb  per  sq  yd;  No.  26,  weighing  23^  lb 
per  sqyd;  and  No.  27,  weighing  2.3  lb  per  sq  yd.  For  such  extraordinary, 
conditions  as  are  found  in  gas-plants,  dye-works  or  places  where  excessive 
moisture  or  salt-air  action  exists,  Hampton  Rust-Resisting  Lath  is  made. 

Key  Expanded-Metal  Lath,  made  by  the  General  Fireproofing  Company, 
Youngstown,  Ohio,  is  furnished  in  sheets  24  by  96  in,  in  Nos.  27,  26,  25,  and  24 
gauge,  weighing  respectively  2.34,  2.50,  3.00,  and  3.40  lb  per  sq  yd. 

Kno-Burn  Lath,  made  by  the  North  Western  Expanded  Metal  Company, 
Chicago,  111.,  is  .furnished  in  sheets  18  by  96  in,  in  Nos,  27,  26,  25,  and  24  gauge, 
weighing  respectively  2},^,  2\'2,  3,  and  3.4  lb  per  sq  yd.  When  made  from  a 
special  acid-resisting  sheet  steel,  this  lath  is  sold  under  the  name  XX  Century 
Expanded  Metal  Lath. 

Herringbone  Expanded  Metal  Lath  (Fig.  72),  made  by  The  General  Fire- 
proofing Company,  Youngstown,  Ohio,  is  furnished  in  three  styles.  A,  AAA,  and 
BB.  Style  A  is  made  in  sheets  13^^  by  96  in  (i  sq  yd),  of  No.  28-gauge  metal, 
weighing  3  lb  per  sq  yd.  Style  AAA  is  made  in  sheets  18  by  96  in,  and  from  27, 
26,  and  24-gauge  metal,  weighing  2.53,  2.81,  and  3.79  lb  per  yd,  respectively. 
Style  BB  is  made  in  sheets  2014  by  96  in  {i^i  sq  yd),  of  Nos.  27,  26,  and  24-gauge 
metal,  weighing  respectively  21^,  2},^,  and  3-%  lb  per  sq  yd.  It  is  made  of  steel, 
American  ingot-iron,  or  galvanized  sheets.  Ribs  are  set  across  studs  and  slope 
down  towards  them. 

Sykes  Expanded  Cup-LatK,  made  by  the  Sykes  Metal  Lath  and  Roofing 
Company,  Niles,  Ohio,  is  furnished  in  sheets  18  by  96  in,  with  an  antirust 
coating,  or  painted  black,  or  galvanized.  It  is  made  of  Nos.  27,  26,  and  24- 
^auge  metal,  weighing  respectively  2.8^  3,  and  3.7  lb  per  sq  yd, 


Expanded-Metal  Lath 


885 


Standard  Rib  Lath,  made  by  the  Truscon  Steel ,  Company,  Detroit,  Mich., 
is  furnished  in  sheets  20H  by  96  in,  in  grades  i,  2,  and  3,  weighing  respectively 
2.74,  3.42,  and  4.10  lb  per  sq  yd.    This  company  makes  also  the  Beaded  Plate 


Fig.  72.     Expanded-metal  Lath,  Herringbone  Mesh 

Rib-Lath,  which  is  about  35%  heavier  and  more  rigid,  permitting  wider  spacing 
of  the  studs. 

Netmesh  Diamond  Expanded-Metal  Lath  is  manufactured  by  the  Mil- 
waukee Corrugating  Company,  Milwaukee,  Wis.  This  lath  is  furnished  in 
sheets,  24  by  96;  in  27,  26,  25,  and  24  gauges,  painted;  and  in  26  and  24  gauges 
only,  hot-galvanized  after  cutting.  This  Company,  also,  makes  corrugated 
OR  SELF-FURRING  LATH,  in  sheets  21 1.^  by  96  in,  same  gauges,  except  No.  25,  as 

for  NETMESH. 

Kno-Fur  Lath,  made  by  the  North  Western  Expanded  Metal  Company, 
Chicago,  111.,  is  furnished  in  sheets  22  by  96  in,  of  Nos.  24,  25,  26,  and  27-gauge 
metal,  weighing  respectively  3.80,  3.36,  2.82,  and  2.62  lb  per  sq  yd.  This  lath 
has  ribs  running  obliquely  across  the  sheets  at  the  same  angle  as  the  strands 
of  the  mesh.  This  corrugation  is  said  to  give  the  lath  greater  rigidity  so  that 
it  can  be  used  on  32-in  centers  for  walls  and  on  24-in  centers  for  ceilings.  The 
corrugations  act  as  furring-strips.  It  is  made  from  a  special  acid-resisting 
STEEL  and  is  always  supplied  painted. 

Integral  Expanded-Metal  Lath.  Truss-metal  lath,  Fig.  73,  made  by  the 
American  Rolling  Mill  Company,  Middletown,  Ohio,  is  furnished  in  sheets 


Fig.  73.     Truss  Metal  Lath 

28  by  90  in,  of  Nos.  26  and  28-gauge  metal,  weighing  respectively  80  and  66.7  lb 
per  100  sq  ft.  A  partition  constructed  of  this  lath  in  one  of  the  test-structures 
at  Columbia  University,  New  York  City,  passed  through  and  withstood,  with- 
out any  sign  of  distress,  the  fire  and  hose-streams  of  five  successive  tests. 

Self-Sentering,  made  by  the  General  Fireproofing  Company,  Youngstown, 
Ohio,  is  furnished  in  sheets  29  in  wide  and  in  lengths  varying  by  i  ft,  from  4  to 


886 


Fireproofing  of  Buildings 


Chap.  23 


12  ft,  of  Nos.  28,  26,  and  24-gauge  metal,  weighing  respectively  0.58,  0.70,  and 
0.93  lb  per  sq  ft.  The  width  of  29  in  is  the  covering  capacity,  as  laps  are  pro- 
vided for  by  outside  ribs.     (See,  also,  page  853.) 

Hy-Rib,  made  by  the  Truscon  Steel  Company,  Detroit,  Mich.,  is  furnished  in 
three  types  known  as  4-Rib,  3-Rib,  and  Deep  Rib.  The  first  is  in  sheets  loj,^ 
in  wide,  and  the  others  in  sheets  14  in  wide.  (See,  also,  page  853.)  All  styles  are 
furnished  in  Nos.  24,  26,  and  28-gauge  metal.  The  standard  lengths  are  6,  8,  10, 
and  12  ft.  Other  lengths  below  12  ft  are  cut,  but  the  waste  is  at  the  cost  of  the 
purchaser.  Hy-Rib  sheets  interlock  at  the  sides  and  ends.  In  ordering,  no 
allowance  need  be  made  for  side  laps,  but  for  end-laps  2  in  should  be  allowed  for 
laps  over  supports,  or  8  in  between  supports. 

Trussit  is  manufactured  by  The  General  Fireproofing  Company,  Youngs- 
town,  Ohio,  in  sheets  19  in  in  width,  and  in  lengths  of  8,  10,  and  12  ft,  from  27, 
26i  and  24  gauge,  weighing  0.57,  0.62,  and  0.83  lb  per  sq  ft,  respectively. 


(2)  Sheet  Lath 

Clinched  Lath,  made  by  the  American  Rolling  Mill  Company,  Middle- 
town,  Ohio,  is  furnished  in  sheets  13 ^  by  96  in  (1  sq  yd),  of  No.  30-gauge  metal, 
weighing  43,4  lb  per  sq  yd. 

Truss-Loop  Lath,  Fig.  74,  made  by  the  Bostwick  Steel  Lath  Company, 
Niles,  Ohio,  is  furnished  in  sheets  13],^  by  96,  161,4  by  80,  and  24  by  96  in, 

weighing  434  lb  per  sq  yd.  This 
lath  is  furnished  painted  unless 
otherwise  specified. 

Genfire  Sheet-Steel  Lath, 
made  by  the  General  Fireproofing 
Company,  Youngstown,  Ohio,  is 
furnished  in  sheets  24  by  96  in, 
weighing  4.6  lb  per  sq  yd,  painted 
unless  otherwise  specified. 

Sykes    Trough     Sheet     Lath, 

made    by   the    Sykes   Metal    Lath 

and  Roofing  Company,  Niles,  Ohio, 

is  furnished  in  sheets  131,2  by  96  in 

(i  sq  yd),  151,^  by  96,  i8l^  by  96,  and  231.^  by  96  in,  weighing  5  lb  per  sq  yd, 

and  made  with  an  antirust  coating,  or  painted  or  galvanized. 

Integral  Sheet  Lath.  Rib-Truss,  made  by  the  Berger  Manufacturing 
Company,  Canton,  Ohio,  is  furnished  in  widths  of  24  in,  and  in  stock  lengths  of 
4,  5,  6,  8,  10,  and  12  ft,  as  follows: 


Fig.  74.     Bostwick  Truss-loop  Lath 


Gauge 


Weight  per  square  yard  in  pounds 


1 3-2-10  rib 

H 

-in  rib 

73 

78 

81 

86 

88 

94 

117 

125 

27 
28 
26 
24 


83 
92 

100 

133 


Woven-Wire  Lath 


887 


(3)  Woven-Wire  Lath 

Woven-Wire  Lath  is  furnished  with  or  without  stiffeners,  which  are  either 
rods  or  V-shaped  ribs  running  through  the  wire  mesh  to  reinforce  and  stiffen  it. 
It  is  suppHed  painted  or  unpainted,  or  it  is  galvanized  after  weaving.  It  can  be 
furnished  to  order  in  any  required  width  up  to  lo  ft.  In  widths  less  than  i8  in, 
there  is  a  small  charge  for  stripping.  Before  ordering,  it  is  very  important  to 
ascertain  the  proper  width,  especially  of  stiffened  lath,  as  it  is  desirable  to  have 
the  edges  of  the  lath  lap  at  the  supports  where  it  is  laced  to  iron  furring.  When 
the  lath  is  not  of  the  proper  width  the  results  are  not  so  good  and  there  is  hable 
to  be  a  waste  of  material.  The  standard  width  of  plain  and  of  V-rib  stiffened 
LATH  is  36  in.  When  beams  or  studs  are  spaced  16  in  from  center  to  center,  the 
lath  should  be  32  or  48  in  wide. 

The  Clinton  Stiffened  Lath  has  corrugated-steel  furring-strips  attached 
every  8  in,  crosswise  of  the  fabric,  by  means  of  metal  clips.  These  strips  con- 
stitute the  FURRING,  and  the  lath  is  applied  directly  to  the  underside  of  the  floor- 
joists,  or  to  planking,  furring,  brick  walls,  etc.  This  lath  is  made  in  36-in  widths, 
with  2)4  meshes  to  the  inch,  and  comes  in  100-ft  rolls.  The  manufacturers  of 
this  lath  make,  also,  a  lath  stiffened  with  round  rods,  H  to  i  in  in  diameter, 
spaced  from  8  to  12  in  apart.  It  can  be  had  either  galvanized  or  japanned,  and 
in  thicknesses  from  18  to  21  gauge.  Clinton  plain  wire  lath  is  furnished  in  roUd 
200  ft  long. 

The  Roebling  Standard  Wire  Lath  (controlled  by  the  New  jersey  Wire 
Cloth  Company,  New  York),  is  made  of  plain  wire  CLOTH,  in  which,  at  intervals 
of  73^  in,  stiffening  ribs  are  woven.  These 
ribs  have  a  V-shaped  section  and  are  made  of 
No.  24  sheet  steel,  H  and  i  in  in  depth.  The 
^-in  rib  is  the  standard  size  for  lathing  on 
Woodwork.  This  lathing  requires  no  furring, 
and  is  applied  directly  to  woodwork  or  to 
walls,  with  steel  nails  driven  through  the  bot- 
tom of  the  V,  as  shown  in  Fig.  75.  The  No. 
20  V-rib  stiffened  lathing  affords  a  satisfac- 
tory surface  for  plastering,  when  attached  to 
Studs  or  beams  spaced  16  in  apart.  The  i-in 
V-rib  lathing  is  used  for  furring  exterior 
walls.  It  provides  an  air-space  between  the 
wall  and  plaster.  Where  this  lath  is  to  be 
applied  to  light  iron  furring,  a  Mo  or  ^-in 
solid  steel  rod  is  substituted  for  the  V-rib, 
and  the  lathing  is  attached  to  light  iron 
furring  with  lacing  wire.  This  lath  is  distinguished  from  the  others  by  the  term 
Solid-Rib  Stiffened  Wire  Lath.  The  Roebling  lath,  whether  plain  or  stiffened, 
is  made  with  2  by  2,  2^^  by '2H,  and  2H  by  4-in  mesh,  the  last  named  being 
known  as  close  warp.  The  2M  by  2%  mesh  is  adapted  to  all  plasters  contain- 
ing the  usual  proportion  of  hair  or  fiber.  The  2H  hy  4-in  mesh  should  be  used 
for  hard  plasters  and  thin  partitions.  The  lath  can  be  furnished  in  widths  up  to 
10  ft,  the  rolls  averaging  50  yd  in  length. 

Wall-Boards.  There  are  various  forms  of  wall-boards  of  an  incombustible 
nature,  most  of  them  made  of  gypsum  in  combination  with  felts.  They  can  be 
used  as  suljstitutes  for  laths.  They  are  very  light  and  require  but  little  plaster- 
ing material  When  this  saving  is  taken  into  account,  wall-boards  cost  less  than 
metal  lath  and  but  little  more  than  wooden  lath  with  three  coats  of  plaster.    The 


Fig.  75.     Roebling  V-rib  Stiffened 
Wire  Lath 


888  Fireproofing  of  Buildings  Chap.  23 

boards  are  generally  32  by  36  in  in  size,  and  }4,  Me,  y^,  or  l^  in  in  thickness. 
The  thinnest  boards  {\i  in)  weigh  i  V2  lb  per  sq  ft,  and  the  thickest  (3^  in)  2  J^  lb. 
Wall-boards  of  asbestos  are  described  on  page  819.  The  best  known  is  transite, 
made  by  the  H.  W.  Johns-Manville  Company,  New  York. 

Sackett's  Wall-Board.  This  is  a  composite  board  of  three  layers  of  pure 
gypsum  and  four  thin  layers  of  wool-felt.  The  boards  can  be  nailed  to  wooden 
studding  or  set  flat  against  solid  beams  or  planks,  and  can  be  cut  with  a  saw. 
For  plastering,  the  best  results  are  obtained  by  applying  first  a  brown  coat  of 
hard  wall-plaster,  34  to  y^  in  thick,  and  when  this  is  thoroughly  set,  finishing  it 
with  a  thin  coat  of  regular  hard  finish  of  lime-putty  and  plaster.  Tests  and 
investigations  at  the  Underwriters'  Laboratories  "have  shown  Sackett  Board, 
Perfection  Brand,  to  be  suitable  as  abase  for  fibered-gypsum  plasters;  and  when 
attached  to  walls,  ceilings,  and  partitions  and  coated  with  V2  in  of  plaster,  possess 
fire-retarding  properties  considerably  higher  than  those  of  wooden  lath  with 
gypsum  or  lime-and-cement  plaster."  The  Perfection  Brand,  Sackett's  Wall- 
Board,  is  H  in  thick,  and  is  attached  with  No.  10^2,  3^-in,  flat-headed,  ^-barbed 
wire  nails,  i  M  in  long,  and  spaced  not  more  than  6  in  at  each  support.  Sackett's 
Board  is  made  by  the  United  States  Gypsum  Company,  Chicago,  111.,  and  the 
Grand  Rapids  Pluster  Company,  Grand  Rapids,  Mich.  Other  makers  of  gypsum 
wall-boards  are  the  J.  B.  King  Company,  New  York  (Diamond  Brand),  the 
Southern  Gypsum  Company,  North  Holston,  Va.  (Economy  Brand),  and  the 
American  Gypsum  Company,  Port  Clinton,  Ohio  (Monarch  Brand), 

Metal-Rib  Plaster-Board  is  composed  of  alternate  layers  of  strong  absorbent 
paper  reinforced  with  fine  annealed  wire  about  2  in  on  centers,  and  stiffened 
transversely  with  3'2-in  iron  bands.  No.  32  gauge,  placed  8  in  on  centers.  The 
material  is  made  up  to  a  total  thickness  of  about  \\&  in,  impregnated  with-  a 
coal-tar  product,  and  provided  every  2  in  with  Me-in  circular  holes  to  key  the 
plaster.  This  is  added  to  the  adhesive  effect  of  the  absorbent  paper.  It  is 
furnished  in  rolls  85  ft  long  and  34  in  wide,  nailed  directly  to  the  studs  or  beams 
set  12  or  16  in  on  centers,  and  lapped  2  in  at  all  joints.  This  board  is  recom- 
mended for  use  with  hard -plaster  mortars  only,  and  forms  a  satisfactory  basis 
for  three-coat  work,  in  which  the  lap-joint  obviates  the  cracking  frequently 
associated  with  ordinary  plaster-board  construction. 

Bestwall.  Bestwall  is  primarily  intended  for  use  as  an  interior  finish  on 
side  walls  and  ceilings  in  buildings  of  all  classes.  It  may  be  used  in  all  situations 
where  finishes  of  lath  and  plaster  may  be  used,  and  in  many  situations  where 
the  latter  finish  is  not  adaptable.  It  consists  of  a  single  layer  of  fiber  calcined 
gypsum,  surfaced  on  each  side  with  specially  prepared  water-proofed  paper  se- 
curely bonded  to  the  surface.  Bestwall  is  ^  in  in  thickness,  and  is  furnished  in  ' 
stock  sizes  47%  in  wide,  and  in  lengths  of  5,  6,  7,  8,  9,  and  10  ft.  The  finished 
product  presents  a  smooth,  true  surface,  which  is  light  cream  in  color  on  the 
face-side  and  gray  on  the  reverse  side.  The  edges  are  sHghtly  beveled  to  pro- 
vide for  the  filling  of  the  joints,  and  are  doubly  reinforced.  Its  weight  is  ap- 
proximately 1850  lb  per  1,000  sq  ft.  Interior  finish  composed  of  Bestwall  is 
applied  by  nailing  the  Bestwall  directly  to  the  joists,  studs,  and  furring,  and 
filling  the  joints  between  the  pieces  of  Bestwall  with  a  specially  prepared  filler 
of  the  same  composition  as  the  core  of  the  board.  For  the  nailing,  threepenny 
fine  wire  nails,  spaced  from  2  to  3  in  at  the  edges  and  from  8  to  1 2  in  at  the  inter- 
, mediate  supports,  are  used.  The  filling  consists  of  two  operations;  first,  rough- 
ing IN  and  then,  troweling  out,  to  a  smooth,  true  finish,  flush  with  the  surface. 
Bestwall  is  cut  and  fitted  either  with  a  saw  or  by  scoring  and  breaking  over  a 
straight-edge.    The  completed  finish  presents  a  smooth,  true,  continuous  surface, 


Deadening  Properties  of  Partitions  889 

without  showing  joints  or  nail-heads,  and  ready  to  receive,  if  desired,  a  decoration  • 
of  paint,  paper,  tint,  etc. 

Shaft-Construction.  The  most  important  partitions  in  a  building  are  those 
inclosing  interior  shafts.  Vertical  openings  through  buildings  form  flues  and 
cause  up-drafts.  In  all  buildings,  fire-proof  as  well  as  non-fire-proof,  therefore, 
they  should  be  inclosed  for  two  reasons:  first,  to  prevent  a  fire  that  would  find 
a  natural  outlet  in  such  openings  from  spreading  to  other  floors;  and  secondly, 
to  prevent,  as  far  as  possible,  a  fire  from  getting  into  these  openings  where  the 
draft  would  greatly  increase  its  fury.  To  be  thoroughly  effective  the  inclosed 
walls  should  be  constructed  of  the  same  materials  as  the  outside  walls  of  the 
buildings,  namely,  brick,  stone,  or  concrete.  While  they  need  not  be  of  the 
same  thickness  as  the  outside  walls,  12  in  is  recommended  as  a  minimum  thick- 
ness. In  less  important  structures  terra-cotta  partitions  are  sometimes  used 
for  such  inclosing  walls.  In  the  walls  inclosing  elevator-shafts  no  openings 
except  those  necessary  for  entrance-doors  should  be  permitted.  The  doors 
should  be  of  fire-proof  construction,  pages  901-2,  and  made  solid.  Glass  lights 
are  sometimes  provided  in  such  doors,  although  this  is  not  good  practice;  if 
they  are  used,  wire-glass,  only,  should  be  used,  in  accordance  with  the  limita- 
tions noted  on  pages  90^-3.  Open  grille-work  for  passenger-elevator  enclosures 
is  being  rapidly  superseded  by  construction  which  is  more  fire-resisting.  The 
architectural  features  of  open  grilles  may  still  be  retained  for  the  fronts  and  doors 
of  such  elevators  by  using  them  in  conjunction  with  approved  wire-glass  con- 
struction. In  interior  light-shafts  and  vent-shafts,  openings  must  necessarily  be 
provided,  but  here  again  the  construction  of  the  window- frames,  sashes,  and 
glazing  should  be  as  far  as  possible  as  described  on  pages  901  to  903.  When- 
ever the  occupancy  of  a  building  admits,  the  stairs,  also,  should  be  inclosed  in 
masonry  walls,  with  fire-proof  doors  at  the  openings.  Unless  so  inclosed  the 
stairways  form  flues  for  the  flames,  and  the  stairs  themselves,  consequently, 
are  exposed  to  intense  heat.  In  such  situations,  even  absolutely  fire-proof  stairs 
could  not  be  used  during  a  fire,  and  possibly  it  is  for  this  reason  that  greater 
pains  have  not  been  taken  to  make  them  fire-proof.  Shaft-walls  should  in  all 
cases  be  carried  3  ft  or  more  above  the  roof. 

Deadening  Properties  of  Partitions.  The  resistance  to  the  passage  of 
sound  thrcaigh  fire-proof  partitions  is  an  important  consideration  in  buildings 
used  for  living-apartments;  and  where  the  rooms  are  to  be  used  as  music-studios, 
it  becomes  a  matter  of  still  greater  importance.  In  January,  1895,  some  tests 
were  made  to  determine  the  relative  deadening  properties  of  the  different 
partitions  shown  in  Fig.  76,  the  object  being  to  decide  upon  the  construction 
that  should  be  used  in  Steinway  Hall,  Chicago,  111.  The  rank  of  the  different 
partitions  tested,  in  sound-proof  i:fficiency,  is  shown  by  the  numbers  at  the 
right  of  the  partition-diagrams.  The  4-in  porous  partition  was  used,  but  was 
not  a  success.  In  the  Fine  Arts  Building,  in  the  same  city,  double  partitions, 
similar  to  No.  i,  were  used,  and  it  is  said  that  they  were  a  great  success.  It  is 
surprising  to  note  that  in  the  tests  above  mentioned,  the  2-in-solid~plaster  par- 
tition. No.  3,  plastered  with  common  mortar,  ranlced  higher  in  sound-deadening 
properties  than  those  with  double  studs.  In  1892  C.  L.  Norton  tested  the 
sound-deadening  properties  of  partitions  of  several  forms,  for  the  purpose  of 
selecting  a  construction  which  was  the  most  fire -resisting  and  sound-proof 
for  the  dormitories  of  the  New  England  Conservatory  of  Music,  in  which  prac- 
tically every  room  is  a  music-studio.*  The  various  partitions  were  rated  by 
Professor  Norton  as  shown  in  the  following  table: 

*  The  results  of  these  tests,  with  a  description  of  the  partitions,  were  published  ii^ 
Insurance  Engineering  for  August,  1902. 


890 


Fireproofing  of  Buildings 


Chap. 


Air  Space 


^Plaster 


Plabter-^ 


^»W' 


c 


Angle  Iron'^         f         ^^  ^^'^'^  ^^*^       Filled  in  solid 
12 "Centers  \  with  EUistei; 

^Wire  Cloth  Laced  to  Rod. 
SOLID  PLASTER  PARTITION 


K 


-2  Studs  16  Centers 


'Wire  Cloth. Laced  to  Rods 

»^"  Rod  12"  Centers'^ 


""y^^^^nu^mnU) '  Centers 


X 


.vNt.,Fijlinj^.  _ 


Expanded-Metal/ 


*  ^%" 


yK"l^od  12  "Centers 


5 


2 "iron  Studs  16* Centers 


^Wire  Cloth  Laced  to  Rod 


\Plaster 


/Iron  16"  Centers 


J^xpanded.Metal- 


Expanded  Metal- 


Mron  IG"  Centers 


Fig.  76.    Relative  Deadening  Properties  of  Partitions 


Furring  for  Outside  Walls  89J 

Table  XVI.     Sound-Deadening  Properties  of  Partitions 


No. 

Room 

Side 

Scale 

I 

E 

Left 

lOO 

2 

E 

Right 

.95 

3 

E 

Rear 

95 

4 

C 

Rear 

85 

5 

C 

Left 

85 

6 

C 

Right 

8o 

7 

D 

Rear 

75 

8 

D 

Right 

75 

9 

B 

Right 

6o 

lO 

A 

Rear 

50 

II 

-    B 

Rear 

50 

12 

A 

Right 

45 

13 

B 

Left 

40 

14 

A 

Left 

40 

IS 

D 

Left 

30 

Composition 


Cabot's  quilt,  3  thick  and  metal  lath 

Cabot's  quilt,  2  thick  and  metal  lath 

Cabot's  quilt,  2  thick  and  metal  lath 

Sackctt  board,  2  felt  on  channels 

Sackett  board,  2  felt  on  channels 

Sackett  board,  2  felt 

Metal  lath  and  paper 

Metal  lath,  paper,  and  felt 

Two  2-in  Keystone  blocks  with  2-in  air-space 

4-in  National  tcrra-cotta  blocks 

3-in  Keystone  blocks 

3-in  National  terra-cotta  blocks 

2-in  Keystone  blocks 

2-in  National  terra-cotta  blocks 

2-in  metal  lath,  solid  plaster 


"Nothing  more  is  to  be  inferred  from  the  numerical  efficiencies,  under  'scale,* 
than  that  the  first  partition  is  about  three  times  as  good  as  the  last,  and  that  the 
numerical  interval  between  any  two  partitions  on  the  list  merely  indicates  the 
order  of  the  magnitude  of  the  difference  between  the  partitions."  Professor 
Norton  recommended  a  partition  of  Sackett  Board  and  plaster  with  two  thick- 
nesses of  Cabot's  ciuilt  between  the  plaster-boards,  and  this  construction  was 
adopted.  The  studding  was  put  up  the  same  as  for  the  2-in  solid  partition,  the 
quilt  secured  to  each  side  of  the  studs,  and  the  plaster-board  wired  on  to  the 
studs  through  the  quilt.  This  makes  as  light  a  partition,  also,  as  it  is  possible  to 
construct.  The  investigations  by  Professor  F.  R.  Watson  of  the  University  of 
Illinois  showed  that  2-in  solid,  metal-lath  partitions  are  more  sound-deadening 
than  3-in  hollow,  gypsum-block  partitions.  Gypsum  tile  has  been  found  to  be 
more  satisfactory  than,  terra-cotta  tile  of  the  same  thickness. 

Furring  for  Outside  Walls.  The  outside  walls  of  fire-proof  buildings  are 
generally  finished  on  the  inside  by  plastering  applied  directly  to  the  masonry. 
When  the  walls  are  of  brick,  it  is  often  desirable  to  fur  them  so  that  there  will  be 
an  air-space  between  the  plaster  and  the  masonry  to  prevent  the  passage  of 
moisture.  This  furring  should  be  either  of  terra-cotta  or  metal,  and  never  of 
wood.  For  this  purpose  furring-bricks  may  be  used.  They  are  made  of  brick- 
clay  and  of  the  same  size  as  common  bricks;  but  they  are  hollow.  They  are 
built  up  with  the  rest  of  the  wall,  on  the  inside  face,  and  bonded  into  the  wall 
by  the  usual  header-courses.  Split  furring-tiles,  also,  are  often  used  on  the  inner 
side  of  brick  walls,  as  shown  in  Fig.  77.  The  tiles  are  either  i  Y^  or  2  in  thick 
and  12  by  12  in  on  the  face.  The  face  is  grooved  to  give  proper  bond  for  the 
plastering.  At  recesses  in  the  walls  partition-blocks  are  substituted  across  the 
openings,  making  a  continuous  wall-surface.  When  using  furring-tiles,  the 
mason  should  be  careful  not  to  drop  mortar  into  the  hollow  spaces.  When  walls 
are  furred  or  lined  with  tile,  solid  porous  terra-cotta  blocks  should  be  built  in 
wherever  nailings  are  required  for  bases,  picture-moldings,  etc.  Wire  lathing, 
also,  with  i-in  V  ribs  woven  in  every  7H  in,  makes  a  good  furring  for  brick 
walls,  as  it  is  easily  applied  and  leaves  air-spaces  between  the  wall  and  plaster. 
All  of  these  devices  also  protect  the  walls  from  being  warped  by  heat  during  a 
fire,  and  prevent  the  passage  of  heat  through  the  walls  in  summer  and  winter. 


892 


Fireproofing  of  Buildings 


Chap.  23 


Metal  Furring.  To  produce  architectural  forms  in  the  interior  decoration 
of  fire-proof  buildings,  metal  furring  and  metal  lath  are  now  almost  uni- 
versally used.    The  furring  is  always  of  a  sham  nature,  and  never  employed 


Fig.  77.     Hollow-Tile  Wall-furring 

to  carry  loads  of  any  magnitude;  so  that  the  only  requirement  is  that  it  shall 
be  incombustible  and  furnish  a  satisfactory  ground  for  attaching  the  metal  lath. 
For  coves,  cornices,  false  beams,  etc.,  the  furring-members  are  made  of  light 
bars,  angles,  tees,  or  channels,  attached  to  the  walls  by  means  of  nails,  staples, 
or  toggle-bolts,  and  to  the  steel  beams  by  means  of  bolts,  hangers,  chps,  etc. 
The  furring-pieces  are  bent  or  shaped  to  the  approximate  outlines  of  the  finished 
plaster-work,  so  that  when  the  lathing  is  applied  it  will  require  not  more  than 
I  ]i  or  2  in  of  plaster  to  give  the  desired  outline.  For  plane  surfaces,  the  furring 
should  be  brought  to  within  %  in  of  the  plaster-line.  Deep  beams,  etc.,  should 
be  braced  by  diagonal  rods,  to  prevent  distortion.  All  structural-steel  members 
should  always  be  fire-proofed  back  of  the  furring.  The  lathing  is  secured  to 
the  furring  by  means  of  No.  i8  galvanized  lacing-wire.  The  spacing  of  the 
furring  should  be  either  12  or  1 6  in,  according  to  the  kind  of  lath  that  is  to  be 
used.  When  chases  in  walls  are  covered  over,  the  covering  should  be  done  with 
metal  furring  and  lath.  The  casings  for  vertical  pipe-lines,  also,  should  be  of 
this  construction  and  the  space  about  the  pipes  at  the  floor-level  should  be  filled 
solidly  with  fire-proof  material,  to  cut  off  all  connection  between  stories. 


7.    Fire-proof  Flooring 

Fire-proof  Flooring.  The  floor-surfaces  of  most  fire-proof  buildings  consist 
of  hard-wood  flooring  secured  in  the  usual  manner  to  nailing-strips  embedded 
in  the  concrete  or  in  the  filling  above  it.  It  is  sometimes  advisable  to  use  in- 
combustible flooring.  The  New  York  City  Building  Code  requires  that  in  all 
buildings  over  150  ft  in  height,  the  floor-surfaces  shall  be  of  stone,  cement, 
tiling,  or  similar  incombustible  material,  or  of  wood  treated  by  some  process 
which  renders  it  fire-proof.  For  warehouses  and  factories,  floors  finished  with 
Portland-cement  mortar  are  about  as  satisfactory  as  floors  with  any  other  over- 
floor  finish;  and  cement  floors  have  been  much  used  for  the  guest-rooms  of 


Fire-proof  Flooring  893 

hotels.  In  the  latter  rooms,  the  floors  are  covered  with  carpets,  which  are 
secured  to  wooden  strips  embedded  in  the  cement  around  the  borders  of  the 
rooms.  This  makes  a  very  sanitary  floor,  and  one  as  easy  for  the  feet  as  a  car- 
peted wooden  floor.  For  pubHc  corridors,  banks,  lobbies,  toilet-rooms,  etc.,  the 
encaustic,  vitreous,  ceramic,  or  marble  tilings  are  generally  used.  In  France  and 
Germany  large  quantities  of  cement  tiles  are  used.  Cement  tiles  have  been  in- 
troduced into  this  country,  also,  but  have  not  yet  been  able  to  compete  with 
the  encaustic  tiles.  In  most  buildings,  however,  the  use  of  stone,  cement,  or  tile 
flooring  is  inadvisable.  These  materials  are  cold  and  trying  to  the  feet.  As  a 
rule,  cement  floor-surfaces  do  not  wear  well.  Asphaltic  flooring  is  sometimes 
used,  but  it  is  not  pleasing  in  appearance.  This  material  and  different  floor- 
tiles  are  discussed  on  pages  1604  to  1609.  The  characteristics  of  fire-proofed 
wood  and  its  availability  for  this  purpose  are  considered  in  the  discussion  of  that 
material  on  page  820. 

Composition  Flooring.  Several  attempts  have  been  made  to  obtain  a 
flooring-material  which  could  be  spread,  without  joints,  over  an  entire  floor, 
and  at  the  same  time  be  elastic,  wear  well,  withstand  water,  acids,  etc.,  and  not 
be  too  expensive.  Various  mixtures  of  magnesite,  asbestos,  fine  sand,  sawdust 
mixed  with  linseed-oil,  and  some  binder  hke  chloride  of  magnesium,  have  been 
put  on  the  market  under  different  names,  all  more  or  less  meeting  the  require- 
ments above  stated  and  being,  also,  fire-proof.  These  materials  are  shipped  in 
the  form  of  a  dry  powder  to  the  place  where  they  are  to  be  used,  and  are  there 
mixed  with  a  speciafly  prepared  liquid.  The  resultant  is  a  plastic  material 
which  is  laid  upon  the  surface  to  be  covered  in  much  the  same  way  that  ordi- 
nary cement  or  plaster  is  put  on.  The  materials  harden  in  from  12  to  24  hours 
in  moderately  dry  weather,  when  the  floor  is  ready  for  use.  When  properly 
laid  the  floor  presents  a  smooth,  fine-grained,  and  continuous  surface,  resem- 
bling linoleum.  These  materials  are  made  in  various  colors,  such  as  red,  white, 
yellow,  brown,  gray,  black,  blue,  and  green,  and  can  be  laid  on  wood,  stone, 
concrete,  asphalt,  cement,  or  metals.  Another  advantage  is  that  they  can  be 
carried  up  on  the  walls  so  as  to  form  a  covered  base,  without  cracks  or  joints. 
Among  the  manufacturers  furnishing  such  floorings  may  be  mentioned:  General 
Kompolite  Company,  Long  Island  City,  N.  Y.;  Marbleoid  Company,  New  York 
City;  Franklyn  R.  Muller  Company,  Chicago,  111.;  and  Ronald  Taylor  Company, 
New  York  City. 

Asphalt  Mastic  Flooring.  This  flooring  is  in  the  nature  of  an  asphaltic 
CONCRETE  consisting  of  natural  asphalt  and  a  well-graded  mineral  aggregate  of 
sand,  gravel,  and  crushed  stone,  ranging  in  size  from  that  which  passes  a  200- 
mesh  screen  to  ^  in.  The  material  is  sent  to  the  building-site  in  blocks  and  is 
there  broken  up,  reheated,  and  mixed  with  the  coarser  aggregate,  the  softened 
mass  being  laid  down  in  one  or  two  courses,  depending  upon  the  thickness 
desired,  and  smoothed  down  by  rubbing  with  wooden  floats.  It  is  laid  without 
construction-joints,  the  usual  thickness  being  ij^  in,  weighing  18  lb  per  sq  ft. 
The  finished  flooring  is  tough,  ductile,  water-proof,  resistant  to  acids,  alkaU  and 
brine,  fire-proof,  noiseless,  and  easy  on  the  feet.  It  is  especially  suitable  for 
factories  and  warehouses.  It  is  manufactured  by  the  H.  W.  Johns-Manville 
Company,  New  York 

8.  Interior  Finish  and  Fittings 

Interior  Finish.  In  buildings  in  New  York  City  in  which  the  flooring  must 
be  of  incombustible  material,  the  interior  finish,  also,  including  the  doors,  door- 
jambs,  window-frames,  sashes,  bases,  and  trims,  must  be  made  of  incombustible 


894  Fireproofing  of  Buildings  Chap.  23 

materials.  The  same  materials  that  are  accepted  for  flooring  can  be  used  for 
this  interior  finish  also.  Several  of  the  largest  buildings  in  New  York  City, 
including  the  Fuller  Building,  have  all  the  trim  constructed  of  fire-proof 
WOOD.  In  the  Hotel  Gotham,  all  the  doors  and  interior  finish  are  made  of 
Alignum. 

Metal  Doors,  Sashes,  Frames,  and  Trim.*  The  effort  to  make  the  interior 
of  buildings  fire-proof  has  resulted  in  metal-covered  wood,  and  in  doors, 
sashes,  frames,  trim,  and  moldings  of  hollow  steel  or  other  metal.  Many  very 
large  buildings  have  in  recent  years  been  equipped  wholly  or  in  part  with  these 
products,  and  the  products  themselves  have  reached  a  stage  of  great  perfec- 
tion of  workmanship  and  efficiency.  Several  cities  in  the  United  States  compel 
the  use  of  these  products  for  certain  parts  of  buildings  which  are  over  a  certain 
height;  and  it  is  probably  only  a  question  of  time  when  other  cities  will  pass 
ordinances  compelling  their  use.  At  the  present  time  cost  enters  largely  into 
the  question  of  substituting  them  for  wood.  Among  the  first  attempts  in  the 
United  States  to  fire-proof  the  interior  trim  of  buildings  were  those  made  in 
New  York  City,  about  the  year  1880,  in  the  form  of  metal-covered  woodwork, 
by  the  firm  of  Campbell  &  Bantossell  of  that  city.  About  this  time,  also, 
there  were  introduced  along  with  various  processes  of  fire-proofing  woodwork, 
FIRE-PROOF  PAINTS.  Later,  fire-proof  wood  was  introduced,  that  is,  wood 
which  has  the  resin  and  other  inflammable  components  extracted  from  it,  and 
the  fiber  left.  In  the  course  of  a  few  years  the  metal-covered- wood  industry 
developed  to  such  a  stage  that  it  was  possible  to  trim  with  its  products  the 
interior  of  a  building  and  keep  a  good  appearance.  Notable  examples  are  the 
Manhattan  Life  Insurance  Company's  Building  and  the  Barclay  Building,  and, 
of  more  recent  date,  the  Metropolitan  Tower,  f  the  Fifth  Avenue  Office-Building, 
the  Germania  Life  Insurance  Company's  Building,  and  the  Var.derbilt  Hotel, 
all  in  New  York  City;  the  Hoge  Building,  Seattle,  Wash.;  the  Hall  of  Records, 
Los  Angeles,  Cal.;  the  Rockefeller  Annex,  Cleveland,  Ohio,  etc.  The  rough, 
unfinished  appearance  of  the  standard  tin-clad  door  set  men  to  seeking  a 
product  for  use  in  interior  finish  which  would  lend  itself  to  rnore  decorative 
effects.  The  Xalamein  iron  and  other  metal-covered  work  resulted. 
In  the  meantime  improvements  were  constantly  being  made  in  hollow 
sheet-metal  doors  and  trim,  and  from  about  the  year  1903  hollow  steel 
construction  for  this  work  came  into  use.  Owing  to  its  generally  superior 
workmanship  and  to  the  splendid  enamel  surfaces  which  can  be  given  it  by 
Various  baking-processes,  this  type  of  interior  finish  has  found  favor  in  the  eyes  of 
the  architects  and  owners  of  modern  offices,  and  mercantile  and  public  buildings. 

Kalamein  Iron.  J  Kalamein  Iron  is  the  trade  name  given  to  one  of  the 
open-hearth  sheet-steel  products  which  is  covered  with  a  thin  alloy  of  tin  and 
lead  in  much  the  same  way  that  galvanized  iron  by  galvanic  immersion  is 
coated  with  zinc.  "The  name  Calamine  (with  Galmci  of  the  Germans)  is 
commonly  supposed  to  be  a  corruption  of  Cadmia.     Agricola  says  it  is  from 

*  For  a  brief  outline  of  this  subject,  illustrated  with  numerous  detail  drawings,  see 
article  on  Metal  Doors,  Sashes,  Frames,  and  Trim,  by  Professor  Thomas  Nolan,  in 
Kidder's  Building  Constructon  and  Superintendence,  Part  II,  Carpenters'  Work. 

t  The  Metropolitan  Tower  has  a  metal-covered  trim  which  is  a  special  bronze-pl^te 
construction  over  a  wooden  core.  This  was  developed  by  The  John  W.  Rapp  Company, 
afterwards  consolidated  with  The  J.  F.  Blanchard  Company  into  the  United  States  Meta? 
Products  Company,  New  York  City. 

t  Among  the  better  known  manufacturers  of  metal-covered  work,  whose  doors  are 
inspected  and  labeled  by  the  Underwriters'  Laboratories,  Inc.,  are  the  United  States 
Metal  Products  Company,  New  York. City  and  the  Thorp  Fireproof  Door  Company, 
Minneapolis,  Minn. 


Interiot  Finish  and  Fitting^  895 

Calamus,  a  reed,  in  allusion  to  the  slender  forms  (stalactic)  common  in  the 
Cadmia  formation."*  The  term  Kalamein  is  often  used  incorrectly,  by  archi- 
tects and  others,  for  any  form  of  metal-covered  woodwork,  whether  the  metal 
is  steel,  copper,  or  bronze,  to  distinguish  metal-covered  from  hollow  metal  con- 
struction; but  the  term  is  obviously  misleading  and  causes  much  confusion.  In 
several  instances  architects  have  specified  Kalamein  material  expecting  bronze 
METAL  to  be  used  in  the  covering,  whereas  the  manufacturer's  interpretation  of 
the  specification  was  that  Kalamein  iron  was  intended. 

Metal-Covered  Doors,  Frames,  and  Trim.  The  cores  of  metal-covered 
doors  and  frames  are  built  up  of  oak  or  white-pine  strips  dovetailed  together 
lengthwise  to  the  grain.  In  gluing  up  the  strips  into  stiles  and  rails  the  grain 
of  each  strip  is  reversed,  in  order  to  resist  the  tendency  of  the  core  to  twist. 
The  stiles  and  rails  are  mortised,  tenoned,  and  box-wedged,  and  the  cores  are 
covered  with  asbestos  paper  or  board  and  enclosed  with  sheet  metal,  either  steel 
(which  may  be  painted  to  match  a  wooden  trim,  or  electroplated  with  copper, 
brass,  or  bronze),  or  soHd  sheet  copper,  brass,  or  bronze.  For  doors  up  to  3  ft 
4  in  in  width  and  8  ft  in  height,  both  sides  are  often  made  of  continuous  sheets 
of  metal,  which  have  the  panels  pressed  into  them  by  hydraulic  pressure  and  are 
without  seam  or  joint.  The  metal  sheets  of  the  two  sides,  in  one  make  of  door,t 
are  made  to  overlap  in  a  depression  on  the  edges  of  the  door  and  are  secured 
in  place  by  screws  which  pass  through  both  face-sheets.  The  standard  thickness 
of  this  door  is  2j^  in.  When  these  doors  are  more  than  3  ft  4  in  in  width,  each 
face  is  generally  made  of  two  sheets  which  meet  over  a  middle  stile  and  lock 
together  with  a  flush  double-lock  joint.  This  makes  a  double  row  of  vertical 
panels. 

Metal-Covered  Window-Frames  and  Sashes.  Window-frames  and  sashes, 
as  well  as  door-frames  and  doors,  are  made  of  metal-covered  wood.  Bronze 
is  the  metal  usually  recommended  and  preferred  although  Kalamein  iron  may- 
be substituted  when  a  much  cheaper  construction  is  necessary.  This  cheaper 
metal  may  be  painted  and  will  give  fair  service  but  it  is  not  recommended. 
Galvanized  iron  and  copper,  also,  are  used.  "  Window-frames  and  sashes  of 
Kalamine  or  of  sheet-metal  over  wooden  cores  are  principally  used  for 
windows  or  skylights  where  the  only  danger  of  fire-contact  is  through 
flying  sparks.  They  are  non-combustible  rather  than  fire-resisting. 
The  lights  are  usually  of  plate  glass,  especially  if  Kalamine  trim  is  used 
simply  to  comply  with  the  law  in  those  cities  where  non-combustible  windows 
and  doors,  etc.,  are  required  in  buildings  of  a  certain  class  or  of  a  height 
a^ove  fixed  Hmits.  Previous  mention  has  been  made  of  their  efficiency  as 
demonstrated  in  the  burning  of  the  Kohl  building  in  San  Francisco,  and  their 
value,  even  as  a  substandard  protection,  has  been  pointed  out;  but  for  efficient 
fire-resistance,  Kalamine  windows,  especially,  are  an  unknown  quantity,  as 
the  resistance  offered  by  the  lighter  members,  such  as  sash-rails,  is  questionable. 
The  better  examples  of  the  work  present  pleasing  workmanship  and  finish.  If 
some  composition  could  be  used.for  the  body  instead  of  wood,  without  producing 
chemical  action  harmful  to  the  metal,  a  superior  type  of  Kalamine  work  would 
result  which  would  be  of  great  value." | 

Hollow  Metal  Finish  in  General. §     The  transition  from  metal-covered 

*  Dana's  Dictionary  of  Mineralogy. 

t  The  Richardson  seamless  door,  made  by  the  Thorp  Fireproof  Door  Company,  Minne- 
apolis, Minn. 

X  Fire  Prevention  and  Fire  Protection,  by  J.  K.  Freitag. 

§  Among  the  better-known  manufacturers  of  hollow,  sheet-metal  doors,  trim,  etc., 
are  the  Dahlstrom  Metallie  Door  Company,  Jamestown,  N.  Y.;  the  National  Automatic 


896  Fireproofing  of  Buildings  Chap.  23 

wood  to  HOLLOW  SHEET  METAL  for  doors,  sashes,  frames,  trim,  moldings,  etc., 
was  naturally  and  easily  made  and  to-day  the  latter  type  of  construction,  when 
expertly  carried  out,  results  in  details  for  interior  work  which  are  very  efficient 
to  resist  fire  and  handsome  in  appearance.  It  would  be  difficult  to  devise  con- 
structional details  which  would  be  more  satisfactory  and  at  the  same  time 
present  greater  possibilities  in  the  way  of  elaborate  design  and  high  finish; 
and  it  is  on  account  of  all  these  advantages  that  this  type  of  construction  is  used 
in  the  interior  equipment  of  many  of  the  best  examples  of  fire-resisting  build- 
ings, especially  for  the  doors,  frames,  sashes,  and  trim  of  corridors,  hallways, 
stair  and  elevator-enclosures,  and  even  for  entire  office-partitions.  Because  of 
the  non-absorbent  character  of  the  baked-enamel  finish  this  material  is  partic- 
ularly sanitary;  and  hollow  metal  doors  are  more  easily  cleaned  than  any  others, 
especially  if  all  moldings  are  omitted  and  panels  made  simply  as  smooth  depres- 
sions. The  thickness  of  standard  hollow  metal  doors  approved  by  under- 
writers, varies  from  iK  to  23^  in. 

Hollow  Metal  Doors.  The  Dahlstrom  patent  sheet-metal  door*  is 
made  from  two  No.  20-gauge-steel  plates,  one  stile  and  one  panel-face  being 
formed  from  each  of  the  sheets,  which  are  connected  by  interlocking  seams  on 
opposite  sides  of  the  panels  and  make  practically  a  double  door.  In  construct- 
ing the  panels  they  are  first  lined  with  a  sheet  of  asbestos  next  to  the  steel  on 
each  side,  and  the  space  between  is  filled  with  a  layer  of  hair-felt  paper,  which 
makes  a  resilient  filling  that  is  a  non-conductor  of  heat.  The  stiles  are  left 
hollow,  but  strips  of  cork  are  laid  perpendicularly  across  the  center  of  each  to 
deaden  the  metallic  ring.  The  panels  are  then  attached  to  each  other  to  form 
the  door  by  planting  on  and  welding  in  place  properly  formed  cross-rails,  at 
the  top  and  bottom,  and  wherever  else  they  may  be  desired;  the  moldings  are 
coped  over  the  molded  stiles  at  the  sides.  The  top  and  bottom  edges  of  the 
door  are  then  reinforced  with  channels  and  bars,  and  the  doors  made  perfectly 
straight  and  rigid.  The  fire-resistance  of  this  construction  is  increased  by 
letting  no  rivets  or  screws  pass  through  from  one  side  of  the  door  to  the  other 
in  the  exposed  parts.  The  transmission  of  heat  is  thus  avoided.  While  the 
door  is  being  put  together,  provision  is  made  for  attaching  the  hardware.  After 
the  doors  have  been  put  together,  they  are  sent  to  the  finishing  department 
where  the  steel  is  thoroughly  cleaned  from  all  rust,  grease,  or  other  impurities. 
They  are  then  given  six  or  eight  coatings  of  enamel,  being  baked  after  the 
application  of  each  coat  in  large  ovens  which  are  heated  to  300°  F.  After 
the  final  coat  of  varnish  is  put  on,  they  are  usually  rubbed  to  an  egg-shell, 
gloss-finish,  equal  in  quahty  to  any  hardwood-finish,  and  more  durable  because 
baked  on.  The  surfaces  can  be  grained  to  imitate  with  wonderful  exactness 
any  wood,  such  as  quartered  oak,  mahogany,  Circassian  walnut,  etc.  If  the 
doors  are  to  receive  glass  panels  they  are  provided  with  detachable  moldings 
to  hold  the  glass  in  place.  Doors  of  the  Dahlstrom,  hollow  metal  type  are 
installed  in  the  corridors  and  partitions  of  the  Singer  Building  and  towerf,  and 
the  United  States  Express  Building,  New  York  City;  the  Bell  Telephone  Ex- 
change Building,  Philadelphia,  Pa.;  the  Seventh  Regiment  Armory,  Chicago, 
111.;  the  Pontchartrain  Hotel,  Detroit,  Mich.;  the  Bank  of  Commerce  Building, 
St.  Louis,  Mo.;  the  First  National  Bank  Building,  Denver,  Col.;  and  the 
Royal  Insurance  Building,  San  Francisco,  Cal.  In  some  of  the  buildings  men- 
Door  Company,  Chicago,  111.;  the  Solar  Metal  Products  Company,  Columbus,  Ohio;  and 
the  Central  Metallic  Door  Company,  Gary,  Ind. 

*  Made  by  the  Dahlstrom  Metallic  Door  Company,  Jamestown,  N.  Y. 

t  A  severe  fire  in  the  twenty-sixth  story  of  this  tower  was  effectually  confined  to  the 
room  in  which  it  originated  by  the  doors  of  this  type  of  construction. 


Interior  Finish  and  Fittings  897 

tioned  in  the  preceding  articles,  hollow  metal  doors,  trim,  and  moldings  are 
accompanied  by  bronze  or  other  metal-covered  wood  window-frames, 
sashes,  etc. 

Hollow  Metal  Door-Frames,  Trim,  and  Moldings.  After  the  hollow 
metal  door  reached  an  advanced  stage  of  construction  the  manufacturers 
turned  their  attention  to  the  problems  involved  in  making  metal  frames  and 
moldings.  It  was  found  that  moldings  made  by  the  ordinary  hot-rolled 
PROCESS  were  too  rough  and  heavy  and  required  too  much  labor  to  smooth 
and  finish  their  surfaces;  and  that  those  pressed  from  light-gauge  steel  by  the 
common  methods  were  not  clear-cut  and  definite  in  their  outhnes,  and  were 
limited  in  length  and  in  variety  of  shapes.  Accordingly,  what  is  known  as  the 
cold-drawn  METHOD  of  making  frames,  trim,  and  moldings,  was  developed  and 
perfected,  and  moldings  made  by  this  process  are  now  used  for  many  kinds  of 
interior  work.  The  cold  metal  is  drawn  through  special  dies  to  give  it  the 
required  shape  and  the  bright  finish  is  retained.  The  corners  and  angles  come 
out  sharp  and  true  and  the  pieces  possess  much  greater  strength  and  rigidity 
than  those  hot-rolled  and  several  times  thicker.  There  are  dies  for  over  a 
thousand  shapes.  Moldings  can  now  be  made  in  lengths  up  to  40  or  even  50 
ft,  but  extra-freight  rates  and  other  drawbacks  make  it  inadvisable  to  ship  it 
in  lengths  of  over  20  ft.  Besides  the  cold-rolled  special  high-grade  steel, 
brass,  bronze,  and  copper  are  used  in  their  manufacture.  The  rolled  shapes 
include  angles,  channels,  and  Z  bars;  moldings  for  bases,  cornices,  wire-conduits, 
door-jambs,  sash-bars,  panels,  and  glass;  picture-frames,  door  and  window- 
casings,  and  trims  of  all  kinds;  wainscoting  and  chair-rails;  and  numerous  miscel- 
laneous sorts.  Wrought-iron  welded  one-piece  door-frames  are  made  for  use 
in  fire-proof  partitions.  These  frames  are  constructed  scientifically  of  specially 
rolled  wrought  iron  in.  several  different  shapes.  The  mitered  corners  are 
welded  together  making  the  frame  one  solid  piece.  They  are  made  for  any 
thickness  or  type  of  door  or  partition,  require  no  bracing,  and  can  be  fitted  with 
invisible  hinges  if  required. 

Hollow  Metal  Window-Frames  and  Sashes.  (See,  also,  Sheet-Metal  for 
Fire-Resisting  Window-Frames  and  Sashes,  page  902).  Hollow  metal  window- 
frames  and  sashes,  as  well  as  those  which  are  made  of  metal-covered  wood 
and  of  cast  iron,  wrought  iron,  drawn  bronze,  cast  bronze,  etc.,  and  glazed  with 
wire-glass,  prism  glass,  electroplated  glass,  etc.,  are  used  in  those  parts  of  build- 
ings in  which  the  exposure  to  fire  is  not  great  enough  to  require  the  use  of  hinged 
or  rolling  shutters,  or  where  a  more  pleasing  appearance  is  demanded  than  that 
resulting  from  the  use  of  hinged  or  rolling  fire-shutters.  Owing  to  many  im- 
provements made  in  recent  years,  both  in  design  and  details  of  manufacture, 
hollow,  sheet-metal  window-frames  and  sashes  are  now  ranked  among  the 
best  types  of  those  of  moderate  cost  for  general  use.  The  National  Fire  Pro- 
tective Association,  by  its  recommendations  and  standardizations,  and  the 
tests  and  labeling  systems  of  the  underwriters'  laboratories,  have  been  largely 
instrumental  in  bringing  about  these  improvements  and  results.  About  the 
only  disadvantage  connected  with  the  use  of  sheet-metal  windows  is  a  relatively 
rapid  deterioration  when  neglected.  The  materials  used  for  making  hollow 
metal  window-frames  and  sashes  are  galvanized  iron  or  steel;  copper;  sheet  metal, 
copper-plated;  and  sheet  metal,  bronze-plated.  The  sashes  are  glazed  with 
plate  or  maze  wire-glass  where  good  appearance  is  an  essential  requirement,  or 
with  RIBBED  OR  ROUGH  wire-glass  where  a  translucent  material  only  is  desired. 
Of  course,  clear  glass,  unwired,  may  be  used  when  additional  fire-resistance  is  not 
the  object.  The  National  Board  of  Fire  Underwriters  fix,  within  certain  limits, 
the  various  constructional  details,  the  maximum  permissible  sizes  of  openings  for 


898 


Fireproofing  of  Buildings 


Chap.  23 


glass,  etc.     The  principal  regulations  have  been  very  conveniently  condensed 
by  Mr.  J.  K.  Freitag.* 

Solid  Steel  Windows.  Where  large  window-surfaces  giving  maximum  light 
are  desired,  as  in  factories,  the  so-called  solid  steel  windows  are  frequently 
used.  They  have  been  given  this  name  because  the  frames  and  muntins  are 
made  of  solid,  rolled-steel  sections,  jointed  at  their  junctions  or  intersections  by 
special  methods,  in  some  cases  oxy-acetylene  welded,  so  as  to  make  strong  and 
stiff  frames.  The  manufacturers  generally  carry  stock  sizes  varying  in  approxi- 
mate widths  from  3  to  6  ft,  and  approximate  lengths  from  3  to  9  ft.  The  glass 
panes  are  about  12  by  18  in.  The  movaJDle  sections,  or  ventilators,  are  pivoted 
on  horizontal  axes,  though  a  counterbalance  type,  also,  is  made  for  use  in 
hospitals  and  public  buildings.  Ventilators  should  not  exceed  5  ft  in  either 
direction,  nor  more  than  18  sq  ft  in  area.  Among  the  principal  makers  are  the 
Detroit  Steel  Products  Company  (Fenestra),  Detroit,  Mich.;  David  Lupton's 
Sons  Company,  Philadelphia,  Pa.;  American  Steel  Window  Company,  Chicago, 
111.;  and  Truscon  Steel  Company,  Youngstown,  Ohio. 

Electroplated  Trim.  This  product  is  made  by  a  process  which  consists  in 
electrically  depositing  a  layer  of  copper  on  the  outer  surface  of  wooden  moldings 
or  doors.  The  metallic  deposit  preserves  the  markings  of  the  grain  of  the  wood 
and  makes  a  very  presentable  door.  A  good  sample  of  this  work  has  been  in- 
stalled in  the  United  Engineering  Building,  New  York  City,  by  the  New  York 
Central  Metal  Company  of  the  same  city.  Some  very  fine  work  of  this  kind  has 
been  done  by  the  Hecla  Iron  Works  of  New  York  City,  by  electroplating  on  a 
fire-proof  material  known  as  Lignolith. 

Cement  Trim.  Keene's  cement  has  been  used  for  many  years  for  running 
base-moldings,  door  and  window-trim,  etc.,  and  in  many  European  buildings 

practically  all  of  the  interior  finish  is  of 
this  material.  Any  molding  can  be  run 
in  it  with  good  sharp  angles,  and  it  is  suf- 
ficiently hard  to  stand  ordinary  usage. 
Fig.  78  shows  a  door-opening  with  a  trim 
of  Keene's  cement.  This  detail  can  be 
further  improved  by  covering  the  wooden 
frame  and  door  with  thin  metal.  The 
metal  and  cement  can  be  painted  as  de- 
sired. 

Molded    Hollow    Tiles    for    Inside 
Finish.     These  are  also  being  substituted 
for    the    ordinary    wooden    finish.      The 
Fig.  78.     Door-jamb  with  Cement  Trim    Amelia    Apartments,    erected    by  H.  B. 

Camp  at  Akron,  Ohio,  in  1901,!  is  built 
almost  entirely  of  hollow  tile.  "The  bases,  the  picture-moldings,  and  the 
architraves  around  the  doors  were  made  of  specially  formed  tiles,  as  shown 
in  Fig.  79.  These  tiles  were  afterward  painted  to  harmonize  with  the  scheme 
of  color-decoration.  All  of  the  floors  throughout  the  building  are  covered  with 
a  cement  composition  composed  of  Sandusky  cement  and  ground  wood,  troweled 
down  smooth  and  level." 

Metallic  Furniture  and  Fittings.  In  offices,  banks,  libraries,  and  public 
buildings,  the  furniture  and  fixtures  are  about  the  only  articles  on  which  a 

*  For  the  principal  regulations,  conveniently  condensed,  see  Fire  Prevention  anrl 
Fire  Protection,  by  J.  K.  Freitag. 

t  Described  in  the  journal,  Fireproof,  July,  1903. 


Interior  Finish  and  Fittings 


899 


fire  can  feed,  if  the  building  itself  is  fire-proof,  and  if  these  are  made  of  incom- 
bustible materials  there  is  no  chance  for  a  fire  to  gain  headway  or  to  do  much 


Fig.  79.    Hollow-tile  Door-trim,  Picture-molding  and  Base 


'^zzzzzz^zkz^ 


^jzmm^^mzz^: 


■^zzzzzz^zzzzz^ 


damage.  Almost  anything  in  the  way  of  furniture  and  fittings,  including  even 
roll- top  desks  and  highly  ornamental  cabinets,  may  now  be  obtained  in  metal; 
and  many  Ubraries,  banks,  and  court-houses  have  been  fitted  up  and  furnished 
entirely  with  incombustible  cabinet-work.  Catalogues  can  be  obtained  from 
the  leading  companies  engaged  in 

the  manufacture  of  metal  fur-  f« 1^— 

NiTURE,  such  for  example  as  the 
Art  Metal  Construction  Company, 
Jamestown,  N.  Y.,  the  Berger 
Manufacturing  Company.  Canton, 
Ohio,  the  Van  Dorn  Iron  Works, 
Cleveland,  Ohio,  and  the  Library 
Bureau,  New  York  City  and  Bos- 
ton, Mass. 

Stairs.  In  a  majority  of  fire- 
proof buildings  the  architects  have 
contented  themselves  with  putting 
in  INCOMBUSTIBLE  STAIRS  of  iron, 

with  perhaps  slate  or  marble  treads.  As  pointed  out  in  the  first  pages  of  this 
chapter,  unprotected  iron  cannot  be  considered  fire-proof,  but  it  is  difficult  to 
protect  the  ironwork  of  a  stairway,  as  it  is  usually  built,  and  at  the  same  time 
preserve  an  ornamental  effect.  If  exposed  metal  construction  is  to  be  used,  cast 
iron  is  much  to  be  preferred  to  steel,  as  the  cast  metal  will  retain  its  shape  under 
severe  heat  far  better  than  thin  facings  or  frameworks  of  steel.  Slate  and  marble 
treads  and  platforms,  unless  supported  underneath,  should  never  be  used  in 
staircase-construction.  When  subjected  to  heat,  marble  and  slate  crack  and  fall 
away,  leaving  the  stairs  impassable.  A  fire-department  captain  in  New  York 
City  lost  his  fife  through  the  collapse  of  a  marble  platform.  If  these  materials 
are  to  be  used,  therefore,  there  should  be  a  subtread  of  iron  or  concrete  beneath 
them.     A  really  fire -proof  staircase  should  be  constructed  with  as  little 


Fig.  80.     Hollow-tile  Steps  for  Staircase 


000 


Fireproofing  of  Buildings 


Chap.  23 


ironwork  as  possible,  and  what  ironwork  there  is,  incased  in  Tire-resisting 
materials.  It  is  possible  and  practicable  to  build  stairs  of  clay  tiles,  bricks,  or 
reinforced  concrete,  that  are  absolutely  fire-proof.  The  stairs  in  the  Pension 
Building  at  Washington,  D.  C,  are  built  of  brick,  with  the  exception  of  the 

treads,  which  are  slate; 


and  in  many  of  the 
earlier  government 
buildings  the  stairs 
are  of  stone.  Stones 
suitable  for  stairs, 
however,  are  not  as 
resistant  as  cast  iron 
to  heat.  Part  I  of 
Building  Construction 
and  Superintendence* 
contains  descriptions 
and  illustrations  of  ' 
brick  stairs.  The  Guas- 
tavino  Company  has 
built  several  stair- 
cases according  to  its 
system  of  construction, 
using  flat  clay  tile  em- 
bedded in  cement.  No 
iron-work  whatever  is 
used  '  in  this  con- 
struction; hence  it  is 
eminently  fire-proof. 
Fig.  80  shows  a  par- 
tial section  of  a  tile  staircase  such  as  was  used  in  the  Amelia  Apartment 
Building,  Akron,  Ohio.  The  blocks  were  of  hard-burned  material,  glazed, 
and  4  ft  long.  They  were  supported  upon  the  partition-walls  and  were  used 
by  the  mechanics  for  carrying  up  material  during  the  erection  of  the  build- 


^■jSar  13'onCentei 


Fig.  81. 


Reinforced-concrete  Stairs,  Government  Printing 
Office,  Washington,  D.  C. 


Fig.  82.     Ferroinclave  Foundation  for  Stair-treads  and  Risers 


ing.  Reinforced  concrete,  with  slate  or  marble  treads,  is  a  good  material  for  the 
construction  of  stairs,  and  permits  of  very  elaborate  and  complicated  construc- 
tion.    Fig.  81 1  shows  the  construction  of  the  stairs  in  the  Government  Printing 

*  By  Frank  E.  Kidder,  rewritten  by  Thomas  Nolan, 
t  From  the  Engineering  Record,  of  Dec.  6,  1902. 


Protection  from  Outside  Hazard  901 

Office  at  Washington,  D.  C.  These  stairs  have  steel  girders  and  strings  enclosed 
in  the  solid  concrete,  which  is  molded  to  form  the  steps  and  risers,  as  shown  in  the 
detail.  The  steel  strings,  however,  are  hardly  necessary,  as  the  reinforcing-bars 
give  sufficient  strength.  Some  excellent  details  for  ornamental  iron  stairs  were 
pubUshed  in  Fireproof,  March,  1903,  in  an  article  by  J.  K.  Freitag.  The  cor- 
rugated sheet  metal,  known  as  Ferroinclave  (page  851),  offers  a  very  conven- 
ient foundation  for  cement  stairs.  When  built  between  walls  or  partitions 
or  with  an  open  string.  Fig.  82  shows  one  way  in  which  the  material  has  been 
used,  the  stairs  being  finished  with  about  2  in  of  cement  over  the  metal  and 
plastered  underneath.  The  Ferroinclave  is  bolted  to  lugs  or  brackets  screwed 
to  or  cast  on  the  strings.  Slate  or  marble  treads  and  risers  may  be  embedded 
in  the  mortar  if  desired.     (See,  also,  pages  947  and  983.) 


9.  Protection  from  Outside  Hazard 

Window-Protection.  To  be  thoroughly  protected  against  the  outside 
hazard,  buildings  must  have  the  openings  in  the  outside  walls  provided  with  some 
means  of  effectively  closing  those  openings  against  flame.  The  same  provision 
should  be  made  for  openings  in  the  partition-walls  of  large  buildings.  Four 
GENERAL  TYPES  of  dcviccs  are  in  use  for  this  purpose:  (i)  tin-covered  wooden 
shutters;  (2)  steel  shutters  or  doors;  (3)  metal  frames  and  sash,  glazed  with 
wire-glass;  and  (4)  v/ater-cur tains. 

Types  of  Window-Protection  Compared.  When  properly  constructed, 
the  TIN-COVERED  WOODEN  SHUTTER  is  Still  the  most  effective  window-protection. 
"In  a  very  severe  fire  in  Lynn,  Mass.,  in  which  the  heat  was  intense  enough  to 
melt  most  of  the  tin  from  the  outside  of  the  tinned  plates  covering  the  shutters, 
it  was  found  afterward  that  the  wood  was  charred  to  a  depth  of  only  about 
%  in.  The  shutters  were  warped  slightly,  but  afforded  sufficient  protection 
against  the  heat  to  allow  men  to  remain  behind  them  to  put  out  such  fire  as 
occasionally  crept  through.  This  would  not  have  been  possible  behind  iron 
shutters  under  similar  conditions."*  Steel  shutters,  under  the  action  of 
heat,  warp  very  readily  and  transmit  considerable  heat.  They  belong  to  the 
cheapest  type  of  window-protection.  "There  is  one  objection  to  the  use  of 
shutters  on  window-openings,  and  that  is  that  they  depend  on  fallible  human 
agency  to  be  effective.  They  must  necessarily  be  open  while  the  building  is 
in  use.  When  the  need  for  them  comes  they  are  apt  to  be  overlooked  and  are  not 
closed.  Certain  it  is  that  on  many  buildings  they  are  not  closed  at  night."* 
The  METAL-FRAME-AND-wiRE-GLASs  WINDOWS  are  not  as  unsightly  as  shutters 
of  almost  any  kind  are  apt  to  be.  They  are  more  likely  to  be  closed  at  night 
and  more  readily  closed  when  necessary.  They  do  not  hide  a  fire  and  are 
more  easily  opened  when  it  is  necessary  to  reach  a  fire.  The  one  serious  objec- 
tion to  them  is  the  intense  radiation  of  heat  from  the  wire-glass,  f 

Tin-covered  Wooden  Fire-Shutters  and  Doors.  The  effectiveness  of 
this  device  depends  on  its  construction.  "Only  well-seasoned  non-resinous 
wood,  dressed,  tongued  and  grooved  in  narrow  boards,  should  be  used.  Wood 
containing  moisture  or  resin  may  generate,  under  heat,  sufficient  ^steam  or  gas 
to  force  off  the  tin  covering  and  expose  the  wood  to  the  flame.  The  body  of 
the  door  should  consist  of  two  or  three  layers  of  such  boards  laid  at  right-angles 
with  each  other  and  fastened  together  by  clinch-nails.  The  best  grade  of  tin 
should  be  used.     No  solder  must  be  used,  and  the  tin  plates  should  be  lock- 

•  Insurance  Engineering,  Dec,  1902. 

t  For  a  consideration  of  water-curtains,  see  page  903. 


902  Flreproofing  of  Buildings  Chap.  23 

jointed,  with  the  nails  in  the  seams.  The  nails  must  be  long  enough,  at  least 
iH  in,  to  secure  a  good  hold  beyond  the  depth  to  which  the  wood  is  likely  to 
char,  which  is  about  %  in.  Under  intense  heat  the  wood  is  certain  to  char,  but 
if  the  nails  are  long  enough  to  hold  the  tin  up  against  the  wood,  and  the  tin 
is  properly  put  on  so  as  to  keep  the  air  out  to  prevent  burning,  the  shutter 
will  stand  under  severe  strains."*  The  hinges,  fastenings,  or  hangers  must  be 
bolted  to  the  door,  not  nailed  or  screwed,  as  nails  or  screws  would  pull  out 
during  a  fire.  If  hung  on  hinges,  the  hinge-hook  should  be  built  into  the  wall. 
This  door  was  designed  for  use  in  mills,  but  it  has  worked  so  satisfactorily 
that  it  is  generally  adopted  wherever  a  fire-proof  door  is  wanted  and  its  ap- 
pearance is  not  olDJectionable.  Fire-proof  shutters,  also,  are  made  in  this  way. 
The  National  Board  of  Fire  Underwriters  issues  complete  specificationsf  for 
this  type  of  door  and  shutter,  and  these  specifications  should  be  closely  fol- 
lowed for  satisfactory  results.  Doors  of  this  type,  provided  for  the  openings 
in  interior  partition-walls,  are  often,  and  wherever  possible  should  be,  hung  on 
inclined  tracks  so  that  they  will  close  automatically.  Where  it  is  desirable  to 
keep  them  open  most  of  the  time,  an  automatic  release  operated  by  a  fusible 
link  is  provided.     (See,  also,  page  778.) 

Metal-coyer^d  Wooden  Doors  as  Fire-Doors.  Wooden  doors  covered 
by  the  Kalamein  or  other  process  (page  894)  are  sometimes  used  as  fire-doors 
yrhere  apf)earance  is  a  consideration.     They  are  not  considered  equal,  however, 

to  the  STANDARD  TIN-COVERED  WOODEN  DOORS. 

Steel  Fire-Doors  and  Shutters.  For  a  satisfactory  steel  fire-door 
g,  yi-'m  sheet  of  steel  should  be  used,  and  it  should  be  reinforced  on  the  back 
with^  frame  of  angle-irons,  not  less  than  iH  by  iH  by  M  in,  and  increasing  in 
size  with  the  door  or  shutter.  These  doors  or  shutters  may  operate  in  one  of 
l^hree  ways:  (i)  swing  on  hinges,  (2)  slide  on  tracks,  or  (3)  roll  vertically. 
The  SWINGING  DOORS  or  shutters  are  the  most  rehable  as  there  are  no  com- 
plicatpd  parts  to  get  out  of  order.  They  should  be  hung  on  eyes  built  into  the 
piiasonry  walls.  Sliding  doors  or  shutters  must  have  the  rails  on  which  they 
pperate  protected  by  metal  shields  to  prevent  obstruction.  For  larger  openings 
the  rolling  shutters  are  generally  preferred.  They  are  made  in  horizontal 
jointed  sectional  strips,  which  wind  up  on  a  roller  placed  in  a  pocket  above  the 
opening,  the  ends  nioving  in  metal  grooves  to  hold  them  in  place.  They  gen- 
erally operate  vertically,  although  some  are  made  to  operate  horizontally, 
the  rollers  being  set  vertically  in  pockets  at  the  sides  of  the  openings.  These 
latter  are  more  apt  to  get  out  of  order.  The  vertically  operated  doors  or 
shutters  are  balanced  by  springs  or  weights  to  make  them  move  easily  up  or 
down.  Where  they  are  intended  to  be  closed  in  case  of  necessity  only,  they 
are  slightly  weighed  and  held  open  by  means  of  fusible  links,  so  that  in  case  of 
fire  they  will  close  automatically. 

Sheet-Metal  for  Fire-resisting  Window-Frames  and  Sashes. J  These 
are  now  made  weather-tight  and  perfectly  practicable  in  all  respects,  and  should 
be  used  wherever  fire-resisting  windows  are  desired.  The  sashes  are  made 
especially  for  holding  wire-glass.  These  sheet-metal  windows  are  made  in 
a  great  variety  of  forms  to  meet  all  purposes  and  the  sashes  may  be  stationary, 
pivoted  eith^  horizontally  or  vertically,  hinged,  or  double-hung  with  weighty, 
like  ordinary  windows.  For  factories,  warehouses,  stairways,  and  elevator? 
shafts,  a  stationary  lower  and  a  pivoted  upper  sash  are  commonly  used,  as  thi? 
is  the  cheapest  type  of  window.    The  double-hung  windows  are  now  made 

*  Insurance  Engineering,  Dec,  1902. 

t  To  be  had  for  the  asking. 

X  S^,  also,  Hollow  Metal  Window-Frames  and  Sashes,  page  897. 


Extinguishing  Devices  and  Precautionary  Measures         903 

to  work  as  smoothly  as  wooden  sashes  in  ordinary  box  frames.  For  offices, 
hotels,  etc.,  a  window  having  two  sashes,  glazed  with  wire-glass,  and  closing 
and  locking  automatically  in  case  of  fire,  and  a  third  inner  sash  glazed  with 
clear  glass,  has  all  of  the  advantages  of  an  ordinary  window  with  the  additional 
advantages  of  fire-protection  and  better  diffusion  of  light.  Metal  fly-screens, 
also,  can  be  used  with  these  windows.  All  movable  sashes,  glazed  with  wire- 
glass,  should  be  provided  with  a  device  by  which  the  sashes  will  close  and  lock 
automatically  in  case  of  fire.  Two  thicknesses  of  wire-glass  are  sometimes  used 
with  a  ventilated  air-space  of  at  least  i  in  between  the  lights. 

10.  Extinguishing  Devices  and  Precautionary  Measures 

Water-Curtains.  "The  vulnerable  portion  of  buildings  generally  is  the 
front,  where  great  window-openings  are  desired  for  purposes  of  light,  and  where 
it  is  considered  objectionable  on  account  of  appearance  to  have  shutters  or 
even  wire-glass  windows.  These  large  window-openings  afford  great  oppor- 
tunities for  the  spread  of  fire  across  streets.  The  danger  of  damage  is  much 
increased  where  the  fronts,  as  is  very  common,  are  made  of  unprotected  metal- 
work.  A  notable  example,  illustrating  such  danger,  was  the  building  of  the 
Manhattan  Savings  Institution,  New  York  City,  which  was  severely  damaged 
and  almost  destroyed  by  a  fire  in  a  six-story  non-fire-proof  building  across  the 
street.  Such  conditions  might  be  overcome  to  some  extent  perhaps,  by  the 
introduction  of  some  system  such  as  the  water-curtains  that  were  placed  on 
the  Chicago  Public  Library.  This  is  practically  a  sprinkler  system  set  along 
the  edge  of  the  cornice  of  the  building,  and  so  arranged  as  to  furnish  a  thin 
sheet  of  water  in  front  of  the  building.  Such  a  sheet  will,  however,-  not  extend 
far  before  it  is  turned  into  spray  and  thus  becomes  practically  useless.  A  similar 
arrangement  placed  at  each  window-opening  might  be  more  useful,  though  it 
is  doubtful  whether  it  would  be  of  much  value  in  any  severe  conflagration."* 
The  rules  of  the  National  Board  of  Fire  Underwriters  for  open  sprinklers 
or  water-curtains  determine  the  sizes  of  piping  and  feed-mains,  and  the  general 
arrangement  of  the  system. 

Precautionary  Measures  in  General. f  No  matter  how  thoroughly  a  build- 
ing is  fireproofed,  if  it  is  filled  with  combustible  goods,  as  a  warehouse,  store,  or 
factory,  there  is  always  the  possibility  of  a  fire,  which,  if  unchecked  when  first 
started,  must  necessarily  entail  a  great  loss  and  more  or  less  damage  to  the 
building.  If  a  fire  is  discovered  and  checked  in  its  incipient  stage  this  loss  is 
avoided.  There  are  now  many  valuable  devices  for  detecting  and  checking 
fires,  which  should  be  installed  in  every  warehouse,  and  which  often  may  be 
placed  with  advantage  in  buildings  used  for  other  purposes.  The  more  imxx)rtant 
of  these  are  automatic  alarms,  automatic  sprinklers,  and  standpipes. 

Automatic  Alarms.  The  prompt  discovery  of  fire  generally  brings  about 
prompt  extinguishment,  but  as  it  is  not  practicable  to  have  someone  on  duty  in 
all  parts  of  a  property  at  all  times,  fires  may  gain  serious  headway  before  being 
discovered,  unless  some  system  of  automatic  notification  is  used.  Next  to  auto- 
matic sprinklers,  approved  automatic  fire-alarm  systems,  thermostats,  are  per- 
haps the  most  important  of  the  fire-protection  devices.  There  are  two  general 
classes  of  thermostats:  one  which  operates  at  a  fixed  or  predetermined 
temperature,  and  the  compensating-type.  The  latter  requires  a  certain  rise 
in  temperature  within  a  given  time.  This  latter  type  is  common  in  Europe,  while 
in  this  country  the  fixed-temperature-type  has  been  preferred.    The  compen- 

*  Insurance  Engineering,  Dec,  1902. 
'  t  ^§§,  al§9,  CJi^J?t#F  :5Qai,  page  7fi§, 


904  Fireproofing  of  Buildings  Chap.  23 

sating-types  seem  to  have  been  used  with  some  success  in  certain  sections,  but 
have  not  proved  altogether  satisfactory.  For  general  use  it  would  appear  that 
the  SOLDER-TYPE  OF  THERMOSTAT  has  many  advantages  when  used  in  connection 
with  a  simple  closed-circuit  system.  The  most  common  type  of  thermostat 
system  is  the  electric  system,  in  which  the  thermostats  are  designed  to  open 
or  close  the  electric  circuit  and  cause  bells  to  be  rung  at  designated  points.  The 
thermostats,  or  circuit-closers,  may  be  of  the  fixed-temperature  type  or  adjusted 
to  operate  at  any  desired  temperature.  The  former  are  chiefly  of  the  solder- 
type,  while  the  most  common  variety  of  the  latter  type  consists  of  a  spring  of 
two  dissimilar  metals,  which  expand  unequally. 

The  Aero  System.  The  best-known  system  of  the  compensating-type  is  the 
aero  system  installed  by  the  Aero  Fire  Alarm  Company,  New  York  City.* 
This  consists  of  a  small  copper  tube  attached  to  the  ceiling.  A  quick  rise  in 
temperature,  as  in  the  case  of  fire,  expands  the  air  in  the  tube  and  acts  on  a  sensi- 
tive diaphragm,  which  latter  makes  an  electrical  connection,  causing  a  trans- 
mitter to  operate  and  send  in  an  alarm. 

The  Reichel  System  is  installed  by  the  Pacific  Fire  Extinguisher  Company, 
San  Francisco,  Cal.  This  system  is  of  the  compensating-type,  the  Reichel 
thermostats*  consisting  of  a  thermopyle  of  special  design  which  is  connected 
in  series  with  an  electric  circuit.  Any  rapid  increase  in  heat  generates  sufficient 
current  to  actuate  a  transmitter.  Slow  changes  in  temperature  do  not  operate 
the  system. 

The  Derby  Automatic  Fire- Alarm  System  is  installed  by  the  American 
Fire  Prevention  Bureau,  New  York  City.  This  system  consists  of  a  tv/o-wire 
closed  circuit,  and  uses  the  Derby  fire-sentinels,*  in  multiple,  across  the 
line.  Any  derangement  of  the  circuit  gives  a  local  or  central  station  trouble- 
alarm.  Upon  the  operation  of  a  sentinel  thermostat,  resistance  is  auto- 
matically cut  out  of  the  circuit,  thereby  causing  the  operation  of  fire-gongs  and 
transmitters.  The  Derby  Fire  Sentinel  can  be  used  on  wiring  systems  utilizing 
primary,  storage,  or  public-service  energy  up  to  no  volts.  The  Sentinels  are 
made  for  attaching  to  open  wiring  and  also  for  use  in  connection  with  concealed 
work. 

The  Watkins  Thermostat  is  installed  by  the  Automatic  Fire  Alarm  Com- 
pany, New  York  City.  It  consists  of  a  perforated  metal  case,  enclosing  a  flat 
SPRING  OF  TWO  DISSIMILAR  METALS.  The  Spring  is  fastened  at  one  end,  and  the 
heat  causes  a  movement,  due  to  the  unequal  expansion  of  the  two  metals. 
Watkins  thermostats  are  wired  in  multiple,  the  wiring  system  being  part  open 
and  part  closed.  The  thermostats  are  adjusted  by  hand.  They  are  likely  to  be 
affected  by  corrosive  influences,  moisture,  and  rough  handling.  This  system, 
however,  has  been  more  largely  installed  than  any  other,  being  the  principal 
type  of  thermostat  used  in  Boston,  New  York,  and  l^hiladelphia,  where,  with 
good  supervision,  its  record  has  been  satisfactory. 

Automatic  Sprinklers.  "An  automatic  sprinkler  is  a  device  for  distribut- 
ing water  by  means  of  a  valve  which  is  arranged  to  open  under  the  action  of 
heat,  as  from  a  fire  which  it  is  intended  to  extinguish.  The  distribution  of 
water  which  results  from  properly  located  sprinklers  occurs  in  the  form  of  a 
rain  of  jets  or  drops,  and  is  sufficient  to  drench  almost  any  inflammable  stock 
beyond  the  point  of  ignition.  The  distribution  is  also  economical,  as  the  water 
is  more  evenly  appHed  than  from  a  nozzle  attached  to  a  fire-hose,  and  the  source 
is  directly  above  the  fire.  Whenever  combustible  merchandise  constitutes 
the  contents  of  a  building,  automatic  sprinklers  are  of  great  value,  and  in 

"Approved  by  the  Underwriters'  Laboratories. 


Extinguishing  Devices  and  Precautionary  Measures  905 

buildings  of  a  height  so  great  as  to  make  the  upper  stories  difficult  of  access, 
especially  if  containing  large  areas  and  very  combustible  contents,  sprinklers 
constitute  the  best  protection  obtainable." *  Sprinkler-systems  may  be  divided 
into  two  general  types:  (i)  the  wet-pipe  system,  or  automatic  sprinklers,  just 
described;  (2)  the  dry-pipe  system.  Where  the  water  cannot  be  kept  from 
freezing  in  the  ordinary  wet-pipe  system,  recourse  is  had  to  the  dry-pipe  system. 
The  sprinkler-pipes  are  filled  with  air  under  pressure,  which  is  automatically 
released  by  the  opening  of  a  head-valve  under  heat.  This  release  of  pressure 
opens  the  dry  valve  in  the  main  supply-pipe,  allowing  water  to  flow  through 
the  sprinkler-pipes  and  the  open  heads.  Automatic  sprinkler-heads  are  made 
to  open  at  various  temperatures:  ordinary,  155°  to  165°;  intermediate, 
212°;  hard,  286°;  and  extra  hard,  360°  F.  The  higher-temperature  sprinklers 
are  put  in  locations  where  the  heat  is  above  normal,  such  as  boiler-rooms  and 
dry-rooms.  Various  types,  made  by  the  following  manufacturers,  have  been 
approved  by  the  National  Board  of  Fire  Underwriters  :t  International 
Sprinkler  Company,  New  York  City;  General  Fire  Extinguisher  Company, 
Providence,  R.  I.;  Automatic  Sprinkler  Company  of  America,  New  York  City; 
Crowdar  Brothers,  St.  Louis,  Mo.;  Esty  Sprinkler  Company  (H.  G.  Vogel 
Company,  New  York,  sole  agents);  Globe  Automatic  Sprinkler  Company, 
Philadelphia,  Pa.;  Independent  Sprinkler  Company,  Philadelphia,  Pa.;  Ohio 
Automatic  Sprinkler  Company,  Youngstown,  Ohio;  and  Rockwood  Sprinkler 
Company,  Worcester,  Mass. 

Sprinkler  Supervisory  Devices.  These  devices  consist  of  apparatus  for 
"transmitting  signals  when  gate- valves  are  closed  or  open;  when  water  in 
tanks  falls  below  or  is  restored  to  a  predetermined  level;  when  pressure  in 
air-tanks  falls  below  or  is  restored  to  a  predetermined  amount;  when  water 
in  tanks  falls  below  or  rises  above  predetermined  temperatures;  also  to  transmit 
water-flow  signals  and  to  withold  signals  from  water-surges  or  variable  pres- 
sures." They  are  used  in  connection  with  central-station  signalling 
systems  for  supervising  the  operation  and  maintenance  of  sprinkler-equip- 
ments. The  devices  of  the  American  District  Telegraph  Company  of  New 
York  City,  are  approved  by  the  National  Board  of  Fire  Underwriters,  f 

Stand-Pipes  and  Hose-Reels.  In  office-buildings,  hotels,  and  apartment- 
houses,  where  sprinkler-systems  are  hardly  suitable,  stand-pipes  with  hose- 
reels  in  each  story  and  on  the  roof,  ready  for  instant  use,  constitute  the  best 
means  of  quickly  controlling  a  fire.  All  buildings  over  certain  heights  should 
be  so  equipped,  the  height  being  fixed  by  the  ability  of  the  local  fire  department 
to  reach  effectively  the  upper  parts  of  the  building  with  its  hose-streams.  The 
stand-pipe  should  be  from  23^2  to  6  in  in  diameter,  according  to  the  size  and 
height  of  the  building,  and  should  be  connected  with  the  water-supply  of  the 
building  and  provided  with  Siamese  connections  at  the  street-level  for  the  fire 
department.  Check-valves  should  be  provided,  so  that  when  the  fire-depart- 
ment engines  are  attached,  their  force  will  be  added  to  the  force  due  to  the  head 
of  water  from  the  fire-tanks,  or  to  the  fire-pumps,  or  to  the  force  of  the  city 
water  system.  Stand-pipes  should  be  placed  within  the  stair-enclosures.  In 
some  cities  the  practise  is  to  attach  them  to  the  outside  fire-escapes  of  the 
building.  The  number  and  location  of  stand-pipes  should  be  such  that  all  parts 
of  the -building  can  be  reached  by  at  least  one  stream  supplied  by  hose  not 
exceeding  100  ft  in  length. 

*  J.  K.  Freitag. 

t  List  of  Fire  Appliances,  National  Board  of  Fire  Underwriters, 


906  Reinforced-Concrete  Construction  Chap.  24 


CHAPTER   XXIV 

REINFORCED-CONCRETE    CONSTRUCTION  * 

By 
RUDOLPH  P.  MILLER 

SUPERINTENDENT    OF    BUILDINGS,    BOROUGH    OF    MANHATTAN,    NEW    YORK    CITY 

I.  Introductory  Notes 

Definition.  The  term  reinforced  concrete  is  defined  in  the  proposed 
standard  regulations  of  the  American  Concrete  Institute  as  "an  approved  mix- 
ture of  Portland  cement,  with  water  and  aggregates  in  which  metal  (generally 
steel)  has  been  embedded  in  proportionately  small  sections,  in  such  a  manner 
that  the  metal  and  the  concrete  assist  each  other  in  taking  stress."! 

Historical  Notes.  The  great  value  of  concrete  as  a  structural  material  when 
subjected  to  compression  only  has  been  recognized  for  centuries.  The  use  of 
reinforced  concrete,  however,  as  a  practicable  and  commercial  form  of  construc- 
tion is  comparatively  recent.  It  is  true  that  as  far  back  as  1869,  Frangois 
Coignet  of  Paris  took  out  letters  patent  on  a  combination  of  iron  and  concrete, 
and  that  even  before  this,  in  1867,  the  principle  of  reinforcing  concrete  with  iron 
had  been  apphed  by  P.  A.  J.  Monier,  a  gardener  of  Paris,  to  the  making  of  large 
flower-pots;  still,  the  general  application  to  building-construction  did  not  occur 
till  about  the  middle  of  the  last  decade  of  the  nineteenth  century.  In  its  develop- 
ment it  was  first  appUed  to  bridge-construction.  The  discussion  of  the  subject 
in  this  chapter  is  confined  to  its  use  in  the  construction  of  buildings.  The 
earliest  example  of  a  building  of  reinforced  concrete  in  this  country,  and  probably 
in  the  world,  is  that  erected  in  1875  bj^  W.  E.  Ward,  near  Port  Chester,  N.  Y., 
in  which  "not  only  all  the  external  and  internal  walls,  cornices,  and  towers  were 
constructed  of  concrete,  but  all  of  the  beams  and  roofs  were  exclusively  made  of 
concrete  reinforced  by  Ught  iron  beams  and  rods."  $ 

The  Erection  of  Reinforced-Concrete  Work.  In  general  outline,  a  build- 
ing operation  in  reinforced  concrete  consists  in  the  usual  preparations  of  the  site 
by  excavation  or  otherwise,  the  provision  of  suitable  foundations  for  walls, 
columns,  or  other  supports,  the  erection  of  a  series  of  wooden  molds  or  forms,  the 
placing  of  the  necessary  steel  reinforcement,  the  pouring  of  the  concrete,  and 
the  removal  of  the  forms  after  the  concrete  has  set  sufficiently  to  sustain  itself 
and  the  load  that  may  come  on  it  during  construction.  From  the  beginning 
of  the  erection  of  the  forms  the  successive  steps  are  progressive,  that  is,  the 
placing  of  the  steel  and  pouring  of  the  concrete  are  going  on  in  the  lower  sec- 
tions or  stories  while  the  forms  are  being  erected  for  the  upper  sections  or  stories. 
So  that  in  a  large  operation  the  carpenters,  the  steel-setters,  and  the  concreters 
may  all  be  working  at  the  same  time,  one  set  shghtly  in  advance  of  the  others, 
without  interference  one  with  the  others.    These  several  steps  in  the  operation 

*  For  Concrete  in  general  and  Mass-Concrete,  see  Chapter  III,  pages  240  to  251;  for 
Strength  of  Concrete  without  Reinforcement,  Chapter  V,  pages  283  to  287;  and  for 
Reinforced-Concrete  Factory-Construction,  Chapter  XXV.  See,  also.  Chapter  XXllI 
pages  817  and  842. 

t  Proc.  Am.  Concrete  Inst.,  Vol.  XV,  1919. 

t  For  a  further  and  more  extended  history  the  reader  is  referred  to  the  larger  treatises 
on  this  subject  and  to  Edwin  Thacher's  article  in  Engineering  News,  March  26,  1903. 


Materials  Used  in  Reinforced-Concrete  Construction  907 

are  considered  in  greater  detail  in  Chapter-Subdivision  7,  page  962,  Erection  of 
Reinforced-Concrete  Construction. 

2.  Materials  Used  in  Reinforced-Concrete  Construction 

The  Materials  used  in  reinforced  concrete  are  concrete  and  steel.  The 
concrete  forms  the  mass  of  the  construction.  Its  proper  use  is  to  resist  com- 
pression. While  it  has  some  tensile  strength  the  amount  is  so  small  and  so 
variable  that  it  should  always  be  neglected.  Steel  is  used  for  the  reinforcing 
material  as  it  furnishes  the  greatest  amount  of  strength  at  the  least  expense. 
Wrought  iron  could  be  used,  but  it  is  practically  unobtainable  under  present 
conditions,  and,  as  already  intimated,  its  use  is  not  economical. 

Concrete.  The  concrete  consists  of  a  mixture  of  cement  and  some  aggre- 
gate, in  definite  proportions,  with  the  necessary  water  to  cause  the  setting  of  the 
cement. 

Cement.  Portland  cement  should  always  be  used  in  reinforced  concrete, 
and  it  should  always  be  tested  before  being  used.  Even  in  small  jobs  it  is  im- 
portant to  know  that  the  cement  is  strong  and  sound.  In  purchasing  the  cement, 
the  certificate  of  some  reliable  testing-laboratory  should  be  made  one  of  the 
conditions  of  acceptance.  Under  all  circumstances,  it  is  always  best  to  have 
the  testing  done  at  some  well-estabhshed  and  properly  equipped  cement-testing 
laboratory.  The  results  of  tests  in  temporary  laboratories  are  often  abnormal 
and  may  lead  to  unnecessary  controversies  with  the  manufacturers.  To  be 
acceptable,  a  cement  should  meet  the  following  requirements  as  called  for  in 
standard  specifications.  * 

Specific  Gravity.  The  specific  gravity  of  the  cement  should  be  not  less 
than  3.10. 

Fineness.  It  should  leave  by  weight  a  residue  of  not  more  than  22%  on  a 
No.  200  sieve. 

Time  of  Setting.  It  should  develop  initial  set  in  not  less  than  45  or  60  min- 
utes, according  as  the  Vicat  or  Gillmore  needle  is  used,  but  must  develop  final 
set  within  10  hours. 

Tensile  Strength.  The  minimum  requirements  for  tensile  strength  for 
briquettes  of  i -in-square  section  should  be  as  follows,  and  should  show  no  retro- 
gression in  strength  within  the  periods  specified: 

Neat  cement 
28  days  (i  day  in  moist  air,  27  days  in  water) 600  lb  per  sq  in 

One  part  cement,  three  parts  standard  Ottawa  sand 

7  days  (i  day  in  moist  air,  6  days  in  water) ; 200  lb  per  sq  in 

28  days  (i  day  in  moist  air,  27  days  in  water) 300  lb  per  sq  in 

Constancy  of  Volume.  Pats  of  neat  cement  about  3  in  in  diameter,  y^  in 
thick  at  the  center,  and  tapering  to  a  thin  edge,  should  be  kept  in  moist  air  for  a 
period  of  24  hours.  The  pat  is  then  exposed  in  an  atmosphere  of  steam,  i  in  above 
boiling  water,  in  a  loosely  closed  vessel,  for  5  hours. 

These  pats,  to  satisfactorily  pass  the  requirements,  should  remain  firm  and 
hard  and  show  no  signs  of  distortion,  checking,  cracking,  or  disintegration. 

*  For  the  complete  standard  specifications  see  the  latest  Year  Book  of  the  Am.  Soc. 
for  Test.  Mats.  See,  also.  Chapter  III,  page  237,  for  the  principal  clauses  of  the  last 
Standard  Specifications  for  Portland  Cement,  adopted  in  1916,  and  effective  January 
I,  1917,  by  the  Am.  Soc.  for  Test.  Mats.  The  tensile  strengths  for  neat  cement  are 
now  omitted. 


^S  Reinforced-Concrete  Construction  Chap.  24 

Sulphuric  Acid  and  Magnesia.  The  cement  should  not  contain  more  than 
2%  of  anhydrous  sulphuric  acid  (SO3)  nor  more  than  5%  of  magnesia  (MgO). 
The  test  for  constancy  of  volume  or  soundness  is  of  particular  importance 
for  reinforced-concrete  work.  When  used  in  large  masses  an  occasional  batch 
of  concrete  made  with  unsound  cement  may  not  seriously  affect  the  final  result, 
but  in  reinforced-concrete  building  operations,  where  the  different  members  of 
the  structures  are  comparatively  small,  the  safety  of  the  entire  building  may 
be  jeopardized  by  the  use  of  a  small  amount  of  unsound  cement  in  some  impor- 
tant part,  such  as  a  column. 

Aggregate.*  By  the  term  aggregate  is  understood  the  materials,  including 
the  sand,  mixed  with  the  cement  to  make  the  concrete.  In  practically  all  cases, 
the  sand  is  a  necessary  element. 

Sand.  "The  sand  should  be  clean.  One  may  obtain  some  idea  of  its  cleanli- 
ness by  placing  it  in  the  palm  of  one  hand  and  rubbing  it  with  the  fingers  of  the 
other.  If  the  sand  is  dirty,  it  will  discolor  the  palm.  Unless  from  a  bank  of 
known  quahty,  a  sand  should  be  tested  for  tensile  strength  of  mortar,  before 
using.  Preference  should  be  given  to  sand  containing  a  mixture  of  coarse  and 
fine  grains.  Extremely  fine  sand  even  if  clean  makes  a  weak  mortar  and  should 
never  be  used  unless  with  a  large  excess  of  cement." f  Mortars  composed  of  one 
part  Portland  cement  and  three  parts  fine  aggregate  or  sand,  by  weight,  should 
show  a  tensile  strength  of  at  least  70%  of  the  strength  of  i  13  mortar  of  the  same 
consistency  and  of  the  same  cement  mixed  with  standard  Ottawa  sand.  The 
New  York  Regulations  specify  that  fine  aggregate  shall  consist  of  sand,  crushed 
stone,  or  gravel  screenings,  passing  when  dry,  a  screen  having  J^-in- diameter 
holes,  and  passing  not  more  than  6%  through  a  sieve  having  100  meshes  per 
Hnear  inch.  The  Chicago  Regulations  specify  that  not  less  than  45%  shall  be 
retained  on  a  screen  of  400  meshes  to  the  square  inch.    (See,  also,  page  241.) 

Coarse  Aggregate.  For  the  coarser  material  of  the  aggregate  many 
materials  are  used  and  many  others  have  been  suggested.  Its  selection  is  gen- 
erally dependent  upon  local  conditions.  If  possible,  gravel  or  crushed  stone 
should  be  used.  Whatever  is  used  should  be  a  clean,  hard  substance  that  will 
secure  to  the  concrete  the  necessary  strength;  that  is,  the  crushing  strength 
of  this  material  should  be  equal  to  or  greater  than  that  of  the  mortar  used,  at 
least  at  the  age  of  28  days.  In  any  case,  where  no  reliable  information  is  to  be 
had  on  the  strength  of  a  concrete  made  from  a  given  aggregate,  careful  investi- 
gation should  be  made  before  such  material  is  used.     (See,  also,  page  241,) 

Gravel.  Gravel,  like  sand,  should  be  clean.  If  dirty  it  should  be  washed 
before  being  used.  To  get  the  most  satisfactory  or  uniform  results,  gravel 
should  be  screened  and  graded  and  then  mixed  in  definite  proportions,  as  the 
RUN  OF  the  bank  will  generally  not  give  uniform  results.     (See,  also,  page  241.) 

Stone.  The  most  satisfactory  stone  that  can  be  used  is  trap-rock  (under 
which  term  are  included  most  of  the  rocks  of  igneous  origin),  because  of  its 
toughness  and  great  compressive  strength.  The  granites,  as  they  are  com- 
mercially known,  are  considered  by  some  equal  in  quality  to  trap-rock  for  the 
making  of  concrete.  The  presence  of  mica  in  considerable  proportion  in  some 
of  the  so-called  granites  would  seem  to  make  them  unsuitable.     Limestones, 

*  See,  also,  Chapter  III,  pages  240  to  251.  The  data  there  on  Aggregates,  Propor- 
tioning Materials,  etc.,  relate  more  particularly  to  mass-concrete,  while  the  data  of 
Chapter  XXIV  is  intended  to  cover,  more  in  detail,  reinforced  concrete. 

t  Treatise  on  Concrete,  Plain  and  Reinforced,  Taylor  and  Thompson,  third  edition, 
T916,  page  12,      . 


Materials  Used  in  Reinforced-Goncrete  Construction  909 

if  the  soft  varieties  are  excepted,  make  excellent  concrete  as  far  as  strength  is 
concerned.  They  would,  however,  seem  to  affect  the  fire-proof  character  of 
the  concrete.  (See  Tables  «n  page  956.)  The  harder  and  more  compact 
SANDSTONES,  also,  may  be  used  successfully,  but  great  care  must  be  exercised 
in  their  selection.  Conglomerate,  which  is  in  reality  a  hard,  coarse  sandstone, 
should  give  very  satisfactory  results.  On  account  of  their  low  crushing  strength, 
SLATE  or  SHALE  should  not  be  used  in  concrete.  Besides  the  stones  thus  far 
mentioned,  broken  brick,  terra-cotta,  furnace-clinker  and  furnace-slag 
have  been  suggested.  In  the  selection  of  broken  brick  or  terra-cotta,  care  must 
be  taken  to  get  hard-burned  material.  The  crushing  strength  of  such  material 
when  well  selected,  is  a  little  more  than  that  of  acceptable  concrete,  28  days 
old.  But  ordinarily,  commercial  brick  or  terra-cotta  will  not  meet  the  require- 
ments for  a  good  aggregate,  and  these  materials  should  be  used  only  as  a  last 
resort  and  then  only  after  careful  investigation.     (See,  also,  page  241.) 

Cinders.  Furnace-clinkers  should  be  clean  and  entirely  free  from  com- 
bustible matter.  Cinders  are  often  used  where  fireproofing  is  the  primary 
consideration,  and  no  doubt  good  constructions  may  be  obtained,  with  extreme 
care,  by  the  use  of  clinker  or  cinder  concrete,  especially  if  the  material  is  ground, 
screened  and  graded  as  suggested  for  gravel.  But  in  general  practice  the  con- 
crete is  not  uniform  in  quality  and  is  unreliable  in  strength.  It  is  therefore  not 
considered  in  this  chapter.  In  Chapter  XXIII,  Fireproofing  of  Buildings,  its 
usj  is  disjcussed  on  pages  817  and  818.     (See,  also,  page  242.) 

Size  of  Aggregate.  The  size  of  the  aggregate  may  vary  from  ^  to  23^ 
in  in  largest  diametrical  dimension,  depending  on  the  particular  purpose  for 
which  it  is  to  be  used.  Where  the  mass  of  concrete  is  comparatively  large  the 
aggregate  may  run  as  high  as  3  in  in  size.  This  may  sometimes  be  the  case 
in  foundations  and  in  large  piers  and  thick  walls.  In  columns,  girders,  beams 
and  slabs,  very  unsatisfactory  results  would  be  obtained  if  so  large  a  stone  were 
used.  For  such  work  no  stone  or  other  aggregate  should  be  used  larger  than 
would  pass  a  i-in  screen.  In  important  girders  and  columns,  especially  when 
the  reinforcing-bars  are  closely  spaced,  the  size  should  be  made  even  smaller  so 
that  a  concrete  of  viscous  consistency  is  produced  "which  will  pass  readily  be- 
tween and  easily  surround  the  reinforcement  and  fill  all  parts  of  the  forms. "  * 

The  maximum  sizes  allowed  for  the  aggregate  in  reinforced  concrete  in  the  dif- 
ferent cities  are  as  follows:  St.  Louis  and  Bufi"alo,  stone  that  will  pass  a  K-in  ring, 
that  is,  "three-quarter-inch  stone";  New  York,  Cleveland  and  Philadelphia, 
stone  that  will  pass  a  i-in  ring;  Chicago,  stone  passing  i -in-square  mesh;  San 
Francisco,  for  floors  and  fireproofing,  i-in  stone,  for  foundations,  2-in  stone. 
(See,  also,  page  241.) 

Water.  "The  water  used  in  mixing  concrete  should  be  free  from  oil,  acid, 
alkalies,  or  organic  matter. "  * 

Proportions  of  the  Materials.  The  proper  proportion  of  the  materials 
entering  into  the  concrete  is  dependent  upon  the  size  and  character  of  the  mate-  • 
rials.  In  cities  in  which  there  are  regulations  governing  reinforced-concrete  con- 
struction, the  mixture  to  be  used  is  generally  specified.  In  the  absence  of  other 
considerations  the  most  satisfactory  and  reliable  mixture  is,  one  part  of  Portland 
cement,  two  parts  of  sand  and  four  parts  of  stone  or  gravel.  It  is  the  mixture 
that  has  been  used  in  most  of  the  experimental  work  on  reinforced  concrete, 
and  there  is  therefore  much  trustworthy  information  to  be  had  concerning  it. 
In  the  case  of  large  or  important  operations,  however,  great  economy  can  often 

*  Trans,  Am.  Soc.  C.  E.,  1917,  Vol.  81,  page  1115- 


910  Reinforced-Concrete  Construction  Chap.  24 

he  effected  by  a  preliminary  study  of  the  materials  to  be  used  and  of  their 
proper  proportions.  In  general,  for  given  materials,  the  most  economical  mix- 
ture is  also  the  strongest.  The  old  method  of  determining  the  proportions  of 
concrete  by  measuring  the  voids  in  the  coarser  particles  by  means  of  water 
poured  into  a  box  containing  i  cu  ft  of  the  material  and  then  providing  that 
quantity  of  finer  material,  assuming  the  cement  the  same  as  sand,  is  not  to  be 
recommended.  It  does  not  give  accurate  or  satisfactory  results.  A  better 
method  is  to  take  the  materials  to  be  used  and  make  trial-mixtures  by  varying 
the  proportions,  always  using,  however,  the  same  amount  of  cement  and  water. 
These  trial-mixtures  are  placed  successively  in  a  measuring  vessel  of  fixed  size 
and  tamped,  and  the  height  to  which  the  vessel  is  filled  for  each  mixture  is 
noted.  The  proportions  that  give  the  lowest  height,  or  result  in  the  smallest 
volume,  will  give  the  most  satisfactory  concrete.  (See,  also,  page  242  and  fol- 
lowing pages.) 

The  best  and  most  scientific  method,  howe-'/'^r,  is  that  known  as  the  IvDECHAN- 
ICAL  ANALYSIS,  devised  by  W.  B.  Fuller.  In  this  method  the  available  materials, 
including  the  cement,  are  separated  into  the  various  sizes  by  means  of  a  series 
of  sieves;  curves  are  plotted  which  indicate  the  p)ercentages  of  the  whole  mass, 
which  pass  the  several  sieves;  and  from  a  study  of  these  curves  the  proportions 
of  the  different  aggregates  are  determined.  For  a  detailed  description  of  this 
method  the  reader  is  referred  to  the  chapter  on  Proportioning  Concrete  in  the 
191 2  edition  of  the  Treatise  on  Concrete,  Plain  and  Reinforced,  by  Taylor  and 
Thompson.  As  an  example  of  the  saving  possible,  the  following  case,  given  in 
the  work  just  referred  to,  will  be  of  interest. 

"The  ordinary  mixture  for  water-tight  concrete  is  about  1:2:4,  which  re- 
quires 1.57  barrels  of  cement  per  cubic  yard  of  concrete.  By  carefully  grading 
the  materials  by  methods  of  mechanical  analysis  the  writer  has  obtained  water- 
tight work  with  a  mixture  of  about  1:3:7,  thus  using  only  i.oi  barrels  of 
cement  per  cubic  yard  of  concrete.  This  saving  of  0.56  barrel  is  equivalent, 
with  Portland  cement  at  $1.60  per  barrel,  to  $0.89  per  cu  yd  of  concrete.  The 
added  cost  of  labor  for  proportioning  and  mixing  the  concrete,  because  of  the 
use  of  five  grades  of  aggregate  instead  of  two,  was  about  $0.15  per  cu  yd, 
thus  effecting  a  net  saving  $0.74  per  cu  yd.  On  a  piece  of  work  involving, 
say,  20000  cu  yd  of  concrete,  such  a  saving  would  amount  to  Si 4  800,  an 
amount  well  worth  considerable  study  and  effort  on  the  part  of  those  in  respon- 
sible charge." 

In  the  ordinances  or  regulations  governing  reinforced  concrete  of  various 
cities  the  proportions  to  be  used  are  generally  prescribed.  In  New  York,  "the 
concrete  for  reinforced-concrete  structures  shall  consist  of  a  wet  mixture  of  one 
part  of  Portland  cement  to  not  more  than  six  parts  of  aggregate,  fine  and  coarse, 
either  in  the  proportion  of  one  part  of  cement,  two  parts  of  fme  aggregate  and 
four  parts  of  coarse  aggregate,  or  in  such  proportion  that  the  resistance  of  the 
concrete  to  crushing  shall  not  be  jess  than  2  000  lb  per  sq  in  after  hardening  for 
28  days."  In  Chicago,  various  grades  of  concrete  arc  specified  with  the  ulti- 
rnate  compressive  resistance,  to  be  developed,  from  a  mixture  of  i  :  i  :  2  and 
an  ultimate  strength  of  2  900  lb  per  sq  in,  to  a  t  :  3  :  7  mixture  with  a  strength 
pf  I  SCO  lb  per  sq  in.  In  Buffalo  and  San  Francisco  the  proportion  is  given 
as  one  of  cement  to  six  of  aggregate;  in  Boston  it  is  one  of  cement  to  five  of 
aggregate. 

Compressive  Strength  of  Reinforced  Concrete.  For  reinforced-concrete 
work  no  mixture  should  be  used  that  docs  not  develop  a  compressive 
STRENGTH  of  at  least  2  000  lb  per  sq  in  at  the  age  of  28  days.  The  crushing 
strength  of  various  concretes  is  shown  in  the  following  table: 


Materials  Used  in  Reinforced-Concrete  Construction 


911 


Table  I 

.     Compressive  Strength  of  Portland-Cement  Concrete  of 

Different  Proportions 

Proportions 

Com- 

Age, 
months 

pressive 

strength 

Authority- 

Cement 

Sand 

Stone 

persq 
in 

I 

0 

4 

4  370 

2 

0 

4 

•2  506 

3 

0 

4 

I  812 

4 

0 

4 

830 

5 

o 

4 

532 

6 

o 

4 

169 

7 

0 

4 

118 

2 

4 

4 

2  178 

3 

4 

6 
8 

4 
4 

I  815 
I  135 

James   E.   Howard,  Tests,   Watertown 
Arsenal 

5 

10 

4 

707 

6 

12 

4 

738 

2 

2 

4 

I  768 

2 

3 

4 

I  911 

2 

4 

4 

2147 

2 

5 

4 

2  452 

2 

6 

4 

2  124 

2 

7 

4 

I  650 

2 

8 

4 

1295 

J 

1 

2 

4 

I 

2399 

G.  A.  Kimball,  Tests  of  Metals,  U.  S.  A. 
(  Taylor  and    Thompson,   Tests,  Water- 
(       town  Arsenal 

2H 

S 

I 

3255 

I  Watertown    Arsenal,    Tests   of    Metals, 
(       U.  S.  A. 

3 

5 

T 

2042 

Working  Stresses  for  Reinforced  Concrete.  Some  formulas  for  the 
strength  of  reinforced-concrcte  construction  provide  for  the  use  of  the  ultimate 
STRENGTH  of  the  concretc  and  the  application  of  a  factor  of  safety.  This 
practice  is  not  to  be  recommended  as  it  necessitates  either  the  test  of  the  con- 
crete or  the  assumption  of  an  ultimate  strength.  While  it  is  undoubtedly  de- 
sirable that  the  concrete  should  be  tested,  this  is  generally  impracticable  when 
the  building  is  being  designed.  It  should  be  done  during  construction  and  is 
done  on  the  best  work,  to  make  sure  that  the  concrete  is  up  to  the  require- 
ments. Various  factors  of  safety  from  two  and  one  half  to  ten  have  been  pro- 
posed. Different  factors  of  safety  are  used  for  different  members  of  a  structure 
or  for  different  conditions.  This  is  another  reason  why  it  would  be  better  to  use 
WORKING  stresses  than  ultimate  stresses.  The  following  working  stresses 
are  recommended  for  reinforced  concrete  that  will  develop  a  crushing  strength 
©f  2  000  lb  per  sq  in  in  28  days: 

Extreme  fiber-stress  in  compression 650  lb  per  sq  in 

Shearing-stress 40  lb  per  sq  in 

Vertical  shearing-stress  when  all  diagonal   tension  is  re- 
sisted   by  the  steel,  and  the    steel-resistance    to   both 

negative  and  positive  moments  is  fully  developed 150  lb  per  sq  in 

Direct  compression Soo  lb  per  sq  in 

Bond-stress  between  concrete  and  plain  reinforcing-bars. .     80  lb  per  sq  in 
Bond-stress  between  concrete  and  suitable  deformed  bars.    100  lb  per  sq  in 
Table  II  gives  the  stresses  allowed  by  various  building  ordinances. 


912 


Reinforced-Concrete  Construction 


03 

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^'o'o  "rt  «^ 

03    'w 

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Materials  Used  in  Reinforced-Concrete  Construction  913 

Steel  Reinforcement.  The  function  of  the  steel  reinforcement  is  to  take  up 
the  longitudinal  and  diagonal  tensile  stresses  and  in  some  cases,  as  in  columns 
and  in  beams  reinforced  at  the  top,  to  give  additional  compressive  strength. 

Mild  or  High  Steel.     Two  grades  of  steel  are  used  for  the  reinforcement, 

MILD  STEEL  and  HIGH-CARBON  STEEL.      MiLD  or  MEDIUM  STEEL  is  USed   for  all 

structural  shapes  and  is  the  ordinary  merchant-steel.  It  has  an  ultimate 
tensile  strength  of  from  60  000  to  70  000  lb  per  sq  in,  and  its  elastic  hmit  is  about 
one  half  the  ultimate  strength.  High-carbon  steel  has  a  greater  percentage 
of  carbon  and  is  therefore  more  brittle.  Its  ultimate  strength  is  about  105  000 
and  its  elastic  limit  about  55  000  lb  per  sq  in.  The  use  of  high-carbon  steel 
would  permit  greater  stresses  in  the  reinforcement,  and  consequently  a  less 
amount  of  steel  and  a  greater  economy  in  construction.  On  account  of  its  greater 
brittleness,  however,  it  is  Hable  to  sudden  failures  under  stress.  It  is  also  often 
found  to  be  cracked  or  broken  when  sent  to  the  work,  and  unless  it  is  very  care- 
fully inspected  there  is  great  Uability  of  defective  material  getting  into  the 
structure.  Furthermore,  much  of  the  so-called  high-carbon  steel  has  been 
found  in  practice,  after  testing,  to  fall  far  short  of  the  specifications.  Its  use  is 
therefore  to  be  avoided,  unless  special  care  is  taken  to  secure  an  absolutely  re- 
liable article  and  to.  have  it  inspected  and  tested.  For  large,  important  work 
this  would  be  desirable.  Ordinarily,  however,  mild  steel  should  be  used,  as  com- 
mercially it  is  manufactured  and  sold  under  such  standard  conditions  that  it  is 
reliable.  As-the  modulus  of  elasticity  of  high-carbon  steel  is  practically  the  same 
as  that  of  medium  steel,  the  deformation  under  any  given  loading  is  the  same 
and  there  is  no  special  advantage  in  the  use  of  one  over  the  other.  Steel  meeting 
the  specifications  of  the  American  Society  for  testing  materials*  for  reinforcing- 
bars  is  recommended.  See  Table  HI.  The  phosphorus  in  the  steel  should  not 
exceed  0.10%  for  Bessemer  steel  nor  0.05%  for  open-hearth  steel.  For  slab  and 
small  beam-reinforcement  where  wire  or  small  rods  are  suitable,  steel  manu- 
factured from  Bessemer  billets  may  be  used  with  a  tensile  strength  of  105  000, 
and  a  yield-point  of  not  less  than  52  500  lb  per  sq  in. 

Working  Stresses  for  Steel.  The  generally  accepted  working  stress  for 
medium  steel  is  16  000  lb  per  sq  in  in  tension.  Tests  have  shown  that  in  cases 
where  the  failure  of  reinforced-concrete  beams  is  due  to  the  failure  of  the  rein- 
forcement, the  stress  in  the  metal  had  not  more  than  reached  the  yield-point. 
This  point  is  somewhat  lower  than  the  elastic  limit.  The  working  stress  in 
the  steel,  therefore,  should  be  a  fixed  proportion  of  the  yield-point  or  the  elastic 
hmit.  It  is  held  by  some  that  this  ratio  should  not  be  as  high  as  one  to  two, 
but  more  nearly  one  to  three,  reducing  the  working  stress  in  mild  steel  as  given 
above  to  10  000  or  12  000  lb  per  sq  in.  In  using  high-carbon  steel  they  would 
advocate  a  similar  ratio  of  the  elastic  limit,  whatever  that  may  be,  according  to 
test.  Ordinarily  20  000  lb  per  sq  in  is  taken  as  the  working  stress  for  high-car- 
bon steel.  Allowable  working  stresses  in  steel  reinforcement  in  various  cities 
are  given  in  Table  II,  page  912. 

Tension-Members.  Reinforcement  is  used  in  a  variety  of  shapes  and  com- 
binations, nearly  all  of  them  patented  and  some  of  them  forming  the  basis  for 
so-called  systems.  Where  the  reinforcement  is  employed  to  take  up  tension, 
as  in  a  beam  or  girder,  the  bond  between  the  concrete  and  the  steel  is  relied  upon 
to  develop  the  tensional  stresses  in  the  steel.  The  plain  bars  depend  entirely 
upon  the  adhesion  of  the  steel  and  the  concrete  for  the  action  of  the  two  mate- 
rials in  combination,  or  the  full  tensile  strength  of  the  rod  is  developed  by  anchor- 
ing the  rods  into  the  concrete  at  the  ends,  in  which  case  the  beam  becomes  more 

*  American  Society  for  Testing  Materials  Standards,  1918. 


914 


Reinforced-Concrete  Construction 


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Materials  Used  in  Reinforced-Concrete  Construction 


915 


analogous  to  a  trussed  beam  with  the  rod  as  the  tension-member.  In  cross- 
section,  plain  bars  are  usually  round  or  square,  though  sometimes  flat  bars, 
angles,  tees,  or  other  shapes  are  used.  In  regard  to  the  use  of  square  bars  and 
some  other  shapes,  it  is  contended  that  the  edges  start  initial  cracks  in  the  con- 
crete as  it  shrinks  in  setting.  Twisted  flat  bars,  when  placed  too  near  the  sur- 
face of  the  concrete,  cause  a  spaUing  or  breaking  out  of  the  concrete  from  between 
the  convolutions,  when  the  steel  is  under  stress. 

Commercial  Sizes.  As  a  result  of  the  shortage  of  steel  during  and  since  the 
world-war,  the  larger  producers  of  reinforcing-bars  have  agreed  to  eliminate 
many  of  the  commercial  sizes  of  bars  formerly  in  use  and  are  now  Hmiting  their 
stocks  of  bars  to  the  following  sizes: 


Area 

Equivalent  to 

Area 

Equivalent  to 

o.  no  sq  in 
o.  196  sq  in 
0.  250  sq  in 
0.307  sq  in 
0 .  442  sq  in 

^-in  round 
K-in  round 
}4-in  square 
^-in  round 
H-in  round 

0.601  sq  in 

0.  785  sq  in 

1 .  000  sq  in 
1 .  266  sq  in 
1 .563  sq  in 

J^-in  round 

I -in  round 

i-in  square 

I  i^-in  square 

I  M-in  square 

Difhculty  in  obtaining  reinforcement  will  be  avoided  to  a  great  extent  by  the 
use  of  these  sizes  in  designing  reinforced  concrete. 

Deformed  Bars.  With  the  deformed  bars  the  adhesion  of  the  concrete  to 
the  steel  is  supplemented  by  a  mechanical  bond  due  to  the  shape  of  the  bar. 
The  following  deformed  bars  have  been  and  are  at  present  widely  used. 

The  Ransome  Bar.  The  Ransome  Twisted  Bars  (Fig.  1)  are  made  of  square 
bars.     Bars  should  be  "twisted  cold  with  one  complete  twist  in  a  length  of  not 


Fig.  1.    The  Ransome  Twisted  Bar 

over  twelve  times  the  thickness  of  the  bar."*  The  work  on  the  bars  in  the  twist- 
ing process  increases  the  elastic  limit  and  the  tensile  strength;  but  the  amount 
of  the  increase  is  not  fixed,  as  variations  in  the  grade  of  rolled  steel  may  result, 
aftei*  twisting,  in  still  wider  variations.  The  users  of  this  bar  generally  assume  a 
working  stress  of  20  000  lb  per  sq  in.  The  patent  on  this  bar  has  expired  and  it 
may  now  be  used  by  anyone.  Strictly  speaking,  this  is  not  a  deformed  bar. 
These  bars  can  be  obtained  in  all  sizes,  varying  by  K  in  from  5^  to  i  M  in.  Larger 
sizes,  also,  can  be  obtained  on  special  order. 


Fig.  2.    The  Buffalo  Deformed  Bar 

The  Buffalo  Deformed  Bar.     The  Buffalo  Steel  Company  of  Tonawanda, 
N.  Y.,  makes  a  square  bar  with  rounded  edges,  thus  eliminating  the  sharp  cor- 

*  American  Society  for  Testing  Materials  Standards,  1918,  pages  149  and  152. 


916 


Reinforced-Concrete  Construction 


Chap.  24 


ners.  The  deformations  consist  of  raised  stars  along  the  sides  of  the  bar,  as 
shown  in  Fig.  2.  It  is  made  in  sizes  of  from  Vg  to  i3^-in  diameter,  and  the 
cross-sectional  areas  are  equal  to  the  areas  of  equivalent  squares.     The  bars  are 

rolled  from  old  railroad  rails 
and  comply  with  the  Standard 
Speciftcations  of  the  American 
Society  for  Testing  Materiyls, 
for    reinforcing-steel    of    that 
kind.      The    steel    is    a   high 
carbon    steel    with    a   tensile 
strength  of  8o  ooo  lb  per  sq  in. 
Corrugated      Bars.     Cor- 
rugated   bars    (Fig.    3),   both 
square    and    round    in  cross- 
section,  are  made  by  the  Cor- 
rugated  Bar    Company,  Inc., 
Buffalo,  N.  Y.,  of  both  medium  and  high-elastic-limit  steel  with  a  yield-point  of 
about  50  000  lb  per  sq  in.     Corr-Bars  are  furnished  either  straight  and  cut  to 
length,  or  bent  ready  for  the  forms.     The  standard  sizes  are  as  follows: 


Fig.  3.     Corrugated  Bars.     Round  and  Square 


Corrugated  Rounds 


Size  in  inches 

H 

K2 

He 

H 

H 

li 

I 

iH 

iH 

Net  area  in  square 
inches 

Weight  per  foot  in 
pounds 

O.II 

0  38 

0  19 
0.66 

0.25 
0.86 

0.30 

I. OS 

0.44 
1.52 

0.60 
2.06 

0.78 
2.69 

0.99 
3.41 

1.22 
4.21 

Corrugated  Squares 


Size  in  inches 

H 

% 

H 

H 

H 

% 

I 

iH 

iH 

Net  area  in  square 
inches 

0.06 
0.22 

0.14 
0.49 

0.25 
0.86 

0.39 

1.35 

0.56 
1.94 

0.76 
2.64 

1. 00 
3.43 

1.26 
4.34 

1.55 
5.35' 

Weight   per  foot  in 
pounds  

Fig.  4.    The  Havermeyer  Bar,  Square  s^nd  Round 


Materials  Used  in  Reinforced-Concrete  Construction 


m 


The  Havermeyer  Bar.  The  Havermeyer  Bar  (Fig.  4),  controlled  by  the 
Concrete  Steel  Company,  Youngstown,  Ohio,  consists  of  square  and  round  bars 
rolled  with  a  series  of  gradual  projections  and  depressions  on  all  sides,  the  defor- 
mations being  so  designed  that  there  is  a  constant  cross-sectional  area.  They 
are  furnished  in  the  following  sizes  and  weights: 


Size  in  inches 

Square  bars 

Round  bars 

Area  in  square 

Weight  per 

Area  in  square 

Weight  per 

inches 

foot  in  pounds 

inches 

foot  in  pounds 

H 

0.0625 

0.212 

0.0491 

0.167 

% 

0.1406 

0.478 

0.1104 

0.375 

H 

0.2500 

0.850 

0.1963 

0.667 

% 

0.3906 

1.328 

0.3068 

1.043 

%      . 

0.5625 

1. 913 

0.4418 

1.502 

% 

0.7656 

2.603 

0.6013 

2.044 

I 

I. 0000 

3.400 

0.7854 

2.670 

iH 

1.2656 

4.303 

0.9940 

3.379 

t3^ 

I  5625 

T    8006 

5.312 
6.428 
7.650 

1.2272 

4.173 

iH 

2.2500 

A  variation  of  5%  under  and  2H%  over  the  above  weights  is  required  for  rolling. 


This  company  also  rolls  a  flat  bar  with  similar  deformations  on  the  wide  faces. 
This  form  is  recommended  where  bars  must  be  bent  in  curves,  as  in  silos,  sewers, 
etc.  In  running  them  through  a  tire-machine  to  bend  them,  the  edges  of  the 
flats  prevent  the  lugs  from  being  damaged. 

The  Diamond  Bar.  The  Diamond  Bar  (Fig.  5),  put  on  the  market  by  the 
Concrete  Steel  Engineering  Company,  New  York,  is  a  bar  of  absolutely  uniform 


Fig.  5.     The  Diamond  Bar 

section.     There  is  consequently  no  waste  of  metal  due  to  the  deformations. 
This  bar  is  practically  a  round  bar,  and  as  sudden  transitions  from  one  section  to 


Fig.  6.    The  Rib-bar 


another  are  avoided,  all  tendency  to  cause  initial  cracks  in  the  concrete  is  over- 
come. The  weights  and  areas  of  Diamond  bars  are  equal  to  those  of  plain  square 
bars  of  Hke  denominations.  Bars  from  }4  to  i  M  in  in  diameter  naay  be  ob- 
tained. 


918 


Reinforced-Concrete  Construction 


Chap.  24 


The  Rib-Bar.  The  Rib-Bar  (Fig.  6)  manufactured  by  the  Truscon  Steel 
Company,  Youngstown,  Ohio,  is  a  rolled  bar  with  a  series  of  cross-ribs.  These 
bars  are  made  with  rectangular  or  round  section  and  are  furnished  in  sizes  of 
from  y^to  1%  in,  the  areas  of  the  cross-sections  being  equivalent  to  squares  of 
equal  denominations;  but  the  weights  are  sHghtly  greater,  and  are  as  follows: 


Sqi 

lare  bars 

Round  bars 

Size, 
in 

Area, 

Weight  per 

Area, 

Weight  per 

sq  in 

linear  foot, 
ib 

sq  m 

linear  foot, 
lb 

Vs 

0.1406 

0.48 

0.1 104 

0.379 

M 

0.2500 

0.86 

0. 1963 

0.674 

H 

0.3906 

1.35 

0.3068 

I  054 

M 

0.562s 

1.9s 

0.4418 

I. 517 

% 

0.7656 

2.6s 

0.6013 

2.065 

I 

I . 0000 

3.46 

0.7854 

2.697 

iH 

1.2656 

4.38 

0.9940 

3.414 

i^ 

1.5625 

5. 41 

Kalman  Grip-Bars.  These  bars  are  similar  in  general  design  to  the  Rib- 
Bars,  differing  from  them  by  having  the  ribs  running  entirely  around  the  bars, 
instead  of  half-way.  They  are  kept  in  stock  in  both  round  and  square  sections 
of  standard  sizes  and  weights,  by  the  Paul  J.  Kalman  Company,  St.  Paul,  Minn. 


Fig.  7.     The  Ovoid  Bar 

The  Ovoid  Bar.    The  Gabriel  Concrete  Reinforcement  Company  of  Detroit, 
Mich.,  furnishes  the  Ovoid  Bar  (Fig.  7),  in  sizes  and  areas  as  follows: 


Size  in  inches 

Vs 

^ 

^ 

¥4. 

% 

I 

iH 

Area  in  square  inches .  .  . 
Weight  ill  pounds 

0. 1406 

0.4940 

0.250 
0.873 

0.3906 
1.3560 

0.5625 
1.9470 

0.7656 

2 . 6430 

I  .000 
3.446 

1.2656 
4.3540 

The  Monotype  Bar.    These  bars  are  cruciform  in  section,  and  have,  at 
intiervals,  ribs  connecting  the  stems.     (Fig.  8.)     The  cross-sectional  areas  are 


Fig.  8.     The    Monotype  Bar 


equivalent  to  those  of  standard  round  and  square  bars.     They  can  be  secured 
trom  the  Edward  A.  Tucker  Company,  Boston,  Mass. 


Materials  Used  in  Reinforced-Concrete  Construction 


919 


Rivet  Grip-Bars.     These  bars  are  rolled  in  sections  equivalent  to  standard 
square  bars.     The  cross-section  is  especially  designed  so  that  shear-members 


Fig.  9.    The  Rivet  Grip-bar 

may  be  rigidly  attached,  as  shown  in  Fig.  9,  thus  securing  such  advantages  as  are 
claimed  for  them.  They  are  handled  by  the  Concrete  Reinforcing  and  Engineer- 
ing Company,  Cleveland,  Ohio. 


Rivet  grip- 
bars, 
size 

Area, 
sq  in 

Perimeter, 
in 

Weight, 

per  foot, 

lb 

3^  in 

^in 

Hin 

14  in 

I  m 

iH  in 

iH  in 

o. 1406 
0.3906 
0.562s 
0.7656 
•  1 . 0000 
1.2656 
1.562s 

1.63 
4.00 
4-25 
4.75 
5. 19 
5.75 
6.50 

0.478 
1.328 
1.913 

2.603 
3.400 
4.303 
5.313 

Wire  Mesh  and  Expanded  Metal.  Other  types  of  tension-reinforcement, 
such  as  WIRE -MESH  FABRIC  and  EXPANDED  METAL  in  various  forms,  have  beeil 
discussed  in  Chapter  XXIII,  Fireproofing  of  Buildings.  Wire  fabric  has  come 
into  very  general  use  as  a  slab-reinforcement,  as  it  resists  temperature-cracks 
and  the  cracking  of  the  concrete  from  impact  or  shock.  It  is  made  in  various 
gauges  with  heavy  longitudinal  or  carrying  wires  and  lighter  transverse  dis- 
tributing, or  tie-wires.  Expanded  metal  is  similar  to  wire  mesh  in  providing 
reinforcement  in  both  directions,  rigidly  spaced  and  attached  or  fastened  to- 
gether. This  additional  advantage  is  claimed  for  it;  it  provides  reinforcement 
in  all  directions,  thus  taking  care  of  concentrated  loads. 

Anchoring.  Different  methods  have  been  used  for  anchoring  the  tension- 
bars  in  reinforced  concrete.  In  the  Hennebique  system  of  construction  (Fig.  10) 
where  plain  bars  are  used,  the  ends  of  the  rods  are  split  and  flared  out.  In  other 
constructions  the  ends  of  the  bars  are  simply  turned  at  right-angles  in  such 
direction  as  is  most  suitable.  In  some  instances  nuts  and  washers  have  been 
placed  at  the  ends  of  reinforcing-rods.  Where  reinforced-concrete  floors  are 
used  in  connection  with  steel  columns  the  rods  are  run  through  the  web-plates 
or  through  angle-brackets  and  secured  with  nuts. 

Adhesion.  The  strengths  of  the  bond  between  concrete  and  steel  for  various 
forms  of  bars  and  differing  conditions  are  shown  in  Table  IV.  After  the  bond 
has  failed,  the  reinforcement  still  acts  in  conjunction  with  the  concrete,  due  to 
a  moving  or  frictional  resistance.    Numerous  tests  nave  shown  this  fric- 


S20 


Reinforced-Concrete  Construction 


Chap.  24 


tional  resistance  to  be  about  two  thirds  of  the  initial  bond-strength.     The 
BOND-STRENGTH  for  ordinary  round  or  square-section  bars  may  be  taken  at  200 


Fig.  10.    The  Hennebique  System 

to  300  lb  per  sq  in,  depending  upon  the  character  of  the  concrete  and  the  degree 
of  roughness  of  the  steel.  Mechanical  bond  depends  upon  the  shape  of  the 
bar  and  the  compressive  and  shearing  strength  of  the  concrete. 


Table  IV.     Results  of  Tests 

on  Adhesion  Between  Concrete  and  Steel 

Kind  of  bar 

Size 
tested  in 
fraction  of 

inch 

Concrete 

Age 

Ultimate  strength 
developed  in  lb 
per  sq  in  of  sur- 
face in  contact 

Round 

% 
•% 
% 
% 
li 
Vs 
■  % 
% 

%    ■ 
% 
% 
% 

% 
% 

H 

H 
'A 

1:2:4 
1:3:6 

60  days 
30  days 
30  days 
90  days 
90  days 

30  days 

31  days 
25  days 

7  mos. 

7  mos. 

7  m.os. 

7  mos. 

7  mos. 

7  mos. 

7  mos. 

7  mos. 

7  mos. 

7  mos. 
31  days 
30  days 

412  (a) 
274  ib) 
437  ic) 
642  (c) 
431  (c) 
294  (c) 
648  id) 
500  (c) 
I  290  (e) 
I  318  (e) 
I  199  (e) 
701  (e) 
796  ie) 
962  ie) 
977  (e) 
934  ie) 
735  ie) 
564  ie) 
640  id) 
646  ic) 

Square 

Square  (rusted) 

Square  (rusted) 

Square 

Square 

Twisted  (Ransome). 
Twisted 

1:2:4 

Twisted 

Neat  cement 

I  :  I 

1 :  2 

1:3 

I  :4 
Neat  cement 

I  :  I 

I  :2 

I  :3 

1:4 
1:2:4 

Twisted .   . . 

Twisted 

Twisted 

Twisted 

Corrugated 

Corrugated 

Corrugated 

Corrugated 

Corrugated 

Corrugated 

Thatcher  (/) 

The  following  are  the  authorities  for  the  above  tests: 

(a)  A.N.Talbot.       (b)  C.  M.  Spofford.        (c)  New  York  City  Rapid  Transit  Co. 

(d)  T.  L.  Condron.  (e)  Testsof 'Metals,  Watertown  Arsenal,  1904. 

if)    No  longer  manufactured. 


Materials  Used  in  Reinforced-Concrete  Construction  921 

Shear-Members.  In  many  of  the  tests  on  full-sized  concrete  beams,  failure 
occurs  by  the  development  of  diagonal  breaks  near  the  supports.  The  first 
diagonal  crack  in  a  beam,  with  nothing  but  horizontal  tension-steel  at  the 
bottom,  is  apt  to  occur  when  the  maximum  vertical  shear  is  from  loo  to  200  lb 
per  sq  in.  Since  the  vertical  shear  is  accompanied  by  a  horizontal  shear  of 
equal  intensity  in  all  parts  of  the  beam,  it  was  formerly  thought  that  this  diag- 
onal failure  was  due  to  these  shearing- forces  at  the  end  of  the  beam  and  vertical 
stirrups  or  bent-up  rods  were  provided  to  resist  the  horizontal  shear.  More 
recent  tests  have  shown  that  the  shearing  strength  of  concrete  is  from  60  to 
80%  of  the  compressive  strength,  and  that  these  cracks  are  diagonal  and  in  the 
direction  which  could  be  expected  from  the  theory  of  diagonal  tension, 
which  attributes  them  to  a  combination  of  the  shearing-stress  with  the  hori- 
zontal tensile  stress.  The  inclined  cracks  which  first  appear  are  due  to  a  rupture 
of  the  concrete  in  tension.  The  most  effective  way  to  prevent  this  rupture  is 
to  provide  reinforcement  in  the  direction  of  the  stress  that  is  inclined  upwards 
toward  the  supports,  as  nearly  as  possible  normal  to  the  line  of  the  diagonal 
crack.  Vertical  reinforcement  could  be  used,  but  it  would  not  act  until  def- 
ormation or  downward  displacement  of  the  concrete  occurred  on  the  side  of  the 
crack  away  from  the  support.  If  vertical  stirrups  are  used  for  this  reinforce- 
ment, they  must  be  spaced  a  less  distance  apart  than  the  effective  depth  of  the 
beam,  and  they  must  l)e  looped  around,  though  not  necessarily  attached  to,  the 
horizontal  bars.  When  inclined  reinforcement  is  used,  it  must  be  rigidly  at- 
tached to  the  longitudinal  members  and  spaced  a  less  distance  apart  than  the 
effective  depth  of  the  beam.  The  reason  for  this  is  that  the  magnitude  and  in- 
clination of  the  diagonal  tension  increases  from  the  middle  toward  the  end  of  the 
beam,  being  inclined  45°  where  the  horizontal  tension  becomes  zero. 

The  Kahn  Bar.  In  the  Kahn  Trussed  Bar  (Fig.  11)  the  attachment  of  the 
stirrups  to  the  tension-member  is  positively  secured.     The, bars  are  square  op 


Fig.  11.    The  Kahn  Bar 

pentagonal  in  cross-section  with  webs  rolled  on  them  at  two  diagonally  opposite 
edges.  The  stirrups  are  formed  by  shearing  these  webs  through  a  part  of  their 
length  and  turning  up  parts,  as  shown  in  the  cut.  These  stirrups  may  be  placed 
so  as  to  turn  up  in  pairs  or  so  as  to  alternate  on  opposite  sides  of  the  bar,  making 
the  spacing-  of  the  stirrups  closer  than  when  turned  up  in  pairs.  Another  advan- 
tage incidental  to  the  use  of  this  bar  is  that  the  greater  effective  cross-section  in 
the  steel  is  at  the  middle,  the  point  of  greatest  bending  moment  with  the  usual 
loading.  Two  disadvantages,  however,  are  the  separation  of  the  concrete  by 
the  wings  above  and  below  the  bar,  and  the  Hmitation  as  to  the  effective  stirrup- 
length  in  deep  beams.  This  bar  is  controlled  by  the  Truscon  Steel  Company, 
Youngstown,  Ohio. 

The  Kahn  Trussed  Bar  can  be  oljtained  in  the  sizes  shown  in  table  on  page 
922. 

Steel  in  Compression.  The  steel  reinforcement  in  reinforced  concrete  is 
used  in  certain  cases  to  assist  in  developing  compressive  strength  when  the 
concrete  is  not  sufficient  for  the  purpose,  as.  in  the  case  of  beams  and  girders  with 


922 


Reinforced-Concrete  Construction 


Chap.  24 


'                Size, 
in 

Weight  per  linear  foot, 
lb 

Area, 
sq  in 

Standard  length 

of  diagonals, 

in 

HXiH 

HX2H6 

^        1HX2M 

1HX2H 

1          2       X3K 

1.4 
2.7 
4.8 
6.8 
10.  2 

0.41 
0.79 
1. 41 
2.00 
3>oo 

12 

12-24 

12-24-36 

36 

36 

rods  placed  above  the  neutral  axis,  and  columns  with  rods  placed  vertically. 
The  use  of  the  steel  reinforcement  in  resisting  compression  will  be  treated  more 
at  length  in  Subdivision  3  of  this  chapter,  in  the  paragraph  Compression  Rods 
in  Beams  and  Girders,  page  941.  On  account  of  the  uncertainty,  however,  of 
the  steel  and  concrete  each  receiving  its  proportionate  share  of  the  load,  the  use 
of  steel  in  compression  should  be  avoided  as  much  as  possible. 

The  Position  of  the  Reinforcement.  The  importance  of  the  exact  posi- 
tion OF  THE  REINFORCEMENT  in  the  concrete  will  become  more  apparent  in  the 
discussion  of  the  design  of  beams.  A  slight  displacement  of  the  steel  will  ma- 
terially affect  the  strength.  If  the  steel  shifts  upward  the  beam  is  weakened,  if 
it  shifts  downward  the  protection  of  the  steel  against  rust  or  fire  is  reduced.  In 
the  so-called  unit  systems  the  reinforcements,  including  the  tension-rods  and 
stirrups,  are  so  tied  and  framed  together  that  after  being  placed  in  the  forms 
the  possibility  of  shifting  their  positions  with  respect  to  the  other  surfaces  of 
the  beam  or  to  one  another  is  practically  entirely  removed. 

The  Unit  System.  The.  particular  advantages  in  the  use  of  a  unit  system 
of  reinforcement  isj  as  already  indicated,  the  assurance  that  each  and  every  part 


Fig.  12.    The  Unit  System 

of  the  reinforcement  is  in  its  exact  relative  position,  and  maintains  that  position 
during  the  placing  of  the  concrete.  The  reinforcement  for  each  beam  or  girder 
is  as  carefully  laid  out  as  the  location  of  cover-plates,  stiffeners,  connection-angles, 
and  rivets  in  a  built-up  steel  girder.  It  can  consequently  be  thoroughly  in- 
spected and  checked  before  being  placed  in  position.  Being  marked,  its  exact 
location  is  easily  determined  by  the  foreman  on  the  job,  from  the  erection- 
plan.  After  it  is  put  in  place  a  quick  inspection  will  show  at  once  whether  it  is 
correctly  placed  or  not,  as  it  must  fit  and  extend  the  full  length  of  the  mold. 
Being  fabricated  off  the  job  there  is  less  interference  between  workmen.    The 


Materials  Used  in  Reinforced-Concrete  Construction  923 

fabrication  can  proceed  while  the  molds  are  being  made,  and  consequently 
greater  speed  in  erection  is  possible.  The  frames  are  readily  transported  and 
less  liable  to  get  mixed  than  loose  rods  sent  to  the  job. 

The  Unit  System  (Fig.  12)  is  the  pioneer  of  this  type  of  construction  and 
is  manufactured  by  the  American  System  of  Reinforcing,  Chicago,  111.  Its  par- 
ticular features  are  the  bending  up  of  some  of  the  longitudinal  reinforcements 
near  the  supports  and  the  use  of  round  U-shaped  stirrups,  wound  around  the  bars 
while  hot  and  allowed  to  shrink  into  place. 

The  Cummings  System  (Fig.  13)  is  manufactured  by  the  Electric  Welding 
Company,  Pittsburgh,  Pa.    The  particular  feature  of  this  system  is  the  forming 


As  fumiehed  and  shipped 
Fig.  13.    The  Cummings  System 


of  the  top  layer  cf  small  rods  into  rectangular  frames  which,  after  being  fastened 
to  the  lower  layer  at  suitable  points,  permit  the  bending  up  of  the  ends  to  act  as 
shear-members  or  stirrups,  thus  utilizing  for  shear  the  steel  that  is  not  required 
for  bending  moments. 

The  Luten  Truss.    The  Luten  Truss  (Fig.  14)  consists  of  longitudinal  rods 
with  alternate  members  bent  diagonally  upwards  across  the  beam  and  con- 


Fig.  14.     The  Luten  Truss 

tinning  along  the  upper  surface  to  the  end  of  the  beam.  Diagonal  members 
are  provided  through  all  the  region  of  diagonal  tension  in  both  ends  of  the  beam. 
This  frame  is  provided  with  a  clamp  and  wedge  that  locks  the  members  together. 
It  is  controlled  by  the  National  Concrete  Company,  Indianapolis,  Ind. 

The  Corr-Bar  Unit.    The  Corr-Bar  Unit,  Fig.  15,  made  by  the  Corrugated 
Bar  Company,  Inc.,  Buffalo,  N.  Y.,  is  provided  with  a  continuous  stirrup  of  both 


Fig.  15.     The  Corr-bar  Unit 


vertical  and  inclined  web-members  with  a  rigid  anchorage  at  both  top  and  bot- 
tom. In  tests  by  Professor  Talbot  on  this  type  of  reinforced  beam,  considerably 
higher  values  than  ordinary  were  obtained  in  vertical  shear. 


924 


Reinforccd-Concrete  Construction 


Chap.  24 


3.  Design  of  Reinforced-Concrete  Construction 

Girders,  Beams,  and  Slabs.  DifTerent  formulas  for  the  design  of  reinforccd- 
concrete  girders,  beams,  slabs,  etc.,  based  on  various  theoretical  considerations, 
have  been  devised  by  different  investigators.  The  formulas  here  given  have  been 
widely  accepted  and  are  offered  because  they  are  simple  in  form  and  give  satisfac- 
tory results.  If  anything,  they  err  on  the  side  of  safety;  and  furthermore,  they 
have  been  found  to  give  results  closely  in  accord  with  actual  tests.  They  are  used 
by  the  New  York  City  Building  Bureau,  and  are  accepted  by  other  authorities. 

Assumptions  in  the  Formulas.  The  formulas  are  based  on  the  following 
assumptions: 

(i)  The  BOND  between  the  concrete  and  steel  is  sufficient  to  make  the  two 
materials  act  together. 

(2)  A  PLANE  CROSS-SECTION  of  a  beam  before  bending  remains  a  plane  section 
after  bending,  and  the  stress  and  strain*  in  any  fiber  of  either  material  are 
directly  proportional  to  the  distance  of  that  fiber  from  the  neutral  axis  of  the 
cross-section. 

(3)  The  MODULUS  OF  ELASTICITY  of  the  concrete  in  compression  remains  con- 
stant within  the  assumed  working  stresses. 

(4)  The  TENSION AL  STRESS  is  taken  entirely  by  the  steel;  that  is,  the  tensile 
strength  of  the  concrete  is  not  considered. 

Fig.  IG  represents  a  longitudinal  section  and  a  cross-section  of  a  reinforced- 
^ncrete  beam  in  a  state  of  flexure  or  bending  under  a  load.     The  fibers  above 


ks-l 


Trace  of  Neutral  Surface 


„        d 


Fig.  16.     Sections  of  Reinforced-concretc  Beam 


the  NEUTRAL  SURFACE  of  the  beam  or  above  the  neutral  axis  of  the  cross-sec- 
tion are  in  compression  and  according  to  the  assumptions  the  stresses  vary  in 
direct  proportion  to  their  distances  from  the  neutral  surface  or  axis,  so  that  the 
total  area  of  compression  in  the  concrete,  representing  the  total  compressive 
STRESS,  may  be  graphically  indicated  by  the  shaded  triangle.  The  total  ten- 
SIONAL  STRESS  may  be  assumed  to  be  concentrated  at  the  center  of  gravity  of  the 
cross-section  of  the  steel  reinforcement.  One  of  the  conditions  of  static  equi- 
librium for  the  beam  is  that  the  algebraic  sum  of  all  the  horizontal  stresses  in 
the  cross-section  shall  be  zero;  that  is,  that  the  sum  of  all  the  compressive 
stresses,  or  the  resultant  compressive  stress  in  the  concrete,  must  equal  the  total 
or  resultant  tensional  stress  in  the  steel. 

Formulas  for  Reinforced-Concrete  Beams.  From  these  assumptions, 
based  upon  theot^etic  and  experimental  laws,  the  following  formulas  are 
derived,  in  which 

St  =  the  allowable  unit  tension  or  working  stress  in  the  steel  in  pounds  per 
square  inch; 

*  Deformation. 


Design  of  Reiiiforced-Concrete  Construction 


925 


Sc  =  the  allowable  unit  compression  or  working  stress  in  the  extreme  fibers 

of  the  concrete  in  pounds  per  square  inch; 
r  =  the  ratio  of  the  modulus  of  elasticity  of  the  steel  to  the  modulus  of 

elasticity  of  the  concrete; 
d  =  the  effective  depth  of  the  beam,  in  inches,  that  is  the  distance  from  the 
center  of  gravity  of  the  steel  reinforcement  to  the  extreme  fibers  in 
compression; 
X  =  the  ratio  of  the  depth  of  the  neutral  axis  from  the  extreme  fibers  in 
compression,  to  the  effective  depth  of  the  beam,  so  that 
xd  =  the  distance  of  the  neutral  axis,  in  inches,  from  the  extreme  fibers  in 
compression; 
b  =  the  width  of  the  beam; 

p  =  the  ratio  of  the  cross-section  of  the  steel  to  the  cross-section  of  the 
beam,  considering  the  beam  all  of  that  part  of  the  concrete  above 
the  center  of  gravity  of  the  steel; 
M  =  the  maximum  bending  moment  at  the  dangerous  section  of  th6  beam; 
Mr  =  the  moment  of  resistance  at  the  dangerous  sectiori  of  the  beam,  and 
must  of  course  be  equal  to  or  potentially  greater  than  the  maximum 
bending  moment;* 
K  =  a.  factor  used  for  simplification  of  the  formulas.    This  factor  is  con- 
stant for  any  given  steel  and  concrete; 
As=  sectional  area  of  the  steel  in  square  inches. 
For  beams  of  rectangular  cross-section 

M==Mr  =  Kbd2  (i) 


the  value  of  K  being  determined  by  the  formula 


K  =  St 


imPwiit'i'-d 


(2) 


which  formula  can  be  deduced  from  the  laws  of  flexure  of  beams  and  the 
assumptions  noted  above. 

In  the  use  of  this  formula  for  the  value  of  K  it  must  be  remembered  that  the 
ratio  of  St  to  Sc  for  any  given  ratio  of  steel  to  concrete,  p,  is  a  constant,  so  that 
corresponding  values  of  St  and  Sc  must  be  used.  This  ratio,  p,  often  spoken  of 
as  the  PERCENTAGE  OF  REINFORCEMENT,  is  the  expression  in  the  first  parenthesis 
of  the  second  member  of  Formula  (2) 


P=- 


(l)0-^£) 


(3) 


*  The  "moment  of  resistance"  or  the  "resisting  moment"  referred  to  any  cross-section 
of  a  beam  in  a  horizontal  position  and  in  a  state  of  flexure  under  a  load  or  loads  is  the 
algebraic  sum  of  the  moments  of  the  internal  horizontal  stresses  with  reference  to  a  point 
in  that  section;  and  the  "bending  moment"  for  that  section  is  the  algebraic  sum  of  the 
moments  of  all  the  external  vertical  forces  on  either  side  of  the  section  with  reference 
to  the  same  point  (the  forces  on  the  left  side  being  usually  taken).  The  resisting 
moments  increase  with  the  bending  moments  and  in  the  flexure  formula,  M^Sl/c  (see 
Chapters  IX  and  X),  they  are  made  equal  to  each  other,  M  being  the  bending  moment 
and  SI /c  the  resisting  moment.  In  the  following  formulas,  M  and  the  expression 
"bending  moment"  generally,  denote  the  maximum  bending  moment,  Mmax  is  often 
used  to  denote  the  latter. 


926  Reinforced-Concrete  Construction 

The  value  of  x  is  derived  from  the  expression 

x  =  rp\ 


•(s/^,-) 


Values  for  K  and  x  for  corresponding  values  of  p,  for  different  conditions 
fixed  by  the  building  authorities  of  different  cities,  are  given  in  Tables  V,  VI, 
VII  and  VIII. 

Table  V.    Values  for  Formulas  for  Reinforced  Concrete 

r  =  12 


p 

X 

K 

5, 

St 

K 

Sc 

St 

K 

Sc 

St 

0.004S 

0.279 

...... 

65.4 

516 

16  000 

0.0050 

0.291 

72.2 

550 

'* 

o.ooss 

0.303 

69.3 

507 

14  000 

79.2 

580 

" 

0.0058 

0.310 

73.0 

525 

" 

83.4 

600 

" 

0.0060 

0.314 

75.2 

535 

" 

86.0 

612 

" 

0.0065 

0.325 

81.2 

560 

" 

92.8 

640 

0.0070 

0.334 

74.7 

503 

12  000 

87.2 

587 

" 

96.5 

650 

15  510 

0.0075 

0.344 

79-5 

523 

" 

93.0 

610 

" 

99.0 

14900 

0.0080 

0.353 

84.7 

544 

" 

98.8 

635 

101.2 

14350 

0.00S5 

0.361 

89.9 

565 

" 

103.3 

650 

13800 

103.3 

13800 

0.0090 

0.369 

94.7 

584 

" 

105.1 

13350 

105.1 

13350 

0.0095 

0.377 

99-6 

60s 

107.0 

^^ 

12900 

107.0 

12  900 

O.OIOO 

0.384 

104.5 

625 

" 

108.8 

12500 

108.8 

12500 

0.0105 

0.392 

109.5 

643 

" 

no. 9 

12  130 

no. 9 

12  130 

O.OIIO 

0.399 

112. 4 

650 

II  790 

112. 4 

II  7QO 

112. 4 

11  790 

il     l\fU 

O.OII5 

0.405 

114. 0 

II  450 

114. 0 

11450 

114. 0 

11450 

0.0120 

0.412 

115-7 

'* 

II  160 

115. 7 

II  160 

115. 7 

II  160 

0.0125 

0.418 

117. 2 

" 

10900 

117. 2 

10900 

117. 2 

10860 

0.0130 

0.424 

118. 2 

" 

10600 

118. 2 

10  600 

118. 2 

10  600 

0.0135 

0.430 

119. 8 

" 

10350 

119.8 

10350 

119. 8 

10350 

0.0140 

0.436 

121. 2 

" 

10  120 

121.2 

10  100 

121. 2 

10  100 

0.0145 

0.441 

122.2 

" 

9890 

122.2 

9870 

122.2 

9870 

0.0150 

0.446 

123.2 

*' 

9660 

123.2 

9660 

123.2 

9660 

0.0155 

0.452 

124.8 

9460 

124.8 

9460 

124.8 

9460 

0.0160 

0.457 

126.0 

9270 

126.0 

9270 

126.0 

9270 

0.0165 

0.462 

127.0 

9  100 

127.0 

9  100 

127.0 

9  100 

0.0170 

0.467 

128.0 

" 

8930 

128.0 

8930 

128.0 

8930 

0.0175 
0.0180 

0.471 
0.475 

129. 1 
130. 1 

" 

8740 

129. 1 

8740 
8580 

129. 1 
130. I. 

8  740 
8580 

8580 

130. 1 

0.0185 

0.480 

131  0 

'\ 

8  440 

131. 0 

8440 

131. 0 

8440 

0.0190 

0.485 

132. 1 

" 

8300 

132.1 

8300 

132. 1 

8300 

0.0195 

0.489 

133  0 

" 

8  150 

133.0 

8  150 

133.0 

8  150 

o.oaoo 

0.493 

134.0 

8010 

134.0 

8010 

134.0 

8  010 

Design  of  Reinforced-Concrete  Construction 
Table  VI.     Values  for  Formulas  for  Reinforced  Concrete 


927 


p 

X 

K 

Sr. 

St 

K 

^"^c 

St 

K 

Sc 

St 

0.0025 

0.217 

51.0 

506 

22  000 

0.0030 

0.235 

55.3 

511 

20  000 

60.8 

S62 

0.0035 

0.251 

57.7 

503 

18  000 

64.2 

558 

70.6 

614 

" 

0.0040 

0.266 

65.7 

542 

" 

72.9 

602 

" 

78.7 

650 

21  610 

0.0045 

0.279 

73.5 

581 

" 

81.6 

645 

" 

82.3 

" 

20  150 

0.0050 

0.291 

81.3 

618 

85.4 

650 

18  910 

85.4 

" 

18910 

0.0055 

0.303 

88.5 

650 

17900 

88.5 

17  900 

88.5 

" 

17900 

0.0060 

0.314 

91-5 

" 

17  000 

91.5 

17000 

91. S 

17  000 

0.0065 

0.325 

94.2 

" 

16250 

94.2 

16250 

94.2 

" 

16250 

0.0070 

0.334 

96.5 

" 

15  510 

96.5 

15510 

96. 5 

" 

15510 

0.0075 

0.344 

99-0 

" 

14900 

99.0 

14900 

99.0 

14900 

0.0080 

0.353 

101.2 

" 

14  350 

101.2 

14350 

101.2 

" 

14350 

0.0085 

0.361 

103.3 

" 

13800 

103.3 

13800 

103.3 

" 

13800 

0.0090 

0.369 

105. 1 

" 

13325 

105. 1 

13325 

105.1 

" 

13325 

0.0095 

0.377 

107.0 

" 

12900 

107.0 

12  900 

107.0 

" 

12900 

O.OIOO 

0.384 

108.8 

" 

12  480 

108.8 

12480 

108.8 

12  480 

0.0105 

0.392 

no. 9 

•• 

12  130 

110.9 

12  130 

110.9 

" 

12  130 

O.OIIO 

0.399 

112. A 

II  790 

112.4 

II  790 

112.4 

11  790 

0.0II5 

0.405 

113. 9 

" 

II  450 

113. 9 

II  450 

113. 9 

" 

11  450 

0.0120 

0.412 

II5-6 

" 

II  160 

115.6 

II  160 

115. 6 

11  160 

0.0125 

0.418 

117. 2 

" 

10900 

117.2 

10900 

117.2 

" 

10900 

0.0130 

0.424 

118. 4 

" 

10  600 

118. 4 

10  600 

118. 4 

" 

10  600 

0.0135 

0.430 

120.0 

" 

10350 

120.0 

10350 

120.0 

" 

10350 

0.0140 

0.436 

121. 2 

" 

10  100 

121. 2 

10  100 

121. 2 

'* 

10  100 

0.0145 

0.441 

122.2 

" 

9870 

122.2 

9870 

122.2 

" 

9870 

0.0150 

0.446 

123.2 

" 

9660 

123.2 

9660 

123.2 

" 

9660 

0.0155 

0.452 

124.8 

" 

9460 

124.8 

9460 

124.8 

" 

9460 

0.0160 

0.457 

126.0 

9270 

126.0 

9270 

126.0 

" 

9270 

0.0165 

0.462 

127.0 

" 

9  100 

127.0 

9  100 

127.0 

" 

9  100 

0.0170 

0.467 

128.0 

" 

8930 

128.0 

8930 

128.0 

" 

8930 

0.0175 

0.471 

129. 1 

" 

8740 

129.1 

8  740 

129. 1 

" 

8740 

0.0180 

0.475 

130. 1 

" 

8580 

130. 1 

" 

8580 

130. 1 

" 

8580 

0.0185 

0.480 

131. 0 

" 

8440 

131  0 

8  440 

131  0 

" 

8440 

0.0190 

0.485 

132. 1 

" 

8300 

132. 1 

" 

8300 

132. 1 

" 

8300 

0.0195 

0.489 

133.0 

" 

8150 

133.0 

" 

8  150 

133.0 

" 

8150 

0.0200 

0.493 

134.0 

8  010 

134.0 

8010 

134.0 

8010 

928 


Reinforced-Concrete  Construction  Chap.  24 


Table  Vn.     Values  for  Formulas  for  Reinforced  Concrete 
r  =  IS 


p 

X 

K 

S, 

St 

K 

5, 

St 

K 

S„ 

St 

0.0050 

0.320 

71.6 

Soo 

16  000 

0.0055 

0.332 

78.3 

530 

*' 

0.0060 

0.344 

85.1 

558 

" 

0.0065 

0.35s 

80.2 

513 

14  000 

91-6 

586 

** 

0.0070 

0.36s 

86.1 

537 

" 

98.3 

614 

0.0075 

0.375 

92.0 

560 

" 

105. 1 

640 

*' 

0.0080 

0.384 

"8^.6     5 

00 

12  000 

97.6 

583 

" 

108.9 

650 

15600 

0.0085 

0.393 

88.6     5 

19 

103.3 

606 

III.O 

15040 

0.0090 

0.402 

93.5      5 

37 

" 

109.0 

627 

" 

113. 2 

14520 

0.0095 

0.410 

98.4      5 

56 

" 

114. 8 

648 

" 

115. 1 

14  020 

O.OIOO 

0.418 

103.3      5 

73 

" 

117. 1 

650 

13600 

117. 1 

13600 

0.0105 

0.425 

108.2      5 

93 

" 

118. 6 

" 

13  ISO 

118. 6 

13  ISO 

O.OIIO 

0.433 

113. I      6 

II 

" 

120.5 

12760 

120.5 

12760 

0.0II5 

0.440 

117. 9     6 

27 

<< 

122.0 

12420 

122.0 

12420 

0.0120 

0.446 

122.7     6 

47 

" 

123-4 

12080 

123-4 

12080 

O.OI2S 

0.453 

125.0     6 

50 

II  780 

125.0 

II  780 

125.0 

11-780 

0.0130 

0.459 

126.8 

II  480 

126.8 

II  480 

126.8 

II  480 

0.0135 

0.46s 

127.7 

II  200 

127.7 

II  200 

127-7 

II  200 

0.0140 

0.471 

128.9 

10  920 

128.9 

10920 

128.9 

10920 

0.0145 

0.477 

130.4 

10690 

130.4 

10  690 

130.4 

10690 

0.0150 

0.483 

131. 7 

10465 

131. 7 

•' 

10465 

131. 7 

10465 

0.0155 

0.488 

133.0 

10  240 

133.0 

10  240 

133 -0 

10240 

0.0160 

0.493 

133.9 

10  010 

133.9 

10  010 

133  9 

10  010 

0.0165 

0.498 

135.2 

9810 

135  2 

9810 

135.2 

9810 

0.0170 

0.503 

136  0 

■  9  620 

136.0 

9  620 

136.0 

9620 

0.0175 

0.508 

1372 

9  435 

137  2 

9  435 

137.2 

9  435 

0.0180 

0.513 

138.2 

9  260 

138  2 

9260 

138.2 

9260 

0.0185 

0.518 

139-4 

9  100 

139-4 

9  100 

139  4 

9  100 

0.0190 

0.522 

140.3 

8940 

140.3 

8940 

140.3 

8940 

0.0195 

0.527 

141. 1 

8790 

141. 1 

8790 

141. 1 

8790 

0.0200 

0.531 

142.0       ' 

8630 

142.0 

8630 

142.0 

8630 

Design  of  Reinforced-Concrete  Construction 


Table  VIII.     Values  for  Formulas  for  Reinforced  Concrete 

r  =■-  15 


p 

X 

K 

.S', 

•5, 

K 

S^ 

Se 

K 

^c 

St 

0.0030 

0.258 

60.3 

512 

22  000 

0.0035 

0.276 

'63.5 

507 

20  000 

69.9 

557 

" 

0.0040 

0.292 

72.3 

548 

79-5 

604 

" 

0.004s 

0.306 

72.7 

528 

18  000 

80.7 

587 

88.8 

646 

" 

0.0050 

0.320 

80.5 

563 

89.4 

626 

" 

92.9 

650 

20  800 

0.0055 

0.332 

88.1 

596 

" 

96.0 

650 

19  610 

96.0 

19  610 

0.0060 

0.344 

95.6 

628 

•* 

99.1 

18620 

99.1 

18620 

0.0065 

0.355 

101.8 

650 

17760 

101.8 

17  760 

101.8 

17760 

0.0070 

0.365 

104. 1 

16950 

104. 1 

16950 

104. 1 

16950 

0.0075 

0.375 

106.7 

16  250 

106.7 

16  250 

106.7 

16  250 

0.0080 

0.384 

108.9 

15600 

108.9 

15600. 

108.9 

15600 

0.0085 

0.393 

III.O 

15  040 

III.O 

15040 

III.O 

15040 

0.0090 

0.402 

113. 2 

14520 

113. 2 

14520 

113. 2 

14520 

0.0095 

0.410 

115. 1 

14  020 

115. 1 

14020 

115. 1 

14  020 

O.OIOO 

0.418 

117. I 

13600 

117. 1 

13600 

117. 1 

13600 

0.0105 

0.425 

118. 6 

13  150 

118. 6 

13  150 

118. 6 

13  150 

O.OIIO 

0.433 

120.5 

12  760 

120.5 

12760 

120.  s 

12  760 

0.0II5 

0.440 

122.0 

12  420 

122.0 

12420 

122.0 

12  420 

0.0120 

0.446 

123  4 

12080 

123.4 

12  080 

123.4 

12  080 

0.0125 

0.453 

125.0 

II  780 

125.0 

II  780 

125.0 

II  780 

0.0130 

0.459 

126.4 

II  480 

126.4 

II  480 

126.4 

II  480 

0.0135 

0.465 

127.7 

II  200 

127.7 

II  200 

127.7 

II  200 

0.0140 

0.471 

128.9 

10  920 

128.9 

10920 

128.9 

10  920 

0.0145 

0.477 

130.4 

10  690 

130.4 

( 

10690 

130  4 

10690 

0.0150 

0.483 

•131. 7 

10  465 

131. 7 

10465 

131  7 

10  465 

0.0155 

0.488 

133.0 

10240 

133.0 

10  240 

133  0 

10  240 

0.0160 

0.493 

133  9 

10  010 

133  9 

TO  010 

133  9 

10  010 

0.0165 

0.498 

135  0 

9810 

135  0 

9810 

135  0 

9810 

0.0170 

0.503 

136.0 

9  620 

136.0 

9620 

136.0 

9620 

0.0175 

0.508 

137.2 

9  435 

137.2 

9  435 

137.2 

9  435 

0.0180 

0.513 

138.2 

9  260 

138.2 

9  260 

138.2 

9260 

0.0185 

0.518 

139  4 

9  100 

139  4 

9  100 

139  4 

9  100 

0 .  0190 

0.522 

140. 1 

8940 

140. 1 

8940 

140. 1 

8940 

0.0195 

0.527 

141. 1 

8790 

141. 1 

8790 

141. 1 

8790 

0.0200 

0.531 

142  0 

8630 

142.0 

8630 

142.0 

8630 

930 


Reinforced-Concrete  Construction 


Cinder  Concrete.  Values  of  K  for  cinder  concrete  are  gix^en  in  Tables  IX 
and  X,  which  are,  however,  recommended  to  be  used  only  for  slabs.  Cinder 
concrete,  though  an  excellent  fireproofing  material,  lacks  strength  and  should 
be  used  as  a  structural  material  for  the  slabs,  only,  between  the  beams. 


Table  IX. 


Values  for  Formulas  for  Reinforced  Cinder  Concrete 
.      r  =  35 


p 

X 

K 

5o 

St 

K 

Sc 

St 

0.0005 

0.170 

7.5 

94 

16000 

7.5 

94 

16000 

o.ooio 

0.232 

14.8 

138 

" 

14.8     • 

138 

16  000 

0.0015 

0.276 

21.8 

174 

" 

18.8 

150 

13800 

0.0020 

0.3II 

28.7 

206 

20.9 

II  633 

0.0025 

0.340 

33.9 

225 

15300 

22.6 

10  200 

0.0030 

0.365 

36.1 

13688 

24.0 

9125 

0.0035 

0.387 

37.9 

" 

12439 

25.3 

8293 

0.0040 

0.407 

39-6 

" 

II  447 

26.4 

7631 

0.0045 

0.425 

41.0 

10625 

27.4 

7083 

0.0050 

0.442 

42.4 

" 

9  945 

28.3 

6630 

0.0055 

0.457 

43.6 

" 

9348 

29.1 

6232 

0.0060 

0.471 

44.7 

" 

8831 

29.8 

5  888 

0.0065 

0.484 

45.7 

" 

8377 

30.4 

5585 

0.0070 

0.497 

46.7 

" 

7988 

31. 1 

5325 

0.0075 

0.508 

47. 5 

" 

7620 

31.6 

5080 

0.0080 

0.519 

48.3 

'* 

7298 

32.2 

4866 

0.0085 

0.529 

49-0 

" 

7  001 

32.7 

4668 

0.0090 

0.539 

49-7 

" 

6738 

33  2 

4492 

0.009s 

0.548 

50.4 

" 

6489 

33.6 

4326 

O.OIOO 

0.557 

51.0 

" 

6266 

340 

4178 

o.oios 

0.56s 

51.6 

6054 

34-4 

4036 

O.OIIO 

0.573 

52.1 

" 

5860 

34.8 

3907 

0.0II5 

0.581 

52.7 

" 

5  684 

35.1 

^^ 

3789 

0.0120 

0.588 

53.2 

5513 

35.5 

3675 

O.OI2S 

0.59s 

53.7 

" 

5  355 

35.8 

3  570 

0.0130 

0.602 

54.1 

" 

5  210 

36.1 

3  473 

0.0135 

0.608 

54.5 

" 

S067 

36.4 

3378 

0.0140 

0.6IS 

55.0 

" 

4942 

36.7 

3295 

0.014s 

0.621 

55-4 

" 

4818 

36.9 

" 

3212 

0.0150 
0.0IS5 

0.626 
0.632 

55.7 
56.1 

" 

4695 

37.1 

3130 

" 

4587 

37.4 

3058 

0.0160 

0.637 

56.4. 

" 

4  479 

37.6 

2986 

0.016s 

0.643 

56.8 

" 

4384 

37.9 

2923 

0.0170 

0.648 

57.2 

" 

4288 

38.1 

2859 

0.0175 

0.652 

57-4 

4  191 

38.3 

2794 

0.0180 

0.657 

57.7 

4  106 

38.S 

2738 

0.0185 

0.662 

58.1 

" 

4026 

38.7 

2684 

0.0190 

0.666 

58.3 

3  943 

38.9 

2629 

0.019s 

0.671 

58.6 

3871 

39.1 

2  581 

0.0200 

0.67s 

58.9 

3  797 

39.2 

2531 

Design  of  Reinrorced-Concrete  Construction 


Table  X.     Values  for  Formulas  for  Reinforced  Cinder  Concrete 
r  =  30 


p 

X 

K 

So. 

6^ 

K 

s. 

s 

K 

6.62 

s. 

St 

0.0005 

0.159 

7.6 

100.6 

16  000 

7.6 

100.6 

16  000 

88 

14000 

O.OOIO 

0.216 

14.9 

148 

" 

14.9 

148 

13.0 

129.5 

o.oois 

0.259 

22.0 

185 

" 

22.0 

185 

" 

19.2 

162 

" 

0.0020 

0.292 

28.8 

219 

" 

28.8 

219 

" 

25.2 

192 

" 

0.0025 

0.319 

35  8 

251 

" 

35.6 

250 

15950 

28.5 

200 

12750 

0.0030 

0.344 

42.6 

279 

" 

38.1 

14300 

30.4 

'* 

II  480 

0.0035 

0.365 

48  .'i 

300 

15620 

40.1 

13030 

32.0 

10  420 

0.0040 

0.386 

50.4 

14480 

42.1 

12  060 

33.6 

9650 

0.0045 

0.402 

52.2 

" 

13400 

43.4 

II  170 

34.8 

8930 

0.0050 

0.418 

54.0 

" 

12540 

45.0 

10450 

36.0 

8360 

0.0055 

0.433 

55.6 

" 

II  810 

46.3 

9860 

370 

7870 

0.0060 

0.447 

57.0 

II  180 

47.5 

9320 

38.0 

7450 

0.0065 

0.460 

58.5 

" 

10  620 

48.7 

8850 

38.9 

7080 

0.0070 

0.472 

59-7 

" 

10  120 

49-7 

8440 

39-8 

6750 

0.0075 

0.483 

60.7 

9660 

50.6 

8  050 

40.5 

6  440 

0.0080 

0.494 

61.9 

" 

9270 

51.6 

7730 

41.3 

6  170 

0.0085 

0.504 

63.0 

" 

8900 

52.5 

7420 

42.0 

5  930 

0.0090 

0.514 

63.9 

". 

8560 

53.3 

7130 

42.6 

5710 

0.0095 

0.523 

64.9 

" 

8250 

54.1 

6870 

43.2 

5500 

O.OIOO 

0.532 

65.7 

7980 

54-7 

6650 

43.7 

5320 

0.0105 

0.540 

66.4 

" 

7710 

55.4 

6420 

44.3 

5  140 

O.OIIO 

0.547 

67.2 

7460 

55.9 

6  220 

44.7 

4970 

O.OII5 

0.555 

67.8 

" 

7240 

56.5 

6  040 

45-2 

4820 

0.0120 

0.562 

68.5 

7020 

57.1 

5850 

45.7 

4680 

0.0125 

0.569 

69.3 

6830 

57.7 

5680 

46.2 

4550 

0.0130 

0.576 

69.8 

" 

6650 

58.2 

5540 

46.5 

4430 

0.0135 

0.582 

70.4 

6460 

58.6 

5380 

46.8 

4310 

0.0140 

0.588 

71.0 

" 

6310 

59-2 

5  260 

47.3 

4  210 

0.0145 

0.594 

71.5 

" 

6  140 

59-5 

5  120 

47-6 

4090 

0.0150 

0.600 

72.0 

" 

6  000 

60.0 

5000 

48.0 

4  000 

0.0155 

0.606 

72.6 

*• 

5860 

60.5 

4880 

48.4 

3910 

0.0160 

0.612 

73.1 

" 

5730 

60.9 

4780 

48.7 

3820 

0.0165 

0.617 

73.6 

'• 

5610 

61.3 

4670 

490 

3740 

0.0170 

0.622 

74.0 

" 

5480 

61.7 

4570 

49-4 

3660 

0.0175 

0.627 

74.5 

" 

5370 

62.0 

4470 

49.6 

3580 

0.0180 

0.632 

74.9 

" 

5270 

62.4 

4390 

49-9 

3SIO 

0.0185 

0.636 

75.3 

" 

5  160 

62.7 

4300 

50.2 

3440 

0.0190 

0.641 

75.7 

" 

5  060 

63.1 

4  220 

50.4 

3370 

O.OT95 

0.645 

76.0 

" 

4960 

63.3 

4  130 

50.7 

3300 

0.020c 

0.649 

76.4 

4870 

63.6 

4060 

50.8 

3240 

Reinforced-Concrete  Beams  of  Rectangular  Cross-Section.  In  determin- 
ing the  SIZE  OF  BEAM  required  for  any  given  case,  r  and  the  limiting  values  of 
Sc  and  St  are  generally  given,  and  K  can  be  determined  for  any  ratio,  p,  of  con- 
crete to  steel.  The  value  of  M,  the  maximum  bending  moment,  that  is,  the 
bending  moment  at  the  dangerous  section  of  the  beam,  is  determined  from 
the  conditions  of  loading,  the  span  and  the  spacing;  and  the  width  and  depth 
of  the  beams  are  to  be  found.  Formula  (i)  may  then  be  put  in  the  more  con- 
venient form. 


d  = 


M_ 
Kb 


(5) 


932 


Reinforced-Concrete  Construction 


Chap.  24 


A  value  for  b  is  assumed  and  the  equation  solved  for  d.  Architectural  or 
structural  reasons  will  often  limit  the  width  or  depth  and  several  trials  may  hav^ 
to  be  made. 

Reinforced-Concrete  Slabs.  For  the  strength  of  slabs  the  same  formulas 
apply.  A  slab  may  be  treated  (i)  as  a  rectangular  beam  of  unusual  width; 
(2)  as  a  series  of  beams  set  one  alongside  the  other,  the  width  of  each  beam  being 
equal  to  the  spacing  of  the  reinforcing-rods,  and  one  rod  being  used  for  each 
beam;  or  (3)  as  a  series  of  beams  of  unit  width,  the  area  of  steel  for  each  beam 
being  the  area  of  reinforcement  per  unit  of  width. 

Check-Formulas.  It  may  sometimes  happen  that  it  is  advisable  to  check 
a  given  or  existing  beam-construction  as  to  strength  or  compliance  with  speci- 
fications for  working  stresses.  In  that  case  the  following  formulas  will  be 
convenient  (see,  also,  page  992): 


(6) 


(7) 


If  the  strength  of  the  beam  for  the  assumed  working  stresses  is  to  be  deter- 
mined, these  values  of  St  and  Sc  are  inserted  in  Formulas  (6)  and  (7),  and  the 
least  value  of  M  is  used.  If  the  values  of  M  resulting  from  these  equations  are 
not  equal,  the  full  benefit  of  one  of  the  materials  is  not  being  obtained.  If  the 
stresses  in  the  steel  or  concrete  due  to  a  given  loading  are  to  be  determined  the 
formulas  are  put  in  the  following  forms: 


St  = 


M 


(8) 


(9) 


These  formulas  apply  to  rectangular  beams  only.  M  in  Formulas  (8)  and 
(9)  is  the  maximum  moment  due  to  the  external  forces,  or  the  maximum  bend- 
ing moment.  The  value  of  x  can  be  determined  from  Tables  V  to  X.  In  For- 
mula (8)  it  will  be  noted  that  the  denominator  of  the  fraction  is  an  expression 
for  the  area  of  the  steel  multipUed  by  the  lever-arm  of  the  resisting  moment, 
that  is,  the  distance  from  the  center  of  gravity  of  the  steel  to  the  center  of  com- 
pression in  the  concrete.  Similarly,  in  Formula  (9),  the  denominator  of  the 
fraction  is  an  expression  for  the  area  of  the  concrete  in  compression  multiplied 
by  the  lever-arm,  x  again  being  determined  by  Formula  (4)  and  M  being  the 
maximum  bending  moment  due  to  the  external  forces. 

Reinforced-Concrete  T  Beams.  Where  beams  or  girders  are  used  in  rein- 
forced-concrete  building-construction  there  are  usually  accompanying  floor-slabs. 
If  these  slabs  are  cast  with  the  beams  or  girders  they  add  very  much  to  the 
strength  of  the  latter,  and  when  adequate  bond  and  shearing-resistance  are  pro- 
vided between  the  slab  and  the  stem  or  beam,  economical  design  requires  that 
the  slab  shall  be  considered  in  determining  the  strength  of  the  beam.  The  width 
of  slab  that  may  be  taken  as  part  of  the  beam  should  not  exceed  one  sixth  the 
span-length  of  the  beam,  and  the  overhanging  part  on  either  side  of  the  web 
or  stem  should  njt  exceed  six  times  the  thickness  of  the  slab.     In  any  case. 


Design  of  Reinforced-Concrete  Construction 


933 


the  flange  must  not  be  considered  wider  than  the  distance  between  the  beams. 
In  ordinary  floor- const  ruction  the  spacing  of  beams,  girders,  and  columns  is  gen- 
erally an  architectural  or  commercial  consideration.  Generally,  the  simplest  pro- 
cedure, therefore,  is  to  first  determine  the  thickness  of  slab  required  for  the  given 
spacing  of  beams,  and  this  determines  the  thickness  of  the  flange  of  the  T  beam. 
In  the  calculation  of  the  girder,  it  is  not  objectionable  to  use  the  same  slab,  or 
as  much  of  it  as  may  be  permissible,  that  has  been  used  in  the  consideration  of 
the  beam  framing  into  that  girder,  as  the  compression-stresses,  in  the  two  cases, 
act  at  right-angles  to,  and  practically  assist,  one  another.  When,  however,  the 
principal  slab-reinforcement  is  parallel  to  the  girder,  in  the  case  of  a  combined 
slag,  beam,  and  girder-construction,  the  slab-action  produces  compression  in  the 
same  direction  as  the  girder-compression  with  a  resulting  overstress  in  the  con- 
crete. In  this  case,  transverse  reinforcement  should  be  provided  at  right-angles 
to  the  girder  and  extending  well  into  the  slab. 

Formulas  for  Reinforced-Concrete  T  Beams.     Fig.  17  shows  a  cross^sec- 
tion  of  a  T  beam  resulting  from  the  use  of  the  slab  as  part  of  the  beam,  and 


I 


xl 


Fig.  17,     Cross-section  of  Reinforced-concrete  T  Beam 

shows  clearly,  also,  the  notation  used  in  the  formulas.     In  a  construction  of  this 
kind  three  cases  may  be  considered: 

Case  I.    The  neutral  axis  may  fall  below  the  flange,  in  which  case 


M^StA 


M-- 


?"('-f) 


(lo) 


(II) 


In  these  formulas  the  small  area  of  concrete  in  compression  below  the  flange 
is  neglected  and  the  center  of  compression  is  assumed  to  be  at  the  center  of 
the  flange.  This  is  done  to  simplify  the  formulas.  The  result  is  not  materially 
afl"ected  and  errs  on  the  side  of  safety.  The  position  of  the  neutral  axis  is  given 
by  Formula  (12) 


2rdAs+yt^ 
^~  2d{rAs-^b't) 
and  the  most  economical  percentage  of  steel  by  Formula  (13) 
_  Scb'i 
^  ~  2  Stbd 


(12) 


(13) 


M'^^StAsid--]  (14) 

and 


934  Reinforced-Concrete  Construction  Chap.  24 

Case  2.  The  neutral  axis  may  coincide  with  the  under  side  of  the  flange,  in 
which  case 

The  economical  value  of  p  in  this  case  is  the  same  as  in  Case  i,  Formula  (13). 

Cas^  3.  The  neutral  axis  may  fall  above  the  lower  edge  of  the  flange.  This 
case  is  the  same  as  Case  2,  since  for  purposes  of  calculation  all  the  concrete  in  the 
flange  below  the  neutral  axis  is  neglected  and  /  becomes  xd  in  this  case  as  in  the 
last. 

Alternate  Solution  for  Cases  2  and  3.  In  Cases  2  and  3  the  section  may 
also  be  considered  as  rectangular,  with  a  depth  d  and  a  width  b',  and  the  for- 
mulas for  rectangular  beams,  (i)  to  (9),  may  be  used.  Tables  V,  VI,  VII,  and 
VIII  are  also  applicable  in  these  two  cases. 

When  the  slab  is  considered  an  integral  part  of  the  beam,  adequate  bond 
and  shearing  resistance  between  the  slab  and  the  web  of  the  beam  must  be  pro- 
vided. The  concrete  is  ordinarily  adequate  to  take  the  vertical  shear  through 
the  flanges  next  to  the  stem,  and  is  further  strengthened  by  placing  horizontal 
steel  reinforcements  across  the  top  of  the  beam  or  girder,  as  described  above. 
Whether  or  not  the  resistance  to  shear  is  adequate  can  be  determined  by  the 
formula 

2tb' 

in  which  Ss  is  the  unit  vertical  shear  at  AB,  and  Sh  is  the  unit  horizontal  shear 
at  BC  (Fig.  17).  This  should  not  exceed  the  safe  unit  shear  for  concrete  unless 
Steel  reinforcement  is  provided.    The  .value  of  Sh  in  the  formula  is 

b{d-  HI) 
which,  it  will  be  noted,  is  the  total  vertical  shear  divided  by  the  effective  area 
of  the  stem. 

Moduli  of  Elasticity.  In  the  derivation  of  all  these  formulas  and  in  the 
determination  of  the  values  of  K,  the  ratio  of  the  modulus  of  elasticity  of 
the  steel  to  that  of  the  concrete  plays  an  important  part.  It  is  necessary  then 
to  know  what  values  to  use.  The  generally  accepted  modulus  of  elasticity  of 
steel  is  30  000  000  lb  per  sq  in.  The  modulus  of  elasticity  of  concrete  varies 
with  many  conditions.  Even  in  the  same  mixture,  the  character  of  the  materials, 
as  well  as  the  manner  of  mixing  and  placing,  affect  it.  The  modulus  increases 
with  the  age  of  the  concrete.  It  also  increases  with  the  richness  of  the  mix- 
ture. It  seems  to  decrease  with  an  increase  in  the  load  on  the  concrete.  It 
should  also  be  noted  that  the  modulus  of  elasticity  as  determined  from  a  beam 
in  flexure  is  greater  than  that  determined  from  compression- cylinders.  More- 
over the  modulus  of  elasticity  as  determined  from  compression  varies  with  the 
point  selected  on  the  stress-strain  cuive.  The  different  values  for  the  ratio  of 
THE  MODULUS  OF  ELASTICITY  of  the  stcel  to  the  modulus  of  elasticity  of  the  con- 
crete to  be  used  in  the  design  of  reinforced-concrete  construction,  as  fixed  by  the 
building  regulations  of  various  cities  and  by  other  authorities,  is  given  in  Table 
II,  page  912.     Values  for  the  modulus  of  elasticity  of  concrete  under  different 


Design  of  Reinforced-Concrete  Construction 


935 


loads  and  for  different  mixtures  determined  by  actual  tests  at  the  Watertown 
Arsenal  are  given  in  Table  XL 

Table  XI.     Elastic  Properties  of  Broken-Stone  Concrete  Twelve-Inch  Cubes 


Composition 


Cement 


Sand 


Broken 

stone 


4 
4 
4 
4 
6 
6 
6 
6 

12 


Age 


7  days 
I  mo 
3  mos 

6  mos 

7  days 
I  mo 

3  mos 
6  mos 
I  mo 
3  mos 
6  mos 


Modulus  of  elasticity  in 

pounds  per  square  inch 

between  loads  of 


100  and 

6oo 
lb  per 
sq  in 


2  593  ooo 

2  662  000 

3  671  000 
3  646  000 

1  869  000 

2  438  000 

2  976  000 

3  608  000 
I  376  000 
I  642  000 
I  820  000 


600  and 
I  000 

lb  per 
sq  in 


2  054  000 

2  445  000 

3  170  000 
3567000 

1  530000 

2  135  000 
2  656  000 
3503000 

I  364  000 
I  522000 


000  and 
2  000 
lb  per 
sq  in 


:  351  000 
:  462  000 
!  158  000 
i  582  000 

:  219  000 
:  805  000 
[  868000 


Tests  made  by 


*  Geo.  A.  Kimball. 


*  Tests  of  metals,  U.  S.  A.,  1899,  page  741. 

Working  Stresses.  The  working  stresses  for  concrete  and  steel  allowed 
by  various  cities  are  given  in  Table  II  on  page  912.  In  the  determination  of 
K  the  values  of  Sc,  St,  and  r  as  taken  from  Table  II  are  substituted  in  Formula 
(2),  or,  the  value  of  K  may  be  taken  directly  from  Tables  V  to  VIII,  pages  926 
to  929  and  substituted  in  Formula  (5).  For  M  in  that  formula,  the  maximum 
BENDING  MOMENT  duc  to  the  external  forces  is  used. 

Bending  Moments  in  Beams.  Beams  and  girders  are  usually  considered 
as  SIMPLE  BEAMS,  that  is,  as  beams  supported  at  both  ends,  but  not  built  in. 


Fig.  18.    Reinforcement  for  Uniformly  Distributed  or  Symmetrically  Placed  Load 


Fig.  19.     Reinforcement  for  Unsymmetrically  Placed  Concentrated  Load 

restrained,  or  continuous,  although  in  many  instances  they  are  actually  carried, 
a^  CONTINUOUS  BEAMS,  over  the  supports.     If  continued  over  a  support,  there 


936  Reinforced-Concrete  Construction  Chap.  24 

is  a  NEGATIVE  BENDING  MOMENT  at  that  support,  and  this  negative  bending  mo- 
ment should  be  taken  care  of  ])y  reinforcements  in  the  upper  part  of  the  beam. 
This  bending  moment  is  one  half  that  at  the  middle  of  a  simple  supported  beam 
loaded  at  the  middle,  and  two  thirds  that  at  the  middle  of  a  simple  supported 
beam,  uniformly  loaded.  In  the  case  of  simple  supported  beams  loaded  either 
at  the  middle  or  with  a  uniformly  distributed  load,  the  bending  moments  de- 
crease toward  the  supports.  For  these  reasons  it  is  advisable  in  arranging  the 
steel  to  be  used  for  the  tensional  reinforcement,  to  select  the  bars  or  rods  in 
pairs,  so  that,  as  the  supports  are  approached,  a  part  of  the  reinforcement  may 
be  turned  up  toward  the  top  and  carried  across  the  supports  near  the  top  as  in- 
dicated in  Figs.  18  and  19.  For  continuous  beams  and  slabs  with  um'formly 
distributed  loads,  the  following  are  recommended  for  maximum  positive  and 

MAXIMUM  NEGATIVE  BENDING  MOMENTS  I 

"For  beams,  the  bending  moment  at  middle  and  at  support  for  interior 
spans,  should  be  taken  equal  to  wl'/ii,  and  for  end  spans  it  should  be  taken 
equal  to  wl^/io  for  middle  and  interior  support,  for  both  dead  and  live  loads. 

"In  the  case  of  beams  and  slabs  continuous  for  two  spans  only,  with  their  ends 
restrained,  the  bending  moment  both  at  the  middle  support  and  over  the  middle 
of  the  span  should  be  taken  equal  to  ie;/Vio-"* 

Beams  simply  supported  at  the  ends  must  be  considered  as  simple  beams 
with  maximum  positive  bending  moments  equal  to  wl^/Z.  In  all  the  above 
values,  w  is  the  load  per  linear  unit  and  /  the  span  in  the  same  unit. 

Bending  Moments  in  Slabs.  As  floor-slabs  are  usually  carried  continuously 
across  the  supports,  the  maximum  bending  moment  due  to  a  uniformly  distrib- 
uted load  is  assumed  to  be  less  than  in  beams  simply  supported  at  the  ends. 
The  New  York  City  Regulations  provide  that  "the  bending  moments  at  the 
center  and  at  intermediate  supports  of  floor-slabs  continuous  over  two  or  more 
supports  shall  be  taken  as  T'F//i2."  The  same  regulations  provide  that  "the  bend- 
ing moments  of  slabs  that  are  reinforced  in  both  directions  and  supported  on 
four  sides  and  fully  reinforced  over  the  supports  (the  reinforcement  passing  into 
the  adjoining  slabs)  may  be  taken  as  Wl/F  for  loads  in  each  direction,  in  which 
F=8  when  the  slab  is  not  continuous  or  when  continuous  over  one  support, 
and  F  =  i2  at  both- center  and  supports  when  the  slab  is  continuous  over  both 
supports."  In  these  expressions  W  is  the  total  distributed  load  and  /  the  span. 
In  square  slabs  with  two-way  reinforcement  it  is  usually  assumed  that  the  load- 
ing is  uniformly  distributed  and  that  half  the  load  is  carried  by  each  system.  In 
rectangular  slabs  the  amount  of  load  carried  by  each  system  of  reinforcement  is 
given  by  the  formula 

r= (i8) 

2   n 

in  which  r  is  the  proportion  of  load  carried  by  the  transverse  reinforcement, 
W  the  total  load  on  the  slab,  and  n  the  ratio  of  its  longer  to  its  shorter  side. 
Using  this  proportion  of  load,  each  set  of  reinforcements  is  calculated  as  a  slab 
with  supports  on  two  sides  only,  and  the  total  number  of  rods  required  is  de- 
termined on  the  assumption  of  equal  spacing.  The  rods  may  then  be  spaced 
uniformly  at  the  usual  spacing  for  the  central  half  of  the  slab  and  gradually  re- 
duced in  number  per  foot  of  width  to  the  edge  of  the  slab,  using  one  half  as 
many  rods  for  the  remaining  two  quarters.  In  this  way,  the  amount  of  reinforce- 
ment is  reduced  25%.  When  the  length  of  the  slab  exceeds  the  breadth  by  50%, 
the  stresses  in  the  longitudinal  steel  become  so  low  that  the  construction  is 

*  Trans.  Am.  Soc.  C.  E.,  1917,  page  1127. 


Design  of  Reinforccd-Concrete  Construction  937 

uneconomical.  The  slab  should  then  be  treated  as  one  with  a  one-way  reinforce- 
ment. 

Shrinkage-Stresses  and  Temperature-Stresses.  In  slabs  resting  on  or 
carried  over  two  support's  some  reinforcement  should  be  provided  at  right- 
angles  to  the  tension-rods  to  provide  against  shrinkage-stresses  and  tem- 
perature-stresses. Incidentally,  this  reinforcement  may  also  serve  to  keep 
the  tension-rods  properly  spaced.  In  general  it  should  not  be  less  than  one 
third  of  one  per  cent  in  amount  and  well  distributed.  It  is  common  practice 
to  use  from  J^  to  ^-in  rods,  spaced  about  2  ft  apart.  Deformed  bars  with  irregu- 
lar surfaces  and  reinforcements  of  small  diameters,  placed  as  close  as  practi- 
cable to  the  surface,  are  most  effective. 

The  Disposition  of  the  Steel.  In  designing  the  reinforcement  for  any 
form  of  loading,  the  full  sectional  area  required  must  be  provided  at  the  point 
of  MAXIMUM  bending  MOMENT.  As  the  supports  are  approached,  part  of  the 
reinforcement,  as  already  indicated,  is  turned  up,  but  care  must  be  taken  to  keep 
it  so  distributed  that  at  any  point  there  is  still  sufficient  reinforcement  below 
the  neutral  axis  to  furnish  the  necessary  tensional  resistance.  The  arrangement 
of  reinforcement  for  a  uniformly  distributed  or  symmetrically  disposed  load  is 
shown  in  Fig.  18,  and  for^an  unsymmetrically  placed  concentrated  load,  in  Fig.  19. 
In  the  first  instance  the  maximum  bending  moment  is  at  the  middle  of  the 
beam,  the  reinforcement  is  symmetrical  about  that  point,  and  as  much  as  one 
half  the  amount  of  reinforcement  may  be  turned  up.  In  the  second  instance 
the  maximum  bending  moment  is  at  some  other  point  than  the  middle,  the  rein- 
forcement must  be  so  disposed  that  the  full  amount  required  will  be  under  the 
load  or  at  the  point  of  maximum  bending  moment,  and  the  turning  up  must 
be  done  between  that  point  and  the  support.  Other  conditions  might  require 
less  than  half  the  reinforcement  to  be  turned  up.  There  is  another  reason  for 
turning  up  the  reinforcements  toward  the  ends.  In  addition  to  the  resistance 
to  the  NEGATIVE  BENDING  MOMENT,  there  is  a  resistance  to  the  shear  offered 
by  the  metal  running  through  the  concrete  at  the  points  where  the  diagonal 

TENSION  occurs. 

The  Percentage  of  Reinforcement.  The  amount  of  the  reinforcement 
in  any  case  is  determined  by  Formulas  (3)  and  (13)  for  rectangular  and  T  beams 
respectively.  The  values  obtained  by  these  formulas  give  the  most  econom- 
ical amount.  This  may  vary  from  1,4%  to  iH%  of  the  cross-section  area  of 
concrete,  but  will  usually  run  about  ^io%-  The  nearest  stock  size  of  rods 
giving  this  amount  or  a  slightly  greater  amount  can  be  selected  from  the  table 
given  on  page  15 14,  or  from  the  catalogues  of  the  manufacturers  of  the  various 
deformed  bars.*  The  number  of  rods  used  to  make  up  the  necessary 
sectional  area  must  be  determined  by  considerations  mentioned  in  the  follow- 
ing paragraphs. 

The  Number  of  Reinforcing-Rods.  As  already  suggested,  an  even  number 
adapts  itself  better  to  a  symmetrical  or  balanced  arrangement  both  in  cross-sec- 
tion and  horizontal  section.  One  rod  does  not  permit  of  the  turning  up  toward  the 
support.  Two  rods  may  be  made  either  to  continue  along  the  lower  edge  of  the 
beam,  or  one  may  start  at  one  support,  run  along  the  lower  part  and  turn  up  be- 
yond the  middle  as  it  approaches  the  second  support;  and  the  second  rod  run 
similarly  along  the  bottom  from  the  second  support  and  turn  up  after  passing  the 
middle  as  it  approaches  the  first  support.  Three  rods  may  be  arranged  so  that 
two  continue  along  the  bottom  and  the  third,  the  middle  one,  turns  up  as  it  ap- 
proaches the  supports.     The  arrangement  for  4,  5,  or  6  rods  will  naturally  suggest 

*  See,  also,  paragraph  on  Commercial  Sizes,  page  915. 


938  Reinforced-Concrete  Construction  Chap.  24 

itself  from  what  "has  been  ah-eady  said.  Too  large  a  number  of  rods  is  not  de- 
sirable, as  a  large  number  of  them  together  acts  more  or  less  as  a  screen  for  the 
coarser  particles  of  the  concrete  and  prevents  a  close  contact  between  it  and  the 
steel.  This  matter  of  complicated  reinforcement  is  one  of  considerable  practical 
importance.  If,  however,  the  steel  is  satisfactorily  incased  with  concrete,  a 
larger  number  of  small  rods  is  preferable  to  a  small  number  of  larger  ones. 
The  AREA  OF  CONTACT  of  a  rod  of  smaller  size  is  proportionately  greater  than 
that  of  a  rod  of  larger  size,  as  the  perimeter  varies  directly  as  the  diameter,  and 
the  sectional  area  as  the  square  of  diameter  of  the  cross-section.  In  order  that 
a  rod  may  not  slip,  the  adhesion  of  the  steel  to  the  concrete  must  be  equal  to 
or  greater  than  the  tension  in  the  steel. 

The  Adhesion  Required.  The  tension  in  a  reinforcing-rod  at  any  point 
having  been  determined  from  the  given  formulas,  it  must  next  be  determined 
if,  in  either  direction  from  that  point,  the  area  of  contact  of  the  steel  is 
large  enough  tc  make  the  total  adhesion  equal  to  or  greater  than  the  tension. 
If  there  is  a  deficiency  in  this  respect  it  must  be  made  up  either  by  a  mechani- 
cal bond  or  by  anchoring  the  reinforcements  at  the  ends.  Safe  values  for 
adhesion  of  concrete  and  steel  are  given  in  Table  II,  page  912.  A  safe  rule 
to  apply,  without  calculation,  to  the  case  of  beams  with  a  maximum  bending 
moment  at  the  middle,  is  to  make  the  diameter  of  the  rods  not  more  than  one 
two-hundredth  of  the  span.  Under  ordinary  conditions,  generally  speaking,  the 
length  of  rod  on  either  side  of  the  point  of  maximum  bending  moment  should  be 
at  least  eighty  diameters  for  plain  rods,  and  not  less  than  fifty  diameters  for 
deformed  bars.  Under  unusual  conditions  the  adhesion  should  be  carefully 
studied.  The  apparent  discrepancy  between  the  first  and  second  statements  of 
this  paragraph  is  explained  by  an  allowance  made  and  based  upon  the  fact  that 
the  tension  in  the  steel  does  not  decrease  uniformly  with  the  decrease  in  dis- 
tance from  the  supports.  The  allowance  is  purely  arbitrary  but  is  considered 
safe.  For  cases  of  unsymmetrically  loaded  beams  it  is  best  to  examine  care- 
fully into  the  conditions. 

The  Separation  of  the  Rods.  It  has  not  been  unusual  in  tests  on  beams 
to  have  the  concrete  split  off  from  the  under  side  along  the  line  of  the  reinforce- 
ment. This  is  due  in  part,  if  not  entirely,  to  an  insufficiency  of  concrete  between 
and  around  the  reinforcement.  To  avoid  this  the  spacing  or  separation  of 
the  reinforcing-rods  in  the  cross-sections  of  the  beams  must  be  such  that  the 
resistance  of  the  concrete  to  shear  at  the  level  of  the  rods  is  at  least  equal  to 
the  ADHESION  of  the  concrete  to  the  steel.  As  a  general  rule  the  rods  should  be 
spaced  not  less  than  two-and-one-half  diameters  on  centers  and  about  two  di- 
ameters from  the  sides  of  beams.  The  clear  distance  between  rods  and  the  space 
between  rods  and  edges  of  beams  should  in  no  case  be  less  than  iH  in.  De- 
formed bars,  if  stressed  to  their  full  tensional  value,  should  be  spaced  farther 
apart,  than  plain  bars.  At  the  middle  of  a  beam,  the  bond-stress  is  low,  but  at 
the  top  of  a  continuous  beam,  over  the  supports,  where  the  negative  moment  de- 
creases rapidly,  the  bond-stress  is  apt  to  be  excessive  and  frequently  limits  the 
diameter  of  the  reinforcement. 

Provisions  against  Shear  or  Diagonal  Tension.  Numerous  tests  of  beams 
reinforced  with  horizontal  rods  without  stirrups  or  inchned  reinforcement  have 
shown  that  diagonal  cracks  occur  when  the  maximum  shear  over  the  cross- 
section  is  from  100  to  200  lb  per  sq  in.  Tests  conducted  on  concrete  with  the 
purpose  of  eliminating  all  other  stresses  but  direct  shear  have  given  a  shearing 
strength  of  concrete  of  from  800  to  i  600  lb  per  sq  in.  The  ordinary  concrete 
beam  has,  therefore,  a  cross-section  of  sufficient  area  to  withstand  a  shearing- 
STRESS  of  200  lb  per  sq  in.     The  cracks  always  occur  at  points  where  a  large 


Design  of  Reinforccd-Concretc  Construction  939 

SHEARING -STRESS  exists  in  combination  with  moment-stresses.  Under  con- 
centrated loads,  diagonal-tension  failure  occurs  under  the  concentration, 
and  in  a  simple  beam  under  a  uniformly  distributed  load,  the  cracks  appear 
near  the  supports.  The  inclination  of  the  diagonal  tension  in  the  concrete  being 
a  resultant  of  two-forces,  changes,  therefore,  with  the  variations  of  shear  and 

TENSION. 

For  beams  with  horizontal  rods  only,  that  is,  beams  in  which  the  wer-stresses 
are  resisted  by  the  concrete,  the  safe  shearing  values  to  be  used  under  various 
building  regulations  are  given  in  Table  II,  page  912.  The  shearing-stress  in 
this  case  is  determined  by  dividing  the  total  vertical  shear  by  the  product  of 
the  effective  depth,  that  is,  the  distance  from  the  center  of  compression  to  the 
center  of  the  steel,  by  the  width  of  the  beam.  The  maximum  shearing-stress 
shouid,  in  this  case,  not  exceed  2%  of  the  compressive  strength  of  the 
concrete.  When  the  resistance  of  the  concrete  to  shear  is  not  sufficient,  web- 
reinforcement  must  be  provided  by  one  of  the  following  methods  or  by  a  com- 
bination of  them: 

(i)  By  attaching  to  or  looping  around  the  horizontal  members,  stirrups  or 
vertical  members; 

(2)  By  securely  attaching  inclined  rods  to  the  horizontals  in  such  manner  as 

to  prevent  slipping;  • 

(3)  By  bending  of  a  part  of  the  longitudinal  reinforcement  at  certain  points, 

thus  providing  against  the  diagonal  tension  and  allowing  a  sufficient 
amount  of  horizontal  steel  to  remain  to  resist  the  direct  tension. 

It  is  customary  to  use  the  calculated  vertical  shearing-stress  as  a  measure 
of  the  diagonal  tensile  or  web-stresses.  In  all  cases,  the  concrete  may  be 
assumed  to  carry  its  safe  load,  and  it  is  ordinarily  assumed  that  two  thirds  of 
the  external  vertical  shear  is  resisted  by  the  web-reinforcement.  For  beams 
reinforced  with  web-members,  the  total  vertical  external  shear  over  the  ef- 
fective section  should  not  exceed  6%  of  the  compressive  strength  of  the  con- 
crete. The  Building  Code  of  New  York  City  specifies  that  the  shearing-stress 
in  concrete,  when  all  the  diagonal  tension  is  resisted  by  steel,  shall  not  exceed 
150  lb  per  sq  in.  For  beams  in  which  part  of  the  longitudinal  reinforcement  is 
in  the  form  of  bent-up  rods,  the  maximum  vertical  shearing-stress  should 
not  exceed  3%  of  the  compressive  strength  of  the  concrete. 

The  stresses  in  web-reinforcements  may  be  determined  by  the  following 
formulas: 

for  stirrups  P  =  Vs/l  (i^) 

for  members  inclined  45°,  not  bent-up  bars, 

P  =  0.7  Vs/l  (20) 

in  which  s  is  the  horizontal  spacing  of  the  web-members,  V  the  total  external 
vertical  shear,  /  the  eflective  depth  from  center  of  compression  to  center  of  steel 
and  P  the  stress  in  a  single  reinforcing-member.  Fixing  the  allowable  tensile 
stress  at  16  000  lb  per  sq  in,  the  spacing  of  web-members  is  expressed  by  the 
following  formulas,  when  A  is  the  cross-section  of  a  web-member: 

s  =16  000  Al/V  (^^) 

and 

s  =  i6ooo  AI/0.7V  (22) 

In  determining  the  length  of  horizontals  necessary  to  pr(^rly  care  for  the 
bending  stresses,  the  same  method  may  be  employed  as  for  plate  girders,  the 


940  Reinforccd-Concrcte  Construction  Chap.  24 

remainder  of  the  bar  being  carried  up  as  an  incHned  member  and  carried  over 
the  top  of  the  supports  in  continuous  beams.  The  rods  remaining  at  any  ix)int 
at  the  bottom  or  top  must  be  of  sufficient  sectional  area  to  carry  the  direct  tension 
beyond  this  point.  There  must  also  be  a  sufficient  length  beyond  this  point  to 
prevent  slipping.  Web-members  must  be  so  spaced  that  therfe  will  be  a  reinforce- 
ment intersecting  every  45°  line  of  rupture  below  the  neutral  axis.  The  New 
York  City  Code  prescribes  that  the  spacing  of  the  web-members  should  not 
exceed  three  fourths  of  the  depth  of  the  beam  in  that  portion  where  the  web- 
stresses  exceed  the  allowable  value  for  shear  in  concrete.  Sufficient  bond- 
strength  of  web-reinforcement  should  always  be  provided  in  the  coivrPRESSiON- 
siDE  of  the  beam.  In  simple  beams,  that  is,  beams  resting  on  two  supports,  the 
ends  of  the  bars  should  preferably  be  bent  into  hooks.  Where  bent  up  through 
large  angles,  web-members  should  extend  horizontally  along  the  upper  part  of  a 
beam  for  some  distance. 

Attached  Shear-Members.  Stirrups  need  not  be  firmly  attached  to  the  ten- 
sional  reinforcement;  but  the  allowable  bond-stresses  and  shearing-stresses 
in  the  concrete  must  not  be  exceeded  in  transmitting  the  stresses  between  stirrups 
and  longitudinal  rods.  The  stirrups  and  inclined  members  must  also  develop 
sufficient  bond-stresses  to  transmit  the  entire  stresses  for  which  they  are  de- 
signed, and  they  must  sometifiies  be  supplemented  with  anchorages  in  the  com- 
pression-side of  the  beam.  It  is,  perhaps,  better  to  have  them  attached,  as 
they  will  certainly  assist  in  anchoring  the  tensional  reinforcement.  Different 
forms  of  stirrups  and  methods  of  attachment  are  used.  In  the  Kahn  system 
(Fig.  11)  the  stirrups  form  a  part  of  the  tensional  reinforcement.  The  U  form, 
either  upright  or  inverted,  is  a  very  common  form  of  stirrup,  and  may  be  a  rod 
of  either  round  or  square  cross-section,  or  a  flat  strap  as  shown  in  Figs.  10  and  13. 
The  Hennebique  system  employs  both  inclined  rods  and  vertical  stirrups.  In 
some  cases,  when  the  slabs  and  beams  are  constructed  together,  the  slab-rein- 
forcement is  carried  through  the  upper  ends  of  the  stirrups. 

The  Bond  between  Steel  and  Concrete.  The  bond  between  the  steel  in 
tension  and  the  concrete  must  not  exceed  the  safe  working  value.  If  the  bond 
is  not  sufficient,  the  rod  will  slip.  Tension-rods  must,  therefore,  never  be  too 
large  to  develop  sufficient  bond-strength  to  transmit  the  stresses.  Where 
bent-up  bars  are  employed,  the  bond-stresses  in  places,  in  both  the  straight 
and  bent  bars,  will  be  higher  than  if  all  bars  are  straight.  In  cantilever  beams, 
the  ends  of  the  bars  at  the  supports  are  fully  stressed  and  the  bars  must  be 
carried  into  the  supports  and  anchored  to  develop  this  stress.  In  anchoring 
bars,  an  additional  length  must  always  be  provided  above  that  required,  on  the 
Assumption  of  uniform  bond-stresses.  Wherever  possible,  adequate  bond- 
strength  should  be  provided  throughout  the  length  of  the  bar  in  preference  to 
end-anchorage.  Between  plain  bars  and  concrete  the  bond-strength  may  be 
assumed  to  be  4%  of  the  compressive  strength  of  the  concrete. 

The  Breadth  of  a  Reinforced-Concrete  Beam  of  Rectangular  Cross- 
Section.  The  breadth  of  a  rectangular  beam,  and  of  the  stem  of  a  T  beam, 
as  already  indicated,  is  generally  dependent  upon  the  amount  of  reinforcement 
necessary,  and  it  is  equal  to  the  sum  of  the  diameters  of  the  tension-rods,  the 
required  spaces  between  them,  and  the  amount  of  concrete  outside  of  the  rods 
needed  to  resist  the  shearing-stresses  and  to  protect  the  steel.  When  no  stirrups 
are  used  in  a  beam  it  is  necessary,  also,  to  make  the  width  of  the  concrete  suffi- 
cient to  resist  the  horizontal  shearing-stresses.  This  width  should  be  at  least 
equal  to  the  sum  of  the  perimeters  of  the  tensional  reinforcing-rods.  The 
amount  of  concrete  to  be  provided  below  the  steel  is  fixed  by  the  requirements 
for  proper  protection  of  the  steel  against  fire  and  corrosion.     (Pages  955-962.) 


Design  of  Reinforced-Concrete  Construction  941 

Compression-Rods  in  Beams  and  Girders.  Steel  reinforcement  in  the 
form  of  rods  is  sometimes  provided  above  the  neutral  axis  in  beams  and 
girders  for  the  purpose  of  providing  additional  compressive  strength  where 
there  is  not  sufficient  concrete  above  the  neutral  axis  to  resist  the  total  com- 
pression. If  steel  reinforcement  is  to  be  used  for  this  purpose,  the  steel  should 
be  placed  as  high  as  possible,  and  the  allowable  unit  compression  in  the  steel 
limited  to  the  actual  compression  in  the  concrete  at  that  point  multiplied  by 
the  ratio  of  the  modulus  of  elasticity  of  the  steel  to  that  of  the  concrete,  as  in 
the  case  of  columns  with  vertical  reinforcement.  The  use  of  steel  in  com- 
pression in  beams  and  girders,  however,  is  not  recommended,  since  at  best  it 
is  very  uneconomical  and  the  steel  has  a  tendency  to  buckle  and  disrupt  the 
concrete. 

Reinforced-Concrete  Columns.  Reinforced-concrete  columns  are  of  three 
general  types:  (i)  concrete  with  vertical  reinforcement  near  the  outer 
surfaces;  (2)  concrete  wrapped  with  spirally-wound  wire  or  with  metal 
bands;  (3)  concrete  with  a  metal  core. 

Lengths  of  Columns.  The  lengths  of  reinforced-concrete  columns  are  vari- 
ously Hmited  by  different  authorities  as  follows,  the  figures  being  in  each  case 
the  ratio  of  the  length  to  the  least  lateral  dimension: 

New  York 15 

Chicago 12 

Philadelphia 15 

St.  Louis IS 

Cleveland 15 

Baltimore 16 

San  Francisco 15 

Buffalo 15 

Detroit 15 

New  York  limits,  also,  the  least  side  or  diameter  to  12  in,  and  San  Francisco 
to  10  in.  , 

Vertically-Reinforced  Columns.  In  determining  the  strength  of  columns 
with  vertical  reinforcement,  the  steel  is  assumed  to  carry  a  load  per  square 
inch  equal  to  the  working  load  per  square  inch  on  the  concrete  times  the  ratio  of 
the  moduli  of  elasticity  of  the  steel  and  concrete.  The  allowable  stresses,  ratio  of 
moduH,  etc.,  are  given  in  Table  II,  page  912.  For  example,  in  New  York  a  load 
of  500  lb  per  sq  in  is  allowed  on  the  concrete,  and  15  times  500,  or  7500  lb  per 
sq  in  on  the  steel,  15  being  the  ratio  of  the  moduli,  as  fixed  by  the  regulations, 
for  1:2:4  concrete  and  steel.  Not  less  than  K%  nor  more  than  4%  of  vertical 
reinforcement  should  be  used  in  reinforced-concrete  columns.  The  reinforcing- 
rods  should  be  tied  together  horizontally  at  intervals  of  not  more  than  the  least 
side  or  diameter  of  the  column.  This  prevents,  to  a  great  extent,  the  buckhng 
of  the  reinforcement  under  load  and  the  consequent  splitting  of  the  concrete. 
The  vertical  reinforcement,  in  order  to  serve  its  purpose  of  taking  up  the 
bending  in  the  column,  should  be  placed  as  near  the  outer  surfaces  of  the  column 
as  possible,  consistent  with  proper  protection  of  the  steel.  (See  page  958.)  If 
tension  is  possible  in  the  longitudinal  steel,  due  to  bending,  the  bars  must  be 
spliced  to  resist  the  stress.  In  the  disposition  of  the  steel-  the  same  pre- 
cautions are  necessary  as  in  the  case  of  beams,  in  order  to  avoid  a  too  close 
spacing  of  the  reinforcing-pieces  or  an  excess  of  reinforcing-material.  (See 
page  937.)  As  the  concrete  in  columns  is  generally  poured  into  the  molds  at 
the  extreme  top,  it  is  particularly  important  to  keep  the  interior^  free  from 
interlacing  steel  across  the  column.    In  columns  in  which  the  steel  is  assumed 


942  Reinforced-Concrete  Construction  Chap.  24 

to  furnish  part  of  the  compressive  strength,  it  should  be  made  continuous 
from  the  columns  of  one  story  into  those  of  the  stories  below.  The  rods 
extending  from  one  column  may  be  connected  with  those  above  or  below  by 
means  of  pipe-sleeves. 

Laterally-Reinforced  Columns.  Tests  made  on  hooped  concrete  columns 
at  the  University  of  lUinois  in  1907,  at  the  Watertown  Arsenal  in  1906,  and  at 
the  University  of  Wisconsin  in  1906  and  1907,  show  that  the  ultimate  compressive 
strength  of  such  columns  is  increased  from  500  to  i  000  lb  per  sq  in  for  each 
percentage  of  hooping  employed.  The  increase  of  strength  is  due  to  the  lateral 
COMPRESSIVE  STRESSES  developed  by  the  restraining  action  of  the  hoops  or 
bands  at  right-angles  to  the  direct  compressive  stresses.  Below  the  limit  of 
elasticity,  however,  very  Httle  stress  is  developed  in  the  lateral  steel,  and  the 
tests  show  that  at  an  early  stage,  the  deformation  or  shortening  of  the  column 
is  equal  to  that  of  plain  concrete.  With  further  loading,  the  laterals  begin  to 
work  and  prevent  failure,  thus  increasing  the  so-called  toughness  of  the  column 
and  the  ultimate  compressive  or  breaking  strength.  This  efifect  has  been  va- 
riously allowed  for  by  considering  the  hooping-metal  equivalent  to  and  replaced 
by  imaginary  longitudinals.  Considere  and  other  investigators  have  shown  that 
the  hooping  is  equivalent  to  2.4  times  as  much  longitudinal  steel.  It  is  gener- 
ally conceded  that  hooping  permits  of  a  somewhat  higher  unit  stress  in  the  con- 
crete. The  New  York  City  Building  Code  permits  an  axial  compression  in  such 
columns,  having  not  less  than  H%  nor  more  than  2%  of  hoops  or  spirals  spaced 
not  farther  apart  than  one  sixth  the  diameter  of  the  enclosed  column  nor  more 
than  3  in,  and  having  not  less  than  1%  nor  more  than  4%  of  vertical  reinforce- 
ment, not  to  exceed  500  lb  per  sq  in  on  the  concrete  within  the  hoops  or  spirals, 
nor  7  500  lb  per  sq  in  on  the  vertical  reinforcement,  plus  a  load  per  square  inch 
on  the  effective  area  of  the  concrete  equal  to  twice  the  percentage  of  lateral 
reinforcement  multipHed  by  the  permissible  tensile  stress  in  the  lateral  reinforce- 
ment. St.  Louis  and  Cleveland  permit  2.4  times  the  volume  of  hooping  to  be 
considered  as  longitudinal  reinforcement;  Chicago  2.5  times;  and  Cincinnati  2.2 
times.  ^ 

New  York  Requirements  Expressed  by  Formulas.  The  safe  loads 
for  reinforced-concrete  columns  according  to  the  requirements  of  the  New 
York  Building  Code  may  be  determined  by  the  following  formulas,  in  which 

W=  total  safe  load,  in  pounds; 
Ae  =  the  effective  cross- sectional  area  of  concrete,  in  square  inches,  which,  in 

the  case  of  columns  with  longitudinal  reinforcement  only,  may  be 

taken  as  the  entire  area,  and  in  the  case  of  hooped  columns  is  limited 

to  the  area  within  the  hoops; 
As—  the  cross-sectional  area  of' the  longitudinal  steel,  in  square  inches; 
p  =  percentage  of  lateral  reinforcement  (hooping),  that  is,  the  volume  of  the 

hooping  divided  by  the  volume  of  the  concrete  enclosed  within  the 

hooping,  for  each  unit  length  of  column; 
Sc=  allowable  compressive  stress  in  the  concrete,  in  pounds  per  square  inch, 

which  is  taken  at  500  for  i  :  2  14  concrete,  and  at  600  for  i  :  i^  :  3 

concrete; 
5s  =  allowabte  compressive  stress  in  the  steel,  in  pounds  per  square  inch, 

which  is  taken  at  7500  when  1:2:4  concrete  is  used,  and  at  7200 

when  I  :  i}4  : 3  concrete  is  used; 
Sh=  allowable  tensile  stress  in  the  hooping  steel,  in  pounds  per  square  inch, 

which  may  be  taken  at  35%  of  the  elastic  limit,  but  not  more  than 

20  000. 


Design  of  Reinforced-Concrete  Construction  943 

For  columns  with  longitudinal  reinforcement  only, 

W  =  AcSc  +  AsSs 

but  the  area  of  the  steel  must  not  be  less  than  i^%,  nor  more  than  4%  of  the 
area  of  the  concrete,  and  the  reinforcement  must  be  secured  against  displacement 
by  34-in  steel  ties  spaced  not  farther  apart  than  15  diameters  of  the  vertical 
rods,  nor  more  than  12  in. 

Example.  What  is  the  safe  carrying  capacity  of  a  12-in  square  column  of 
1:2:4  concrete,  reinforced  in  each  corner  with  %-m  square  bars? 

Solution.  The  area  of  the  concrete  may  be  taken  at  12X12  =.144  sq  in. 
A  K-iu  square  bar  has  a  sectional  area  of  0.7656  sq  in.  The  area  of  the  steel 
is  4  X  0.7656  =  3.06  sq  in,  a  little  over  2%  reinforcement.  The  allowable 
stresses  for  concrete  and  steel  are  500  and  7500  lb  per  sq  in,  respectively.     Hence 

W  =  144  X  500  +3-o6  X  7  500  =  94  950  lb  =  473^  tons 

For  hooped  columns, 

W  =  AcSc  +  AsSs-^2pAcSfi 

with  longitudinal  reinforcement  not  less  than  1%,  nor  more  than  4%,  and 
hooping  not  less  than  }4%,  nor  more  than  2%,  the  hooping  being  spaced  not 
farther  apart  than  one  sixth  of  the  diameter  of  the  enclosed  column,  and  at 
most,  3  in. 

Example.  Determine  the  maximum  load  that  should  be  placed  on  a  24-in 
round  column  of  i  :  i}4  -^  concrete,  with  spiral  hooping  of  Mo-in  cold-drawn 
wire,  having  a  3-in  pitch,  and  reinforced  longitudinally  with  six  i-in  round 
bars,  equally  spaced  just  inside  the  hooping,  and  fastened  to  it,  the  concrete 
being  2  in  thick  outside  the  hooping. 

Solution.  The  effective  sectional  area  of  the  concrete  has  a  diameter  of 
20  in,  and  is  therefore  20 X2o>:o. 7854  =314.16  sq  in.  For  an  inch  in  height, 
the  cubic  contents  of  the  concrete  is  314.16  cu  in.  The  area  of  a  i-in  round 
bar  is  0.7854  sq  in.  The  area  of  longitudinal  steel  is  6X0.7854=4.71  sq  in, 
about  i}4%.  The  cross-sectional  area  of  yie-in  wire  is  0.0767  sq  in.  The 
length  of  one  turn  of  wiqe  is  62.75  iu,  and  as  the  turn  is  made  in  a  height  of 
3  in,  the  cubic  contents  for  an  inch  of  height  of  the  column  is  K  X  62.75  X  0.0767 
=  1.60  cu  in,  about  H%.  The  working  stress  per  square  inch  for  the  con- 
crete is  600  lb,  for  the  longitudinal  steel  7  200  lb,  and  for  the  hooping  20  000  lb. 
Hence 

W  =  (314-16  X  600)  +  (4.71  X  7  200),+  (2  X  o.oos  X  314-16  X  20  000) 
=  285  240  lb,  or  142.6  tons 

Details  of  Lateral  Reinforcement.  At  the  top  or  base  of  the  columns  in 
each  story,  the  wrapping  should  be  made  to  continue  through  the  floor-con- 
struction. Under  certain  conditions,  when  the  floor-construction  is  practically 
silid  about  the  columns,  thus  affording  good  lateral  support,  equal  to  the 
wrapping,  it  may  be  better  to  omit  the  wrapping  and  avoid  the  possible  com- 
plication of  steel  reinforcement  from  column,  girder,  and  floor-construction  and 
the  consequent  breaking  of  the  bond  of  the  concrete.  The  materials  used  for  the 
wrapping  are  either  steel  wire  or  steel  bands.  When  wire  is  used  it  is  spirally, 
wound  and  continuous  through  the  full  length  of  the  column.  The  ends  of  the 
wire  are  turned  into  the  column  and  turned  down  to  such  an  extent  that  when 
the  concrete  has  been  poured  and  set,  there  will  be  sufficient  anchorage  to  resist 


944 


Reinforced-Concretc  Construction 


Chap.  24 


the  tension  in  the  wrapping  due  to  the  outward  pressure  of  the  concrete.  When 
metal  bands  are  used,  as  in  the  Cummings  system,  care  must  be  taken  to  make 
the  riveted  joints  in  the  bands  as  strong  as  the  bands  themselves.  A  form  of 
wrapping  that  has  the  merits  of  rapidity  and  ease  of  erection  is  shown  in  the 
columns  used  in  the  Bush  Terminal  Warehouse,  Borough  of  Brooklyn,  New 
York  City,  described  on  page  958. 


'ilh. 


Fig.  20.    Concrete  Column  with  Steel  Core 


Metal-Core  Columns.  The  object  of  this  type  of  column  is  to  provide  a 
construction  for  tall  or  heavily  loaded  buildings  that  will  have  the  necessary 
strength  and  yet  not  encroach  too  seriously  on  the  floor-space.  For  this  form 
of  column  some  engineers  advocate  placing  a  steel  core  through  the  axis  of  the 
concrete,  the  steel  taking  the  bulk  of,  if  not  all  of,  the  load.*  "A  rational  basis 
of  design  is  to  determine  the  strength  of  the  steel  column  by  the  use  of  the  column- 
formula  for  the  proper  l/r  of  the  column  and  to  consider  the  concrete  of  the  core- 

•  Trans.  Am.  Soc.  C.  E..  Vol.  XIV,  Part  E,  page  556. 


Design  of  Reinforced-Concrete  Construction  945 

section   to   have   a   stress-value   proportional   to   the   strength  of   plain    con- 
crete." * 

William  H.  Burr  designed  a  column  (Fig.  20)  for  the  McGraw  Building,  New 
York  City.  The  steel  core  has  sufficient  strength  as  a  column,  independent  of 
any  concrete,  to  carry  the  entire  dead  load  coming  upon  it,  the  stresses  in  the 
steel  being  in  no  case  greater  than  those  allowed  on  steel  columns  under  the 
New  York  Building  Code,  consideiing  the  ratio  of  length  to  radius  of  gyration. 
Furthermore,  those  stresses  were  not  allowed  to  exceed  9  000  lb  per  sq  in  in  any 
case.  The  Uve  loads  were  provided  for  by  placing  enough  concrete  within  the 
steel  framework  to  prevent  the  stress  on  the  concrete  from  exceeding  750  lb 
per  sq  in.  This  is  one  twelfth  of  the  maximum  allowable  load  on  the  steel. 
The  concrete  outside  of  the  steel  was  considered  only  as  a  protection  against  fire 
and  corrosion.  Columns  of  this  type  should  be  designed  with  caution.  The 
concrete  should  not  be  rehed  upon  to  tie  the  steel  units  together  or  to*  transmit 
stresses  from  one  unit  to  another.  The  units  should  be  tied  together  by  tie- 
plates  or  lattice-bars  in  conformity  with  the  standard  practice  for  structural 
steelwork.  For  high  percentages  of  steel,  the  concrete  will  develop  low  unit 
stresses,  and  caution  should,  therefore,  be  used  in  placing  dependence  upon  the 
concrete,  t 

Rich  Mixtures  of  Concrete.  Increasing  the  proportion  of  cement  in  a 
mixture  increases  the  ultimate  strength  of  the  concrete  projx)rtionally  and  is 
effective  in  designing  columns  with  smaller  cross-sectional  area.  The  increased 
compressive  strength  is  also  accompanied  by  a  higher  modulus  of  elasticity. 
Furthermore,  the  employment  of  a  rich  mixture  also  permits  of  higher  propor- 
tional stresses  in  the  steel  and  consequently  a  more  economical  design.  The 
internal  stresses  in  a  monoHthic  member,  however,  may  be  considerably  com- 
plicated by  the  excessive  shrinkage  of  rich  mixtures,  which  have  a  tendency  to 
crack.  The  New  York  Building  Code  provides  that  "in  concrete  columns  the 
compression  on  the  concrete  may  be  increased  twenty  per  cent  when  the  fine  and 
coarse  aggregates  are  carefully  selected  and  the  proportion  of  cement  to  total 
aggregate  is  increased  to  one  part  of  cement  to  not  more  than  four  and  one-half 
parts  of  aggregate,  fine  and  coarse,  either  in  the  proportion  of  one  part  of  cement, 
one  and..one-half  parts  of  fine  aggregate,  and  three  parts  of  coarse  aggregate, 
or  in  such  proportion  as  will  secure  the  maximum  density.  In  such  cases,  how- 
ever, the  compressive  stress  in  the  vertical  steel  shall  not  exceed  seven  thousand 
two  hundred  pounds  per  square  inch." 

Cummings  Lateral  Reinforcement.  Robert  A.  Cummings  of  Pittsburgh, 
Pa.  (Electric  Welding  Company),  following  a  European  practice,  has  applied  a 
method  of  reinforcing  compression-members  by  placing  horizontal  wire  spirals 
in  planes  at  right-angles  to  the  main  compressive  stresses.  This  practice  is  based 
on  the  theory  that  the  failure  of  a  concrete  prism  will  take  place  along  Hues 
parallel  to  the  direction  of  the  applied  load.  The  method  has  been  very  success- 
ful in  reinforcing  the  heads  of  precast  concrete  piles,  driven  by  hammer. 

Cast-Iron  Columns.  When  a  building  for  any  reason  need  not  be  treated 
as  a  fire-proof  structure,  space  and  time  may  be  saved  by  using  cast-iron  or 
STEEL  COLUMNS.  In  such  cases  the  column-connections  must  be  designed  with 
suitable  bearings  for  the  concrete  construction  and  so  that  there  will  be  a  con- 
tinuity in  that  construction;  for  the  great  advantage  in  reinforced-concrete 
construction  lies  in  its  monolithic  character.  When  cast-iron  columns  are 
used,  the  heads  of  the  columns  may  be  cast  with  openings  through  which  the 

*  tlniversity  of  Illinois  Bulletin,  No.  56,  1912. 
t  Proc.  Am.  Soc.  C.  E.,  Feb.,  1913,  page  153. 


946 


Reinforced-Concrete  Construction 


Chap.  24 


reinforcement  may  pass  from  one  side  to  the  other.  Fig.  21  nhows  how  this  has 
been  done  in  a  building  at  Gay  and  Christopher  Streets,  New  York  City  with- 
out impairing  the  strength  of  the  columns  at  the  connections. 


Granolithic  ^Finish 
Cinder  Concrete 


^—^ 


-:^ 


.1st  Story/ 
Column 


W 


Pintles  P  to  have  a  combined 
Area  equal  to  the  Area  of  the 
Column  they  have  to  Support, 
to  be  cast  on  at  top  of  Support-, 
^  Basoraent    ing  Column. 
Column 


Fig.  21,     Connections  for  Cast-iron  Columns  and  Reinforced-concrete  Construction 


Steel  Columns.  In  steel  columns  it  is  simpler  to  provide  connections 
between  the  reinforcing-rods  and  the  steel  shapes  of  the  columns.  When  the 
reinforcement  does  not  go  through  the  columns,  some  rods  should  be  placed 
outside  of  them  to  tie  as  much  as  possible  the  concrete  on  one  side  to  that  on 
the  other. 

Eccentric  Loads.  Bending  stresses  due  to  lateral  and  eccentric  loads 
must  be  computed  so  that-  the  combined  direct  and  bending  stress  does  not 
exceed  the  allowable  maximum  stress  for  axial  compression.  Formulas  for 
eccentric  loading  on  columns  are  given  in  Chapter  XIV,  pages  453  and  486. 

Concrete  Walls.  If  not  reinforced,  concrete  walls  are  generally  required  to 
be  of  the  same  thickness,  for  given  conditions,  as  brick  walls.  Under  such  cir- 
cumstances they  are  not  as  economical  as  brick  walls.  If  reinforced  and  used  as 
bearing-walls,  they  can  be  reduced  to  about  two  thirds  the  thickness  of  brick 
walls,  provided,  however,  that  the  bad  on  the  concrete  does  not  exceed  the  safe 
load  per  square  inch  permitted  on  reinforced  columns.  The  ratio  of  unsupported 
height  to  thickness  should  not  exceed  that  fixed  for  columns.  For  spandrel- 
walls,  supported  entirely  on  girders,  the  minimum  thickness  should  be  4  in. 
Such  walls  should  be  reinforced  with  not  less  than  %  lb  of  steel  per  square  foot 
of  wall,  in  the  form  of  rods  placed  vertically  and,  less  frequently,  horizontally. 

Reinforced-Concrete  Footings.  (See,  also,  pages  186,  225,  and  226.)  The 
principles  underlying  the  design  and  construction  of  reinforced-concrete  footings 
are  the  same  as  those  applied  to  other  types  of  footings.  In  wall,  pier,  or  column- 
footings,  the  overhang  or  off-set  must  be  considered  as  an  inverted  cantileveK 
loaded  uniformly  with  a  load  per  square  foot  equal  to  the  load  per  square  foot 
imposed  on  the  underlying  soil.  The  reinforcing-rods  will  then  necessarily  be 
placed  near  the  lower  surface  of  the  footing  and  the  size  and  number  determined 
by  formulas  given  on  page  925.     A  detail  often  overlooked  in  reinforced-con- 


Design  of  Rein  forced -Concrete  Construcdon  947 

Crete  footings  is  the  tendency  to  shear  at  the  edge  of  the  wall,  pier,  or  column 
supported.  When  footings  would  otherwise  become  very  eccentric,  cantilevers 
should  be  resorted  to,  the  same  as  for  steel  construction.  (See  pages  165  to  169, 
and  978  to  982).  The  maximum  bending  moment  on  the  cantilever  is  deter- 
mined and  the  concrete  girders  designed  as  described  on  page  925.  Steel  in 
footings  should  be  protected  by  at  least  3  in  of  concrete. 

Economy  of  Reinforced-Concrete  Footings.  Great  economy  over  steel- 
grillage  or  other  types  of  footings  may  often  be  effected  by  the  use  of  rein- 
FORCED-coNCRETE  FOOTINGS.  The  cost  of  the  latter  type  will  vary  from  20  to 
40%  of  the  cost  of  a  corresponding  steel-grillage  footing.  This  difference 
is  easily  accounted  for.  The  amount  of  excavation  for  the  reinforced  footing  is 
generally  much  less  than  for  the  steel  grillage.  A  smaller  amount  of  concrete 
is  used,  and  this  concrete  is  considered  in  the  calculations  for  strength;  whereas 
in  the  steel  grillage,  the  concrete  is  chiefly  provided  for  incasing  and  protecting 
the  steel.  The  amount  of  steel  is  much  less,  being  used  only  to  supply  the  ten- 
sional  resistance  of  the  construction,  .the  compressive  strength  ])eing  supplied 
by  the  much  cheaper  material,  concrete.  Incidentally,  the  protection  of  the 
steel  in  the  reinforced  footing  is  generally  more  certain  than  in  the  steel -grillage 
footing. 

Concrete  Piles.  Concrete  piles  are  discussed  in  Chapter  IT,  pages  196  to 
200,  and  some  of  the  types  are  there  described. 

Connections  in  Reinforced-Concrete  Construction.  Much  good  Judgment 
can  be  displayed  and  must  be 'exercised  in  the  design  of  the  details  in  these 
connections.  The  great  value  of  reinforced-concrete  construction  over  other 
types  is  the  possiinlity  of  securing  great  rigidity.  This  can  only  be  attained 
when  the  result  is  as  nearly  monolithic  as  possible.  We  than  have  mass  to 
take  up  vibration  and  this  advantage,  in  the  case  of  workshops  or  factories  in 
which  there  is  machinery,  is  readily  seen.  The  reinforced-concrete  buildings 
that  came  through  the  severe  San  Francisco  earthquake  in  May,  1906,  in  good 
condition,  were  those  in  which  attention  had  been  given  to  the  details  and  con- 
nections. ITo  secure  a  monolithic  character  requires  continuity  not  only  in  the 
concrete,  but  also  in  the  reinforcement.  This  often  means  that  there  is  a  net- 
work of  steel  at  the  connections.  If  this  is  carried  to  excess,  the  bond  and  con- 
tinuity of  the  concrete  is  apt  to  be  broken,  even  when  the  spaces  between  the 
steel  units  are  thoroughly  filled.  But  when  there  is  such  a  network  of  steel 
it  also  acts  like  a  sieve  and  the  spaces  are  not  readily  filled.  For  this  reason  it 
is  well  to  use  a  richer  mixture  at  the  columns  and  to  keep  the  aggregate  as  small 
as  possible.  The  connections  of  floor  system  to  columns  are  particularly  trouble- 
some in  this  respect,  and  partly  for  this  reason  and  partly  to  insure  rigidity, 
brackets  should  be  provided  under  the  girders  at  the  columns,  with  metal  rein- 
forcement near  the  inclined  surfaces  of  these  brackets. 

Reinforced-Concrete  Stairs.*  Some  of  the  most  interesting  work  that  has 
been  done  in  reinforced  concrete  has  been  the  construction  of  stairs.  The  rein- 
forcement, being  in  the  form  of  comparatively  small,  hmber  bars,  can  be  adapted 
to  almost  any  shape  for  which  molds  can  be  constructed,  and  when  a  wet,  rich 
concrete  with  small  aggregate  is  used,  little  or  no  difficulty  need  be  experienced 
in  casting.  As  an  example  of  such  work,  the  stairs  in  the  residence  of  G.  W. 
Vanderbilt,  in  New  York  City,  may  be  cited.  When  these  stairs  were  five 
weeks  old  a  test  of  their  strength  was  made,  without  distress,  by  dropping  a 
bundle  of  four  bags  of  cement,  weighing  about  380  lb,  from  the  floor  aliove  to 

*  See,  also,  pages  9cx>  and  983. 


948  '    Reinforced-Concrete  Construction  Chap.  24 

the  intermediate  platform,  a  distance  of  ii  ft.    No  injurious  effects  were  no- 
ticed.* 

4.  Types  of  Reinforced-Concrete  Construction  f 

Mill-Construction.  In  locaHties  where  the  cost  of  labor  is  high  and  where 
the  conditions  cause  more  or  less  congestion,  it  is  probably  more  economical  to 
use  brick  instead  of  concrete  for  the  walls.  In  such  cases  the  type  of  construc- 
tion is  similar  to  ordinary  mill-construction.  Provision  must  be  made  to  an- 
chor the  beams  and  girders,  and  this  can  be  done  by  bending  the  ends  of  the 
reinforcing-rods  so  that  they  will  extend  horizontally  into  the  walls  on  each  .side. 

Skeleton  Construction.  The  skeleton  type  of  construction  seems  to  be 
the  form  best  adapted  to  reinforced  concrete.  A  framework  of  columns,  girders, 
beams,  and  flooring  is  built,  as  in  steel  construction,  the  wall-girders  and  columns, 
of  course,  being  designed  to  carry  the  weights  of  the  outside  walls  as  well  as 
that  part  of  the  floor-loads  and  live  loads  which  comes  on  them.  The  work,  in 
this  type  of  construction,  can  generally  progress  more  steadily  than  in  the  mill- 
construction  since  the  concrete  work  need  not  be  stopped  at  any  time  to  wait 
for  the  brickwork  to  be  carried  up,  if  brick  is  used  for  the  walls.  In  the  skele- 
ton construction  any  type  of  outside  wall  may  be  used;  brick,  concrete,  tile, 
etc.  In  some  cases  the  panels  are  simply  filled  in  with  brickwork,  8  or  12  in* 
thick,  leaving  the  concrete  columns  and  girders  showing  between  the  brick 
panels.  For  walls  situated  on  property -lines  where  adjoining  buildings  are  likely 
to  be  erected,  this  is  not  objectionable.  If  the  wall  remains  exposed  and  a  good 
appearance  is  a  consideration,  the  columns  and  girders  can  be  treated  architec- 
turally to  set  off  the  brickwork;  or  the  brickwork  may  be  continued  as  a  facing 
over  the  outside  of  the  columns  and  girders.  This  was  done  in  some  of  the  Bush 
Terminal  Warehouses,  Borough  of  Brooklyn,  New  York  City. J  To  thoroughly 
secure  this  brick  facing,  galvanized  anchors  were  placed  in  the  concrete  columns 
and  girders  as  they  were  erected,  projecting  sufficiently  to  bond  into  the  brick- 
joints.  In  using  concrete  for  the  panels  the  sides  of  the  columns  are  cast  with 
pockets,  grooves,  or  recesses  to  receive  the  panels,  which,  as  in  the  case  of  brick- 
work, are  most  satisfactorily  and  most  economically  built  after  the  removal  of 
the  molds  from  the  skeleton  frame.  In  the  Marlborough-Blenheim  Hotel,  at 
Atlantic  City,  N.  J.,  the  panels  are  filled  in  with  hard-burned  terra-cotta  tiles 
and  a  stucco  applied  on  the  outside.  This  makes  a  comparatively  light  con- 
struction and  affords  good  insulation.  The  particular  advantage  in  the  skele- 
ton TYPE  of  construction,  especially  for  workshops  and  factories,  is  the  possibihty 
of  large  window-areas  affording  light  and  ventilation. 

System  M.  A  type  of  construction  known  as  System  M  has  been  developed 
by  the  Standard  Concrete  Steel  Company  of  New  York  City  (Fig.  22).  It  con- 
sists of  a  light  steel  skeleton  frame  designed  to  carry  the  dead  load  of  the  entire 
structure,  except  that  the  columns  are  designed  to  carry  the  gross  loads.  The 
structure  is  incased  in  concrete,  making  ultimatelya  reinforced-concrete  construc- 
tion. §  Its  advantage  consists  in  its  adaptation  to  the  erection  and  inspection  of 
the  steel  reinforcement  before  even  the  centers  or  molds  are  placed  in  position. 
Under  congested  conditions,  such  as  prevail  in  large  cities,  it  is  a  rapid  form  of 

*  For  a  detailed  description,  see  Cement,  Jan.,  1904,  and  Engineering  Record,  Dec.  12, 
1903.     P'or  other  examples  of  stair-construction,  see  Engineering  News,  June  30,  1904. 

t  See,  also,  Chapter  XXV. 

i  For  a  description  of  this  building,  see  Engineering  Record,  March  3,  1906. 

§  For  fuller  description,  see  Engineering  News,  April  25,  1907,  and  Engineering  Record, 
June  22,  1907. 


Types  of  Reinforced-Concrete  Construction  949 

construction.  The  use  of  the  steel  in  this  type  is,  however,  not  economical. 
In  order  to  get  the  necessary  strength  in  the  steel  framework,  shapes  must  be 
used  which  do  not  offer  the  amount  of  adhesion  that  should  result  from  the 


Fig.  22.     System  M  Type  of  Jleiuforced -concrete  Construction  j 

amount  of  metal  used.  Furtliermore  such  shapes  must  necessarily  be  subjected 
to  some  bending,  which  tends  to  break  the  bond  between  concrete  and  steel. 

Flat-Slab  Construction.*  In  this  form  of  construction  beams  and  girders 
are  eliminated  almost  completely,  if  not  entirely,  and  the  slab  is  made  to  rest 
directly  on  the  columns;  the  tops  of  the  columns  are  enlarged  into  extended  caps. 
This  system  of  construction  employs  a  shallower  floor-construction  than  is  ordi- 
narily attainable.  The  floor-centering,  too,  for  purposes  of  erection,  is  somewhat 
simpler,  especially  in  those  forms  of  slabs  in  which  the  lower  surface  is  all  in  one 
plane.  The  slab  may  be  of  uniform  thickness  between  the  edges  of  the  column- 
capitols,  or  a  portion  of  it,  symmetrical  about  the  columns,  may  be  thickened  to 
form  a  column-drop,  or  the  slab  may  be  thickened  to  form  a  band  or  shallow 
beam  between  columns,  with  a  paneled  ceiling  at  the  center  of  the  panel. 

Based  on  the  method  of  reinforcing  the  slab  and  columns,  a  number  of  systems 
have  been  developed  which  may  be  divided  into  four  general  classes:  (i)  the 
TWO-WAY  system;  (2)  the  four-way  system;  (3)  the  three-way  system;  and 
(4)  the  circumferential  system.  In  the  tw^o-way  system,  the  reinforcement 
is  placed  in  direct  bands  between  thf^  columns  in  both  directions,  with  an  interior 
system  of  two-way  rectangular  bands  on  the  remaining  panel-area  at  the  center. 
In  the  four-way  system,  the  reinforcement  is  placed  in  two  direct  bands  in  the 
two  rectangular  directions,  and  in  two  diagonal  bands  which  cross  the  panel 
diagonally  between  columns.  In  the  three-way  system  the  reinforcement 
is  placed  in  bands  directly  connecting  the  columns  and  passing  over  the  column- 
heads.  In  the  circumferential  system,  circumferential  reinforcement  is 
placed  around  the  columns,  with  bars  radiating  from  the  column-centers.  Con- 
centric rings  of  reinforcement  are  also  placed  at  the  center  of  the  sides  joining 
column-centers,  which  overlap  the  circumferential  reinforcement  at  the  columns, 
and  the  center  of  the  panel  is  reinforced  in  a  similar  manner.  Some  of  the 
systems  developed  are  modifications  of  the  above  or  a  combination  of  two  or  more 
of  the  general  types  described.  The  principles  of  design  are  based  on  empirical 
analyses  determined  by  extensometer  tests  made  on  completed  buildings. 

Akme  System.  This  is  a  two-way  system  developed  by  the  Condron 
Company,  Chicago,  III.  It  is  constructed  either  with  a  slab  of  uniform  thick- 
ness, with  a  drop-panel,  or  with  a  paneled  ceiling.     Each  panel  of  the  slab  is 

*  See,  also,  Girderless  Floors,  Chapter  XXV,  page  993. 


950  Reinforced-Concrete  Construction  Chap.  24 

divided  into  two  sets  of  strips,  called  the  main-slab  strips  and  the  mid-slab 
STRIPS,  which  are  designed  as  flat,  shallow  beams. 

Corr-Plate  System.  This  type  of  construction  has  been  developed  and  in- 
stalled by  the  Corrugated  Bar  Company,  Buffalo,  N.  Y.  The  construction  is 
similar  to  other  two-way  systems  and  is  installed  either  with  or  without  drops. 
The  reinforcement  is  distributed  across  the  entire  slab,  with  varying  spacing  to 
resist  the  stresses  determined  experimentally. 

Mushroom  System.  The  mushroom  system,  invented  by  C.  A.  P.  Turner, 
MinneapoUs,  Minn.,  is  one  of  the  earliest  of  the  flat-slab  constructions.  The 
striking  and  essential  feature  which  gives  this  system  its  name  is  the  gradual 
spreading  out  of  the  column  at  the  top  to  form  a  cap,  the  diameter  of  which  is 
seven  sixteenths  of  the  sum  of  the  distances  between  columns  in  the  direction  of 
the  sides  of  the  slab.  The  longitudinal  column-reinforcement  is  bent  to  follow 
the  curved  outer  surface  of  the  cap,  and  the  cap  is  reinforced  both  radially  and 
circumferentially.  The  slab-reinforcement  is  placed  at  the  top  of  the  slab  over 
the  columns  and  allowed  to  sag  to  a  catenary  curve  with  the  low  point  near  the 
bottom  of  the  slab  at  the  middle  of  the  span.  The  thickness  of  the  slab  varies 
from  \ii5  to  y20  of  the  shorter  distance  between  the  column-centering.  This  is 
essentially  a  four-way  systJ'.m  with  the  added  features  described  above. 

The  Cantilever  Flat  Slab,  designed  by  the  Concrete  Products  Company, 
Chicago,  111.,  is  another  type  of  four-way  system.  It  differs  from  the  one  de- 
scribed in  the  preceding  paragraph  mainly  in  the  construction  of  the  column-cap. 
The  column-bars  are  not  bent  to  the  shape  of  the  cap  but  continue  up  straight. 
The  horizontal  cap-reinforcement  is  provided  by  a  shop-made  frame  of  radial 
bars,  held  together  by  a  Diamond  Bar  which  is  intended  to  resist  the  circum- 
ferential stresses.  The  diameter  of  the  cap  is  about  yio  the  span  and  the  thick- 
ness of  the  slab  about  Hs  the  span.  Whenever  necessary  to  provide  for  large 
shearing-stresses  and  bending-stresses  around  the  column,  the  slab  is  increased 
in  thickness  at  that  point,  forming,  in  appearance,  an  extended  cap  at  the 
column-head,  l.ater  extensometer  tests  have  proved  the  use  of  radial  rods 
with  rings  around  the  column-heads  to  be  inefficient,  and  they  therefore  have 
been  abandoned. 

Three-Way  System.  This  system  was  invented  and  patented  by  David  W. 
Morrow,  Cleveland,  Ohio.  The  columns  are  located  at  the  apexes  of  equilateral 
triangles,  making  equal  the  bands  of  steel  between  the  columns.  The  reinforce- 
ment over  the  columns  is  placed  in  three  instead  of  the  four  layers  of  the  four- 
way  systems.  Flaring  circular  caps,  with  hexagonal  or  circular  drops,  are  pro- 
vided over  the  columns. 

S.  M.  I.  System.  This  systeni  was  Invented  and  patented  by  Edward 
Smulski,  and  is  controlled  by  the  S.  M.  I.  Engineering  Company,  Boston,  Mass. 
Circumferential  and  radial  reinforcement  is  placed  in  both  the  top  and  bottom 
of  the  slab,  with  trussed  bars  extending  both  rectangularly  and  diagonally  be- 
tween the  columns  (Fig.  23).  The  radial  bars  are  provided  with  a  semicircular 
hook  to  transfer  the  stresses  into  the  concrete  by  loond,  and  to  engage  the  ring  of 
reinforcement  in  the  center  of  the  panel.  To  prevent  cracking  on  the  top  of  the 
slab  between  columns,  additional  short,  straight  bars  are  sometimes  used. 

Patents  for  Flat-Slab  Construction.  In  1901  and  1902  patents  were 
granted  to  O.  W.  Norcross,  covering  girderlcss  floor-construction  reinforced  with 
bands  of  wire  netting  extending  from  column  to  column.  AppH cation  for  the 
original  C:  A.  P.  Turner  patents  was  made  in  1905.  In  1915  the  United  States 
Courts  held  that  the  Norcross  patents  covering  girderless  floors  were  funda- 
mental, and  that  bands  of  bars  were,  to  all  intents  and  purposes,  the  same  as 


Types  of  Reinforced-Concrete  Construction] 


mx 


Fig.  23.    S.  M.  I.  Flat-slab  System 


hands  of  wire  netting.  It  would  seem,  therefore,  that  any  system  of  floor-con- 
struction depending  upon  bands  of  bars  running  either  diagonally  or  crosswise 
from  column  to  column  constitutes  an  infringement  of  the  Norcross  patents. 
The  leading  promoters  of  flat-slab  construction  in  the  United  States  are  now 
licensed  under  the  Norcross  patents;  but  several  other  United  States  patents 
have  been  granted  covering  special  methods  of  construction  and  reinforcement. 
*  Combination  Hollow-Tile  and  Reinforced-Concrete  Construction.  In 
seeking  to  minimize  the  cost  of  centering,  the  floor-construction  shown  in  Fig.  24 
has  been  devised.  It  consists  of  a  series  of  rein  forced-concrete  beams  with 
clear  spaces  between  them  of  the  width  of  the  holiow-tile  blocks.    In  erection,  a 


952 


Reinforced-Concrete  Construction 


Chap:  24 


flat  centering  is  used,  which,  however,  need  not  even  be  continuous.  Planks,  a 
few  inches  wider  than  the  concrete  beams,  are  placed  under  the  spaces  to  be  filled 
by  the  beams,  and  the  tiles  are  laid  in  rows  and  supported  along  their  edges  by 
the  planks,  thus  forming  the  sides  of  the  molds  for  the  beams.  The  reinforce- 
ment is  placed  and  the  concrete  poured,  with  or  without  floor-phtes,  as  the  neces- 
sities of  the  case  may  require.     Care  must  be  taken  in  pouring  the  concrete 


Fig.  24.     The  Combination  Tile  and  Reinforced-concrete  System 

that  the  tiles  are  not  displaced  sidewise.  The  tiles  should  fit  closely  at  their 
joints,  otherwise  the  finer  particles  of  the  concrete  are  liable  to  flow  into  them, 
either  making  the  concrete  porous  or  requiring  more  cement  and  sand  than  is 
necessary.  This  form  of  construction,  besides  being  economical  in  centering, 
offers  the  advantages  of  a  flat  ceiling  without  the  application  of  lath  and,  in  roof- 
construction  partic\flarly,  of  freedom  from  condensation. 

The  Floretyle  Systems.  A  floor-construction  similar  to  the  hoflow-tile 
construction  just  described  has  been  devised  by  the  Truscon  Steel  Company, 
Youngstown,  Ohio,  in  which  forms  of  corrugated  sheet  steel,  called  floeetyles, 
replace  the  hollow  tiles.  The  Floretyles  are  furnished  in  lengths  of  283^  and  45 
in,  and  in  depths  of  6,  8,  10,  and  12  in.  The  width  at  the  base  is  20V2  in,  with  the 
sides  tapering  at  an  angle  of  7°  30'.  They  are  furnished  in  two  types,  either  with 
serrated  edges  for  use  with  the  company's  Hy-rib  lath  for  ceilings,  or  with  straight 
edges  for  use  where  paneled  ceilings  are  required.  Other  makes  of  metal  forms 
used  in  the  construction  of  reinforced-concrete  floors  are  the  g  f  steel  tiles  of  the 
General  Fireproofing  Company,  Youngstown,  Ohio,  and  the  wiscoforms  of  the 
Witherow  Steel  Company,  Pittsburgh,  Pa.  Besides  a  reduction  in  weight  of 
finished  floors,  the  additional  advantages  in  the  use  of  these  steel  tiles  or  forms 
over  the  terra-cotta  fillers  are:  Greater  economy  in  centering,  larger  covering 
capacity,  less  bulk  in  shipment  because  the  forms  can  be  nested,  and  less  danger 


6  in 

8  in 

10  in 

12  in 

14  in 

Average    weight,  in  pounds 

40.100 

0.278 

58.300 

46.000 

0.319 

61 .700 

S3-SOO 

0.371 

63 . 000 

61 .000 

0.423 

63.800 

72.600 

0.50s. 

62 . 200 

Cubic    feet    of    concrets  per 

.    square  foot  of  floor 

Core-area,  percentage  of  sec- 

Types  of  Reinforced-Concrete  Construction  953 

of  absorption  of  water  from  the  concrete  and  of  the  flooring-out  of  the  cement  at 
the  joints.  A  concrete  floor  of  G  F  steel  tiles,  spaced  so  as  to  make  4-in  con- 
crete beams,  24  in  on  centers,  and  liaving  2  in  of  concrete  above  the  tiles,  with- 
out ceiling,  is  said  to  have  the  properties  shown  in  the  table  on  page  952, 
according  to  the  depth  of  tiles  used. 

Two- Way  Tile  Systems.  Similar  in  general  principle  but  using  reinforce- 
ment in  two  directions,  at  right-angles  with  one  another,  is  the  combined  hol- 
LOW-TiLE-AND-coNCRETE  FLOOR,  Controlled  by  the  Republic  Fireproofing  Com- 
pany, Inc.,  New  York  City,  under  the  Burchartz  patents  (Fig.  25).  This  system 
employs  terra-cotta  blocks,  channels,  and  soffits,  providing  uniform  flat  ceilings 
to  which  plaster  can  be  applied  without  the  use  of  metal  lath.  -  In  this  case  the 
floor  is  calculated  as  a  slab  supported  on  four  sides.  (See  page  936.)  The  con- 
crete is  prevented  from  running  into  the  hollow  spaces  of  the  tile  by  the  use 
of  the  terra-cotta  channels  as  shown. 

Floredomes.  In  the  floredome  -construction,  put  on  the  market  by  the 
Truscon  Steel  Company,  Youngstown,  Ohio,  the  tile  spacing-blocks  of  the  two- 
way  tile  SYSTiSM  are  replaced  by  rectangular  dome- shaped  steel  forms  with  the 
under  side  open.  Lightness  in  floor-weight,  ease  and  rapidity  of  installation,  and 
no  breakages  are  the  advantages  claimed.  The  ceiling-treatment  in  this  con- 
struction is  similar  to  that  in  the  Floretyle  system.  The  base  of  the  domes  is 
uniformly  21.5  in  square;  the  depth  varies,  being  6,  8,  10,  or  12  in. 

Strength  of  Combination  Systems.  While  the  tiles  may  under  favorable 
conditions  add  to  the  strength  of  the  combined  floor-construction,  the  chances 
of  unsatisfactory  workmanship  are  too  great  to  consider  them  in  the  calculations 
for  strength.  In  the  floors  reinforced  in  one  direction,  the  construction  should 
be  treated  as  a  series  of  either  rectangular  beams,  or  T  beams,  as  the  concrete 
extends  either  to  or  above  the  top  face  of  the  tiles.  The  two-way  reinforced 
construction  should  be  treated  as  if  it  consisted  of  a  slab  supported  on  four 
sides,  or  as  a  series  of  intersecting  rectangular  beams,  or  T  beams.  If  the  con- 
struction is  to  be  treated  as  a  series  of  T  beams  or  as  a  slab,  the  concrete  should 
extend  at  least  2V^  in  above  the  top  surface  of  the  slab  and  the  tiles  or  fillers  should 
not  exceed  60%  of  the  volume  of  the  construction. 

Separately-molded  Construction.  The  unit  or  separately-molded  con- 
struction consists  of  precast  reinforced-concrete  members,  columns,  girders, 
beams,  or  slabs,  either  molded  at  the  site  of  the  building,  or  made  at  the  factory 
and  shipped  to  the  site  ready  for  use.  The  various  members  are  swung  into 
place  in  much  the  same  manner  as  steel  is  erected,  and  fitted  together  in  the 
structure  by  interlocking  reinforcement  and  poured  grouting.  Great  economy 
is  claimed  for  this  method  of  erection  on  account  of  the  saving  of  forms.  Maxi- 
mum economy,  however,  cannot  be  obtained  on  a  building  operation  of  less  than 
80  000  sq  ft,  as  economy  is  obtained  by  the  greater  use  of  the  forms  and  the 
familiarity  of  the  erecting-crews  with  the  particular  type  of  building.  But 
under  good  conditions,  economy  can  also  be  shown  on  an  operation  involving 
as  Httle  as  50  000  sq  ft.  The  advantages  of  this  construction  are  said  to  be: 
The  great  number  of  uses  possible  of  one  set  of  forms,  especially  on  a  large  opera- 
tion; the  small  number  of  men  required,  due  to  the  extensive  use  of  locomotive- 
cranes,  motor  trucks,  derricks,  etc.;  the  ease  with  which  the  units  may  be  in- 
spected while  being  poured  and  before  entering  the  building;  and  the  fact  that  all 
shrinkage  takes  place  before  the  units  enter  the  structure,  thus  eliminating 
shrinkage-cracks  in  the  building.  The  disadvantage  of  such  a  system,  however, 
appears  to  lie  in  the  lack  of  sufficient  rigidity  in  tall,  separately-molded  unit  " 
structures.  All  floor-members  must  be  designed  and  cast  as  simple,  non-con- 
tinuous units,  with  the  reinforcement  left  projecting  at  both  ends  to  serve  for 


Reinforccd-Concrete  Construction 


Chap.  24 


Fire-Resistance  of  Rcinforced-Concrete  Construction  955 

tying  the  structure  together.  These  junctures  are  made  after  the  units  are 
hoisted  into  place,  and  supported  by  a  pouring  of  rich  concrete.  For  tall  struc- 
tures it  is  more  feasible  to  erect  a  light  structural-steel  frame  and  employ  the 
precast  floor-units  only.  (See  Chapter  XXITI,  page  854.)  The  saving  in  cost 
is  noted  particularly  in  low  buildings,  and  more  especially  in  one-story  struc- 
tures,* such  buildings  having  been  erected  at  a  saving  of  from  10  to  20%  over 
MONOLITHIC  construction.  Methods  of  interlocking  the  units  and  providing 
satisfactorj''  details  are  constantly  being  improved  and  a  series  of  tests  of  the 
efficiency  of  such  connections  is  being  carried  on  by  the  Unit  Construction 
Company  of  St.  Louis,  Mo.  There  are  under  construction,  or  already  completed, 
many  buildings  of  this  type  installed  by  the  above  company,  including  five-story 
buildings  for  the  National  Lead  Company,  at  St.  Louis,  Mo.,  Kansas  City, 
Mo.,  and  Pittsburgh,  Pa.;  a  three-story  l^uilding  for  the  Ohio  Cultivator  Com- 
pany, at  Belleville,  Ohio;  five  acres  of  car-barns  at  Philadelphia,  Pa.;  and  approx- 
imately thirteen-and-a-half  acres  of  cotton-warehouses  at  Memphis,  Tenn. 
The  Ransome  Engineering  Company  cvf  New  York  City  has  erected  five-story 
and  six-story  buildings  with  its  Unit  system,  in  Boston,  Mass, 

5.  Fire-Resistance  of  Reinforced-Concrete  Construction 

Non-Conductivity  of  Reinforced  Concrete.  Concrete  is  a  poor  conductor 
of  heat,  and  in  this  fact  lies  whatever  virtue  it  has  as  a  fire-proof  material.!  A 
series  of  tests  made  by  Professor  Woolson  of  Columbia  University,  New  York 
City,  and  reported  at  the  1907  meeting  of  the  American  Society  for  Testing  Mate- 
rials, shows  the  following  results:  — | 

(i)  "That  all  concrete  mixtures  when  heated  throughout  to  a  temperature? 
of  I  000°  to  I  500°  F.  will  lose  a  large  proportion  of  their  strength  and  elasticity, 
and  that  this  fact  must  be  well  remembered  in  designing." 

(2)  "That  all  concretes  have  a  very  low  thermal  conductivity,  and  therein 
lies  their  well  known  heat  resisting  properties." 

(3)  "That  as  a  result  of  this  low  thermal  conductivity,  two  to  two  and  one- 
half  inches  of  concrete  covering  will  protect  reinforcing  metal  from  injurious 
heat  for  the  period  of  any  ordinary  conflagration  (provided,  of  course,  that  the 
concrete  stays  in  place  during  the  fire)." 

(4)  "That  reinforcing  metal  exposed  to  the  fire  will  not  convey  by  conduc- 
tivity an  injurious  amount  of  heat  to  the  embedded  portion." 

(5)  "That  the  gravel  concrete  was  not  a  reliable  or  safe  fire-resisting  aggre- 
gate." t 

Loss  of  Strength  of  Reinforced  Concrete.  If  its  non-conductivity  were 
all  that  is  involved  in  the  fire-proof  character  of  concrete,  the  minimum  thick- 
ness required  for  the  protection  of  the  steel  could  be  easily  determined.  But 
the  STRENGTH  of  the  concrete  is  more  or  less  affected  when  exposed  to  extreme 
heat.  An  effort  has  been  made  to  determine  this  effect  and  a  summary  §  of  the 
results  as  reported  by  Professor  Woolson  of  Columbia  University,  New  York 
City,  is  given  in  Tables  XII  and  XIII. 

*  Engineering  Record,  Vol.  60,  page  643;  Engineering  News,  Vol.  58,  page  5;  Pro- 
ceedings National  Association  of  Cement  Users,  1910,  page  391. 

t  It  must  be  remembered  that  in  this  and  succeeding  paragraphs  on  the  fire-resisting 
properties  of  concrete,  only  such  material  as  is  used  in  reinforced  concrete,  is  considered. 
The  value  of  cinder  concrete  as  a  fire-proof  material  is  discussed  in  Chapter  XXIII, 
page  817. 

X  Engineering  News,  Aug.  15,  iQo?,  page  168. 

§  Proc.  Am.  Soc.  for  Test.  Mats.,  Vol.  IV,  page  433- 


956 


Reinforced-Concrete  Construction 


Chap.  24 


Fire  Tests  on  Reinforced  Concrete.  The  effect  of  fire  on  reinforced 
concrete  has  l)een  studied  in  a  number  of  tests  made  by  the  building  authorities 
of  New  York  City  and  Philadelphia,  and  in  some  of  the  conflagrations  in  this 
country,  notably  at  San  Francisco.  The  tests  to  which  the  sample  full-size 
constructions  have  been  subjected  are  similar  to  the  test  described  in  Chapter 
XXIII,  page  827.* 


Table  XII.    Tests  of  Concrete  Blocks  Heated  on  All  Sides  f 

Specimens,  6  by  6  by  14-in  prisms;   proportions  1:2:4 
Age  2  months;  temperature  1500*  F. 


Treatment 

Aggregate 

Limestone 

Trap-rock 

Cinder 

Gravel 

Modulus  of  elasticity, 
At  200  lb  per  sq  in: 

Unheated 

6  000  000 
200  000 

3  430  000 
150  000 
129  000 

4  355  000 
222  CXX) 
188000 

4  355  000 
348000 

3140 

I  400 

997 

I  090  000 
49500 
571000 

960  000 

8000000 

Heated  3  hours 

Heated  5  hours 

At  400  lb  per  sq  in: 

Unheated   

6000  000 
285  000 

6  887  000 

Heated  2  hours 

Heated  5  hours 

At  800  lb  per  sq  in: 

Unheated 

5  647  000 
425  000 

2740 

I  345 

870 

915  000 

6  000  000 

Heated  3  hours . . 

Breaking-load  in  lb  per  sq  in: 

Unheated 

Heated  3  hours 

I  400 
547 
504 

2  780 

Heated  5  hours 

Table  XIII.     Concrete  Blocks  Heated  on  One  Face  Only  t 

Specimens,  6  by  6  by  14-in  prisms;  proportions  1:2:4 
Age  2  Months;    temperature  i  500"  F. 


Treatment 

Aggregate 

Limestone 

Trap-rock 

Modulus  of  elasticity.   (Blocks  heated  5  hrs.) 
At  200  lb  per  sq  in     

293  400 

521  700 

730  700 

I  840 

200000 
268000 
379000 

I  705 

At  400  lb  per  sq  in 

At  800  lb  per  sq  in     .             

Breaking-load  in  lb  per  sq  in 

•  For  a  partial  list  of  thef.e  tests,  see  Table  in  Proc.  Am.  Soc.  for  Test.  Mats.,  Vol.  VI, 
page  128.     Several  tests  have  been  made  since  that  report  was  submitted, 
t  Proc.  Am.  Soc.  for  Test.  Mats.,  Vol.  VI,  page  446. 
I  Proc.  Am.  Soc.  for  Test.  Mats.,  Vol.  VI?  page  448. 


Fire-Resistance  of  Reinforced- Concrete  Construction         057 

The  conclusion,  from  a  study  of  the  tests  in  detail,*  shows  that  to  a  depth 
averaging  about  i  in,  the  concrete  is  seriously  impaired  and  easily  \yashed  off  by  a 
hose-stream  applied  to  the  surface.  Any  stone  containing  an  appreciable  per- 
centage of  carbonate  of  lime  will  calcine  and  may  cause  failure.  Where  the  con- 
struction is  poorly  designed,  allowing  an  excessive  deflection,  the  fine  cracks 
in  the  concrete  below  the  steel  will  open  to  such  an  extent  as  to  permit  the  heat 
to  reach  the  metal  reinforcements.  When  the  reinforcement  is  such  as  to  pro- 
duce a  plane  of  weakness  in  the  concrete  there  is  Hable  to  be  a  flaking  off  of  the 
concrete  and  a  consequent  exposure  of  the  metal. 

Actual  Fire  Tests  of  Reinforced  Concrete.  The  earliest  test  of  a  re- 
inforced-concrete  building  in  an  actual  fire  occurred  in  1902,  in  the  four-story 
factory  of  the  Pacific  Coast  Borax  Company,  at  Bayonne,  N.  J.  The  roof  of 
this  building  was  of  wood,  and  with  the  contents  of  the  building,  was  destroyed 
by  the  fire.  The  only  damage  suffered  was  a  break  in  the  top  floor  caused  by 
the  fall  of  a  heavy  tank  that  had  been  supported  by  the  roof.  At  the  same 
time  an  adjoining  building  constructed  with  unprotected  steel  posts  and  beams 
was  twisted  into  a  tangled  mass  of  metal. 

Tests  in  the  Baltimore  Fire.  In  the  Baltimore  fire  there  was  but  one 
reinforced  -concrete  building  of  the  three  exposed  to  the  fire,  from  which  any  fair 
conclusion  can  be  drawn.  In  one  of  the  buildings,  the  concrete  construction 
was  entirely  destroyed,  but  this  was  probabl^^  due  to  the  falling  walls  and  the 
failure  of  other  non-fire-proof  parts.  In  a  second  building,  the  heavy  rein- 
forced-concrete  floor  of  a  banking-room  came  out  practically  unharmed;  but  it 
was  not  exposed  to  severe  fire.  The  third  structure  was,  however,  exposed  to 
severe  fire.  The  contents  of  the  building  were  destroyed  and  a  large  part  of  the 
outside  brick  walls  fell.  The  floors,  five  in  number,  were  all  of  reinforced  con- 
crete supported  on  concrete  columns,  having  replaced  an  old  wooden-joist  con- 
struction. A  test  made  after  the  fire  showed  that  the  floors  were  still  strong 
enough  to  sustain  the  loads  for  which  they  were  designed,  although  the  floor- 
slabs  were  cracked.  The  girders  were  cracked  longitudinally  near  the  lines  of 
the  reinforcement,  and  the  columns  were  spalled  to  such  an  extent  as  to  expose 
most  of  the  reinforcement.  It  would  have  been  difficult  to  restore  the  building 
so  that  it  would  resist  another  such  attack,  f 

Tests  in  the  San  Francisco  Firfe.  The  effects  of  the  fire  on  concrete 
construction  in  the  conflagration  immediate^''  following  the  San  Francisco  earth- 
quake in  1906  are  summed  up  in  the  following  paragraph  from  the  report  of  a 
committee  of  engineers  that  investigated  the  subject. 

"  Concrete  floors  generally  had  hung  ceilings,  and,  where  thus  protected,  were 
uninjured.  Where  exposed,  the  concrete  is  in  most  cases  destroyed,  for  instance, 
in  the  Sloan,  Rialto,  and  the  Aronson  Buildings,  and  the  Crocker  Warehouse. 
The  concrete  is  dry,  and  while  in  many  cases  hard,  yet  all  the  water  has  been 
burned  out  and  it  may  be  said  to  be  destroj^ed,  even  if  able  to  support  weights. 
Floor-coverings  of  wood  invariably  burned,  adding  to  the  destruction.  Sleepers 
were  generally  burned.  Surfaces  of  cement  mortar  fared  much  better,  the  lino- 
leum covering  remaining  practically  intact." t 

In  discussing  the  report,  Mr.  A.  L.  A.  Himmelwright,  who  made  a  personal 
inspection  of  the  ruins,  concludes  that  reinforced  concrete  is  inferior  as  a  fire- 
resisting  construction  to  any  form  of  steel  construction  with  concrete  floors  and 

*  The  detailed  reports  are  on  file  in  the  Bureau  of  Buildings,  Borough  of  Manhattan, 
New  York. 

t  Captain  Sewell  in  his  report  on  this  building  draws  a  different  conclusion.  See 
Engineering  News,  March  24,  1904,  page  276. 

t  Proc.  Am.  Soc.  C.  E;,  March,  1907,  page  330. 


958  Relnforced-Concrete  Construction  Chap.  24 

concrete  column  and  girder-protection,  but  superior  to  steel  construction  with 
terra-cotta  floor  and  terra-cotta  column  and  girder-protectiort.  "Where  this 
method  was  used,  a  very  slight  attack  of  fire  was  generally  sufficient  to  cause  the 
rupi:ure  of  the  concrete  underneath  the  reinforcing-metal,  so  that  it  fell  away, 
exposing  the  metal.  There  were  comparatively  few  l)uildings,  however,  in  which 
this  method  of  construction  was  used."* 

Thickness  of  Concrete  Required.  From  a  study  of  the  tests  and  fires  just 
referred  to,  the  fair  conclusions  as  to  the  amount  of  protection  against  fire 
would  seem  to  be  as  follows:  (i)  In  all  columns  and  in  large  and  iniix)rtant 
girders,  trusses,  or  other  supports,  at  least  2  in  of  concrete  outside  of  all  reinforce- 
ments; (2)  in  girders  and  beams  and  in  slal)s  of  long  spans,  about  1^  in  of  con- 
crete outside  of  all  reinforcements;  (3)  in  stair-work,  floor-slabs  of  short  span, 
and  walls  and  partitions,  from  54  to  i  in  of  concrete  outside  of  all  reinforcement. 
The  provisions  recommended  in  the  Building  Code  of  the  National  Board  of 
Fire  Underwriters  are  :  "  Steel  reinforcement  shall  have  a  minimum  pro- 
tection of  concrete  on  all  sides  as  follows:  In  columns  and  girders,  2  mches; 
in  beams  and  walls,  iH  in;  and  in  floor  slabs,  i  inch.  The  steel  in  footings  for 
walls  and  columns  shall  have  a  minimum  protection  of  4  inches  of  concrete. 

"The  minimum  thickness  of  concrete  surrounding  and  reinforcing  members 
one-quarter  inch  or  less  in  diameter  shall  be  one  inch;  and  for  members  heavier 
than  one-quarter  ineh  the  minimum  thickness  of  protecting  concrete  shall  be 
four  diameters  taking  that  diameter,  in  the  event  of  bars  of  other  than  circular 
cross-section,  wliich  lies  in  the  direction  in  which  the  thickness  of  the  concrete 
i3  measured;  but  no  protecting  concrete  need  be  more  than  fcur  inches  thick 
for  bars  of  any  size;  and  provided,  further,  that  all  columns  and  girders  of  rein- 
forced concrete  shall  have  at  least  one  inch  of  material  on  all  exposed  surfaces 
over  and  above  that  required  for  structural  purposes;  and  all  beams  and  floor 
slabs  shall  have  at  least  three-quarters  inch  of  such  surplus  material  for  fire-re- 
sisting purposes." 

Other  Forms  of  Protection  for  Reinforced  Concrete.  Because  of  the 
effects  produced  by  fire  on  reinforced  concrete,  as  above  described,  and  the 
difficulty  of  restoring  the  construction  where  so  affected,  various  suggestions 
have  been  made  to  protect  the  concrete  construction  with  other  materials.  On 
account  of  its  excellent  fire-resisting  quahties  (see  page  817),  cinder  concrete 
naturally  suggests  itself.  This  material  is  out  of  the  question  where  strength 
is  required.  But  its  use  may  be  combined  with  that  of  stone  concrete,  by 
placing  a  sufficient  thickness  for  protective  purposes  on  the  outside  of  the  rein- 
forcements in  columns,  below  the  neutral  axis  in  l)eams  and  girders, f  and  on  the 
under  surface  of  floor-.slabs.  Difficulties  are  likely  to  be  encountered;  however, 
in  placing  two  kinds  of  concrete  in  the  same  mold,  but  these  difficulties  are 
not  insurmountable.  Careful  inspection  is  required  to  see  that  the  poorer 
material  is  not  put  in  place  of  the  stronger.  One  kind  of  concrete  should  follow 
the  other  immediately  in  order  to  secure  a  bond  between  the  two.  This  sug- 
gestion, serving  at  the  same  time  another  purpose,  was  satisfactorily  applied  to 
the  column-protection  in  the  Bush  Terminal  Warehouses  in  the  Borough  of 
Brooklyn,  New  York.  The  steel-wire  wrapping  for  the  columns  was  prepared 
in  sections  2  ft  in  height.  Metal  lath  with  about  a  J^-in  mesh  was  placed  outside 
the  wrapping  and  secured  to  it.  This  was  then  placed  in  a  cylindrical  wooden 
mold  2  ft  in  height  and  with  a  diameter  4  in  larger  than  the  wrapping,  thus 
forming  an  inner  side  of  the  mold.  The  space  between  the  wrapping  and  the 
wooden  mold  was  then  filled  with  cinder  concrete.     When  set  and  the  mold 

*  Trans.  Am.  Soc.  C.  E.,  1907,  Vol.  LTX,  page  305. 
t  Trans.  Am.  Soc.  C.  E.,  Vol.  LVI,  page  284. 


Fire-Resistance  of  Reinforccd-Concrctc  Construction         959 

removed,  the  result  was  a  hollow  cylinder  of  cinder  concrete,  2  in  thick  and  2 
ft  high,  with  the  column-wrapping  attached  to  the  inside.  These  cylinders 
were  set  one  over  the  other  in  the  building  till  the  proper  column-height  was 
reached,  such  vertical  rods  as  were  wanted  were  put  in,  and  the  interior  filled 
with  concrete.  Thus  was  produced  a  fire-proof,  wrapped  column,  without 
expense  and  inconvenience  of  any  column-molds  in  the  building. 

A  form  of  fire-protection,  advocated  by  the  National  Fire  Proofing  Company 
of  Pittsburgh,  Pa.,  is  shown  in  Fig.  26.     Here  columns,  beams,  and  girders  are 


Fig.  2G.     Tile  Protection  for  Reinforced  Concrete 

completely  incased  with  hollow-tile  blocks.  Being  either  laid  in  the  molds 
or  forming  them,  their  rough  and  furrowed  porous  surfaces  cause  them  to  adhere 
firmly  to  the  concrete.  They  afford  as  efficient  protection  here  as  they  do  for 
steel  columns,  and  if  destroyed  the  blocks  can  be  replaced. 

Effect  of  Aggregate  on  Fire-Resistance.  Fire  tests  on  full-size  reinforced- 
concrete  columns,  conducted  by  Walter  A.  Hull  at  the  Pittsburgh  laboratories  of 
the  Bureau  of  Standards,  show  that  the  nature  of  the  aggregate  plays  an  impor- 
tant part  in  resistance  to  fire.  Silicious  gravels  appear  to  make  unsatisfactory 
concrete  from  the  standpoint  of  fire-resistance.  Limestone  concretes  are  superior 
to  other  materials  tested,  including  trap-rock  and  blast-furnace  slags.  Coatings 
of  cement  plaster,  i  in  thick,  and  secured  by  a  light,  metal  lath,  protected  the 
columns  so  effectively  that  the  strength,  after  a  four-hour  fire  test,  was  as  much 
as  four  times  that  of  the  unplastered  columns  after  the  test,  and  about  90%  of 
that  of  the  column  which  had  not  been  subjected  to  fire.  Other  forms  of  pro- 
tective coverings  investigated  and  proved  effective,  were  a  roofing-material  of 
Portland  cement,  sand,  and  asbestos,  and  cylindrical  forms  of  cast  gypsum,  3  in 
thick,  made  and  applied  in  a  manner  similar  to  those  of  cinder  concrete  described 
on  page  958. 

The  unsuitability  of  gravel  concrete  as  fire-proof  construction,  was  pointed  out  • 
by  Ira  H.  Woolson  as  early  as  1907*  and  appears  to  have  been  later  confirmed 

*  Proc.  Am.  Soc.  for  Test.  Mats.,  1907. 


960  Reinforced-Concrete  Construction  Chap.  24 

by  an  actual  fire  in  a  reinforced-concrete  warehouse  at  Far  Rockaway,  N.  Y.,  in 
1916.  From  this  the  conclusion  was  drawn  that  "all  concrete  specifications 
should  contain  a  definite  warning  against  the  use  of  quartz  gravel  in  concrete 
liable  to  be  exposed  to  high  heat."* 

6.  Protection  Against  Corrosion  in  Reinforced-Concrete  Construction. 

Thickness  of  Reinforced  Concrete.  The  thickni:ss  of  concrete  required 
for  protection  against  fire  has  been  found  to  be  also  ample  for  protection  against 
CORROSION.  It  is  well  established  that  steel  embedded  in  neat  cement  will  not 
corrode.  C.  L.  Norton  of  the  Massachusetts  Institute  of  Technology,  Boston, 
Mass.,  draws  the  following  conclusions  from  a  series  of  experiments  made  in 
1902  and   1903.1 

(i)  Steel  embedded  in  neat  cement  is  secure  against  corrosion; 

(2)  Steel  embedded  in  a  dense   concrete  mixture  is  safe  against  corrosion; 

(3)  To  assure  a  thorough  coating  of  the  steel  the  concrete  should  be  mixed  wet; 

(4)  Porous  concrete  allows  the  admission  of  moisture  and  will  not  protect  the 
steel  thoroughly; 

(5)  A  coating  of  rust  is  not  a  protection  against  further  corrosion,  as  has  been 
sometimes  claimed. 

In  these  experiments  the  steel  was  incased  in  concrete  i?/^  in  thick  on  all  sides. 
From  this  it  would  appear  that 

(6)  The  steel  of  reinforced  concrete  is  secure  against  corrosion,  provided  it  is 
thoroughly  embedded  in  concrete,  and 

(7)  A  slight  coating  of  rust  on  the  steel,  where  embedded,  does  no  harm, 
as  the  cement  is  strongly  alkaline  and  will  counteract  the  acidity  of  the  iron 
oxide  and  prevent  further  corrosion. 

"In  practical  deygn  the  most  important  question  which  arises  is  how  far 
a  concrete  may  be  cracked  (due  to  bending  of  beams)  without  exposing  the  steel 
to  corrosive  influences.  In  this  respect  it  seems  to  the  writer  that  the  minute 
cracks  which  appear  in  the  early  states  of  the  tests  can  have  very  little  in- 
fluence." t  This  means  that  within  the  safe  working  limits,  there  is  no  danger 
from  corrosion  on  account  of  the  fine  cracks  due  to  tension  in  beams  and  girders. 

Corrosion  of  Steel  in  Cinder  Concrete.  Cases  are  on  record  of  serious 
CORROSION  OF  STEEL  embedded  in  cint)er  concrete.  In  a  report  to  the  Struc- 
tural Association  of  San  Francisco,  Cal.,§  the  committee  investigating  the  sub- 
ject states  that  in  cinder  concrete  "the  extent  of  the  corrosion  is  great  enough 
to  seriously  endanger  the  safety  of  the  floors,  and  it  is  not  probable  that  the 
floors  would  have  supported  their  loads  more  than  one  to  three  years  longer." 
The  committee  recommended  "that  the  Structural  Association  try  to  amend 
the  present  building  law  so  as  to  exclude  the  use  of  cinder  concrete  in  floor- 
slabs  or  for  fireproofing." 

Mr.  William  H.  Fox  in  his  investigations  |I  on  this  same  subject  finds  that 
'*  after  about  forty  days'  treatment,  the  specimens  were  broken,  and  the  steel 
carefully  examined  for  corrosion.  With  but  one  exception,  one  or  more  of  the 
three   steel  pieces  in  each  specimen  showed  unmistakable  signs  of  corrosion. 

*  Report  to  National  Board  of  Fire  Underwriters,  on  the  fire  in  question, 
t  Reports  Nos.  4  and  9,  Insurance  Experiment  Station  of  the  Boston  Manufacturers 
Mutual  Tire  Insurance  Company. 

X  Professor  Turneaure  in  Trans.  Am.  Soc.  for  Test.  Mats.,  Vol.  IV,  page  505. 
§  Engineering  News,  Nov.  i,  1906,  page  458. 
!i  Engineering  News,  May  23,  1907,  page  569. 


Protection  Against  Coirosion  in  Rein  forced-Concrete  Construction  961 

Apparently  it  made  no  difTerence  how  the  concrete  was  mixed,  wet  or  dry,  tamped 
or  imlamped,  whether  the  steam  or  water  treatment  was  used,  the  result  was 
the  same,  rust  streaks  and  spots  were  found;  the  difference  in  the  amount  of 
corrosion  being  imperceptible."  He  concludes  that  "to  secure  a  dense  homo- 
geneous cinder  concrete,  a  thorough  tamping  is  necessary.  A  rich  mixture, 
either  1:1:3  or  one  in  which  the  proportion  of  cement  to  aggregate  is  larger, 
should  be  used  in  all  cases.  The  greatest  of  care  should  be  taken  in  mixing  the 
materials,  and  it  may  be  necessary  to  resort  to  the  seemingly  imj^ractical  method 
of  coating  the  reinforcement  with  grout  before  placing  in  the  concrete." 

In  a  series  of  chemical  and  physical  tests,*  made  by  George  Borrowman  of 
the  University  of  Nebraska,  it  was  found  that  disintegration  of  cinder  concrete 
was  caused  by  the  oxidation  of  iron  and  sulphur  producing  internal  stresses 
and  consequent  cracking  with  occasional  efflorescence  of  ferrous  sulphate  on  the 
surface.  From  these  tests,  it  was  concluded  that  cinders  with  much  sulphide 
and  sulphate  sulphur  are  likely  to  give  unsatisfactory  results,  especially  if  there 
is  much  coke  or  porous  material  present;  also  that  such  material  (cinders)  may 
be  improved  if  allowed  to  weather  with  occasional  washing,  until  the  ferrous 
iron  and  sulphur  have  been  washed  and  leached  out  of  the  cinders.  The 
cinders  used  in  these  tests  were  from  carefully  screened  steam  coal  and  slack. 
The  analysis  showed  considerable  ferrous  iron  and  sulphur  as  sulphide  and  sul- 
phate. 

On  the  question  of  the  corrosion  of  steel  in  cinder  concrete  Professor 
Norton  concludes:  "There  is  one  limitation  to  the  whole  question,  that  is,  the 
possibility  of  getting  the  steel  properly  incased  in  concrete.  Many  engineers 
will  have  nothing  to  do  with  concrete  because  of  the  difficulty  in  getting  'sound' 
work.  This  is  especially  true  of  cinder  concrete,  where  the  porous  nature  of 
the  cinders  has  led  to  much  dry  concrete  and  manj^  voids,  and  much  corrosion. 
I  feel  that  nothing  in  this  whole  subject  has  been  more  misunderstood  than 
the  action  of  cinder  concrete.  We  usially  hear  that  it  contains  much  sulphur 
and  this  causes  corrosion.  Sulphur  might,  if  present,  were  it  not  for  the  presence 
of  the  strongly  alkahne  cement;  but  with  that  present  the  corrosion  of  steel 
by  the  sulphur  of  cinders  in  a  sound  Portland  concrete  is  the  veriest  myth,  and 
as  a  matter  of  fact  the  ordinary  cinders,  classed  as  steam  cinders,  contain  only  a 
very  small  amount  of  sulphur.  There  can  be  no  question  that  cinder  concrete 
has  rusted  great  quantities  of  steel,  but  not  because  of  its  sulphur,  but  because 
it  was  mixed  too  dry,  through  the  action  of  the  cinders  in  absorbing  moisture, 
and  that  it  contained,  therefore,  voids;  and  secondly,  because  in  addition  the 
cinders  often  contain  oxide  of  iron  which,  when  not  coated  over  with  the  cement 
by  thorough  wet  mixing,  causes  the  rusting  of  any  steel  which  it  touches.  There 
is  one  cure  and  only  one,  mix  wet  and  mix  well.  With  this  precaution  I  would 
trust  cinder  concrete  quite  as  quickly  as  stone  concrete  in  the  matter  of  cor- 
rosion."! 

In  1902  the  Pabst  Building  in  New  York  City,  an  eight-story  steel  skeleton 
construclioi,  was  taken  down  after  standing  for  about  four  yeirs.  The  floor- 
filling  betwji  n  the  steel  I  beams  in  this  case  consisted  of  cinder  concrete  on 
metal  lath,  built  in  segmental  form.t  The  steelwork  generally  was  found  to  be 
free  from  rust,  though  it  should  be  remembered  that  all  the  steel  had  been 
painted. §     Taking  all  things  into  consideration  it  is  probably  safe  to  use  cinder 

♦Journal  of  Industrial  and  Enpineerinp;  Chemistry,  June,  1912. 

t  Report  No.  9,  Insurance  Experiment  Station,  Boston  Manufacturers  Mutual  Firo 
Insurance  Company. 

J  Roeblinc;  system,  now  obsolete. 

§  Trans.  Am.  Soc.  C  E.,  Vol,  L.  page  297. 


962  Reinforced-Concretc  Construction  Chap.  24 

concrete,  if  care  is  taken  to  provide  a  proper  mixture  and  careful  and  thorough 
workmanship. 


7.  Erection  of  Reinforced-Concrete  Construction 

Forms  for  Reinforced  Concrete.  For  the  erection  of  reinforced  concrete, 
it  is  generally  necessary,  first,  to  construct  molds  or  centerings  for  the  col- 
umns, floors,  etc.  Wood  is  the  material  used  for  this  purpose.  Sheet-metal 
centering  has  been  used  with  questionable  success  and  economy.  In  the  selec- 
tion of  the  wood  for  the  molds  a  clean  grade  of  dressed  pine  should  be  used. 
It  should  be  thick  enough  to  resist  warping  and  to  resist  deflection  between  sup- 
ports.   It  must  be  coated  on  its  surface  with  soap  or  some  other  satisfactory 


Fig.  27.    Wooden  Form  for  Reinforced-concrete  Column 

substance  to  prevent  it  from  sticking  to  the  concrete.  The  forms  or  molds  must 
be  erected  carefully,  the  exact  size  of  the  proposed  parts,  and  must  be  true  in 
position  and  direction.  For  floor-molds,  sufficient  supports  must  be  provided, 
not  only  to  carry  safely  the  heavy  wet  concrete,  but  also  such  materials  as  are 
liable  to  be  placed  on  the  floors  up  to  the  time  when  the  concrete  has  set  suflEi- 
ciently  to  carry  such  loads.  The  supports  must  have  sufficient  rigidity  to  prevent 
deflection  in  the  molds.  The  molds  should  be  so  constructed  that  they  can 
])e  easily  removed  when  the  concrete  has  set.  Sharp  corners  should  be  avoided 
as  much  as  possible,  as  the  wood  is  Hable  to  stick  in  them.  Where  there  are 
reentrant  angles  in  the  finished  concrete-work,  the  molds  should  have  beveled 
edges,  and  at  salient  edges  of  the  finished  concrete-work,  triangular  strips  should 
be  nailed  in  the  corners  of  the  molds  to  produce  a  beveled  edge  in  the  concrete. 


Erection  of  Reinforced-Concrete  Construction  963 

To  prevent  the  spreading  of  the  sides  of  the  molds,  cleats  must  be  provided  at 
sufficient  intervals.  In  the  case  of  beams  and  girders,  these  are  gen- 
erally secured  by  nailing.  In  the  case  of  columns  and  piers  and  often  in  walls, 
the  cleats  are  so  notched  at  the  ends  that  long  bolts  *  with  washers  may  be 
used  to  hold  them  in  place,  as  shown  m  Fig.  27.  In  removing  the  form  the  bolts 
are  loosened  and  the  cleats  and  the  rest  of  the  form  are  ready  to  use  again.  In 
some  cases,  particularly  in  the  construction  of  walls,  the  cleats  are  held  in  place 
by  wires  running  through  the  mold.  These  wires  become  embedded  in  the 
concrete  and  in  removing  the  molds  they  are  cut  and  the  portions  iji  the  con- 
crete are  allowed  to  remain.  The  items  of  molds  and  centerings  needed  in  the 
erection  of  reinforced-concrete  buildings  form  a  considerable  part  of  the  cost  of 
construction.  Economy  in  this  respect  can  l^e  affected  in  designing  and  planning 
by  making  the  floor-panels  throughout  a  building  uniform  in  size  and  by  repeat- 
ing, as  far  as  possible,  such  parts  as  piers,  walls,  etc.  Successful  attempts  have 
been  made  to  dispense  with  the  erection  of  timber  molds  and  centering  by  casting 
the  various  members  of  the  construction  on  the  ground  and  assembling  and 
erecting  them  in  the  same  way  that  wood  or  steel  columns,  beams,  and  floors  are 
assembled  and  erected.     (See  page  953.) 

Concrete  Mixing.  In  all  reinforced-concrete  work  the  concrete  should  be 
MIXED  MPXHANICALLY.  Satisfactory^  hand-mixing  can  be  obtained  and  might  be 
resorted  to  in,  very  small  jobs,  where  it  would  be  uneconomical  to  set  up  a 
MACHINE-MIXER.  But  a  much  more  uniform  product  will  result  from  machine- 
mixing,  and  most  types  of  mixers  are  mounted  on  wheels  so  as  to  be  easily  moved 
to  a  job.  IVIechanical  mixers  are  either  continuous  mixers  or  batch-mixers. 
In  the  continuous  mixers  the  materials  are  fed  sometimes  by  hand  and  sometimes 
mechanically,  and  the  concrete  issues  continuously.  The  product,  however,  is 
not  Ukely  to  be  as  uniform  as  that  from  the  batch-mixer;  for  when  the  latter 
is  used  it  is  under  constant  supervision,  whereas  when  the  continuous  mixer  is 
used  the  machine  is  relied  upon.  Of  the  batch-mixers  the  rotary  type  is  the 
one  giving  most  general  satisfaction.  Among  the  efficient  examples  of  this 
type  may  be  mentioned  the  mixers  made  by  the  Ransome  Concrete  Machinery 
Company,  New  York  City,  and  the  T.  L.  Smith  Company,  Chicago,  III.  They 
are  made  in  different  sizes  and  with  capacities  varying  from  about  10  to  60  cu  yd 
per  hour. 

Charging  Concrete-Mixers.  In  charging  a  concrete-mixer  the  materials 
for  each  batch,  carefully  measured,  are  dumped  into  the  mixer  and  the  machinery 
started.  After  completing  a  definite  number  of  revolutions,  sufficient  to  thor- 
oughly mix  the  ingredients,  the  concrete  is  discharged  into  wheelbarrows  or 
other  implements  for  carrying  it  to  the  molds.  Each  batch  should  be  completed 
before  another  is  started.  To  obtain  uniform  results  the  number  of  revolutions 
in  each  operation  should  be  the  same.  It  is  not  well  to  trust  to  the  judgment  of 
the  man  in  charge  of  the  machine,  as  to  when  the  mixing  has  been  thorough. 
He  should  be  instructed  to  count  the  revolutions  each  time.  A  good  plan  is  to 
attach  a  gong  which  rings  when  the  fixed  number  of  revolutions  has  been  com- 
pleted. The  Code  of  the  National  Board  of  Fire  Underwriters  cafls  for  "at 
least  20  revolutions,"  and  the  "speed  of  the  mixer  shah  not  exceed  20  revolutions 
per  mmute." 

Wet  Concrete  Mixture.  The  water  is  introduced  during  the  process  of 
mixing.  The  amount,  also  measured,  should  be  such  as  to  produce  what  is 
known  as  a  wet  mixture,  that  is,  a  mixture  that  has  the  consistency  of  molasses 
and  that  will  readily  flow  around  and  thoroughly  incase  all  steel  to  be  embedded. 
It  may  be  necessary  to  vary  the  amount  of  water  somewhat  in  placing  a  large 
mass  of  concrete,  as  in  walls,  since  the  water  generally  works  itself  upward 


064  Reinforced-Coiicrete  Construction  Chap.  24 

through  the  successive  layers.  For  transporting  the  concrete  from  the 
mixer  to  the  mold,  steel  wheelbarrows,  each  holding  about  2  cu  ft,  are  generally 
employed.  A  larger  vehicle,  holding  about  6  cu  ft,  is  made  by  the  Ransome 
Concrete  Machinery  Company,  Dunellen,  N.  J.,  and  is  found  very  economical 
in  larger  work.  When  the  conditions  will  permit,  concrete  may  also  be  distrib- 
uted by  means  of  chutes,  but  care  must  be  exercised  to  secure  a  consistency, 
that  will  prevent  the  separation  of  the  coarse  aggregate  from  the  mortar.  The 
transporting  through  the  chutes  may  be  done  either  by  gravity  or  by  com- 
pressed air.  Tests  have  shown  that  an  excess  of  water  tends  to  decrease  the 
strength  of  concrete,  so  that  care  must  be  taken  not  to  use  more  water  than  is 
necessary  to  place  the  concrete  properly. 

Pouring  the  Concrete.  Ideal  conditions  would  obtain  if  the  process  of 
PLACING  CONCRETE  could  be  CONTINUOUS.  This  is  not  generally  practicable; 
so  it  is  important  that  the  point  at  which  work  is  stopped  each  day  shall  be  so 
selected  and  predetermined  that  the  strength  of  the  construction  shall  suffer 
least.  In  smaller  buildings,  with  floor-areas  not  exceeding  about  3  000  sq  ft,  it 
should  be  possible  to  so  arrange  the  progress  of  the  work  that  each  entire  floor- 
construction  may  be  placed  in  one  day.  In  larger  work  it  is  necessary  to  lay 
off  a  certain  area  to  be  completed  within  the  time  of  concreting  for  the  day. 
Work  should  not  leave  off  across  important  beams  or  girders,  and  the  tempo- 
rary stopping  should  be  arranged  for  when  the  work  is  at  the  middle  of  slabs 
or  minor  floor-beams.  If  any  parts  of  floor-slabs  are  considered  in  the  calcula- 
tions for  the  strength  of  the  beams  or  girders,  such  parts  must  be  concreted 
at  the  same  time  and  must  be  considered  parts  of  such  beams  or  girders. 
Joints  in  columns  should  be  made  perpendicular  to  the  axes  of  the  columns, 
and,  as  far  as  possible,  at  the  lower  side  of  girders.  Columns  should  be  .allowed 
to  set  for  at  least  two  hours  before  girders  are  cast  on  them,  in  order  to  provide 
for  settlement  and  shrinkage. 

Ramming  the  Concrete.  As  soon  as  the  concrete  has  been  poured  into  the 
molds,  and  during  the  process  of  pouring,  it  should  be  continually  rammed  to 
secure  complete  filling  of  the  molds,  density  in  the  finished  product,  and  thor- 
ough adhesion  to  the  reinforcement.  In  wet  concrete,  such  as  is  used  for  build- 
ings, this  ramming  should  be  done  with  a  flat  steel  spatula  at  the  end  of  a  handle 
long  enough  for  comfortable  manipulation.  For  column-work  the  handle  is 
lengthened  out  so  as  to  reach  to  the  bottom  of  the  forms.  Ordinary  spades 
are  sometimes  employed,  and  where  no  special  tools  are  provided,  rammers  are 
sometimes  made  of  2  by  3-in  scanthngs,  rounded  off  at  the  top  end  to  make 
a  handle.  Where  a  smooth  surface  is  de.sired  the  spatula  rammer  should  be 
used,  particularly  at  the  sides  of  the  molds.  The  honeycombed  appearance 
that  results  from  improper  ramming  is  difficult  to  remedy  afterward  without  a 
surface  of  patches.  After  having  been  placed,  the  concrete  should  be  kept 
damp  by  sprinkling  it  with  a  hose  until  it  has  thoroughly  hardened.  The  tap- 
ping of  the  forms  with  a  hammer  while  the  concrete  is  still  plastic  and  before  it 
has  begun  to  set  will  cause  it  to  flow  more  freely  into  place  in  intricate  forms  and 
around  reinforcing-bars,  especially  when  a  dryer  concrete,  recommended  by 
recent  investigators,  is  used.  Tapping  after  it  has  started  to  set,  however,  tends 
to  weaken  the  concrete.* 

Removing  the  Forms  from  Reinforced  Concrete.  No  fixed  rule  can  be 
given  for  the  remoxal  of  the  forms,  as  the  time  required  for  the  setting  of 
concrete  varies  with  the  consistency  of  the  mixture,  and  the  climatic  and  other 

y:-^SiBe  "Effect  of  Vibrations,  etc.,"  by  Duff  A.  Abrams,  Proc.  Am.  Concrete  Inst. 
Vol.  XV,  1919- 


Erection  of  Reinforced-Concrete  Construction  965 

conditions.  Numerous  failures  of  reinforced  concrete  have  been  attributed  to 
the  too  early  removal  of  forms.  In  warm  weather  concrete  will  set  more  quickly 
than  in  cold.  The  setting  process  may  be  somewhat  accelerated  after  a  day  or 
two,  by  removing  the  boards  forming  the  sides  of  beams  or  girders  and  leaving 
in  the  planks  on  the  underside  and  the  props  supporting  them. '  In  cold  weather 
it  is  advisable  to  warm  the  building  during  the  setting  process  by  means  of 
salamanders. 

The  Finish  of  Concrete  Surfaces.  The  faposed  surfaces  of  concrete 
walls  are  variously  treated  in  attempts  to  produce  a  satisfactory  appearance. 
Where  no  special  provision  is  made,  the  marks  of  the  lumber  used  in  the  forms 
are  almost  certain  to  show,  and  the  lines  of  demarcation  between  successive 
layers  are  clearly  defined.  To  eliminate  these  lines,  grooves  are  sometimes 
purposely  formed,  by  tacking  on  the  sides  of  the  molds  triangular  or  trapezoidal 
strips  that  produce  sunk  joints  in  the  wall,  and  give  it  an  ap])earance  resembling 
dressed  stone.  The  successive  layers  of  concrete  arc  in  such  cases  stopped  at 
these  hues  so  that  the  junction  of  the  two  layers  is  hidden.  In  some  cases 
the  surface  is  purposely  left  rough  and  scratched  like  the  scratch-coat  in  plaster- 
ing, and  then  stuccoed  with  a  neat  cement  or  a  rich  cement  mortar.  In  this 
form  of  finish  there  is  always  some  danger  that  the  stucco  will  flake  off.  The 
surface,  as  it  comes  from  the  mold,  is  sometimes  hammer-dressed,  or  rather 
picked  with  a  special  hammer.  This  hammer  has  an  edge  at  right-angles  to 
the  handle,  and  the  edge  is  indented  and  made  a  series  of  points.  A  roughened 
face  is  thus  produced  which  in  time  shows  a  uniform  texture.  Another  method 
is  to  remove  the  forms  as  soon  as  the  concrete  is  sufficiently  hard  and  to  rub  the 
surface  with  a  plasterer's  float  or  a  block  of  carborundum,  concrete,  or  stone, 
using  a  thin  grout  or  fine  sand  with  plenty  of  water  between  the  float  and  the 
wall-surface.  Brushing,  also,  may  be  resorted  to,  consisting  in  scrubbing  the 
surface,  while  still  green,  with  a  wire  brush,  and  a  mixture  of  one  part  of  hydro- 
chloric acid  to  six  parts  of  water.  A  similar  finish  may  be  obtained  by  sand- 
blasting after  the  concrete  has  thoroughly  hardened. 

The  Finish  of  Reinforced-Concrete  Floors.  If  the  floor-stirfaces  are 
not  to  be  covered  with  a  wooden  flooring,  a  satisfactory  finish  may  be  obtained 
by  placing  over  the  surface,  before  the  concrete  has  had  time  to  set  thoroughly, 
a  mortar  finish  from  i  to  iH  in  thick,  and  troweling  to  make  it  smooth  and 
level.  If  the  finish  is  attempted  after  the  concrete  has  set,  the  new  and  the  old 
work  will  probably  not  bond;  and  there  is  always  danger  of  flaking  off  unless  the 
finish  itself  is  of  considerable  thickness. 

Bonding  Old  and  New  Concrete.  Various  fluids  and  special  cementitious 
materials  have  been  put  on  the  market  for  the  purpose  of  bonding  new  and  old 
CONCRETE  SURFACES.  Whether  or  not  these  materials  have  any  special  merits, 
it  is  now  generally  accepted  that  a  good  rich  cement  mortar  will  form  sufficient 
bond  between  two  concrete  surfaces,  providing  the  surfaces  are  clean.  If  the 
stress  is  compressive,  the  old  surface  of  the  concrete  should  be  cleaned  and 
wet,  and  the  surface  may  be  roughened.  Joints  y^hich  are  subject  to  tension 
should  be  coated  with  a  i  :  i3^^  or  a  i  :  2  cement  mortar  before  the  new  concrete 
is  cast.  In  building  walls  which  must  be  water-tight,  the  structure  should  be 
made  monolithic  And  if  it  cannot,  all  dirt  and  laitance  should  be  removed, 
and  a  thin  layer  of  very  rich  mortar  placed. 

Inspection  of  Reinforced-Concrete  Work.  In  all  reinforced-concrete  work 
it  is  of  extreme  importance  to  have  competent  and  thorough  inspection  or 
SUPERINTENDENCE.  The  iuspcctor  should  be  familiar  with  the  nature  and  qual- 
ities of  the  different  materials  entering  into  the  construction.    He  should  have 


9G6  Reinforced-Concrete  Construction  Chap.  24 

a  knowledge  of  the  underlying  principles  of  the  design  of  reinforced-concrete 
structures,  so  that  he  may  reaUze  the  importance  of  carrjdng  out  all  the  details, 
and  particularly  of  placing  the  reinforcement  exactly  as  planned.  He  must  be 
sufficiently  alert  and  active  to  see  that  the  work  of  the  contractor  is  progressing 
properly;  so  that,  for  instance,  work  shall  not  have  to  be  rebuilt  because  of  error 
in  the  forms.  The  materials  used  in  the  construction,  particularly  the  cement, 
should  be  tested  as  the  work  progresses.  Cubes  of  the  concrete  as  used  should 
be  made  up  each  day  and  at  the  end  of  seven  days  should  be  tested  for  com- 
pression, and  if  necessary  again  at  the  age  of  twenty  eight  days.  This  record 
will  serve  as  a  guide  in  the  acceptance  of  the  work,  or  in  deciding  on  the  neces- 
sity for  a  load  test  of  the  finished  structure.  Under  no  circumstances,  however, 
should  it  replace  or  serve  as  an  excuse  to  omit  the  testing  of  the  cement  upon 
delivery  or  before  acceptance.  In  addition  to  the  details  discussed  in  this 
chapter,  details  which  require  the  attention  of  the  inspector  on  the  work,  a  few 
others  may  be  especially  mentioned  here: 

(i)  In  JOINING  NEW  WORK  with  that  which  is  already  in,  and  wliich  has  begun 
to  set,  the  surface  must  be  thoroughly  cleaned  and  wet.  In  stopping  off  work,  it 
is  good  practice  where  possible,  to  cast  a  groove  in  a  surface  that  is  to  be  joined 
with  another,  so  that  when  the  work  is  afterward  continued,  a  tongue-and- 
groove  junction  is  effected. 

(2)  All  FORMS  or  MOLDS  must  be  carefully  cleaned  out  just  before  the  concrete 
is  poured.  The  bottoms  of  the  column-molds  must  be  especially  watched  for 
this,  as  shavings,  sawdust,  and  even  blocks  of  wood  are  liable  to  fall  into  them 
unobserved.  It  is  well  to  leave  off  a  small  piece  of  one  side  of  the  column-mold 
at  the  bottom,  for  purposes  of  observation  and  cleaning,  and  to  close  it  up  just 
before  pouring  the  concrete. 

(3)  Great  care  should  be  excerised  in  pouring  and  ramming  concrete  in  deep 
molds,  such  as  for  columns,  walls,  etc.,  in  order  to  get  the  molds  thoroughly 
filled  at  the  bottom.  In  careless  work  it  is  not  unusual  to  find  in  such  places 
very  porous  concrete,  if  not  large  pockets.  This  is  particularly  liable  to  occur 
when  there  is  considerable  rcinforcing-stecl  in  the  construction. 

(4)  It  should  be  remembered  that  concrete  shrinks  in  setting.  Hollow  spaces 
at  the  tops  of  columns  are  sometimes  found  to  be  due  to  this  cause.  As  these 
are  not  always  observable  from  the  outside  after  the  forms  are  removed,  great 
care  should  be  exercised  to  guard  against  them.  In  pouring,  therefore,  the 
molds  should  be  filled  to  overflowing  to  the  top  of  deep  molds. 

(5)  The  exact  position  of  the  rein  forcing-steel  in  the  concrete  is  of  such  vital 
importance  that  particular  mention  is  again  made  of  it  here.  In  loose-bar  con- 
struction the  greatest  care  must  be  exercised,  in  the  first  place,  to  have  the  rein- 
forcement carefully  placed,  and  then  to  avoid  its  being  shifted  out  of  position 
by  the  pouring  and  the  ramming  of  the  concrete. 

(6)  The  REiNFORCiNG-STEEL  of  thosc  systems  in  which  the  advantage  of  at- 
tached stirrups  is  claimed,  is  often,  for  convenience  in  shipping,  sent  with  the 
stirrups  laid  flat  or  close  to  the  main  bar.  It  Is  intended  that  in  placing 
them  on  the  job  the  stirrups  shall  be  turned  up  to  their  proper  positions.  Unless 
carefully  inspected,  this  is  liable  to  be  neglected. 

(7)  The  use  of  a  unit  type  of  construction  (see  page  922)  practically  obviates 
these  two  last-mentioned  dangers,  as  the  enlire  reinforcement  comes  framed  to- 
gether, so  that  the  relative  positions  of  reinforcing-rods  or  bars  cannot  be  changed; 
and  a  glance  will  show  whether  the  fkame  is  complete  or  has  been  damaged,  and, 
when  placed  in  the  molds,  whether  it  fits  or  not.  In  this  type  of  construction 
the  parts  are  all  assembled  in  the  shop  from  details  carefully  drawn  and  checked, 
in  much  the  same  wcty  that  steel  beams,  girders,  columns,  etc.,  are  fabricated  from 


Erection  of  Reinforced-Concrete  Construction  907 

detailed  shop  drawings.  The  work  of  the  inspector  or  superintendent  on  the  job 
is  very  much  simplified,  and  hence  the  liability  of  error  reduced  to  a  minimum. 
Load  Tests  on  Reinforced-Concrete  Construction.  Load  tests  on  the 
finished  structure  should  only  be  resorted  to  when,  all  reasonable  care  having 
been  exercised  to  obtain  good  results,  some  doubt  still  exists  as  to  the  results. 
Such  tests,  however,  should  not  be  accepted  in  place  of  a  strict  compliance  with 
the  specifications.  The  architect  should  know  beforehand  that  his  building  is 
correctly  designed  and  safe,  and  should  empk>y,  if  necessary,  an  engineer.  The 
contractor  should  understand  at  the  outset  that  the  structure  has  been  designed 
for  certain  definite  purposes  and  loads,  and  that  the  materials  and  details  of 
construction  specified  are  not  to  be  changed.  If  the  contractor  furnishes  the 
design,  as  he  sometimes  does,  a  practice  thoroughly  condemned,  the  architect 
should  prescribe  in  his  specifications  that  such  design  shall  be  checked  and 
approved  by  an  engineer  appointed  by  him.  A  fair  load  to  be  applied  in  a  test  is 
one  half  the  weight  of  the  construction  plus  one-and-one-half  times  the  working 
live  load.  The  stresses  in  the  construction  are  then  equal  to  one-and-one-half 
times  the  working  stresses  assumed  in  designing.  Under  these  conditions  there 
should  not  be  any  evidences  of  distress,  and  the  deflections  should  not  exceed 
Hfio  the  span.  The  material  used  for  the  load  test  should  he  so  selected  and 
placed  that,  when  uniformly  distributed,  as  required,  it  will  not  arch  and  assist 
the  compressive  strength  of  the  beam  or  floor.  Pig  iron  is  a  very  good  material 
to  use.  Bricks  are  more  generally  available,  but  must  often  be  piled  very  high 
to  get  the  required  load,  consuming  much  time  and  labor  in  making  the  test. 
When  bricks  are  used  they  should  be  set  in  vertical  piles  with  spaces  of  2  or  3  in 
between  them,  thus  avoiding  all  arching  of  the  load. 


968      Reinforced-Concrete  Factory  and  Mill-Construction     Chap.  25 


CHAPTER  XXV 

REINFORCED-CONCRETE  FACTORY  AND   MILL- 
CONSTRUCTION  * 

I  Bv      -      -/ 

EMILE   G.   PERROT 

MEMBER  OF  AMERICAN  SOCIETY  OF  CIVIL  ENGINEERS 

General  Principles.  The  problem  involved  in  the  proper  design  of  a  rein- 
forced-concrete  factory  or  mill  is  a  far  more  difficult  one  than  might  appear 
from  a  superficial  examination  of  the  finished  structure.  This  applies  to  build- 
ings constructed  wholly  or  in  part  of  reinforced  concrete,  and  is  due  to  the  fact 
that  maximum  economy  and  efficiency  in  production  can  only  be  obtained 
when  the  building  is  thoroughly  adapted  to  a  given  occupancy  and  use.  Laymen, 
and  even  some  architects,  look  upon  the  factory  as  a  mere  workshop,  consisting 
of  four  walls  with  floors  and  roof.  To  them  it  seems  an  easy  matter  to  locate 
the  structure  with  reference  to  the  lot  or  site  and  then  supply  it  with  stairways, 
elevators  and  kindred  features.  This,  however,  is  not  the  case.  Each  industry 
uses  processes  pecuHar  to  itself.  The  ease  with  which  these  processes  can  be 
employed  renders  the  profit-making  more  or  less  successful;  hence  it  is  neces- 
sary to  design  the  building  to  suit  them.  However,  as  the  purpose  here  is  to 
explain  what  constitutes  proper  design,  as  appHed  to  the  reinforced-concrete 
construction  of  a  factory  or  mill-building,  a  typical  case  will  serve  to  make  clear 
the  principles  involved.  This  chapter,  therefore,  deals  with  such  general  types 
as  would  seem  to  meet  the  needs  of  the  greatest  number  of  persons. 

Walls,  Floors  and  Roofs.  Reinforced-concrete  construction  may  be  used 
for  walls  and  floors,  or  for  floors  and  roofs  only,  in  the  latter  case  substituting 
for  reinforced-concrete  walls  some  masonry  construction  such  as  brick  or  stone. 
It  is  not  always  advisable  to  use  reinforced  concrete  for  walls.  Circumstances 
very  frequently  arise  in  which  it  is  more  suitable  and  economical  to  use  brick 
walls  or  piers. 

Types  of  Floor-Construction.  The  floor-construction  may  be  divided 
into  two  general  types,  the  beam-and-slab  type  and  the  girderless  type. 
The  beam-and-slab  type  may  in  turn  be  divided  into  varieties.  For  example,  it 
may  consist  of  beams  supported  by  columns,  with  slabs  spanning  from  beam  to 
beam.  This  arrangement  corresponds  to  simple  mill-construction  in  wood,  where 
the  heavy  timbers  run  across  the  building  every  8  or  lo  ft.  The  timbers  rest 
on  the  wall  at  one  end  and  on  a  post  at  the  other,  with  3  or  4-in  splined  planks 
spanning  from  beam  to  beam.  The  earlier  types  of  reinforced-concrete  floors 
were  patterned  after  this  system.  The  next  method  was  the  introduction  of 
girders  running  from  column  to  column,  and  the  placing  of  the  columns  farther 
apart,  say  twice  the  distance  common  to  the  former  system.  The  beams  are 
gpaced  as  formerly.  This  may  be  called  the  beam-and-girder  system.  Still 
another  variation  of  the  beam-and-slab  type  is  the  square-panel  system,  in 

*  For  Concrete  in  general  and  Mass-Co^erete,  see  Chapter  III,  pages  240  to  251; 
for  Strength  of  Concrete  without  Reinforcement,  Chapter  V,  pages  283  to  287;  and 
for  Reinforced-Concrete  Construction  in  General,  see  Chapte?  XXIV,  the  paragraphs  of 
which,  corresponding  to  the  same  det^s  4iscuss^4  Uere,  shQuW  ?^l3Q  t>?  Te^4.  See,  alse; 
Chapter  XXUI,  p£«es  8;;  ^nd  844. 


Number  and  Arrangement  of  Columns 


969 


which  the  beams  are  arranged  along  four  sides  of  a  square,  a  column  being 
placed  at  each  of  the  four  corners.  The  simplest  type  of  reinforced- concrete 
construction  for  factories  is  some  form  of  the  beam-and-slab  type  with  walls  and 
piers  of  reinforced  concrete.  The  girderless  type  consists  of  a  heavy  flat  slab 
supported  on  columns  without  the  use  of  beams  or  girders.  The  column-head 
is  enlarged  to  form  a  large  bearing-surface  and  the  columns  are  spaced  so  as  to 
form  square  bays  as  near  as  possible.  A  typical  example  is  worked  out  at  the 
end  of  this  chapter. 

Columns.  In  general,  as  few  columns  as  possible  should  be  used  to  support 
a  floor,  in  order  that  they  may  not  interfere  with  the  placing  of  machinery,  and 
to  insure  the  most  economical  use  of  the  floor-space.     From  the  standpoint  of 


i^-n— r 


IT   i r 


I       I       r 


^ 


T 1  '       I        III 


■T 1 r 


T       I        n 


I       I 


T       I        n 


Jr 


Fig.  1.     Cross-section  of  Building 


economy  of  construction,  however,  the  use  of  one  column  to  not  more  than 
400  sq  ft  of  floor-space  has  been  found  to  meet  average  requirements.  This, 
of  course,  does  not  include  construction  of  a  special  class.  Adopting  this,  then, 
as  the  standard,  and  bearing  in  mind  the  fact  that  the  nearer  a  building  comes 
to  being  square  in  plan  the  less  is  the  total  length  of  exterior  wall  required  to 
enclose  a  given  area,  it  can  be  assumed  that  a  four-story  building  75  ft  wide 
with  tv/o  rows  of  columns,  making  three  spans  across  the  building,  is  a  suitable 
one  for  many  purposes.     (See  Fig.  1.) 

The  Lighting  of  a  Building  of  this  width,  with  story-heights  of  14  ft, 
top  to  top,  will  be  ample  for  most  purposes.  There  are  always  some  parts  of 
the  floor-space  for  which  a  strong  light  is  not  absolutely  essential  and  which 
can  be  devoted  to  aisles  and  to  the  storing  of  material  in  process  of  manufacture. 
The  central  part  of  the  floor-space  is  generally  used  for  this  purpose,  while  the 


970       Reinforced-Concrete  Factory  and  Mill-Construction     Chap.  25 

machinery  is  placed  nearer  the  windows  where  the  hght  is  best  and  where  the 
work  is  done.  It  is  usually  better,  therefore,  not  to  have  a  row  of  columns 
along  the  central  axis  of  the  building,  unless  it  is  definitely  known  that  such  an 
arrangement  will  not  interfere  with  the  proper  use  of  the  lloor-space.  In  a 
building  75  ft  wide,  two  rows  of  columns,  with  spans  of  25  ft  crosswise  of  the 
structure,  leave  the  central  part  of  the  floor-space  free.  Dividing  25  into 
400  sq  ft,  the  floor- space  allowed  for  each  column,  gives  16  ft  as  the  distance 
between  columns,  measuring  lengthwise  of  the  building. 

Bays.  The  reason  in  this  instance  for  making  the  bays  rectangular  instead 
of  square  is  that  there  would  be  another  row  of  columns  if  a  square  bay  with 
a  maximum  of  20  ft  in  either  direction  were  assumed.    This  would  be  likely  to 

End  of  Building 


s 
W 


Fig.  2.     Part  Floor-plan  of  Building 


interfere  with  the  judicious  placing  of  machinery  and  would  result  in  a  row  of 
columns  along  the  central  axis  of  the  building.  This  is  not  considered  good 
practice  r*nd  should  be  avoided,  except  when  there  is  to  be  only  one  row  of 
columns  in  the  building. 

Example  of  a  Typical  Bay,  The  design  of  a  typical  bay  of  the  size  men- 
tioned above,  25  by  16  ft,  will  now  be  considered.  Referring  to  the  illustrations 
(Figs.  1  and  2),  it  is  seen  that  the  windows  occupy  the  major  portion  of  the  wall- 
area,  the  sill  being  set  much  lower  than  is  usual  in  brick  buildings.  This  is 
done  to  avoid  the  necessity  of  the  construction  of  an  extra-high  spandrel  beam, 
as  the  lintel  over  the  windows  below  performs  the  double  function  of  supporting 
the  floor  and  forming  a  curtain  wall.  The  head  of  the  window  is  carried  up 
to  the  under  side  of  the  floor-slab  to  simplify  the  construction  of  tlie  bottom 


Design  of  a  Typical  Floor-System  971 

of  the  lintel  and  at  the  same  time  permit  the  window  to  extend  to  the  ceiling, 
thereby  introducing  the  light  at  the  highest  possible  point  and  allowing  the  rays 
to  project  far  into  the  room.  The  first  beam  should  be  set  as  far  back  as  possible 
from  the  outside  wall  and  windows,  so  that  the  angle  of  the  direct  rays  of  light 
will  be  as  nearly  horizontal  as  practical^le.  It  will  be  found  best  to  have  the 
main  girders  run  across  the  building,  bearing  on  the  walls  and  interior  columns. 
These  girders  may  be  made  as  deep  as  economy  of  design  suggests,  as  they  run 
parallel  with  the  light-rays  and  do  not  interfere  with  the  lighting-scheme.  Again, 
a  deep  girder  is  relatively  very  economical.  It  also  acts  as  a  stiffener  across  the 
narrower  dimension  of  the  building,  thus  increasing  the  resistance  to  vibration 
caused  by  moving  machinery. 

Design  of  Floor-System.  The  various  elements  of  the  floor-system  consist 
of  columns,  girders,  beams  and  slabs.  Each  cf  these  will  be  considered  sepa- 
rately. A  live  load  of  1 20  lb  per  sq  ft  is  ample  for  light  manufacturing  purposes. 
This  is  the  load  prescribed  by  the  Building  Regulations  of  the  City  of  Phila- 
delphia. 

The  Slabs.  The  spacing  of  the  beams  should  be  governed  both  by  economy 
of  the  form-construction  and  the  maximum  distance  a  slab  will  span  while 
carrying  the  load  safely.  It  is  impractical  to  make  a  slab  less  than  3  in  thick. 
Its  dead  weight,  with  concrete  weighing  150  lb  per  cu  ft,  is  s7H  lb  per  sq  ft. 
Allowing  for  a  i-in  cement  finishing-coat,  weighing  12^/12  lb  per  sq  ft,  to  be  laid 
on  the  concrete,  the  total  live  and  dead  load  which  the  slab  must  carry,  if  it  is  3 
in  thick,  is  120  lb  +  50  lb  =  170  lb  per  sq  ft.  Referring  to  the  diagram  of  the 
strength  of  reinforced-concrcte  slabs  (Fig.  18),  calculated  on  a  basis  of  the 
bending  moment  equaling  Wl/ 10,  no  curve  is  found  in  the  3-in  diagram  for  a 
span  of  6  ft  to  carry  a  load  of  1 70  lb  per  sq  ft.  Some  other  slab  must  be  used, 
therefore,  to  carry  the  load. 

The  Slab-Reinforcement.  Referring  to  the  diagram  of  the  4-in  slab  in 
Fig.  18  and  following  the  6-ft  line  until  it  intersects  the  horizontal  line  opposite 
187  ^i  lb  per  sq  ft,  it  is  found  that  a  4-in  slab,  reinforced  with  0.195  sq  in  per  lin 
ft,  or  two  Me-in  square  bars  per  foot,  will  carry  slightly  more  than  is  required  for 
the  slab  in  question.  The  total  load,  if  the  slab  is  4  instead  of  3  in  thick,  is 
182 i/i  lb  per  sq  ft,  and  as  the  i87H-lb  Ime  is  the  nearest  to  this  load,  the  4-in 
slab,  reinforced  as  above,  is  adopted.  The  reinforcing-rods  are  placed  i  in  from 
the  bottom  of  the  slab  and  are  of  sufficient  length  to  extend  over  two  spans  and 
lap  18  in  at  each  end;  the  joints  are  made  over  the  beams  and  not  in  the  space 
between  them  (Fig.  3). 

The  Beams.  The  beams  running  from  girder  to  girder  are  considered  next 
(Fig.  2).  The  span,  center  to  center  of  girders,  is  16  ft,  and  the  distance  apart 
6  ft  3  in,  making  an  area  of  100  sq  ft  carried  by  each  beam.  To  the  load  per 
square  foot  of  1821^  lb  must  be  added  the  weight  of  the  beam  itself,  which  is 
assumed  to  be  15  lb  per  sq  ft  of  floor-area,  rnaking  a  total  of  19  7 1/^  lb  per  sq  ft 
to  be  carried  by  the  beam.  This  multipHed  by  the  area,  100,  equals  19  750  lb. 
The  bending  moment  caused  by  this  load  on  the  beam,  based  on  the  formula  M  = 
Wl/10,  which  for  partially  restrained  beams  is  the  one  generally  used,  is  379  200 
in-lb.  The  slab  acts  with  the  stem  or  beam  to  form  a  T  beam  and  hence  is  as- 
sumed to  be  the  compression-flange  of  the  girder;  and  as  the  slab  is  4  in  thick,  the 
depth  of  the  beam  and  the  amount  of  reiniforcement  can  readily  be  found  by  refer- 
ring to  Fig.  21,  which  is  the  diagram  of  the  strength  of  T  beams  having  a  4-in 
slab.  The  beam-depth  in  the  diagram  is  the  depth  of  the  stem  below  the  slab. 
In  the  diagram  opposite  the  center  of  the  space  between  350  000  and  400  000 
on  the  left-hand  side,  the  depth  of  beam  that  best  suits  the  conditions  can  be 
selected,  and  at  the  bottom  of  the  diagram  is  given  the  total  area  of  steel  to 


072      Rclnforced-Goncrete  Factory  and  Mill-Construction     Chap.  25 

be  used  in  the  reinforcing-rods.  As  the  depth  of  a  beam  from  the  standpoint  of 
economical  use  of  material  should  be  about  one-twelfth  the  span,  a  beam  14 
or  16  in  deep  is  found  to  comply  with  this  rule.  Below  the  space  where  the  line 
representing  the  14-in  depth  of  beam  intersects  the  line  representing  the  bend- 
ing moment,  it  is  seen  that  the  area  of  steel  necessary  is  1.8  sq  in.     Distributing 


Fig.  3.     Plan  of  One  Bay,  Showing  Reinforcing 

this  over  four  bars,  each  bar  should  contain  0.45  sq  in.  The  area  of  one  ^Vie-in 
square  bar  is  0.47  sq  in,  and  hence  a  beam  14  in  deep,  reinforced  with  four  ^Vic-in 
square  bars,  is  used.  The  width  of  the  beam  should  be  6  in.  A  safe  rule  to 
determine  the  width  of  the  beam-stem  is  to  allow  Il^  in  of  concrete  iireproofmg 
on  the  sides  of  the  bars  and  arrange  the  bars  in  two  rows,  if  the  beams  have 
three  or  more  bars.  The  distance  in  a  horizontal  direction,  center  to  center  of 
bars,  should  be  2V^  times  the  diameter,  but  in  any  case  there  should  be  a  i  in 
space  between  the  bars  horizontally,  to  permit  the  concrete  to  thoroughly  incase 
them. 

Arrangement  of  the  Bars.  Assuming  the  bars  to  be  twisted,  the  distance, 
center  to  center,  of  the  two  bars  is  1%  in.  Addnig  to  this  the  diameter  of  the 
bars  on  their  diagonal,  which  is  about  iVs  in,  and  3  in  for  the  fireproofmg,  the 
sum  is  6  in  as  the  width  of  the  beam  required  in  this  case  (Fig.  6).  It  would  be 
perfectly  practicable  to  arrange  the  four  bars  in  one  row  across  the  bottom  of 
the  beam;  but  the  width  would  have  to  be  9%  in,  which  is  wider  than  safety 
requires.  An  additional  objection  to  the  latter  arrangement  is  that  it  requires 
more  concrete,  thus  adding  to  the  dead  weight  of  the  construction.  There 
should  be  2  in  of  concrete  under  the  bottom  of  the  rods  for  hreproofing. 

Width  of  Beam.  Of  course,  the  width  of  the  beam  must  be  sufficient  to 
permit  easy  pouring  of  the  concrete.  Where  wooden-box  forms  are  used,  it  is 
not  good  practice  to  make  beams  narrower  Ihan  6  in.  If  the  beam  is  very  deep, 
say  36  in,  6  in  would  be  too  narrow  a  width  in  which  to  place  the  steel  and 
clean  out  the  beam-forms.  Practical  considerations  very  frequently  govern 
the  width  of  beams. 


Stirrups  and  Reinforcing-Bars 


973 


Stirrups.  There  should  be  in  each  beam  and  girder  a  sufi&cient  number  of 
stirrups,  made  of  at  least  %6-in  round  bars,  bent  U-shaped,  run  under  the 
bottom  rods  and  extended  up  into  the  slab  with  an  angle-bend  6  in  long.  If 
the  beam  or  girder  is  short  and  excessively  deep,  %-in  round  or  heavier  stirrups 
should  be  used.  The  function  of  stirrups  is  to  unite  mechanically  the  slab  to 
the  beam,  so  that  perfect  T-beam  action  will  result,  and  also  to  assist  in  the 
resistance  to  diagonal  tension  or  shear  as  it  is  commonly  called.  The  num- 
ber of  stirrups  in  a  beam  should  be  approximately^  one  for  each  foot  of  the  span, 
center  to  center,  but  the  spacing  should  be  as  stated  below.  Thus,  a  i6-ft 
beam  should  have  not  less  than  sixteen  stirrups,  that  is,  eight  on  each  side  of 
the  center  line. 

Stirrup  Spacing  for  Distributed  Loads.  For  beams  with  distributed 
loads,  the  stirrups  are  to  be  spaced  so  that  the  minimum  distance  between  them 
will  be  6  in  in  ordinary 
cases,  and  the  maximum 
distance  not  more  than  36 
in  at  the  middle  of  the 
beam.  Each  half  of  the 
beam  should  be  divided 
into  three  parts.  The 
division  nearest  the  sup- 
port should  contain  ap- 
proximately one-half  the 
number  of  stirrups  allotted 
to  one-half  the  beam,  or 
one-fourth  the  total  num- 
ber. The  middle  division 
should  contain  one- sixth 
the  total  number,  and  the 
division  next  to  the  cen- 
ter line  one-twelfth  the 
total  number,  as  shown  in 
Fig.  4.  If  the  distribution 
does  not  work  out  evenly 
the  spacing  which  comes 
the  nearest  to  this  should 
be  used. 

Stirrup-Spacing  for  Concentrated  Loads.  When  there  are  concentrated 
loads  the  stirrups  should  be  designed  to  suit  the  loading,  but  in  any  case, 
for  a  distance  equal  to  about  one-fifth  the  span  from  each  end,  the  stirrups 
should  be  spaced  at  least  from  4  to  6  in  on  centers.  A  good  rule  to  follow  is 
to  err  on  the  side  of  safety  and  to  put  in  plenty  of  stirrups,  if  the  determination 
of  the  exact  number  is  in  doubt,  as  there  should  be  a  sufficient  number  of  them 
to  resist  that  part  of  the  diagonal  tension  not  safely  resisted  by  the  concrete. 

The  Arrangement  of  the  Bars  in  the  Beam  is  shown  in  Fig.  4.  The 
two  upper  bars  are  bent  upwards  near  the  supports  to  resist  the  negative  bending 
moment,  which  causes  tension  at  the  top  of  the  beam  near  the  supports.  These 
bars  should  extend  into  the  next  span  at  least  30  in  to  form  a  tie.  As  rein- 
forced concrete  is  of  a  monolithic  character,  it  is  necessary  to  introduce  metal 
bars  wherever  the  concrete  is  subjected  to  tensile  stresses.  While  it  is  not 
necessary  to  provide  as  much  steel  at  the  top  of  the  beam  over  the  supports  as 
the  formula,  for  restrained  beams  gives,  if  50%  of  the  area  in  the  beam  is  carried 


F'vj.  4.     Section  Showing  Elevation  of  Beam 


974      Reinforced-Concrete  Factory  and  MiU-Construction    Chap.  25 

to  the  top  and  over  the  supports,  as  shown  in  the  illustration,  the  beam  will  be 
perfectly  safe  when  calculated  on  a  basis  of  M  equaling  Wl/io.  In  some  cities, 
beams  must  be  calculated  on  the  basis  o(  M  =  Wl/S.  Then  it  is  only  neces- 
sary to  have  about  one-fourth  the  number  of  the  bars  bent  up  near  the  supports. 
These  bars,  however,  should  extend  at  least  30  in  beyond  the  center  of  the 
girder  or  column  to  tie  the  building  together. 

For  Simple  Beams  with  Uniformly  Distributed  Loads,  all  rods  for 
60%  of  the  span  should  be  straight  and  the  truss-rods  should  bend  up  from  the 
points  so  determined. 

For  Beams  or  Girders  with  Concentrated  Loads,  all  bars  are  run  straight 
as  far  as  the  concentrated  loads  extend.  Beyond  these  loads,  towards  the  sup- 
ports, one-half  the  number  of  bars  may  be  bent  up  as  above. 


-    Plan  of  Wall 
Qplumn  Footings. 


Plan  of  Interior 
Column  Footings. 


Fig.  5.     Elevation  of  Girder  and  Plans  of  Column-Footings 


The  Girders.  The  girders  running  across  the  building  arc  calculated  on  the 
basis  of  carrying  their  own  weight  as  a  uniformly  distributed  load  and  con- 
centrated loads  at  the  points  where  the  beams  frame  into  them.  Referring  to 
the  illustrations.  Figs.  2  and  5,  it  will  be  noticed  that  there  are  three  beams  on 
each  side  supported  by  the  girder,  the  fourth  beam  being  carried  by  the  column. 
Each  concentrated  load  equals  the  total  load  on  the  beams,  or  19  750  lb.  The 
weight  of  the  girder  can  be  assumed  as  20  lb  per  sq  ft  of  area  carried,  20  X  400 
=  8  000  lb.    This  acts  as  a  distributed  load.    Oac-haU  the  span  oi  25  ft,  or  12  ft 


Girders  and  Lintels 


975 


6  in,  is  ISO  in.    The  bending  moment  at  the  middle  of  the  girder  from  the  con- 
centrated and  distributed  loads  is 


M  =  (29  625  X  150)  -  ( 19  750  X  75)  + 


8  000  X  300 


3  262  500  in-lb 


Reinforcing-Bars  and  Width  of  Girder.  Referring  again  to  Fig.  21,  in 
the  center  of  the  space  opposite  3  300  000  and  3  250  000,  the  line  of  a  26-in  deep 
beam  is  shown  to  intersect  the  vertical  line  representing  8  sq  in  of  steel.  Hence 
eight  I -in  square  bars  arranged  in  two  horizontal  rows  are  used.  The  width  of 
girder  must  be  12  in  in  order  to  have  the  proper  distance  between  the  bars  and 
at  the  same  time  have  1I/2  in  of  concrete  fireproofing  on  the  sides  (Fig.  7). 


Cemeut  Top, 


)/^aSq-i 


mmm 


Cement  Top         Kg  Sq.  Bars 


jjjj  "  Stirrups 
Fig.  0.     Cross-section  of  Beam 


,L 


-%°  Stirrups 


iH' 


8- 1  Sq.  Cars 

J. 


-12''—^. 


Fig.  7.     Cross-section  of  Girder 


The  Width  of  the  Concrete  Slab  over  the  Girder  is  found  by  multiplying 
the  area  of  the  steel  liy  the  number  on  the  hne  of  the  26-in  beam,  which  is 
8.7.  This  constant  is  used  for  any  area  of  steel  when  the  beam  is  26  in  deep;  the 
constants  on  the  other  beams  are  to  l)e  hkewise  used  for  their  respective  beams. 
In  the  case  of  this  girder,  the  width  of  the  T  beam  is  8.7  X  8  =  69.6  in,  or  34.8 
in  on  each  side  of  the  middle  of  the  girder.  The  portion  of  the  slab  used  at 
the  T  flange  of  the  girder  or  beam  should  not  exceed  on  each  side  of  the  beam 
ten  times  the  slab- thickness,  nor  one- third  the  span.  In  the  case  now  being 
considered,  the  Umit  is  not  exceeded.  Similarly  the  width  of  the  slab  acting  as 
the  compression-flange  of  the  14-in  beam  is  1.8  X  12  =  21.6  in,  twelve  being  the 
constant  for  14-in  beams. 

The  Lintels.  The  next  member  to  design  is  the  lintel,  or  spandrel  beam  over 
the  window  (Figs.  2,  5,  and  8).  This  should  be,  for  practical  considerations,  6  in 
thick.  As  the  bottom  of  the  lintel  is  flush  with  the  bottom  of  the  slab,  the  slab- 
rods  must  run  into  the  hntel  over  the  top  of  the  hntel-rods.  In  addition  to  the 
stirrups  in  the  Hntel  there  should  be  bars  of  the  same  size  as  the  stirrup-bars, 
spaced  about  12  in  apart  and  bent  at  right-angles,  one  leg  extending  up  12  in 
into  the  lintel  and  the  other  18  in  out  into  the  slab;  or  else  the  slab-bars  should 
be  bent  up,  extending  into  the  lintel  12  in.  These  make  a  perfect  tie  between 
the  slab  and  lintel.  The  bottom  of  the  lintel  should  be  made  with  a  rebate  to 
receive  the  head  of  the  window-frame.  The  load  carried  by  the  Hntel  is  the 
load  from  the  slab,  the  weight  of  the  window  and  the  dead  weight  of  the  Hntel. 
The  load  from  the  floor-slab  is  13  H  ft  (the  clear  span  of  the  lintel)  X  3  f t  =  40  3^ 
sq  ft  X  182  1/^  lb,  the  load  ix^r  square  foot  on  the  floor-slab,  or  a  total  load  from 
the  floor-slab  of  7  371  lb.  The  total  height  of  the  Hntel  to  the  top  of  siH  is  3  ft. 
As  it  is  6  in  thick  this  makes  the  weight  per  Hn  ft  75  X  3  ='225  lb,  the  total 
weight  of  the  Hntel  being  225  X  13  M  =  3  038  lb.  For  the  window  10  lb  per  sq  ft 
is  allowed.     The  area  being  X3H  X  n  ft,  the  height  of  the  window,  or  in  even 


076      Reinforced-Concrete  Factory  and  Mill-Construction    Chap.  25 


figures  149  sq  ft,  the  weight  is  149  X  10  lb  =  i  490  lb.    The  total  load  on  the 
lintel,  then,  is  7  371  +  3  038-}-  i  490=  11  899  lb. 

The  Lintels  Figured  as  Rectangular  Beams.  By  referring  to  the  paragraph 
Explanation  of  Diagrams  and  Formulas,  page  992,  for  the  strength  of  rectangular 
beams,  it  is  seen  that  when  reinforced  with  0.5%  of  steel  the  safe  load  carried  by 


the  beam  is  W  =  wl  ■■ 


=  48—. 


Hence,  a  6  by  (36  —6) -in  beam  will  carry  48- 


6X27- 


13-5 


=»  15  552  lb.  The  depth  27  is  used,  as  it  is  taken  to  the  center  of  action  of 
the  steel.  This  is  more  than  the  load  upon  the  lintel  and  hence  the  lintel  is 
safe.     A  reinforcement  of  0.5%  equals  0.005  of  162  sq  in,  the  area  of  the  concrete, 

or  0.81  sq  in;  and  if  two  bars  are  used, 
each  must  be  of  0.4-sq-in  sectional  area. 
Two  %-in  square  bars,  each  having  an 
area  of  0.39  sq  in,  will  be  used.'  These 
should  be  located  2  in  from  the  bottom, 
and  run  straight.  There  should  be  two 
%-in  square  bars  near  the  top  of  the 
lintel,  running  the  full  length,  and  fourteen 
%6-in  stirrups,  as  shown  in  the  illustra- 
tion (Fig.  8).  The  top  bars  take  the 
place  of  bent  bars  and  also  prevent 
vertical  cracks  which  are  liable  to  occur 
from  shrinkage  near  the  middle  of  the 
lintel. 


Sq.  Bars 


Stin-ups 


Bend  up  Ends  of  Slab-Bars 
Cement  Top 


m 


The    Columns.     Having    established 
the  design  of  the  lloor-system,  the  dimen- 
sions of  the  wall  piers,  interior  columns 
and    footings    are    next    determined.     A 
Fig.  8.     Vertical  Section,  Showing  Lintel    schedule    of    the    loads    on    the    interior 

cohmins  will  now  be  made. 
The  Load  from  the  Roof.  Assuming  a  live  roof  load  of  30  lb  per  sq  ft 
and  10  lb  additional  for  accidental  load  from  overhead  shafting,  the  total  Hve 
load  is  40  lb  per  sq  ft.  The  weight  of  the  slab,  if  3  in  thick,  which  is  as  thick 
as  is  usually  required,  is  37^^  lb  per  sq  ft.  The  beams  and  girders  weigh  another 
30  lb  per  sq  ft  (12  plus  18),  making  a  total  dead  load  of  70  lb,  including  the 
covering.  Adding  the  live  load  of  40  lb  to  this  gives  1 10  lb  per  sq  ft  as  the  total 
dead  and  live  load. 

The  Load  on  the  Fourth-Story  Column,  then,  is  400  times  no  lb  or 
44  000  lb,  not  counting  the  weight  of  the  column  itself.  For  practical  reasons 
no  column  should  be  made  less  than  10  by  10  in  in  cross-section.  Allowing, 
therefore,  500  lb  per  sq  in  unit  stress  on  the  concrete  for  columns,  which  is  the 
unit  stress  allowed  by  the  Philadelphia  Building  Bureau  in  reinforced-concrete 
columns  with  vertical  reinforcement,  the  carrying  capacity  of  a  10  by  lo-in 
column  is  100  times  500,  or  50  000  lb,  which  is  in  excess  of  the  load  to  be  carried. 
(See  Table  I.) 

The  Load  on  the  Third-Story  Column  is  the  load  from  the  one  above 
of  44  000  lb  plus  the  load  of  one  bay  of  the  fourth  floor,  which  is  217  lb  X  400 
=  86  800  lb,  being  the  total  dead  and  live  load;  or  86  800 -+-  44  000  =130  800  lb,  to 
which  mu§t  be  added  the  weight  of  the  column,  which  is  assumed  to  be  300  lb  per 
lin  ft.  As  it  is  about  1 1  ft  long  in  the  clear,  the  weight  of  the  column  is  3  300  lb, 
which,  added  to  130  800  lb,  equals  134  100  lb.  The  area  of  the  cross-section  of 
a  16  by  i6-in  column  is  256  sq  in,  which,  at  500  lb  per  sq  in,  gives  128  000  lb  as 


Columns  and  PierS 


977 


the  safe  carrying  capacity.  While  this  is  6  loo  lb  less  than  the  load  to  be  carried, 
it  is  within  4y2%  of  the  required  strength.  It  is  customary  to  make  a  reduc- 
tion of  the  load  to  be  cariied  on  the  columns  in  proportion  to  the  amount  of 
floor-area  carried,  the  reduction  being  greater  as  the  floor-area  increaseSi  Usu^ 
ally  a  5%  reduction  of  the  live  load  per  floor,  with  a  maximum  not  exceeding 
50%  on  the  bottom  columns  for  high  buildings,  is  considered  good  practice. 

Table  I.  Strength  of  Reinforced-Concrete  Columns.     Length,  Fifteen  Diameters 

Columns'  with  vertical  bars.     Safe  working  stress  on  concrete  500  lb  per  sq  in,  the 
strength  of  the  rods  being  neglected  in  figuring  the  columns 


Size 

Area 

Total  safe 
loads  in  lb. 

Size 

Area 

Total  safe 
loads  in  lb 

8X  8 

64 

32  000 

18X18 

324 

162  000 

9X  9 

81 

40  500 

■19X19 

361 

180  500 

10X10 

100 

50000 

20X20 

400   ■ 

200  000 

iiXii 

121 

60  500 

21X21 

441 

220  500 

12X12 

144 

72  000 

22X22 

484 

242000 

13X13 

169 

84500 

23X23 

529 

264  500 

14X14 

196 

98  000 

24X24 

576 

288000 

iSXiS 

225 

112  500 

25X25 

625 

312500 

16X16 

256 

128  000 

26X26 

676 

338  000 

17X17 

289 

144  500 

27X27 

729 

364  500 

The  Load  on  the  Second-Story  Column  is  134  100  lb  plus  the  load  from 
the  third  floor  and  the  weight  of  the  columns,  all  of  which  is  assumed  as  being 
equal  to  the  fourth-floor  load  and  weight  of  column,  or  90  100  lb,  making  tht 
load  224,200  lb.  A  21  by  21-in  column  will  carry  441  times  500  lb  per  sq  in, 
or  220  500  lb. 

The  Load  on  the  First-Story  Column  is  224  200  lb  plus  the  second-floor 
load  of  86  800  lb  and  the  weight  of  the  column,  which,  at  600  lb  per  lin  ft,  is 
6  600  lb,  or  a  total  of  317  600  lb.  A  25  by  25-in  column  will  carry  625  times 
500  lb  per  sq  in,  or  312  500  lb,  which  is  almost  the  required  strength.  The 
column-schedule  then  becomes 

For  the  first  story  25  x  25  in  in  cross-section. 
For  the  second  story  21  x  21  in  in  cross-section. 
For  the  third  story  16  x  16  in  in  cross-section. 
For  the  fourth  story  10  x  10  in  in  cross-section.       '' 

The  Reinforcement  in  the  Columns  should  consist  of  eight  %-in  round 
rods  in  the  two  lower  and  four  in  the  two  upper  stories,  with  ties  of  i^-in  round 
wire  every  12  in,  as  shown  in  Fig.  9.  It  is  the  custom  to  use  the  same  unit 
stress  on  reinforced-concrete  columns  up  to  15  diameters,  and  not  to  use  columns 
whose  length  exceeds  15  diameters. 

The  Wall  Piers.  The  schedule  of  all  the  wall  piers  is  made  by  the 
method  used  for  the  interior  columns.  The  details  of  the  calculations  are  not 
gone  into  here,  results  only  being  given.  The  size  of  the  wall  piers  is  deter- 
mined by  the  architectural  effect  desired  and  by  practical  considerations. 
Assuming  30  in  as  the  smallest  face-dimension  of  the  piers,  this  size  should 
be  carried  up  the  full  height  of  the  building  (Fig.  10).  The  reveal  of  the  piers 
to  the  spandrels  is  6  in,  and  the  spandrels  should  line  up  flush  with  the  inside 
sf  the  piers  if  by  so  doing  they  are  not  made  extremely  thick.    Reinforced- 


978      Relnforced-Concrete  Factory  and  Mill-Construction     Chap.  25 

concrete  spandrels  may  be  6  in  thick  and  give  good  results.  It  is  not  wise  to 
make  them  thinner  than  this,  on  account  of  the  difficulty  of  constructing  them. 
It  is  to  be  noticed,  also,  that  the  hntels  or  spandrel  beams  act  as  ties  from  one 
wall  pier  to  another.  They  should  be  of  sufficient  strength  not  only  to  carry  the 
vertical  loads  coming  upon  them,  but  also  to  act  as  braces  to  take  up  any  vibra- 


\i  Wire  Ties, 
spaced  12  apart 


;        Rciuf.  G--r?  Kods      '■  i 

1                                     ■       ■        ■               o 

'.  *■../  *    --'^  .' 

1 


Keiuf.  8-%'''Kods 


^  Wire  Ties,  spaced  12  apart) 
Fig.  9.     Interior  Column  Fig.  10.    First-story  Wall  Pier 


tion  in  the  direction  of  the  length  of  the  buildin^?;  just  as  the  deep  cross-girders 
resist  the  vibration  in  the  direction  of  the  width  of  the  building.  Very  fre- 
quently the  main  girders  are  run  lengthwise  of  the  building,  that  is,  spanning 
the  shortest  distance,  while  the  beams  run  across  the  building.  Sometimes 
this  will  make  the  construction  more  economical;  but  the  reduced  height  of 
the  windows  in  the  side  walls  due  to  the  necessity  of  lowering  the  window-heads 
to  permit  the  beams  to  be  carried  by  a  lintel  running  over  them,,  is  objectionable, 
as  the  light  from  the  windows  in  this  position  is  not  as  effective  as  when  they 
are  run  up  to  the  under  side  of  the  floor-slab  or  ceiling. 

The  wall-pier  schedule,  figured  on  the  assumption  above,  becomes 

For  the  first  story  30  x  16  in  in  cross-section. 
For  the  second  story  30  X  12  in  in  cross- section. 
For  the  third  story  30  x  12  in  in  cross-section. 
For  the  fourth  story  30  x  12  in  in  cross-section. 

It  will  be  noticed  that  the  piers  in  the  three  upper  stories  are  of  the  same 
dimensions.  This  is  due  to  practical  requirements,  the  reveal  of  the  pier  to 
the  spandrel  being  6  in  and  the  minimum  spandrel-thickness  6  in.  The  pier 
must  be  1 2  in  in  order  to  be  flush  on  the  inside  of  the  building. 

Spread  Foundations.  The  use  of  reinforced  concrete  for  the  footings  of 
a  building  results  in  economical  construction  when  it  is  necessary  to  project  the 
base  or  footing  more  than  is  customary  or  permissible  without  reinforcement  of 
some  kind.  In  order  to  give  sufficient  information  for  the  design  of  the  founda- 
tions for  the  building  under  discussion  in  this  chapter,  as  well  as  for  other  types 
of  construction  met  with  in  practice,  several  examples  are  worked  out  in  the 
following  pages.  The  simplest  form  of  reinforced  concrete  spread  footing  is 
shown  in  Fig.  5  and  consists  in  considering  the  overhanging  portions  of  the 
footings  as  cantilever  beams.  The  footings  of  the  interior  columns  are  de- 
signed as  explained  in  the  following  paragraphs. 

The  Load  on  the  Footing.  The  load  on  the  footing  is  assumed  to  be 
317  000  lb  and  the  safe  bearing  value  of  the  soil  7  000  lb  per  sq  ft.  This  requires 
a  spread  footing  of  317  coo  lb  divided  by  7  000,  or  45  sq  ft.  The  side  of  the 
square  which  comes  the  nearest  to  this  area  is  6  ft  9  in  and  its  area  is  45.5  sq  ft. 

The  Design  of  the  Footing.  The  footing  is  designed  as  follows:  As  each 
square  foot  of  footing  sustains  an  upward  pressure  of  7  000  lb,  the  overhanging 
portion  is  treated  as  a  cantilever  beam  uniformly  loaded.    The  load  directly 


Footings  and  Foundations  979 

under  the  column  proper  causes  no  bending,  and  this  load  is  neglected  in  finding 
the  bending  moment.  The  rods  should  be  run  as  shown  in  Fig.  5,  some  diago- 
nally and  some  at  right-angles  to  the  sides,  the  first  layer  located  3  in  from  the 
bottom  of  the  footing.  The  size  of  the  rods  on  the  diagonal  is  now  to  be  de- 
termined and  the  others  are  to  be  made  the  same  size.  The  longest  length  of 
the  i-ft-wide  diagonal  cantilever  is  4  ft,  measured  from  the  center  of  the  column 
to  the  intersection  of  the  i-ft-wide  strip  with  the  side  of  the  square.  The  bend- 
ing moment  on  this  strip  is  equal  to  the  load  on  an  area,  outside  of  the  column, 
3  ft  long  and  i  ft  wide,  or  (3  X  7  000  =21  000  lb)  X  30  in  =  630  000  in-lb,  30  in 
being  the  distance  from  the  axis  of  the  column  to  the  center  of  gravity  of  the 
area. 

Assuming  the  footing  to  be  24  in  thick  over-all,  the  center  of  action  of  the 
steel  will  be  about  5  in  up  from  the  bottom,  making  an  epfective  depth  of  19  in. 
As  the  lever-arm  for  the  steel  is  nine-tenths  of  the  depth  when  the  stress  in  the 
concrete  is  600  lb  per  square  inch,  the  resulting  stress  per  square  inch  in  the  steel 
(maximum  stress  16  000),  is  16000  X  0.9  =14  400.  As  the  bending  moment 
is  630  000  in-lb,   the   number  of   square  inches  of   steel   necessary   per  foot 

630  000 

in  width  is   '-=  2.34  sq  in.     This  formula  is  for  rectangular  beams 

14  400  X  19 
when  the  bending  moment  is  given.  (See  Formula  (i),  page  992.)  Spacing  the 
rods  4  in  on  centers  requires  three  rods  per  foot,  each  requiring  a  cross-section 
area  of  0.78  sq  in.  As  a  %-in  square  bar  has  a  section-area  of  0.76  sq  in,  this 
size  will  be  used.  The  bars  in  the  layers  at  right-angles  to  the  side  are  made  the 
same  size  and  spaced  as  above,  so  as  to  avoid  complications  in  the  construction 
of  the  footing.  It  would  be  possible  to  space  these  farther  apart,  but  this  re- 
finement is  unnecessary,     (See  Fig.  5.) 

When  the  load  on  a  column  is  such  as  to  require  a  footing  more  than  2  ft  thick, 
it  is  customary  to  slope  the  top  of  the  footing,  thus  saving  in  the  quantity  of 
concrete,  or  else  to  provide  a  concrete  plinth  or.  block  at  the  bottom  of  the 
column  on  top  of  the  footing  so  as  to  reduce  the  projection  of  the  footing  and 
thereby  make  a  more  economical  design.  If  steel  column-cores  or  hooped 
columns  with  vertical  reinforcements  are  used,  a  metal  base-plate  is  necessary 
on  top  of  the  footing  of  sufficient  size  to  limit  the  direct  stress  on  the  footing  to 
500  lb  per  sq  in. 

The  Foundations  for  the  Outside  Walls  may  be  designed  in  either  of 
two  ways:  first,  as  continuous  footings  such  as  are  usual  in  ordinary  construc- 
tion, and  secondly,  as  isolated  piers  under  the  wall  columns.  In  the  first  case 
it  is  necessary  to  reinforce  the  footings  and  foundation-walls,  as  these  act  as 
continuous  beams  loaded  at  each  column,  and  must  be  made  strong  enough  to 
distribute  the  loads  from  the  columns  uniformly  over  the  entire  length. of  the 
footings.  The  foundation-walls  and  footings  can  be  treated  as  inverted  con- 
tinuous beams  (Fig.  11),  the  upward  reaction  of  the  earth  being  considered  a 
uniformly  distributed  load  on  the  beams,  and  the  wall  piers  being  considered  a* 
columns  supporting  tlie  beams,  with  the  load  on  each  pier  as  equal  to  the  load  on 
such  supports.  Fig.  12  shows  the  arrangement  of  the  reinforcing-rods.  Their 
size  is  determined  as  explained  in  the  following  paragraph. 

Since  the  load  per  running  foot  of  the  foundation  is  equal  to  the  load  from  a 
pier  divided  by  the  distance  apart  of  the  piers,  omitting  the  weight  of  the  spandrel 
below  the  first-story  windows,  this  load  per  running  foot  =191  140  lb,  the  load 
from  the  pier -^  16  ft  =  11  946  lb.  As  great  refinements  in  calculations  are  not 
required  in  footing-work  of  this  kind,  because  of  the  advisability  of  large  factors 
of  safety  for  this  part  of  the  building  and  the  small  reduction  in  cost  due  to  any 
such  refinement,  the  strength  of  this  continuous  beam  is  calculated  by  the  formula 


980      Reinforced-Concrete  Factory  and  Mill-Construction     Chap.  25 

M  =.  ir//8,  assuming  /  to  be  the  clear  distance  between  the  piers,  or,  in  this  case, 
13  ft  6  in  (Fig.  12).  Therefore,  W  =  13HX  11  946  =  161  271  lb  and  the  bend- 
ing moment  M  =  (161  271  X  i62)/8  =  3  265  737  in  lb.  As  the  size  of  the  beam 
is  determined  by  the  tliickness  of  the  wall  and  its  depth,  all  that  is  necessary  is  to 


!otal,  191140  lb. 


Total,  191U0  Ib^ 


Total,  191U0  lb: 


T  T  IT  T  T  t  T  T  T  T  T  T  T  T  T  T  ?  t  T-  T  T 11  n  n  T 1 1  IT  T  T  T  T  T  n  I  r 

Load  per  Running  Foot  119i6  lb. 
Fig.  11.     Foundation-wall  an  Inverted  Continuous  Beam 

find  the  area  of  the  steel  by  referring  to  Formula  (i),  page  992,  which  gives 

M  3  265  737 

A  = -,  ov  A  =  ■ =  4.3  sq  in,  distributed  in  eight  %-in  square 

14400  a  14400X52 

bars  with  a  total  area  of  cross-section  of  4.48  in.     These  are  in  two  layers,  four 

running  straight  and  four  bent  as  shown  in  Fig.  12.     The  top  layer  is  placed  2  in 


Center  Line  of  Column. 


Center  Line  of  Column- 


'-r     EourHi'^    I       ^•2-9^1  "VT¥-y^;  .  I  i'*'"'"  Bars,  I       ;^2'9^~1     j 

/  I        ^^^A^Two  liars'^  /  V-WTwoBars^     ' 


5^^=^^=^ 


-V-V-yiy-: 


SECTION  A-A 


^--M^ 


Fig.  12 


Arrangement  of  Rods  in  Foundation-wall 


from  the  top  of  the  concrete.  The  footing  is  made  wider  than  the  wall  to  keep 
the  load  on  the  soil  within  the  safe  limit  of  7  000  lb  per  sq  ft.  The  width  is 
determined  as  follows.  As  the  column-spacing  is  16  ft,  center  to  center,  7  000  X  16 
=  112  000  lb,  the  load  the  foundation  i  ft  wide  and  16  ft  long  will  carry;  hence 
to  carry  212  120  lb  (the  load  from  the  pier,  plus  20980  lb,  the  weight  of  the 
spandrel  and  footing),  212  120  is  divided  by  112  000,  giving  1.9  ft  for  the  width 
of  the  footing,  or  i  ft  11  in,  nearly. 

Isolated  Piers.  In  the  second  case,  a  spread  footing  is  provided  under 
each  wall  column  in  the  same  manner  as  under  the  interior  columns,  but  designed 
for  the  lighter  load.  The  foundation  or  spandrel  wall  is  not  made  as  heavy  as 
in  the  first  case,  as  it  carries  no  load  except  its  own  weight  and  the  wall  or  window 
above  it.  (See  Fig.  5.)  Where  the  soil  is  bad  and  of  low  carrying  capacity, 
the  pier-method  is  found  to  make  an  economical  foundation,  especially  where  it 
is  necessary  to  use  piling  under  the  building,  as  the  piles  can  be  grouped  under 
the  piers  and  columns,  and  capped  with  reinforced  concrete.  The  foundation  or 
spandrel  walls,  properly  reinforced,  can  be  carried  from  pile-cap  to  pile-cap,  as 
they  do  not  depend  on  the  soil  directly  under  them  to  sustain  the  load. 

Combined  Column-Footings.  It  very  frequently  happens  that  a  build- 
ing is  to  be  built  adjacent  to  and  abutting  on  a  property-line,  and  as  the 
foundations  must  not  encroach  upon  the  adjacent  property  the  columns  must  be 


Combined  Column-Footings 


981 


built  on  the  edge  of  the  footings.  In  order  to  secure  uniform  soil-pressure  it  is 
often  necessary  to  combine  an  interior  with  an  exterior  column-footing  so  as  to 
distribute  the  load  uniformly  from  the  two  columns  to  the  soil  below.  Some- 
times it  is  necessary  to  combine  the  footings  of  more  than  two  columns.  Fig.  13 
shows  the  details  of  an  actual  construction  and  may  be  regarded  as  typical.  The 
loads  from  the  columns  in  this  case  are  almost  identical,  one  being  700  000  lb 


fk 


jC: 


C0IN0.2  700,0001b. 


r==^T 


^<-4 4S. 


Present  Stoue  Wall- 
Col  No.  1  700,000  IbT' 
Col.  5a*x25!__^ 


>oint  o£  Maximum 
IJending  Moment 


Five  Bars  bent  up — -sJI    I 
Five  Bars  bent  up — Jin!  I 
Five  Bars  bent  down. 
Fifteeli  1  '.4""tw^Bar8 


L  ^'Stirrupsl '  \, 


I 


f  M  It  f  t  t  M  t  -r  t  ^  t  t  M  t 
SIDE   ELEVATION 


Party  Line-  'H 


;fc:-13' 


Fig.  13. 


PLAN 
Combined  Column-footing 


and  the  other  790  000  lb,  so  that  the  shape  of  the  combined  footing  in  plan  can 
be  RECTANGULAR,  as  the  center  of  gravity  of  the  two  loads  is  practically  at  the 
middle  of  the  span.  When  one  column  is  more  heavily  loaded  than  the  other, 
the  center  of  gravity  of  the  loads  is  no  longer  at  the  middle  of  the  span,  but 
nearer  one  column;  hence  it  is  necessary  to  make  the  combined  footing  trape- 
zoidal in  plan  so  that  the  center  of  gravity  of  the  trapezoid  will  coincide  with 
the  line  of  action  of  the  resultant  of  the  loads  from  the  columns. 

The  following  calculations  for  the  design  of  this  footing  are  the  actual  ones 
made,  and  serve  as  a  good  example  of  the  necessity  of  assuming  certain  sizes  at 
the  start  which  the  final  calculations  may  change.  The  width  of  the  founda- 
tion being  determined  by  the  load-limit  on  the  soil,  which  in  this  case  is  not  to 
exceed  7  000  lb  per  sq  ft,  and  the  size  of  the  column-base  being  known,  we  may 
proceed  to  determine  the  bending  moment  in  the  footing.  We  assume  an  area 
of  7  X  32  ft  =  224  sq  ft,  giving  a  soil-pressure  of  i  490  000  lb  -h  224  sq  ft  =  6  650 
lb  per  sq  ft,  or  6  650  X  7  =  46  550  lb  per  running  foot.  The  point  of  maximum 
bending  moment  is  where  the  vertical  shear  is  zero  and  is  determined  by  the 
equation  700  000/46  550  =  15  ft.     Also,  15  ft  —  1.05  ft  =  13.95  ft.     Hence 

Minax  =  [(700  000  X  13-95)  =  9  765  000  ft  lb]  -  [(46  550  X  15  X  7H) 
=  5  236  875  ft  lb]  =  (4  528  125  X  12)  =  54  337  500  in  lb 


982      Reinforced-Concrete  Factory  and  Mill-Construction     Chap.  25 

The  I. OS  ft  is  one-half  the  column- width,  2  ft  i  in. 

We  may  determine  the  depth  of  the  foundation  by  assuming  a  cross- 
sectional  area  of  the  reinforcing-steel  and  solving  in  Formula  (i),  page  992,  for 
the  depth.  For  practical  considerations  square  bars  larger  than  iJ4  in  square 
bhould  not  be  used;  hence  by  trial  we  hnd  that  thirty  iH-in  square  bars  with  a 
ocction-area  of  46.8  sq  in,  placed  in  two  rows  in  the  top  part  of  the  foundation, 
will  space  out  just  right  for  a  width  of  beam  of  64  in,  which  is  6  in  wider  than 
the  58-in  dimension  of  Column  No.  i.     The  depth  then  by  this  formula  is 


M                       54  337  500        o    . 
,  or  d= —  =  80  m, 


14  400  A 


14  400  X  46.8 


the  depth  from  the  center  of  the  steel  to  the  bottom  of  the  concrete.     Therefore, 
80  +  4  =  84  in,  the  total  depth  of  the  foundation. 
The  WIDTH  of  the  footing  at  the  base  must  be  increased  to  keep  the  unit 


|1  Cenienl 


Fig.  14.     Section  through  Flight  of  Reinforced-concrete  Stairs 


stress  on  the  concrete  in  compression  within  the  allowable  stress,  600  lb  per  sq  in. 
As  the  total  horizontal  compression  in  the  beam  must  equal  the  total  tensioii  in 
order  to  satisfy  the  requirements  for  equilibrium,  we  have  total  tension  =16  000 
lb  per  sq  in  X  46.8  sq  in  =  748  800  lb.  From  Table  V,  page  930,  Chapter  XXIV, 
the  depth  of  the  area  of  the  concrete  in  compression  is  equal  to  0.31  X  80 
=  24.8  in.  The  width  is  found  by  dividing  748  800  by  (300  X  24.8  =  8  440) 
the  resistance  of  the  concrete  per  inch  in  width  of  the  beam,  which  gives  89  in  for 
the  width  of  the  concrete  at  the  bottom  of  the  footing,  300  lb  being  the  average 
unit  stress  on  the  area  of  the  concrete  in  compression,  since  the  stress  actually 


Reinforced-Concrete  Stairs 


983 


varies  from  600  lb  on  the  outside  upper  surface  of  the  concrete  to  zero  at  the 
neutral  axis. 

The  Stairs.  The  ease  with  which  stairs  can  be  built  of  reinforced  concrete  has 
led  to  its  general  adoption  for  this  purpose  in  reinforced-concrete  buildings.  As 
stairs  are  generally  enclosed  in  stair-towers  or  shafts,  their  construction  usually 
takes  the  form  of  the  double  run  or  half-pace  type  (Fig.  14).  This  reduces  the 
length  of  the  run  so  that  the  construction  does  not  become  too  heavy.  Each  run 
of  stairs  is  considered  as  an  inclined  beam  and  is  so  figured,  being  supported  at 
the  top  and  bottom  on  the  stair-landing  header-beam.  The  rods  are  placed 
near  the  bottom  of  the  slab  and  run  continuously  from  top  to  bottom..  The 
depth  of  the  beam  is  considered  to  be  equal  to  the  distance  from  the  sofht  of 
the  stairs  to  the  corner  formed  by  the  tread  and  rise,  as  shown  by  the  letter  D 
in  Fig.  14.  The  landings  are  figured  the  same  as  floor-slabs.  Their  supporting 
beams  are  calculated  to  carry  the  load  coming  upon  them  from  the  landing  and 
from  the  upper  stair-run,  which  starts  from'  the  landing-beam.  The  lower  stair- 
run,  coming  up  under  the  landing-beam,  acts  as  an  inclined  strut  and  supports 
one-half  of  this  beam.  Hence  the  span  of  the  landing-beam  is  equal  to  the  dis- 
tance from  the  wall  of  the  stair- 
tower  or  shaft  to  the  inside  edge  of 
the  stair-run  from  below,  and  is  a 
Httle  more  than  one-half  the  width 
of  the  stair-shaft.  This  makes  the 
design  of  reinforced-concrete  stairs 
very  economical.     (See  page  905.) 

Example  in  Stair-Design.  It  is 
assumed  that  each  of  the  runs  is  4  ft 
wide,  and  that  the  maximum  live 
load  that  can  come  upon  the  stairs 
in  a  crush  is  one  person,  weighing 
150  lb,  for  each  2  ft  of  step,  or  75 
lb  per  lin  ft  of  step.  With  steps  4 
ft  wide  the  live  load  is  300  lb  per 
step  or,  for  ten  steps,  10  times  300 
or  3  000  lb  per  run  for  the  live  load. 
The  dfead  load  is  approximately  400 

lb  per  step,  or  4  000  lb  for  the  run.  This  makes  a  total  load  on  the  inclined  beam 
of  7  000  lb.  The  span  in  calculating  inclined  beams  is  taken  at  the  horizontal 
distance  between  supports;   hence  in  our  example  the  span  is  8  ft  9  in.     The 


"  Wood  Form 
^"    .I'CemcutTop 


Fig.  15.     Detail  of  Reinforced-concrete  Steps 


maximum  bending  moment,  therefore,  is 


7  000  X  105 


=  73  SCO  in-lb,  figuring 


the  run  as  partially  restrained.     Assuming  the  thickness  of  the  slab  to  be  5  in,  the 
effective  depth  is  4  in,  and  the  area  of  steel  per  foot  of  width  for  this  depth  and 

bending  moment  as  above  is  ■ 


■  =  1.3  sq  in,  approximately.     If  %-in 


4  X  14  400 

square  bars  are  used  having  a  section  area  of  0.56  sq  in,  they  should  be  spaced 
S^k  in  apart.  It  is  customary,  also,  to  run  14-in  square  bars,  spaced  2  ft  on 
centers,  at  right-angles  to  the  main  rods,  as  shrinkage-bars.  It  is  also  customary 
to  run  the  rods  which  reinforce  the  run  of  the  stairs,  from  the  wall-edge  of  plat- 
form at  the  top  to  the  wall-edge  at  the  bottom,  bending  the  rods  to  make  them 
come  in  the  bottom  of  the  landing-slabs  and  act  as  their  reinforcement.  This 
makes  a  very  rigid  and  economical  construction.  The  treads  should  be  finished 
with  a  I -in  top  surface  of  cement  and  grits;  and  the  risers  can  be  brushed  smooth 


984      Reinforced-Concrete  Factory  and  Mill-Construction     Chap.  25 


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Fig.  16.     Diagram  for  Strength  of  Rcinforced-concrete  Slabs 


when  their  forms  are  removed.  The  riser-forms  should  be  removed  as  soon 
as  the  concrete  has  set  sufficiently  to  hold  its  shape,  so  that  the  top  of  each  step 
or  tread  can  be  incorporated  into  the  concrete.  Top-surfacing  applied  after 
the  concrete  has  set  hard  is  very  likely  to  become  loose  and  break  off.  A  very 
good  form  of  step  is  shown  in  the  detail^  Fig.  15.     When  the  stair-runs  arp 


Strength  of  Rcinforced-Concrete  Slabs 


985. 


very  long  and  cannot  be  carried,  at  bottom  and  top  where  the  steps  start  and 
stop,  on  header  beams,  a  reinforced-concrete  beam,  forming  an  outside  string, 
should  be  used  and  the  stair-reinforcement  run  parallel  with  the  risers  from  the 
string  to  the  v/all.  The  lieam  forming  the  string  can  be  made  any  convenient 
height  and  width,  and  reinforced  to  suit  the  load. 


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Fig.  17.     Diagram  for  Strength  of  Reinforced-concrete  Slahs 

Explanation  of  Diagrams  and  Formulas.     Figs.  16,  17,  18  and  19  are  to 

be  used  in  designing  reinforced-concrete  slabs.  These  diagrams  are  plotted 
from  calculations  made  in  accordance  with  the  1907  Regulations  of  the  Phila- 
delphia Bureau  of  Building  Inspection,  which  permit  a  unit  compressive  stress 
of  600  lb  per  sq  in  in  the  concrete  and  a  tension  of  16  000  lb  per  sq  in  in  the 
?teel,  with  a  ratio  of  the  moduli  of  elasticity  of  steel  to  concrete  equal  to  12, 


986      Reinforced-Concrete  Factory  and  Mill-Construction     Chap.  25 

These  unit  stresses  give  a  factor  of  safety  of  4,  based  on  the  ultimate  strengths 
of  the  materials  and  have  been  found  to  give  results  in  practice  which  are  con- 
sistent with  safety  and  economical  construction,  the  concrete  being  a  i  :  2  :  4 


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Fig.  18.     Diagram  for  Strength  of  Reinforced-concrete  Slabs 


9        10 


^=10 


mixture  and  the  aggregate  a  good  hard  stone.  The  building  laws  of  various 
cities  usually  specify  the  allowable  unit  stresses  to  be  used  in  designing  reinforced- 
concrete  structures,  and  when  they  differ  from  those  used  in  the  calculations. 


Strength  of  Relnforced-Concrete  Slabs 


987 


corrections  will  have  to  be  made  in  the  results  obtained  when  using  the  diagrams. 
However,  when  one  has  the  option  of  choosing  his  own  method  of  calculating, 
the  diagrams  may  be  used  with  absolute  safety. 

Figs.  20,  21,  22  and  23  are  diagrams  of  the  strength  of  T  beams.    The  cal- 
culations in  these  diagrams  are  based  on  the  same  unit  stresses  as  above;  but 


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Span  in  feet 

Fig.  19.     Diagram  for  Strength  of  Reinforced-concrete  Slabs 


the  effective  depth  of  the  beam  is  taken  as  the  distance  from  the  center  of  action 
of  the  steel  to  the  center  of  the  concrete  slab  and  not  to  a  point  one-third  the 
thickness  of  the  slab  from  the  top.  The  beam-depths  in  the  diagrams  are  the 
depths  of  the  stems  below  the  slab.  The  width  of  the  slab  in  compression  is 
found  by  multiplying  the  area  of  the  steel  by  the  constant  given  in  the  dia- 
grams for  the  corresponding  depth  of  beams. 


Reinforced-Concrete  Factory  and  Mill-Construction     Chap.  25 

2.500,000  DIAGRAM  OF  STRENGTH  OF  T  BEAMS 


j 

2.400.000 

/ 

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2,300.000 

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12  3  4  5 

Area,  A,  of  steel,  square  inches. 
pi|.  20.    Diagram  for  Strength  of  T  Beam§ 


Strength  of  Reinforced-Concrete  T  Beams  989 

iooooo  DIAGRAM  OF  STRENGTH  OF  T  BEAMS 


3,400.000 

1 

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r 

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3.300.000 

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f 

2,600.000 

00 

/"i 

/ 

, 

f 

>-/ 

/ 

/ 

1 

2.500.000 

/ 

ao/ 

/ 

f 

/ 

/ 

i 

y 

1 

2,400.000 

/ 

1 

-/ 

/ 

/ 

r 

' 

a> 

1 

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2,300.000 

) 

1 

CjJ 

1 

/ 

/ 

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L 

2,200,000 

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/  ° 

7 

f 

/ 

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4 

2.100.000 

r  , 

1 

1 

n 

/ 

/ 

1 

1 

/ 

2,000.000 

/ 

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1 

^ 

f 

/ 

k/ 

1,900,000 

1 

1 

J 

1 

1.800.000 

1 

1 

1 

^ 

/ 

/ 

1 

1 

'^'  1 

1,700,000 

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1 

/ 

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y 

/ 

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1,000,000 

/ 

f 

y 

1 

/ 

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/ 

1,500,000 

1 

/ 

^ 

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/ 

1 

'  / 

f 

/ 

q 

V 

1,400.000 

rh 

/ 

y 

f 

W-^ 

rr 

1 

/ 

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/ 

1,300,000 

/ 

If 

. 

/ 

/ 

/ 

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/ 

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1.200,000 

11 

1  i 

r  "v/ 

/ 

/ 

II 

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^ 

/ 

^ 

1.100,000 

, 

II 

/  i 

^/ 

/ 

S- 

/ 

/ 

f  1 

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y 

1.000,000 

11 

II 

1 1 

/ 

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900,000 

It 

1 1 

J 

/ 

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II 

1  i 

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800.000 

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If 

1 

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1 1 

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J 

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700,000 

If. 

1 

/ 

/ 

/ 

If 

1 . 

f 

r 

600.000 

If 

/ 

/ 

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/  . 

500.000 

I 

// 

/ 

/ 

/// 

f  ^ 

/ 

400.000 

/ 

/ 

rIK 

h- 

Jla 

|g 

V 

300.000 

/ 

200,000 

I 

iW. 

7 

100,000 

m 

133456789      10 
Area,  A,  of  steel,  square  inches. 
Fig.  21.    Diagram  for  Strength  of  T  Beams 


990       Reinforced-Concrete  Factory  and  Mill-Construction     Chap, 
DIAGRAM    OF  STRENGTH   OF  T  BEAMS 


.  25 


2       3       i       5       6        7       8        9      10      11      12      13     li      15 

Area,  A ,  of  steel,  square  inches. 
Fig.  22.     Diagram  for  Strength  of  T  Bearos 


Strength  of  Reinforced-Concrete  T  Beams 
DIAGRAM   OF    STRENGTH   OF  T    BEAMS 


991 


3       1       5       f)       T        8        9      10      H     12      13     14. 

Area,  A,  of  steel,  square  inches. 
Fig.  23.    Diagram  for  Strength  of  T  Beams 


^92      Reinforced-Concrete  Factory  and  Mill-Construction    Chap.  25 

The  following  formulas  are  for  the  strength  of  rectangular  beams  or  slabs, 
based  on  various  percentages  of  steel,  the  beams  being  considered  to  be  as  simply- 
supported  at  the  ends.  They  are  calculated  in  accordance  with  the  Philadelphia 
requirements,  and  can  be  used  in  investigating  the  strength  of  rectangular 
beanis  and  slabs  without  obtaining  the  bending  moment.  They  are  very  con- 
venient in  checking  up  a  design  already  made,  or  in  establishing  the  area  of  the 
steel  reinforcement  when  the  size  of  the  concrete  beam  or  slab  is  fixed,  aS  shown 
by  the  example  given. 

7V  =  load  in  pounds  per  runnmg  foot; 

b  =  breadth  of  beam  in  inches; 

d  =  depth  to  center  of  action  of  steel  in  inches; 

/  =  span  in  feet; 

p  =  percentage  of  steel  to  area  of  concrete  above  center  of  steel  to  top  of  beam. 

When  P  =  o.5%     then    w  =  4S-—- 

bd^ 
p  =  0.6%  w^  =  56  — 

rr.  bd^ 


p  =  0.8%  W  =  62 

P  =  o-9%  w^  =  64.5 


/2 

bd^ 
bd^ 

/2 


/,=  !%  ^^67_ 

Example.     Find  the  total  load  per  square  foot  that  can  be  carried  by  a  4-in 

slab,  with  a  5-ft  clear  span,  reinforced  with  0.8%  of  steel  per  running  foot. 

Solution. 

12x32       -        108        ^^^,, 

w  =  62  X =  62  X  —  =  266.6  lb 

5=^  25 

From  this  must  be  deducted  the  weight  of  slab  and  floor-finish  to  obtain  the 
live  load.  If  finished  with  i-in  cement  top  coat  laid  directly  on  the  concrete 
the  total  dead  weight  is  621^  lb,  which,  deducted  from  266.6  lb,  leaves  204.1  lb. 

Note.  If  the  total  load  carried  by  the  beam  is  desired,  iise  /  instead  of  /^ 
in  the  formula.  These  formulas  are  based  upon  the  stress  in  the  concrete  not 
exceeding  600  lb  per  sq  in  and  a  tension  in  the  steel  of  16  000  lb  per  sq  in,  with 
a  ratio  of  the  moduli  of  elasticity  of  the  concrete  and  steel  equal  to  12. 

Formula  for  the  Resisting  Moment  of  Rectangular  or  T  Beams.    This 
is  Formula  (6),  page  932,  Chapter  XXIV,  only  in  a  different  form,  and  is  to  be 
used  when  the  percentage  of  steel  is  not  greater  than  0.58  of  1%. 
M  =  the  maximum  bending  moment  in  inch-pounds; 

d  =  the  depth  from  the  top  of  the  beam  to  the  center  of  action  of  the  steel  in 
inches; 

A  =  the  area  of  the  sum  of  the  cross-sections  of  the  steel  bars  in  square  inches. 

M 

M  =  Ax  16  000  X  o.g  d  ov  A  = 

14400  a 

or  d='  — 7       (i) 

14  400  A 


Girderless  Floors  993 

Example.  Given  a  bending  moment  of  217  728  in-lb  and  a  depth  (over  all) 
of  beam  of  16  in,  to  find  the  sectional  area  of  steel  necessary  to  make  the  resisting 
moment  equal  to  the  bending  moment. 

Solution. 

M  ,  217  728 

A  = or  ^  = =  1. 12  sq  m. 

14  400  d  i4  400Xi33'i 

Using  two  round  bars  of  -Xt-in  diameter  we  have  0,56  sq  in  X  2,  or  1.12  sq  in. 
Allowing  2  in  for  fireproofing  and  y2  in  to  the  center  of  the  bars,  the  effective 
depth  of  the  beam  is  reduced  to  13}^^  in.  For  the  width  of  the  beam  we  can  use 
Formula  (5),  page  931,  Chapter  XXIV,  substituting  for  K  the  value  correspond- 
ing to  the  unit  stresses  and  the  ratio  of  the  moduli  of  elasticity  for  the  con- 
crete and  steel  we  have  been  using,  namely,  600  and  16  000  lb  per  sq  in  for  the 
unit  stresses  and  12  for  the  ratio.  This  value  of  K,  from  Table  V,  page  926, 
Chapter  XXIV,  is  83.4  and  M  =  83.4  bd^.    Transposing,  we  have 

M  ,  217  728        .      217  728 

0  = ,  or  0  =  = =  1A..7,  m 

83.4  d''  83.4  X  (i3K>)2      83.4  X  182.2 

The  beam  therefore  will  be  i43'i  in  X  16  in  in  cross-section,  reinforced  with  two 
%-m  round  rods  placed  so  that  there  will  be  2H  in  from  the  bottom  of  the  beam 
to  their  center.  As  the  width  of  this  beam  is  excessive  for  the  number  of  rods 
used,  it  is  uneconomical.  It  would  be  better  to  design  the  beam  with  a  T  section 
reducing  the  width  to  6  in  for  the  stem  and  making  the  top  flange  143^^  in  wide 
and  13.5  X  0.31  =  4.18  in  thick.  The  ratio  of  the  distance  of  the  neutral  surface 
below  the  top  of  the  beam  to  the  effective  depth  of  the  beam,  for  the  values  we 
have  been  using  is  0.31  (see  Table  V,  page  926,  Chapter  XXIV),  and  in  order  to 
have  sufficient  concrete  in  compression  at  the  top  of  the  beam  to  balance  the 
tensile  stress  in  the  steel,  the  head  or  flange  of  the  T  must  extend  from  the  top 
to  the  line  of  the  neutral  surface. 

Girderless  Floors.*  In  order  to  familiarize  the  student  with  the  design  of 
GIRDERLESS  FLOORS,  an  example  is  worked  out,  in  which  the  area  of  a  panel  or  bay 
is  assumed  to  be  400  sq  ft,  the  same  as  that  of  a  typical  bay  in  the  factory -build- 
ing already  considered  in  this  chapter.  The  column-spacing  is  made  the  same 
in  both  directions,  so  that  the  panels  are  square,  with  a  length  of  side  of  20  ft. 
Without  discussing  the  various  methods  of  computing  the  strength  of  flat,  re- 
inforced-concrete  plates,  we  will  use  one  under  consideration  by  the  Bureau  of 
Building  Inspection  of  Philadelphia. f  This  is  a  conservative  jnethod. .  It  has 
been  carefully  worked  out  in  all  its  details  and  applications  and  gives  results 
consistent  with  safety  and  economical  design.  The  following  paragraphs  set 
forth  the  notation  and  equations  of  this  method  as  published  by  the  Philadelphia 
Bureau  which  calls  it  the  drop-construction. 

L  =  the  length,  center  to  center  of  columns,  of  the  longest  of  straight  bands 

in  inches. 
Li  =  the  distance  or  width,  edge  to  edge,  between  capital-heads  in  inches. 
w  =  the  total  dead  and  live  load  per  square  foot. 
d  —  the  distance  from  the  center  of  action  of  the  concrete  in  compression  to 

the  center  of  the  steel  at  the  drop  in  inches. 
di  =  the  distance  from  the  center  of  action  of  the  concrete  in  compression  to 

the  center  of  the  steel  at  the  center  of  the  slab  in  inches. 

*  See,  also,  Chapter  XXIV,  pages  949  to  951.  Flat-Slab  Construction, 
t  To  Edwin  Clark,  Chief  of  the  Bureau  of  Building  Inspection,  Philadelphia,  Pa.,  is 
due  the  credit  for  working  out  and  perfecting  the  practical  applications  of  this  method. 


994      Reinforced -Concrete  Factory  and  Mill-Construction     Chap.  25 

If  the  drop-construction  is  not  used,  d  =  di. 

Sufficient  depth  of  slab  is  to  be  provided  for  shearing-stresses  as  well  as  for 
bending-stresses. 

Width  of  capital-head  =  not  less  than  ^io  L. 
Width  of  drop  =  WiooL. 
Width  of  bands  =  ^Moo  L. 

X  =  the  area  of  section  of  steel  over  the  capital-head. 
xi  =  the  area  of  section  of  steel  in  center  of  bay. 
—  M  =  the  bending  moment  at  the  edge  of  the  capital-head. 
+  M  =  the  bending  moment  at  the  center  of  the  span. 

^,     ,      ,         ...       .       .    .  w,       ,      total  bay  —  capital-head 

The  load  carried  by  the  straight  band  = X  iv 

2 

total  bay  —  capital -head     wLi 
-M  = X 

2  12 

total  bay  —  capital-head     wLi 
+  M= X 

2  24 

Width  of  concrete  to  resist  compression  at  edge  of  capital-head  =  width  of 

drop. 

WLi 

Width  of  concrete  to  resist  compression  when  negative  moment  = 

24 

=  width  of  band,  in  which  T  =  the  thickness  of  slab. 

Width    of    concrete    to  resist   compression   at  middle  of   span  =  width  of 

band. 


dX  16  000 

Place  66%  of  x  in  straight  bands  ,  .    ,  ,      1 

™  ^     ,     .     ,.  ,  ,       ,    f  over  capital-head. 

Place  43%  of  X  in  diagonal  bands  j 


di  X  16  000 

Place  66%  of  xi  in  straight  bands    .  . ,  „      . 

T^,  -...-.  ,,       ,    >  at  middle  of  span. ' 

Place  43%  of  xi  in  diagonal  bands  ] 


M 


The  drop  equals  the  abacus  outside  of  the  capital-head,  or  the  increased  thickness 
of  the  concrete  to  obtain  the  necessary  compression  in  the  concrete.  TMs  is  not 
*?encrally  necessary  when  the  live  load  of  the  floor  is  light,  say  120  lb  per  sq  ft 
and  the  span  is  not  excessive.  To  determine  d  and  di  deduct  from  the  total 
thickness  of  the  slab  i  in  to  the  center  of  the  steel  when  the  rods  are  H  in  or  less 
in  diameter;  if  over  %  in  deduct  iy2  in;  and  multiply  the  result  by  0.9.  The 
result  will  be  the  distance  from  the  center  of  the  steel  to  the  center  of  action  of 
the  compressive  stresses  in  the  concrete. 

The  depth  h  is  the  distance  from  the  top  of  the  slab  to  the  center  of  the  steel 
and  is  used  in  finding  the  thickness  of  the  slab.  Applying  the  above  formulas  to 
the  example  considered,  using  a  floor-load  of  120  lb  per  sq  ft  as  in  the  previous 
example,  and  assuming  an  average  slab-thickness  of  8  in  with  a  i-in  top  finish- 
coat  of  cement,  the  dead  load  is  100  lb  4-  13  lb  =  113  lb,  which  added  to  the  hve 
load  =  233  lb,  total. 

The  arrangement  of  the  bands  is  shown  in  plan,  Fig.  24,  the  width  being  Mo  L, 
or  H  the  span  of  20  ft,  which  is  to  ft.  The  diameter  of  the  column-head  is  Via  L, 
or  4  ft.    The  width  of  the  drop  is  3^00  L,  or  7  ft  7  in. 


995 


A  N 

Fig.  24.     Arrangement  of  Bands  in  Girderless  Floor 

The  total  area  of  the  bay  =  20^  =  400  sq  ft. 

The  area  of  the  capital-head  =  42  =  16  sq  ft.     Then,  by  the  formula,  the  load 


carried  by  the  straight  bands  = 
44  736  X  U 


400—  16 


X  233  =  44  736  lb 


-M^- 


44  736  X  16  X  12 


+   ilf  : 


44  736  X  L\      44736X16X12 


=  715  776  in-lb 
357  ^8  in-lb 


24  24 

The  bending-moment  diagram  is  shown  in  Fig.  25. 

It  is  necessary  next  to  find  the  thickness  of  the  concrete  at  the  drop.  The 
formula  used  to  find  the  depth  of  a  beam  when  the  bending  moment,  the  width 
of  the  beam  and  the  allowable  stresses  are  given,  is  as  follows,  in  which  h  equals 
the  total  depth  of  the  slab  from  the  center  of  the  steel  to  the  top  of  the  concrete: 


V  0.27  X  hSa      V  0.27  X  91 


5776  _,/-— 


=  V  100  =  10  in 
X  600 

In  this  formula  h  =  the  width  of  the  drop  and  Sr.  =  600  lb  per  sq  in.     The 
depth  of  the  drop  over  all,  therefore,  is  10+  i  =  11  in  (Fig.  26). 

M 
The  steel  over  the  column  at  the  drop  =  x  =  — in  which  d=  o.g  h 


or  0.9  X  lo  =  9. 


715776 
9X  16000 


dX  16  000 


=  4.9  in,  or  about  5  in 


996      Reinforced-Concrete  Factory  and  Mill-Construction     Chap.  25 


The  straight  band  will  have  66%  of  5  or  s-S  sq  in  of  steel.     A  H  round  rod  has 

a  cross-sectional  area  of  o.ii  sq  in.     Therefore,  there  will  be  -^—  =  30  bars  over 

0.1 1 
the  capital-head  in  the  straight  band.     As  the  bars  from  the  adjoining  span  over- 
lap the  column-head,  extending  into  the  next  span  as  far  as  the  edge  of  the  drop, 
each  straight  band  over  the  column  will  have  3^^  or  fifteen  bars.    The  diagonal 


■  Center,  line  of  Column 


Top  Surface 


Fig.  25.     Bending-moment  Diagram  for  Girder- 
less  Floor 


Fig.  26.     Capital-head  and  Slab 
in  Girderless  Floor 


bands  will  have  43%  of  5  or  2.15  sq  in,  which  will  require  twenty  5i-in  round 
rods  over  the  column,  or  ten  on  each  side,  lapped  as  above.  The  thickness  of 
the  slab  at  the  middle  of  the  span  is  found  by  the  formula  given  above,  substi- 
tuting the  proper  values  for  the  letters.     The  formula  becomes 


T    0,27 


X357^ 


X  138  X  600 


:  V32=  5.6  in 


The  total  depth  is  5.6  -f  i  in  =  6.6  in,  or  about  7  in. 
The  width  of  the  band  =  10  ft-f-  (3  X  6  =  18)  =  138  in. 
For  the  steel  at  the  center  of  the  span 

M  .       ,  .  ,    ,  ,  ^     . 

ic  =  + m  which  di  =  0.9  A  or  0.9  X  7  =  6.3  in 

di  X  16  000 

357  888 


"     c     V.    ^    ^  =3.5  sqm 
6.3  X  16  ocx> 

The  straight  bands  will  have  66%  of  3.5  or  2.31  sq  In  of  steel  which  will  re- 
quire — ^^ —  =  twenty-one  %-in  round  bars  or  six  bars  more  for  the  middle  of  the 
o.n 

span  than  for  the  band  set  over  the  column. 

In  practice  the  rods  are  made  the  full  length  of  the  span,  from  column  to 
column,  plus  the  width  of  the  drop,  or  in  this  example  20  ft-}-  7  ft  7  in  =  27  ft  7  in 
for  the  fifteen  rods.  Six  additional  rods,  13  ft  long  or  about  the  distance  from 
the  edge  of  one  drop  to  the  edge  of  the  next  one,  must  be  used  with  the  fifteen  to 
make  the  twenty-one  required  for  the  middle  of  the  span.  The  diagonal  bands 
will  have  in  the  center  43%  of  3.5  sq  in  =  1.5  sq  in  which  require  fourteen  ^^-in 
round  rods  or  four  more  than  one  set  of  rods  over  the  column  These  four,  how- 
ever, are  to  be  added  at  the  middle  of  the  span  between  the  drops.  The  rods 
are  bent  up  over  the  column-head  so  as  to  be  near  the  top  of  the  slab  to  take  care 
of  the  negative  bending  moment,  the  bars  extending  horizontally  near  the  top 
of  the  slab  the  full  width  of  the  drop.  It  is  necessary  to  provide  bent  radial  rods 
extending  down  into  the  column  and  outwards  as  far  as  the  outer  ring  with  two 


Girderless  Floors  997 

or  more  rings  as  reinforcements  of  the  column-head.  The  size  and  number  of 
these  varies  with  the  span  and  load;  but  for  the  floor  under  consideration  there 
should  be  eight  i-in  radial  rods  as  near  the  top  of  the  slab  as  practicable,  the 
diameter  of  the  outer  one  being  equal  to  the  width  of  the  band  and  that  of  the 
inner  one  being  equal  to  the  capital-head.  It  will  be  noticed  in  the  above  analysis 
that  before  any  calculations  could  be  made  certain  assumptions  were  necessary, 
such  as  the  thickness  of  the  slab,  which  was  assumed  as  8  in,  in  order  to  obtain 
the  dead  load;  whereas  in  the  finished  design  the  thickness  of  the  slab  is  7  in  and 
the  drop  1 1  in,  which,  however,  does  not  affect  the  practical  results  materially. 
It  is  for  this  reason  that  the  design  of  flat  slabs  should  be  intrusted  only  to  those 
who  have  wide  experience  in  the  design  of  reinforced  concrete,  as  good  judgment 
enters  into  the  making  up  of  a  successful  design;  and  one  who  is  inexperienced 
should  consult  a  specialist  in  this  particular  system  of  construction,  if  a  design 
is  to  be  put  into  execution. 

Among  the  best  methods  of  determining,  girdless  floors  is  that  embodied 
in  the  Chicago  Rulings  Governing  the  Design  and  Construction  of 
Concrete  Flat  Slabs,  which  went  into  effect  March  1,1918.  The  following 
are  some  of  these  rulings:  The  least  dimensions  of  concrete  columns  shall  be 
not  less  than  |'l2  the  panel-length,  nor  less  than  K12  the  clear  height  of  the 
column.  The  minimum  total  thickness  of  the  slab,  in  inches,  shall  be  deter- 
mined by  the  formula,  t  =  -y/w/Ai,  in  which  /  is  the  total  thickness  of  the 
slab  in  inches,  and  W  the  total  live  and  dead  load,  in  pounds,  on  the  panel, 
measured  center  to  center  of  columns;  but  in  no  case  shall  the  thickness  be 
less  than  L/32  (L  is  the  panel  length,  center  to  center  of  columns)  for  floors, 
nor  less  than  L/40  for  roofs,  nor  shall  a  less  thickness  than  6  in  be  used.  The 
allowable  unit  punching  shear  on  the  perimeter  of  the  column-capital  shall 
be  Ho  of  the  ultimate  compressive  strength  of  the  concrete.  The  allowable 
unit  shear  on  the  perimeter  of  the  drop-panel  shall  be  Moo  of  the  ultimate 
compressive  strength  of  the  concrete. 

"For  the  purpose  of  establishing  the  bending  moments  and  the  resisting 
moments  of  a  square  panel,  the  panel  shall  be  divided  into  strips  known  as 
strip  A  and  strip  B.  Strip  A  shall  include  the  reinforcement  and  slab  in  a 
width  extending  from  the  center  hne  of  the  columns  for  a  distance  each  side 
of  this  center  Hne  equal  to  one-quarter  of  the  panel-length.  Strip  B  shall  include 
the  reinforcement  and  slab  in  the  half  width  remaining  in  the  center  of  the 
panel.  At  right  angles  to  these  strips,  the  panel  shall  be  divided  into  similar 
strips  A  and  B,  having  the  same  widths  and  relations  to  the  center  line  of  the 
columns  as  the  above  strips.  These  strips  shall  be  for  designing  purposes  only, 
and  are  not  intended  as  the  boundary  lines  of  any  bands  of  steel  used." 

Bending-Moment  Coefficients  for  interior  panels  for  two-way  and  four- 
way  systems,  wall  panels  and  panels  without  drops  or  capitals,  are  given  in 
detail.  When  the  length  of  panel  does  not  exceed  the  breadth  by  more  than 
5  per  cent,  all  computations  shall  be  based  on  a  square  panel  whose  side  equals 
the  mean  of  the  length  and  breadth.  In  no  rectangular  panel  shall  the  length 
exceed  the  breadth  by  more  than  one-third  of  the  latter.  Wall  columns  in 
skeleton  construction  shall  be  designed  to  resist  a  bending-moment  of  PFZ/6g 
at  the  floor  and  WL/so  at  the  roof.  Interior  columns  must  be  analyzed  for 
the  worst  condition  of  unbalanced  loading.  The  Point  of  Inflection;  Tensile 
Stress  in  Steel  and  Compressive  Stress  in  Concrete;  Rectangular  Panels, 
Four-way  System;  Rectangular  Panels,  Two-way  System;  Placing  of  Steel; 
are  considered  under  their  respective  headings. 


998  Types  of  Roof-Trusses  Chap.  26 

CHAPTER  XXVI 
TYPES  OF  ROOF-TRUSSES 

By 
MALVERD   A.  HOWE 

PROFESSOR  EMERITUS  OF  CIVIL  ENGINEERING,  ROSE  POLYTECHNIC  INSTITUTE 

1.     Definitions 

Use  of  Trusses.  Whenever  the  distance  between  the  side  walls  of  a  build- 
ing exceeds  about  thirty  feet,  and  there  are  no  intermediate  walls  or  columns,  it 
is  usually  necessary  to  support  the  roof  on  trusses.  The  ceilings  of  large  rooms, 
assembly-halls,  etc.,  also,  require  trusses  for  their  support.  In  many  cases  the 
roof  and  a  ceiling  are  carried  by  the  same  trusses. 

^  Truss  is  a  framework,  composed  of  straight,  or  sometimes  curved,  mem- 
bers or  pieces  so  arranged  that  the  structure  as  a  whole  acts  as  a  beam.  Since 
a  triangle  is  the  only  figure  which  cannot  be  changed  in  shape  without  changing 
the  length  of  one  or  more  of  its  sides,  it  follows  that  the  pieces  forming  a  truss 
must  be  arranged  so  as  to  form  triangles.  The  members  of  a  truss  are  usually 
subjected  to  longitudinal  stresses  only,  either  compressive  or  tensile.  Curved 
members  and  members  which  act  as  beams  supporting  loads  are  subjected  to 
additional  bending  stresses.     Each  member  of  a  truss  is  either  a  tie  or  a  strut. 

A  Tie  is  a  member  which  has  developed  in  it  a  longitudinal  tensile  stress. 

A  Strut  is  a  member  which  has  developed  in  it  a  longitudinal  compressive 
stress.     When  vertical,  struts  are  sometimes  called  posts  or  columns. 

The  Top  Chord  of  a  truss  is  composed  of  the  upper  outside  members.  In 
some  forms  of  roof -trusses  top  chords  are  called  rafters  (Fig.  2). 

The  Bottom  Chord  of  a  truss  is  composed  of  the  lower  outside  members 
(Fig.  2).     In  roof-trusses  the  bottom  chord  is  commonly  called  the  tie-beam. 

The  Web-Members  are  those  connecting  the  chords  (Fig.  2). 

A  Joint  is  the  point  of  intersection  of  two  or  more  members  of  a  truss  (Fig.  2). 

A  Panel  is  the  distance  between  two  adjacent  joints  in  either  the  upper  or 
lower  chords  (Fig.  2). 

Purlins.  Whenever  possible  all  roof -loads  and  ceiling-loads  should  be^  trans- 
ferred to  trusses  at  the  joints.  This  usually  requires  beams  spanning  the  space 
between  trusses  at  corresponding  joints.  These  beams,  when  supporting  the 
roof,  are  called  purlins  (Fig.  2). 

2.  Types  of  Wooden  Trusses 

The  Simplest  Truss  that  can  be  built  is  that  shown  in  Fig.  1.  It  consists 
of  three  members  forming  a  triangle.  As  the  unsupported  length  of  a  strut, 
for  economical  reasons,  should  not  exceed  12  feet,  such  a  truss  is  not  suitable 
for  spans  exceeding  from  20  to  24  ft;  and  even  for  a  span  of  20  ft  there  should 
be  a  center  rod,  as  shown  by  the  dotted  line  R,  to  support  the  tie-beam.  To 
utilize  this  truss  for  spans  greater  than  24  ft,  it  is  necessary  to  brace  the  rafters 
from  the  foot  of  the  center  rod,  as  shown  in  Fig.  2.  This  gives  us  the  king-rod 
truss,  the  modern  type  of  the  old-fashioned  king-post  truss  which  is  shown 


Types  of  Wooden  Trusses 


999 


in  Fig.  3  and  which  was  built  wholly  of  wood  except  for  the  iron  straps  at  S 
and  P. 

Rods  and  Braces.     When  the  tie-beam  supports  a  ceiling  or  attic-floor,  rods 
should  be  inserted  at  RR,  Figs.  2  and  4,  to  support  the  load  on  the  tie-beam. 
By  increasing  the  number  of  rods  and  braces,  as  in  Figs.  4  and  5,  this  type  of 
truss  may  be  used  for  spans  up 
to    64   ft,   and    even   for   greater 
spans;    but    on   account    of    the 
increased    length    of    the    center 
struts    and    rods    it  •  is    not    an 
economical  type  when   the   span 
exceeds  60  ft.    When  there  is  no 
load    on    the    tie-beam    the    rods 
RR,  Figs.  4  and  5,  merely  sup- 
port the  tie-bc£nn  and  are  often 
omitted. 

Triangular  Howe  Trusses. 
The  trusses  shown  in  Figs.  4  and 
5     are     sometimes    called   Howe 


Simplest  Three-piece  Truss,  j  Spans  up 
to  Twenty-four  Feet 


TRUSSES  as  the  character  of  the  stresses  in  the  web-members  corresponds  with 
that  of  the  stresses  in  the  web  in  the  standard  form  of  Howe  truss.  They  are 
also  called  triangular  Howe  trusses  to  distinguish  them  from  the  standard 
Howe  truss  with  parallel  chords. 


Principal  oi 
^  Rafter 


Fig.  2.    King-rod  Truss.    Spans  up  to  Thirty-six  Feet 

Queen-Rod  Truss.  The  rise  of  the  rafter  in  any  of  the  trusses,  Figs.  1  to 
5,  should  never  be  less  than  6  in  in  12  in  or  261.^°;  a  Vs  pitch,  or  a  rise  of  8  in 
in  12  in,  is  generally  the  most  economical.  When  the  span  exceeds  36  ft,  it  is 
more  economical  to  cut  off  the  top  of  the  truss  as  in  Fig.  6,  which  shows  the 
modern  type  of  the  ancient  queen-post  truss.  This  truss  is  frequently  used 
for  the  support  of  deck  roofs,  although  it  may  also  be  used  for  a  pitched  roof 
with  a  ridge.  When  the  top  chord  is  more  than  12  ft  long,  the  size  of  the 
member  may  be  considerably  reduced  by  using  a  center  rod  and  a  pair  of  struts 
as  shown  in  Fig.  7.  The  center  rod  will  be  especially  needed  if  the  bottom 
chord  or  tie-beam  is  subject  to  a  bending  stress.  The  center  rod  should  never 
be  used,  however,  without  the  braces. 


1000  Types  of  Roof-Trusses  Chap.  26 

Counters.  The  truss  shown  in  Fig.  6  differs  from  those  shown  in  Figs.  1 
to  5,  in  not  being  composed  entirely  of  triangles  and  in  having  a  rectangle  in 
the  middle.    Assuming  the  joints  to  be  pin-connected  and  without  friction,  it 


FOR  SPANS  FROM  25  TO  35  FT. 
Fig.  3.    Modem  King-post  Truss 


Fig.  4.    Six-panel  Triangular  Howe  Truss.    Spans  from  Thirty-six  to  Fifty  Feet 


Eight-panel  Triangular  Howe  Truss.    Spans  from  Forty-eight  to  Sixty  Feet 


is  evident^hat  a  very  small  inequality  in  the  position  or  magnitude  of  the  load- 
ing will  cause  the  failure  of  the  truss  since  the  rectangle  will  not  retain  its  shape. 
This  is  easily  verified  by  means  of  a  cardboard  model  fastened  at  the  joints 


Types  of  Wooden  Trusses 


1001 


with  ordinary  eyelets.     When  the  joints  at  the  corners  of  the  rectangle  are  not 
perfectly  free  to  turn  they  have  a  tendency  to  prevent  distortion.    When  the 


Fig.  6.    Queen-rod  Truss.    Spans  from  Thirty  to  Forty-five  Feet 

loading  is  entirely  upon  the  left  of  the  center  the  truss  itself  tends  to  assume  a 
form  similar  to  that  shown  in  Fig.  8.  The  distortion  of  the  rectangle  may  be 
prevented  by  the  introduction  of  a  diagonal  member  as  shown  in  Fig.  9.    For 


^-Top  Chord 


Fig.  7.    Queen-rod  Truss.    Spans  from  Forty  to  Fifty-two  Feet 

the  loading   shown,   the   diagonal  is  in  compression   and  is  usually   called   a 

COUNTERBRACE.     If  the  piece  were  in  tension  it  would  be  called  a  countertie. 

Unsymmetrical  Loads.     Although  roof-trusses  of  the  type  shown  in  Fig.  9, 

supporting  symmetrical  loads,  do  not  theoretically  require  counters,  it  is  never- 


Fig.  8.    Distorted  Queen-rod  Truss 


theless  advisable  to  brace  the  rectangle  along  both  diagonals  to  insure  stability 
under  accidental,  unsymmetrical  loading  and  to  relieve  the  joints  from  any 
stresses  due  to  the  latter,  which  is  usually  caused  by  wind,  snow  and  floor-loads.' 


1002 


Types  of  Roof-Trusses 


Chap.  26 


Reversal  of  Stresses.  In  some  trusses  subjected  to  different  loadings  at 
different  times,  the  diagonal  web-members  near  the  center  may  be  subjected  to 
tension  for  one  loading  and  compression  for  another  loading.     In  such  cases  it 


Fig.  9.     Counterbraced  Queen-rod  Truss 

is  advisable  to  introduce  a  member  following  the  other  diagonal  of  the  quadri- 
lateral containing  the  member  subjected  to  the  two  kinds  of  stress,  to  assist  the 
main  member.  This  piece,  also,  is  called  a  counterbrace  br  countertie 
according  to  the  kind  of  stress  it  has  to  resist.     If  this  is  not  done,  the  member 


Iron  Strap 


Span  45  4,  Pitch  of  Rafter  9H  in  1  foot 


Fig.  10..    Queen-post  Truss.    Massachusetts  Charitable  Mechanics'  Association  Build- 
ing, Boston,  Mass. 

which  is  subjected  to  two  kinds  of  stress  must  be  designed  for  both  tension  and 

compression  and  the.  ends  connected  at  the  joints  to  meet  the  same  conditions. 

An  Ornamental  Queen-Post  Truss,  supporting  a  portion  of  the  roof  of  the 

Massachusetts  Charitable  Mechanics'  Association  building  in  Boston,  Mass.,  and 


Types  of  Wooden  Trusses 


1008 


designed  by  Mr.  William  G.  Preston,  is  shown  in  Fig.  10.  The  truss-members, 
which  are  of  long-leaf  yellow  pine,  were  worked  from  limbers  of  the  dimensions 
given.  In  this  truss  wooden  members  instead  of  rods  are  used  for  the  vertical 
ties,  and  are  bolted  and  tenoned  to  the  tie-beam  and  secured  to  the  rafters  by 
iron  straps.     The  curved  ribs  take  the  place  of  counterbraces. 


-2>^"Rod       |[<-lXEod       [J«-2XRod 
Fig.  11.     Queen-rod  Truss.     Museum  of  Fine  Arts,  St.  Louis,  Mo. 

A  Queen-Rod  Truss  from  the  Museum  of  Fine  Arts,  St.  Louis,  Mo., 
designed  by  Peabody  &  Stearns,  is  shown  in  Fig.  11.  It  supports  the  floor 
below  by  means  of  three  rods.  The  truss-rods  have  nuts  and  washers  below  the 
tie-beam,  and  the  threads  on  the  rods  are  long  enough  to  receive  turnbuckles 
which  connect  the  suspension-rods  with  the  truss.  This  is  generally  the  best 
method  of  suspending  a  floor  from  a  truss. 
Fig.  11a  shows  a  detail  of  joint  A  of  the 
truss  in  Fig.  II. 

Counters  Omitted  for  Special  Reasons. 
Fig.  12  shows  a  truss,  sometimes  used  when  it 
is  desired  to  keep  the  middle  part  of  an  attic 
free  from  .obstructions.  In  building  this 
truss  it  is  advisable  to  construct  the  lower 
part  of  the  rafters  of  two  timbers,  thoroughly 
bolted  together,  as  shown.  What  has  been 
said  in  regard  to  counterbraces  in  queen-rod 
trusses  applies  also  to  this  truss,  although  in 
the  latter  the  continuous  rafter  aids  very 
materially  in  resisting  distortion  from  wind- 
pressure;  so  that  for  ordinary  construction 
and  for  spans  not  exceeding  40  ft  it  is  safe  to 
omit  counterbraces. 

Manner  of  Supporting  Common  Rafters.  Before  describing  other  types 
of  trusses,  it  may  be  well  to  consider  the  manner  of  supporting  the  common 
rafters  by  the  trusses.  Occasionally  it  is  desirable  to  span  the  common  rafters 
from  truss  to  truss,  but  as  a  general  rule  it  is  better  construction  to  support 
them  by  means  of  large  beams  or  purlins  which  themselves  span  from  truss 
to  truss,  as  shown  in  Fig.  13. 

Purlins.  The  trusses  can  be  designed  so  that  the  purlins  need  not  be  more 
than  10  ft  apart,  and  very  often  not  more  than  6  or  8  ft  apart;  so  that  the 
common  rafters  need  not  be  more  than  2  by  4  or  2  by  6  in  in  cross-section,  while 
the  trusses  may  be  spaced  12,  14,  or  i6  ft  on  centers.     As  a  rule  a  spacing  of 


Fig.  1 1  A.    Detail  of  Joint  A ,  Fig.  1 1 . 


1004 


Types  of  Roof-Trusses 


Chap.  26 


about  14  ft  for  the  trusses  and  of  9  ft  6  in  for  the  purlins  is  found  to  be  the 
most  economical  arrangement.  Another  advantage  in  the  use  of  purlins  is 
that  where  they  are  placed  at  the  truss-joints  no  bending  stresses  are  developed 
in  the  truss-rafters  or  chords;  and  hence  the  latter  may  be  made  Ughter  than  if 


;Ilafter8 


Fig.  12.    Queen-rod  Truss  with  Middle  Part  Clear.     Spans  up  to  Forty-two  Feet 

they  supported  the  common  rafters.     For  wooden  trusses  of  60  ft  or  greater 
span,  purUns  should  always  be  used. 

Supports  for  Purlins.     Purhns  may  be  placed  with  their  sides  either  vertical 
or  at  right-angles  to  the  plane  of  the  roof,  as  shown  in  Figs.  2  and  13.    The 

ends  of  the  purUns  may 
be  supported  by  means 
of  beam-hangers,  des- 
cribed in  Chapter  XXI; 
by  double  stirrups;  by 
3-in  planks  bolted  and 
spiked  to  the  sides  of 
the  trusses;  or  they 
may  rest  on  the  top 
chords  themselves.  The 
ceiling- joists  or  floor- 
joists  are  usually  sup- 
ported at  the  sides  of 
the  tie-beams,  as  at  ^ , 
Fig.  13,  or  simply  rest 
Fig.  13.    Manner  of  Supporting  Common  Rafters  and  Purlins    on  them,  as  at  J?.  When 

they  support  an  attic 
floor  it  is  better  to  use  the  latter  construction.  In  the  case  of  scissors  trusses 
it  is  sometimes  more  economical  to  support  the  ceiling- joists  by  purlins;  but 
when  the  tie-beams  are  horizontal  it  is  more  economical  to  use  them  for  the 
direct  support  of  the  ceiling-joists  or  floor-joists.  All  chords  which  support 
rafters,  ceihng-joists  or  floor-joists  must  be  designed  for  bending  stresses  as 
well  as  for  longitudinal  stresses. 

Trusses  with  Horizontal  Chords.     For  the  support  of  flat  roofs,  with  or 
without  a  ceiling  below,  and  for  conditions  such  that  horizontal  trusses  are 


Types  of  Wooden  Trusses 


1005 


practicable,  the  types  shown  in  Figs.  14  to  17  are  undoubtedly  the  most  satis- 
factory for  wooden  construction,  when  the  span  does  not  exceed  8o  ft;  and 
except  in  localities  where  the  cost  of  iron  rods  is  relatively  great,  it  is  as  econom- 
ical as  any.  In  this  work  the  name  Howe  truss  is  given  to  this  type,  as  it  is 
an  adaptation  of  the  Howe  bridge- truss  to  building-construction;  and  the 
term  horizontal  truss  is  also  sometimes  used.    Trusses  of  this  type  can  be 


Bottom  Chord 
Fig.  14.    Five-panel  Howe  Truss 
,  Counter  Braces  ^^ 


Fig.  15.    Six-panel  Howe  Truss 

A_ B  Top  Chords  C 


Fig.  16.    Ten-panel  Howe  Truss 


Fig.  17.    Six-panel  Howe  Truss  with  Top  Chord  Inclined 

made  strong  enough  for  spans  up  to  150  ft;  but  when  the  span  exceeds  100  ft 
it  is  generally  cheaper  to  use  a  steel  truss  of  the  Pratt  type  in  which  the  verti- 
cals are  in  compression  and  the  diagonals  in  tension.  When  a  Howe  truss  is 
placed  in  the  longitudinal  direction  of  a  flat  roof,  the  top  chord  may  be  given 
the  inclination  of  the  roof  itself,  so  as  to  support  the  rafters  without  the  blocking 
as  shown  in  Fig.  17.  For  deck  roofs  the  top  chord  may  be  inclined  upwards 
toward  the  center  or  deck-ridge,  to  conform  to  the  shape  of  the  roof,  as  shown  in 


1006  Types  of  Roof-Trusses  Chap.  26 

Fig.  18.  For  deck  roofs  and  mansard  roofs  the  middle  panels  should  have 
counterbraces,  as  shown  in  Fig.  18,  to  resist  the  wind-pressure  against  the 
sides  of  the  roof  and  any  unequal  distribution  of  snow. 

Height  of  a  Howe  Truss.  The  height  of  the  truss,  measured  from  center 
to  center  of  the  chords,  should  never  be  less  than  one-ninth  the  span  for 
spans  up  to  36  ft,  nor  less  than  one-tenth  the  span  for  spans  from  36  to  80  ft. 


Fig.  18.    Howe  Truss  for  Deck  Roofs 

As  a  general  rule  a  height  of  from  one-seventh  to  one-sixth  the  span  will  be 
most  economical.  When  the  top  chord  is  inclined,  as  in  Fig.  17,  the  height  at 
X,  that  is,  at  the  shortest  rod,  should  not  be  less  than  the  limit  given  above. 

Number  of  Panels  in  a  Howe  Truss.  In  this  type  of  truss  a  panel  is 
the  space  between  two  adjacent  rods  or  between  an  outer  rod  and  the  end- 
joint  (Fig.  14).  As  a  rule,  the  number  of  panels  should  be  such  that  the  diag- 
onals will  have  an  inclination  of  from  36°  to  60°,  an  incHnation  of  about  45** 
being  the  most  economical.  It  is  not  material  whether  there  is  an  even  or  an 
odd  number  of  panels.  If  the  position  of  one  or  more  of  the  purhns  is  fixed 
by  some  special  requirement,  then  the  panels  should  be  so  arranged  that  the 
upper  joints  come  under  the  purhns,  and  the  inclination  of  none  of  the  diagonals 
is  less  than  36°.  Although  it  is  generally  better  to  have  the  truss  symmetrical 
about  the  center,  it  is  not  absolutely  necessary;  nor  is  it  necessary  to  make  the 
panels  of  uniform  width.  When  the  truss  is  not  symmetrically  loaded,  however, 
it  may  be  necessary  to  reverse  the  brace  in  one  of  the  center  panels.  This  point 
is  considered  in  Chapter  XXVII,  page  1 102,  under  the  subject  of  unsymmetri- 

CALLY  LOADED  TRUSSES. 

Counterbraces  in  a  Howe  Truss.  If  there  is  any  chance  of  the  truss 
being  more  heavily  loaded  on  one  side  of  the  center  than  on  the  other,  counter- 
braces,  that  is,  braces  inchned  in  the  opposite  direction  from  that  of  the  regular 
braces,  should  be  placed  in  the  center  panels,  as  shown  by  the  dotted  Imes  in 
Fig.  15.  If  the  truss  is  deep  and  the  diagonals  long  it  is  economical  to  counter- 
bi'ace  each  panel  as  shown  in  Fig.  18.  If  the  number  of  panels  is  odd,  as  shown 
in  Fig.  14,  no  diagonals  are  required  in  the  middle  panel  when  the  braces  and  the 
loading  are  symmetrical;  but  it  is  good  practice  to  cross-brace  this  panel  to 
provide  for  any  accidental  unsymmetrical  loading. 

Spacing  of  Trusses.  The  most  economical  spacing,  center  to  center,  of  the 
trusses,  all  things  considered,  is  usually  from  12  to  16  ft  for  spans  up  to  60  ft, 
and  from  14  to  20  ft  for  greater  spans. 

Spacing  of  Purlins.  Purlins  should  always  be  placed  as  near  the  truss- 
joints  as  possible;  they  should  also  be  spaced  so  as  to  effect  the  greatest  economy 
in  rafter-construction.  Their  spacing,  therefore,  determines,  to  a  large  extent, 
the  number  of  panels.  When  the  height  of  the  truss  is  not  more  than  one-ninth 
or  one-tenth  the  span,  it  is  often  more  economical  to  place  a  purlin  over  every 
other  joint,  as  in  Fig.  16. 


Types  of  Wooden  Trusses 


mi 


Table  I.     Dimensions  for  Six-Panel  Howe  Trusses,  Symmetrically  Loaded 

Timber,  Norway  pine,  Douglas  fir,  or  eastern  spruce.    (See  Fig.  15) 


TJnds 

1 

Dis- 

Braces 

not  upset 

Span 

tance 
apart 

Total 
height 

Top 
chord 

Bottom 
chord 

ctoc 

A 

B 

C 

D 

E 

F 

ft 

ft 

ft 

in 

in 

in 

in 

in 

in 

in 

in 

in 

12   j 

6 

7 

6X  6 

6X  8 

6X  6 

6X4 

6X3 

}lV8 

% 

% 

S 

2 

GX  8 

6X  8 

6X  6 

GX6 

6X4 

36 

15   I 

6 

8 

6X  8 

GX  8 

GX  6 

6X4 

6X3 

}iVi 

74 

54 

S 

2 

8X  8 

8X  8 

8X  6 

6X6 

6X4 

'/8 

78 

18   { 

6 

8 

6X  8 

GX  8 

6XS 

6X6 

6X4 

jiVi 

Va 

f'4 

5 

2 

8X  8 

8X  8 

8X  8 

6X6 

6X4 

/8 

/8 

12   1 

7 

7 

8X  6 

8X  8 

8X6 

8X4 

6X4 

}lu 

% 

R/« 

5 

II 

8X  8 

8X  8 

8X  6 

8X5 

8X4 

/» 

42- 

7 

8 

8X  8 

8X  8 

8X  6 

8X5 

6X4- 

}  1% 

Va 

»'i 

15   j 

S 

II 

8X  8 

8X  8 

8X  8 

8X6 

8X4 

78 

/■i 

18   1 

7 

8 

8X  8 

8X  8 

8X  8 

8X6 

8X4 

}lV2 

«Vi 

6 

I 

8X10 

8X10 

8X  8 

8X6 

8X4 

I 

/■i 

8 

8 

8X  8 

8X  8 

8X  8 

8X6 

8X4 

}l% 

1 1% 

12   ] 

6 

8 

8X  8 

8X  8 

8X  8 
8X  8 

8X6 
8X6 

8X4 
8X4 

% 

% 

48. 

8 

8 

8X  8 

8X  8 

%^ 

IS    j 

6 

10 

8X10 

8X10 

8X  8 

8X6 

8X4 

I 

18    { 

8 

8 

8X  8 

8X  8 

8X  8 

8X6 

8X4 

}  iVa 

% 

6 

10 

8X10 

8X10 

8X10 

8X6 

8X4 

I 

9 

8 

8X  8 

8X  8 

8X  8 

8X6 

8X4 

}  1% 

-/ 

«/i 

12    1 

7 

6 

8X  8 

8X10 

8X  8 

8X6 

8X4 

/8 

/Jr 

9 

8 

8X  8 

8X  8 

8X  8 

8X6 

8X4 

}  1% 

8/." 

54" 

15    1 

7 

7 

8X10 

8X10 

8X  8 

8X6 

8X4 

I 

74 

18    { 

9 

10 

8X10 

8X10 

8X10 

8X8 

8X6 

1 1% 

1V8 

% 

7 

7 

10X10 

10X10 

10X8 

8X8 

8X4 

10 

9 

8X  8 

8X10 

8X  8 

8X6 

6X6 

1 1% 

I 

%  ■' 

12    \ 

8 

4 

8X10 

8X10 

8X10 

8X6 

8X4 

GO- 

ID 

10 

8X10 

8X10 

8X10 

8X6 

6X6 

}  1V2 

1V8 

^i 

15    i 

8 

4 

10X10 

10X10 

loX  8 

10X6 

8X4 

18    { 

10 

10. 

10X10 

10X10 

loX  8 

10X6 

8X6 

[  IVi 

jT,^ 

0/ 

8 

4 

10X10 

10X10 

10X10 

10X6 

8X6 

12 

G 

8X10 

8X10 

8X10 

8X6 

6X6 

]iVj 

% 

12    j 

9 

7 

10X10 

10X10 

loX  8 

10X6 

8X6 

^ 

TO' 

15    1 

12 
9 

6 
9 

10X10 
10X12 

10X10 
10X12 

loX  8 
10X10 

10X6 
10X8 

8X6 
10X6 

}  1% 

I^^ 

% 

18    { 

12 

6 

10X10 

10X10 

10X10 

10X6 

8X6 

]  iVs 

iV-L 

% 

9 

9 

10X12 

10X12 

10X12 

10X8 

10X6 

14 

2 

10X10 

10X10 

10X10 

10X6 

8X6 

}  T% 

iy8 

% 

12    j 

ID 

10 

10X10 

10X10 

10X10 

10X6 

8X6 

8o- 

IS    { 

14 
II 

2 
0 

10X10 
10X12 

10X10 
10X12 

10X10 
10X10 

10X8 
10X8 

8X6 
10X6 

}  1% 

1V4. 

Vs 

18  { 

14 

4 

10X12 

10X12 

10X12 

10X8 

8X6 

[2 

1% 

II 

I 

10X12 

10X14 

10X12 

10X8 

10X6 

1008 


Types  of  Roof-Trusses 


Chap.  26 


Bearing  on  "Wall  or  Post.  The  point  where  the  axial  lines  of  the  end 
brace  and  of  the  tie-beam  intersect  should  always  come  over  the  support,  and 
if  possible  over  the  axis  of  the  supporting  wall  or  post. 

Stresses  in  a  Howe  Truss.  The  stresses  in  the  chords  are  always  greatest 
at  the  middle  of  a  truss,  diminishing  towards  the  supports,  while  the  stresses  in 
the  rods  and  diagonals  are  greatest  at  the  ends  of  a  truss. 

Table  of  Dimensions  for  a  Howe  Truss.  In  symmetrical  trusses 
having  panels  of  uniform  width  and  uniformly  loaded,  the  stresses  in  the  differ- 
ent members  are  proportional  to  the  span,  number  of  panels,  height  of  truss, 
spacing  of  trusses  and  load  per  square  foot.  It  is  therefore  possible  to  prepare 
tables  giving  the  proper  dimensions  of  the  members  of  such  trusses.  Table  I 
gives  the  dimensions  for  six-panel  trusses  for  heights  of  one-sixth  and  one-eighth 
the  span  and  for  three  different  spacings.  These  dimensions  are  for  a  flat 
roof  covered  with  tin,  sheet  iron,  or  composition;  a  snow-load  of  1 6  lb  per  sq  ft, 
equivalent  to  about  24  in  of  light,  dry  snow;  also  for  a  lath-and-plaster  ceiling 
supported  by  the  bottom  chord.  The  chords  and  braces  are  of  Norway  pine 
and  the  rods  of  wrought  iron.    These  dimensions  apply  only  when  the  rafters 


,   A -^s^  /\^  y^<^  /V\_/^^    XV 


;    V    000 


H 


F  i 


v^  vv  W  w 


4.Pins 
Bolt 


-Spaa 


Fig.  19.    Lattice  Truss 


are  supported  on  purlins  placed  at  the  upper  joints,  as  in  Figs.  15  and  16. 
When  the  rafters  rest  on  the  top  chord,  as  in  Fig.  17,  the  dimensions  of 
the  latter  must  be  increased  and  special  calculations  made  for  it.  The  dimen- 
sions given  in  the  table  may  be  used  for  trusses  of  greater  height  than  that 
given,  but  not  for  trusses  of  less  height,  as  the  less  the  height  the  greater  the 
stresses  in  the  chords  and  braces.  When  the  conditions  of  load,  span,  height 
and  spacing  are  not  exactly  as  given  above  and  in  the  table,  the  stresses  should 
be  determined  and  the  members  of  the  truss  proportioned  accordingly;  but 
even  in  such  cases  the  table  will  serve  somewhat  as  a  check  on  the  com- 
putations. 

Lattice  Trusses.  In  localities  where  timber  is  not  expensive  the  lattice 
TRUSS  (Fig.  19)  is  often  fomid  economical  for  supporting  flat  roofs.  This  type 
of  truss  was  invented  for  bridges  by  Ithiel  Towne  in  1820  and  a  large  number  of 


Types  of  Wooden  Trusses 


1009 


railroad  bridges  have  been  constructed  with  trusses  of  this  type,  some  of  which 
are  in  service  now  (19 15)  in  New  England.  The  principal  objections  to  the 
truss  are  its  tendency  to  twist  sidewise,  hke  a  thin  board  on  edge,  its  flexibility 
in  a  vertical  plane  and  the  difficulty  of  getting  sufficient  bearing  material  at 
the  supports.  As  indicated  in  Fig.  19,  the  truss  is  composed  of  top  and  bottom 
chords,  usually  parallel,  connected  by  lattice  bracing.  The  chords  are  com- 
posed of  four  planks,  two  being  on  one  side  and  two  on  the  opposite  side  of  the 
web.  For  the  bottom  chord  the  planks  should  be  as  long  as  can  be  obtained 
and  arranged  so  that  no  two  splices  are  near  the  same  point.  The  available 
area  of  the  bottom  chord  to  resist  tension  is  the  area  of  three  planks  less  the  area 
cut  out  at  the  joints  by  the  connecting  pins  or  bolts.  Each  member  of  the  web 
consists  of  a  single  plank  arranged  as  shown  in  Fig.  19.  The  braces  are  inclined 
at  an  angle  of  about  45°  and  usually  three  sets  are  sufficient,  as  shown  in  the 
figure.  The  connections  are  best  made  with  American-locust  pins,  which  give 
large  bearing  areas  without  much  extra  weight.  Modern  construction  employs 
bolts,  which  are  expensive  and  add  considerable  weight,    There  should  be  at 


Bottom  Chor^ 


Fig.  20.     Vertical  Section  of 
Truss  Shown  in  Fig.  19 


Fig.  21.    Lower  Joint  5  of  Truss  Shown  in 
Fig.  19 


least  two  pins  at  each  connection,  if  the  planks  are  wide  enough  to  permit,  and 
three,  at  least,  at  the  chord-joints.  Since  about  one-half  the  web  planks  resist 
tensile  stresses,  the  web  projects  beyond  the  chord  at  least  4  in  to  provide 
sufficient  longitudinal  shearing  area.  The  ends  are  reinforced  by  vertical  tim- 
bers cut  in  between  the  chords  and  each  set  of  diagonals  is  thoroughly  fastened 
to  these  timbers.  In  some  cases  it  is  necessary  to  add  timbers  on  the  outside 
of  this  and  extend  them  down  to  the  lower  face  of  the  bottom  chords  to  relieve 
them  of  excessive  bearing-stresses  where  they  rest  on  the  supports.  The  methods 
of  determining  the  stresses  in  this  truss  are  considered  in  Chapter  XXVII, 
pages  1089  to  1091.     Figs.  20  and  21  show  details  of  this  lattice  truss. 

Wooden  Trusses  with  Raised  Bottom  Chords.  All  of  the  trusses  thus 
far  described  have  horizontal  bottom  chords;  and  this  construction  is  the  most 
desirable  as  well  as  the  most  economical  and  should  be  used  whenever  condi- 
tions do  not  necessitate  a  greater  height  of  ceiling.  In  roofing  churches,  public 
halls,  etc.,  raised  ceilings  are  often  desirable  as  they  increase  the  general  height 
of  a  room  without  increasing  the  height  of  its  side  walls. 


lOlU 


Types  of  Roof-Trusses 


Chap.  26 


Table  11.     Dimensions  for  Lattice  Trusses,  Uniformly  Loaded 

Timber,  Norway  pine,  Douglas  fir,  and  yellow  pine.     (Fig.  19) 


Span 

Spacing 
of  trusses 

Height 
out  to  out 
of  chords 

No.  of 
spaces 

No.  and 
size  of 
pes  of 

bottom 
chord 

No.  and 
size  of 

pes  of  top 
chord 

Size  of 
braces 

No.  and 
diameter  of 
treenails  or 
bolts,  joints 
1-5.  Fig.  19 

ft 

ft 

ft     in 

in   in 

in    in 

in    in 

in 

5      6 

i6 

4    2X  6 

4    2X  6 

2X  6 

4    I 

12 

7        2 

12 

4    2X  6 

4    2X  6 

2X6 

4    I 

5      7 

i6 

4    2X  6 

4    2X  8 

2X  6 

4    I 

40' 

14 

7      3 

12 

4    2X  6 

4    2X8 

2X  6 

4     I 

i6 

5      8 

i6 

4    2X  8 

4    2X  8 

2X  8 

4     iH 

. 

7      4 

12 

4    2X  8 

4    2X  8 

2X  8 

4          lV4: 

c 

6      8 

i6 

4    2X  8 

4    2X  8 

2X10 

4    iM 

12 

8      8 

12 

4    2X  8 

4    2X  8 

2X10 

4     1V4 

__,  J 

6      8 

i6 

4    2X  8 

4    2X  8 

2X10 

4    iH 

50^ 

14 

8      8 

12 

4    2X  8 

4    2X  8 

2X10 

4    iVi 

i6 

6      9 

i6 

4    2X  8 

4    2X10 

2X10 

4     i^ 

8      8 

12 

4    2X  8 

4    2X  8 

2X10 

4     iH 

12 

8      4 

i6 

4    2X10 

4    2X10 

2X10 

4     1% 

10      10 

12 

4    2X10 

4    2X10 

2X10 

4    1% 

6o- 

8      4 

i6 

4    2X10 

4    2X10 

2X10 

4     1% 

14 

10      10 

12 

4    2X10 

4    2X10 

2X10 

4     1% 

i6 

8      4 

i6 

4    2X10 

4    2X10 

2X10 

4    1% 

10      10 

12 

4    2X10 

4    2X10 

2X10 

4     1% 

9      5 

i6 

4    2X10 

4    2X12 

2X10 

4     1% 

14 

12       4 

12 

4    2X10 

4    2X10 

2X10 

4     1% 

70- 

i6 

9      5 
12      4 

i6 

12 

4    2X10 
4    2X10 

4     2X12 
4    2X10 

2X10 
2X10 

4     1% 
4    1% 

i8 

9      6 

i6 

4    2X12 

4    2X12 

2X10 

4    2 

r 

12       6 

12 

i6 

4     2X1*2 
4    2X12 

4    2X12 
4    2X12 

2X10 
2X12 

4     2 
4    2 

14 

II        0 

14      0 

12 

4    2X12 

4    2X12 

2X12 

4    2 

80- 

i6 

II        2 

i6 

4    2X14 

4    2X14 

2X12 

4    2 

14      0 

12 

4    2X12 

4    2X12 

2X12 

4    2 

18 

II        2 

i6 

4    2X14 

4    2X14 

2X12 

4    2 

14      1 

12 

4    2X12 

4    2X14 

2X12 

4     2 

Note.  All  joints  should  be  thoroughly  spiked  and  packing  blocks  used  where  neces- 
sary. When  treenails  are  used  each  chord-joint  should  have  in  addition  one  %-in 
bolt  as  shown  in  Fig.  21. 

Scissors  Trusses.  For  the  roofs  described  in  the  preceding  paragraph  some 
form  of  the  scissors  truss,  so  named  from  its  resemblance  to  a  pair  of  scis- 
sors, is  most  often  used.  When  correctly  designed,  with  members  of  the  proper 
size,  and  with  joints  carefully  proportioned  to  the  stresses,  it  is  a  very  good 
truss  for  supporting  roofs  over  halls  and  churches,  up  to  a  span  of  48  ft;  but 
for  greater  spans  it  should  be  used  with  caution,  as  the  stresses  become  very 
great  and  the  joints  difficult  to  make.  Figs.  22  to  27  show  different  forms  of 
this  truss  and  modifications  of  it  adapted  to  different  spans  and  roof-pitches. 
None  of  these  trusses  exerts  a  large  horizontal  thrust  if  the  members  are  of 
ample  size  and  the  joints  properly  made.     The  members  having  a  plus  sign  on 


Types  of  Wooden  Trusses 


1011 


Fig.  22.     Simple  Scissors  Truss.     Spans  up  to  Thirty  Feet 


Fig.  23.    Scissors  Truss.     Spans  Exceeding  Thirty  Feet 


Fig.  24.     Scissors  Truss.     For  Steep  Roofs.     (See  Chapter  XXVIII,  Figs.  18  and  19) 


1012 


Types  of  Roof-Trusses 


Chap.  26 


or  close  to  them  are  in  compression,  while  those  having  a  minus  sign  are  in 
TENSION.  The  determination  of  the  actual  horizontal  thrust  is  considered 
on  pages  1085-1087.    The  members  indicated  by  a  single  line  should  be  rods, 


Fig.  25.    Modified  Scissors  Truss.    For  Medium  Pitch.     (See,  also,  Chapter  XXVIII, 
Figs.  18  and  19) 


except  in  the  case  of  bottom  chords.  Fig.  22  shows  the  simplest  form  of  the 
SCISSORS  truss,  which  is  suitable  for  spans  up  to  30  ft.  When  the  span  exceeds 
30  ft,  it  is  more  economical  to  use  two  purlins  on  each  side  to  support  the  com- 


-32  Span.  laApait 


Fig.  26.    Finished  Cambered  Truss.     (See,  also.  Chapter  XXVIII,  Figs.  18  and  19) 

mon  rafters;  and  additional  supports  from  the  bottom  chords  are  generally 
required,  calling  for  additional  rods  and  braces,  as  shown  in  Fig.  23.  For  a 
gt^ep  roof  the  arrangement  shown  in  Fig  24  is  generally  the  best,  and  for  9 


Types  of  Wooden  Trusses 


1013 


flatter  roof  that  shown  in  Fig  25,  in  which  the  scissors  pieces  do  not  cross  nor 
run  through;  Fig.  26  shows  a  finished  truss,  built  on  somewhat  the  same  lines 
as  the  one  shown  in  Fig.  25  but  with  only  one  purhn.  This  truss  can  hardly 
be  classified  as  a  scissors  truss  but  is  shown  here  for  convenience.  It  is  really 
the  same  type  as  that  of  the  truss  shown  in  Fig.  33.  The  truss  shown  in  Fig; 
27  is  similar  to  that  shown  in  Fig.  24,  with  the  peak  cut  off>  but  for  spans 


Fig.  27. 


Modified    Scissors    Truss.    Spans    Exceeding  Thirty-six    Feet.     (See,    also, 
Chapter  XXVIII,  Figs.  18,  19  and  20) 


exceeding  36  ft,  is  more  economical.  It  can  also  be  used  where  the  roof  is 
hipped.  With  this  form  it  is  better  to  use  ceiling-purlins  to  support  the  ceiling- 
joists  than  to  span  the  latter  from  truss  to  truss. 

Hammer-Beam  Trusses.  Two  of  the  principal  characteristics  of  the  Gothic 
style  of  architecture  are  the  relatively  elaborate  ornamentation  of  structural 
parts  and  the  exposure  to  view  of  the  construction  of  a  building  as  a  whole. 
As  the  pointed  arch  and  steep  roof  were  developed  the  roof-truss  became  an 
important  feature  in  the  ornamentation  as  well  as  in  the  construction  of  Gothic 
halls  and  churches.  The  trusses  of  this  period  were  built  almost  entirely  of 
wood  and  generally  of  very  heavy  timbers,  to  give  the  appearance  of  great 
strength.  One  of  the  most  common  types  of  these  Gothic  trusses,  and  also 
the  most  ornamental,  was  the  hammer-beam  truss,  still  often  used  in  churches 
designed  in  the  Gothic  style.  Figs.  28  and  29  show  early  English  forms  of  this 
truss,  which  takes  its  name  from  the  horizontal  beam  H,  called  the  hammer- 
beam,  at  the  foot  of  the  principal  rafter.  In  the  more  ornamental  trusses  this 
hammer-beam  was  usually  carved  to  represent  royal  personages  or  angels. 
These  trusses  differ  in  principle  from  those  thus  far  described,  in  having  no 
bottom  chord  and  no  substitute  for  one.  In  fact  the  trusses  shown  in  Figs. 
28  and  29  do  not  come  within  the  scope  of  the  definition  of  a  truss  given  at  the 
beginning  of  this  chapter.  Although  the  rafters  or  principals  are  connected 
near  the  top  of  the  truss  by  a  short  collar-beam,  this  offers  but  httle  resistance 
to  the  tendency  of  the  rafters  to  spread  at  their  lower  ends;  and  hence  the 
truss  depends  either  upon  the  transverse  strength  of  the  rafters  or  upon  the 
resistance  of  the  walls  to  keep  it  intact  and,  generally,  upon  both.  This  form  of 
truss  is  actually  that  of  an  arch,  as  vertical  loads  produce  inclined  reactions  at  the  . 
supports.    In  the  halls  and  churches  of  the  Gothic  period  the  walls  were  generally 


1014 


Types  of  Roof-Trusses 


Chap.  26 


very  thick'  and  usually  reinforced  on  the  outside  by  buttresses  built  against 
them  and  directly  opposite  the  roof-trusses.  In  most  cases  such  a  wall  possesses 
sufficient  stability  to  withstand  the  thrust  of  the  truss,  and  hence  the  bottom 
chord  may  be  dispensed  with;  but  in  a  wooden  building  the  walls,  unless  tied 
at  the  top,  offer  no  resistance  whate^>er  to  being  thrust  out  and  hence,  in  such 
buildings,  no  truss  which  exerts  an  outward  thrust  on  the  walls  should  be  used. 


=i=it=!t=jt=iyb^- 


m 


^SECTION  OF  SECTION  OF 

^PRINCIPAL  RAFTER    COLLAR  BEAM 

r 


ROOF    OVER    NAVE 

CHAPEL.  SUFFOLK,  ENG. 

Span  \  8  ft. 


Fig.  28.    Hammer-beam  Truss.    Early  English  Form 


It  is  therefore  generally  impracticable  to  use  a  hammer-beam  truss  in  a  wooden 
building.  Where  these  trusses  are  used,  the  ceiling  is  generally  formed  of  matched 
sheathing,  nailed  to  the  under  side  of  the  jack-rafters  between  the  purhns, 
thus  allowing  the  latter  to  be  seen.  The  purlins  are  generally  decorated,  and 
f  alse  ribs  are  often  placed  vertically  between  them,  to  divide  the  ceihng  into 
PANELS.  The  main  rafters  should  be  made  very  large  to  prevent  them  from 
breaking  at  the  point  A,  Figs.  28  and  29. 


Types  of  Wooden  Trusses 


1015 


Truss  for  First  Church,  Boston,  Mass.  An  excellent  example  of  a 
hammer-beam  truss  adapted  to  modern  conditions  is  shown  in  Fig.  30,  which 
represents  one-half  of  one  of  the  trusses  designed  by  Ware  &  Van  Brunt,  for 


Fig.  29.    Hammer-beam  Truss.    Early  English  Form 

the  First  Church,  Boston,  Mass.  The  truss  is  finished  in  black  walnut  and  has 
the  effect  of  being  very  strong  and  heavy.  Fig.  31  shows  the  framing  of  the 
same  truss  without  the  casing  and  falsework.  It  should  be  noticed  that 
inside  the  turned  column  in  the  upper  part  of  the  truss.  Fig.  30,  there  is  an  iron 


Typfes  df  Roof-Trusses 


Fig.  30.    Hammer-beam  Truss.    First  Church,  Boston,  Mass. 


Types  of  Wooden  Trusses 


1017 


rod,  Fig.  31,  which  resists  the  tensile  stress.  In  this  form  of  truss  the  line  of 
outward  thrust  of  the  arch  enters  the  wall  just  above  the  corbel,  K;  and,  as. 
its  direction  is  inclined  only  about  30°  from  the  vertical,  its  tendency  to  over- 
throw the  wall  is  not  very  great,  and  may  be  resisted,  in  this  particular  case^^ 


FRAMING  OF  HAMMER 
BEAM  TRUSS 


Span  61  feet 

DISTANCE  BETWEEN  TRUSSES 

ABOUT  15  feet 


Fig.  31.    Framing  of  Truss  Shown  in  Fig.  30 


by  a  wall  20  in  or  2  ft  thick,  thoroughly  reinforced  by  a  buttress  of  proper 
dimensions  built  on  the  outside.  In  trusses  of  this  kind,  the  various  members 
should  be  securely  fastened  together  wherever  they  cross  or  touch  each  other, 
and  the  structure  as  a  whole  made  as  rigid  as  possible.  No  dependence  should 
be  placed  upon  the  casings  and  panel-work  for  any  extra  strength. 


1018 


Types  of  Roof-Trusses 


Chap.  26 


Truss  for  Emmanuel  Church,  Shelburne  Falls,  Mass.  Fig.  32  shows 
another  form  of  truss  designed  by  Van  Brunt  &  Howe,  for  Emmanuel  Church, 
*>helbume  Falls,  Mass.     It  is  probably  a  variation  of  the  hammer-beam 


Fig.  32.     Truss  for  Emmanuel  Church,  Shelburne  Falls,  Mass. 
.'Casting 


Fig.  33.     Wooden  Truss  with  Iron  Ties.     Spans  up  to  Thirty-six  Feet 

form  and  when  securely  bolted  together  at  all  the  joints  can  be  designed  so  as 
to  exert  very  little  thrust  on  the  walls.  The  rafters  and  cross-tie  are  each 
formed  of  two  pieces  of  timber,  separated  but  bolted  together,  the  small 
•upright  members  passing  between  these  pieces.     The  hammer-beams  are  carved 


Types  of  Wooden  Trusses 


1019 


to  represent  angels.     The  action  of  the  stresses  in  hammer-beam  trusses  i^ 
explained  in  Chapter  XXVII,  pages  1087  to  1089. 

Wooden  Trusses  with  Iron  Ties.     Where  there  is  no  ceiling  beneath  the 
roof  and  it  is  desirable  to  make  the  trusses  as  light  in  appearance  as  possible, 


Near  Rod  C 


Fig.  33a.     Detail  of  Joint  B, 
Fig.  33 


Fig.  33b. 


Alternate  Detail  of  Joint  at 
Ridge,  Fig.  33 


wrought-iron  or  steel  rods  may  be  used  for  the  ties,  and  the  wooden  *  rafter- 
pieces  and  struts  retained.  For  moderate  spans  such  trusses  are  cheaper  than 
steel  trusses;  and  where  the  rafters  and  puriins  are  of  wood  they  are  about  as 
good.  Figs.  33  and  34  show  forms  of  trusses  well  adapted  to  many  roofs.  The 
dimensions  given  in  Fig.  34  are  for  yellow-pine  or  Douglas-fir  timber  and  wrought- 


DETAILi 
CASTINGS 
ON  STRUTS 


ir^ 


^Z-1%"' 


2K  Pin 


-24  0- 


10  ti&tteT9-..,^^^^S)r  ^ 

\ 

m^^Mvin 

-■-■/ 

\j      I-1JK'° 

2«-Pto          C     "^ 

^Hook 

Fig.  34.    Wooden  Truss  with  Iron  Ties 


iron  rods,  and  are  ample  for  a  slate  roof,  the  trusses  being  spaced  from  12  to 
14  ft  on  centers.  Trusses  of  the  form  shown  in  Fig.  33  are  sometimes  made 
with  the  rods  C  and  D  continuous.  They  should  not  be  made  in  this  way, 
however,  unless  the  entire  rod  is  proportioned  for  the  stress  in  C,  as  this  stress 
is  greater  than  that  in  D.    The  best  construction  for  the  joint  B  is  illustrated 


1020 


Types  of  Roof-Trusses 


Chap.  26 


Fig.  35.    Hammer-beam  Truss  for  Grace  Chap)el, 
New  York  City 


in  Fig.  33a,  which  shows  a  cast-iron  shoe  fitted  to  the  end  of  the  strut  to 
receive  the  pin.  For  the  truss  shown  in  Fig.  34,  a  shoe  made  as  shown  in  the 
detail  drawing  makes  a  better  connection  for  the  rods,  two  of  the  latter  being 
placed  outside  of  the  brackets  and  three  between  them.  For  a  truss  with  a 
single  strut,  a  turnbuckle  on  the  rod  E  serves  to  tighten  the  rods.     When 

there  are  three  struts,  there 
should  be  five  turnbuckles,  as 
in  Fig.  34.  A  cast-iron  shoe 
should  be  made  to  receive  the 
foot  of  the  rafter  and  the  rods 
secured  to  a  pin  passed  through 
shoe  and  rafter.  At  the  apex, 
also,  of  the  truss  shown  in  Fig. 
34,  there  should  be  castings  to 
receive  the  ends  of  the  rafters, 
and  pins  for  the  tie-bars.  The 
apex-joint  of  the  truss  (Fig. 
33)  may  be  made  either  by 
crossing  the  rods  through  a 
CAST  WASHER,  or  as  shown  in 
Fig.  33b.  The  pins  at  the 
joints  should  be  computed  for 
shear,  bearing  and  flexure. 
More  modern  construction  re- 
places the  cast  iron  shown  with  steel  plates  and  pins.  When  a  hammer- 
beam  truss  is  to  be  supported  on  a  clerestory-wall  which  is  not  very  thick 
nor  braced  from  the  outside,  a  truss  of  the  form  shown  in  Fig.  35  may  be 
used  to  advantage.  It  has  the  appearance  of  a  hammer-beam  truss  and  when 
placed  over  a  high  nave  the  effect  of  the  rods  is  not  objectionable.  These 
tie-rods  should  extend 
through  the  hammer- 
beams  to  their  outer 
ends. 

Truss  for  Grace 
Chapel,  New  York 
City.  The  curved  ribs 
a,  a,  Fig.  35,  have  a  ten- 
dency to  bend  at  their 
smallest  section  and 
braces  under  the  ham- 
mer-beams are  necessary 
to  prevent  vertical  deflec- 
tion in  the  latter.  A 
truss  similar  to  this  was 
used  in  Grace  Chapel, 
New  York  City. 

Truss  for  Metropolitan  Concert-Hall,  New  York  City.  Fig.  36  shows 
a  form  of  truss  used  to  support  the  roof  of  the  Metropolitan  Concert-Hall,  New 
York  City,  George  B.  Post,  architect.  The  span  is  about  54  ft  and  the  propor- 
tions are  about  as  shown.  The  arch  between  rafters  and  raised  rib  is  orna- 
mented with  sawed  work  and  the  truss  has  a  very  light  and  airy  appearance. 
The  tie-rod  is  kept  from  sagging  by  a  vertical  rod  from  the  crown  of  the 
arch, 


Fig.  36.    Truss  for  Metropolitan  Concert  Hall,  New  York 
City 


Types  of  Wooden  Trusses 


1021 


Wooden  Arched  Ribs  with  Iron  or  Steel  Ties.  For  roofing  large  halls 
or  rooms  a  segmental  timber  arch,  with  an  iron  or  steel  tie  to  take  up  the 
horizontal  thrust,  is  about  the  cheapest  construction,  especially  where  there  is 
no  ceiling  to  be  supported.    Figs.  37  and  38  are  good  examples  of  this  form  of 


j-xloVerTr^i!! 


Fig.  37.    Segmental  Timber  Arch 

truss,  the  arched  ribs  supporting  all  the  load  and  the  tie-rods  preventing  tha 
ends  of  the  arch  from  the  spreading  which  would  result  without  them. 

Truss  for  M.  C.  M.  A.  Building,  Boston,  Mass.  This  truss  is  shown  in 
Fig.  37  and  the  framework  shown  above  the  arch  is  simply  to  support  the  pur^ 
lins  and  rafters  and  carry  the  load  directly  to  the  arch.  It  does  not  assist  the 
truss  in  any  way  in  carrying  the  load. 


Fig.  38.     Segmental  Timber  Arch 

Trusses  for  the  Fifth  Avenue  Riding-School,  New  York  City.     The 

method  of  supporting  the  roof  of  the  Fifth  Avenue  Riding-School,*  New  York 
City,  was  rather  unusual  and  very  ingenious;  and  as  it  is  an  excellent  example 
of  the  advantage  of  the  arched  form  of  truss,  a  brief  description  is  added.  The 
plan  of  the  riding-room,  which  is  io6  ft  6  in  long  by  73  ft  wide,  is  shown  in  Fig.  39. 
This  space  is  kept  free  from  columns,  the  entire  roof  being  supported  by  two 
large  trusses,  one  of  which  is  shown  in  Fig.  38.  The  entire  roofing  is  supported 
by  smaller  trusses  resting  on  these  two  large  ones,  each  of  the  latter,  however, 

♦  Remodeled  in  1905.     The  old  trusses  were  used  in  the  altered  structure. 


10'22 


Types  of  koof-Trusses 


Chap.  26 


Fig.  39.    Plan  of  Truss-framing  of  Fifth  Avenue  Riding-school,  New  York  City 


.}  IRON  TIE  TO  OPPOSITE  COLUMN 
106  6  DISTANT 


FSj  40.     Detail  of  Iron  Skewback  and  Post  of  Truss  Shown  in  Fig.  3£ 


Types  of  Wooden  Trusses 


iD2S 


eventually  carrying  a  roof -area,  equal  to  about  2  930  sq  ft,  and  a  great  amount 
of  extra  framework.  The  method  employed  to  resist  the  thrust  of  these  large 
arches  without  the  use  of  rods  showing  in  the  room  is  very  ingenious.  Opposite 
the  upper  ends  of  the  iron  posts  which  receive  the  arched  ribs  are  oak  struts 


Fig.  41.    Arched  Wooden  Truss.     City  Armory,  Cleveland,  Ohio.     Span  79  feet 

held  in  place  by.  iron  tie-bars  and  heavy  iron  beams  and  together  forming  a 
horizontal  truss  at  each  end.  These  two  trusses  are  prevented  from  being  pushed 
out  by  two  3  by  i-in  iron  tie-bars  in  each  side  wall,  as  shown  in  the  plan  (Fig.  39). 
The  lower  ends  of  the  two  iron  posts  are  tied  together  by  iron  rods  running  under 


Fig.  42.    Arched  Wooden  Truss,  Sanger  Hall,  Philadelphia,  Pa. 

the  floor  the  whole  length  of  the  room.  Altogether  this  gives  for  the  tie-rods 
of  each  truss  two  3  by  i-in  iron  bars  and  one  ii/^-in-diam  iron  rod,  equivalent 
to  two  3%  by  I-in  tie-bars.  Enlarged  sections  of  the  ribs,  uprights  and  braces 
are  shown  in  Fig.  38.  It  should  be  noticed  that  the  uprights  have  iron  rods 
through  their  axes,  holding  the  two  ribs  together.     Fig.  40  shows  a  detail,  or 


1024 


Types  of  Roof-Trusses 


Chap.  26 


enlarged  view,  of  the  iron  skewback  and  post  at  each  end  of  the  truss  shown  in 
Fig.  38. 

Truss  for  City  Armory,  Cleveland,  Ohio.*  Fig.  41  shows  the  method 
adopted  for  supporting  the  roof  and  gallery,  the  arch  being  of  wood. 

Truss  for  Sanger  Hall,  Philadelphia.!  Fig.  42  shows  one-half  of  an 
ARCHED  WOODEN  TRUSS  which,  with  seventeen  others,  was  designed  to  support 
the  roof  over  the  central  bay  of  Sanger  Hall,  Philadelphia,  Hazelhurst  &  Huckel, 
Line 


,;2-3  X  6 


126  0  C-C  Pins 


2-ljS^  ® 


2^4  Rollers  ' 


Stone  2'6"x4'0" 


Fig.  43.     Three-centered  Curved  Wooden  Truss.     O.  N.  G.  Armory,  Cincinnati,  Ohio 


architects.  This  building  was  erected  in  1897  for  the  use  of  the  Eighteenth 
National  Siingerfest,  and  was  intended  only  for  temporary  vise.  With  the 
dimensions  slightly  increased,  however,,  these  trusses  would  be  suitable  for 
permanent  use.  They  were  spaced  20  ft  center  to  center.  A  description  of 
the  building. and  trusses  was  published  in  the  Engineering  Record  of  January  9, 
1897. 

Truss  for  the  O.  N.  G.  Armory,  Cincinnati,  Ohio.  Fig.  43  shows  a  truss 
used  in  this  building.  The  curve  of  the  axial  line  of  the  arch-truss  is  a  three- 
centered  ellipse.  Hannaford  &  Sons  were  the  architects  of  the  building  and 
G.  Bouscaren  was  the  designer  of  the  trusses.  (See  the  Engineering  and  Build- 
ing Record,  December  7,  1889.) 

*  The  building  has  been  remodeled  and  is  now  used  for  commercial  purposes, 
t  This  building  was  torn  down  immediately  after  the  meeting. 


Types  of  Steel  Trusses 


1025 


3.   Types  of  Steel  Trusses 

Trusses  for  Pitched  Roofs.  For  ordinary  conditions  and  for  spans  under 
lOO  ft,  some  one  of  the  types  shown  in  Figs.  44  to  55  will  generally  meet  the 
requirements  of  strength  and  economy.  Trusses  of  these  types  are  composed 
of  rolled  plates  and  angles 
and  have  riveted  joints.  This 
is  not  only  a  cheaper  con- 
struction than  a  combination 
of  shapes  and  rods  with  pin- 
joints  but  is  also  much  more 
rigid.  Where  one  dimension 
of  the  trusses  does  not  exceed 
about  10  ft  they  can  be 
completely  riveted  up  in  the 
shops.  In  case  they  are 
large  a  little  judgment  will 
divide  them  into  parts  which 
can  be  shipped  by  rail,  leaving 
but  few  joints  to  be  riveted  at  the  building;  but  entire  trusses  having  spans  even 
of  loo  ft  can  be  raised  from  the  ground  and  put  in  place.  Occasionally  a  struc- 
ture is  of  such  magnitude  that  this  is  not  feasible,  in  which  case  the  trusses 
must  be  raised  in  parts  and  riveted  afterwards.     For  a  narrow  shed  or  shop  a 


Fig.  44.    Truss  for  a  Narrow  Shed  or  Shop 


Fig.  45.     Simple  Fink  Truss.     Spans  from  Twenty  to  Thirty-six  Feet 

truss  of  the  shape  shown  in  Fig.  44  is  the  most  economical,  the  truss  proper 
being  that  portion  enclosed  within  the  points  A,  B,  C.  This  truss  is  practically 
the  same  as  that  shown  in  Fig.  45.  For  spans  of  from  24  to  48  ft,  and  inclina- 
tions not  exceeding  6  in  to  the  foot,  the  types  shown  in  Figs.  46  and  47  are  the 
most  suitable.     Trusses  of  the  types  represented  by  these  two  figures  are  called 


Fig.  46.     Fan  Truss.     Spans  from  Thirty-six  to  Fifty  Feet 

FAN  TRUSSES.  The  truss  shown  in  Fig.  45  is  known  as  a  simple  Fink  truss. 
The  truss  shown  in  Fig.  47  is  supported  on  columns,  the  knee-braces  B  and  the 
pieces  A  being  stressed  only  when  the  building  is  subjected  to  wind-pressure. 
A  sag-tie,  shown  by  the  middle  dotted  line,  Fig.  46,  is  generally  inserted. 
"When  the  roof-construction  demands  three  purlins  on  each  side  of  the  truss, 


1026 


Types  of  Roof-Trusses 


Chap.  26 


one  of  the  fonns  shown  in  Figs.  48,  49,  50,  or  51  should  be  used.  The  term 
French  appears  to  be  generally  given  to  those  trusses  in  which  the  tie-beam  is 
raised  or  cambered  in  the  middle.     The  truss  shown  in  Fig.  51  may  be  called 


Fig.  47.     Fan  Truss  with  Knee-braces.     Spans  from  Forty  to  Sixty  Feet 


a  TRIANGULAR  Pratt  TRUSS  as  the  web  is  composed  of  verticals  in  compression 
and  diagonals  in  tension.  This  truss  is  not  as  economical  as  the  Fink  truss, 
except  when  the  inclination  of  the  rafter  is  less  than  ^^4.  pitch.  This  is  on 
account  of  the  great  length  of  the  web-members  in  compression.     In  designing 


Fig.  48.    Fink  Truss.     Spans  from  Forty  to  Eighty  Feet 

steel  trusses  it  is  desirable  to  have  as  many  members,  and  especially  as  many 
long  members,  in  tension  as  possible,  as  a  given  weight  of  steel  resists  a  much 
greater  stress  when  in  tension  than  when  in  compression.  The  great  economy 
of  Fink  trusses  and  fan  trusses  lies  in  the  fact  that  most  of  the  members 


Fig.  49.    French  Truss.     Spans  from  Forty  to  Eighty  Feet  ] 


are  in  tension  and  the  struts  are  short.  By  comparing  Figs.  50  and  51,  it  is 
seen  that  the  inner  strut  in  Fig.  50  is  only  one-half  as  long  as  the  strut  in  Fig. 
61.  If  the  roof  is  hipped  it  is  desirable  to  have  vertical  members  in  the  hip- 
trusses  to  receive  the  short  trusses  or  trussed  purlins. 


Types  of  Steel  Trusses 


im 


Fig.  50.     Fink  Truss  with  Vertical  Struts 


Depth  of  Fink  and  Fan  Trusses.  The  depth  of  these  trusses  at  the 
middle  is  usually  determined  by  the  roofing-material.  Thus  slate  should  not  be 
used  on  a  roof  in  which  the  rise  is  not  equal  to  one-third  the  span.  For  wooden 
shingles  the  rise  should  be  not  less  than  one-fourth  and  for  corrugated  iron  not 
less  than  one-fifth  the  span.  Steel-roll  roofing  may  be  used  where  the  rise  is 
but  one- twelfth  the  span.  There  are  many  kinds  of  so-called  ready  roofing 
put  up  in  rolls  which  may 
be  used  for  any  slope  ex- 
ceeding 34  in  to  the  foot. 
Tar-and-gravel  roofing 
should  never  be  used  on  a 
slope  exceeding  %  in  to  the 
foot.  Considering  the  con- 
struction of  the  roof  and 
the  weight  of  the  trusses,  the  most  economical  pitch  for  a  roof  is  about  one- 
fourth  the  span,  or  what  is  commonly  called  a  quarter-pitch,  the  rise  of  the 
rafters  being  6  in  for  each  12  in  of  run,  or  26°  34'.  When  the  rise  is  less 
than  one-sixth  the  span  some  other  type  of  truss  is  generally  required. 
When  the  inclination  of  the  roof  is  determined  almost  entirely  by  the  question 
of  economy  the  rise  is  generally  made  from  6  to  7  in  in  12  in.     With  Fink 

TRUSSES      or      FAN      TRUSSES 

having  inclinations  for  the 
rafters  not  exceeding  30°,  it 
is  more  economical  to  employ 
a  horizontal  chord  or  tie.  A 
truss  whose  bottom  chord 
has  a  rise  of  2  or  3  ft,  as  in 
Fig.  49,  presents  a  better 
appearance,  however,  than  one  with  a  horizontal  chord.  Raising  the  bottom 
chord  also  materially  increases  the  stresses  in  the  truss-members  and  hence 
increases  the  cost.  For  steep  roofs,  however,  it  is  generally  as  economical  to 
raise  the  bottom  chord,  because  of  the  shortening  of  the  members. 

Number  of  Panels.     The  number  of  panels  that  should  be  used  in  each 
half  of  the  truss  is  determined  in  great  measure  by  the  construction  of  the  roof. 


Fig.  51.    Triangular  Pratt  Truss 


Fig.  52.     Fink  Truss  with  Knee-braces.     Span  Sixty-eight  Feet 


If  jack-rafters  and  purlins  are  used  the  length  of  a  panel  may  be  as  great  as  12  ft; 
if  there  are  no  jack-rafters  and  the  planking  of  the  roof  is  nailed  directly  to  the 
purlins,  the  latter  are  placed  not  more  than  8  ft  apart;  and  if  the  roof  is  covered 
with  corrugated  iron  secured  to  the  purlins,  the  purlins  should  be  not  more  than 
5  ft  on  centers.  Whenever  the  purhns  are  more  than  4  ft  apart  they  should 
be  placed  at  the  truss-joints  to  prevent  large  bending-stresses  in  the  top  chord. 


1028 


Types  of  Roof-Trusses 


Chap.  26 


The  spacing  of  the  purlins,  therefore,  generally  determines  the  number  of  panels 
in  each  half  of  the  truss.  For  this  reason  also,  the  same  form  of  truss  may  be 
required  for  spans  of  40  and  80  ft;  but  of  course  the  members  will  not  be  as 
heavy  in  the  40-ft  truss  as  in  the  one  with  greater  span.  Most  of  the  trusses 
shown  in  Figs.  45  to  55  are  drawn  from  executed  designs  and  give  a  good 
idea  of  the  most  economical  division  for  different  spans. 

Truss  over  Car-Barn,  Newark,  N.  J.     When  stresses  due  to  flexure  are 
developed  in  the  truss-rafters,  that  is,  when  they  are  loaded  between  the  joints 


Fig.  53.     Fink  Truss.     Span  Fifty-one  Feet  Six  Inches 

the  distance  between  the  latter  should  not  exceed  9  ft,  and  preferably  7  or  8  ft 
depending  somewhat  upon  the  distance  between  the  trusses  themselves.  The 
diagram  shown  in  Fig.  55  represents  one-half  of  one  of  the  steel  trusses  used  in 
roofing  a  car-barn  for  the  North  Jersey  Railway  Company,  Newark,  N.  J.  There 
are  13  of  these  trusses  spaced  19  ft  2^4  in  on  centers,  each  having  a  span  of 
9814  ft  between  the  centers  of  the  supporting  columns,  to  which  they  are  riveted 
by  splice-plates  engaging  the  end  connection-plates  and  the  webs  of  the  columns. 
The  dimensions  of  the  principal  members  of  these  trusses  are  indicated  in  con- 


Fig.  54.     Fink  Truss  with  Vertical  Struts,  for  Drill-hall.     Span  Eighty  Feet 

nection  with  Fig.  55.  There  is  a  more  complete  description  in  the  Engineering 
Record  of  June  22,  1901.  These  trusses  were  shipped  in  four  sections,  which 
were  assembled  on  the  ground  in  a  horizontal  plane  and  riveted  up  complete. 
The  bottom  chord  was  stiffened  by  rails  lashed  on  each  side  of  its  entire 
length,  and  a  sling  being  attached  to  the  apex  of  the  top  chord,  the  truss  was 
hfted  and  set  on  top  of  the  columns  by  a  gin-pole,  50  ft  in  length.  The 
roofing  consists  of  corrugated  iron  supported  by  5-in  I-beam  purlins,  weighing 
10  lb  to  the  foot,  spanning  from  truss  to  truss  and  bolted  to  the  rafters  with 


Types  of  Steel  Trusses 


1029 


two  bolts  at  each  end.  The  general  spacing  of  the  purlins  is  4  ft  9%  in.  This 
is  a  good  example  of  an  extremely  hght  roof,  the  weight  of  each  truss  being  about 
4  200  lb  and  the  entire  weight  of  truss,  purlins,  bracing  of  lower  chord  and 
corrugated-iron  roofing  being  only  8  lb  for  each  horizontal  foot  of  surface  cov- 
ered. 

Table  III.    List  of  Descriptions  of  Different  Types  of  Roof-Trusses 

Engineering  Record 


Date 


March  19,  1892 

July  20,  1901 

January  4,  1902 

February  22,  1902.. 

August  12,  1905 

September  2,  1905 . 
September  16,  1905 
November  2,  1907 . 
September  16,  1911 
October  7,  191 1 


Type 


Howe 

Fink 

Fan 

Fink 

Pratt 

Fan 

Fan 

Fink 

Truss 

Truss 

Fink 


Number  of 
panels 


16 
12 
16 


Truss  over  Drill-hall.  The  truss  shown  in  Fig.  54  was  designed  for  the  roof 
of  a  drill-hall  having  a  span  of  80  ft  and  a  spacing  between  trusses  of  20  ft.  The 
roof  was  to  be  constructed  with  2  by  8-in  rafters  supported  by  purlins  at  the 


Main  Tie  l-4i  2  5"x 

3J^  X  %  L's 

„    \ 

t 

i> 

b 

" 

"       "  4-5. 

2-3^ 

x2H"xVi6"L's 

a^-^ 

\ 

sb 

i_ 

Rafter,  1-2. 

2-5  "x 

3M"x  Vie  L's 

T 

b 

\ 

"      2-3. 

2-5"  X 

8}<j"x  M"  L's 

b      J 

ff 

y 

^ 

\^ 

a,  a,  a, 

2-2H" 

yil\)i'    L's 

ct 

-=f^ 

y 

^ 

fe,  6,  b. 

1-214' 

^i\%'    L's 

> 

\  rA 

c, 

2-3"x 

2yi\y^'  L's 

J 

<r 

< 

d,d, 

2-SH" 

x2><^'x  5/16  L's  2 

^ 

€> 

1) 

\ 

y 

b 

>-yf 

a 

/ 

v-'r  \ 

/ 

/ 

4 

/ 

b 

/:; 

\ 

.y^   ^ 

<*Cfcl* 

\ 

/ 

\ 

/ 

25  5% 


J  4 
49'lK- 


Jl.. 


J8K 


Fig.  55.    Truss  over  Car-bam,  Newark,  N.  J.     Span  Ninety-eight  Feet,  Three  Inches. 
(See,  also,  Chapter  XXVIII,  Fig.  25) 

points  A,  B,  C,  D,  E  and  F.  Sashes  were  to  be  placed  in  the  rise  CD,  to  light 
the  interior  of  the  building.  The  joint  at  X  was  located  with  reference  to  the 
position  of  the  gallery-rod;  but  if  there  had  been  no  gallery  it  would  have  been 
more  economical  to  space  the  vertical  struts  uniformly,  as  in  Fig.  50.  In  all 
the  trusses  illustrated  the  plus  sign  adjacent  to  a  member  denotes  that  the 
member  is  in  compression,  while  the  minus  sign  denotes  that  it  is  in  tension. 
The  members  above  the  main  rafter,  as  CD,  DE  and  EF,  in  Fig.  54,  and  a  and  b 
in  Fig.  55,  do  not  form  a  part  of  the  truss  proper,  but  are  merely  a  framework  to 


1030 


Types  of  Roof-Trusses 


Chap.  26 


support  the  elevated  roof,  and  in  drawing  the  stress-diagram  for  the  vertical 
Ipads  they  would  be  omitted. 

In  the  issues  of  the  Engineering  Record  given  in  Table  III  may  be  found  de- 
scriptions and  illustrations  of  several  types  of  roof-trusses,  including  the  forms 
described  above. 

Fink  Trusses  with  Pin- Joints.  The  use  of  pin-joints  in  ordinary  roof- 
trusses  has  practically  been  abandoned,  even  for  long-span  heavy  trusses.  In 
the  Engineering  Record  of  March  12,  1892,  there  is  a  description  of  a  Fink  truss, 
with  pin-joints.  The  truss  is  heavy  and  is  built  entirely  of  rolled  metal.  The 
tension-members  are  5,  6  and  7-in  eye-bars.    The  span  is  about  105  ft. 

Trusses  for  Flat  Roofs.  For  supporting  flat  roofs  or  roofs  having  a  fall 
not  exceeding  i  in  to  the  foot,  one  of  the  types  shown  in  Figs.  5G  to  60  will  gen- 


Fig.  5G.     Warren  Truss  with  Verticals.     Span  Fifty-six  Feet 

erally  be  found  economical,  the  choice  of  the  particular  type  depending  somewhat 
on  the  span  and  on  whether  the  truss  is  supported  by  columns  or  by  brick  or 
stone  walls.  For  spans  up  to  about  50  ft,  either  of  the  forms  shown  in  Figs.  56 
or  57  answer  all  practical  requirements.  The  truss  shown  in  Fig.  56  is  intended 
to  be  used  where  the  slope  of  the  roof  is  at  right-angles  to  the  truss.  It  can  be 
built,  however,  with  the  top  chord  incHned  as  in  Fig.  57.  The  end-diagonals 
in  Fig.  56  are  in  tension,  while  in  Fig.  57  they  are  in  compression.  The  portions 
of  the  lower  chord  between  the  end-joints  and  the  walls  (Fig.  56)  have  no  stress 


Fig.  57.    Warren  Truss  with  Verticals  and  Knee-braces.     Spans  from  Thirty  to 
Fifty  Feet 


from  the  roof -load,  but  are  put  in  to  add  rigidity  to  the  construction  as  a  whole. 
In  trusses  supported  by  brick  walls  this  type  is  preferable  to  that  shown  in  Fig.  57, 
while  the  latter  is  more  suitable  when  the  roof  is  supported  by  columns.  The 
vertical  A,  Fig.  57,  is  inserted  to  receive  the  tension  or  compression  from  brace 
B,  and  has  no  stress  from  the  roof-loads. 

Double  Warren  Truss.  The  truss  shown  in  Fig.  58  is  known  as  a  double 
Warren  truss,  and  is  desirable  where  it  is  important  to  make  the  trusses  as 
.^^llpw  as  practicable.    It  can  be  built  )yith  light  members,  anc}  i^  a  ypry  s^fi 


Types  of  Steel  Trussps 


im 


truss,  being  especially  suitable  for  roofs  supported  by  steel  columns.  Fig.  58 
is  drawn  from  a  truss  in  actual  use.  The  member  in  the  middle  indicated  by  the 
dotted  line  should  never  be  omitted,  although  examples  may  be  found  where  it 
has  not  been  included.  Fig.  59^  also,  represents  a  roof-truss  which  was  con- 
structed with  a  span  of  57  ft  and  supported  by  steel  columns.  The  entire  lo^d 
on  the  truss  is  transmitted  to  the  columns  at  the  intersection  of  the  diagonals 


Rafterss. 


Fig.  58.    Double  Warren  Truss 

BB  and  the  top  chord.  Fig.  60  shows  a  truss  of  96-ft  span  over  a  pier-shed. 
New  York  City,  the  trusses  being  spaced  20  ft  apart.  They  are  about  10  ft 
high  and  weigh  i  300  lb  each.  They  were  delivered  from  the  shops  completely 
assembled  and  riveted,  and  were  raised  and  set  in  position  by  falls  suspended 
from  two  masts.  The  dimensions  of  these  trusses  are  given  in  the  Engineering 
Record  of  January  18,  1896. 


Fig.  59.    Pratt-truss  Type.     Span  Fifty-seven  Feet 


The  Plus  and  Minus  Signs  in  these  illustrations,  as  has  been  mentioned 
before,  indicate  compression  and  tension,  respectively,  under  a  uniformly  dis- 
tributed dead  load.  The  plus  and  minus  signs  used  together  indicate  that 
the  member  may  be  subject  to  either  tension  or  compression  according 
to  the  direction  of  the  wind  or  to  the  manner  of  distribution  of  the  snow.  In 
most  of  these  trusses  unsymmetrical  loads  may  change  the  stresses  in  the 


Fig.  60.    Warrep-truss  Type.    Pier-shed,  New  York  City.    Span  Ninety-six  Feet 

diagonals  near  the  middle  of  the  truss.  This  changing  of  stresses  due  to 
unequal  loading  is  considered  on  pages  1096  to  1104.  The  trusses  shown  in 
Figs.  56  to  60  are  almost  invariably  built  with  riveted  connections  and  with 
angle  or  channel -shapes  for  all  members. 

The  Pratt  Truss,  shown  in  Figs.  61  and  62,  is  the  form  of  steel  truss 
best  adapted  to  support  floor-loads,  the  members  indicated  by  double  lines 
being  in  compression  and  those  indicated  by  single  lines  in  tension*    When 


1032 


Types  of  Roof-Trusses 


Chap.  26 


supporting  floors  are  subject  to  moving  loads,  counterties  should  be  inserted 
where  indicated  by  dotted  lines.     For  trusses  of  this  type  piN-connections  are 
generally  employed  and  are  preferable  to  riveted  connections. 
.     The  Quadrangular  Truss.    The  truss  shown  in  Fig.  63  is  known  as  a  quad- 
^iiANGULAR  TRUSS,  and  has  the  proportions  of  the  truss  over  the  amphitheater 


/\ 

\ 

\  / 

\/ 

/ 

/ 

\ 

/  \ 

\ 

/\ 

/\ 

/ 

/ 

\ 

..:  Fig.  61.    Pratt  Truss 

of  the  Madison  Square  Garden,  New  York.  Figs.  64  and  66,  also,  show  variations 
of  this  type,  differing,  however,  from  the  latter  in  having  all  the  diagonals  in 
each  half-truss  inclined  in  the  same  direction.  In  the  typical  truss  their  direction 
is  usually  reversed  at  about  the  middle  of  each  half-span  in  order  to  keep  them 
in  tension.    The  plus  and  minus  signs  indicate  the  kind  of  stress  produced  in 


Fig.  62.    Suspended  Pratt  Truss 

a  member  by  a  uniformly  distributed  dead  load.  It  should  be  noticed  that  the 
middle  diagonals  of  trusses  64  and  66  are  in  compression.  These  trusses  are 
well  adapted  to  steel  construction  and  to  spans  up  to  180  ft.  When  the  span 
exceeds  100  ft  one  end  of  the  truss  should  be  supported  on  rollers  to  allow  for 
the  EX^^^^j  pr^fiONTRACTiON  in  the  steel.     In  these  trusses  the  load  is  trans- 


Fig.  G3.     Quadrangular  Truss.     Amphitlieater,   Madison   Square   Garden,   New  York 

City 

%rtt:eidfo'tl^'tbp  of  the  column-support,  the  truss  proper  being  included  within 
•the  points^,  jB,  C,  D  and  E,  Figs.  64  and  65.  The  continuation  of  the  bottom 
chord  to  the  columns  is  for  the  purpose  of  bracing  the  roof  from  the  latter,  there 
being  no  stresses  in  these  end-chord  members  due  to  vertical  loads.  This  mem- 
ber B,  Fig.  63,  and  the  corresponding  member  in  Figs.  64  and  65  should  be  con- 
structed to  resist  both  tension  and  compression.     For  short  spans  the  lower 


Types  of  Steel  Trusses 


1033 


Fig.  65.    Ouadrangular  Truss 


rj7 

V    + 

\     1 

H 

1871 

[7 

^ 

V 

V 

•^^i-«-13'8^| 

t-..i 

^ 

.i_.._ 

"f--^ 

^16^^ 

^12 

^^- > 

^16^'  • 

DIAGRAM  OF  TRUSS 


Fig.  66.     Diagrams  of  Trusses  in  Auditorium,  Kansas  City,  Mo.    Plan  of  Two  Trusses 
Showing  Lateral  Bracing 


1034 


Types  of  Koof-Trusses 


Chap.  26 


chord  may  be  made  in  the  shape  of  a  semicircle  or  half-ellipse  so  as  to  give 
more  of  an  arch-eflfect.     There  are  numerous  examples  in  this  country  of  quad- 


lladius  -113'2»/ie 
SPanels  9'9=78'0  =Spaa 


Fig.  67.    Riveted  Truss  with  Broken  Top  Chord.     Power-house,  Interborougli  Rapid 
Transit  Company,  New  York  City 


3«J.4    n 


3%" 

-  ? 

Radiu3^3l2  0       } 


Fig.  68.     Pin-connected  Truss  Over  Drill-hall,  71st  Regiment  Armory,  New  York  City 

rangiilar  trusses  having  spans  of  from  loo  to  i8o  ft.  For  the  wider  spans  it  is 
customary  to  build  the  trusses  with  pin-connections,  eye-bars  being  used  for 
the  ties.     When  this  is  done  it  is  usually  necessary  to  insert  counterbraces 


Arched  Trusses 


m^ 


in  two  panels  of  each  half  of  the  truss  as  shown  by  the  dotted  lines,  Fig.  63, 
as  under  an  unsymmetrical  or  wind-load  the  stresses  in  the  diagonals  arc  gener- 
ally reversed.  For  spans  less  than  loo  ft,  the  trusses  may  be  built  with  riveted 
CONNECTIONS.  In  this  case  the  diagonals  are  generally  made  of  angles  capable 
of  resisting  both  tension  and  compression,  the  counterbraces,  therefore,  not 
being  required.  For  this  type  of  truss  the  stresses  due  to  wind  and  snow  should 
be  computed  independently  of  the  dead  load  and  the  membefs  computed  for 
the  maximum  stresses  produced  by  every  possible  combination  of  loading. 

Trusses  for  the  Auditorium,  Kansas  City,  Mo.  A  description,  with 
illustrations,  of  the  truss  shown  in  Fig.  66,  which  is  a  diagram  of  one  of  the  trusses 
over  the  Kansas  City  Auditorium,  may  be  found  in  the  Engineering  Record  for 
July  22,  1899,  and  in  the  Engineering  News  of  November  2,  1899. 

Riveted  Truss  with  Broken  Top  Chord.  A  description  is  given  in  the 
Engineering  Record  of  October  15,  1904.  The  span  is  78  ft  between  centers 
of  the  supporting  columns  (Fig.  67). 

Truss  for  Drill-Hall,  New  York  City.  A  pin-connected  truss,  over  the 
drill-hall  of  the  71st  Regiment  Armory,  New  York  City,  has  a  span  of  190  li 
4  in  and  full  descriptions  of  it  are  given  in  the  Engineering  News  of  June  16, 
1904,  and  in  the  Engineering  Record  of  July  2,  1904  (Fig.  68). 


i.   Arched  Trusses 

Difference  Between  an  Arched  Truss  and  a  Trussed  Arch.  For  sup- 
porting the  roof  of  very  large  spaces  such  as  drill-halls,  riding-halls,  railway 
train-sheds,  etc.,  trusses  in  the  form  of  arches  or  arches  composed  of  trussea 
members  are  often  employed .  The  essential  difference  between  an  arched  truss 
and  a  trussed  arch  is  that  under  vertical  loads  the  supporting  forces  of  an  ardied 
truss  are  vertical,  while  for 
a  trussed  arch  they  are 
incHned. 

Bowstring  Trusses.  Pre- 
vious to  the  year  1880  most 
of  the  wrought-iron  trusses 
of  wide  span  were  built  in 
the  form  of  a  bow,  from 
which  the  term  bowstring 
was  derived.  Trusses  of  this  type  were  built  with  spans  of  from  88  to  211 
ft  and  with  a  rise  at  the  middle  of  from  Vs  to  V4,  the  span.     At  that  time  this 

type  was  considered  the  most 
economical  for  spans  exceed- 
ing 120  ft,  but  in  recent 
years  they  have  been  com- 
paratively Httle  used.  Fig. 
69  is  the  diagram  of  a  bow- 
string truss  with  a  span  o^ 
153  ft  6  in.  The  trusses  iri 
this  particular  case  ares 
spaced    21    ft    6    in    apart. 


Fig.  69.    Bowstring  Truss 


Fig.  70.     Bowstring  Truss 


The  arched  top  chord  consists  of  a  wrought-iron  deck-beam  9  in  deep,  with 
a  10  by  ii4-in  plate,  riveted  to  its  upper  flange.  Towards  the  springing 
this  rib  is  strengthened  with  7  by  Vs-in  plates  riveted  on  each  side  of  the 
deck-beam.  The  struts  are  wrought-iron  I  beams  7  in  deep.  The  bottom 
chord  has  a   sectional  area  of  6^^   sq  in  and  each  diagonal  tension-rod  Jl 


1036  Types  of  Roof-Trusses  Chap.  26 

diameter  of  iV4  in.  Each  truss  is  fixed  at  one  end  and  rests  on  rollers 
at  the  other,  allowing  free  expansion  and  contraction  due  to  changes  of  tem- 
perature in  the  metal.  Fig.  70  shows  a  similar  truss  having  a  span  of  212  ft. 
It  consists  of  BOWSTRING  PRINCIPALS  Spaced  24  ft  apart.  The  rise  is  one-fifth 
the  span,  the  middle  of  the  bottom  chord  rising  17  ft,  and  of  the  top  chord  4oy2  ft 
above  the  springing.  The  top  chord  is  a  15-in  wrought-iron  I  beam  and  the 
bottom  chord  a  round  rod  in  short  lengths,  4  in  in  diameter  and  thickened  at 
the  joints.  The  ties  of  the  bracing  are  of  plate  iron  from  5  to  3  in  in  width,  and 
%  in  thick.  The  struts  are  formed  of  bars  having  the  form  of  a  cross.  During 
the  last  ten  or  twelve  years  a  number  of  roofs  have  been  supported  on  trusses 
which  can  hardly  be  classed  as  simple  trusses;  and  yet  it  is  questionable  if 
they  are  true  arches.  Probably  the  frames  act  partially  as  simple  trusses 
and  partially  as  arches. 

Trusses  for  the  Conservatory  Building,  Garfield  Park,  Chicago,  111. 

Engineering  News,  August  27,  1908.  The  roof  is  supported  by  pointed  trusses 
spaced  12  ft  6  in  on  centers.  The  truss-span  is  80  ft  6  in,  center  to  center  of 
end-supports.  The  chords  of  the  trusses  are  parallel  and  connected  by  Warren 
BRACING.  Both  ends  of  the  trusses  are  bolted  to  the  supports  and  consequently 
there  must  be  some  horizontal  thrust  under  certain  conditions.  The  trusses 
are  riveted  at  all  joints  and  have  no  hinges  or  pins. 

Trusses  for  the  Chicago  and  North  Western  Railway  Station,  Chicago, 
111.  Engineering  Record,  June  18,  19 10.  The  roof  over  the  main  waiting-room 
is  carried  by  trusses  each  having  a  span  of  90  ft  4  in  and  a  rise  of  31  ft  and  being 
riveted  to  columns  about  27  ft  6  in  apart.  All  connections  are  riveted.  The 
clear  height  of  the  bottom  chords  at  the  middle  is  84  ft. 

Trusses  for  the  Peoria  and  Pekin  Union  Railway  Trains-Shed,  Peoria, 
111.  Engineering  Record,  December  8,  1900.  The  trusses  are  riveted  to 
columns  about  30  ft  above  the  floor  and  spaced  20  ft  apart.  The  truss-span  is 
109  ft  4  in,  center  to  center  of  end-supports,  with  a  clear  rise  of  about  10  ft. 
The  depth  at  the  middle  is  18  ft  and  at  the  end  6  ft.    All  connections  are  riveted. 

Trusses  for  the  New  Union  Station,  Washington,  D.  C.  Engineering 
Record,  February  6,  1904.  The  concourse-roof  is  supported  by  crescent 
trusses,  each  having  a  span  of  132  ft  514  in  and  a  clear  rise  of  22  ft  SV2  in.  They 
are  spaced  about  39  ft  4  in  apart.  One  end  of  each  truss  rests  upon  masonry 
and  the  other  is  riveted  to  a  heavy  plate  girder.  All  connections  are  riveted. 
The  bottom  chord  at  the  middle  is  45  ft  above  the  floor.  The  trusses  over  the 
waiting-room  of  the  same  station  have  a  span  of  137  ft  8  in  and  a  rise  of  45  ft 
5  in.  The  chords  are  parallel  and  the  ends  are  anchored  with  bolts  to  the 
masonry. 

Trusses  for  the  Riding-Hall,  Armory  for  Squadron  C,  National  Guard, 
Brooklyn,  N.  Y.  Engineering  News,  August  29,  1907.  The  main  trusses  have 
a  span  of  179  ft  2  in  and  a  rise  of  about  66  ft  in  the  clear.  The  total  depth  of 
the  truss  at  the  middle  is  14  ft,  while  at  the  ends,  where  the  chords  approach 
each  other  and  finally  become  vertical,  it  is  3  ft  3  in.  One  end  is  anchored  to 
the  masonry  and  the  other  is  on  rollers.  The  trusses  are  in  pairs  10  ft  ii^/^  in 
on  centers  and  the  pairs  are  spaced  38  ft  8^/^  in  on  centers.  All  connections  are 
riveted. 

Trusses  for  the  New  Rock  Island  Terminal  Station  Train-Shed,  Chicago, 
111.  Engineering  Record,  September  12,  1903.  Engineering  News,  August  6, 
1903.  The  trusses  over  the  tracks  have  a  span  of  221  ft  i  in  center  to  center  of 
the  end-pins,  a  rise  of  28  ft  and  a  depth  at  the  middle  of  25  ft  6  in.     They  are 


Arched  Trusses 


10^/ 


supported  bjT  columns  and  are  spaced  from  lo  ft  3  In  to  19  ft  6  in  apart.  All 
principal  connections  are  made  with  pins. 

Curved  Trusses  with  Horizontal  Ties.  Curved  or  arched  trusses  are 
often  constructed  with  a  horizontal  member  connecting  the  ends  at  the  supports. 
This  makes  the  structure  as  a  whole,  including  the  horizontal  member,  usually 
called  the  tie-rod,  a  simple  truss  requiring  only  vertical  supporting  forces 
for  vertical  loads,  provided  one  end  is  free  to  move,  as  it  is  when  placed  on 
rollers.  When  the  trusses  are  supported  by  long  columns  it  may  be  assumed 
that  the  ends  have  freedom.  A  few  examples  are  given,  some  of  which  are 
commonly  classed  as  true  arches. 

Trusses  for  the  Sullivan  Square  Station,  Elevated  Railway,  Boston, 
Mass.     Engineering  Record,  June  15,  1901.     Fig.  71.    These  arches  spring 


K— 


4_.^1.,,. _. 


// 


Fig.  71.    Arched  Truss  for  Sullivan  Square  Station,  Elevated  Railway,  Boston,  Mass. 


from  steel  columns  and  are  provided  with  tension-rods  which  take  up  the  thrust. 
The  arch  proper  rests  on  two  4iA-in  pins  at  each  end,  as  indicated  in  the  diagram, 
the  tie-rods  being  connected  to  them.  The  bracing  below  each  pin  is  riveted 
to  the  column  and  the  arch  itself  is  built  of  angles  and  plates  with  riveted  con- 
nections. Fig.  71a  shows  the  joint  at  A  where  the  tie-rods  are  connected  and 
held  up  by  a  i-in  suspension-rod  from  the  crown  of  the  arch.  This  construc- 
tion is  the  same  in  principle  as  that  of  the  wooden  arch  shown  by  Fig.  42. 

United  States  Express  Company's  Receiving  Station,  New  York  City. 
Engineering  Record,  October  22,  1904.  The  roof -trusses  in  this  building  are 
supported  on  24-in  brick  walls  at  the  level  of  the  second-story  floor  and  have 
their  ends  connected  by  I  beams  which  form  a  part  of  the  floor-framing  of  the 
second  story.  Each  truss  has  a  span  of  74  ft  4  in  and  a  clear  rise  of  27  ft.  They 
are  spaced  about  24  ft  5  in  apart  and  have  all  connections  riveted.    Since  the 


1038 


Types  of  Roof-Trusses 


Chap.  26 


tjes  are  very  heavy  one  might  be  led  to  classify  these  trusses  with  true  arches, 
fixed  at  the  ends;  but  as  the  condition  of  fixed  ends  rarely  obtains  in  practice, 
it  is  better  to  consider  this  type  of  structure  as  an  arched  truss  with  a  tic-rod, 
or  possibly  as  similar  to  the  type  shown  in  Fig.  75. 


Table  IV.     General  Dimensions  of 

a  Few  Three-Hinged  Arches 

Location 

Span 
ft     in 

Rise 
ft       in 

Tie 

Syracuse  University     

lOI     4 

106    0 
121  10 
134    0 
149    9 
163    6 
172    0 
178    6 
181    0 
184    0 

189  8 

190  4 

191  4 
215    0 
227    0 
230    0 
252    8 
259    0 
300    8 

363    0 

"56    2i4 

96    3 

32    6 

66    6 

73    5% 

69    9V2 

80    0 

90    2V2 

94  (about) 
103    aV^ 

88    oj 

84    0 

73    0 

94    0 

89'  9% 
88    3V2 
100    4 

206    4 

Floor-b^ms 
No  tie 
tTwo  1%  X  iVs 

t2V2X2y2 

tTwo  2%  round  rods 

9-in  I  beam 

No  tie 

No  tie 

No  tie 
tTwo  1%-in  round  rods 

Two  channels 
tTwo  4  X  %-m  plates 

t9  X  Via-in  plate 
Two  i2-in  I  beams 

Lawson  Riding-Academy 

Machinery  Hall,  Chicago  Exp ; . 

22nd  Reg.  Armory,  New  York 

Coliseum    Chicago  (new)   . . 

Newark,  N.  J.,  Armory 

Government  Bldg.,  St.  Louis  Exp.. 
Coliseum,  St.  Louis 

Hartford,  Conn.,  Armory 

Frankfort,  Germany,  Train-Shed... 
69th  Reg.  Drill- Hall,  New  York. . . 
5th  Reg.  Armory,  Baltimore,  Md.. . 
47th  ^eg.  Armory,  Brooklyn,  N.  Y. 
Coliseum,  Chicago  (old) 

74th  Reg.  Arpiory,  Buffalo,  N.  Y. . 

Coal-Shed,  Wende,  N.J 

Jersey  City  Train-Shed. 

Philadelphia  Train-Shed 

Broad  Streef;  Station,  Phila 

Manufacture^    and    Liberal   Arts 
Bldg.,  Chicago  Exp 

Location 

Distan 
c 

ce,  center  to 
enter* 

Reference 

Syracuse  University 

17  ft 

32  ft 
50  ft 
II  an 
22V2 
31  an 

35  ft 

36  ft 
6  an 

33  ft 

6%£ 

iiK'  in 

0  in 

Sin 
d52ft 
.0  25  ft 
d  26V2  ft 

0  in 

8  in 
d  52%  ft 

6  in 
ind  38^/4  ft 

R.  Aug.  22,  1908 
R.  Dec.  31.  1904 
R.  Dec.  24,  1892 
N.  May     5,  1910 
N.  Sept.  14^  1899 
R.  May  26,  1900 
N.  Sept.  29,  1904 
N.  Aug.  10,  1899 
R.  Sept.  12,  1908 
R.  Mar.     5, 1892 
R.  June     3,  1905 
R.  May  14,  1904 
R.  Dec.  23,  1899 
N.  Nov.  12,  1896 
R. June     9, 1900 
R.  Oct.     3.  1908 
N.  Sept.  25,  1899 
R.  July    16,  1892 
R. June    10, 1893 

N.  Sept.    I,  1892 

Lawson  Riding-Academy         

Machinery  ii^l\,  Chicago  Exp 

22nd  Reg.  Armory,  New  York 

Coliseum,  Chicago  (new) 

Newark,  N.  J.,  Armory 

Government  Bldg.,  St.  Louis  Exp.. 
Poliseum.  St.  Louis 

Hartford,  Conn.,  Armory 

Frankfort,  Germany,  Train-Shed... 
69th  Reg.  DriU-Hall,  New  York  . . 
5th  Reg.  Armory,  Baltimore,  Md.. 
47th  Reg.  Armory,  Brooklyn,  N.  Y. 
Coliseum,  Chicago  (old) 

34  ft 
46  ft 

4  in 

5  in 

74th  Reg.  Armory,  BufTalo,  N.  Y.. 

Coal-Shed,  Wende,  N.  J 

Jersey  City  Train-Shed 

22  ft 

14^2  £ 

loU  in 
md  43^1'  ft 

Philadelphia  Train-Shed. 

Broad  Street  Station,  Phila 

Manufactures    and    Liberal   Arts 
Bldg.,  Chicago  Exp 

*  Center  to  center  of  end-supports. 

X  To  lower  chord.  N.  Engineering  News. 


t  Dimensions  in  inches. 
R.  Engineering  Record. 


Arched  Trusses 


Sj^Pin         '2-l>g  Plates 
Fig.  71a.    Detail  at  A,  Fig.  71. 


Trusses  for  Drill-Hall,  13th  Regiment  Armory,  Scranton,  Pa.  Engi- 
neering Record,  August  24,  1901.  These  roof-trusses  are  about  5  ft  deep  and 
are  spaced  about  12  ft  on  centers.  The  truss-span  is  156  ft,  over  all,  with  a  rise 
of  47  ft  in  the  clear.  The  ends  rest  on 
flat  plates  and  are  connected  by  a  tie 
consisting  of  two  i%-in  round  rods. 
Freedom  of  motion  is  provided  at  one 
end  by  slotting  the  holes  for  the  anchor- 
bolts. 

Trusses  for  Armory  Drill-Hall, 
Providence,  R.  I.  Engineering 
Record,  April  13,  1907.  The  type  of 
roof-truss  used  in  this  building  is  com- 
monly called  a  three-hinged  arch, 
there  being  a  pin  at  each  support  and 
one  at  the  crown;  but  the  two  end-pins 
are  connected  by  a  tie  and  one  end-shoe 
is  provided  with  rollers  and  hence  the 
structure  is  a  simple  truss  composed  of  three  members,  two  of  which  are 
trusses  in  themselves.  The  truss-span  is  166  ft  8  in  and  the  rise  about  61  ft. 
The  trusses  are  riveted  and  spaced  about  26  ft  i  in  on  centers. 

Trusses  for  the  Pennsylvania  Railway  Train-Shed,  Pittsburgh,  Pa. 
Engineering  Record,  August  23,  1902.  The  trusses  have  three  hinges  and  a 
TIE  and  a  roller-bearing  at  one  end.  The  truss-span  is  255  ft  %  in  between 
end-pin  centers,  the  rise  93  ft  between  pin-centers  and  the  depth  at  the  cente^- 
7  ft.  The  trusses  are  riveted  and  stand  in  pairs  9  ft  on  centers  and  the  pairs 
are  spaced  49  ft  6  in  on  centers. 

The  Three-hinged  Arch  as  employed  for  supporting  the  roofs  over  large 
rooms,  train-sheds,  drill-halls,  etc.,  is  composed  of  two  curved  trusses,  usually 
of  the  same  form  and  dimensions,  resting  upon  pins  at  the  supports  and  con- 
nected by  a  pin  over  the  middle  of  the  span.  The  supports  are  assumed  to  be 
fixed  in  position  and  are  often  connected  by  a  tie  to  insure  stability  and  take 
up  the  horizontal  thrust  of  the  arch.  While  a  metal  tie  between  masonry  sup- 
ports does  not  make  these  supports  fixed  in  position  imder  all  or  any  conditions 
of  loading,  yet  for  all  practical  purposes  they  may  be  so  considered;  and  these 
three-hinged  structures  which  have  ties,  provided  there  is  no  arrangement 
for  horizontal  end-movement  due  to  roller-bearings,  etc.,  may  be  classified  with 
those  whose  supports  must  resist  all  horizontal  as  well  as  all  verticq,!  forces. 
The  bottom  pins  are  usually  placed  below  the  floor-level  so  that  the  tie-rods, 
when  used,  may  be  concealed  by  the  floor  or  even  made  a  part  of  its  framing. 
Under  certain  conditions  the  arches  can  be  so  designed  that  the  horizontal  thrust 
will  be  quite  small  and  the  supports  designed  without  the  use  of  the  hofizontal 
tie.  The  special  advantages  of  the  three-hinged  arch  for  the  class  of  build- 
ings above  mentioned  are  economy  and  a  maximum  amount  of  clear  space 
beneath  the  truss.  Much  of  the  economy  results  from  the  omission  of  support- 
ing columns.  The  base  of  the  arch  being  very  near  the  ground-level,  it  is  also 
well  designed  to  resist  wind-pressure.  Another  advantage  of  this  type  is  the 
free  movement  allowed  under  temperature-changes  without  causing  additional 
stresses  in  the  members  of  the  structure,  the  middle  part  rising  or  falling  freely 
with  a  slight  rotation  of  the  half-trusses  about  the  pivots.  In  the  case  of  the 
arches  of  the  buildings  of  the  Paris  Exposition,  it  was  estimated  that  a  range  of 
temperature  of  100°  F.  would  produce  a  change  in  level  of  2%  in  at  the  center 
pivot.     The  arched  ribs  are  usually  built  of  plates,  angles,  or  channels,  yti^ 


1040 


Types  of  Roof-Trusses 


Chap.  26 


riveted  connections  and  frequently  with  a  solid-plate  web  at  the  bottom.  The 
determining  of  the  stresses  and  detailing  of  the  members  and  joints  require  the 
services  of  a.  competent  structural  engineer;  but  the  illustrations  given  will 
enable  the  architect  to  decide  on  the  general  shape  of  the  trusses  for  the  purpose 
of  making  preUminary  drawings  and  the  computations  and  detail  drawings  can 
be  made  later. 


-2  Square  bars 


Three-hinged  Arch.     Manufactures  and  Liberal  Arts  Building, 
Chicago  Exposition 


Fig.  72.    Half  Truss. 


Trusses  for  Railway  Station,  Frankfort-on-the-Main,  Germany.    The 

first  suggestion  for  hinging  the  ribs  at  the  crown  was  made  by  M.  Manton, 
a  French  engineer.  The  writer  believes  that  the  first  application  of  this  principle 
to  roof-trusses,  at  least  on  a  large  scale,  was  made  in  the  train-sheds  of  the  Union 
Railway  Station  completed  in  the  year  i888at  Frankfort-on-the-Main,  Germany. 
These  trusses  have  a  span  'of  about  184  ft.  Engineering  Record  of  September 
12,  1891,  and  March  5,  1892. 

Trusses  for  Machinery  Hall,  Paris  Exposition.     The  large  roof  of  the 
Machinery  Hall  of  the  Paris  Exposition  of  1899  was  supported  by  trusses  of 


Arched  Trusses 


mi 


this  type,  the  span  being  368  ft  and  exceeding  anything  hitherto  attempted  in 
roof-trusses.  Since  then  trusses  of  this  kind  have  been  frequently  used  for 
roofing  large  exhibition-halls,  train-sheds,  armories,  and  similar  buildings. 

Trusses  for  Manufactures  and  Liberal  Arts  Building,  Chicago  Exposi- 
tion. Fig.  72  shows  the  half-truss  of  one  of  the  three-hinged  arches  sup- 
porting the  roof  of  the  Manufactures  and  Liberal  Arts  Building  of  the  Chicago 
Exposition.     Engineering  News,  September  i,  1892. 

Trusses  for  Drill-Hall,  Brooklyn,  N.  Y.  Fig.  73,  in  a  similar  manner, 
shows  the  half-truss  of  one  of  the  three-hinged  arches  over  the  drill-hall  of 


^2  Bars  4  X  % 
Fig.  73.     Half  Truss,  Three-hinged  Arch,  Drill-hall,  Brooklyn,  N.  Y. 


the  47th  Regiment  Armory,  Brooklyn,  N.  Y.  Engineering  Record,  December 
23,  1899.  A  description  of  the  arch  shown  in  Fig.  74  is  given  in  the  Engineering 
Record  of  November  19  and  December  24,  1892.  The  horizontal  thrust  due  to 
the  dead  load  is  small. 

Two-hinged  Arches.  When  there  are  only  two  pins,  usually  at  the  sup- 
ports, the  trusses  become  two-hinged  arches.  As  in  the  case  of  three-hinged 
erches,  there  may  be  a  tie  or  the  supports  may  be  entirely  depended  upon  to 
resist  the  horizontal  thrust. 

Trusses  for  Live-Stock  Pavilion,  Chicago,  111.  In  the  Engineering  News 
of  June  28,  1906,  there  is  a  description  of  the  two-hinged  arches  supporting 
the  roof  of  this  building.  The  arch  span  is  198  ft,  the  rise  54  ft  and  the  truss- 
spacing  42  ft.     Each  truss  has  a  tie  consisting  of  one  2^l6-in  round  rod. 

Trusses  for  Railway  Station,  Cologne,  Germany.  This  station,  owned 
by  the  Prussian  Railways,  has  two-hinged  arches  supporting  the  roof  of  the 
train-shed.  The  arch-span  is  209  ft  6  in  and  the  rise  79  ft.  There  is  a  brief 
mention  of  it  in  the  Engineering  News,  October  6,  1892.     A  number  of  roofs 


1042 


Types  of  koof-Trusses 


Chap.  26 


-121-10- *| 

JH'«g.  74.    Three-hinged  Arch,  Machinery  Hall,  Chicago  Exposition 


Fig.  75.    Two-hinged  Arch,  Exposition  Hall,  Providence,  R.  I. 


Cantilever  Trusses 


1043 


are  supported  by  structures  similar  to  that  shown  in  Fig.  75.  While  such  a  frame 
is  not  strictly  a  two-hinged  arch,  owing  to  the  lack  of  freedom  at  the  supports, 
it  may,  however,  for  all  practical  purposes,  be  so  considered. 

Table  V.    List  of  Buildings  with  Trusses  of  the  Two-Hinged-Arch  Type 


Name 

Span 

Spacing 

Armory,  Pawtticket,  R.  I 

ft 
82 
92 
96 

100 

104 
ii8 

120 
122 

176 
196 

ft 

24 
25 
24 
24 
25 

24.5 
23  to  25 
30 
24.5 
35 

Armory,  Portland,  Me 

Phoenix  Hall,  Brockton,  Mass 

Armory,  Northampton,  Mass. 

Palace  Rink,  Hartford,  Conn 

Exposition  Hall,  Providence,  R.  I 

Armory,  Cleveland,  Ohio 

Armory,  Boston,  Mass.    . . 

Armory,  22d  Reg.,  New  York  City 

Armory,  Brooklyn,  N.  Y 

These  structures  are  described  in  Building  Construction  and  Superintendence,  Part 
HI,  by  F.  E.  Kidder  and  are  similar  to  the  type  shown  in  Fig.  75. 

Fixed  Arches,  or  arches  without  hinges,  are  seldom  employed  in  buildings. 
In  a  number  of  examples  cited  above  the  structures  have  the  appearance  of  being 
fixed  at  the  ends,  but  a  closer  inspection  indicates  that  they  are  not  sufficiently 
anchored  to  warrant  their  being  classed  as  fixed  arches.  -.^ 


5.   Cantilever  Trusses 

General  Principles.  A  cantilever  beam  or  cantilever  truss  is  that 
portion  of  a  larger  beam  or  truss  which  extends  beyond  one  of  the  supports,  as 
B  in  Figs.  76  to  79  and  A  in  Fig.  80.  The  overhanging  portion  B  is  called  the 
cantilever-arm  and  the  portion  C  the  anchor-span.  The  cantilever-arm  may 
support  at  its  end  another  beam  or  truss.  The  term  cantilever  was  originally 
used  to  designate  a  projecting  beam  which  served  as  a  bracket;  in  engineering 
it  is  used  to  denote  a  beam  or  girder  fixed  at  one  end,  by  being  either  built  into 
a  wall,  or,  as  is  more  commonly  the  case,  extended  a  sufficient  distance  beyond 
its  support  to  form  an  anchorage.  Thus  in  Fig.  76,  which  shows  a  beam  resting 
on  two  supports,  B  is  the  cantilever  or  cantilever-arm  and  C  the  anchor-span  or 
anchorage.  It  is  obvious  that  if  this  entire  beam  were  uniformly  loaded  the 
support  P  would  carry  the  greater  part  of  the  total  load;  and  also,  that  an 
additional  load  W,  at  the  end  of  the  cantilever,  might  cause  a  negative  reaction 
or  upward  pull  at  the  support  D,  in  which  case  the  reaction  at  P  would  exceed 
the  load  on  the  beam,  unless  the  negative  reaction  at  D  is  considered  as  an 
additional  load.  Although  both  conditions  of  loading  occur  in  practice,  the 
cantilever  end  of  the  truss  usually  requires  an  anchorage  rather  than  a  support 
at  the  inner  end.  As  apphed  to  roof-construction  some  such  arrangement  as 
is  shown  in  Fig.  77  is  generally  required  to  make  this  method  of  support  prac- 
ticable; that  is,  a  wide  middle  span,  with  shorter  spans  or  aisles  on  each  side  of 
it.  Each  cantilever-arm  is  usually  made  from  V4  to  V&  the  middle  span  and  a 
simple  middle  truss,  represented  by  S,  supported  by  the  arms  of  the  canti- 
levers, is  used  to  support  the  rest  of  the  roof.  In  all  such  cases,  therefore,  can- 
tilever trusses  must  be  used  in  pairs,  one  on  each  side  of  the  building;  and  there 
must  be  room  or  passages  outside  of  the  principal  span  to  permit  the  use  of  the 


1044 


Types  of  Roof-Trusses 


Chap.  26 


outer  or  anchor-spans.  This  arrangement  is  generally  found  in  auditoriums, 
armories,  exhibition-halls  and  similar  buildings,  and  is  sometimes  conveniently 
adapted  also  to  other  classes  of  structures.  Of  course,  in  a  large  building  a  beam 
consisting  of  a  single  member  such  as  is  shown  in  Fig.  77  could  not  be  used; 


Fig.  79 
Figs.  76  to  80. 


Fig.  80 
Cantilevers  and  Cantilever  Trusses 


but  the  principle  of  construction  is  the  same  whether  the  cantilever  is  a  single 
member  or  a  large  truss.  Fig.  78  is  the  diagram  of  a  truss  which  takes  the  place 
of  the  beam  CB  in  Fig.  77,  the  single  lines  representing  the  tension-members 
and  the  double  lines  the  compression-members.  Fig.  81  shows  the  complete 
arrangement  of  two  of  these  trusses  with  the  accompanying  middle  truss,  for  an 


Fig.  81.     Suggestion  for  Wooden  Cantilever  Truss 

entire  roof.  The  truss-principle  shown  in  these  figures  may  be  developed  to 
almost  any  extent.  The  lower  chord  may  be  curved,  but  the  general  outline 
of  the  truss  is  best  adapted  to  those,  roofs  in  which  a  wide  middle  part  is  to 
be  supported  by  cantilevers.  For  bridge-trusses  or  floors  the  form  shown  in 
Fig.  79  may  be  used;  whik  for  shed  and  platform-roofs,  open  on  one  side,  trusses 


Cantilever  Trusses 


1045 


of  the  form  shown  in  Fig.  80  are  about  the  only  ones  practicable.  In  this  latter 
truss  the  proportions  of  the  arms  are  such  that  only  a  slight  support  is  required 
at  W,  and  a  consequent  compressive  stress  developed  in  the  lower  portion  of  the 
rafter. 

Advantages  and  Disadvantages  of  the  Cantilever  Truss.  The  cantilever 
truss  possesses  some  special  advantages.  The  clear  height  in  the  middle  is  greater 
than  can  be  obtained  with  any  other  type  excepting  the  three-hinged  arch;  its 
appearance  is  light  and  graceful,  and  there  is  no  horizontal  thrust  and  conse- 
quently no  necessity  for  tic-rods.  The  particular  advantage  of  this  truss  for  very 
great  spans  is  that  it  can  be  erected  without  scaffolding  under  the  middle  part, 
and  in  bridge-work  this  is  considered  as  its  only  advantage.  It  is  claimed  by 
some  prominent  engineers  that  the  cantilever  type  of  truss  is  not  an  economi- 
cal one  and  not  as  desiral^le  for  spans  of  150  ft  or  more  as  the  three-hinged 
ARCH.  It  does  not  as  readily  lend  itself  to  methods  of  allowing  for  expansion 
and  contraction  as  the  three-hinged  arch,  the  bowstring  truss,  or  the  quad- 
rangular TRUSS.  For  certain  classes  of  buildings,  however,  and  especially 
where  the  middle  span  does  not  exceed  150  ft,  it  can  perhaps  be  used  with 
better  architectural  effect  than  is  possible  with  other  types,  the  cost  remaining 
about  the  same.  For  roofing  platforms,  grand-stands,  etc.,  where  an  outer 
support  is  not  desired,  it  is  the  only  type  available. 

Truss  for  Grand-Stand,  Monmouth  Park,  N.  J.  Fig.  82  is  a  diagram  of 
one  of  the  cantilever  trusses  supporting  the  roof  of  the  grand-stand  at  this 


Fig.  82.     Cantilever  Truss,  Grand-staud,  Monmouth  Park,  N.  J. 

racing-track,  the  details  of  which  were  published  in  Architecture  and  Building, 
in  February,  1890.  This  is  an  instance  in  which  the  cantilever  was  the  only 
type  of  truss  that  could  be  used  and  the  form  adopted  is  both  simple  and  economi- 
cal. As  will  be  seen  from  the  drawing,  the  main  supporting  column  extends  to 
the  top  of  the  truss,  as  is  usually  the  case  with  cantilever  trusses,  and  the  truss 
is' riveted  to  each  side  of  it.  The  upper  and  lower  chords  are  made  of  two  angles 
and  a  web-platc.  The  bracing  consists  of  angle-bars  used  in  pairs  and  varying 
from  3  by  2  by  i/4  in  to  3  by  3  by  %6  in,  the  whole  frame  being  connected  by 
rivets. 

Trusses  for  the  Fore  River  Ship-building  Shed,  Quincy,  Mass.  In 
the  Engineering  Record,  July  26,  1902,  there  is  a  description  of  the  roof  of  this 
building,  in  which  the  cantilever  trusses  have  an  overhang  of  60  ft. 

Roof-Trusses  for  Grand-Stand,  Empire  City  Trotting  Association, 
Yonkers,  N.  Y.  These  trusses  have  cantilever-arms  at  each  end,  25  ft  6  in 
on  one  end  and  15  ft  6  in  on  the  other.  The  intermediate  truss  has  a  span  of 
50  ft.  This  structure  is  described  in  the  Engineering  Record,  February  10, 
1900.  Other  examples  of  cantilever  roofs  are  given  in  Building  Construction 
and  Superintendence,  Part  III,  by  F.  E.  Kidder. 


1046 


Stresses  in  Roof-Trusses 


Chap.  27 


CHAPTER  XXVII 

STRESSES  IN  ROOF-TRUSSES 

By 
MALVERD  A.  HOWE 

PROFESSOR  EMERITUS  OF  CIVIL  ENGINEERING,  ROSE  POLYTECHNIC  INSTITUTE 

1.   Roof-Loads.     Data,  Weights,  Materials,  Methods 

Data  for  Roof-Trusses.     Before  the  stresses  in  a  roof-truss  can  be  deter- . 
inined  it  is  necessary  to  decide  upon  the  character  of  the  roof-covering,  the 
method  of  supporting  it  between  the  trusses,  the  geometrical  shape  and  span 
of  the  trusses  and  the  spacing  of  the  trusses. 

Roofing  Materials  for  Pitched  Roofs.  The  materials  suitable  for  covering 
pitched  roofs  are  slate,  burnt-clay  tiles,  metal  tiles  or  shingles,  wooden  shingles, 
corrugated  iron,  tin  with  standing  seams,  standing-seam  steel  roofing  and 
various  kinds  of  ready  roofing.  The  least  slope  to  which  these  materials  may 
be  laid  without  danger  of  leaks,  the  weight  per  square  foot  of  roof  and  the  com- 
parative cost  are  indicated  in  Table  I.  The  cost,  however,  can  only  be  considered 
as  approximate,  as  it  varies  for  different  materials,  locahties  and  the  scales  of 
wages. 

Table  I.     Covering  Materials  for  Pitched  Roofs 


Material 


Slates,  black 

Slates,  green 

Slates,  red 

Burnt-clay  tiles,  interlocking  pattam 

Tin  shingles,  painted 

dalvanized-iron  tile,  painted 

Cedar  shingles,  stained  or  painted. . . 

Corrugated  iron,  painted 

Standing-seam  steel  roofing,  painted. 
Ready  roofing 


Least  rise 

Comparative 

of  rafter 

cost  per 

m  12  m 

square 

8 

$7.00  to  $12.00 

8 

7.00  to    10.00 

8 

12.00  to    17.00 

7 

15.00  to    25.00 

6 

8.00  to    10.00 

6 

13.00  to    IS. 00 

6 

3.80  to      7.20 

3 

4.00  to     4-50 

2 

4.00  to     4-50 

I 

3.50  to     4.50 

Roofing  Materials  for  Flat  Roofs.  Flat  roofs  or  roofs  having  a  fall  of 
Irom  1^  to  %  in  to  the  foot  are  usually  covered  with  tar  and  gravel,  asphalt, 
ready  roofing,  or  tin  with  lock-and-solder  joints.  A  good  tin  roof  costs  about 
$8.00  a  square,  not  including  the  painting.  The  other  kinds  vary  from  $3.50 
to  $4.50  a  square. 

Manner  of  Supporting  the  Roof  from  the  Trusses.  Wooden  roofs,  sup- 
ported by  wooden  trusses,  require  common  or  jack-rafters  to  support  the  sheath- 
ing or  slate,  and  generally  purlins  to  support  the  rafters,  although  in  some  cases  it 
may  be  more  economical  to  span  the  rafters  from  truss  to  truss  (Fig.  17,  Chapter 
XXVI).  When  slates  or  burnt-clay  tiles  are  used  on  steel  roofs,  they  are  usually 
secured  to  steel  angles,  running  parallel  with  the  walls  and  spaced  from  8  to 
ioy2  in  apart,  as  may  be  necessary  to  accommodate  the  size  of  the  slates  or 


koof-Loads.    Data,  Weights,  Materials,  Methods  1047 

tiles.  If  the  span  is  not  more  than  6  or  7  ft,  the  angles  may  be  fastened  to  thd  ' 
truss-rafters.  As  a  rule,  however,  when  slates  or  tiles  are  to  be  used,  it  is  cheaper 
to  space  the  trusses  from  16  to  20  ft  apart,  and  to  use  purlins  and  jack-rafters  to 
support  the  smaller  angles.  Quite  often,  wooden  rafters  and  sheathing  are 
used  with  steel  trusses.  This  is  more  economical,  but  of  course  increases  the 
fire-risk.  Unprotected  steel  is  little  if  any  better  than  wood.  If  corrugated 
iron  is  to  be  used  for  roofing,  the  most  economical  construction  for  steel  roofs  is 
to  space  the  trusses  from  16  to  20  ft  apart,  and  to  use  light  I  beams  for  purlins, 
spaced  about  4%  ft  on  centers,  as  in  Fig.  52,  Chapter  XXVI,  the  corrugated 
iron  being  secured  to  the  purlins  by  straps.  If  warm  air  comes  in  contact  with 
the  underside  of  a  corrugated  roof,  either  the  roofing  should  be  laid  on  boards, 
or  some  kind  of  anticondensation  lining  should  be  provided,  as  otherwise  the 
moisture  in  the  air  will  condense  and  fall  on  the  floor  or  objects  below.  Flat 
roofs  always  require  rafters  and  sheathing,  or  fire-proof  filling  between  the 
rafters. 

Spacing  of  Trusses.  From  the  above  it  is  seen  that  the  economical  spacing 
of  the  trusses  depends  to  a  great  extent  upon  the  kind  of  roofing  that  is  used, 
and  also  upon  the  span.  As  a  general  rule,  however,  the  most  economical 
spacing  is  about  as  follows: 

For  WOODEN  TRUSSES  under  80-ft  span,  from  12  to  16  ft  on  centers. 

For  WOODEN  TRUSSES  over  80-ft  span,  from  16  to. 24  ft  on  centers. 

For  STEEL  TRUSSES  Under  80-ft  span,  from  16  to  20  ft  on  centers. 

For  STEEL  TRUSSES  over  80-ft  span,  from  20  to  40  ft  on  centers. 

The  SPACING  of  a  number  of  steel  trusses  of  wide  span  is  given  in  Chap- 
ter XXVI.  When  the  distance  between  the  trusses  exceeds  16  ft  for  wooden 
roofs  or  20  ft  for  steel  roofs,  it  is  generally  necessary  to  use  trussed  purlins. 
Having  decided  upon  the  kind  of  truss  to  be  used,  the  spacing  of  the  trusses  and 
the  roof-construction,  a  section-drawing  of  the  roof  should  be  made,  showing 
an  elevation  of  the  truss,  the  points  at  which  the  purlins  are  to  be  supported, 
the  manner  of  supporting  the  ceiling,  if  there  is  one,  and  any  other  loads  that 
are  to  be  supported  by  the  trusses.  The  section  and  truss-drawing,  with  the 
tables  of  the  weights  of  roofing-materials,  will  furnish  the  necessary  data  for 
computing  the  loads  at  each  joint.  Until  the  stresses  have  been  determined, 
the  sizes  of  the  members  computed,  and  the  joints  detailed,  an  exact  drawing 
of  the  truss  cannot,  of  course,  be  made;  but  in  order  to  compute  the  loads  and 
stresses,  it  is  necessary  to  know  the  positions  of  the  joints,  and  these  can  be 
indicated  with  sufiicient  accuracy  before  the  exact  sizes  of  the  members  are 
determined.  Chapter  XXVI  gives  suflSicient  information  regarding  the  various 
types  of  trusses  to  enable  one  to  decide  upon  the  height  and  the  number  and 
arrangement  of  the  struts  and  ties;  and  the  sizes  of  the  members  can  be  approx- 
imated for  the  preliminary  drawings. 

Roof  and  Ceiling-Area  Supported  at  Any  Joint.  Calculations  for  the 
stresses  in  a  truss  are  always  based  on  the  assumption  that  the  loads  are  trans- 
ferred to  the  joints,  and  that  the  members  are  free  to  move  at  the  joints  as  if 
hinged,  although  the  actual  joints  may  be  made  with  riveted  or  other  connec- 
tions. The  loads  at  the  joints  are,  of  course,  equal  to  the  reactions  of  the  pur- 
lins, or  of  the  tie-beams  or  principals,  if  these  receive  the  ceiling-joists  or  rafters. 
When  the  load  on  the  roof  or  ceiling  is  uniformly  distributed,  as  is  usually  the 
case,  the  simplest  method  of  computing  the  joint-loads  is  to  determine  the  roof 
or  ceiling-area  contributory  to  the  joint,  and  to  multiply  this  area  by  the  weight  or 
load  per  square  foot.  The  area  contributory  to  any  joint  is  equal  to  the  product 
of  the  distance  measured  half-way  to  the  next  joint,  on  each  side,  by  the  dis- 
tance measured  half-way  to  the  next  truss  or  wall  on  each  side.    Thus  if  Fig.  1 


104a 


Stresses  in  Roof-Trusses 


Chap.  27 


*  represents  truss  i,  of  Fig.  2,  the  roof-area  contributory  to  joint  2  is,  in  square  feet, 

8+14  -r,  ,  ,     ,  ,  ...        14+    12 

•  X  a.     For  truss  2,  the  area  supported  by  the  same  joint  is  '  X  fl; 


or,  if  we  let  D  represent  the  length  in  feet  of  roof  or  ceiling  supported  at  each 
joint,  the  area  in  square  feet  supported  by  joint  2  is  aXD,  and  the  area  sup- 


Fig.  1. 


Rafters  and  Ceiling  Joi8tS-2  x  8" 
16*on  centers. 
King-rod  Truss 


.vy/-x- -,v/.'  '//w^^^^wjawajm;/www//mww/.'m.w'  ,< 


-y— 


-f- 


r 


ported  by  joint  3  is  2  ^  X  Z).  In  the  same  way,  the  ceiling-area  supported  at 
joint  6  is  c  X  -D,  the  arrow-heads  being  half-way  between  the  joints.  It  makes 
no  material  difference  in  the  joint-loads  whether  the  common  rafters  are  sup- 
ported on  purlins  or  whether  they  rest  on  the  top  chord  of  the  truss,  provided 

the  purlins  come  at  or  close  to  the  joints 
and  the  load  is  uniformly  distributed. 
Thus  the  width  of  the  ceiling  contrib- 
utory to  joint  7  (Fig.  3)  is  equal  to  c, 
just  the  same  as  in  Fig.  1.  The  arrange- 
ment in  Fig.  1  produces  cross-bending 
stresses  in  the  tie-beam,  while  that  in 
Fig.  3  does  not.  When  the  trusses  are 
spaced  a  uniform  distance  apart,  D,  Fig. 
2,  is,  of  course,  equal  to  the  distance 
between  centers  of  trusses.  When  the 
trusses  are  not  spaced  uniformly,  D  is 
equal  to  one-half  the  distance  from  the 
center  of  the  truss  on  the  left  to  the 
center  of  the  truss  on  the  right.  When  a 
purlin  is  more  than  12  in  from  a  joint,  or 
the  roof-area  is  not  symmetrical,  as  is 
often  the  case  at  hips  and  valleys,  the 
joiiit-load  is  determined  by  the  principle 
of-  the  REACTION  OF  BEAMS,  as  explained  in 
Chapter  IX.  Examples  showing  the  computation  of  joint-loads  are  given  a 
little  farther  on. 

Roof-Load  per  Square  Foot.    By  the  term  roof-load  is  meant  the  weight  of 
the  materials  composing  the  roof,  trusses  and  purlins,  an  ample  allowance  for 


4- 

-r-  — 
[       Truss  1 


^ 


A.. 


^4 


%/^//////UAA/^/M////mw/m/MMm^^^^ 


Fig.  2.    Plan  of  Wall  and  Trusses 


Roof-Loads.     Data,  Weights,  Materials,  Methods 


1049 


snow  and  also  an  allowance  for  wind-pressure.  The  weight  of  the  materials 
is  called  the  dead  load.  Snow  is  generally  considered  a  live  load,  acting 
vertically.  The  pressure  due  to  the  wind  is  always  assumed  to  act  normal  to, 
or  at  right-angles  to,  the  surface  of  the  roof;   but  for  trusses  of  less  than  loo-ft 


2'x  6*Raftera 
16"0.C. 


^  H^ e=i2  2- A  ye  X 12" 

^ -12'2^^ ^H 12  2''-—, -+  — 

J QiJ    6--^ 


.,.-^-4 


-36  6--. -^ 

Fig.  3.    Queen  Truss.     (See,  also,  Figs.  12,  53  and  54  and  Chapter  XXVIII,  Fig.  1)— 

span  it  is  usually  combined  with  the  dead  load,  wind-load  and  snow-load  and 
treated  as  one  vertical  load.  This  does  not  apply  to  the  Fink  and  fan  types. 
(See  page  1109.) 

Data  for  Computing  Dead  Loads.     The  dead  load  of  any  roof  may  be 
estimated  with  sufl5cient  accuracy  from  the  following  data: 

Table  n.     Weights  per  Square  Foot  of  Roof-Surface 


Shingles,  common,  2V2  lb;   18  in,  3  lb 

Slates,  %6  in  thick,  7V*  lb;  -"/i  in  thick,  9.6  lb  (the  common  thickness  is  %e  in  for 
sizes  up  to  10  by  20  in) 

Plain  tiles  or  clay  shingles,  11  to  14  lb 

Roman  tiles,  old  style,  two  parts,  12  lb;  new  style,  one  part,  8  lb 

Spanish  tiles,  old  style,  two  parts,  19  lb;  new  style,  one  part,  8  lb 

Improved  Oriental  tilesr  11  lb 

Ludowici  tiles,  8  lb 

For  tiles  laid  in  mortar  add  10  lb  per  sq  ft 

Copper  roofing,  sheets,  i^i>  lb;  tiles,  1%  lb 

Tin  roofing,  sheets  or  shingles,  including  one  thickness  of  felt,  i  lb 

Corrugated  iron,  painted  or  galvanized.  No.  26,  i  lb;  No.  24,  1.3  lb;  No.  22, 1.6  lb; 
No.  20,  1.9  lb;  No.  18,  2.6  lb;  and  No.  16,  3-3  lb 

Standing-seam  steel  roofing,  i  lb 

Five-ply  felt  and  gravel  roof,  6  lb  ; 

Four-ply  felt  and  gravel  roof,  5^1j  lb 

Three-ply  ready  roofing  (elaterite.ruberoid,  asphalt,  etc.).  from  0.6  to  i  lb 

Skylights  with  galvanized-iron  frame,  i/4-in  glass,  ^¥2  lb;    %6-in,  5  lb;  %-in,  6  lb 

Sheathing,  i  in  thick.  3  lb  per  sq  ft  for  white  pine,  spruce,  or  hemlock;  4  lb  for  yel- 
low or  pitch  pine 


1050  Stresses  in  Roof-Trusses  Chap.  27 

Table  HI.     Weights  of  Rafters  per  Square  Foot  of  Roof-Surface 


Size  of 
rafter  in 
inches 

Spruce,  hemlock,  white  pine. 

Spacing  in  inches,  center 

to  center 

Hard  pine.     Spacing  in  inches, 
center  to  center 

i6 

20 

24 

16 

20 

24 

2X  4 
2X  6 
2X  7 
2X  8 
2Xio 

lb 
1V2 
2V4 

2^/8 

3 

38/4 

lb 
1,2 
1.8 
2,1 
2.4 
3 

lb 

I 

1V2 

1% 
2 

2V2 

lb 

2 

3 

3V2 

4 

5 

lb 
1.6 
2.4 
2.8 
3.2 
4 

lb 
iVs 
2 

2% 
3V3 

Wooden  purlins  weigh  about  2  lb  per  sq  ft  of  roof-surface  when  the  span  is  between 
12  and  16  ft. 

For  steel  roofs  the  sizes  and  weights  of  the  purlins  and  rafters  should  be  computed  for 
each  particular  case. 

Weight  of  Truss.  To  the  weight  of  the  roof-construction  proper  should 
be  added  an  allowance  for  the  weight  of  the  truss.  If  trusses  could  be  built 
in  exact  accordance  with  the  theoretical  requirements  their  weight  would  be 
directly  proportional  to  the  roof-load  and  span;  but  as  there  is  always  some 
extra  material,  it  is  impossible  to  determine  the  weight  of  the  truss  exactly  until 
it  is  completely  designed.  Several  tables  for  the  weights  of  wooden  trusses 
and  formulas  for  steel  trusses  have  been  published,  but  hardly  any  two  of  them 
are  alike.    The  following  are  some  of  the  formulas  in  use: 


For  Wooden  Trusses 


W  =  0.04  L  -\-  0.000167  L^ 
W  =  0.50  -I-  o.o7sL 


(  N.  C.  Ricker,  for  trusses  like  Figs.  4 
(      and 


and  5,  Chapter  XXVI. 
H.  S.  Jacoby. 


For  Steel  Trusses 

fF=  0.75  4-0.075  L  Mansfield  Merriman  and  Jacoby. 

PT  =  0.6  4-  0.06  L,  for  heavy  loads  {  ^  ^  ^     ,      r    '  t-  1  ^ 

Tjr  ,  r    f     1-  w  1     J       (  ^'  E.  Fowler,  for  Fmk  trusses. 

py  -  0.4  +  0.04  L,  for  light  loads     )  ' 

^^  P  /  L    \  (  M.  S.  Ketchum,  for  steel  mill-build- 

45  \        SVJ/  (      ing  trusses. 

W  =  0.05  L-\-i2/A  H.  G.  TyrreU. 

In  the  above  formulas,  W  —  weight  of  truss  in  pounds  per  square  foot  of  hori- 
zontal projection  of  the  roof  supported,  L  =  span  in  feet,  A  =  distance  between 
trusses,  and  P  =  capacity  of  truss  in  pounds  per  square  foot  of  horizontal  pro- 
jection. 

Tables  IV  and  V,  compiled  from  a  comparison  of  other  tables  and  formulas, 
and  from  the  weights  of  actual  trusses,  are  sufficiently  accurate  for  the  purpose 
of  determining  stresses.  The  weights  given  are  probably  slightly  in  excess  of 
the  actual  weights  of  average  trusses,  as  it  is  preferable  to  have  the  error,  if  any, 
on  the  safe  side.  It  should  be  noted  that  the  weights  are  for  each  square  foot 
of  roof-surface,  and  not  for  the  horizontal  area.  Table  VI  gives  the  actual 
weights  of  a  number  of  large  steel  roofs. 


Roof-Loads.     Data,  Weights,  Materials,  Methods  1051 

Table  IV.     Weights  of  Wooden  Trusses  per  Square  Foot  of  Roof-Surface* 


Span 

ft 
Up  to   36 

36  to    50 

so  to    60 

Goto    70 

veto    80 

Soto    90 

90  to  100 

100  to  no 

no  to  120 


V'j.  pitch 


V'i  pitch 


H  pitch 


Flat 


lb 

3 

3V4 

3% 

5 

5% 


lb 

^^ 

3% 

4 

4V2 

5 

6 

6% 

7V3 

8K' 


lb 
3«/4 
4 

4% 

5V2 

7 


lb 
4 

4^^ 

4% 

5V1 

6 

7 


Table  V.     Weights  of  Steel  Trusses  per  Square  Foot  of  Roof-Surface 


Span 


ft 
Up  to  40 
40  to  50 
so  to  60 
60  to  70 
70  to  80 
80  to  100 
100  to  120 
120  to  140 


y%  pitch 


lb 

lb 

5.25 

6.3 

5 

75 

6.6 

6 

75 

8.0 

7 

25 

8.5 

7 

75 

9.0 

8 

5 

10. 0 

9 

5 

II. 0 

10 

0 

II. 6 

Vz  pitch 


^/4  pitch 


lb 
6.8 
7.2 
8.6 
9-2 
9-7 
10.8 
12.0 
12.6 


Flat 


lb 
7.6 
8.0 
9.6 
10.2 
10.8 
12.0 
13.2 
14.0 


Table  VI.     Weights  and  Spacing  of  Some  Steel  Roofs  of  Wide  Span,  Including 
Trusses,  Purlins  and  Braces,  but  not  Roof-Covering  or  Rafters 


Name  of  building 

Type  of 
truss 

Span 
ft 

Spacing, 
center  to 
center  of 
trusses, 
ft 

Weight 
per  sq  ft 
sloping 
surface, 
lb 

Weight 
of  one 
truss, 
tons 

Armory,  Pawtucket,  R.  L. . 

Armory,  Portland,  Me 

Phoenix     Hall,     Brockton, 
Mass 

Fig.7St 

82 
92 

96 

100 

104 
118 
120 
122 

24 
25 

24 

24 

25 

241/3 

23-25 

30 

241/2 

35 

8.7 
9-7 

8.6 

8.0 

II. 8 

9-5 

12.4 

6.7 
9 

10 
8.5 

II. 5 

12. s 

21 

Armory,    Northampton , 
Mass 

Palace      Rink,      Hartford, 
Conn                                 . .    • 

Ex.  Hall,  Providence,  R.  I.. 
Cleveland,  Ohio,  Armory.. 
Armory,  Boston,  Mass 

Armory,  22d  Regt.,  N.  Y.  .. 
Armory,  Brooklyn,  N.  Y.... 

'• 

176 
196 

*  For  scissors  trusses,  increase  one-third, 
t  Chapter  XXVI. 


1052 


Stresses  in  Roof-Trusses 


Chap.  27 


The  data  for  the  first  seven  buildings  in  Table  VI  were  compiled  by  H.  G. 
Tyrrell,  who  states  that  all  of  the  seven  roofs  were  proportioned  for  slate 
and  plank  roofing  resting  on  wide  rafters  2  ft  apart,  supported  by  st^4  purlins 
about  10  ft  apart.  The  spans  given  are  measured  from  center  to  center  of  side 
bearings.  Stresses  were  computed  for  a  dead  load  of  25  lb  per  sq  ft,  a  snow-load 
of  10  lb  per  sq  ft  of  sloping  surface,  and  a  horizontal  wind-load  of  40  lb  per  sq  ft  or 
a  28-lb-per-sq-ft  normal  pressure.  Data  for  computing  the  weights  of  floors  and 
floor-loads  supported  by  trusses,  and  for  fire-proof  construction,  may  be  found  in 
Chapters  XXI  and  XXIII. 

Snow-Loads.  As  a  basis  for  making  an  allowance  for  snow,  Table  VII  is 
perhaps  as  good  a  guide  as  any  that  can  be  given.  When  snow-guards  are 
placed  on  a  roof,  the  same  allowance  is  made  for  a  half-pitch  as  for  a  one-third 
pitch. 

Table  VII.     Allowance  for  Snow  in  Pounds  per  Square  Foot  of  Roof-Surface 


Location 


Southern  states  and  Pacific  slope 

Central  states 

Rocky  Mountain  states 

New  England  states 

Northwest  states 


Pitch  of  roof 


V2 


*  t 
a-  o 
o-  5 

0-10 

o-io 
0-12 


V3 


*      t 

o-  5 
7-10 
10-15 
lo-is 
12-18 


*     t 
o-  5 
IS-20 
20-25 

20-25 
25-30 


%       Vq  or  less 


5 
30 
35 

40 
45 


Columns  headed  by  an  asterisk  (*)  are  for  slate,  tile,  or  metal;  those  headed  by  a 
dagger  (f)  are  for  shingles. 

Wind-Pressure.*  For  roofs  having  a  pitch  of  5  in  or  more  to  the  foot,  an 
allowance  must  be  made  for  wind-pressure.  For  trusses  of  the  Fink,  fan,  king, 
or  QUEEN  TYPES,  the  usual  practice  is  to  include  the  wind-pressure  with  the 
vertical  loads,  and  to  make  a  single  allowance  for  both  wind  and  snow,  as  during 
a  gale  snow  is  not  likely  to  stay  on  a  steep  roof.  When  the  wind-pressure  is 
added  to  the  vertical  loads,  the  allowance  for  wind  and  snow  combined  should 
not  be  less  than  indicated  in  Table  VIII. 


Table  VIII. 


Allowance  for  Wind  and  Snow  Combined  in  Pt)unds  per 
Square  Foot  of  Roof-Surface 


Location 


Northwest  states 

New  England  states 

Rocky  Mountain  states 

Central  states 

Southern  and  Pacific  states . 


Pitch  of  roof 


60° 


30 
30 
30 
30 
30 


30 
30 
30 
30 
30 


Vs 


25 
25 
25 
25 
25 


30 
25 

25 

25 
25 


37 
35 

27 


V^ 


45 
40 
35 
30 


No  roof -truss  should  be  proportioned  for  a  total  load  of  less  than  40  lb  per  sq  ft 
of  roof-surface  except  flat  roofs  in  warm  climates.  For  trusses  having  spans 
exceeding  100  ft  (except  trusses  for  flat  roofs)  and  for  trusses  in  which  a  partial 

f  (See,  also,  Chapter  XXX,  page  1199,  and  pages  1394  and  1717-) 


Roof-Loads.    Data,  Weights,  Materials,  Methods  1053 

load  may  produce  maximum  stresses,  or  call  for  counterbracing,  as  is  the  case 
in  QUADRILATERAL  TRUSSES,  and  trusses  with  CURVED  CHORDS,  the  stresses  for  all 
the  different  loadings  should  be  found  separately  and  each  member  of  the  truss 
proportioned  for  the  maximum  stress  to  which  it  may  be  subject  under  any 
possible  combination  of  loads.  For  determining  the  stresses  due  to  wind-pres- 
sure alone  the  force  of  the  wind  is  usually  assumed  to  act  in  a  direction  normal, 
that  is,  at  right-angles,  to  the  slope  of  the  roof.  This  force  is  commonly  based  on 
a  horizontal  wind,  producing  a  pressure  of  30  lb  against  a  vertical  surface.  This 
corresponds  to  a  wind-velocity  of  nearly  100  miles  per  hour.  According  to 
Marvin's  formula, 

P  =  0.0032  F2 

where  P  =  the  pressure  in  lb  per  sq  ft  against  a  surface  normal  to  the  direction 
of  the  wind  and  V  =  the  velocity  in  miles  per  hour.  For  P  =  30  lb,  V  =  96.3 
miles.  The  normal  pressure  per  square  foot  of  roof-surface  corresponding  to 
pressures  of  20  and  30  lb  per  sq  ft  against  a  vertical  surface  is  given  in  Table  IX. 

Table  IX.     Wind-Loads  in  Pounds  per  Square  Foot  of  Roof-Surface* 


Inclination  of  roof 


5  

10° 

15° 

21°  48'  =  i,^-pitch 
26°  34'=i4-pitch 

30° 

33°  4i'=V3-pitch 

40° 

45°  0'= 1/2  pitch. 
60°  and  above. . , 


Normal  pressure  P„, 
pounds  per  square  foot 


P=30  lb 


S.I 
10. 1 
14.6 
19.8 
22.4 
24.0 
25. 5 
26.7 
28.3 
30.0 


P  =  20lb 


35 

6.8 
9-6 
13  I 
14.0 
16.0 
17.0 
18.2 
18.9 
20.0 


The  values  in  Table  IX  are  based  on  Duchemin's  formula, 


^'^"^H-sin^^ 

in  which  P  is  the  pressure  per  square  foot  on  a  vertical  surface,  Pn  the  normal 
component  of  pressure  and  0  the  angle  of  inchnation  of  the  roof  wfth  the  hori- 
zontal. The  wind  not  only  produces  a  pressure  upon  the  windward  side  of  the 
roof  but  a  suction  upon  the  leeward  side;  therefore  all  roof-covering  should  be 
securely  fastened,  all  joints  in  the  trusses  so  constructed  that  they  will  resist 
tension  and  compression,  and  the  trusses  themselves  securely  anchored  to  the 
supports. 

Variations  in  Loading  for  which  Stresses  should  be  Found.  To  deter- 
mine the  maximum  stresses  under  any  possible  condition  of  loading,  stresses 
should  be  found  for  the  following  cases: 

(i)  Stresses  due  to  permanent  dead  loads, 

(2)  Snow  covering  only  one  side  of  roof, 

(3)  Snow  covering  entire  roof,  ». 

(4)  Wind  on  side  of  truss  nearer  the  expansion-end, 

(5)  Wind  on  side  of  truss  nearer  the  fixed  end. 

♦  (See,  also,  Chapter  XXX,  page  1199,  and  pages  1394  and  171 7.) 


1054  Stresses  in  Roof-Trusses  Chap.  27 

\t  is  generally  assumed  that  the  maximum  wind-pressure  and  the  snow-load 
cannot  act  on  the  same  half  of  the  truss  at  the  same  time;  hence  the  combina- 
tions for  maximum  stress  will  be  either  cases  i  and  3  or  cases  i,  2,  and  4  or  5. 
If  the  trusses  are  supported  on  iron  columns  instead  of  on  walls  the  wind-force 
is  transferred  to  the  foundations  through  the  columns,  producing  a  bending 
moment  in  the  columns.  The  stresses  in  the  columns,  trusses  and  knee-braces 
sliould  therefore  be  determined  for  the  wind-pressures  against  the  side  of  the 
building  and  roof.  These  pressures  are  obtained  by  multiplying  the  area  of 
the  vertical  surfaces  by  the  full  pressure  per  square  foot  and  the  area  of  the 
roof  by  the  normal  component,  given  in  Tabic  IX. 

Kansas  City  Auditorium.  For  the  trusses  supporting  the  roof  of  the  Kan- 
sas City  Auditorium  (Fig.  66,  Chapter  XXVI)  stresses  were  computed  for  the 
following  conditions:  First,  full  dead  and  live  load  on  both  galleries  and  the 
roof-garden,  and  wind-pressure  due  to  a  velocity  of  45  miles  an  hour;  second, 
full  dead  load,  snow-load,  and  gallery  live  load,  wind-pressure  10  lb  and  no 
load  on  roof -garden  floor;  third,  full  dead  load  and  50  lb  wind-pressure;  fourth, 
full  dead  load  and  wind-pressure  at  45  miles  an  hour,  and  full  live  loads  on 
gallery  and  roof -garden  on  one  side  only.  Snow-loads  throughout  were  taken 
at  one- third  of  the  dead  load.  Examples  showing  manner  of  combining  the 
stresses  due  to  different  conditions  of  loading  are  given  on  pages  1114  and  11 23-8. 

2.   Examples  of  the  Computation  of  Roof-Loads* 

King-Rod  Truss.  Example  i.  The  first  example  considers  the  roof  and 
truss  shown  in  Fig.  1,  page  1048,  which  it  is  assumed  represents  truss  2  of  Fig.  2. 
It  is  assumed  that  the  timber  is  to  be  common  white  pine  and  that  the  roof  is 
to  be  covered  with  %6-in  slate  of  medium  size  on  %-in  sheathing.  The  ceiling 
is  to  consist  of  lath  and  plaster.  The  dead  load  of  roof  and  truss  per  square 
foot  of  roof -surf  ace  is  made  up  as  follows: 

lb  per  sq  ft 

For  slate 7^/4 

For  sheathing. •. 3 

For  rafters 3 

For  purlins .• 2 

For  truss 3 

Total 18V4. 

For  wind  and  snow-load  combined  there  should  be  allowed  about  28  lb  (the 
pitch  being  about  40°),  which  makes  a  total  roof-k)ad  of  46^/4  lb.  To  avoid 
fractions,  however,  the  load  is  assumed  to  be  48  lb  per  sq  ft.  As  the  distance 
to  truss  I,  Fig.  2,  is  14  ft  and  to  truss  3,  12  ft,  the  length  of  roof  supported  by 
the  truss  is  13  ft.  The  roof-area  supported  by  the  purlins  at  joint  2  is  equal  to 
the  distance  a  multiplied  by  13  ft;  and  a  is  one-half  the  distance  from  the  wall- 
plate  to  the  ridge-purlin,  or  22  ft  8  in  divided  by  2,  or  11  ft  4  in,  or  nV^  ft. 
Hence  the  roof-area  supported  at  joint  2  is  11 V^  by  13  ft,  or  i47V^  sq  ft.  The 
roof-area  supported  by  the  purlins  at  joint  3  is  2  6  by  13  ft,  or  12%  by  13  ft,  or 
i6oi.^  sq  ft.  Multiplying  the  roof-areas  by  the  load  per  square  foot,  48  lb,  there 
results  7  072  lb  for  the  load  at  joint  2;  and  7  696  lb  for  the  load  at  joint  3.  The 
load  at  joint  4  is  equal  to  that  at  2,  as  the  truss  is  symmetrical.  The  ceiling- 
loads  at  joints  6  and  7  are  computed  next.  The  ceiling-area  supported  at  joint 
6  is  c  X  13  ft,  o*  8^  by  13  ft,  or  107^4  sq  ft.  The  area  supported  at  joint  7  is  8% 
by  13  ft,  or  114%  sq  ft.     The  actual  weight  of  the  ceiling  i>er  square  foot  is 

*  In  the  following  five  examples  all  loads  are  considered  as  acting  vertically. 


"J 


Examples  o£  the  Computation  of  Roof-Loads  1055 

3  lb  for  the  joists  and  lo  lb  for  the  lath  and  plaster;  but  where  there  is  a  large 
attic-space  liable  to  be  used  for  storage  it  is  well  to  make  a  small  allowance, 
say  5  lb  per  sq  ft,  for  any  extra  attic-load.  Therefore,  i8  lb  per  sq  ft  is 
allowed  for  the  weight  of  the  ceiling,  which  makes  the  weight  at  joints  6  and 
8,  107^4  sq  ft  by  18  lb  per  sq  ft,  or  i  930  lb;  and  the  weight  at  joint  7,  114%  sq 
ft  by  18  lb  per  sq  ft,  or  2  067  lb.  As  soon  as  computed,  the  roof  and  ceiling- 
loads  should  be  marked  on  a  truss-diagram,  as  in  Fig.  10.  The  roof  and  ceiling- 
loads  at  joint  I  are  transmitted  directly  to  the  wall  and  need  not  be  taken  into 
account  in  determining  the  stresses  in  the  truss. 

Queen  Truss.  Example  2.  It  is  required  to  compute  the  joint-loads  for 
the  truss  shown  in  Fig.  3,  page  1049.  ^'l  timber  is  to  be  of  spruce  and  the  roof 
is  to  be  covered  with  shingles  on  i-in  sheathing.  The  ceiling  is  to  be  of  lath 
and  plaster.     The  dead  load  is: 

lb  per  sq  ft 

Weight  of  shingles 2  V^ 

Weight  of  sheathing 3 

Weight  of  rafters. 2^4 

Weight  of  purlins 2 

Weight  of  truss 3 

Total  dead  load  per  sq  ft 1 2% 

Allowance  for  wind  and  snow. * 30 

Total  roof-load  in  pounds  per  square  foot 42% 

For  the  weight  of  the  ceiHng  it  is  well,  for  a  truss  of  this  kind,  to  allow  at  least 
20  lb  per  sq  ft.  It  will  be  assumed  that  the  trusses  are  to  be  spaced  uniformly 
15  ft  on  centers.  Then  the  roof-area  supported  at  joint  2  is  9%  by  15  ft,  or 
147^2  sq  ft,  and  the  load  at  this  joint  is  6  306  lb.  The  purlin  at  joint  3  supports 
the  roof,  from  a  point  midway  to  joint  2,  to  the  ridge,  or  6  =  4  ft  1 1  in  -|-  8  ft  5  in, 
or  13  ft  4  in.  The  roof-area  supported  at  this  joint  is  isVs  by  15  ft,  or  200  sq 
ft,  and  the  load  is  8  550  lb.  The  loads  at  joints  4  and  5  are  equal  respectively 
to  those  at  3  and  2.  For  the  ceiling-loads  at  joints  7  and  8  there  is  an  area  to  be 
supported  equal  to  12%  by  15  ft,  or  182 V2  sq  ft,  which,  multiplied  by  20,  gives 
3  650  lb. 

Scissors  Truss.  Example  3.  For  this  example  the  church-roof  shown  in 
section  in  Fig.  4  is  considered.  In  this  roof  the  trusses  take  the  place  of  the 
rafters  and  ceiling-beams,  the  sheathing  spanning  from  truss  to  truss  and  the 
laths  for  the  ceiling  being  nailed  to  iV4  by  2V^-in  furring  strips,  spaced  12  or  16  in 
on  centers.  Assuming  that  the  parts  of  the  trusses  have  the  dimensions  indi- 
cated in  the  figure,  and  that  the  wood  is  white  pine,  the  actual  weight  of  one 
truss  is  about  i  200  lb.  The  roof-area  supported  by  one  truss  is  170  sq  ft,  and 
hence  the  weight  of  the  trusses  is  about  7  lb  per  sq  ft  of  roof-surface.  This 
weight  is  more  than  twice  that  given  in  Table  IV,  owing  principally  to  the  close 
spacing  of  the  trusses  and  also  to  the  small  dimensions  of  their  members.  The 
weight  of  the  sheathing  and  shingles  is  about  5^^  lb  and  30  lb  is  allowed  for  wind- 
pressure.  The  roof  is  too  steep  for  snow  to  lodge  on  it.  This  gives  a  total  roof- 
load  of  421.^  lb  per  sq  ft  of  sloping  surface.  For  the  weight  of  the  ceiling  12  lb 
per  sq  ft  is  ample,  as  no  load  other  than  its  own  weight  is  likely  to  come  upon  it. 
The  roof-area  supported  at  joint  2  is  10%  by  2V2  ft,  or  27  sq  ft.  The  area  sup- 
ported at  joints  4  and  5  is  equal  to  12^3  by  2^^  ft,  or  31  sq  ft  for  each.  The 
ceiling-area  supported  at  joint  3  is  14^^  by  2I/2  ft,  or  35V2  sq  ft.  Multiplying 
each  joint-area  by  the  corresponding  loads  per  square  foot,  there  results  i  148  lb 


1056 


Stresses  in  Roof-Trusses 


Chap.  27 


*  for  the  load  at  joint  2,  i  318  lb  for  each  load  at  joints  4  and  5,  and  426  lb  for 
the  load  at  joint  3. 

Truss  over  Car-Barn.  Example  4.  In  this  example  the  roof  is  of  corru- 
gated iron,  supported  by  a  steel  truss  of  the  shape  shown  in  Fig.  55,  Chapter 
XXVI.  This  truss  supports  nothing  but  the  corrugated  iron,  the  purlins  and 
the  pressure  due  to  wind  and  snow,  the  use  of  the  building  not  requiring  the 
suspending  of  any  load  from  the  trusses.  In  figuring  the  dead  loads  for  such 
a  roof,  the  sizes  of  the  purhns  and  the  gauge  of  the  iron  should  first  be  definitely 


Fig.  4.     Scissors  Truss.     (See,  also,  Fig.  24  and  Chapter  XXVIII,  Fig.  2) 


fixed,  so  that  the  weight  per  square  foot  of  roof  may  be  accurately  determined. 
In  this  instance  the  purlins  are  5-in  I  beams  spaced  4  ft  9  in  on  centers,  and 
weighing  10  lb  per  linear  foot.  The  weight  of  the  purlins  per  square  foot  of 
roof  is  therefore  equal  to  10  lb  divided  by  4%,  or  2.1  lb.  For  a  span  of  4  ft  9  in 
the  corrugated  iron  should  be  No.  18  gauge  (see  Corrugated  Iron,  Part  III,  page 
i6ot)  weighing  2  lb  per  sq  ft.  For  the  weight  of  the  truss  and  bracing  the  weight 
taken  is  that  given  in  Table  V  for  a  span  of  100  ft  and  V4-pitch,  10.8  lb.*  This 
gives  a  total  dead  load  of  14.9  lb  per  sq  ft  of  sloping  surface. 

For  wind  and  snow  we  should  allow  22  lb  per  sq  ft  if  the  building  is  situated 
in  the  Central  states,  making  the  totiil  roof-load  36.9  lb  per  sq  ft.  It  is  quite 
generally  recommended,  however,  that  no  roof  should  be  designed  for  a  load 
less,  all  told,  than  40  lb  per  sq  ft;  the  joint-loads,  therefore,  should  be  computed 
on  that  basis.  The  only  loaded  joints  in  this  truss  are  those  under  the  purlins. 
The  trusses  are  spaced  19  ft  2^4  in  and  the  purlins  4  ft  9  in  on  centers,  the  roof- 
area  supported  at  each  upper  joint  being  91  sq  ft.  The  joint-loads,  therefore, 
should  be  figured  at  3  640  lb.     Even  for  the  locality  in  which  it  was  built,  this 

♦  The  actual  weight  of  this  truss  and  bracing  was  4  lb  per  sq  ft  of  sloping  surface, 
which  is  remarkably  small. 


Examples  of  the  Computation  of  Roof-Loads  1057 

is  a  very  light  roof;    and  it  would  hardly  be  considered  safe  for  states  further 
north  or  west. 

Truss  for  Flat  Roof.  Example  5.  This  truss  is  for  a  flat  roof  (Fig.  5). 
The  timber  is  of  spruce  and  there  is  a  five-ply  gravel  roof  and  a  plastered  ceiling. 
For  the  dead  load  we  have, 

lb  per  sq  ft 

Weight  of  roofing 6 

Weight  of  sheathing 3 

Weight  of  rafters 2^4 

Weight  of  purlins 2 

Weight  of  truss,  about , 4^4 

Total  dead  load  in  pounds  per  square  foot 17^/^ 

No  allowance  is  required  for  wind-pressure,  but  the  snow-load  is  a  large  per^ 
centage  of  the  total  load  in  any  of  the  Northern  states,  as  indicated  in  Table  VII. 


■^ g'l^ ^ ^g". ^1     o'x  e'Rafters 


Fig.  5.     Howe  Truss 


Assuming  that  the  building  is  located  in  one  of  the  Central  states,  30  lb  per  sq 
ft  should  be  allowed  for  snow,  making  the  total  roof-load  47!/^  lb.  The  plaster 
ceiling  and  the  ceiling- joists  weigh  about  12^/4  lb  and  as  the  roof-space  is  not 
likely  to  be  used  for  storage,  13  lb  per  sq  ft  is  a  sufficient  allowance  for  the  ceil- 
ing. Assuming  that  the  trusses  are  to  be  uniformly  spaced,  14  ft  on  centers, 
the  roof-area  supported  at  joint  2  is  9V^  by  14  ft,  or  133  sq  ft,  and  the  area  sup- 
ported at  joint  4,  9%  by  14  ft,  or  135^/^  sq  ft.  The  ceiling-area  supported  at 
joint  3  is  91^^  by  14  ft,  or  130%  sq  ft  and  at  joint  5,  9  by  14  ft,  or  126  sq  ft.  Mul- 
tiplying each  of  these  areas  by  the  corresponding  load  per  square  foot,  we  have 
6  317  lb  for  the  load  at  joint  2,  6  428  lb  at  joint  4,  i  699  lb  at  joint  3,  and  i  638  lb 
at  joint  5.  In  practice  it  is  hardly  worth  while  to  compute  the  stresses  closer 
than  100  lb,  so  that  the  loads  may  as  well  be  put  down  at  an  even  50  or  100  lb 
above  the  loads  obtained  by  computation.  When  the  roof  is  supported  by 
purlins,  there  are  often  some  joints  of  the  truss  which  have  no  load.  Thus  for 
the  truss  shown  in  Fig.  16,  Chapter  XXVI,  there  are  no  loads  on  joints  2,  6  and 
10.  The  roof-area  supported  at  joint  4  (Fig.  16)  is  equal  to  one-half  the  distance 
OB  multiplied  by  the  distance  halfway  to  the  truss  on  each  side.  If  the  lower 
chord  supports  ceihng-joists,  there  is  a  load  at  each  of  the  joints  3,  5,  7,  9,  etc. 
Stress-diagrams  can  be  drawn  for  any  arrangement  of  loads,  the  important 
point  being  to  compute  the  loads  exactly  as  they  are  placed  on  the  truss. 

These  five  examples  illustrate  fairly  well  the  method  of  computing  the  loads 
on  different  types  of  trusses.  Other  special  cases  of  loading  should  be  com- 
puted on  the  same  principles. 


1058 


Stresses  in  Roof-Trusses 


Chap.  27 


3.   Determination  of  Stresses  by  Computation 

Stresses.  To  determine  the  stresses,  a  diagram  of  the  truss,  composed 
of  single  lines  representing  the  central  axial  or  median  lines  of  the  truss-members, 
should  first  be  carefully  drawn  to  a  scale  and  the  loads  at  the  different  joints 
indicated  by  arrows  and  numbers  as  in  Figs.  10  and  12.  If  the  center  lines  of 
the  members,  as  they  are  actually  placed,  do  not  intersect  at  common  points, 
they  must  be  made  to  do  so  in  the  diagram,  as  the  stresses  can  be  computed  only 
on  the  assumption  that  the  center  lines  of  all  members  meeting  at  any  joint 
intersect  at  a  common  point.  In  wooden  trusses  it  is  not  always  practicable  to 
place  the  members  so  that  their  center  hues  meet  in  a  common  point  at  each 
joint;  but  this  condition  should  obtain  as  nearly  as  practicable,  and  in  steel 
trusses  the  joint-connections  should  be  made  so  that  the  hnes  passing  through 
the  centers  of  gravity  of  the  cross-sections  of  the  members  meeting  at  a  joint 
intersect  in  the  same  point. 

Table  X.     Coefficients  for  Determining  the  Stresses  in  Simple  Fink  and 
Fan  Trusses 

,  WHEN   PANEL-LOADS    ARE    ALL   EQUAL 


^\ 

< 1  =  span 

R^=^1.5  P 

i^span 

|R^=2.5P 

Simple  Fink  Truss  Simple  Fan  Truss 

To  find  the  stress  in  any  member,  multiply  its  factor  by  the  panel-load,  P 
SIMPLE   FINK   TRUSS 


Member 


A 
B 
D 
F. 
G. 
K 

A 
B. 
C. 
D 
E. 
F. 
G. 
K 


Kind  of  stress 


.Compression 
Tension 


//A=3 


2.70 
2.15 
0.83 
2.25 
1.50 
0.75 


//A =3. 464 
=  30° 


300 
2.50 
0.87 
2.60 
1.73 
0.87 


//A=4 


3  35 

2.91 
0.89 
3  00 
2.00 
I  00 


l/h=S 


4.04 
3.67 
0.93 
3.7s 
2.50 
1. 25 


SIMPLE   FAN  TRUSS 


Compression 

451 

5.00 

5. 59 

6.73 

3.54 

4.00 

4-55 

5.59 

" 

3.40 

4.00 

4.70 

5.99 

0.93 

I. CO 

1.08 

1. 21 

" 

0.93 

1. 00 

1.08 

1. 21 

Tension 

3. 75 

4.33 

5.00 

6.25 

" 

2.25 

2.60 

3.00 

3.75 

1.50 

1.73 

2.00 

2.50 

Determination  of  Stresses  by  Computation 


1059 


Computation  of  Stresses.  As  a  general  rule^  the  stresses  in  a  roof-truss  can 
be  determined  much  more  readily  by  the  graphic  method  than  by  mathemati- 
cal COMPUTATIONS  and  with  as  close  a  degree  of  accuracy  as  is  necessary.  Inhere 
are  a  few  forms  of  trusses,  however,  for  which  the  stresses  can  be  more  easily 
determined  by  computation.  Such  trusses  must  be  symmetrical  in  shape 
and  the  joint-loads  all  alike,  as  is  quite  frequently  the  case  with  simple  steel  roofs 
having  no  ceiling-load. 

Tables  X  to  XIII  give  constants  by  which  the  stresses  in  Fink  and  fan 
trusses  may  be  readily  computed  simply  by  multiplying  the  constant  by  the 
panel  or  joint-load.  These  tables  apply,  however,  only  when  the  rafter  is 
divided  by  the  struts  into  equal  spaces,  giving  equal  panel -loads.  For  any 
other  conditions  the  stresses  should  be  determined  by  the  graphic  method. 


Table  XI.     Coefficients  for  Determining  the  Stresses  in  an  Eight-Panel 
Fink  Truss 

WHEN    PANEL-LOADS    ARE    ALL   EQUAL 


C^AZ 


-^  =  span 


Ri=3.5P 

Eight-panel  Fink  Truss 
To  find  the  stress  in  any  member,  multiply  its  factor  by  the  panel-load,  P 


Member 


Kind  of  stress 


//A=3 


^^=3.464 
=30° 


//A=4 


l/h  =  5 


A. 
B. 
C. 
D. 
E. 
F. 
G. 
I.. 
K. 
L. 
M. 
N. 
O. 
P. 


Compression 


Tension 


I  tt/ij  no  bjioi 


6.31 
5.76 

5-20 

4-6s 
0.83 
I  66 
0.83 
0.-7S 
0.7s 
I. SO 
2.25 
5. 25 


7.00 
6.50 
6.00 
5.50 
0.87 
1.73 
0.87 
0.87 
0.87 
1.73 
2.60 
6.06 


>\  h 


7.83 
7.38 
6.93 
6.48 
0.89 
1.79 
0.89 
1. 00 
1. 00 
2.00 
300 
7.00 


942 

9  OS 
8.68 
8.31 
0.93 
1.86 
0.93 
1. 25 
1.25 
2.50 
3-75 

%.n 


1060 


Stresses  in  Roof-Trusses 


Chap.  27 


Table  XII.     Coefficients  for  Determining  the  Stresses  in  Cambered  Fink 
and  Fan  Trusses 

WHEN  PANEL-LOADS   ARE   ALL   EQUAL   AND   THE   CAMBER   EQUALS   ONE- 
SIXTH   THE   RISE 


Fig.E 
To  find  the  stress  in  any  member,  multiply  its  factor  by  the  panel-load,  P 


TRUSS   LIKE   FIG.   A 


Member 


Kind  of  stress 


l/h-- 


///i=3  464 
=  30° 


l/h=4 


l/h  =  5 


A 
B. 
D 
F. 
G. 
K 


Compression 
Tension 


3.64 
3-09 
0.83 
3.07 
1.80 
1.43 


4.13 
3.63 
0.87 
362 
2.08 
1.69 


4.70 
4.25 
0.89 
4.24 
2.40 
1.98 


5. 78 
5-41 
0.93 
5.40 
3  00 
2.52 


TRUSS   LIKE   FIG.   B 


A. 
B. 
C. 
D. 
E. 
F. 
G. 
K. 


Compression 

6.09 

6.88 

7.83 

9.64 

•• 

4.89 

5. 63 

6.48 

8.10 

•• 

4.96 

5.88 

6.93 

8.89 

" 

1.04 

1. 15 

1.26 

1.49 

" 

1.04 

LIS 

1.26 

1.49 

Tension 

5.12 

6.03 

7.07 

9.01 

2.70 

3.12 

3.60 

4.50 

2.66 

3.13 

3.67 

4.69 

Table  XIV  gives  coefficients  which  are  general  for  any  span  and  depth  for 
eight-panel  roof-trusses  with  the  Howe  and  Pratt  types  of  bracing.  Tables  XV 
and  XVI  give  .formulas  for  computing  the  stresses  in  symmetrical  Howe  and 
Pratt  trusses  which  are  symmetrically  loaded.  The  coefficients  are  given  for 
trusses  having  an  odd  number  of  panels.  For  the  Howe  truss  with  an  even 
number  of  panels  the  coefficients  for  the  center  load  on  the  top  chord  are  each 
d'iv5ued  by  two.  For  the  center  load  on  the  bottom  chord  the  coefficients  are 
also  divided  by  two,  except  that  for  the  center  vertical,  which  remains  unity. 


Determination  of  Stresses  by  Computation 


1061 


For  the  Pratt  truss  with  an  even  number  of  panels  the  coefficients  are  divided 
by  two  for  the  center  loads  for  all  pieces,  except  that  for  the  center  vertical 
for  loads  on  the  top  chord,  the  coefficient  remains  unity.  For  the  young  architect 
or  engineer  these  tables  will  be  found  useful  in  furnishing  a  check  upon  stresses 
determined  by  graphic  methods. 


Table  Xin.     Coefficients  for  Determining  the  Stresses  in  an  Eight-Panel 
Cambered  Fink  Truss 


Sc- 


WHEN  PANEL-LOADS   ARE   ALL  EQUAL   AND   CAMBER  EQUALS   ONE-SIXTH   THE 
TOTAL   RISE 


1« i 


Rf  3.5  P 

To  find  the  stress  in  any  member,  multiply  its  factor  by  the  panel-load,  P 


Member 


A, 
B. 
C. 
D 
E. 
F. 
G. 
I. 
K 
L. 
M 
N. 
O. 
P. 


Kind  of  stress 


Compression 


Tension 


l/h=3 


8.49 
7-94 
7-39 
6.83 
0.83 
1.66 
0.83 
1.02 
1.02 
2.87 
3.89 
7.17 
6.15 
3.60 


^/A= 3.464 
=30° 


9  63 
9.13 
8.63 
8.13 
0.87 
1.73 
0.87 
1,21 
1. 21 
3.37 
4.58 
8.44 
7-23 
4.16 


l/h=4 


10.96 
10. SI 
10.06 
9.61 
0.89 
1.79 
0.89 
1. 41 
1. 41 
3.96 
5.37 
9.90 
8.48 
4.80 


//A=5 


13.49 
13. II 
12.74 
12.37 
0.93 
1.86 
0.93 
1.80 
1.80 
5.04 
6.8s 
12.61 
10.81 
6,00 


1002  Stresses  in  Roof-Trusses  Chap.  27 

Table  XIV.     Coefficients  for  Eight-Panel  Roof-Tnisses 


Sec   g^^L^^w^-HlT        Triangular  Howe  Trues 


Triangular  Pratt  Trusfl 


Spa.n-nh=l- 


Ceiling- 
loads, 


Length  of 
member 


.75V«-+4 

o.i25AVw2-t-4 

.SoV«2+4 

" 

.25Vw2+4 

.OoV«-4-4 

•♦ 

1.75  « 

0.125  nh 

1.75  n 

" 

1.50  n 

" 

o.i25A's/«2-f64 


Stress  =  coeflBcient  X  P  or  p. 

For  a  half-truss  supported  at  A  and  B,  reduce  all  top  chord  coefficients  by  \^n^-{-  4 
and  all  bottom-chord  coefficients  by  n.  The  coefficients  for  the  web-m«mbers  used 
remain  unchanged. 


Determination  of  Stresses  by  Computation 


1063 


Table  XV.     Coefficients  for  Howe  Trusses  which  are  Symmetrical  About 
the  Center  of  the  Span  and  Symmetrically  Loaded 


Member 


L]  and  U^ 
Li  and  C/3 
L3  and  f/4 

U 

D^ 

D^ 

Dz 

r>i 

Fi 

F2 

F3 

Fx 

Vi. 

F3 


7  panels 


Pi 


P2 


i.o  • 

1.0 


1.0 
1.0 


1.0 
1.0 
1.0 


5  panels 


Pi 


1.0 
1.0 


3  panels 


Px 


a^h 


For  loads  Pi,  P2,  etc.,  the  coefficients  for  the  chords  and  diagonals  are  the  same  as 
given  for  the  loads  Pi,  Po,  etc.  The  coefficients  for  the  verticals  for  loads  Pi,  P2,  etc.. 
are  given  in  the  supplementary  table  below  the  general  table.  Tension  is  indicated 
in  the  truss  diagram  by  light  lines. 


1064 


Stresses  in  Roof-Trusses 


Chap.  27 


Table  XVI.     Coefficients  for  Pratt  Trusses  which  are  Symmetrical  About 
the  Center  of  the  Span  and  Symmetrically  Loaded 


P,      p,-      p,  p,      p,      p. 


Member 


Li and  L2 
Lz  and  Ui 
L4  and  Uz 

u,=u... 

Di 

D2 

Dz 

D, 

Vi 

V2 

F3 


V2. 
Vz. 


7  panels 


Pi 


{a+b+c)^h 
y/b^+h^^h 


i.o 
i.o 


5  panels 


Pi 


{a-\-b)^h 


3  panels 


Pi 


a-^A 


For  loads  Pi,  p^,  etc.,  the  coefficients  for  the  chords  and  diagonals  are  the  same  as 
given  for  the  loads  Pi,  P^,  etc.  The  coefficients  for  the  verticals  for  loads  pi.  Pi,  etc., 
are  given  in  the  supplementary  table  below  the  general  table.  Tension  is  indicated 
in  the  truss-diagram  by  light  lines. 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1065 

4.   Examples  Showing  Use  of  tables  in  Stress-Computations 

Simple  Fan  Truss.  Example  i.  In  this  example  a  simple  fan  truss  of 
36-ft  span  is  considered.  The  distance  on  centers  of  trusses  is  12  ft.  The 
height  of  truss  is  9  ft,  or  l/h  =  4.  The  total  load  per  square  foot  of  roof  is  40  lb. 
The  length  of  rafter  is  20  ft,  nearly.  The  panel-load,  P=2%xi2X40  = 
3  200  lb.     Then  from  Table  X, 

Stress  in  lower  end  of  rafter  ^  =  3  200  x  5.59  =  17  888  lb 
Stress  in  ends  of  main  tic  Z*"  =  3  200  x  5.00  =  16  000  lb 
Stress  in  center  of  main  tie  G  =  3  200  x  3.00  =  9  600  lb 
Stress  in  braces  D  and  £  =  3  200  X  1.08  =  3  456  lb 
Stress  in  tie  K  =  s  200  x  2  =  6  400  lb 

Five-Panel  Howe  Truss.  Example  2.  (Table  XV.)  A  five-panel  Howe 
truss  is  considered,  for  which  ^  =  6  ft,  a  =  9  ft,  6  =  10  ft  and  c  =  12  ft.  Let  the 
trusses  be  spaced  10  ft  on  centers,  the  roof-load  be  40  lb  per  sq  ft  and  the  ceiling- 
load  15  lb  per  sq  ft.     The  panel-loads  become: 

Pi=  V2(  9+10)  (ioX4o)  =  3  8oolb  )   _  ,, 

/'I  =¥2(9+10)  (10X15)  =  1400  lb  j   -5  200 ID 
P2  =  ¥2(10+12)  (10X40)  =  4  40olb  (^  _  „ 

p2=V2  (10+  12)  (loX  15)  =  I  700  lb  S    -^  '°^^^ 
Li  and  i/2  =  %  X  5  200  +  %  \  6  100  =17  000  lb 
Z2  and  f/3  =  %  X  5  200  +  ^%  X  6  100  =  27  100  lb 
Di  =  10.82/6  (5  200  -f-  6  100)  =  20  400  lb 
D2  ==  1 1.66/6  X  6  100  =11  90b  lb 
Fi  =  4  400  -f-  I  400  +  I  700  =  7  500  lb 
F2  =  I  700  lb 
In  the  above  results  all  values  between  50  and  100  have  been  considered  100. 
5.    Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods 
The  Graphic  Method  is  the  simplest  and  in  most  cases  the  quickest  method 
of  determining  the  stresses  in  a  roof-truss;    and  it  has,  besides,  the  additional 
advantage  of  being  applicable  to  any  true  truss-form  or  any  arrangement  of 
loads.     There  is  also  less  chance  of  making  a  mistake  in  the  graphic  method 
than  in  the  method  of  numerical  computation,  as  an  error  in  the  graphical 
analysis  almost  always  becomes  manifest.     When  the  principles  are  under- 
stood, STRESS-DIAGRAMS  cau  be  very  quickly  drawn,  without  the  aid  of  books 
or  tables.     For  the  forms  of  trusses  in  common  use,  the  method  of  drawing  the 
stress-diagrams  is  quite  simple;   and  a  careful  study  of  the  following  examples, 
supplemented  by  a  little  practice  in  drawing  the  diagrams,  should  enable  any 
architect,  draughtsman,  or  builder  to  understand  the  principles  involved  in  the 

GRAPHICAL  ANALYSIS  OF  ROOF-TRUSSES. 

Principles  Upon  Which  the  Graphic  Method  is  Based.  To  thoroughly 
understand  this  method,  a  knowledge  of  the  composition  and  resolution  of 
FORCES,  as  explained  in  Chapter  VI,  is  essential;  and  before  studying  this 
subject  the  student  should  read  carefully  pages  288  and  289. .  The  theorems 
stated  and  explained  on  these  pages  form  the  basis  of  graphic  statics. 
In  the  graphic  method  all  forces,  including  the  loads,  are  represented 
by  straight  lines,  and  the  directions  of  the  forces  must  be  constantly  kept  in 
mind.  Often  it  is  of  assistance  to  indicate  the  direction  of  a  force  by  an  arrow- 
head, as  explained  on  page  289.  The  direction  in  which  a  force  acts  with  refer- 
ence to  a  body  indicates,  also,  whether  it  is  a  pushing  or  a  pulling  force,  or 
whether  the  member  on  which  the  force  or  in  which  the  stress  acts  is  in  compres- 
sion or  TENSION.  This  is  more  fully  explained  in  the  following  pages,  and  also 
in  connection  with  several  of  the  stress-diagrams. 


1066  StFesses  in  Roof-Trusses  Chap.  2T 

Forces  and  Stresses  which  Act  On  and  In  a  Truss.  Every  stress-dia- 
gram represents  three  sets  of  forces,  viz.,  the  external  loads,  the  supporting 
forces  or  reactions,  and  the  stresses  in  the  truss-members. 

Supporting  Forces  or  Reactions.  For  a  truss  to  remain  in  place,  two  ot 
the  conditions  for  equilibrium  are  that  the  algebraic  sums  of  the  vertical  and 
horizontal  components  of  all  the  forces  acting  upon  the  truss  must  respectively 
equal  2sero.  Then  the  horizontal  and  vertical  components  of  the  supporting 
forces  or  reactions,  taken  together,  must  respectively  equal  the  horizontal  and 
vertical  components  of  the  loads.  The  lo.vds  and  reactions  are  considered 
as  the  external  forces  acting  on  the  truss  and  form  part  of  the  stress-diagram. 

Symmetrical  Loads.  When  the  loads  or  vertical  forces  are  symmetrical  on 
each  side  of  the  middle  of  the  span,  the  supporting  forces  are  equal,  and  each  is 
equal  to  one-half  the  total  load  on  the  truss. 

Unsymmetrical  Loads.  When  the  loads  are  not  symmetrical  about  the 
middle,  either  in  regard  to  point  of  application  or  to  magnitude,  the  supporting 
forces  are  unequal  and  in  most  cases  must  be  determined  before  the  stress-dia- 
gram can  be  drawn.  The  supporting  forces  for  unsymmetrically  loaded  trusses 
may  be  computed  by  the  method  of  the  moments  of  forces,  explained  on 
pages  322  to  324. 

Stress-Diagrams  for  Vertical  Loads.  Before  the  stress-diagram  for  a  truss 
can  be  drawn,  it  is  necessary  to  make  a  skeleton  drawing  of  the  truss,  representing 
the  central  or  median  lines  of  the  members  as  explained  on  page  1058.  This 
diagram,  called  the  truss-diagram,  should  be  drawn  on  the  same  sheet  of 
paper  as  the  stress-diagram,  for  convenience  in  drawing  the  latter.  The 
truss-diagram  should  also  have  all  of  the  loads  which  come  on  the  truss  indicated 
by  arrows  and  figures,  as  in  the  following  examples. 

Supporting  Forces.  The  supporting  forces,  also,  should  be  indicated  on 
ithe  truss-diagram  as  in  Fig.  10.  These  forces  are  determined  as  explained 
on  pages  322  to  324. 

Lettering  the  Truss-Diagram.  After  the  truss-diagram  is  drawn,  it  is  con- 
venient to  letter  it  according  to  the  method  known  as  Bow's  Notation,  which 
allows  a  ready  comparison  of  the  truss-diagram  and  the  stress-diagram, 
and  also  enables  the  student  to  readily  draw  the  stress-diagram  and  to  immedi- 
ately determine  the  ch.vracter  as  well  as  the  magnitude  of  the  stresses.  The 
essential  principle  of  this  method  is  the  lettering  of  each  space  on  each  side 
of  every  external  force  and  of  every  member  of  the  truss,  so  that  on  the  truss- 
diagram  a  truss-member  or  external  force  is  denoted  by  the  letters  on  each 
side  of  it.  When  the  stress-diagram  is  drawn,  it  will  be  found  that  the  same 
letters  come  at  the  ends  of  the  lines  representing  the  external  forces  and  the 
stresses  in  the  truss-members. 

The  Simple  Triangular  Frame  is  much  used  in  building  construction,  and 
most  forms  of  roof-trusses  are  combinations  of  such  triangles.  It  is,  therefore, 
worth  while  to.  show  how  easily  the  above  principles  may  be  used  to  determine 
the  stresses  in  such  a  frame.  Diagram  i,  Fig.  6,  represents  the  truss-diagram 
of  a  triangular  frame  properly  lettered.  A  load  of  100  lb  is  applied  at  the  apex. 
The  weight  of  the  frame  is  disregarded.  In  diagram  2,  a  vertical  line  ab  is  drawn, 
1  in  long  (say  to  a  scale  of  100  lb  to  the  inch),  representing  the  force  AB. 
From  b,  bd  is  drawn  equal  to  R2  and  from  d,  da  equal  to  Ri.  These  three  lines 
represent  the  external  forces  acting  on  the  truss,  and  the  polygon  abda,  called 
the  force-polygon,  is  always  a  closed  figure  if  the  forces  are  in  equilibrium. 
Since  the  force  AB  is  vertical  and  Ri  and  R2  are  parallel  to  AB,  the  figure  abda  is 
a  straight  Une,  bd  and  da  coinciding  with  ab.    If  the  external  forces  form  a  closeo 


Determination  of  Stresses   in  Roof-Trusses  by  Graphic  Methods     1067 

I'OLYGON  when  laid  ofif  to  scale,  usually  in  order,  the  frame  or  truss  upon  which 
they  act  will  not  be  moved  either  vertically  or  horizontally  by  the  forces.  The 
FORCE-POLYGON  should  always  be  drawn  and  closed  before  any  attempt  is  made 
to  determine  the  stresses  in  the  members  of  the  truss.  The  stresses  in  the 
members  of  the  truss  will  now  be  found,  beginning  with  those  meeting  at  joint  r. 
Pieces  A  C  and  CD  meet  at  this  joint.  The  stresses  in  these  two  pieces  and  Ri  are 
in  EQUILIBRIUM  and,  consequently,  if  laid  off  in  order  will  form  a  closed  pigure 
as  shown  in  Chapter  VI.  In  diagram  2,  da  represents  Ri  in  magnitude  and 
direction.     From  a  draw  a  line  parallel  to  ^C  and  from  d  a  line  parallel  to  CD 


O 


1.  Tt-uss-diagratn 

Fig.  6.     Triangular  Frame 


2.  Stress-diagram 


and  prolong  them  until  they  intersect  at  c.  ac  is  the  stress  in  AC,  and  cd  that 
in  CD.  ac,  cd  and  da,  or  Ri,  are  in  equilibrium  since  they  form  a  closed  fig- 
ure. Taking  the  forces  in  order,  da,  or  Ri,  is  known  to  act  towards  the  joint. 
The  direction  ac  is  also  towards  the  joint  and  hence  the  stress  is  of  the  same 
character  as  the  force  Ri  and  the  piece  ^C  is  in  compression.  AC  pushes 
against  the  joint  as  Ri  does.  Continuing  around  the  stress-polygon  dac,  in  the 
same  direction,  cd  acts  away  from  the  joint  and  the  stress  in  CD  is  opposite  in 
character  to  the  force  R\,  or  CD  is  in  tension.  CD  pulls  away  from  joint  i*. 
At  joint  2,  the  stresses  in  the  pieces  BC  and  CA  and  the  force  AB  are  in  equi- 
librium. The  sides  of  the  stress-polygon  are  ah,  he  and  ca  (diagram  2).  The 
force  ah  which  represents  the  load  of  100  lb  acts  down  and  towards  the  joint, 
he  and  ca  also  act  towards  this  joint,  showing  that  the  stresses  in  BC  and  CA 
are  of  the  same  character  as  the  force  AB,  or  that  the  pieces  push  against  the 
joint  and  that  each  is  in  compression.  At  joint  3,  the  two  pieces  meeting  are 
DC  and  CB.  The  stress-polygon  is  hdc.  Here  hd  acts  towards  the  joint,  dc 
away  from  the  joint,  and  ch  towards  the  joint.  As  found  before,  the  stress  in 
DC  is  tension  and  that  in  CB,  compression.  Diagram  2  is  made  up  of  three 
stress-polygons,  one  for  each  of  the  joints  shown  in  diagram  i.  Each  of  these 
polygons  is  considered  independently  when  determining  the  magnitude  and 
character  of  the  stresses  or  forces.  This  is  important  to  remember  when  the 
stress-polygons  are  combined  as  in  diagram  2.  In  determining  the  character 
of  the  stress  in  AC,  for  example,  from  the  stress-polygon  dac  for  joint  i,  the 
force  ac  acts  towards  joint  i,  while  from  the  stress-polygon  ahc  for  joint  2,  ca 
acts  towards  joint  2.  In  both  cases  the  piece  ^C  is  pushing  against  the  joints 
at  its  ends  and  is  in  compression.  If  arrow-heads  are  used  in  indicating  the  di- 
rections of  the  forces  in  the  stress-polygons,  they  should  be  erased  as  soon  as 
the  characters  of  the  stresses  for  the  joint  being  considered  have  been  found; 
otherwise,  where  polygons  are  combined  as  in  diagram  2,  each  line  will  have  two 
arrow-heads  pointing  in  opposite  directions,  leading  to  confusion.  .  Arrow-heads 
may  be  placed  upon  the  truss-diagram.  Each  piece  will  have  two  arrow-heads, 
one  at  each  end,  referring  to  the  joint  at  the  end.     When  the  arrow-heads  point 


1068 


Stresses  in  Roof-Trusses 


Chap.  2\ 


Piece  in  Tension 


away  from  each   other   the  piece  is   in  compression,   and  when  they  poin 
towards  each  other  the  piece  is  in  tension. 

It  is  important  to  keep  in  mind  the  direction  in  which  the  forces  and  stresse 
are  considered  in  order,  in  going  around  the  truss  or  around  a  joint.  In  Figs 
6  and  8  the  curved  arrows,  show  that  a  clockwise  direction  has  been  chosen 
This  makes  the  stress-Hnes  of  the  stress-diagram  come  on  the  left  of  the  load 
line.  This  direction  has  been  taken  for  all  the  trusses  in  this  chapter,  excep 
for  a  few  diagrams  for  wind-loads.  The  stresse 
could  have  been  deterrnined  just  as  well  b] 
taking  a  contra-clockwise  direction. 

If  two  men  pull  on  the  two  ends  of  a  rope 
exerting  pulling  forces  of  equal  intensity,  thi 
TENSiONAL  STRESS  in  every  cross-section  of  th 
rope  is  equal  to  the  force  with  which  one  mai 
pulls;  and  each  end  of  the  rope  pulls  away  fron 
the  man  holding  it,  with  a  force  equal  in  magnitude  to  that  which  he  exerts 
Thus  if  each  man  exerts  a  force  of  loo  lb  the  stress  in  the  rope  is  loo  lb  an( 
each  end  of  the  rope  pulls  away  with  a  force  of  loo  lb.  If  the  men  push  agains 
the  two  ends  of  a  piece  of  timber  with  a  force  of  loo  lb,  the  timber  pushe 
against  each  man  with  a  force  of  loo  lb,  although  the  entire  compressivj 
stress  in  every  cross-section  of  the  timber  is  but  loo  lb.  Consequentl: 
stress-lines  are  sometimes  drawn  with  arrow-heads  pointing  towards  eacl 
other,  as  at   A,  Fig.  7,    denoting    tension;   or   with   arrow-heads   pointin] 

b      +58      d 


D^ 


Fig.  7. 


Piece  in  Compression 

Indication  of  Character 
of  Stress 


D 

1             +58 

p=ioo 
C 

2   -1-58 

3 

^^\   B 

0 

1 
4- 

1/ 

2=66^ 


o 


1.  Truss-diagram 

c 


1             +58 

2                3 

\,^^ 

B 

0 

A  / 

0 

\ 

P=100 

' 

R2=6 


3.  Truss-diagram 


Fig.  8.     Trussed  Beam 


4.  Stress-diagram 


in  opposite  directions,  as  at  B,  denoting  compression.  It  is  better,  however 
to  omit  arrow-heads  on  stress-lines,  putting  them .  on  lines  representing 
external  forces  only.  The  stress  in  any  member  of  a  truss  acts  ir 
opposite  directions  at  the  two  ends  of  the  piece.  This  is  an  important  trutl 
to  remember  jn  drawing  stress-diagrams. 

The  Trussed  Beam.     Fig.  8  shows  a  load  supported  by  a  beam,  post  or  strut 
and  two  ties  instead  of  by  two  struts  and  a  tie.     The  effect  on  the  rod  forming 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1069 

the  two  ties  is  the  same  whether  the  load  is  applied  as  shown  in  diagram  i,  or 
as  shown  in  diagram  3.  Considering  the  case  shown  in  diagram  i:  The  force- 
polygon  is  dcod  (diagram  2);  the  sides  of  the  stress-polygon  for  joint  1  are  od, 
db  and  ho,  the  stress  in  DB  being  compression,  and  that  in  BO,  tension.  For 
joint  2  the  sides  of  the  stress-polygon  are  dc,  ca,  ah  and  hd,  the  stress  in  CA  be- 
ing compression;  that  in  AB,  compression;  and  that  in  BD,  compression.  For 
joint  3  the  sides  of  the  stress-polygon  are  ac,  co  and  oa.  The  stress  in  ylC  is  com- 
pression; and  that  in  OA,  tension.    The  condition  shown  in  diagram  3,  where 


1.  Truss-diagram 
Fig.  9. 


Crane  Truss 


2.   Stress-diagram 


7700 


H— -SlO- 


-- 'rr;  -^  r-T — Tt:  r^'ir^Vfi 


\ 


the  load  is  suspended  from  joint  4,  leads  to  a  different  form  of  stress-diagram, 
but  the  method  of  construction  remains  the  same.  The  stresses  in  the  pieces 
are  the  same  with  the  exception  that  the 'stress  in  the  piece  A  Bis  zero  for  the  case 
shown  in  diagram  3. 

The  Crane  Truss.  Fig.  9,  diagram  i,  shows  the  truss-diagram  of  a  crane 
carrying  a  vertical  load  at  joint  2.  The  external  forces  acting  on  the  frame 
are,  the  load  at  joint  2,  the  supporting  force  at  joint  3,  and  the  stress  in  the 
guy  CA .  Since  the  frame  is  in  equilibrium  under  the  action  of  these  three  forces, 
they  meet  in  a  point. 
This  provides  a  ready 
method  for  determining 
the  direction  and  magni- 
tude of  the  supporting 
force  at  joint  3 .  Prolong 
the  line  CA  and  draw  a 
vertical  line  through 
joint  2  until  it  intersects 
the  line  CA,  prolonged,  at 
O;  then,  since  the  sup- 
porting force  must  pass 
through  jofnt  3,  sO  is 
the  direction  of  this 
force.  The  force -poly- 
gon is  now  drawn.  The  sides  of  this  polygon  are  he,  ca  and  ah.  ca  is  the  stress 
in  the  guy  CA  which  is  in  tension.  The  stress-polygons  for  each  joint  can  now 
be  readily  drawn  and  the  stresses  in  the  members  of  the  frame  determined 
(diagram  2). 

The  following  examples,  worked  out  in  detail  and  with  considerable  repeti- 
tion, will  enable  the  student  to  grasp  the  principles  of  the  graphic  method 
for  determining  stresses  in  framed  structures. 

King-Rod  Truss.  Example  i.  Fig.  10  shows  the  truss-diagram  of  tho 
truss  represented  in  Fig.  1,  properly  drawn,  lettered  and  figured,  ready  for 


R2=U785 


Fig.  10.    King-rod  Truss.    Truss-diagram 


1070 


Stresses  in  Roof-Trusses 


Chap.  27 


drawing  the  stress-diagram.  The  supporting  force  at  the  left  is  SM,  the  load 
at  joint  I  is  MA,  the  bottom  of  the  rafter  isAE,  the  left  portion  of  the  tie-beam 
or  bottom  chord  is  ES,  etc.  The  loads  acting  at  joints  i,  2,  3,  4  and  5  are 
designated  as  MA,  AB,  BC,  CD  and  DN  respectively,  and  those  at  joints  8,  7 
and  6  as  OP,  PQ  and  QS  respectively.  It  makes  no  difference  what  letters 
are  used,  except  that  it  is  better  to  first  letter  the  outside  spaces  consecutively 
and  then  the  inside  spaces. 

Force-Polygon.    The  force-polygon  is  now  constructed  by  laying  off  to 
scale  (Fig.  10a)  the  external  forces  in  order,  beginning  with  the  force  MA,  and 
..^  following  with  AB,  BC,  CD,  DN  laid  off 

downward,  NO  laid  off  upward,  OP,  PQ, 
QS  laid  off  downward,  and  SM  laid  off 
upward.  If  the  work  is  correct,  these 
forces  form  a  closed  figure. 

Stress-Diagrams.  The  stress-dia- 
gram is  drawn  by  taking  the  forces  acting 
on  the  joints  in  consecutive  order,  com- 
mencing at  one  of  the  supports.  It  is 
convenient  to  start  with  the  support  at 
the  left,  or  at  joint  i.  In  actual  com- 
putations it  is  not  necessary  to  number 
the  joints,  but  in  order  to  refer  to  them 
in  the  description  it  is  necessary  to  num- 
ber them  in  the  illustrations.  Commenc- 
ing at  joint  I,  the  first  step  in  drawing 
the  STRESS-DIAGR.4M  js  to  draw  a  vertical 
line  to  a  scale  of  pounds-to-tiie-inch  to 
Stress-  represent  the  supporting  force  SM.  This 
hne  is  the  line  sm  already  drawn  in  con- 
structing the  force-polygon  (Fig.  10a) 
which  might  be  drawn  to  the  scale  of  16  000  lb  to  the  inch.  It  is  best  to 
use  a  scale  as  large  as  convenient  in  order  to  have  a  relatively  small  stress- 
diagram.  An  engineer's  scale,  one  divided  to  loths,  2oths,  30ths,  etc.,  of  an 
inch,  is  found  most  convenient  for  these  drawings.  The  small  letter  s  is  placed 
at  the  bottom  of  the  line  sm,  and  the  letter  m  at  the  top.  From  m  is  laid  off  ma 
representing  the  load  MA .  A  line  is  then  drawn  from  a,  parallel  to  the  rafter 
AE,  and  a  line  from  s  parallel  to  the  tie-beam  ES.  The  two  lines  meet  at  e, 
and  ae  represents  the  stress  in  AE  and  es  the  stress  in  ES.  The  supporting  force, 
represented  by  sm,  acts  upward,  and  the  others  follow  in  rotation,  showing  that 
ae  acts  towards  joint  i  and  that  the  member  ^£  is  in  compression,  and  show- 
ing that  es  acts  from  joint  i  and  that  the  member  ES  is  in  tension.  Consider 
next  the  stresses  at  joint  6.  Commencing  at  the  bottom  of  the  joint  and  going 
around  to  the  left,  the  first  force  that  is  known  is  the  load  QS,  or  i  930  lb,  which 
is  measured  to  the  scale  used  from  g  to  s,  downward,  as  the  loads  act  downward. 
The  point  ^  was  located  in  drawing  the  stress-polygon  for  joint  i,  and  q  and  s 
in  constructing  the  force-polygon  for  the  external  forces.  The  next  stress 
that  is  known  is  the  stress  se  which  has  just  been  determined.  As  this  stress 
acts  to  the  right  from  joint  i,  it  will  act  to  the  left  from  joint  6,  as  the  stresses 
in  the  two  ends  of  a  strut  or  a  tie  act  in  opposite  directions,  as  explained  on  page 
1068.  The  stresses  in  EE'  and  E'Q  are  not  known,  so  from  e  a  line  is  drawn 
parallel  to  EE'  and  extended  so  that  a  line  drawn  from  its  extremity  e'  and 
parallel  to  E'Q  closes  on  q.  The  lines  ee'  and  e'q  are  thus  found,  which  repre- 
sent the  stresses  in  EE'  and  E'Q  respectively.    Starting  with  $e,  tl>e  stress  i^ 


Fig.  .;JOiU>jTfiing-rod    Truss. 
.,,;.       ,,|j     diagram 


Determination  of  Stresses  in  Roof-Trusses  Dy  Graphic  Methods    1071 

SE,  known  to  be  tension  and  acting  from  joint  6,  and  going  around  the  diagram 
in  rotation,  EE'  and  E'Q  are  found  to  be  in  tension.  At  joint  2  the  stresses 
in  E'E  and  EA  and  the  force  or  load  AB  are  known,  leaving  the  stresses  in  BF 
and  FE'  to  be  detennined.  From  a  lay  oflf  downward  ab  equal  to  the  force  or 
load  AB.  From  b  draw  a  line  parallel  to  BF,  and  from  e'  a  line  parallel  to 
FE'.  Prolong  these  lines  until  they  intersect  at  /;  then  bf  is  the  stress  in  BF 
and  fe'  that  in  FE'.  Both  members  are  in  compression.  At  joint  3,  the  un- 
known forces  or  stresses  are  the  stresses  in  CG  and .  GF.  From  c  draw  a  Una 
parallel  to  CG,  and  from  /  a  line  parallel  to  GF.  The  two  lines  intersect  at  g, 
and  eg  is  the  stress  in 


CG  and  gf  that  in  GF. 
CG  is  in  compression 
and  GF  in  tension. 
Since  the  truss  is  sym- 
metrical and  symmetri- 
cally loaded,  the  stresses 
in  the  members  on  the 
right  of  the  middle  are 
the  same  as  in  those  on 
the  left.  The  stresses  in 
the  members  on  the  left 
of  the  middle  have  been 
determined  so  that  it  is 


Roof  Load  iS  lb.  per  Bq.ft. 
Ceiling  Load  181b.  per  sq.ft. 


R,=  11785 


1930  2070  1930 

Fig.  11.    King-rod  Truss.     Stresses 
not  necessary  to  draw  the  stress-polygons  for  joints  4,   5,   8  and  7 


R2=  H785 


It 


is  good  -practice  to  complete  the  stress-diagr.\m  including  the  stresses  for 

every  joint  in  the  truss.     A  closed  symmetrical  figure  will  result,  unless  some 

error  is  made  in  the  construction,  thus  checking  the  work.     The  scale  is  now 

applied  to  the  different  lines  of  the  stress-diagram  and  the  magnitudes  of 

the  stresses  obtained  as  indicated  on  the  corresponding  lines  of  the  truss-dia- 

GR/\M  (Fig.  11),     In  practice  the  diagrams  of  Figs.  10  and  11  are  combined  in 

■  'n\j  lo  T 

C 


Queen  Truss. 


Truss-diagram.      (See,  also,  Figs.  3,  53  and  54  and  Chapter 
XXVIII,  Fig.  1) 


one  drawing.  They  are  shown  separately  here  merely  to  indicate  the  succes- 
sive steps  in  the  drawing  of  the  diagrams  and  in  the  determination  of  the  stresses. 
The  Queen  Truss.  Example  2.  The  diagram  in  Fig.  12  represents  the 
center  lines  of  the  members  of  the  queen  truss  shown  in  Fig.  3;  and  the 
loads  indicated  are  those  found  in  example  2,  page  1055.  The  middle  braces  in 
the  middle  panel  are  indicated  by  dotted  lines  in  the  truss-diagram,  because 
imder  a  symmetrical  load  there  are  no  stresses  in  these  members,  and  they  are 
therefore  not  represented  by  lines  in  the  stress-diagram.    As  the  truss  is  sym- 


1072 


Stresses  in  Roof-Trusses 


Chap.  27 


ii\iUi    J I 


metrically  loaded,  each  supporting  force  or  reaction  is  equal  to  one-half  the  total 
load,  or  1 8  500  lb.  There  are  no  purlins  at  joints  i  and  6  to  carry  rafters  and 
ceiling-joists,  which  are  supported  by  the  walls  of  the  building,  so  there  are  no 
external  loads  at  these  joints  as  in  the  previous  example.  The  very  small  dead 
load  due  to  the  truss  itself  is  neglected.  To  draw  the  force-polygon,  first  draw 
the  vertical  line  qa  (Fig.  12a)  equal  in  leiigth,  to  some  scale,  to  the  magnitude 
of  the  left  supporting  force;  then  in  rotation  and  at  the  same  scale  lay  off  the 
distances  ab,  be,  cd  and  dg,  downward;  go,  equal  t6  the  right  supporting  force, 
upward;  and  op  and  Pq  downward,  closing  the  figure  at  q.  To  construct  the 
combined  stress-diagram  using  the  force-polygon  just  drawn,  as  a  foundation, 
first  consider  joint  i.  From  a  draw  a  line  parallel  to  AE  and  from  q  a  line 
parallel  to  EQ.  The  triangle  qae  represents  the 
three  forces  in  equilibrium,  meeting  in  a  point  and 
acting  at  joint  i.  As  the  supporting  forces  act 
upward,  the  arrow-head  on  qa  points  upward.  Fol- 
lowing the  sides  of  the  stress-polygon  qae  in  rotation, 
ae  acts  towards  the  joint  and  eq  from  the  joint, 
showing  that  ae  is  in  compression  and  eq  in  tension. 
Next  determine  the  stresses  acting  at  joint  2.  The 
stress  in  EA  is  now  known  and  represented  by  the 
line  ea,  and  as  the  stress  at  joint  2  acts  in  a  direction 
opposite  to  that  at  joint  i,  it  now  acts  upward 
towards  joint  2.  The  next  force  is  the  load,  6  300 
lb,  which  acts  downward.  The  point  b  has  already 
been  found  by  measuring  from  a  a  distance  equal  to 
6  300  lb  at  the  same  scale  as  used  in  drawing  qa. 
There  now  remain  two  stresses  to  be  found  for  joint 
2,  those  in  BF  and  FE.  Draw  bf  parallel  to  BF,  and 
fe  parallel  to  FE,  the  two  lines  intersecting  at  /. 
Then  the  sides  of  the  polygon  abfe  represent  respectively  the  magnitudes 
of  the  four  forces  acting  at  joint  2;  and  the  character  of  the  stresses  is 
determined  by  the  directions  in  which  the  stress-lines  are  drawn,  in  order, 
in  going  around  the  joint.  In  this  case  they  all  act  toward  the  joint, 
and  EA,  BF  and  FE  are  in  compression.  The  stresses  acting  at  joint  3  or  7 
may  be  determined  next,  as  only  two  of  them  are  unknown  at  either  joint. 
Considering  the  external  force  and  the  three  stresses  acting  at  joint  3,  the  stress 
in  FB  has  been  determined  and  is  represented  by  the  line  fb,  which  is  drawn  up- 
ward for  this  joint.  The  load  or  force  BC,  8  550  lb,  is  known  and  is  represented 
by  be.  ch  is  drawn  parallel  to  CH,  and  hf  parallel  to  IIF,  closing  the  polygon. 
The  length  of  ch  determines  the  magnitude  of  the  stress  in  CH  and  hf  the  stress 
in  HF.  The  stresses  in  all  the  truss-members  but  HP  are  now  determined. 
This  stress  is  found  by  considering  the  force  and  stresses  acting  at  joint  7.  At 
this  joint  the  force  PQ,  or  3  650  lb,  and  the  stresses  in  QE,  EF  and  FH,  represented 
respectively  by  pq,  qe,  ef  and  fk,  have  been  determined.  The  line  hp,  represent- 
ing the  stress  in  HP,  completes  the  polygon  for  j/ftint  7.  Hence  hp  determines 
the  stress  in  HP,  and  as  ho  is  drawn  from  left  to  right,  from  the  joint,  HP  is  m 
tension.  With  reference  to  joint  3,  the  line  ch  is  drawn  towards  joint  3  and 
hence  CH  is  in  compression.  Scaling  the  lines  in  the  stress-diagram  (Fig.  12a) 
the  figures  shown  by  the  side  of  the  lines  are  obtained.  They  indicate  the  mag- 
nitude of  each  stress  in  pounds,  the  -f  sign  denoting  compression,  and  the  —  sign, 
tension.  The  two  foregoing  examples  illustrate  the  method  of  drawing  the 
stress-diagrams  for  simple  symmetrical  trusses,  symmetrically  loaded.  The 
truss-diagrams  should  be  diavfxx  in  accordance  with  the  measurements  give^, 


Fig. 


1!2a'.  '   Qu6fen    Truss. 
Stress-diagram 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1073 

but  to  a  scale  of  not  less  than  Vs  in  to  the  foot;  and  the  stress-diagram  should 
be  drawn,  line  by  line,  in  accordance  with  the  foregoing  directions  and  the 
results  obtained  and  compared  with  those  given  in  the  figures.  A  variation  of 
loo  or  200  lb  for  small  stresses  and  less  than  1%  for  large  stresses  may  be  ex- 
pected, but  a  greater  variation  indicates  either  that  sufficient  care  has  not  been 
exercised  in  drawing  the  stress-Unes  exactly  parallel  to  the  corresponding  lines 
of  the  truss-diagram,  or  that  an  error  has  been  made  in  drawing  the  truss-dia- 
gram, or  in  scaling  the  lines  of  the  stress-diagram.  After  these  two  examples 
have  been  worked,  a  number  of  the  following  examples,  also,  should  be  solved, 
until  the  principles  are  fully  understood. 

Truss  for  Museum  of  Fine  Arts,  St.  Louis,  Mo.    Example  3.    Fig.  13 
represents  the  truss-diagram  of  the  truss  shown  in  Fig.  11,  Chapter  XXVI, 


f  S^ 


O      ie'o'l 
-    Ro^4iai;o 


Fig.  13.     Truss-diagram.     Museum  of  Fine  Arts,  St.  Louis,  Mo. 
Fig.  13a.     Stress-diagram 


the  loads  indicated  being  approximately  those  due  to  the  roof  and  suspended 
floor  below.  The  loads  being  symmetrically  disposed,  each  supporting  force  is 
equal  to  one-half  the  total  load,  or  41  040  lb.  The  counterb races  CC,  shown 
in  Chapter  XXVI,  are  omitted  from  the  truss  because  they  have  no  stress  when 
the  truss  is  uniformly  loaded.  To  draw  the  stress-diagram  (Fig.  13a),  first 
draw  to  scale  the  vertical  line  sa,  equal  to  41  040  lb,  equal  to  Ri;  and  then  ab 
and  bs  parallel  respectively  to  AB  and  BS  and  representing  the  stresses  acting 
at  joint  I.  At  joint  2,  the  line  ba  represents  the  stress  in  BA ;  ac,  equal  to  7  200 
lb,  the  load  AC;  cd,  the  stress  in  CD;  and  db  the  stress  in  DB.  The  polygon 
bacdb  represents  the  forces  in  equilibrium  acting  at  joint  2.  At  joint  3  there  are 
three  unknown  forces;  and  as  three  unknown  forces  out  of  five  in  one  polygon 
cannot  be  determined,  joint  4,  where  dc  and  the  load  CF  are  known,  is  considered 
next.  Measuring  oQ  the  load  cf,  equal  to  12  240  lb,' the  stresses  in  FE  and  ED 
only  are  to  be  determined.  These  are  found  by  drawing /g  parallel  to  FE,  and 
ed  parallel  to  ED,  the  two  lines  intersecting  at  e.  At  joint  3,  sb,  bd,  de  and  the 
force,  qs  are  known,  and  eg  and  gq  are  drawn  to  close  the  polygon  sbdegs.     At 


1074 


Stresses  in  Roof-Trusses 


Chap.  27 


joint  lo  the  force  pq,  equal  to  12  000  lb,  and  qg  are  known;  and  gg'  and  g'p  are 
drawn  to  close  the  polygon.  At  joint  5,  g'g,  ge  and  ef  are  known  and  ih  and  hg' 
are  drawn  to  close  the  polygon.  Since  there  is  no  load  at  joint  5,  /  and  i  fall  at 
the  same  point  in  the  stress-diagram.  The  stresses  in  pounds,  in  the  various 
members  of  the  truss,  are  given  in  numbers  on  the  corresponding  lines  in  the 
stress-diagram  (Fig.  13a). 

Triangular    Howe   Truss.     Example  4.     Consider  the  skeleton  triangular 
Howe  truss  represented  in  Fig.  14  loaded  as  shown  by  the  weight  of  the  roof 

10320 
10320  M     £  ^^'ioS20 


[L   10320 


^^  10.320' 


^.    Q   «ooa  P   3000  o   3000  N*  3000  1^  3000    C>  sooo   ^ 
Fig.  14.     Triangular  Howe  Truss.     Truss -diagram 


^soooIX 


Fig.  14a.     Triangular  Howe  Truss. 


above  and  a  ceiling  t>elow.  To  draw  the  stress-diagram,  first  draw  to  scale 
the  supporting  force  qj,  equal  to  46  620  lb.  Then  lay  off  jk  equal  to  10  320  lb, 
kl  equal  to  10  320  lb,  etc.  Then  draw  the  lines  Ja  and  aq,  and  the  three  forces 
Bt  the  left  support  are  known.  At  joint  0,  pq  and  qa  are  known  and  ab  and  bp 
are  drawn  to  close  the  polygon.  At  joint  i,  ba,  aj  and  jk  are  known  and  kc 
and  cb  are  drawn  to  close  the  polygon.  At  joint  2,  op,  pb  and  be  are  known 
and  cd  and  do  are  drawn  to  close  the  polygon.  At  joint  3,  dc,  ck  and  kl  are  known 
and  le  and  ed  are  drawn.     At  joint  4,  no,  od  and  de  are  known  and  ef  and  /«  are 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods    1075 


drawn  to  close  the  polygon.  At  joint  ^,  /e,  el  an.d  Im  are  known  and  mg  and  gj 
are  drawn.  Joint  7  is  considered  next,  for  at  joint  6  there  are  three  unknown 
stresses;  and  by  the  graphic  method  three  out  of  five  forces,  meetiiig  in  a  point 
and  in  equilibrium,  must  be  known  in  order  to  determine  the  other  two.  At 
joint  7,  gm  and  mm'  are  known  and  mg'  and  g'g  are  drawn  to  close  the  polygon. 
This  completes  the  determination  ot  the  stresses  in  all  the  pieces  for  one-half 
of  the  truss  and  of  course  the  stresses  for  each  half  are  the  same  as  the  loading 
is  symmetrical. 

Eight-Panel  Howe  Truss.     Example  s-     For  the  next  example  a  Howe 
TRUSS  is  considered,  whose  center  lines  give  the  diagram  shown  in  Fig.  15. 


Fig.  15.     Howe  Truss.     Truss-diagram 

This  truss  is  used  for  a  span  of  64  ft,  and  it  supports,  in  addition  to  a  flat  roof, 
a  plaster  ceiling  below  the  bottom  chord  and  a  gallery  on  each  side.  The  loads 
at  the  different  joints  are  about  as  indicated  in  Fig.  15.  To  draw  the  stress- 
diagram  (Fig.  15a),  first  construct  the  force-polygon  by  laying  off  to  scale  in 
rotation  the  external  forces,  commencing  with  the  left  reaction  34  200  lb.  Next, 
commencing  at  joint  o,  the  supporting  force  sa  is  known,  the  stress  in  the  rafter 
is  ap,  and  the  stress  in  the  tie  ps,  closing  the  polygon.     At  joint  i,  pa  and  ab 


+500U  i 


Fig.  15a.    Howe  Truss.    Stress-diagram 

are  known  and  hn  and  np  are  drawn,  closing  the  polygon.  At  joint  2,  gs,  sp  and 
pn  are  known  and  nm  and  mg  are  drawn.  At  joint  3,  w«,  nh  and  be  are  known 
and  d  and  Im  are  drawn.  The  stresses  at  the  remaining  joints  are  found  in  the 
same  way  as  those  at  3  and  4.  The  stresses  in  pounds  in  the  various  members 
of  the  truss  are  noted  in  figures  in  the  stress-diagram  (Fig.  15a). 

Howe  Truss  Loaded  at  Alternate  Joints.     Example  6.     (Fig.  16.)    This 
example  of  a  Howe  truss  is  selected  to  show  how  to  proceed  when  there  is  no 


1076 


Stresses  in  Roof-Trusses 


Chap.  27 


load  at  one  or  more  of  the  joints.  F[g<  16  represents  the  center  lines  of  a  truss 
50  ft  in  span  and  only  5  ft  in  height.  In  order  to  give  the  braces  an  inclination 
approximating  45°,  the  truss  is  divided  into  ten  panels;  but  purlins  are  placed 
over  every  other  joint,  as  in  Fig.  16,  Chapter  XXVI.  The  loads  from  these 
purlins  are  about  5  000  lb.  The  stresses  at  joint  i  are  found  in  the  same  manner 
as  in  the  previous  example,  always  starting  with  the  supporting  force.  At 
joint  2  the  stress-line  da  is  already  drawn;  and  as  there  is  no  load  at  this  joint, 


5000 


Ri=aoooo 


Fig.  16.    Howe  Truss.    Truss-diagram 


a  line  is  drawn  from  a  parallel  to  AE  (A  covers  the  entire  space  from  joint  i 
to  joint  4),  and  a  line  from  d  parallel  to  ED,  the  two  lines  intersecting  at  e. 
The  force-lines  and  stress-lines  are  as  follows: 

At  joint  3:  od,  de,  ef  a.ndfo; 

At  joint  4:  fe,  ea,  ab,  bg  and  gf; 

At  joint  5:  of,  fg,  gh  and  ho] 

At  joint  6:  hg,  gb,  bi  and  ih; 

At  joint  7:  oh,  hi,  ij  Siudjo; 

At  joint  8:  ji,  ib,  be  and  ck; 
the  latter  line  extending  to  the  point  of  beginning,  j,  showing  that  there  is  no 
stress  in  kj:    At  joint  9  the  only  stresses  are  oj  and  lo,  for  as  there  is  no  stress 

e  -fioooo 


Fig.  16a.    Howe  Truss.     Stress-diagram 

in  JK,  for  equilibrium  there  can  be  none  in  KL.  There  is,  also,  no  stress  in  the 
middle  rod.  Although  these  members  have  no  stress,  it  is  advisable  to  insert 
them  in  the  truss  in  order  to  stiffen  the  top  and  bottom  chords.  They  may 
be  made  very  light,  say  ^4  in  in  diameter  for  the  rods  and  3  by  6  in  in  cross- 
gection  for  the  braces, 


Determination  of  Stresses  in  Roof -Trusses  by  Graphic  Methods     1077 

Howe  Truss  with  Slanting  Top  Chord.  Example  7.  In  order  to  give  a 
slope  to  the  roof  it  is  often  desirable  to  incline  the  top  chord  of  a  Howe  truss 
as  in  Fig.  17,  Chapter  XXVI.  Fig.  17  shows  the  truss-diagram  for  such  a  truss, 
and  Fig.  17a  the  stress-diagram.  The  latter  is  drawn  in  the  same  way  as  the 
stress-diagram  in  Example  5,  but  because  the  top  chord  is  not  level,  the  stress- 
diagram  is  not  symmetrical.  When  the  stress-diagram  is  not  symmetrical  it  is 
necessary  to  complete  the  entire  diagram,  so  as  to  show  the  stress  in  every  mem- 
ber of  the  truss.     The  stress-lines  for  joint  9  are  om,  nin,  nr  and  ro.     This  leaves 


R2  =  10000 


Fig.  17.     Howe  Truss  with  Slanting  Top  Chord.     Truss-diagram 


Fig.  17a.     Howe  Truss  with  Slanting  Top  Chord.     Stress-diagram 


only  the  line  rj  to  complete  the  diagram;  and  if  the  diagram  has  been  correctly 
drawn,  a  Hne  joining  r  and  /  will  be  exactly  parallel  to  RF.  There  is  no  stress 
in  the  rod  //. 

Pratt  Truss.  Inclined  Ties.  Example  8.  (Fig.  18.)  This  truss  has  the 
same  dimensions  as  the  truss  shown  in  Fig.  14,  but  the  diagonals  incline  in  the 
opposite  direction  and  are  in  tension,  while  the  verticals,  except  the  middle  one, 
LL',  are  in  compression.  This  form  of  truss  is  sometimes  used  in  wooden  con- 
struction to  avoid  the  long  middle  braces  shown  in  Fig.  14.    Long  ties  are,  as  a 


1078 


Stresses  in  Roof-Trusses 


Chap.  27 


rule,  more  economical  thail  long  struts.  The  construction  of  the  stress-diagram 
requires  no  additional  explanation  after  that  given  for  the  stress-diagram  in 
Fig.  14a.  The  student  should  compare  the  magnitude  of  the  stresses  scaled 
and  marked  in  Fig.  18a  with  those  in  Fig.  14a,  and  note  the  eflect  of  the  change 
in  the  direction  of  the  braces.  The  truss  represented  by  Fig.  14  requires  a  very 
much  larger  rod  in  the  middle  than  is  required  for  KL  and  K'L'  in  the  truss  of 
Fig.  18.    The  middle  rod  for  the  truss  shown  in  Fig.  18  may  be  made  very  light. 


Fig.  I 8a.     Pratt  Truss.  Inclined  Ties.     Stress-diagram. 

This  truss,  however,  requires,  for  good  construction,  special  cast-iron  washers 
for  the  rods. 

Simple  Fan  Truss.  Example  9.  (Fig.  19.)  This  figure  shows  the  skeleton 
of  a  simple  fan  truss  with  rafters  inclined  30°  and  divided  into  three  equal 
panels,  making  the  loads  AB,  BC,  CC,  etc.,  equal.  The  stress-diagram  is 
drawn  according  to  the  principle  already  explained  and  requires  no  special 
treatment.  As  the  loads  are  equal,  the  stresses  in  this  truss  may  be  readily 
figured  by  means  of  Table  X,  and  the  student  should  compare  the  stresses  thus 
determined  with  those  obtained  by  scaling  the  stress-diagram. 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1079 

Cambered  Fink  Truss.  Example  lo.  (Fig.  20.)  The  inclmation  of  the 
rafters  is  30°  and  the  distance  between  the  trusses  20  ft.  The  loads  are  cal- 
culated for  a  slate  roof  on  boards  or  on  angle-iron  purlins.  Commence  the 
stress-diagram  by  drawing  a  vertical  line  equal  to  the  supr)orting  force  Ri,  ot 
56  350  lb,  and  lettering  the  lower  end  of  the  line  0  and  the  upper  end  c,  as  these 


R,=5000 


Fig.  19.    Fan  Truss.    Truss-diagram 


are  the  letters  on  each  side  of  the  supporting  force  at  joint  o.  an  and  no  are 
drawn  parallel  to  AN  and  NO.  For  joint  i,  na  is  drawn  upward;  ab  is  laid  oflf 
equal  to  16  100  lb  and  bm  and  mn  are  drawn  parallel  to  BM  and  MN.  At  joint  2 
on  and  mm  are  known,  and  ?nl  is  drawn  parallel  to  ML,  the  sides  of  the  stress- 
polygon  being  on,  nm,  ml  and  lo. 
not  found  in  any  of  the  preced- 


At  joint  3  a  new  condition  is  met,  which  is. 

T 


ing    examples     and     which     is 

peculiar  to  this  form  of  truss, 

viz.,  three  apparently  unknown 

forces.     From    a    study  of   the 

truss-diagram,    however,    it    is 

seen  that  LM  and  IK   act  as 

parts  of  BELLY-RODS,  taking  up 

the  thrust  from  the  lower  ends 

of  the  struts  at  joints  2  and  5; 

and  as  the  loads  at  joints  i  and 

6  are  equal  and  NM  and  IH  are 

the  same  length,   the   stress  in 

IK  is  the  same  as  the  stress  in 

LM,   which   is   already   known. 

This    reduces    the    number    of 

unknown   forces   at  joint   3   to 

two.     The  first  force  known  at 

this  joint  is  Im,  the  next  mb  and 

the  next  be,  equal  to  16  100  lb. 

From  c  a  line  is  drawn  parallel  to  CI  and  from  /,  the  initial  point,  a  line 

parallel  to  KL.     Between  these  two  lines  there  must  be  a  line,  ik,  parallel  to 

IK  and  equal  in  length  to  ml;  and  this  Hne  is  determined  by  means  of  the 

dividers  and  a  parallel  ruler  and  straight-edge.     If  correctly  drawn,  the  joint  i 

will  fall  in  line  with  nm.     The  sides  of  the  stress-polygon  for  joint  3  are,  then, 

hn,  mb,  be,  ci,  ik  and  kl. 


Fig.  19a.     Fan  Truss. 


Stress-diagram 


1080 


Stresses  in  Roof-Trusses 


Chap.  27 


At  joint  4  the  stress-lines  are  ol,  Ik,  kg  and  go. 

At  joint  5  the  stress-lines  are  gk,  ki,  ih  and  hg. 

At  joint  6  the  stress-lines  are  hi,  ic,  cd  and  dh. 
If  the  stress-diagram  is  accurately  drawn,  a  line  from  d  parallel  to  the  rafter 
will  pass  through  the  point  h.     The  vertical  tie  GG'  (Fig.  20)  has  no  stress 
and  its  only  purpose  is  to  prevent  the  horizontal  tie  from  sagging. 


Fig.  20.     Cambered  Fink  Truss.     Truss-diagram 

1' 


Fig.  20a.     Cambered  Fink  Truss.     Stress-diagram 

Cambered  Fink  Truss.  Example  ii.  (Fig.  21.)  This  is  the  truss  shown 
in  Fig.  20,  with  two  additional  loads.  Steel  trusses  of  this  shape  are  often 
required  to  support  loads  from  below.  In  Fig.  21  there  are  two  loads  of  4  tons 
each,  supported  at  joints  s  and  9,  in  addition  to  the  roof-loads.  The  stress- 
diagram  is  drawn  in  exactly  the  same  way  as  in  Fig.  20a,  except  that  at  joint  s 
the  first-known  force  ro,  parallel  to  RO,  4  tons,  is  laid  ofif,  locating  r.  At  this 
joint,  then,  ro,  ol  and  Ik  are  known  and  kg  and  gr  are  drawn  to  close  the  polygon. 
It  should  be  noticed  that  the  stresses  in  NM,  IH,  ML,  KI  and  LK  are 
not  affected  by  the  ceihng-load.  This  is  evident  by  comparing  Fig.  21a  with 
Fig.  20a.  All  of  the  other  stresses,  however,  are  increased  because  of 
the  increase  in  the  supporting  forces,  the  greatest  increase  being  in  KG  and  HG. 


Detennination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1081 

8 


8 


B 


4^ 


(H 


^ 
''H/^ 


<^!x^V  ^  L    rA/         -38.0 


c' 


>3— ^^9^f — ^^oeJ^I    Span  =So'o"      Ti" 
O  \  R 


A' 


o' 


Pj=  32       • 


Fig.  21.     Cambered  Fink  Truss.     Truss-diagram 


R|=32 


Fig.  21a.     Cambered  Fink  Truss.     Stress-diagram 
5200      ^'V, 


Fig.  22.    Scissors  Truss.    Truss-diagrara  Fig.  22a.    Scissors  Truss.     Stress-^ 

diagram 


1082 


Stresses  in  Roof-Trusses 


Chap.  27 


Simple  Scissors  Truss.  Example  12.  (Fig.  22.)  This  is  the  truss- 
diagram  of  the  truss  shown  in  Fig.  22,  Chapter  XXVI,  which  is  the  simplest  form 
of  the  SCISSORS  TRUSS.  The  truss-dia^ram  is  drawn  by  commencing  with  the 
line  oa  equal  to  the  supporting  force,  9  600  lb,  and  then  in  order  the  forces  ah, 
bb',  b'a',  a'r  and  ro,  forming  the  polygon  of  the  external  forces.  At  joint  i,  oa 
is  known  and  ad  and  do  are  drawn,  closing  the  polygon.  At  joint  2,  da  and  ab 
are  known  and  be  and  ed  are  drawn,  closing  the  polygon.  At  joint  3,  eb  and  bb' 
are  known  and  b'e'  and  e'e  are  drawn.  This  determines  the  stresses  in  one-half 
the  truss.  Those  for  the  other  half  are,  of  course,  of  the  same  magnitude  and 
character,  but  the  stress-diagram  should  be  continued  for  the  second  half  of  the 
truss  as  a  check. 

Scissors  Truss.  Example  13.  Fig.  23  is  the  truss-diagram  of  the  truss 
shown  in  Fig.  23,  Chapter  XXVI,  with  the  loads  figured  about  as  they  would 


Ri =  1*600 


B' 

6400 

.j*°i 

V*' 

~' 

o'^ 

^"i. 

T 

J 

R2=  U600 

-^    '<:^ 


Fig.  23.     Scissors  Truss.    Truss-diagfam 


Fig.  23a.     Scissors  Truss.     Stress- 
diagram 


be  for  a  slate  roof  and  wooden  ceiling  and  for  a  spacing  of  1 2  ft  on  centers.  The 
stress-diagram  is  begun  by  drawing  the  line  oa  equal  to  the  supporting  force 
at  joint  I  C14  600  lb).  The  sides  of  the  stress-polygons  for  the  different  joints 
are  as  follows: 

At  joint  i:  oa,  ae  and  eo; 

At  joint  2:  ea,  ab,  bf  and  fe; 

At  joint  3:  oe,  ef,  Jh  and  ho; 

At  joint  4:  hfyjb,  bk  and  kh\ 

At  joint  5:  TO  {1  100  lb),  oh,  hk,  Id  and  Ir; 

At  joint  6:  Ik,  kb,  be  (5  400  lb),  cm  and  ml', 

At  joint  7 :  mc,  cc'  (5  \oq  lb),  c'm'  and  m'm. 

The  student  should  notice  how  much  the  stresses  in  the  principal  members  of 
this  truss  exceed  the  supporting  forces  or  loads,  and  particularly  the  great  stress 
in  the  middle  rod.  For  these  reasons  this  is  not  an  economical  type  of  trugs  for 
spans  exceeding  36  ft. 


■Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1083 

Scissors  Truss.  Example  14.  Fig.  24  is  the  truss-diagram  of  the  truss 
shown  ill  Fig.  4,  page  1056,  arid  for  which  the  roof  and  ceiling-loads  are  computed 
in  Example  3,  page  1055.  The  truss  shown  in  Fig.  4  is  built  of  planks  spiked 
and  bolted  together,  but  the  stresses  are  found  in  precisely  the  same  way  if  the 
truss  is  made  of  heavy  timbers  and  supports  a  greater  roof-area.  It  should  be 
remembered  that  only  the  shape  of  the  truss  and  the  loads,  including  their  point 
of  application,  affect  the  stress-diagram.  The  stresses  at  joints  i  and  2  are 
readily  found,  commencing  with  oq,  equal  to  R\.  At  each  of  joints  3  and  4, 
however,  there  are  three  unknown  forces.  We  cannot  obtain  the  stresses  at 
joint  4  until  those  acting  at  joint  3  have  been  determined.  The  known  forces 
at  3  are  the  load  RO,  equal  to  430  lb,  and  the  stresses  acting  in  OE  and  EF\  and 
the  unknown  forces,  those  acting  in  FU,  HK  and  KR.  UK  and  KR  are  in  ten- 
sion and  serve  to  hold  joint  3  from  falling  down  and  outwards.  Either  one, 
but  not  both,  may  be  omitted,  and  the  greater  the  stress  is  in  one  the  less  it  is  in 
the  other.     The  only  way  to  complete  the  stress-polygon  for  joint  3  is  to  fix  the 


Ri=3fi00  Ror=3600  +'J^ 

Fig.  24.     Scissors  Truss.    Truss-diagram.     (See,  also,      Fig.    24a.      Scissors    Truss. 
Fig.  4  and  Chapter  XXVIII ,  Fig.  2)  Stress-diagram 

amount  of  6ne  of  the  unknown  stresses  arbitrarily.  The  most  satisfactory 
analysis  seems  to  be  to  make  the  stress  in  HK  equal  to  that  in  KR.  This  is 
done  as  follows:  The  first  known  force  at  joint  3  is  the  load  represented  by  ro, 
the  point  r  being  obtained  by  measuring  upwards  from  0,  430  lb;  next,  the  Hues 
oe  and  ef  are  known.  From  /  a  line  is  drawn  parallel  to  FH  and  from  r,  a  line 
parallel  to  KR.  These  two  lines  must  be  connected  by  a  third  line  parallel  to 
HK.  This  fine  should  be  drawn  so  that  its  length  is  equal  to  ^r,  which  can  be 
done  by  means  of  dividers.  Lettering  the  ends  of  this  line  h  and  k  the  sides 
of  the  completed  stress-polygon  for  joint  3  are  ro,  oe,  ef,  Jh,  hk  and  kr.  Knowing 
the  stress  in  UF,  there  are  but  two  unknown  forces  at  joint  4,  and  these  are  readily 
found.  The  sides  of  the  stress-polygon  for  joint  5  are  Ic,  cc'^  c'V  and  VI.  Cona- 
paring  this  stress-diagram  with  that  of  Fig.  23a,  it  is  seen  that  the  stress  in  the 
middle  rod  is  much  less  in  proportion  to  the  loads  for  the  truss  shown  in  Fig.  24 
than  for  the  one  shown  in  Fig.  23,  this  reduction  being  due  to  the  horizontal  tie 
RK.  For  light  trusses  built  of  planks,  spiked  or  bolted  together,  the.  form  of 
truss  shown  in  Fig.  24  is  preferable  to  that  shown  in  Fig.  23. 

Scissors  Truss.     Example  15.    Fig.  25  is  the  truss-diagram  of  the  scissors 
TRUSS  shown  in  Fig.  27  of  Chapter  XXVI.    The  line  EF  in  Fig.  25  does  not 


1084 


Stresses  in  Roof-Trusses 
7800  7spo 

< -K'g 


Chap.  27 


■w 


;iS= -26500 


c;i=. +26500 


.../], 


l^ 


i^ 


"t 


•?! 


O' 

-s-\c    1 


4-t 


6    ! 


(*i'_i 


aT^    a 


+6500      / 


pig.  25a.     Scissors  Truss.     Stress-diagram 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods    1085 

correspond  with  the  center  line  of  the  strut  in  Fig.  27,  because  the  inner  end  of 
this  strut  is  dropped  slightly  on  account  of  the  detail  of  the  joint;  but  in  truss- 
diagrams  all  lines  must  go  from  joint  to  joint,  otherwise  the  stress-diagram  can 
not  be  drawn.  There  are  no  stresses  in  the  middle  diagonals  under  a  symmetrical 
vertical  load;  hence  they  are  shown  by  dotted  lines  in  Fig.  25.  As  no  complica- 
tions arise  in  drawing  the  stress-diagram  of  this  truss,  a  detailed  description  is 
unnecessary.  The  sides  of  the  stress-polygons  for  the  different  joints  are  as 
follows: 

For  joint  I :  oa,  ad,  do; 

For  joint  2:  ro,  od,  de,  er; 

For  joint  3:  ed,  da,  ah,  bf,fe; 

For  joint  4:  fb,  be,  ch,  hf; 

For  joint  5 :  sr,  re,  ej,  fh,  hs. 
ch  and  hs  coincide,  showing  that  the  compression  in  CH  is  equal  to  the  tension 
in  US.     The  plus  and  minus  signs  in  Fig.  26,  as  in  all  the  other  diagrams, 
denote  compression  and  tension  respectively. 


Truss  without  Tie- 
Stress-diagram 


Truss  Without  Tie-Beam.  Example  16.  Fig.  26  shows  a  truss  which  is 
neither  a  scissors  truss  nor  a  hammer-beam  truss,  yet  this  form  can  be  made 
to  appear  similar  to  the  hammer-beam  truss  by  inserting  a  curved  brace  below 
joint  3,  and  replacing  the  pieces  OH  and  OH'  by  curved  members.  There  is  no 
difficulty  in  drawing  the  stress-diagram  shown  in  Fig.  26a. 

The  Horizontal  Thrust  of  Scissors  Trusses.  In  the  examples  just  given 
it  has  been  assumed  that  the  reactions  are  vertical  and  consequently  that  there 
is  no  HORIZONTAL  THRUST.  Tliis  would  be  true  if  the  materials  composing  the 
frames  were  absolutely  rigid.  This  is  not  the  case,  however,  and  all  trusses 
built  along  the  geometrical  lines  of  their  shape  change  in  shape  after  the  full 
load  is  applied.  In  the  scissors  truss  this  changes  the  length  of  the  span, 
making  it  longer  and  permitting  the  rafters  to  sag.  If  the  trusses  are  con- 
structed with  a  camber  in  the  rafters  and  the  span  made  a  little  short,  the  thrust 
against  the  supports  can  be  practically  eliminated  by  fastening  one  end  of  the 
truss  and  providing  for  a  movement  at  the  other,  so  that  when  the  full  roof  and 
ceiling-loads  have  been  placed  on  the  truss  the  span  will  have  its  correct  length. 
In  order  to  do  this  we  must  know  how  much  the  span  will  change  in  length 
under  the  full  load.    This  can  be  determined  in  the  manner  shown  in  the  follow- 


1086 


Stresses  in  Roof-Trusses 


Chap.  27 


ing  example  and  by  referring  to  Fig.  26b.  Let  Diagram  i  represent  a  simple 
SCISSORS  TRUSS  loaded  as  shown  with  i  ooo  pounds  at  each  top-chord  joint, 
and  let  the  left  end  be  assumed  to  rest  u[3on. rollers.  Then  both  reactions  will 
be  vertical  and  the  stresses  in  each  member  can  be  foimd  from  the  usual  stress- 
diagram  shown  in  Diagram  2.  Let  S  be  the  stress  in  any  member  as  found 
from  Diagram  2;  u,  the  stress  in  any  member  produced  by  one  pound  acting 
horizontally  at  K  and  from  L  as  found  from  Diagram  3;   A,  the  area  of  any 


1000, 


^=1500 


Fig.  26b.,    Simple  Scissors  Truss  and  Stress-diagrams 


member,  in  square  inches;'  /,  the  length  of  any  member,  in  inches;  E,  Young's 
modulus  of  elasticity  of  the  material  Composing  any  member  and  D,  the  total 
CHANGE  IN  LENGTH  OF  SPAN  when  the  truss  is  subjected  to  its  full  load.    Then, 


If  H  is  the  HORIZONTAL  FORCE  applied  at  K,  which  is  necessary  to  make  the 
value  ol  D  =  o 

•  Theory  and  Practice  of  Modern  Framed  Structures,  Johnson,  Bryan  and  Turneaure 
(John  Wiley  &  Sons);   Roofs  and  "Bridges,  Merriraaa  and  Jacoby  (John  Wiley  &  Sons). 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1087 

The  detailed  calculations  for  Fig.  26b  are  given  in  Table  XVII,  assuming  that 
all  members,  excepting  FG,  are  composed  of  6  by  6-in  white  pine  timbers  with 
£  at  I  ooo  coo  lb  per  sq  in,  and  that  FG  is  an  upset  round  steel  rod  having 
an  area  of  0.785  sq  in  with  E  equal  to  30  000  000  *  lb  per  sq  in  for  steel. 


Table  XVII.     Computations  for  D  and  H  for  a  Particular  Scissors  Truss 


(I) 

Member 

(2) 

s, 

Dia- 
gram 2 

(3) 
A 

/4) 
S-^A 

(5) 

M, 

Diagram  3 

(6) 

(7) 
Sul 

AE 

(8) 
uH 
AE 

AE 

BF 

CG 

DH....... 

EM 

HM 

EF 

FG 

GH 

+3160 
+2100 
+2100 
+3160 

—  2360 
-2360 
+  800 

—  1980 
+  800 

36 
36 
36 
36 
36 
36 
36 
0.785 
36 

87.8 
58.3 
58.3 
87.8 
65.5 
65.5 
22.2 

25.22 
22.2 

+0.71 
+0.71 
+0.71 
+0.71 
-1.58 
-1.58 

0 
—  1. 00 

0 

84.8 
84.8 
84.8 
84.8 
126. 5 
126.5 
63.2 
80.0 
63.2 

0.00528 

0.00351 

0.00351 

0.00528 

0.01316 

0.01316 

0.0 

0.00672' 

0.0 

0.00000118 

0.00000118 

0.00000118 

0.00000118 

0 . 00000875 

0.00000875 

0.0 

0.00000340 

0.0 

0.05062 

0.00002562 

D  =  0.05062  in  and  //  =  0.05062  ~  0.00002562  =  1975,  or,  approximately, 
2  000  lb.  This  shows  that  the  span  would  lengthen  about  ^0  in,  if  allowed  free 
movement  at  one  end;  or,  if  fixed,  there  would  be  a  horizontal  force  of 
2  000  lb  tending  to  push  the  supports  out.  In  column  4  it  is  seen  that  the 
stresses  per  square  inch  are  only  about  one- tenth  of  those  permissible.  Assum- 
ing that  the  loads  become  10  000  lb  at  each  apex-joint,  the  horizontal  deflec- 
tion becomes  about  V^  in,  and  the  horizontal  thrust  becomes  20000  lb. 
This  shows  conclusively  that  a  large  excess  of  material  must  be  employed  in  the 
scissors  truss,  particularly  in  the  members  em  and  hm  which  contribute  over 
one-half  the  value  of  D  as  shown  in  column  7,  if  the  horizontal  deflection  is 
to  be  made  so  small  that  its  effect  may  be  neglected.  As  stated  before,  if  the 
truss  is  permitted  to  deflect  horizontally  until  fully*  loaded,  the  walls  or  supports 
will  have  sensibly  no  horizontal  thrust  to  resist. 

The  Hammer-Beam  Truss.  As  usually  constructed  the  hammer-beam 
TRUSS  is  expected  to  exert  more  or  less  horizontal  pressure  at  the  supports; 
and  this  is  provided  for  by  heavy  walls  and  buttresses.  The  diagram  of  such 
a  truss  is  shown  in  Fig.  27,  in  which  the  curved  braces  usually  built  in  the 
middle  part  of  the  truss  are  not  shown,  as  they  are  considered  to  be  purely  orna- 
mental and  for  vertical  loading  have  no  stresses.  The  brace  OM  is  drawn  as 
though  it  were  straight;  but  a  curved  brace  may  be  used  instead,  without  alter- 
ing the  diagram.  The  stress  in  the  curved  piece  is  that  found  from  the  stress- 
diagram,  increased  by  the  bending  stress  due  to  its  curvature.  To  determine 
stresses  in  the  members  of  this  truss  it  is  necessary  to  first  find  the  horizontal 
thrust  of  the  truss  against  the  wall.  To  do  this  all  the  truss-members  from 
joint  o  to  joint  4  are  considered  to  form  a  framed  brace,  or  assemblage  of 
pieces  supporting  the  upper  portion  of  the  truss  at  joint  4,  or  a  single  brace, 
shown  by  the  broken  line  04,  Fig.  27,  is  assumed  to  have  the  same  effect  on  the 
wall  as  all  the  pieces  put  together  in  the  framed  strut;   that  is,  the  truss  is 

*  If  29000000  lb  per  sq  in  is  used  for  the  value  of  E  for  steel  the.  values  of  D  and 
B  will  be  slightly  changed.     See  Table  I,  page  664. 


1088 


Stresses  in  Roof-Trusses 


Chap.  27 


considered  to  have  the  same  horizontal  thrust  as  the  truss  shown  in  Fig.  27a. 
The  load  at  joint  4  is  evidently:  12  000  lb,  plus  the  load  at  joint  5,  plus  hali 
the  load  at  joint  6,  plus  half  the  load  at  joint  2;   making  in  all,  36  000  lb.    To 

find     the    horizon- 
^^^^.  TAL  THRUST  and  the 

stresses  the  proce- 
dure is  as  follows: 
ab  (Fig.  27b)  is  laid 
off  equal  to  the  load 
at  joint  2,  be  equal  to 
the  load  at  joint  4, 
cd  equal  to  the  load 
at  joint  5,  and  dd' 
equal  to  the  load  at 
joint  6.  Then  the 
load  at  joint  4  (Fig. 
27a)  =  V2ab  +  bc-\- 
cd+y2  dd';  and  if  a 
horizontal  Une  is 
drawn  from  x  to  the 
left,  and  from  the 
center  of  ab  a  line 
parallel  to  the  Una 
4-0  (Fig.  27a)  these 
two  lines  will  intersect  at  m,  and  mx  is  the  magnitude  of  the  horizontal 
THRUST  exerted  on  the  wall  at  the  joint  o.  Having  obtained  this  thrust,  it 
is  easy  to  determine  the  stresses  in  the  pieces.     At  joint  o  the  four  forces  in 


R  1=42000 
Fig.  27.    Hammer-beam  Truss.    Truss-diagram 


H  =18000 


R.f42000 


n'  "  18000 

Fig.  27a.    Hammer-beam  Truss.     Truss-diagram  Fig.  27b.     Hammer-beam 

Truss.     Stress-diagram 


equilibrium  are  the  resistance  to  the  thrust,  mx,  the  vertical  supporting  force 
mn  and  the  stresses  ao  and  om,  closing  the  polygon.  At  joint  i,  oa,  af  and  fo  are 
the  stresses  in  OA,  AF  and  FO.  At  joint  3  the  stresses  are  mo,  of,  fg  and  gm; 
at  joint  2  they  d,Tefa,  ab,  bg  and  gf;  at  joint  4  the  stresses  are  mg,  gb,  be  a.nd  ci. 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1089 

closing  the  polygon.  It  will  be  noticed  that  the  polygon  closes  without  allow- 
ing any  line  to  be  drawn  parallel  to  IM;  hence  there  is  no  stress  in  IM,  with 
vertical  loading.  When  there  are  wind-loads  there  is  some  compression  in  /i/, 
and  this  member  is  a  necessary  part  of  the  truss.  At  joint  5  there  are  the  stresses 
ic,  cd,  dk  and  ki,  and  at  joint  6.  kd,  dd',d'k'  and  k'k,  which  complete  the  stresses  for 
one-half  the  truss,  which  are  all  that  are  needed.     Comparing,  now,  the  diagram 


10  tons 


Span  =-48'0" 
Fig.  28.     Suspended  Pratt  Truss.     Truss-diagram 


\ 

"'/ 

0 

+  12.8 

/ 

\ 

A 

\ 

/ 

\/V'=-8       / 

/ 

a'' 

\-  UA  / 

/ 

\          / 

s' 

X 

/    V* 

•1- 

.<? 

h 

/ 

+  12.8 

\ 

/     \ 

r 

( 

1' 

/ 

/      .. 

\ 

aT"T 


I 


R2 


of  stresses,  Fig.  27b,  with  Fig.  26a,  it  is  seen  that,  in  general,  the  magnitudes 
OF  THE  STRESSES  in  the  truss,  Fig.  27,  are  much  less  than  those  of  the  stresses 
in  the  truss.  Fig.  26;  while,  on  the  other  hand,  the  latter  truss  may  be  so  con- 
structed as  not  to  exert  the  outward  thrust  on  the  walls,  exerted  by  the  truss 
shown  in  Fig.  27.  If  curved  members  are  introduced  between  joints  3  and 
12  and  II  and  12,  they  should  be  lightly  secured  at  the  ends  or  the  stresses  deter- 
mined in  the  manner 
outlined  for  the  scissors 

TRUSS. 

Suspended    Pratt 
Truss.     Example    17. 

Let  Fig.  28  be  the 
truss-diagram  of  a  sus- 
pended Pratt  truss, 
uniformly  loaded  at  top 
and  bottom,  with  2  tons 
at  each  joint.  The 
stress-diagram  is  drawn 
in  exactly  the  same  way 
as  for  a  Howe  truss, 
except  that  the  diagonals 
run  in  the  opposite  direc- 
tion. The' stresses  should  be  drawn  for  the  joints  in  the  order  in  which  they 
are  numbered.  In  this  truss  the  verticals  are  in  compression  and  the  diagonals 
in  tension. 

Warren  Truss.  Example  18.  Fig.  29  is  the  truss-diagram  of  a  light  iron 
Warren  truss  of  32-ft  span,  intended  to  support  a  tar-and -gravel  roof,  the 
slope  being  at  right-angles  to  the  line  of  the  trusses.  The  stress-diagram  is 
drawn  as  in  the  previous  examples,  taking  the  joints  in  the  order  in  which  they 
are  numbered. 

Double  Warren  Truss,  or  Lattice  Truss.  Example  19.  The  truss-dia- 
gram shown  by  Fig.  30  is  best  analyzed  by  considering  it  as  built  up  of  tWQ 


<*'jl1, 


Fig.  28a.     Suspended  Pratt  Truss.     Stress-diagram 


1090 


Stresses  in  Roof-Trusses 


Chap.  27 


2G0O     2G00     2G00     2r.0O     2600 


R2=  9100 


Pi  =  9100  Span=32'0' 

Fig.  29.    Warren  Truss.    Truss-diagram 


Fig.  29a.     Warren  Truss.     Stress-iliagram 
2  2 


j<    -4.0      2     -10.0     4     -U.0     6     -16.0     8 
Pj  =  3.0  +  4.0  --  7.0  Span  =  40'0" 


R„  =3.0-^  4.0  =  7.0 


Fig.  30.    Double  Warren  Truss.    Truss-diagram 
2 


Fig.  31.     Warren  Truss.     Truss-diagram 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1091 


Warren  trusses,  laid  one  over  the  other,  the  full  lines  indicating  a  truss  such 

as  is  shown  in  Fig.  31,  and  the  dotted  lines  a  truss  as  shown  in  Fig.  32.     Three 

of  the  seven  loads  would  come  on  the  first  truss  and  four  on  the  second.     The 

stresses  are  found  for  each  truss  separately 

and  then  combined  for  the  top  and   bottom 

chords.     Thus   the  stress  in   the  top   chord 

from  I  to  3,  Fig.  30,  would  be  that  in  AD, 

P'ig.  SI,  or  3  tons;  from  3  to  5  it  would  be 

equal  to  the  stress  in  AD,  Fig.  31,  plus  that 

in  BE,  Fig.  32,  or  9  tons;  from  5  to  7  it 

would  be  equal  to  the  stress  in  BF,  Fig.  31, 

plus  the  stress  in  BE,  Fig.  32,  or  13  tons, 

and  so  on,  the  stress  in  the  bottom  chord 

being  found  in  the  same  way.     The  diagonal 

struts    and  ties    act  independently  of    each 

other,  and  the  stresses  are  those  indicated  on  the  stress-diagrams.     The  plus 

signs  denote  compression  and  the  minus  signs  tension.     In  Fig.  32  the  sides 

of  the  stress-polygon  for  joint  7  are  fe,  eh,  be,  and  ge,  which  closes  without 

any  room  for  a  line  parallel  to  GF,  showing  that  there  is  no  stress  in  the  two 


Fig.  3lA. 


d' 

Warren  Truss, 
diagram 


Stress- 


Fig.  32.     Warren  Truss.    Truss-diagram 

inner  diagonals  except  that  due  to  the  weight  of  the  bottom  chord.  This  truss 
is  usually  constructed  of  steel  angles.  When  wood  is  employed,  three  or  four 
Warren  trusses  are  combined  forming  the  lattice  truss  shown  in  Fig. 
19,  page    1008.      It    is    entirely   unnecessary    to    use    graphical   methods    in 

determining  the  stresses,  as  the  chords 
and  web-members  are  respectively  uni- 
form in  size.  For  the  chords  the  maxi- 
mum bending  moment  divided  by  the 
distance,  center  to  center,  of  the  chords 
gives  the  designing-stress  for  the  chords. 
The  maximum  vertical  shear,  usually  the 
reaction,  divided  by  the  number  of 
simple  Warren  trusses  combined  gives 
the  vertical  component  for  which  the 
web-planks  are  designed.  This,  of  course, 
leads  to  a  waste  of  material  as  far  as 
resisting  stresses  is  concerned,  but  for 
stiffness  and  economy  in  labor,  the  extra 
material  is  well  used.  This  truss  can  be  extended  indefinitely  by  giving  it 
sufficient  height  for  the  span.     (See,  also,  pages  1008  and  1009.) 

Quadrangular  Truss.  Example  20.  Fig.  33  is  the  truss-diagram  of  a  truss 
similar  to  that  shown  in  Fig.  59,  Chapter  XXVI,  the  panel-loads  being  taken  at 
2  tons  each,  and  the  analysis  being  the  same  for  any  other  loads.     The  stress- 


Warren  Truss, 
gram 


1092 


Stresses  in  Roof-Trusses 

2 


Chap.  27 


Ro=9.o 


Fig.  34a.    Quadrangular  Truss.    Stress-diagram 


Detennination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods    1093 

diagram  is  drawn  exactly  as  in  the  previous  examples,  commencing  with  the 
supporting  force  oa  and  considering  the  joints  in  the  order  in  which  they  are 
numbered.  In  this  truss  the  diagonal  web-members  are  all  in  tension  and  the 
verticals  in  compression.  It  will  be  noticed  that  the  inclination  of  the  diagonals 
in  the  two  panels  nearest  the  middle  of  the  truss  is  opposite  to  that  of  the  diagonals 
in  the  outer  panels.  This  is  due  to  the  inclination  of  the  top  chord,  which  causes 
compressive  stresses  in  the  inner  diagonals  when  they  incline  the  other  way. 
The  stress  in  LM,  however,  is  so  small  that  a  single  steel  angle  resists  either  a  com- 


Fig.  35.    Quadrangular  Truss.    Truss-diagram 

pressive  or  tensile  stress.  The  truss  shown  in  Fig.  34  is  very  similar  to  that  shown 
in  Fig.  33,  the  principal  difference  being  that  the  slope  of  the  top  chord  is  less 
in  the  former  than  in  the  latter.  In  Fig.  34,  the  diagonals  in  the  two  middle 
panels  only  incline  from  the  top  of  the  middle  vertical,  and  the  stress  in  these 
diagonals  is  very  small.  With  a  still  less  inclination  to  the  top  chord,  the  stresaL 
in  NR  becomes  zero;  and  with  a  horizontal  top  chord  the  character  of  the  stress 
in  NR  is  reversed.  To  keep  it  in  tension,  its  direction  should  be  changed,  as  in 
the  Pratt  truss.  Fig.  28.  Comparing  the  stresses  in  these  two  trusses,  it  is 
seen  that  while  the  stresses  in  the 
end-panels  are  less  in  Fig.  34a  than  in 
Fig.  33a,  the  stresses  in  the  chords  at 
the  middle  are  considerably  greater. 
As  a  rule,  the  less  the  height  of  a 
truss  in  proportion  to  the  span,  the 
greater  the  stresses  in  the  chords, 
especially  at  the  middle  of  the  truss. 
Quadrangular  Truss.  Example 
21.  Fig.  35  is  a  truss-diagram 
similar  to  the  truss  shown  in  Fig.  66, 
Chapter  XXVI.  The  truss-diagram 
is  drawn  as  in  the  previous  examples, 
except  that  in  this  case,  as  the 
bottom  chord  has  different  inclina- 
tions in  the  different  panels,  the  stress-lines  do  not  lie  over  each  other,  but 
radiate  from  o,  the  lines  in  the  stress-diagram  being  parallel  to  the  corresponding 
lines  in  the  truss-diagram.  In  this  truss  the  character  of  the  stresses  in  the 
diagonal  web-members  is  reversed  in  the  two  panels  nearest  the  middle.  Thus 
the  sides  of  the  stress-polygon  for  joint  4  are  Ik,  kb,  be,  cm  and  ml,  the  stress  ml 
acting  from  the  joint  and  hence  denoting  tension.  At  joint  8  the  sides  of  the 
stress-polygon  are  rp,  pd,  de,  es  and  sr,  the  latter  line  acting  towards  the  joint, 
and  hence  denoting  compression.  Under  irregular  loading,  the  character  of 
the  stress  in  SR  would  probably  be  reversed,  so  that  the  piece  would  be  in  ten- 


Quadrangular   Truss, 
diagram 


1094 


Stresses  in  Roof-Trusses 


Chap.  27 


sion  instead  of  in  compression.  The  stresses  in  members  of  trusses  like  Figs.  33, 
34  and  35  should,  therefore,  always  be  computed  for  snow  on  one-half  of  the 
truss  only  and  also  for  wind-pressure. 

Quadrangular  Truss.  Example  22.  In  Fig.  36  is  shown  the  diagram  of 
ihe  truss  illustrated  in 'Fig.  65,  Chapter  XXVI.  This  truss  is  similar  to  that 
shown  in  Fig.  34,  except  for  the  secondary  bracing  in  the  panels  and  for  the 


Ra'SOOO 


Fig.  36.    Quadrangular  Truss.    Truss-diagram 


curved  bottom  chord.  The  stress-diagram  presents  no  difficulties.  In  drawing 
the  lines  from  0  parallel  to  the  members  of  the  bottom  chord  the  latter  should 
be  considered  as  made  up  of  straight  lines  connecting  the  joints.  Thus  om  is 
drawn  parallel  to  an  imaginary  straight  line  connecting  joints  8  and  4.  As  there 
is  no  load  over  the  center  of  the  two  panels  next  to  the  middle  of  the  truss,  there 
are  no  stresses  in  the  truss-members  between  X  and  /  and  /  and  //.    When 

the  bottom  chord  is  straight, 
as  in  Fig.  34,  there  is  no 
stress  in  YY';  but  when  the 
chord  is  curved,  a  tensional 
stress  develops,  in  YY',  the 
magnitude  of  this  stress  being 
indicated  by  yy'  (Fig.  36a). 
When  the  diagram  is  com- 
pleted for  the  entire  truss,  it 
is  symmetrical  about  a  hori- 
zontal line  drawn  through  0. 
Bowstring  Truss.  Example 
23.  The  span  of  this  truss  is 
90  ft;  the  distance  between 
trusses  from  centers,  20  ft; 
and  the  rise  of  the  arched 
rafter  or  upper  chord,  20  ft. 
The  form  of  truss  represented 
■  in  Fig,  37  is  one  of  the  most 

economical  for  very  great  spans.  In  trusses  similar  to  the  one  explained  in  this 
example,  the  top  chord  is  curved  and  is  the  only  piece  that  is  in  compression. 
All  the  other  members  are  in  tension.  Under  a  steady  load  only,  such  as  the 
weight  of  the  roof  itself,  the  diagonals  drawn  with  solid  lines  and  placed  as 
shown  in  Fig.  37  are  all  that  are  needed;  but  when  there  is  a  severe  wind-pres- 
sure on  one  side  of  the  roof  only,  it  is  necessary  to  have  the  additional  set  of 
diagonals  shown  by  the  dotted  lines.    These   counterbraces,    as  they  are 


Fig.  36a.    Quadrangular  Truss.     Stress-diagram 


Detennination  of  Stresses  in  Roof-Trusses]  by  Graphic  Methods    1095 

called,  forrrring  the  additional  set,  are  not  stressed  when  there  is  a  vertical  load 
only  and  they  are  omitted  in  drawing  the  stress-diagram.  To  draw  the  stress- 
diagram,  the  loads  are  laid  off  on  a  vertical  line,  as  in  all  the  previous  examples, 
the  point  o  being  half-way  between  e  and  e'  (Fig.  37a).  oa  is  the  supporting 
force  at  joint  i.  In  drawing  the  stresses  at  the  different  joints,  those  at  joint  i 
are  first  drawn  and  then  those  at  joints  2,  3,  4,  5,  etc.,  in  the  order  in  which  they 
are  numbered  (Fig.  37).     In  the  stress  diagram,  oa,  equal  to  the  supportirkg 


15000 


Fig.  37a.     Bowstring  Truss.     Stress-diagram 


force  at  joint  i,  is  known  and  from  a  a  line  is  drawn  parallel  to  AG,  and  from 
0  a  line  parallel  to  GO.  These  two  lines  intersect  at  g.  The  lines  repre- 
senting the  stresses  in  the  curved  members  of  the  truss  are  drawn  parallel 
to  straight  lines  connecting  the  two  ends  of  each  curved  piece.  Thus  ag  is 
drawn  parallel  to  1-3  and  og  parallel  to  1-2.  At  joint  2,  og  is  known,  gh  is  drawn 
parallel  to  GH  and  ho  parallel  to  HO.  At  joint  3,  hg  and  ga  have  been  drawn, 
the  load  ab  is  known  and  bi  and  ih  are  drawn.  At  joint  4,  oh  and  hi  have  been 
drawn,  and  ik  and  ko  are  next  drawn  to  close  the  polygon.  The  stress-lines  for 
joints  6  and  8  are  drawn  in  a  similar  way,  and  those  for  5,  7  and  9  similarly  to 
those  at  joint  3.  After  drawing  the  stress-lines  for  joint  9,  joint  10  is  next  con- 
sidered; and  after  the  stress-lines  for  that  joint  are  determined  the  stresses  in 
all  the  members  of  the  truss  are  known.  The  stresses  in  this  particular  example 
are  given  in  pounds  on  the  respective  lines  in  the  stress-diagram.     It  will  be 


1096 


Stresses  in  Roof-Trusses 


Chap.  27 


noticed  that  the  stresses  are  very  great  in  the  top  and  bottom  chords,  but  very 
small  in  the  bracing.  The  latter  stresses  are,  in  fact,  so  small  that  it  is  just  as 
well  to  make  all  the  diagonal  braces  the  same  size  and  of  dimensions  sufficient 
to  resist  the  stress  in  ///,  which  has  the  greatest  stress;  or  IH  and  KL  may  be 
made  the  same  size  and^iV  and  PR  a  smaller  size.  The  verticals  or  radiating 
pieces  may  all  have  a  sectional  area  sufficiently  large  to  safely  resist  the  stress 
in  NP.  The  great  advantage  of  this  truss  lies  in  the  fact  that  all  its  parts  are 
in  tension  excepting  the  upper  chord,  which,  of  course,  is  in  compression.  The 
manner  in  which  stresses  act  may  be  described  in  general  by  saying  that  the 
upper  chord  carries  all  the  load,  like  an  arch,  and  is  prevented  from  spreading 
out  at  the  ends  by  the  lower  tie;  and  that  the  object  of  the  bracing  and  the 
vertical  pieces  is  only  to  keep  the  bottom  chord  in  its  curved  position. 

Trusses  Unsymmetrically  Loaded.     Now  that  the  principles  have  been 
explained  according  to  which  the  stress-diagrams  may  be  drawn  for  several 


Fig.  38.    Unsymmetrical  Truss.    Truss-diagram 


Fig.  38a.     Unsymmetrical 
Truss.    Force-polygon 


forms  of  trusses  symmetrically  loaded,  it  may  be  well  to  consider  the  subject 
in  a  more  general  manner.  It  will  now  be  assumed  that  there  are  no  restrictions 
as  to  SYMMETRY  in  the  form  of  the  truss  and  its  loading;  and,  furthermore,  it 
will  not  be  assumed  that  all  of  the  loads  act  as  vertical  forces  as  in  the  problems 
just  solved.  Fig.  38  shows  an  unsymmetrical  truss  unsymmetrically 
loaded  and  with  loads  or  forces  which  are  not  parallel.  In  the  previous  problems 
the  supporting  forces  or  reactions  have  been  equal  and  each  equal  to  one-half 
the  load.   In  this  problem  such  is  not  the  case.   The  first  step,  then,  is  the  deter- 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1097 


MiNATiON  OF  THE  REACTIONS.  If  the  truss  remains  in  position  it  follows  that 
all  the  forces  acting  upon  the  truss,  such  as  the  loads  and  reactions,  must  be 
in  equilibrium;  also  since  by  definition  a  truss  must  act  as  a  beam,  the  truss 
may  be  replaced  by  a  beam  in  considering  the  outside  forces.  In  Fig.  38, 
prolong  the  lines  representing  the  direction  of  the  forces,  as  shown,  until  they 
cut  the  Une  ^T  and  assume  52'  to  be  a  simple  beam  loaded  with  the  forces  AB, 
BC,  etc.  Beginning  with  AB,  to  some  convenient  scale  lay  off  the  forces  in 
order  as  shown  in  Fig.  38a.  The  broken  line  VU  represents  the  forces  in  magni- 
tude and  direction.  For  equilibrium,  forces  equivalent  to  UV  are  required. 
This  is  evident  when  we  remember  that  the  algebraic  sum  of  the  vertical  and 
horizontal  components  of  all  the  forces  acting  must  respectively  equal  zero. 
Assuming  that  the  supports  at  S  and  2\  Fig.  38  are  similar  in  every  respect  we 
may  assume  that  the  reactions  Ri  and  R2  act  in  the  same  direction  and  that  they 
are  parallel  to  UV.  This  does  not  determine  the  magnitudes  of  Ri  and  R2.  These 
may  be  found  as  follows:  In  Fig.  38A,  assume  any  point  W  and  draw  the  lines  i, 
2,  3,  etc.  In  Fig.  38,  starting  at  any  point  on  Ri  draw  the  line  i  parallel  to  the 
line  I  in  Fig.  38a,  and  extend  it  until  it  cuts  the  direction  or  line  of  action  of  the 
force  yl  5  as  shown;  from  this  point  draw  a  line  parallel  to  2  in  Fig.  38a,  and  extend 
it  until  it  cuts  the  direction  of  BC  as  shown,  and  so  continue  until  line  6  is  drawi^ 

P., 


Fig.  38b.     Unsymmetrical  Truss.    Truss-diagram 

cutting  R2.  Draw  line  7  in  Fig.  38  and  then  in  Fig.  38a  draw  a  line  parallel  to 
this  from  W  until  it  cuts  UV.  This  point  divides  UV  into  two  parts,  the  upper 
being  the  magnitude  of  i^i  and  the  lower  the  magnitude  of  R2.  No  trouble  will 
be  experienced  in  applying  the  above  method  if  the  following  rule  is  obeyed  to 
the  letter.  In  Fig.  38,  the  parallels  to  any  three  lines  in  Fig.  38a  which  form  a 
triangle  must  meet  in  a  point.  For  example,  in  Fig.  38a  lines  i,  2,  and  Fi, 
or  ab  form  a  triangle,  and  in  Fig.  38,  their  parallels  meet  in  the  point  A'.  In 
this  method  it  is  not  necessary  that  the  forces  AB,  BC,  etc.,  be  used  in  order  in 
Fig.  38a,  but  considering  them  in  order,  on  a  simple  beam,  makes  the  graphical 
construction  in  Fig.  38  less  complex  and  avoids  many  chances  of  error.  The 
method  outlined  above  is  general  and  can  be  used  for  forces  acting  in  any  direc- 
tion. If  the  forces  are  parallel  then  the  load-line  ab,  be,  cc,  etc.,  in  Fig.  38a,  and 
the  line  UV  will  coincide;  but  the  method  of  procedure  remains  unchanged. 
Now  that  all  the  forces  acting  upon  the  truss  have  been  determined,  for  con- 
venience, they  will  be  shown  in  character,  in  Fig.  38b,  and  the  stresses  in  the 
members  composing  the  truss  will  be  found.  First  lay  off  the  forces  in  exact 
order  to  see  that  they  form  a  closed  figure,  which  must  be  the  case  if  they  are 
in  equilibrium.    The  lines  with  arrow-heads  in  Fig.  38c  show  this  construction. 


1098 


Stresses  in  Roof -Trusses 


Chap.  27 


which  checks  the  values  of  Ri  and  R2  obtained  above.  This  figure  remains  the 
■siame  regardless  of  the  interior  arrangement  of  the  truss.  The  construction  of 
the  stress-diagram  follows  the  methods  given  in  the  previous  examples  until 
point  3  is  reached.  Here  there  are  three  unknowns,  CM,  ML  and  LK,  and  it 
cannot  be  assumed  that  ML  is  the  same  as  JK,  as  was  done  in  examples  10  and 
II.  Let  the  truss  be  cut  as  shown  in  Fig.  38d,  and  the  actual  stresses  in  the  cut 
pieces  assumed  to  act  against  the  cut  ends,  then  the  frame  shown  in  Fig.  38d 
and  the  forces  Ri,  AB,  BC,  CE,  EN,  NO,  OG  and  GU  will  be  in  equilibrium. 


,1  2"Jiiil  'JiiJ  f/i.ii)  ini 


Fig.  38c.    Unsymmetrical  Truss.     Stress-diagram        Fig, 


38d.     Unsymmetrical  Truss. 
Truss-diagrams 


The  frame  may  be  of  any  form  as  long  as  it  is  rigid  so  the  bracing  may  be  changed 
as  shown  in  Pig.  38d  and  the  stress-diagram  proceeded  with  as  in  Fig.  38c, 
until  the  stresses  in  EN,  NO  and  OG  have  been  found.  This  will  locate  the 
point  0.  Returning  to  Fig.  38b,  it  is  found  that  at  joint  4  all  the  stresses  but 
KL  and  LO  are  known;  hence  these  can  be  found  in  the  usual  manner.  Joint  3 
is  next  considered  and  so  on  until  the  diagram  is  complete.  The  line  qf  in  Fig. 
38c  will  pass  through  /  if  the  work  is  correct.  Although  the  method  for  deter- 
mining the  CHARACTER  OF  THE  STRESSES  has  been  explained,  it  will  be  repeated 
^here  in  a  more  general  manner.  Take,  for  example,  joint  8,  in  Fig.  38b,  which 
is  in  equilibrium  under  the 


111 


action  of  the  stresses  go, 
op,  pq  and  qg,  as  indicated 
in  Fig.  38e.    The  stress - 


-^Cf 


Fig.^38E.  Unsymmetrical  ^^^gram  for  this  joint  is_^Fig.  33^.  Unsymmetrical 
Truss.  Forces  at  Joint  8  shown  m  Fig.  38f,  sepa-  Truss.  Stress-polygon  , 
rated  from  Fig.  38c.  It  is 
assumed  that  the  stress  in  GO  is  tension.  Then  in  Fig.  38f,  starting  at  g  we  lay 
off  go,  op,  pq  and  qg,  placing  the  arrow-heads  as  shown.  Transferring  these 
arrow-heads  to  the  ends  of  the  cut  pieces  in  Fig.  38e  indicates  at  once  the 
KIND  OF  STRESS.     The  following  examples  illustrate  the  above  methods. 

Unsymmetrically-loaded  Truss.  Example  24.  Fig.  39  represents  the  dia- 
gram of  a  truss  similar  to  that  shown  in  Fig.  1,  but  of  a  greater  span  and  having 
a  gallery  supported  from  it  at  one  side  only.  The  approximate  roof  and  ceiling- 
ioads  are  indicated  by  the  figures  near  the  arrows,  and  the  weight  coming  on 
one  truss  from  the  gallery  would  be  about  9  000  lb.  The  first  step  towards 
drawing  the  stress-diagram  is  to  determine  the  reactions  at  the  two  ends  of  the 


Detemiinalion  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1009 

truss,  which  will  give  the  supporting  forces.  This  is  readily  done  in  this  example 
by  the  method  of  moments  explained  on  pages  322  to  324.  Moments  are  first 
taken  about  joint  i.  As  the  loads  at  joints  2  and  3  have  the  same  arm,  they 
are  added  together  before  multiplying  by  the  arm.     The  loads  at  joints  4  and  $ 


Fig.  39.     King-rod  Truss.     Truss-diagram  and  Equilibrium-polygon 
h 


Fig.  39a.     King-rod  Truss.     Stress-diagram 

and  at  joints  6  and  7  are  treated  the  same  way.   The  moments  about  joint  i  will 

then  be: 

[(8  000  f  4  500-1-9  000)  =  21  500]  lb  X  I2l^  ft  =      268  750  ft-lb 
[(80004-4500)  =  12  500]  lb  X  25      f t  =      312  500  ft-lb 

[(8000-1-4500)  =  12  5oo]lbX37y2  ft=      468  750  ft-lb 


The  sum  of  the  moments 


I  050  000  ft-lb 


.'I 


The  sum  of  these  clockwise  moments  about  joint  i  must  be  balanced  by  the 
CONTRA-CLOCKWISE  MOMENT  of  R2,  the  LEVER-ARM  of  which,  with  reference  t6 
joint  I,  is  50  ft.  Knowing  the  arm,  50  ft,  the  force  R2  is  obtained  by  dividing 
the  sum  of  the  moments  of  the  loads  by  the  span.     Dividing  i  050  000  ft-ib  by 


lioo 


Stresses  in  Roof-Trusses 


Chap.  27 


50  ft,  the  resuh  Is  21  000  lb,  which  is  the  reaction  or  supporting  force  at  joint  8; 
and  Ri  must  equal  the  difference  between  the  sum  of  the  loads  and  R2.  The 
sum  of  the  loads  is  46  500  lb  and  subtracting  from  this  21  000  lb,  the  remainder, 
25  500  lb,  is  the  value  of  Ri.  The  stress-diagram  (Fig.  39a)  may  now  be  drawn. 
First  draw  a  vertical  line  oa  equal  to  Ri,  25  500  lb.  From  a  and  0  draw  lines 
parallel  respectively  to  ^£  and  EO,  locating  the  point  e.  For  the  stress-lines 
at  joint  2  measure  up  from  0  a  distance  equal  to  the  load  at  that  joint,  13  500  lb, 
which  gives  the  point  r,  and  from  e  and  r  draw  lines  parallel  to  EF  and  FR, 
which  intersect  at  /.  At  joint  3,  the  sides  of  the  stress-polygon  are  fe,  ea,  ab, 
bg  and  gf.    Draw  the  stress-polygons  for  joints  4,  5,  and  6  in  the  order  in  which 


I 
j 

I 

I 
I 

Fig.  40.     Unsymmetrical  Truss.     Truss-diagram  and  Equilibrium-polygon 


they  are  numbered.  At  joint  6  the  sidrs  of  the  strcss-iwlygon  are  ih,  he,  cd,  dj 
and//.  If  the  diagram  has  been  correctly  drawn,  the  line  ij  will  be  just  equal 
to  the  load  at  joint  7.  The  sides  of  the  stress-polygon  for  joint  7  are  ts  equal  to 
4  500  lb,  si,  ij  andj/,  the  only  line  to  be  drawn  being ^7,  which  must  be  parallel 
to  JT.  Consequently  i  must  be  exactly  opposite  /,  or  the  polygon  will  not  close. 
The  distance  dt  should  be  equal  to  R2. 

Unsymmetrically-loaded  Truss.  Example  25.  Fig.  40  is  the  diagram  of 
a  wooden  roof-truss.  The  actual  loads  were  about  as  given  on  the  diagram. 
There  were  purlins  at  joints  3  and  5  only,  and  the  ceiling  below  was  suspended 
by  rods  from  joints  4  and  7,  joint  4  being  fixed  by  the  framing  of  the  ceiling. 
The  moments  of  the  loads  about  joint  i  are: 


Determination  of  Stresses  in  Roof -Trusses  by  Graphic  Methods     1101 

3  200  lb  X    8V2  ft  =    27  200  ft-lb 
5  5oolbXi5V2ft=    85  250  ft-lb 

4  100  lb  X  19     ft  =    77  900  ft-lb 

5  500  lb  X  24     ft  =  132  000  ft-lb 

Sum  of  moments    =  322  350  ft-lb 

Dividing. the  sum  of  the  moments  by  the  distance  between  the  supporting  forces, 
there  results  9  768  lb  as  the  value  of  R2. 
The  sum  of  the  loads  is  18  300  lb.  Sub- 
tracting 9  768  lb,  8  532  remains  as  the 
value  of  Ri.  To  draw  the  stress-diagram, 
start  with  o"a  equal  to  8  532  lb  equal 
to  Ri  and  draw  ae  and  eo".  The  sides  of 
the  stress-i)olygon  for  joint  2  are  ea,  ab,  bf, 
fe'  and  ce' .  At  joint  3, /6  is  known  and 
be  is  measured  down  and  made  equal  to 
5500  lb.  eg  and  gf  are  then  drawn.  At 
joint  4,  start  by  measuring  upwards  from 
<?,  4  100  lb,  locating  point  0'  and  draw  gh 
and  ho'.  At  joint  5,  hg  and  gc  are  now 
known,  cd  equals  5  500  lb  and  a  line  from  d 
is  drawn  parallel  to  DH.  This  should  pass  through  h,  completing  the  diagram. 
The  stress  in  rod  2-7  is  the  load  at  joint  7. 


40a.       Unsymmetrical 
Stress-diagram 


Truss. 


10000 


6700 


Fig.  41.     Unsymmetrical  Truss.     Truss-diagram  and  Equilibriun^-polygon 

Unsymmetrically-loaded  Truss.  Example  26.  Fig.  41  is  the  truss-diagram 
of  another  truss  in  the  same  building  in  which  the  truss  shown  in  Fig.  40  was 
used.    Taking;  moments  about  joint  i,  there  results,  for  the  sum  of  the  moments, 


1102 


Stresses  in  Roof-Trusses 


Chap.  27 


41a.       Unsymmetrical 
Stress-diagram 


Truss. 


406  050  ft-lb;  and  dividing  this  by  33  ft  gives  1 2  304  lb  as  the  value  of  R2.  The 
sum  of  the  loads  is  28  600  lb,  which  leaves  16  296  lb  for  the  value  of  Ri.  The 
stress-diagram  Fig.  41a,  is  drawn  in  the  same  manner  as  in  Fig.  40.  Starting 
with  o"a  equal  to  Ri,  ab  is  drawn  equal  to  the  load  at  joint  2,  and  the  actual 
stress  in  EF  h  6  000  lb,  or  the  length  of  the  line  ef.  If  the  stress-diagram  is 
correctly  drawn,  a  line  through  d  parallel  to  KD  will  pass  through  the  point  k, 
previously  determined.    The  character  of  the  stresses  is  indicated  by  the 

PLUS  AND  MINUS  SIGNS  in  Fig.  41,  plus 
denoting  compression.  If  the  stress-dia- 
grams in  the  last  three  examples  are 
compared  with  those  for  symmetrically 
loaded  trusses  of  similar  shape  it  is  found 
that  while  the  stress-diagrams.  Figs.  39a, 
40a  and  41a,  are  unsymmetrical,  they 
are  of  the  same  general  character,  and 
the  stresses  are  all  of  the  same  kind  as 
when  the  supporting  forces  are  equal. 
This  condition  holds  true  for  most  trian- 
gular trusses,  but  for  trusses  with  hori- 
zontal or  curved  chords,  unsymmetrical 
loading  usually  causes  a  reversal  of  the  stress  in  kind  in  one  or  more  of  the 
diagonals  or  verticals;  and  if  the  truss  contains  any  four-sided  panels,  an  addi- 
tional diagonal  is  generally  required.  This  is  particularly  true  of  the  Howe 
truss;  and  as  this  truss  is  very  extensively  used  by  architects  and  builders,  it 
will  now  be  considered  at  some  length  with  special  reference  to  the  effect  of 
unsymmetrical  lo.ading. 

Howe  Trusses,  Unsymmetrically  Loaded.  When  a  Howe  truss  is  loaded 
symmetrically  on  each  side  of  the  middle,  all  of  the  braces  incline  downward 
from  the  center,  as  in  Figs.  14  to  17,  Chapter  XXVI;  and  if  there  is  an  odd 
NUMBER  OF  PANELS,  the  middle  panel  needs  no  brace.  When  a  load  of  much 
ma'^nitude  is  placed  on  one  side  of  a  truss  having  an  odd  number  of  panels 
without  a  corresponding  load  on  the  other  side,  a  brace  is  always  required  in 
the  middle  panel  and  the  brace 
should  incline  downward  from  the 
side  which  is  most  heavily  loaded. 

Howe  Truss  with  Even  Num- 
ber of  Panels.  When  the  truss 
has  an  even  number  of  panels,  . 
an  unsymmetrical  load  causes  a 
greater  stress  in  the  braces  on 
one  side  of  the  truss  than  on  the 
other;  and  if  there  is  a  sufficient 
difference  in  the  loads  on  the  two  sides  of  the  truss,  it  causes  compressive  stresses 
in  one  or  more  of  the  rods  and  tensile  stresses  in  one  or  more  of  the  braces.  As 
this  truss  is  especially  designed  with  the  idea  of  having  the  braces  in  com- 
pression and  the  verticals  I^f  tension,  whatever  the  loading  causes  tension 
in  a  brace,  or  compression  in  a  rod,  the  direction  of  the  brace  should  be  reversed, 
causing  it  to  be  in  compression  again.  Consider,  for  example,  the  truss  shown 
in  Fig.  42,  divided  into  6  panels  of  equal  width  and  loaded  with  4  tons  at  each 
of  the  upper  joints  and  9  tons  at  the  second  lower  joint  from  the  left.  With- 
out the  bottom  load  of  9  tons,  the  brace  in  the  third  panel  should  incline  down- 
ward from  the  middle  joint,  as  shown  by  dotted  line  at  B;  but  when  the  load  of 
9  tons  is  added,  it  causes  a  tensile  stress  in  B  and  a  compressive  stress  in  R.    To 


q?    ; 

y    : 

y^R^ 

\ 

\ 

\ 

Rl=^l6 

A 

9 

^2=13 

Fig.  42.    Howe  Truss.    Truss-diagram 


Determination  of  Stresses  in  Roof-Trusses  by  Graphic  Methods     1103 


avoid  this,  the  direction  of  the  brace  is  reversed,  as  shown  by  the  full  line. 
It  is  then  in  compression  and  the  vertical  R  has  no  stress  except  that  caused  by 
the  direct  load  of  9  tons.  There  are  the  same  results  when  the  load  of  9  tons 
is  applied  at  the  joint  directly  above,  instead  of  at  the  lower  joint,  although  in 
this  case  there  is  no  stress  at  all  in  R  except  that  due  to  the  weight  of  the  tie-beam. 
When  the  load  of  9  tons  is  reduced  to  6  tons,  no  brace  is  required  in  the  third 
panel;  and  when  the  bottom  load 
is  less  than  6  tons,  a  brace  in  the 
normal  direction  is  required,  as 
shown  in  Fig.  43.  (See  page  1006.) 
Howe  Truss  with  Uneven 
Number  of  Panels.  In  the  five- 
panel  truss,  shown  in  Fig.  44,  a 
load  of  7.5  tons  at  A  requires 
the  arrangement  of  braces  shown 
by  the  full  lines,  and  when  the  load  at  A  is  increased  to  more  than  15  tons, 
the  brace  R  needs  to  be  reversed,  as  shown  by  the  dotted  Hne.  The  stress- 
diagram  always  shows  in  which  direction  any  brace  should  be  placed  to  be  in 
compression;  but  this  may  be  determined  also  by  the  following  rule.  When  the 
sum  of  the  loads  to  the  left  of  any  section,  taken  between  Ri  and  the  middle,  is 
greater  than  the  reaction  Ri,  the  direction  of  the  brace  cut  by  that  section  must 
be  reversed  from  its  normal  direction.  When  the  sum  of  the  loads  is  less  than 
Ri  the  brace  should  be  in  its  normal  position.  When  the  sum  of  the  loads,  to 
the  left  of  the  section,  is  just  equal  to  Ru  no  brace  is  required.     For  example, 

consider  a  section  at  x,  Fig.  44.     Here 
3  3  3 

^  4  y    i 


Fig.  43 


R2  =  ll-6| 

Truss-diagram 


Fig.  44.     Howe  Truss.    Truss-diagram 


the  sum  of  the  loads  to  the  left  is  10.5 
tons,  which  sum  is  less  than  Ru 
hence  the  brace  should  be  in  its 
normal  direction.  If  the  section  is 
at  y,  the  sum  of  the  loads  to  the 
left  is  13.5  tons,  which  sum  is  greater 
than  Ri;  hence  a  brace  is  required, 
slanting  downward  from  the  more 
heavily  loaded  side.     When  the  sec- 


tion is  at  X,  Fig.  42,  the  load  to  the  left  is  4  tons,  an  amount  less  than  R^; 
hence  the  brace  in  that  panel  should  be  in  its  normal  position.  When  the  sec- 
tion is  at  y,  the  sum  of  the  loads  is  greater  than  Ri;  hence  the  brace  in  that 
panel  must  be  reversed.  When  the  section  is  at  y,  Fig.  43,  the  sum  of  the 
loads  to  the  left  is  less  than  Ri;  hence  the  brace  should  be  in  its  normal  posi- 
tion. By  this  rule  the  proper  direction  of  the  brace  in  any  panel  is  indicated, 
regardless  of  the  complication  of  the  loading  and  of  the  width  of  the  panels;  but 
in  applying  the  rule,  it  is  first  necessary  to  determine  the  supporting  forces, 
which  can  be  found  either  by  the  method  of  moments,  as  explained  in 
Example  24,  or  by  the  graphical  method. 

Unsymmetrical  Howe  Truss.  Example  27.  As  an  example  of  an  unsym- 
metrical  Howe  truss  unsymmetrically  loaded,  the  truss  represented  in  Fig.  45 
is  considered.  This  truss  is  supposed  to  support  a  flat  roof  and  a  wooden  tower 
located  as  shown.  The  position  of  the  tower  necessitates  a  division  of  the  panels 
as  indicated,  so  that  the  truss  is  quite  unsymmetrical.  It  is  assumed  that  the 
weight  of  the  roof,  snow,  and  tower  constitute  the  loads  in  pounds  at  the  upper 
joints,  indicated  by  the  figures.  The  graphical  determination  of  the  reactions 
and  stresses  is  clearly  shown  in  Figs.  45  and  45a.  The  only  panels  of  this  truss 
in  which  there  is  any  question  as  to  the  direction  of  the  braces  are  the  third  and 


1104 


Stresses  in  Roof-Trusses 


Chap.  27 


fourth.  Taking  a  section  at  x,  the  sum  of  the  loads  to  the  left  is  greater  than 
Ru  hence  the  brace  should  be  placed  as  drawn.  A  section  taken  through  C 
makes  the  sum  of  the  loads  to  the  left  less  than  Ri;  and  hence  the  brace  should 
be  in  its  normal  position.  The  stress-diagram  of  this  truss  is  readily  drawn, 
starting  with  wa  equal  to  Ri,  and  going  from  joint  to  joint  as  in  previous  exam- 
ples.   The  completed  stress-diagram  is  shown  in  Fig.  45a. 


Tower  _ 


23  ;oo.«=Ri 


Fig.  45.    Howe  Truss.    Truss-diagram 


Fig.  45a.    Howe  Truss.     Stress-diagram 


Counterbraces.  These  are  extra  braces  that  are  put  in  a  truss  when 
stresses  are  reversed  in  character  by  a  load  which  may  be  applied  for  a  time 
and  then  removed.  For  illustration,  consider  the  truss  represented  in  Figs.  42 
and  43.  Here  it  has  already  been  shown  that  when  the  load  at  A  is  less  than  6, 
the  brace  in  the  third  panel  should  be  in  the  position  shown  in  Fig.  43;  while, 
when  the  load  is  greater  than  6,  the  brace  should  be  in  the  position  shown  by 
the  full  line,  Fig.  42.  Now,  if  the  load  at  A  represents  the  weight  of  a  crowded 
gallery  or  a  hoist  raising  a  heavy  load,  or  in  fact  if  it  represents  any  live  load, 
it  is  evident  that  when  this  live  load  is  absent  the  brace  in  the  third  panel  should 
be  in  its  normal  position;  and  that  when  this  maximum  load  is  present  a  brace 
is  needed  in  the  opposite  direction.  As  it  is  not  practicable  to  move  the  brace 
to  suit  the  changing  conditions  of  the  loading,  it  is  necessary  to  put  in  two 
braces,  only  one  of  which,  however,  is  in  action  at  a  time.  The  stresses 
in  a  Howe  truss,  therefore,  which  is  subject  to  a  variable  and  unsymmetrical 
loading,  should  be  computed  for  at  least  two  conditions  of  loading:  first, 
for  the  condition  resulting  from  the  application  of  thjb  maximum  load;  and 


Determiriation  of  Stresses  in  Roof-Trusses  by  Graphic  Methods    1105 

secondly,  for  the  condition  resulting  from  the  removal  of  the  variable  load. 
The  truss  should  be  designed  to  resist  both  conditions.  Snow  is  a  variable 
LOAD,  to  which  such  trusses  are  often  subjected;  but  as  it  is  nearly  uniformly 
distributed  over  the  roof,  it  does  not  change  the  character  of  the  stresses 
in  any  of  the  members.  If  a  truss,  therefore,  is  designed  for  a  maximum  snow- 
load,  it  is  more  than  strong  enough  when  there  is  no  snow.  Moreover,  the 
transverse  strength  of  the  chords  is  usually  sufficient  to  resist  any  slight  inequality 
in  the  loading.  The  principal  variable  vertical  loads,  therefore,  to  which 
a  roof-truss  may  be  subjected  and  which  require  counterbraces,  are  those  due 
to  the  weight  of  people,  merchandise,  etc.,  these  loads  being  either  suspended 
from  the  truss  by  rods  or  brought  upon  the  truss  by  a  floor  supported  by  the 
bottom  chord.  The  truss  shown  in  Fig.  45,  also,  is  an  instance  of  such  loading. 
The  weights  given  by  the  figures  indicate  merely  the  combined  dead  loads  and 
snow- loads.  During  a  high  wind  the  weight  on  the  leeward  side  of  the  tower 
is  much  increased  and  on  the  windward  side  decreased,  so  that  when  the  wind 
blows  from  the  right,  the  load  at  4  is  greater  and  at  8  less  than  indicated;  while 
when  the  wind  blows  from  the  left  the  load  is  increased  at  8  and  decreased  at  4. 
This  requires  counterbraces  in  both  the  third  and  fourth  panels.  As  counter- 
braces  do  no  harm,  even  if  never  brought  into  action,  it  is  always  well  to  use 
them  in  the  middle  panels  wherever  the  loads  are  at  all  variable. 

Cantilever  Trusses.  These  trusses  may  be  considered  as  unsymmetrically 
loaded  trusses,  for  although  the  loads  may  be  symmetrical  in  relation  to  the 
truss,  they  are  usually  unsymmetrical  in  relation  to  the  supports.  The  method 
of  computing  the  supporting  forces  and  drawing  the  stress-diagrams  is  shown 
by  the  following  examples: 


s 6-^--^ — 6- — ^ — 6^—4^ — 6-- 

^  d 

Rl=  6125  R2=875 

Fig.  40.     Cantilever  Truss.    Truss-diagram 


Cantilever  Truss.  Example  28.  Fig.  46  is  the  diagram  of  a  cantilever 
truss  such  as  might  be  used  to  support  the  roof  over  a  grand  stand  or  railway- 
station  platform  and  may  be  constructed  either  of  wood  or  steel,  steel  being 
preferable.  The  first  "step  towards  determining  the  stresses  is  to  find  the  sup- 
porting forces.  For  this  purpose  the  panel-loads  have  been  made  i  000  lb  each, 
all  panels  being  of  equal  width.  These  assumed  loads  simplify  the  problem  and 
serve  as  well  as  the  actual  loads  to  explain  the  method  of  procedure.  In  canti- 
lever trusses  the  loads  at  the  ends  of  the  trusses,  as  well  as  the  intermediate 
loads,  should  be  taken  into  account.  These  end-loads  are  each  equal  to  one-half 
of  the  panel-loads.  To  find  the  supporting  forces  moments  are  taken  about 
joint  13.  The  sum  of  the  moments  of  the  external  vertical  forces  is  147  000  ft-lb. 
These  moments  must  be  resisted  by  the  moment  of  the  force  Ri,  which  acts  in 
a  contrary  direction  with  reference  to  the  same  point  and  with  a  lever-arm  of 
24  ft.    Dividing  147  cx)o  ft-lb  by  24  ft,  there  results  6  125  lb  as  the  value  of  Rii 


1106 


Stresses  in  Roof-Trusses 


Chap.  27 


and  as  the  total  load  is  7  cxx)  lb,  Ri  must  be  875  lb.  The  stress-diagram  may  be 
commenced  either  with  the  forces  at  joint  i  or  with  those  at  joint  13;  but  as 
the  external  loads  were  laid  off  from  left  to  right  in  the  preceding  examples,  the 
same  order  is  used  here.  Commencing  then 
with  joint  i,  lay  off  on  a  vertical  line  the  load 
oa  equal  to  500  lb,  which  acts  down,  and 
draw  ai  and  io  parallel  respectively  to  AL 
and  10.  The  forces  act  from  o  to  a,  from  a 
to  i  (from  the  joint)  and  from  itoo  (towards 
the  joint),  showing  that  ^1/  is  in  tension  and 
10  in  compression,  a  reversal  of  the 
CHARACTER  OF  THE  STRESSES  developed  in 
the  corresponding  members  of  a  truss  sup- 
ported at  both  ends.  Next,  at  joint  2,  the 
stress  ia  is  now  known,  and  ab  equal  to  i  000 
lb  is  laid  off;  then  bj  and  ji  are  drawn,  BJ 
being  in  tension  and  J I  in  compression. 
The  forces  at  joint  3  are  next  drawn  and 
then  those  for  the  remaining  joints,  in  the 
order  in  which  they  are  numbered.  At  joint 
6,  the  first  force  known  is  the  supporting  force 
Ri,  represented  by  o'o  laid  off  equal  to  6  125 
lb  and  acting  upward.  The  sides  of  the 
polygon  of  forces  for  joint  6  are  o'o,  om,  mn 
and  no'.  The  stress  in  MN  is  equal  to  the 
supporting  force  o'o,  which  is  evident  from 
the  truss-diagram.  In  practice,  Ri  would 
probably  b'e  a  column  continued  to  the 
apex  of  the  truss.  At  joint  12  the  stresses 
aheady  determined  are  vu,  uf,  and  fg  equal 
gv  must  close  the  polygon.    It  will  be  noticed  that  gv  acts  toward  joint 

If  a  line  drawn  from  g, 
if  it  does 


Fig.  46a.    Cantilever  Truss, 
diagram 


Stress- 


to  I  000  lb 

12;  hence  the  rafter  in  the  end-panel  is  in  compression. 

parallel  to  the  rafter,  passes  through  v,  the  stress-diagram  is  correct 

not  pass  through  v,  then  either  the  stress-diagram  has  not  been  drawn  with 


Rl  —  6,400 
Fig.  47.     Cantilever  Truss.    Truss-diagram 


R2  =  1(500 


sufficient  accuracy  or  an  error  has  been  made  in  computing  the  supporting  forces. 
In  drawing  the  stress-diagram  for  cantilever  trusses,  it  is  important  to  keep 
in  mind  the  direction  in  which  the  forces  act,  in  order  to  determine  which 
members  are  in  compression  and  which  in  tension. 


Determination  ot  Stresses  in  Roof-Trusses  by  Graphic  Methods     1107 


Cantilever  Truss.  Example  29.  Fig.  47  is  the  diagram  of  a  truss  similar 
in  outline  to  that  shown  in  Fig.  46,  but  with  the  diagonal  braces  inclined 
IN  THE  OPPOSITE  DIRECTION,  SO  as  to  cause  them  to  be  in  compression  and  the 
verticals  in  tension.  The  supporting  forces  are  found  by  the  same  methods 
used  in  Example  28,  and  the 
stress-diagram,  also,  is  drawn  by 
the  methods  used  for  Fig.  46a. 
In  this  tj^uss,  however,  the  stress 
in  the  vertical  post  MN  is  con- 
siderably less  than  the  reaction 
Ri  because  a  large  portion  of 
the  loads  is  transmitted  to  joint 
6  bj^  the  struts  LM  and  NR, 
In  this  truss  three  sections  of 
the  rafter  on  the  right  side  are 
in  compression  and  three  sec- 
tions of  the  bottom  chord  are 
in  tension.  This  is  because  in 
this  truss  the  projection  of  the 
overhang  in  proportion  to  the 
anchor-span  is  less  than  it  is  in 
Fig.  46.  When  the  stress-lines 
pass  to  the  left  of  the  load-line 
(Fig.  47a),  the  stresses  are 
REVERSED  IN  KIND.  This  truss 
is  better  adapted  to  wooden 
construction  with  vertical  rods 
than  is  the  truss  shown  in 
Fig.  46. 

Anchored  Cantilever  Truss.  * 
Example  30.  In  this  example. 
Fig.  48,  is  shown  a  truss  with 
an  anchorage  at  the  outer  end 
to  hold  it  down,  so  that  Ri  acts 
downward.  To  determine  the 
magnitude  and  character  of  the  supporting 
joint  6  as  follows: 

Sum  of  moments  of  loads  to  the  right  of  joint  7,  the  figures  on  the  force-arrows 
of  the  truss-diagram  indicating  thousands  of  pounds: 

(5  X  8).-t-  (s  X  16)  -I-  (s  X  24)  -F  (12.5  X  32)  =  640000  ft-lb 

Sum  of  moments  of  loads  to  the  left  of  joint  7 : 

(2.5  X  24)  H-  (5  X  16)  -h  (5  X  8)  =  180000  ft-lb 

As  these  moments  act  in  opposite  direction  with  reference  to  the  center  of 
moments,  joint  6,  the  smaller  sum,  is  subtracted  from  the  larger,  leaving  an 
unbalanced  moment  of  640000  ft-lb  -  180000  ft-lb  =  460000  ft-lb,  tending 
to  turn  the  truss  down  on  the  right  of  R2.  at  joint  6  and  to  lift  it  up  on  the  left. 
This  moment  must  be  resisted  by  the  moment  of  the  reaction  Ru  which  has  an 
arm  of  24  ft.  Dividing  460  000  ft-lb  by  24  ft,  19  250  lb  results  as  the  reaction 
Ri.  That  is,  it  requires  a  downward  force  of  this  magnitude  to  maintain  the 
truss  in  equilibrium.  As  the  support  at  6  must  resist  this  downward  pull  a^ 
well  as  the  loads,  R2  will  equal  the  sum  of  the  loads  plus  the  pull  i?i,  or  45  000  lb 


Fig.  47a. 


Cantilever  Truss. 


forces 


Stress-diagram 
moments  are  taken  about 


1108 


Stresses  in  Roof-Trusses 


Chap.  27 


+  19  250  lb  =  64  250  lb.     Having  obtained  the  value  of  the  supporting  forces 
the  stress-diagram  is  drawn  by  laying  off  on  a  vertical  line  oa  downward,  equal 


k ^8-->|<--8'-^--8'- 


Rl- -19,250 


- -8- -  "4^  -  8- -  >|<- - -8  — >[<— -8- -  >| 


R2  =  64,259 
Fig.  48.     Cantilever  Truss.     Truss-diagram 


to  19  250  lb  equal  to  Ry.     The  next  force  is  the  load  of  2  500  lb,  which  also  acts 
down,  and  which  locates  the  point  b.     From  b  a  line  parallel  to  BI  is  drawn  and 

from  0  a  line  parallel  to  70, 
locating  the  point  i.  bi  acts 
from  joint  i  and  to  towards 
it,  showing  that  BI  is  in 
tension  and  10  in  compression. 
The  remainder  of  the  stress- 
diagram  is  drawn  by  the  same 
methods  employed  for  the 
diagrams  of  Figs.  46a  and 
47a.  At  joint  6  the  force- 
polygon  is  begun  with  the 
force  R2  or  o'o,  which  acts 
upward,  and  the  upper  end 
of  which  must  be  at  o.  Con- 
sequently 0'  is  located  by 
measuring  downward  from  0, 
64  250  lb.  The  sides  of  the 
stress-polygon  for  this  joint 
are  o'o,  o?n,  mn  and  no'. 
After  gh,  the  load  at  joint  13 
is  laid  off,  the  remaining  dis- 
tance ho'  should  be  just  equal 
to  the  load  at  joint  14,  or 
12500  lb.  If  Ri  and  Rz  have 
been  correctly  computed  and  the  stress-diagram  accurately  drawn,  the  points 
^,  u  and  TV  will  fall  in  the  line  no'.  l^^i 


Fig.  48a.     Cantilever  Truss.     Stress-diagram 


Determination  of  Wind-Load  Stresses  1109 

6.   Determination  of^ind-Load  Stresses 

Wind-Loads.  Thus  far  the  stresses  due  to  vertical  loads  only  have  been 
considered,  the  pressure  of  the  wind  being  combined  with  the  dead  load  and 
considered  as  acting  vertically.  For  triangular  and  Fink  trusses  this 
method  is  sufficiently  accurate,  as  the  wind-pressure  never  causes  a  maximum 
stress  in  excess  of  that  obtained  by  the  method  explained  in  connection  with  the 
foregoing  examples.  For  trusses  with  curved  chords  and  in  fact  for  almost 
all  forms  of  steel  trusses  except  those  of  the  Fink  and  fan  types,  it  is  not 
safe  to  consider  wind-pressure  as  acting  vertically,  because  the  wind  acts  gen- 
erally in  a  direction  at  right-angles  to  the  roof-surface,  and  upon  but  one  side  of 
the  roof  at  a  given  time,  thus  loading  the  truss  unsymmetrically  and  often  caus^ 
ing  stresses  of  an  opposite  kind  from  those  produced  by  a  vertical  loading. 
Braces  which  are  inactive  under  a  vertical  load  may  therefore  be  necessary  to 
resist  the  force  of  the  wind,  or  the  total  stress  due  to  wind  and  vertical  load 
combined  may  be  greater  than  it  would  be  if  the  wind-pressure  were  considered 
as  a  vertical  load.  To  design  a  roof-truss  correctly,  therefore,  it  is  necessary 
to  determine  the  stresses  due  to  vertical  loads  and  wind-loads  separately 
and  then  combine  them  so  as  to  get  the  greatest  stress  that  may  be  produced 
under  any  probable  conditions.     (See  statement  on  page  1049.) 

Curved  Chords.  In  the  calculation  of  trusses  with  curved  chords  it  is 
the  usual  practice  to  find  the  stresses  for  the  following  different  loadings  and 
then  combine  them  to  obtain  the  maximum  stress:  Stresses  due  to  the  wind  on 
the  side  of  the  truss  nearer  the  expansion-end;  stresses  due  to  the  wind  on  the 
side  of  the  truss  nearer  the  fixed  end;  stresses  due  to  the  permanent  dead  loads; 
stresses  due  to  snow  covering  the  entire  roof  or  only  one-half  of  the  roof;  and,  in 
special  cases,  stresses  due  to  snow  covering  only  a  small  area  of  the  roof  on  one 
side. 

Wind  and  Snow.  It  is  generally  assumed  that  the  maximum  wind-pressure 
and  the  snow-load  can  not  act  on  the  same  half  of  the  truss  at  the  same  time. 
For  trusses  with  straight  rafters  it  will  generally  be  sufficient  to  find  the  stresses 
due  to  the  permanent  dead  load,  and  to  the  wind  from  both  directions,  disregard- 
ing the  snow-load  when  the  pitch  of  the  roof  is  45°  or  greater.  For  the  Northern 
states,  when  the  pitch  is  less  than  30°,  it  is  well  to  consider  that  a  heavy  sleet 
may  be  on  both  sides  of  the  roof  at  the  time  of  a  heavy  wind  and  to  add  about 
10  lb  per  sq  ft  of  roof-surface  to  the  dead  load  to  allow  for  it.  In  localities  where 
heavy  snowfalls  may  be  expected,  the  stresses  due  to  the  full  snow-load  should 
also  be  found,  as  these  combined  with  the  permanent  dead  load  may  exceed 
those  due  to  dead  load,  sleet  and  wind-pressure. 

Wind  Stress-Diagrams.  These  are  affected  by  the  manner  in  which  the  truss 
is  supported.  If  both  ends  of  the  truss  are  fixed,  the  wind-reactions  are  paral- 
lel to  the  resultant  wind-load;  if  one  end  is  free  to  move  horizontally,  that  is, 
on  rollers  or  supported  on  a  rocker,  the  reaction  at  the  roller-end  is  vertical 
and  that  at  the  fixed  end  inclined.  ''If  one  end  be  fixed  and  the  other  merely 
supported  upon  a  smooth  iron  plate,  the  reaction  at  the  free  end  may  have  a 
horizontal  component  equal  to  the  vertical  component  multiplied  by  the  coeffi- 
cient OF  friction,  which  is  about  one-third." 

Fixed  and  Free  Ends  of  Trusses.  Wooden  trusses  may  be  considered  as 
fixed  at  the  ends.  Steel  trusses,  when  supported  on  masonry  walls,  should 
have  one  end  fixed  and  the  other  free  to  move;  and  when  the  span  exceeds 
70  ft  the  free  end  should  be  supported  on  rollers  to  permit  of  expansion  or 
contraction.  When  steel  trusses  are  supported  by  steel  columns,  as  in  steel  mill- 
buildings,  the  trusses  are  rigidly  attached  to  the  columns  and  no  provision 


1110 


Stresses  in  Roof-Trusses 


Chap.  27 


is  made  for  expansion.     In  such  buildings  the  wind-pressure  causes  a  bending 
STRESS  in  the  columns,  which  must  be  provided  for. 

Truss  with  Fixed  Ends.  Example  31.  Wind -pressure  is  usually  assumed 
to  be  applied  uniformly  over  one  side  of  the  roof  and  to  act  at  right-angles  to 
the  surface  of  the  roof.  The  joint-loads  or  panel-loads,  therefore,  are  proportional 
to  the  roof-areas  supported.  When  the  joints  divide  the  ra  fter  into  panels  of  equal 
length,  the  joint-loads  are  uniform,  except  for  the  joints  at  the  edges  of  the  roof. 
The  actual  wind-pressure  is  obtained  by  multiplying  the  roof  surface  by  the 
values  given  in  Table  IX,  page  1053.  For  this  example  the  triangular  truss  shown 
in  outline  by  Fig.  49  is  considered  and  it  is  assumed  that  the  span  and  spacing 
of  the  truss  are  such  as  will  give  a  load  of  i  ocx)  lb  at  joints  2  and  4.  The  loads 
at  joints  i  and  5  are  only  one-half  of  those  at  2  or  4.  To  find  the  supporting 
forces  or  reactions,  draw  a  line  representing  the  resultant  of  the  loads,  cutting 
the  bottom  chord  at  A''.  As  the  loads  aVe  symmetrical  the  resultant  acts  at  the 
middle  of  the  rafter  and  at  right-angles  to  it.  The  reactions  Ri  and  Rt  are 
inversely  proportional  to  the  two  segments  into  which  a  horizontal  line  joining 
the  points  of  support  is  divided  by  the  resultant,  or  iii  this  case  to  X-7  and  i-X, 


3000 
\R  1000 


Fig.  49.    Triangular  Truss.    Truss-diagram 


Fig.  49a.    Triangular  Truss. 
Stress-diagram 


the  greater  reaction  being  at  joint  i.  The  sum  of  the  reactions  are  equal  to  the 
sum  of  the  loads.  To  find  the  reactions  graphically,  draw  a  line  from  joint  i, 
at  any  angle,  say  from  30°  to  45°,  and  measure  off  a  distance  equal  to  the  total 
load.  In  Fig.  49  the  line  1-8  represents  3  000  lb.  Join  7  and  8,  and  from  X 
draw  a  line  parallel  to  7-8,  intersecting  1-8  at  X'.  Then  S-X'  is  the  reaction  at 
joint  I  and  X'-i  the  reaction  at  joint  7.  To  draw  the  stress-diagram,  Fig.  49a, 
first  draw  the  load-line  ae  equal  to  the  sum  of  the  loads,  in  this  case  3  000  lb,  and 
perpendicular  to  the  rafter  1-5,  and  divide  it  so  that  ao  is  equal  to  A''-8.  Then, 
at  joint  I,  oa  is  the  supporting  force,  ab  is  500  lb  and  hf  and  fo  are  drawn  parallel 
respectively  to  BF  and  FO,  intersecting  at  /.  The  external  forces  and  stresses 
act  in  the  direction  oa,  ab,  bf  and  fo,  showing  that  BF  is  in  compression  and  FO 
in  tension.  At  joint  2  the  stress-lines  lire  fh,  be  equal  to  i  000  lb,  eg  and  gf.  The 
stress-lines  at  joint  3  are  of,  fg,  f^h  and  ho;  at  joint  4,  hg,  gc,  ed,  di  and  ih;  and  at 
joint  5,  id,  de,  ck  and  ki.  If  the  load-line  has  been  correctly  divided  at  0,  and 
the  stress-lines  have  been  drawn  exactly  parallel  to  the  lines  of  the  truss,  the  point 
k  will  fall  vertically  above  the  point  i.  At  joint  6  the  stress-lines  are  oh,  hi,  ik  and 
ko.  As  the  figure  must  close  by  a  horizontal  line  through  o,  it  is  evident  that  the 


Determination  of  Wind-Load  Stresses 


nil 


line  KIC  of  the  truss-diagram  cannot  be  represented,  and  therefore  there  can  be 
no  stress  in  this  member  when  the  wind  is  from  the  left.  At  joint  7  the  reaction 
eo  is  known,  acting  up,  and  ok  and  ke  must  close  the  figure,  showing  that  the  line 
he  represents  the  stress  in  the  entire  length  of  the  right  rafter,  and  that  there  is 
no  stress  in  the  bracing  on  that  side  of  the  truss  when  the  wind  is  from  the  left. 
When,  however,  either  the  lower  chord  or  the  rafter  is  not  straight,  some  of  the 
braces  on  that  side  come  into  action.  By  noting  the  character  of  the  stresses  in 
Fig.  49a,  it  is  seen  that  the  different  members  of  the  truss  have  the  same  kind 
of  stress  as  is  produced  by  vertical  loads.  As  the  wind  may  blow  from  either 
direction,  it  is  evident  that  both  sides  of  the  truss  must  be  made  alike.  This 
example  illustrates  the  method  of  drawing  the  stress-diagram  for  any  truss  with 
a  straight  rafter  when  both  ends  of  the  truss  are  fixed. 

Truss  on  Rollers.  Example  32.  When  one  end  of  the  truss  is  free  to 
MOVE,  the  reaction  at  that  end  must  always  be  practically  vertical,  and  this 
condition  gives  a  considerable  variation  of  stress  when  the  wind  is  on  different 
sides  of  the  roof;   so  that  it  is  necessary  to  draw  two  wind-stress  diagrams,  one 


Fig.  50.    Triangular  Truss.    Truss-diagram  and  Stress-diagram,  Wind  Left 

tor  WIND  FROM  THE  LEFT,  marked  W.L,  and  one  for  wind  from  the  right, 
marked  W.R.  It  is  customary  with  authors  when  writing  on  this  subject  to 
consider  that  the  rollers  are  always  under  the  right-hand  support,  and  this 
custom  is  followed  here.  In  practice  the  rollers  may  be  placed  under  either 
end,  as  both  sides  of  the  truss  are  usually  proportioned  to  the  maximum  stresses. 
For  this  example  we  will  take  the  same  truss-diagram  that  was  used  in  Fig.  49, 
illustrating  it  again  in  Fig.  50,  which  is  drawn  to  show  wind  from  the  left. 
Lay  off  the  load-line  1-8  and  divide  it  at  X',  as  in  example  31.  Draw  a  hne  ae, 
perpendicular  to  the  rafter  and  equal  to  1-8  in  length,  and  divide  it  into  two 
segments  of  the  same  proportions.  Through  x'  on  ae  draw  a  horizontal  line, 
and  through  e  a  vertical  line,  the  two  intersecting  at  0.  Then  eo  represents  the 
vertical  reaction  at  joint  7  and  oa  the  reaction  at  joint  i.  The  stress-lines  at 
joint  I  are:  oa,  ab  equal  to  500  lb,  hj  and/(?.  At  joint  2:  Jh,  he,  eg  and  gf.  The 
remainder  of  the  diagram  W.L.  is  completed  exactly  as  described  for  Fig.  49a, 
the  only  difference  between  the  two  being  the  location  of  point  0,  which  givei 
increased  stresses  in  the  bottom  chord  for  the  truss  of  Fig.  50.  Fig.  51  represents 
the  same  truss  with  wind  from  the  right.  To  draw  the  stress-diagram  W.R. 
start  with  id,  perpendicular  to  the  rafter  and  equal  to  the  total  load,  3  000  lb. 
Divide  the  line  at  x'  into  two  segments  of  the  same  proportions  as  the  segments 


1112 


Stresses  in  Roof -Trusses 


Chap.  27 


of  the  line  1-8,  Fig.  50,  the.longer  segment  being  at  the  top.  To  find  the  reac- 
tions draw  a  horizontal  Hne  through  x'  and  a  vertical  Hne  through  t,  the  two  lines 
intersecting  at  0.  Then  do  is  the  reaction  at  joint  i,  and  ol  the  reaction  at  joint 
10.  For  this  diagram  it  is  better  to  start  with  joint  10  and  take  the  forces  in 
the  reverse  order  from  that  in  which  they  were  taken  before.  The  stress-lines 
at  joint  10  are  ot,  is  equal  to  500  lb,  sn  and  no\  at  joint  9,  ns,  sr,  rm  and  mn; 
at  joint  8:  on,  nm,  ml  and  lo;  at  joint  7,  Im,  mr,  re,  ek  and  kl;  and  at  joint  5, 


Fig.  51.     Triangular  Truss.    Truss-diagram  and  Stress-diagram,  Wind  Right 

ke,  ed,  di  and  ik.  If  the  diagrams  have  been  correctly  drawn  the  point  i  will 
fall  vertically  above  the  point  k.  On  comparing  the  two  diagrams  for  W.L. 
and  W.R.  it  is  seen  that  the  stress-lines  for  the  rafters  and  braces  are  of  the  same 
length  and  that  the  stresses  are  of  the  same  character  in  both,  but  that  the  stress 
in  the  bottom  chord  is  considerably  less  when  the  wind  is  from  the  right.  This 
condition  does  not  apply  to  all  trusses,  however,  so  that  it  is  best  to  draw  the 
two  stress-diagrams  for  wind  from  both  directions. 

Queen  Truss.  Example  33.  Fig.  52  represents  the  outline  of  a  queen-rod 
TRUSS  for  a  roof  having  a  rise  of  14^^  in  in  12  in.  As  the  truss  is  of  wood  the 
supports  are  considered  fixed.  Joint  2  divides  the  rafter  into  two  equal  parts, 
consequently  the  wind-load  at  this  joint  is  twice  that  at  joint  i  or  4.  For 
convenience  it  is  assumed  that  the  wind-load  at  joint  2  is  i  000  lb  and  at  joints  i 
and  4,  500  lb.  The  resultant  is  2  000  lb  acting  through  joint  2  and  intersects 
the  tie-beam  at  X.  To  find  the  supporting  forces,  draw  the  line  1-8  equal  to 
2  000  lb  and  connect  7  and  8.  From  X  draw  a  line  parallel  to  7-8  intersecting 
1-8  at  X'.  Then  8-X'  is  Ri  or  the  supporting  force  at  joint  i  and  X'-i  or  R2 
the  supporting  force  at  joint  7.  Begin  the  stress-diagram  (Fig.  52a)  by  drawing 
the  line  ad  at  right-angles  to  the  rafter  1-4,  and  equal  in  length  to  1-8  or  2  000  lb. 
By  means  of  dividers  locate  the  point  0  so  that  oa  equals  S-X'.  Then  the  stress- 
lines  for  joint  i  arc  oa,  ab,  be  and  eo;  at  joint  2,  eb,  be,  cf  a.ndfe;  at  joint  3,  oe^ 
ef,fh  and  ho;  and  at  joint  4,  hf,  fc,  cd,  dk  and  kh.  It  is  seen  that  the  force-poly- 
gon at  joint  4  will  not  close  without  the  brace  KH,  because  the  initial  point  in 
drawing  the  polygon  is  at  h,  and  a  horizontal  line  through  d  does  not  pass 


Determination  of  Wind-Load  Stresses 


in3 


trirough  h.  A  queen-rod  truss,  therefore,  requires  braces  in  the  middle  panel 
lo  resist  the  wind-stress.  With  the  wind  from  the  fight,  a  brace  is  required  from 
ioint  .3  to  joint  6.  At  joint  5  the  stress  lines  are  oh,  hk,  kl  and  lo.  It  should  be 
noticed  that  lo  acts  towards  the  joint,  showing  that  LO  is  in  compression.     At 


Fig.  52.     Queen  Truss.     Truss-diagram 


Fig.  52a.     Queen  Truss.     Stress* 
diagram,  Wind  Left 


first  it  would  seem  as  though  this  could  not  be  true,  but  if  we  glance  at  joint  7 
we  see  that  Ri  is  thrusting  in  on  the  joint,  and  that  a  strut  is  required  to  keep 
the  joint  in  position.  This  condition  is  true  only  when  the  inclination  of  the 
rafter  is  greater  than  45°.     When  the  inclination  of  the  rafter  is  exactly  45% 


Fig.  53.     Queen  Truss.     Truss-diagram.     (See.  also,  Figs.  3,  12  and  54  and  Chapter 
XXVIII,  Fig.  1) 


there  is  no  stress  in  LO,  and  when  the  inclination  is  less  than  45°,  LO  is  in  ten- 
sion. The  stress-lines  for  jomt  6  are  Ik,  kd  and  dL  If  no  errors  are  made,  a 
line  through  d  parallel  to  DL  passes  through  the  point  /,  previously  obtained.  A 
very  slight  inaccuracy  vr^  io'-ating  the  point  X',  or  in  drawing  the  stress-diagram, 


1114 


Stresses  in  Roof-Trusses 


Chap.  27 


however,  causes  the  line  through  d  to  pass  to  one  side  or  the  other  of  point  /; 
and  if  this  happens,  it  shows  that  there  has  been  some  inaccuracy  somewhere. 
In  practice,  a  slight  divergence  does  not  materially  affect  the  stress.  At  joint  7 
the  sides'  of  the  stress-polygon  are  ol,  Id  and  do  =  Ri,  the  lines  being  already 
drawn. 

Combination  of  Stresses.  Example  34.  For  the  purpose  of  showing  how 
the  stresses  due  to  wind  and  vertical  loads  are  combined,  the  truss-diagrams  in 
Figs.  53  and  54  are  shown,  being  the  same  as  in  Fig.  12,  and  representing  the 


Fig.  53a.     Queen  Truss.    Stress- 
diagram 


Fig.  54.     Queen  Truss.  Truss-diagram.    (See,  also, 
Figs.  3,  12  and  53  and  Chapter  XXVIII,  Fig.  1) 


truss  shown  in  Fig.  3.  The  stresses  first  determined  are  those  due  to  the  weight 
of  the  roof  and  ceiling  and  to  an  allowance  of  10  lb  per  sq  ft  for  sleet.  On 
page  1055  the  roof-area  supported  at  joint  2  was  found  to  be  147^^  sq  ft  and  at 
joint  3,  200  sq  ft.  On  page  1055  the  weight  of  the  roof  was  estimated  at  12%  lb 
per  sq  ft,  and  allowing  10  lb  for  sleet,  there  results  22%  lb  as  the  greatest  dead 
load  under  a  heavy  wind.  This  gives  3  360  lb  for  the  lead  at  joint  2  and  4  550  lb 
for  the  load  at  joint  3.  The  ceiling-loads  will,  of  course,  be  the  same  as  in  Fig.  12. 
Fig.  53  shows  the  loads  due  to  weight  of  materials  and  sleet,  as  computed  above, 
and  the  ceiling-loads.  Fig.  63a  is  the  stress-diagram  for  these  loads,  with  the 
stresses  indicated  by  figures.  This  diagram  is  drawn  exactly  in  the  same  way 
as  the  stress-diagram  in  Fig.  12,  page  107 1. 

Wind-Stresses.  The  inclination  of  the  roof  is  very  close  to  45°,  and  from  Table 
IX,  page  1053,  the  normal  wind-pressure  for  that  angle  is  found  to  be  28  lb.  Multi- 
plying^ the  roof-area  at  joints  2  and  3  by  28,  the  wind-loads  indicated  in  Fig.  54 
are  obtained.  The  wind-load  at  joint  i,  also,  must  be  found.  The  rcof-arca 
suppvMled  at  this  joint,  allowing  17  in  for  eave-projection  (Fig.  3)  is  6M1  by  15  ft, 
or  95  sq  ft,  which  makes  the  wind-load  2  660  lb.  The  next  step  is  to  find  the 
point  at  which  the  resultant  of  these  loads  cuts  the  rafter.  As  the.  loads  are  I 
not  symmetrical  or  uniform  on  the  rafter,  the  point  through  which  the  resultant 
acts  must  be  determined  by  means  of  moments  about  joint  i.  The  arms  of  the 
loads  at  joints  2  and  4  are  figured  on  the  truss-diagram  (Fig.  54).  The  moments 
are 

4  140  lb  X  9^/12  ft  =     38  9<^S  ft-lb 

5  600  lb  X  i8iA  ft  =   102  200  ft-lb 

The  sum  of  the  moments    =   141  185  ft-lb 


Determination  of  Wind-Load  Stresses 


im 


The  resultant  is  the  sum  of  all  the  loads,  or  12  400  lb,  and  the  distance  of  its  point 
of  application  from  i  is  found  by  dividing  the  sum  of  the  moments  by  the  result- 
ant force,  or  141  185  ft-lb  divided  by  12  400  lb  =  ii.4-  ft.  Measuring  off  11.4  ft 
on  the  rafter  from  joint  i  and  drawing  a  line  at  right-angles  to  it  intersecting  the 
tie-beam,  the  point  X  is  determined.  From  i  the  line  1-8  is  drawn  at  any 
angle  and  equal  in  length  to  the  sum  of  the  loads,  12  400  lb,  and  7-8  is  drawn. 
From  X  a  line  is  drawn  parallel  to  7-8,  intersecting  1-8  at  X'.  Then  8-X'  is 
Ri  or  the  supporting  force  at  joint  i  and  ^ -r  is  R2  or  the  supporting  force  at 
joint  7. 

Supporting  Forces  Computed  by  Moments.  The  supporting  forces  ipay  also 
be  computed  by  moments.  The  moments  of  the  loads  about  joint  i  tend  to 
rotate  the  truss  from  left  to  right.  To  prevent  this  rotation  there  is  the  moment 
of  the  supporting  force  R2  acting  vX  joint  7  to  rotate  the  truss  from  right  to  left. 
To  maintain  equihbrium,  the  moment  of  i^2  about  joint  i  must  just  equal  the  sum 
of  the  moments  of  the  loads  about  the  same  point.  This  sum  was  found  above  to 
be  141  185  ft-lb.  The  arm  of  R2  is  the  perpendicular  distance  between  its  hne 
of  action  and  joint  i.  Continue  i?2  to  meet  the  dotted  line  at  P.  The  dis- 
tance from  force  i?/l  to  P  scales,  say  26.5  ft.  (By  trigonometry,  26  ft.)  Knowing 
the  arm,  the  value  of  R2  is  obtained  by  dividing  the 
sum  of  the  moments  of  the  loads,  141  185,  by  the 
arm,  or  26.5  ft.  This  gives  5  344  lb.  As  the  sum 
of  Ri  and  R2  must  equal  the  total  load,  Ri  equals 
12  400  less  5  344  lb,  or  7  056  lb.  The  distance 
S-X'  and  X'-i  should  scale  reasonably  close  to  these 
figures.  Knowing  the  supporting  forces,  the  stress- 
diagram,  Fig.  54a,  is  drawn  exactly  as  described  for 
Fig.  52a.  As  the  inclination  of  the  rafters  is  a 
little  greater  than  45°,  0£'  is  in  compression,  but 
the  stress  is  very  small.  The  figures  on  Fig.  54a 
indicate  the  stresses  in  pounds.  The  stresses  may 
now  be  tabulated  and  should  be  arranged  as  in  the  following  table.  In 
tabulating  the  wind-stresses,  it  should  be  remembered  that  the  wind  may  blow 
against  either  side  of  the  truss,  and  the  greatest  stress  liable  to  occur  should  be 
put  in  the  table. 


.cbW 

;^/  ^-3600 

Fig.    64a.     Queen    Truss. 
Stress-diagram,  Wind  Left 


Table  XVra. 

Stresses  for  the  Trusses  Shown  in  Figs.  12,  53  and  54 

Members 

Dead  weights 
and  sleet 
(Fig.  53.4) 

Wind-stresses 
(Fig.  54) 

Totals 

Stresses 
(Fig.  12) 

AEor  A'E' 

BF  or  B'F' 

c//'or  cn 

EF 

////' 

+  16  150 
+  13  800 
+  9600 
+  2350 
0 

—  5  400 

—  IT   200 

—  9  600 

+5  100 
+5  100 
+3  600 
+4100 
+5  100 
-3  700 
-5  950 
-3  150 

+21  250 
+18900 
+  13  200 
+  6450 
+  5  100 
—  9  100 
-1/  150 
-12  750 

+  25  600 
+  21  300 
+  14  700 
+  4400 
0 

—  6900 

—  17  60c 
-147CJ 

FH  or  F'H' 

EO    .      . 

HP 

The  truss-members  are  lettered  as  in  Fig.  54.  Thus  the  stress  in  the  rafter  F'B' 
is  greater  than  in  the  rafter  on  the  other  side,  and  this  stress  acts  through  the 
entire  length  of  the  rafter;  hence  the  stress  for  AE  and  BF  should  be  entered 
as  5  100  lb,  the  stress  in  F'B'.    In  the  same  way  the  stress  in  the  rod  H'F'  is 


1116  Stresses  in  Roof-Trusses  Chap.  27 

greater  than  in  F/7;  hence  the  stress  in  H'F'  should  be  tabulated.  The  stress 
in  OE'  slightly  reduces  the  tension  due  to  the  dead  load,  but  as  the  stress  in  EQ 
increases  it,  the  stresses  in  EQ  and  HP  should  be  tabulated.  Both  sides  of  the 
truss  should  of  course  be  made  alike,,  and  two  l)races  should  be  inserted  in  the 
middle  panel.  In  the  fifth  column  of  the  table  are  given  the  stresses  due  to  the 
ceiling-load  and  a  vertical  load  on  the  roof  of  42%  II)  per  sq  ft,  as  obtained  from 
the  stress-diagram.  Fig.  12.  Comparing  the  stresses  in  the  fourth  and  fifth 
columns,  it  is  seen  that  except  for  the  brace  EF,  and  for  the  two  rods,  the  stresses 
obtained  by  combining  snow  and  wind  and  adding  to  the  dead  weight  are  greater 
than  thQ  totals  due  to  wind,  dead  weight  and  sleet.  Vertical  loads,  of  course, 
cause  no  stresses  in  the  braces  of  the  middle  panel,  and  unless  the  wind-stresses 
are  drawn,  it  is  necessary  to  estimate  the  sizes  of  these  braces.  The  stresses  in 
these  braces,  however,  are  so  small  that  large  pieces  of  timber  are  not  required. 
The  stresses  given  in  the  fourth  column  are  unquestionably  nearer  what  the 
real  stresses  are  likely  to  be  than  those  in  the  fifth  column.  If  the  roof  is  erected 
in  a  warm  climate  where  there  is  no  sleet,  these  stresses  may  be  further  reduced 
by  omitting  the  10  lb  per  sq  ft  added  for  sleet.  If,  on  the  other  hand,  the  in- 
clination of  the  roof  is  less  than  30°,  the  stresses  produced  by  a  heavy  fall  of 
snow  without  wind  generally  exceed  the  sum  of  those  due  to  dead  weight,  sleet 
and  wind;  and  for  such  roofs  the  stresses  due  to  the  maximum  snow-load  should 
always  be  computed. 

Reactions.  The  reactions,  or  supporting  forces  of  the  truss  shown  in  Fig.  54, 
are  very  much  inclined  from  the  vertical.  As  the  dead  load,  however,  is  always 
acting  on  the  truss,  the  inclination  of  the  real  reaction  is  never  so  great,  but 
more  nearly  vertical;  and  when  there  is  no  wind  the  reactions  are  exactly  ver- 
tical. The  theoretical  reaction,  due  to  both  wind-load  and  dead  load,  is  the 
diagonal  of  a  parallelogram,  the  two  adjacent  sides  of  which  are  the  reactions 
for  the  dead  load  and  wind-load  drawn  to  the  same  scale.  Thus  if  a-7,  Fig.  54, 
represents  the  reaction  due  to  the  wind  and  h-^  the  vertical  reaction,  due  to  the 
dead  load  and  drawn  to  the  same  scale,  then  R'^  is  the  resultant  reaction,  modified 
somewhat,  however,  by  friction.  Examples  31,  32  and  s^  serve  to  show  the 
general  method  of  drawing  wind  stress-diagrams,  and  are  sufficient  to  enable 
the  student  to  draw  those  diagrams  for  most  trusses  v/ith  straight  rafters.  For 
trusses  with  curved  rafters  the  diagrams  become  more  complicated,  and  the 
reader  is  referred  to  Graphical  Analysis  of  Roof  Trusses,  by  Charles  E.  Greene 
and  to  other  standard  handbooks  on  the  subject. 

7.   Trusses  with  Knee-Braces 

Knee-Braces  are  generally  used  to  give  greater  stability  to  the  structure  as  a 
whole  when  roof-trusses  are  supported  by  columns.  Under  the  action  of 
vertical  loads  the  stresses  in  these  members  are  usually  assumed  as  zero,  which 
would  be  true  if  the  materials  composing  the  truss,  knee-kraces  and  columns 
were  rigid.  This  discussion  will  deal,  however,  with  the  effect  of  wind  blowing 
against  one  side  of  the  building  and  roof.  The  actual  stresses  in  the  knee- 
braces,  columns  and  truss-members  will  probably  never  be  known  exactly,  as 
there  are  so  many  variable  factors  entering  into  the  problem.  In  the  usual 
construction,  in  which  columns  are  bolted  to  masonry  pedestals  at  the  bottom, 
either  riveted  or  bolted  to  the  trusses  at  the  top,  and  in  which  the  knee-braces 
are  riveted  at  both  ends,  the  degree  to  which  these  connections  may  l)e  considered 
fixed  is  a  question  leading  to  many  arguments  and  differences  of  opinion.  This 
will  not  be  discussed  at  all;  but  it  will  be  shown  how  the  stresses  in  all  members 
of  the  framework  can  be  found  under  given  assumptions.  Assume,  for  example, 
that  the  bottoms  of  the  columns  are  sufficiently  fixed,  so  that  a  powt  of  no* 


Trusses  with  Knee-Braces 


1117 


MOMENT  is  midway  between  the  bottom  of  the  knee-brace  and  the  masonn^ 
pedestal  (equivalent  to  assuming  a  pin  at  this  point),  and  so  that  the  top  attach- 
ments and  those  of  the  knee-braces  may  be  considered  as  pin-connections. 
Taking  the  truss  and  loading  shown  in  Fig.  55,  it  is  clear  that  the  outside  forces 
must  be  in  equilibrium,  and,  unless  the  points  M  and  N  are  unlike  in  some 


l5oa. 


Fig.  55.    Truss  with  Kn^-braces.    Truss-diagram 


particular,  the  reactions  at  these  points  will  be  parallel  to  the  direction  of  the 
resultant  of  the  wind-forces.  Lay  off  to  any  convenient  scale  the  wind-forces 
in  order,  as  shown  in  Fig.  55a.  Then  XY  is  the  direction  and  magnitude  of  the 
resultant  wind- pressure  and  also  the  direction  of  Ri  and  Ri.  The  magnitudes 
of  i?i  and  Ri  are  found  by  meansof  the  equilibrium  polygon  explained  on  page  1097. 
Rx  is  equal  to  SX  and  R2  to  YS.  These 
reactions  are  correct  in  direction  and  mag- 
nitude unless  some  condition  is  imposed  to 
change  them.  If  there  are  no  moments  at 
M  and  N  and  these  points  are  restrained 
from  moving  vertically,  the  vertical  com- 
ponents of  R\  and  R2  must  remain  constant, 
even  in  the  extreme  case  where  M  may  be 
assumed  as  a  pin-connection  and  N  as 
resting  on  rollers.  Any  assumption  may  be 
made  as  to  the  magnitudes  of  the  horizontal 
components  at  these  points  as  long  as  the 
sum  of  the  two  equals  the  sum  of  the 
horizontal  components  of  Rx  and  R^.  It  is 
customary  to  assume  these  as  equal.  In 
this  case  the  reactions  at  M  and  N  are  TX  and  YT,  respectively.  The  next  step 
is  to  find  the  effect  of  these  reactions  at  the  points  O,  Q,  P  and  R.  The  vertical 
components  Vi  and  Vz  act  as  vertical  forces  at  O  and  P.  The  horizontal  com- 
ponents produce  bending  moments  at  O  and  P,  and,  in  effect,  horizontal  forces 
at  O,  P,  Q  and  R.  Taking  the  left  column,  the  8  100  lb  acting  towards  the  left 
would  move  the  column  to  the  left  if  not  prevented  by  the  joints  at  O  and  Q. 


55a.    Truss  with  Knee-braces. 
Force-polygon 


Ills 


Stresses  in  Roof-Trusses 


Chap.  27 


If  the  member  MQ  is  considered  to  act  as  a  lever  with  a  fulcrum  at  O,  a  hori- 
zontal force  of  8  loo  lb  acting  towards  the  left  at  M  will  produce  a  pressure,  or  a 
force  acting  from  left  to  right  at  Q  which  equals,  by  the  method  of  moments,  the 
center  of  moments  being  at  O,  8  loolbX  7.5  ft -t-  5  ft  =  12  150  lb.  At  0,  in  like 
manner,  taking  the  center  of  moments  at  Q,  8  100  lb  X  12.5  ft  -h  5  ft  =  20  250  lb 


A\     v# 

12150  ^^150o\^^^ 


Fig.  56.    Truss  with  Knee-braces.     Truss-diagram 


/  Fig.  57.     Truss  with  Knee-braces.     Stress-diagram 

is  produced,  acting  from  right  to  left .  These  forces  are  shown  in  Fig.  56.  When 
combined  with  those  shown  in  Fig.  55  they  give  the  forces  acting  at  O,  Q,  R 
and  P  which  are  used  in  constructing  the  stress-diagram  shown  in  Fig.  57. 


8.   Arched  Trusses 

An  Archied  Truss  is  one  which  has  the  form  of  an  arch  and  which  is  so 
supported  at  the  ends  that  the  reactions  produced  by  vertical  forces  are  vertical. 
This  is  usually  accomplished  by  placing  pin-connections  at  the  supports  and 
providing  rollers  at  one  end  to  permit  horizontal  movement. 

Stresses  in  an  Arched  Truss.  The  determination  of  the  stresses  in  the 
members  of  an  arched  truss  is  readily  accomplished  by  following  the  methods 
given  in  the  previous  examples. 

Arched  Truss  with  Roller-Support.     Example  35.     In  Fig.  58  is  shown 
the  left  half  of  an  arched  truss  and  the  roller-support.     This  truss  has  the  ' 
shape  and  dimensions  of  a  truss  in  the  Live  Stock  PaviUon,  Union  Stock- Yard 


Arched  Trusses 


1119 


and  Transit  Company,  Chicago,  III.  It  is  discussed  in  the  Engineering  News  of 
June  28,  1906.  The  loading  shown  is  symmetrical  about  the  middle  of  the 
span  and  hence  each  reaction  equals  one-half  the  total  load.     Fig.  58a  shows 


Ri=195  0(X) 

Fig.  58.     Live  Stock  Pavilion,  Chicago,  111.     Truss-diagram 


24  +535000 


110-11-12 


18-19 
Fig.  58a.    Live  Stock  Pavilion,  Chicago,  111,     Stress-diagram  for  Truss 


the  stress-diagram  for  one-half  of  the  truss.     The  stresses  upon  the  right  of  the 
middle  are  the  same  as  those  upon  the  left. 

The  HORIZONTAL  DEFLECTION  of  this  truss  is  measured  by  the  movement  of 
the  ROLLER-END.  This  movement  is  computed  in  the  manner  explained  for  the 
SCISSORS  TRUSS,  pages  1085-7,  by  the  formula  D  =i:{Sul  ^AE).  '  Where  D  is  the 


1120  Stresses  in  Roof-Trusses  Chap.  27 

HORIZONTAL  MOVEMENT,  5  the  stress  in  any  member  as  given  by  the  stressKliagram 
shown  in  Fig.  58a,  m  the  stress  in  any  member  produced  by  the  unit  load  applied 
at  the  roller  end  of  the  truss  and  acting  in  a  horizontal  direction  (Fig.  58b), 
I  the  length  of  any  member,  A  the  area  of  any  member,  E  Young's  modulus  of 
elasticity  for  the  material  composing  any  member  and  S  the  sign  of  summation, 
and  when  limits  are  not  designated,  the  formula  indicates  that  S(5w/  -i-  AE)is  to 
be  taken  for  each  member  of  the  truss.  For  the  loads  and  areas  indicated  in 
Fig.  58,  the  rollers  will  move  about  lo  in  when 
i(vii-i2     yjv  £  is  30  000  000  lb  per  sq  in.     In  order  that  a 

given  span  may  obtain  under  a  given  load, 
each  tension-member  must  be  constructed 
shorter  than  its  geometrical  length  by  an 
amount  which  it  is  lengthened  by  the  stress 
which  it  resists,  and  each  compression-member 
must  be  lengthened  in  a  hke  manner.  Any 
Fig.  58b.  Live  Stock  Pavilion,  ^^her  loading  will  produce  a  change  in  the 
Chicago,  111.  Stress-diagram  length  of  the  span.  To  reduce  the  horizontal 
DEFLECTION  without  changing  the  lengths  of 
the  members  they  would  have  to  be  made  excessively  heavy.  A  truss  of  the 
form  shown  in  Fig.  58  is  not  economical  as  an  arched  truss  on  rollers  but 
may  be  satisfactorily  used  by  connecting  the  two  end -pins  by  a  tie- rod. 

Arched  Truss  with  Tie-Rod.  When  a  tie-rod  is  employed  the  members 
become  much  lighter  and  can  be  built  according  to  their  geometrical  lengths. 
The  stress  in  the  tie-rod  may  be  found  from  the  formula 

in  which  St  is  the  stress  in  the  tie- rod.  A'  the  area  of  the  tie-rod,  I'  the  length  of 
the  tie-rod  and  E'.  Young's  modulus  of  elasticity  for  the  material  composing 
the  tie-rod.  The  other  symbols  have  the  significance  given  above  for  the 
expression  for  D.  Since  the  stress  and  area  of  the  tie-rod  appear  in  the  above 
equation  it  is  necessary  to  assume  an  area  and  then  compute  the  value  of  St. 
If  this  produces  a  unit  stress  in  the  tie-rod  differing  greatly  from  the  allowable 
value,  a  new  trial  must  be  made.  Having  found  the  stress  in  the  tie-rod,  the 
resulting  stresses  in  the  truss-members  can  be  found  graphically  from  a  stress- 
diagram  which  will  be  of  the  form  shown  in  Fig.  58b,  which  was  constructed  for 
a  horizontal  force  of  i  000  lb.  The  stresses  can  be  found,  also,  by  multiplying 
the  stresses  produced  by  one  pound  b^'  the  value  of  St.  The  stresses  produced 
by  St  combined  algebraically  with  those  obtained  from  Fig.  58a  give  the  final 
stresses.  These  stresses  differ  but  little  from  those  which  obtain  for  a  two- 
hinged  arch  of  the  form  shown  in  Fig.  58,  and  such  structures  with  the  tie- 
rod  are  often  classed  as  two-hinged  arches. 

Assumption  of  Areas.  Since  the  deflection  of  the  truss  shown  in  Fig.  58 
depends  upon  the  areas  of  the  members,  it  is  evident  that  they  must  be  either 
known  or  assumed  before  the  formulas  for  D  or  St  can  be  applied.  For  a  new 
structure  the  areas  are  of  course  unknown  and  the  problem  of  determining  the 
stresses  becomes  one  which  is  sometimes  classed  as  cut-and-try.  For  the  first 
trial,  the  areas  may  be  assumed  as  unity  and  the  corresponding  value  of  St 
found  and  then  the  combined  stresses.  The  members  may  now  be  designed  as 
to  area  and  a  new  trial  made  with  these  areas.  Usually  the  second  trial  is 
sufficient,  as  a  slight  change  in  areas  does  not  materially  affect  the  values 
of  St. 


Trussed  Arches 


1121 


9.    Trussed  Arches 

Symmetrical  Trussed  Arches.  The  three-hinged  arch  is  the  simplest 
form  of  TRUSSED  ARCH,  and,  as  used  in  buildings,  it  is  usually  symmetrical  in 
form,  consisting  of  two  trusses  connected  by  a  pin  over  the  middle  of  the  span  and 
resting  on  a  pin  at  each  support.  The  stresses  in  the  truss-members  are  found 
by  the  ordinary  graphical  methods  after  the  reactions  have  been  determined. 

^ 82-3^^ >| 


1^— ll-O"  >K     1-1-0-^ — ^11-C— >|^— 1-1-0^UJ< — l-l-o'    >k  .1-1-0^ — ^l-l'ol^>|-5'3'^ 

1       !       !      J      i!      i|  «  I  h±1l44 


Fig.  59.    Three-hinged  Arch.    Truss-diagram 
Fig.  59a.     Stress-diagram 

The  SUPPORTING  FORCES  are  inchned  and  may  be  resolved  into  two  components, 
one  vertical  and  the  other  horizontal.  For  symmetrical  loading  the  two  reac- 
tions are  equal  in  magnitude.  The  vertical  components  are  each  equal  to  one- 
half  the  vertical  loading.  The  horizontal  components  are  equal  in  magnitude 
and  opposite  in  character.  The  following  examples  illustrate  the  methods  to 
be  followed  in  the  determination  of  the  stresses. 


1122 


Stresses  in  Roof-Trusses 


Chap.  27 


Trussed  Three-hinged  Arch.  Example  36.  Fig.  59  shows  one-half  of  a 
TRUSSED  THREE-HINGED  ARCH  with  a  Vertical  load  of  I  000  lb  per  top-chord 
joint.  Fig.  59a  shows  the  stress-diagram  for  this  loading;  but  before  it  can  be 
drawn,  the  vertical  and  horizontal  reactions  at  the  left  support  must~be  deter- 
mined. The  vertical  reaction  is  (7  X  i  000)  -|-  500  =  7  500  lb  or  one-half  the  ver- 
tical load.  The  horizontal  component  or  the  horizontal  thrust  of  the  arch 
may  be  found  by  moments.    The  center  of  moments  will  be  taken  at  the  middle 


H,«| 


O 
Vi=  457,750 

Fig.  60.    Liberal  Arts  Building,  Chicago,  111.     Truss-diagram 
Fig.  60a.     Stress-diagram 

pin  at  the  crown  as  at  this  point  the  moment  is  zero.  The  equation  of  moments 
is  III  X  72.5  +  I  000  (5.25  -\- 16.25  -H  27.25  -\-  38.25  -H  49.25  4-  60.25  +  71.25) 

-f  500  X  82.25  -  7  500  X  78.75  =  o, 
or  III  =  281  750  ^  72.5  =  3  886  lb 

Having  determined  Vi  and  Hi,  the  stress-diagram  shown  in  Fig.  59a  can  be 
readily  constructed.  Since  the  arch  is  symmetrical,  it  is  necessary  to  draw  but 
one-half  the  stress-diagram.  If  the  right  half  of  the  arch  is  removed  and  in  its 
place  a  horizontal  force  applied  at  the  middle  pin,  the  magnitude  of  this  force  i& 


Trussed  Arches 


1123 


equal  to  the  horizontal  thrust  Ih,  since,  for  equilibrium,  the  algebraic  sum 
ot  the  horizontal  forces  is  zero. 

Trussed  Three-hinged  Arch.  Example  37.  Fig.  60  represents  one-half  of 
a  TRUSSED  THREE-HINGED  ARCH  used  in  the  Liberal  Arts  Building  of  the  Colum- 
bian Exposition,  Chicago,  111.,  1893.  (See  Engineering  Record,  July  9,  1892.) 
Fig.  60a  is  the  stress-diagram  for  the  loading  shown  in  Fig.  60. 

Combination  of  Stresses.  In  Examples  35  and  36  only  the  efifect  of  vertical 
loads  has  been  considered.  Where  three-hinged  arches  are  employed  they 
must  be  designed  to  carry  dead,  snow  and  wind-loads.     The  dead  and  snow- 


.g    <0 


its 


^'^^.M  ''""m 


"32000^ 

FD.ft 


43.48- 


: — ^Z: 


■:<^S: 


.65.66- g.(2^< 


T5.54 

84.43- 


— — i"lt 


11 

/22    ^ 

ll 

\^21 
20     JS 

> 

^y^j 

18  yf 
All 

JT 

/     1 

t 

W^'  sp 

3  8H  -'■ 


Fig, 


Fig.  61.     5th  Regiment  Armory,  Baltimore,  Md.     Truss-diagram 
Fig.  61a.     Stress-diagram 


I 


loads  are  vertical  loads  but  the  snow-load  is  not  symmetrical  in  all  cases.     The 
wind-load  is  usually  considered  as  acting  normal  to  the  roof.     In  order  to  be 
sure  that  the  maximum  stresses  are  obtained,  the  stresses  for  the  following  con- 
ditions of  loading  must  be  found  and  combined, 
(a)  For  dead  load  only, 
(6)  For  snow-load  covering  left  half  of  roof, 
(c)  For  snow-load  covering  right  half  of  roof, 
{d)  For  wind-load  acting  normal  to  roof  on  left  of  center, 
(e)  For  wind-load  acting  normal  to  roof  on  right  of  center. 


1124 


Stresses  in  Roof-Trusses 


Chap.  27 


^21     .22  o. 


Fig.  61b.    5th  Regiment  Armory, 
Baltimore,  Md.     Stress-diagram 


Snow  on  Bight 
ofCrowi^ 


Fig.  61c.    6th  Regiment  Armory,  Baltimore, 
Md.    Stress-diagram 


J^- 

\ 

S^^,^.-3u_,. 

S.o    S„ 

J3^ 

13 

■pj^- 

\ 
\ 

i\ 

^kJ^^C^) 

i    3^^^/ 

>^ 

r\" 

^ 

9/ 

J<:;;^\3T^ 

A 

\r"29 

^ 

/ 

%«/28 

vV 

/ 

K 

6/\     27 

y^ 

coi  % 

y  26    \      y 

/ 

-/ 

/ 

/ 

C/ 

''X      25     / 
24    X/' 

/ 
/ 
/ 

7 

/ 

•^  i/\ 

23     / 

/ 

/ 
/ 
/ 

\i>/h 

=13200 

1% 

1 

Fig.  61d.     5th  Regiment  Armory,  Baltimore.  Md.     Truss-diagram 


Trussed  Arches  1125 

The  stresses  for  the  above  conditions  of  loading  are  to  be  found  for  one-half 
of  the  arch.  In  combining  the  stresses  those  which  occur  at  the  same  time  are 
to  be  used  in  determining  maximums.  Many  engineers  do  not  consider  snow 
and  wind-loads  acting  on  the  same  portion  of  the  roof  simultaneously. 

Trussed  Three-hinged  Arch.  Example  38.  Fig.  61  shows  one-half  of  a 
TRUSSED  THREE-HINGED  ARCH  with  the  dead,  snow  and  wind-loads  indicated  at 
each  of  the  upper-chord  joints.  This  form  of  truss  supports  the  roof  of  the 
5th  Regiment  Armory,  Baltimore,  Md.,  described  in  the  Engineering  Record 
of  May  14,  1904.  The  stresses  for  the  loadings  specified  above  will  be  deter- 
mined and  it  will  be  shown  how  these  are  to  be  combined. 

Dead-Load  Stresses.  The  reactions  are  obtained  by  the  method  used  in 
Example  35.  Vi  is  77  900  lb  and  Hi  32  000  lb.  -Fig.  61a  is  the  stress-diagram 
for  the  members  shown  in  Fig.  61. 

Snow  on  Left  Half  of  Span.  Assuming  that  the  snow  covers  the  portion  of 
the  arch  shown  in  Fig.  61  and  taking  the  center  of  moments  at  the  middle  pin, 
it  is  found  by  moments  that  Vi  is  equal  to  26  700  lb  and  H^  is  equal  to  15  000  lb. 
Beginning  at  the  support  the  stress-diagram  shown  in  Fig.  61b  is  readily  drawn. 

Snow  on  Right  Half  of  Span.  With  the  snow  on  the  right  of  the  crown,  the 
portion  of  the  span  shown  in  Fig.  61  is  unloaded.  The  total  snow-load  is 
41  200  lb  and  it  has  just  been  found  that  the  vertical  reaction  at  the  support 
adjacent  to  the  loading  is  26  700  lb;  hence  the  vertical  reaction  at  the  other 
support  is  41  200  less  26  700  lb  or  14  500  lb  or  Vi  for  the  case  considered.  Since 
the  moment  at  the  middle  pin  is  zero,  Vi  (half  the  span)  less  Hi  (rise  of  the  arch) 
equals  zero,  or  14  500  X  95 -16  —  ^1 X  92.0  =  o;  and 
Hi  =  (14  500  X  95-i6)  -^  92  =15  000  lb  which  is  the 
same  as  found  above.  As  before,  beginning  at  the 
left  support,  the  stress-diagram  is  constructed  as 
shown  in  Fig.  61c.  |  |j 

Snow  Covering  Entire  Span.     The  algebraic  sum    d  ]!  , 
of  the  stresses  found  from  the  two  cases  above  for    >  1 1 

snow-loads  will   give   the  stresses  produced  by  a       j.1 

snow-load  covering  the  entire  span.  I  pj^"^ 

Wind-Load  on  Left  of  Crown.     Here  no  two  of       | 
the  loads  are  parallel.     This  condition  increases  the       I   _ 
labor  in  finding  the  reactions.     These  may  be  com-       |     ~'*"~^"j — — ^ 

puted    by   moments,   but   a   graphical  method  is       ' '*"'hVi8^^^^'^^ 

found  more  convenient.     The  direction  and  mag-  KthH    '       t  A  ■> 

nitude  of  the  resultant  of  the  wind-forces  are  first  ^^ory,  Baltimore^MT  Force' 
found  by  graphics.  As  shown  in  Fig.  61e,  the  wind-  polygon 
loads  are  laid  off  in  order.  Then  3-13  is  the  direc- 
tion and  magnitude  of  the  resultant.  Next,  from  any  point  O  draw  the  strings 
Si,  S2,  S3,  etc.,  and  construct  the  equilibrium  polygon  shown  in  Fig.  6 Id,  begin- 
ning by  drawing  string  Si  from  A,  and  so  on  until  string  Sn  cuts  the  line  BC 
passing  through  the  middle  pm  and  the  pin  at  the  right  support.  This  is  the 
direction  of  the  reaction  at  the  right  support.  In  Fig.  61  e,  from  13  draw  a  line 
parallel  to  BC  and  from  0  a  line  parallel  to  So  in  Fig.  6 Id,  and  prolong  them  until 
they  meet  at  i.  Then  1-3  is  the  reaction  at  A  and  13-1  that  at  the  right  support. 
Resolving  these  into  vertical  and  horizontal  components,  Vi  equals  23  400  lb, 
Hi  equals  13  200  lb,  F2  equals  18  000  lb  and  H2  equals  18  600  lb.  Fig.  61f  shows 
the  stress-diagram  from  the  left  support  up  to  the  crown. 

Wind-Load  on  Right  of  Crown.    Since  the  reaction  at  A,  Fig.  61d,  produced 
by  this  load,  must  pass  through  the  hinges,  or  pins  A  and  C,  th^  stress-diagram 


1126 


Stresses  in  Roof-Trusses 


Chap.  27 


will  be  exactly  similar  in  shape  to  that  shown  in  Fig.  61c;  but  the  values  of  Fa 
and  Hi  will  be  i8  ooo  lb  and  i8  6oo  lb  respectively.  The  stresses  will  bear  a 
direct  proportion  to  the  stresses  found  from  Fig.  61c,  and  hence  a  new  diagram 
is  not  necessary. 


;.  61p.    5tb  Regiment  Armory,  Baltimore,  Md.     Stress-diagram 


%. 


Combination  of  Stresses.  The  maximum  stresses  may  now  be  determined, 
To  illustrat^-^e  m<^tho(|,  consider  ihe  lower  chord  1-37.   . 

>*''    ■'   '    /^     '  ''■      ,."■,  -^  ..,  ^  '.,  ..Vt  Jb 

(a)  Dead-load  stress,  +22  100 

(h)  Snow  on  left  of  crown,  —  14  300 

(c)   Snow  on  right  of  crown,  +  37  800 

((/)  Wind-load  on  left  of  crown,  —  31  6oq 

{e)  Wind-loAd  on-  right  of  crown,  -f  46  900 

(/)   Snow  over  all,  +  23  500 

Total  stress  without  wind,  +59  900 

(a)  +  (e),  +  69  000 

(a)  +  W,  -    9500 

The  maximum  stresses  are  69  000  lb  compression  and  9  500  lb  tension,  assum- 
ing that  the  wind  and  snow-loads  are  not  considered  to  act  on  the  same  side  of 
the  crown.  If  no  such  restriction  is  made,  the  maximum  stresses  are  106  800  lb 
compression  and  23  800  lb  tension.  In  a  like  manner  the  maximum  stress  in 
each  member  of  the  truss  is  determined.  Tables  XIX  and  XX  give  the  max- 
imum STRESS  for  the  members  shown  in  Fig.  61. 

Stress-Diagrams  for  Three-hinged  Arches.  The  stress-diagrams  in  the 
above  cases  are  very  difhcult  to  construct  owing  to  the  great  number  of  lines 
and  the  difficulty  in  drawing  them  exactly  parallel  to  the  Hnes  of  the  truss- 
diagram.  One  or  more  members  should  be  computed  as  a  check  on  the  graph- 
ical work. 

Three-hinged  Arch  with  Tie-Rod.  The  introduction  of  a  tie-rod  connect- 
ing the  end-pins  of  a  three-hinged  arch  and  placing  rollers  under  one  end 


Trussed  Arches 


1127 


practically  changes  the  arch  into  a  simple  truss  composed  of  three  members, 
two  trussed  rafters  and  a  horizontal  tie.  Under  vertical  loading,  the  support- 
ing forces  are  vertical,  but  for  wind-loads  the  supporting  force  at  the  end  with- 
out rollers  is  inclined.  The  stresses  in  the  truss-members  are  the  same  as  found 
above  for  the  three-hinged  arch.  Th*e  stress  in  the  tie-rod  equals  the  hori- 
zontal thrust  found  above  at  the  roller-end  for  the  given  loading.  The  support 
at  the  roller-end  is  designed  for  vertical  forces  only,  while  the  support  at  the  other 
end  must  resist  the  vertical  reaction  and  the  total  horizontal  component  of  the 
forces  acting  on  the  structure,  or  for  roofs  the  horizontal  component  of  the  wind- 
forces.  This  is  very  much  smaller  than  the  horizontal  force  which  must  be 
resisted  when  the  structure  is  without  a  tie-rod  or  a  true  three-hinged  arch. 

Table  XIX.    Three-hinged  Arch.     Chord-Stresses 

Thousand  pounds 


Snow  on 

Snow  on 

Wind 

Wind 

Max.  stresses     | 

Member, 

Dead 
load, 

left  of 

right  of 

Snow 
over  all 

on  left 
of 

on  right 
of 

Fig.  61 

Fig.  61a 

crown, 
Fig.  6lB 

crown, 
Fig.  61c 

the  roof 

crown. 
Fig.  6lF 

crown,* 
Fig.  61c 

Ten 
sioi 

Com- 
i      pression 

3-14 

+  25.2 

+  6.1 

-2.1 

+    4.0 

+25.6 

-  2.6 

50.8 

3-16 

-    6.3 

-  7.0 

—  14.0 

—  21.0 

+32.8 

-17.4 

30. 

7          26.5 

3-18 

-  18.7 

-13.2 

-21.4 

-  34.6 

+42.6 

-26.5 

58. 

i         23.9 

3-20 

—  190 

-13.9 

-22.8 

-  36.7 

+45.8 

-28.3 

61. 

2          26.8 

4-22 

-  22.4 

-15. 5 

-28.0 

-  43.5 

+58.7 

-34.7 

72. ( 

3          36.3 

5-24 

-  26.8 

-15.8 

-35.1 

-  50.9 

+73.8 

-43.5 

86. 

[         47-0 

6-26 

-  26.6 

—  II. 2 

-41.0 

—  42.2 

+85.3 

-50.8 

88. ( 

i          58. 7 

7-28 

—  22.0 

-3.9 

-44.6 

-  48.5 

+90.7 

-55.3 

81. 

2         68.7 

8-30 

-  13.3 

+  7.8 

-44.8 

-  37.0 

+89.6 

-55.6 

68. c 

)          76.3 

9-32 

-    3.7 

-1-20.2 

-41.7 

-  21. 5 

+81.9 

-51.7 

55.^ 

i          78.2 

10-34 

+    6.4 

+30.0 

-33.5 

-     3.5 

+67.2 

-41.5 

35. 

[          73.6 

11-36 

+  14.3 

+30.0 

—20.6 

+    9.4 

+47.2 

-25.5 

II.- 

2         61. 5 

12-38 

+  18.7 

+19.3 

-  2.8 

+  16. 5 

+23.3 

-  3.5 

42.0 

13-39 

-f  21.8 

H-22.6 

-  3.3 

+  19-3 

+27.8 

-  4.1 

49.6 

1-39 

+  18.8 

-    5.4 

+21.9 

+  16.5 

-  6.7 

+27.2 

46.0 

1-37 

-1-  22.1 

-14.3 

+37.8 

+  23.5 

-31.6 

+46.9 

9.. 

)         69.0 

I-3S 

+  33.3 

-II. 3 

+51 .9 

+  40.6 

-53.2 

+66.0 

19-^ 

)         99.3 

1-33 

+  47.7 

+  2.1 

+61.0 

+  63.1 

-69.5 

+75.6 

21. { 

i        125.4 

1-31 

+  63.0 

-I-18.1 

+64.8 

+  82.9 

-78.3 

+80.4 

15.. 

I        161. 5 

1-29 

+  18.4 

+31. 5 

+65.1 

+  96.6 

-80.1 

+80.7 

61.' 

1        130.6 

1-27 

+  90.3 

+41  I 

+61.8 

+102.9 

-75.0 

+76.6 

208.0 

I-2S 

+  98.7 

+45.7 

+55.8 

+101. 5 

-62.8 

+69.2 

213.6 

x-23 

'-^-102. 6 

-^46.0 

+48.5 

+  94.5 

-46.3 

+60.1 

208.7 

1-2 1 

-I-101.8 

+42.9 

.  +40.0 

+  82.9 

—26.0 

+49.6 

194.3 

I-I9 

+102.3 

+42.3 

+37.9 

+  80.2 

-20.3 

+47.0 

191. 6 

1-17 

+  86.7 

+34.8 

+29.3 

+  67.7 

-  9.6 

+36.3 

157.8 

l-IS 

+  59-5 

-t-22.4 

+16.2 

+  38.6 

+  3.9 

+20.1 

102.0 

I-I4 

+  77-4 

+29,2 

+21.0 

+  50.2 

+  5.2 

+26.0 

132.6 

By  proportion,  18  600  :  15  000. 


Tie-Rod  and  no  Rollers.  If  the  rollers  are  omitted  and  a  tie-rod  is  used, 
the  stress  in  the  tie-rod  and  the  reactions  are  indeterminate.  They  depend  upon 
the  relative  rigidities  of  the  tie-rod  and  the  material  composing  the  supports. 
If  the  tie-rod  is  made  very  heavy  so  that  its  stretch  will  be  very  small  whea 


1128 


Stresses  in  Roof-Trusses 


Chap.  27 


stre.ssed,  the  stresses  in  all  members  of  the  structure  may  be  taken  the  same  as 
found  for  the  condition  where  rollers  are  used,  and  the  horizontal  component  of 
the  wind-load  equally  divided  between  the  supports. 


iM.M   .i.,     .         Table  XX.     Three-hinged  Arch.     Web-Stresses 
5io<-iqj.»«  v'f!i'  Thousand  pounds 


Snow  on 

Snow  on 

Wind 

Wind 

Max.  stresses 

Member, 
Fig.  61 

Dead 

load, 

Fig.GlA 

.  left  of 
crown, 
Fig.eiB 

right  of 
crown. 
Fig.  61C 

Snow 
over  all 
the  roof 

on  left 

of 
crown. 
Fig.  61f 

on  right 

of 
crown,* 
Fig.  61c 

Ten-, 
sibii 

Com- 
pression 

39-38 

-  4.9 

-  3.8 

+  2.1 

-  1.7 

-13-7 

+  2.6 

16. 5 

36-37 

+10.4 

+  0.3 

+14.5 

+14.8 

-18. 5 

+18.0 

8.1 

28^7 

34-35 

+14.5 

+  8.3 

+13.0 

+21.3 

-18.6" 

+16. 1 

4.1 

38.9 

32-33 

+17.8 

+12.7 

+10.6 

+23.3 

-15.4 

+13. 1 

43.6 

30-31 

+19-7 

+13.8 

+  7.6 

+21.4 

-10.7 

+  9.4 

42.9 

28-29 

+20.3 

+12.3 

+  4.7 

+17.0 

-  4-9 

+  5.8 

38.4 

26-27 

+18.7 

+  9.3 

+  1.2 

+10.5 

+  3.4 

+  1.5 

29.5 

24-25 

+15.3 

+  5.4 

-  1.8 

+  3.6 

+10.8 

—  2.2 

26.1 

22-23 

+10.2 

+  1.5 

-  S-i 

-  3.6 

+19.0 

-  6.3 

29.2 

20-21 

+  9-9 

+  3.5 

+  2.0 

+  5.5 

+  2.4 

+  2.5 

15.9 

18-19 

-  0.7 

-  9-3 

-  2.7 

—  12.0 

+  6.6 

-  3.3 

13.3 

5.9 

16-17 

-13.6 

-  6.8 

-  8.1 

-14.9 

+10.9 

-10. 0 

30.4 

14-IS 

-42.3 

-15.9 

-II. 4 

-27.3 

+  2.8 

-14. 1 

72.3 

37-38 

-  7.1 

+11. 2 

—22.0 

—  10.8 

+29.8 

-27.3 

23.2 

22.7 

35-36 

-12.9 

-  3-5 

-16.3 

-198 

+24.9 

—20.2 

36.6 

12.0 

33-34 

-16.8 

-IS. 8 

-10.4 

-26.2 

+18.8 

-12.9 

45. 5 

2.0 

31-32 

-17  9 

-19.2 

-  4.2 

-23.4 

+10.0 

-  5.2 

42.3 

29-30 

-17.9 

-17.0 

+  0.6 

—  16.4 

+  1.4 

+  0.7 

34.9 

27-28 

-14. 1 

-11.6 

+  5.0 

-  6.6 

-  7.4 

+  6.2 

25.7 

25-26 

-  9-4 

-  5.3 

+  8.7 

+  3.4 

-17.0 

+10.8 

26.4 

1.4 

23-24 

-  4.7 

+  0.4 

+11. 0 

+11. 4 

-23.3 

+13.6 

28.0 

9-3 

21-22 

+  3.0 

+  5.2 

+13. 1. 

+18.3 

-29.5 

+16.2 

26.5 

24.4 

19-20 

+  0.8 

+  1.6 

+  3.1 

+  4.7 

—  7.4 

+  3.8 

6.6 

6.2 

17-18 

+18. 5 

+  9.2 

+10  9 

+20.1 

-14.8 

+13.5 

41.2 

15-16 

+36.3 

+16.8 

+17.8 

+34.6 

-19-1 

+22.1 

75.2 

j  *  By  proportion,  18  600  :  15  000.  i 

j  Changes  in  Temperature  do  not  seriously  affect  the  stresses  in  the  members' 
of  a  TRUE  THREE-HINGED  ARCH,  or  one  with  a  tie-rod  and  rollers  at  one  end,j 
as  the  change  in  geometrical  shape  is  quite  small.  For  the  arch  with  a  tie-rod i 
and  no  rollers,  the  effect  of  changes  in  temperature  may  affect  the  supporting' 
forces  if  the  tie-rod  is  not  so  protected  that  it  will  change  but  little  from  its 
average  temperature.  In  most  structures  this  is  the  case  as  the  tie-rod  is  iii  or 
under  the  floor  of  the  building. 

The  Two-hinged  Arch  differs  essentially  in  construction  from  the  three- 
Hinged  ARCH  in  having  only  two  pins  or  hinges  which  are  placed  at  the  supports.; 
Fig.  62  shows  the  form  of  truss  which  will  be  used  in  explaining  the  method  for- 
finding  the  stresses  in  the  members  of  the  truss. 

Supporting  Forces.  The  supporting  forces  are  inclined  but  can  be  re- 
solved into  vertical  and  horizontal  components.  The  vertical  components  are 
readily  found  as  they  are  the  same  as  for  a  simple  truss  on  two  supports.  The 
horizontal  components  depend  upon  the  areas  of  the  members  and  their  modul^ 
OF  elasticity  when  the  dimensions  of  the  truss  and  the  loading  are  known.    '  •• 


Trussed  Arches 


1129 


Horizontal  Thrust  for  Vertical  Loads. 


-■=XS-2 


This  can  be  found  from  the  formula 

AE 

where  the  symbols  have  the  significance  given  on  page  1086.  But  this  contains 
the  unknown  area  A  for  each  piece.  For  a  preliminary  trial  the  procedure  is  as 
follows:  In  the  truss  shown  in  Fig.  62,  divide  the  span  into  twenty  equal  parts 
and  at  the  centers  of  the  divisions  erect  verticals.  Through  the  points  on  these 
verticals,  midway  between  the  chords  of  the  truss,  draw  a  smooth  curve  as  shown. 
This  line  will  be  designated  the  axis  of  the  arch.    Number  the  points  desig- 


Mi. 


%s 


^£ 


'c?"!^ 


13  /> 


''^ 


v-^SS 


k--9.9- 


^^  _^ tfl  -^JlI.  _^^  _5_&i-^  _  1^ 


24 


25 


-r'TF 


1  I 


Fig.  62.    Two-hinged  Arch.    Truss-diagram 


L_^-. 


nated  above,  i,  2,  3,  etc.,  as  shown  in  Fig.  62,  and  let  x  and  y  be  their  coordi- 
nates with  the  left  support  as  the  origin.  Scale  the  length  of  the  curve  between 
the  centers  of  the  divisions  so  that  y  is  practically  the  ordinate  of  the  center  of 
the  short  length  of  curve,  and  call  this  length  of  the  curve  5^.  On  a  radial  line 
at  each  point  numbered  i,  2,  3,  etc.,  scale  the  distances  between  the  upper  and 
lower  chords,  calling  the  distance  h  and  compute  V2  h^=  I,  which  expresses, 
approximately,  the  moment  of  inertia  of  the  section  when  the  chord-areas 
are  unity  and  the  web-members  are  neglected.  Let  M  represent  the  bending 
MOMENT  at  any  point  having  the  abscissa  x,  of  the  loads,  considering  the  truss  as 
a  simple  beam  on  two  supports;  or,  for  a  single  load  P,  M  =  Rx—  P  (x—  a), 
X  being  greater  than  a,  where  a  is  the  distance  of  the  load  P  from  the  left  sup- 
port. Then  if  5.9  -^  EI  is  represented  by  <}>  the  horizontal  thrust  can  be  found 
from  the  formula, 


1130 


Stresses  in  Roof-Trusses 


Chap.  27 


For  the  vertical  loading  shown  in  Fig.  62,  the  value  of  Hi  is  io8  ooo  lb,  and  Vu 

being  one-half  the  total  load,  is  195  000  lb.  The  stresses  in  the  members  of  the 
truss  can  now  be  found  by  the  usual  graphical  method.  The  snow-load,  if  any, 
must  be  treated  in  a  Hke  manner.  The  computations  are  considerably  shorter, 
since  2y20  remains  unchanged,  regardless  of  the  loading. 

Wind-Loads.  For  wind-loads  the  process  is  not  changed  very  much.  The 
value  of  M  is  the  moment  of  the  wind-loads,  assuming  the  truss  as  hinged  at 
the  right  support  and  on  rollers  at  the  left  support.  The  value  of  Vi,  which  is 
vertical,  is  found  by  taking  the  sum  of  the  moments  of  the  wind-loads  about 
the  hinge  at  the  right  support  and  dividing  this  by  the  length  of  the  span. 
The  value  of  Hi  is  found  from  the  formula  given  above,  and  then  the  stresses 
are  found  by  the  ordinary  stress-diagram.  The  maximum  stresses  are  now  found 
and  the  proper  areas  of  the  members  determined. 

The  True  Horizontal  Thrust.  The  method  just  given  is  a  close  approxi- 
mation to  determine  the  areas  of  the  pieces  so  that  the  correct  formula  for  Hi 
can  be  applied.    This  formula  is 

SSid      ^  uH 
AE^'MAE 

where  the  symbols  have  the  meaning  already  given.  Applying  this  formula 
for  the  dead  load  shown  in  Fig.  62  and  areas  shown  in  Fig.  58,  the  value  of  //j 

is  no  600  lb,  which  is  but 
httle  different  from  the  value 
found  by  the  approximate 
method. 

Dead-Load  Stresses.  The 
stress-diagram  for  the  dead 
LOAD  is  shown  in  Fig.  62a. 
Considerable  care  must  be 
exercised  in  drawing  the  stress- 
diagrams,  and  their  correct- 
ness should  be  checked  by 
computing  the  stresses  in  one 
or  more  pieces.  Compare  Fig. 
62a  with  Fig.  58a. 

Changes  in  Temperature. 
Unlike  the  three-hinged  arch 

the       TWO-HINGED       ARCH       is 


Fig.  62a.    Two-hinged  Arch.     Stress-diagram 


affected  by  changes  in  temperature  an4  the  stresses  which  are  produced  by 
such  changes  must  be  provided  for.  Vi=  O  and  ^1  is  determined  from  the 
formula 

where  e  is  the  coefficient  of  expansion  for  the  material  composing  the  truss, 
t°  the  number  of  degrees  change  in  temperature  and  L  the  span  of  the  truss. 
The  other  symbols  have  the  significance  already  given.  The  above  formula 
assumes  that  the  truss-members  are  of  the  same  kind  of  material.  After  Hi 
has  been  found,  the  stresses  can  be  determined  by  constructing  the  stress-dia- 
gram which  will  be  of  the  shape  shown  in  Fig  58b. 

Tie-Rod.  If  a  tie-rod  connects  the  two  supports  of  a  two-hinged  arch 
the  remarks  made  concerning  such  an  arrangement  for  the  three-hinged 
arch  apply  here. 


Trussed  Arches 


1131 


The  Fixed  Arch  has  no  hinges  and  is  a  type  which  is  seldom  employed  by 
architects  in  the  truss-form.  The  rigid  analysis  of  a  trussed  fixed  arch  is 
very  long  and  tedious,  so  a  few  formulas  will  be  given,  necessary  for  the  solution 
of  ARCHES  WITH  SOLID  WEBS,  sucli  as  PLATE-GIRDER  ARCHES.  These  formulas 
may  be  applied  to  truss-forms,  where  the  chords  are  approximately  parallel, 
without  serious  error.  Midway  between  the  top  and  bottom  chords  draw  a 
smooth  curve,  called  the  arch-axis,  and  designate  the  distance  between  its  ends 
as  L  or  the  span  of  the  axis.  Divide  the  span  into  n  equal  parts  and  at  the 
centers  of  these  divisions  draw  perpendiculars  until  they  cut  the  arch-axis. 


C.L. 


Fig.  63.     Fixed  Arch.     Truss-diagram 


Number  the  points  i,  2,  3,  etc.,  as  shown  by  Fig.  63,  which  also  indicates  the 
nomenclature  employed. 

Determination  of  Hu  Vi  and  Hiifi.  The  equilibrium-polygon  for  a  single 
inchned  load  is  shown  in  Fig.  63,  in  its  true  position  with  reference  to  the  arch- 
axis.  This  locates  the  point  of  application  of  Ih.  The  following  formulas  are 
very  close  approximations  for  arches  having  a  rise  greater  than  one-eighth  the 
span. 

Hi  =  ZmxyA"  ^  XyA" 

'  XK  j 
XyK        (  "EniryK       l^mxyK{z  —  n) 


..{: 


E%yi 


Hi 


XK 


Vi  = 


Hiy2  —  //2J/2 


ZK 


+  ri 


S/i 


Hi 


yi  is  measured  down  from  A  when  Hiyi  is  negative.  S  is  the  sum  of  quantities 
lit  governs  for  each  point  on  the  arch-axis  numbered  i,  2,  3,  .  .  .  «.  For 
'example 


-(i),-(i).-(i), 


-hetc. 


1132 


Stresses  in  Roof-Trusses 


Chap.  27 


/  is  the  moment  of  inertia  of  the  chords  about  an  axis  midway  between  them. 

The  sections  of  the  chords  are  to  be  taken  on  radial  lines  passing  through  points  i, 

2,  3,  etc.  X  and  y  are  the  coordinates  of 
the  points  i,  2,  3,  etc,  in  Fig.  63 

dx  L 

x  =  z—  =  z  — 
2  2n 

mxy  is  the  moment  at  the  point  on  the 
arch-axis  having  the  coordinates  xy  assum- 
ing that  the  given  loading  is  supported  by 
the  axis  hinged  at  the  right  end  and  on 
rollers  at  the  left  end.  n  is  the  reaction 
at  the  left  support  under  the  conditions 
specified  for  mxy.  In  the  above  formulas 
the  only  terms  which  depend  upon  the 
loading  are  those  containing  mxy  and  ri, 
the  others  being  constant  for  any  given 
arch.  While  but  one  load  has  been  used, 
any  number  may  be  used  by  considering 
mxy  and  r\  as  the  sum  of  the  respective 
quantities  for  each  load. 

Stresses.     The  stresses  in  the  truss- 
members  can  be  found  by  the  ordinary 
graphical  methods  when  //i,   Fi  and  Hyi 
are   known.     For    example,    assume   the 
numerical  values  shown  in  Fig.  64.     The 
resultant  of   Vi  and  Hi  is  resolved  into 
two  components  parallel  and  perpendic- 
ular  to   the    bottom-chord    member    at 
the  support.    Then  T  must  act  at  the 
upper-chord  joint  as  shown.     The  two  reactions  parallel  to  the  bottom  chord 
are  found  by  moments.     The  stress-diagram  can  now  be  drawn  beginning  with 
these  forces  and  proceeding  until  the  right  support  is  reached. 

Symmetrical  Loading.     When  the  loading  is  symmetrical,  Hiyi  = 
hence  Fi  =fi.     Also 


Fig.  64.     Fixed  Arch.     Reactions 


=n2i/t    and 


-Hi 


XK 


XK 


Changes  of  Temperattire.    For  temperature-changes, 
Ht  =  e/°L  -^  XyA" 

Hxyi  =  Hiyi  =  Ht  -^^ 


yi  = 


HyK 


F,  =0 


10.  Arches  with  Solid  Ribs 

■  \\ 

Arches  with  Solid  Ribs.    While  this  chapter  considers  trusses  only,  ifc 

may  not  be  out  of  place  to  briefly  consider  arches  having  solid  ribs.     The 

computations  for  Vi,  Hi  and  Hiyi  remain  unchanged,  excepting  that  /  now  is 

the  moment  of  mertia  of  the  radial  section  of  the  rib  at  points  i,  2,  3,  etc. 


Arches  with  Solid  Ribs  1133 

Fiber-Stresses.  If  x  and  y  are  the  coordinates  of  any  point  on  the  gravity- 
axis  of  the  rib,  which  should  coincide  with  the  arch-axis,  the  bending  moment 
at  this  point  is,  for  each  load, 

Mx  =  Ihyx  +  Vxx  -  Thy  -P{pc-a)-Q{y  -  b) 

Ihyi  is  negative  when  y\  is  measured  below  A  in  Fig.  64. 

Mxyc    ,  Nxy 
^  -~I~  '^   A 

where  c  is  the  distance  from  the  gravity-axis  to  the  outermost  fiber.  For  the 
TWO  and  three-hinged  arches,  Hiyi  =o. 

Radial  Shear.  Let  Hx  be  the  algebraic  sum  of  all  the  horizontal  components 
on  the  left  of  the  section,  Vx  the  algebraic  sum  of  all  the  vertical  components 
on  the  left  of  the  section  and  6  the  angle  which  the  radial  section,  upon  which 
the  shear  is  wanted,  makes  with  the  vertical.    Then  Tx  =  Vx  cos  6  —  Hx  sin  0. 

Two-hinged  Parabolic  Arch.  If  the  center  line  of  the  solid  rib  is  a  par- 
abola, when  EI  cos  0  is  a  constant,  the  following  simple  formulas  give  the 
values  of  Vi  and  Hi'. 


o  '. 
V  11 


F.  =  P(i-i)-Q^*(i-A)  .o,uinor,ri, 


and 


Hx  =  %-P[k{i-2k^  +  k')]-Q  1 1 -^[5(1 -^-2^  +  4^3) -8H 


in  which  k  =  a^  L  (Fig.  63),  /  is  the  rise  of  the  axis,  P  is  the  vertical  load  acting 
down,  Q  is  the  horizontal  load  acting  from  left  to  right  and  h  is  the  moment  of 
inertia  of  the  section  of  the  rib  at  the  crown. 

Fixed  Parabolic  Arch.  In  like  manner  the  following  formulas  apply  for 
the  arch  without  hinges: 

V=P{l-kY{^-\-2k)-^Q{k-  ^2)2 
Hi  =  — ^  P)^2  (l  -  i^)'  -  Q  {  I  +  ^U  -  15  +  50  ^  -  60  ^2  +  24  ^3)  I 

Hiyx  ==-  Pk  {i  -  k)H5k-  2)  -fQ\  2  k  {1  -  k)H2  -  7  k^Sk^)] 
2 

Ht=^.EI,et''         Htyx=  —.El^ef 
AJ  27 

The  values  of  the  factors  containing  k  in  the  above  formulas  are  given  in  tabular 
form  in  A  Treatise  on  Arches.* 

Circular  Arches,  with  solid  ribs  of  constant  cross-section  and  the  center  line 
an  arc  of  a  circle,  may  be  considered  by  using  formulas  somewhat  similar  to 
those  given  for  parabolic  arches  but  very  much  longer  and  more  complex. 
Formulas  and  tables  for  their  solution  are  given  in  the  treatise  on  arches  referred 
to  above. 

♦  A  Treatise  on  Arches,  by  Malverd  A.  Howe,  John  Wiley  &  Sons,  Inc.,  New  York. 


1134 


Stresses  in  Roof-Trusses 


Chap.  27 


11.  Influence-Lines  for  Simple  Beams  and  Trusses 

An  Influence-Line  is  a  line  showing  the  variation  in  any  function  at  anj 
section  of  a  beam  or  for  any  member  of  a  truss,  caused  by  a  single  load  moving 
across  the  span.    For  convenience  the  load  is  usually  considered  as  unity. 


A 

P 

Q 

B 

Ri' 

H 

X — 

>: 

a 

•           \d 

CL 

1^ 

-^^ 

t 

uior!  ^^^„,„— . 

Fig.  65.    Influence-lines.     Reactions  for  Beams 

Reaction  for  a  Single  Load.  If  the  load  P,  Fig.  65,  moves  from  A  towards 
B,  the  left  reaction,  when  P  is  distant  x  from  B,  is  expressed  algebraically  b> 
Ri=  Px-7-  L,  which  is  an  equation  of  a  straight  Hne.  If  x  =  o,  Ri=  o,  and 
ii  X  =  L,  Ri  =  P.  If  we  make  ac  =  P  and  draw  the  two  straight  lines  ab  and  cb 
the  ordinate  de  immediately  below  P  is  the  value  of  Ri  for  this  position  of  P 
11  ac=  unity,  then  Ri  =  P  {de). 


R  R,  P^ 

A     0     Q     Q 


4 


Fig.  66.     Influence-lines.    Reactions  for  Beams 


|< a '->H-  -^^-' — . S^ —>-»->] 

Fig.  67.     Influence-lines.    Moments  for  Beams 


:    Reaction  for  More  than  One  Load.    The   reaction  for  any  number  ol 

^ncentrated  loads  can  be  found  as  shown  in  Fig.  66. 

The  moment  at  C,  Fig.  67,  when  F 

.  (a)  jb] 
L 


Bending  Moment  for  a  Single  Load. 
Pxa 
<s  on  the  right  of  C,  is  M  =  R^a  =  — .    When  the  load  is  at  C,  il/  = 


Influence-Lines  for  Simple  Beams  and  Trusses 


1135 


and  when  at  5,  M  =  o.    For  all  positions  of  P  upon  the  left  of  C,  if  =  Rih 
^  ^  (L-^^    When  P  is  at  A,  M  =  o,  and  when  at  C,  M=P^^""^^^ 


L 

,  (a)  (b) 


If  in  Fig.  67  the  figure  mng  is  drawn  with  fg  =  — - — ,  then  the 


L     '    "'°'  "  °~" °  ""^         L 

moment  at  C  for  any  load  in  any  position  is  P  (de). 

Bending   Moment  for  Any   Number   of    Concentrated   Loads.     The 
moment  at  the  point  C  for  the  loading  shown  in  Fig.  68  is^^  =  JPi,a^,+  .^2aa   < 

Q   Q O 


j^ a >\< -6, -»J 

Fig.  68.     Influence-lines.     Moments  for  Beams 


+  Pads  +  P^idi.  This  gives  the  moment  at  C  for  a  given  position  of  the  loads, 
but  this  is  not  necessarily  the  greatest  moment  which  these  loads  may  cause, 
as  some  other  position  may  cause  a  greater  moment.  The  greatest  moment  at 
C  will  obtain  when  some  concentration  is  at  C.     Let  P  be  this  concentration  and 


^ a -^ — b 

Fig.  69.    Influence-lines.     Moments  for  Trusses 

assume  it  to  be  divided  into  two  parts,  nP  and  mP  so  that  n-\-,m=  i,  and  n  is 
greater  than  zero  and  less  than  i.     The  maximum  moment  at  C  will  occur  when 

Pi  +  P2  +  P3-fP4     Px  +  nPi  ■ 


The  point  in  the  beam  where  any  given  moving  load  causes  the  greatest 
POSSIBLE  MOMENT  is  SO  situated  that  the  middle  of  the  span  is  half-way  between 
it  and  the  center  of  gravity  of  the  load..  Since  a  concentration  will  always  be 
at  the  point,  a  few  trials  will  determine  the  proper  concentration  to  use.  For 
example,  two  equal  concentrated  loads  should  be  placed  on  the  beam  so  that 


1136 


Stresses  in  Roof-Trusses 


Chap.  27 


the  middle  of  the  span  is  at  the  quarter-point  between  the  concentrations.  The 
MAXIMUM  MOMENT  falls  Under  the  concentration  nearer  the  middle  of  the  span. 

Chord- Member  in  Truss  with  One  Set  of  Web-Members  Vertical.  In 
Fig.  69  the  top  chord  member  UiUz  has  its  center  of  moments  at  L2  and  the 
bottom  chord  member  X1L2  at  Ui.  The  influence-diagram  for  the  moments 
at  L2  and  U2  is  precisely  the  same  as  shown  in  Fig.  67.  The  moment  produced 
by  any  load  P  is  P  {de).  As  long  as  one  set  of  web-members  is  vertical  the 
INFLUENCE-DIAGRAM  wifl  be  identical  with  that  shown  in  Fig.  69,  regardless 
of  the  inclination  of  the  diagonals  or  the  chord-members. 

Chord-Members  in  Truss  with  Inclined  Web-Members.  The  moments 
at  points  in  the  loaded  chord,  Fig.  70,  have  influence-diagrams  identical  with 


C    Uo 


^ 5 ^ 

Fig,  70.     Influence-lineg.    Moments  for  Trusses 
2  Us    I     Va 


Ui 


Ur. 


Ill  > 


Fig.  71.    Influence-lines.    Shear  for  Trusses 


that  shown  by  Fig.  69.  For  the  unloaded  chord  a  slight  modification  must  be 
made.  For  example  let  U2  be  a  center  of  moments,  then  if  the  loads  were  on  a 
beam,  mgn  would  be  the  influence-diagram  (Fig.  70).  For  all  loads  on  the 
left  of  Li  and  on  the  right  of  Li  the  diagram  is  correct  and  the  moments  at  f/2 
=  Pi^i  and  Piaz.  For  loads  between  Li  and  Li  draw  the  line  rs.  The  moment 
at  /72  is  P2a2. 

Web-Members  of  Trusses  with  Parallel  Chords.    Fig.  71.    The  stress 
in  UiLz  equals  the  shear  in  the  panel  LiLz  multiplied  by  the  secant  of  Q»    The 


Secondary  Stresses  in  Truss-Members  1137 

INFLUENCE -DIAGRAM  will  be  drawn  for  the  shear.  For  any  load  between  L3 
and  B,  the  shear  in  this  panel  equals  R2',  hence,  with  ah  as  a  reference-line,  ha' 
is  the  INFLUENCE-LINE  for  i?2  and  the  shear  is  Pia.u  Psas,  etc.,  until  the  point  L3 
is  reached.  In  Hke  manner  af  is  the  influence-line  for  Ri  and  the  shear  for 
loads  on  the  left  of  Z2  is  Pia\.  The  shear  for  the  loads  P2  between  L2  and  L3 
is  Rx  less  the  amount  of  P2  which  is  transferred  to  L2.  The  influence-diagram 
for  the  reactions  of  P2  on  a  span  L2L3  is  ff'e.  The  shear  in  this  panel  due  to  P2 
is  P2{dd')  less  P2  (d'c)  or  ^2^2-     A  load  at  k  produces  no  shear  in  the  panel. 

12.  Secondary  Stresses  in  Truss-Members  * 

Secondary  Stresses.  In  the  determination  of  stresses  in  a  truss  it  is 
usually  assumed  that  they  act  along  the  gravity-axis  of  each  member;  that 
the  gravity-axes  of  all  members  at  any  joint  meet  at  a  common  point;  that 
the  members  are  free  to  turn  around  this  point,  the  joints  being  considered 
frictionless;  and  that  all  loads,  including  the  weights  of  the  members,  are 
applied  at  the  joints  only.  The  stresses  determined  with  these  assumptions 
are  axial  or  direct  stresses,  sometimes  called  primary  stresses  or  main  stresses. 
The  assumptions  made  are  not  realized  in  practice  and  other  stresses,  called 
secondary  stresses,  are  induced.  An  eccentricity  causing  bending  moment 
occurs  in  the  common  case  of  the  rivet-line  not  coinciding  with  the  gravity- 
axis  where  angles  connected  with  one  leg  only  are  used  to  resist  direct  stress. 
If  the  gravity-axes  of  members  about  a  joint  do  not  intersect  at  the  same  point 
bending  moments  are  induced.  The  resistance  of  a  joint  to  free  angular  move- 
ment as  the  truss  deflects  also  induces  bending  moments.  The  weights  of 
horizontal  and  inclined  members  add  slight  bending-stresses  to  the  direct 
stresses  in  these  members.  At  the  supports  there  will  be  a  resistance  to  hori- 
zontal deformation  from  temperature-changes  and  the  deflection  of  the  truss. 
The  degree  of  this  resistance  depends  upon  the  coefiicient  of  friction  between 
the  truss  and  the  support,  the  vertical  loads  and  the  length  of  span.  Members 
not  straight  and  imperfect  workmanship  are  other  causes  of  secondary  stresses. 
:With  care  in  the  design  and  fabrication  secondary  stresses  in  ordinary  roof-trusses 
from  the  above  causes^  need  not  be  considered  seriously.  The  main  causes, 
'however,  of  secondary  stresses  are  faulty  details.  The  actual  shearing- 
stress  sometimes  found  in  details  is  much  more  than  the  direct  shearing-stress, 
because  of  eccentricity  in  the  lines  of  stress-action.  Eccentric  riveted 
connections  may  not  be  wholly  avoided  but  they  should  be  reduced  to  a  mini- 
mum. The  history  of  bridge  and  building-failures  is  mostly  a  story  of  faulty 
details.  A  structure  has  seldom  given  way  for  lack  of  strength  in  the  main 
members.  But  if  the  strength  of  a  structure  is  measured  by  the  strength  of 
its  weakest  part,  it  can  be  only  as  strong  as  the  weakest  detail.  Because  of 
this,  connections  that  induce  large  secondary  stresses,  insufficient  lacing  of 
compression-members  and  careless  grouping  of  rivets,  have  all  invited  disaster. 
The  importance  of  the  detailer's  work  is  often  underrated.  What  is  usually 
considered  the  designing  of  a  structure  may  be  comparatively  easy  while  the 
detailing  may  be  difficult.  A  well-designed  structure  may  be  spoiled  by 
poor  detaiUng.  The  detailer  should  be  a  designer,  that  is,  a  designer  of  details, 
and  at  the  same  time  the  designer  should  be  thoroughly  familiar  with  detaihng. 

♦  From  Notes  by  Robins  Fleming. 


1138 


Design  and  Construction  of  Roof-Trusses 


Chap.  28 


CHAPTER  XXVIII 

DESIGN  AND  CONSTRUCTION   OF  ROOF-TRUSSES 

By 
MALVERD  A.  HOWE 

PROFESSOR  EMERITUS  OF  CIVIL  ENGINEERING,  ROSE  POLYTECHNIC  INSTITUTE 

1.   Design  of  Wooden  Trusses 

Proportioning  the  Members.  In  Chapter  XXVII  it  has  been  shown  how 
the  STRESSES  in  the  members  of  a  truss,  supporting  known  loads,  may  be  found. 
The  next  step  is  to  proportion  the  members  for  the  stresses  which  they  have 
to  resist.  The  methods  employed  and  the  allowable  unit  stresses  are  given 
in  detail  in  Chapters  XI  to  XVI,  inclusive.  For  example,  tension-members  are 
considered  on  pages  385  to  400;  steel  strut-beams  and  tie-beams  on  pages  571 
and  572;  and  wooden  strut-beams  and  tie-beams  on  page  633.  As  a  matter 
of  convenience  the  unit  stresses  used  in  this  chapter  are  given  in  the  following 
table  in  a  condensed  form.     White  pine  is  here  used  for  the  wooden  trusses. 

Table  I.     Allowable  Unit  Stresses  Used  in  Truss-Design  * 


Material 

Kind  of  stress 

Safe  unit  stress 
lb  per  sq  in 

White  pine 

Tension  with  the  grain 

700 

50 

I  100 

200 

200 

I  100 

100 

500 

700  J 

12  000 

7SOO 

15  000 

15  000 

16  000 
10  000 
20  000 

?4  000 

16  000 

10  000 

Tension  across  the  grain 

Compression  on  end-fibers        .         

Compression  across  the  grain 

Compression  across  the  grain,  round  pins. . 
Columnsf  under  15  diam  long 

Shear  with  the  .grain 

Shear  across  the  grain 

Transverse,  fiber-stress 

Wrought  iron 

Rolled  steel 



Bolts  in  bearing                              

Rods  in  tension 

Bolts  in  shear 

Bolts  in  bearing                                  

Bolts  in  bending,  fiber-stress 

Beams  in  bending,  fiber-stress 

Beams  in  shear 

♦  See  also,  the  tables  on  pages  376,  412,  449,  454,  557.  647  and  1200.  These  must  be 
modified,  when  necessary,  to  comply  with  building  laws.  White  pine  is  used  for  the 
examples  in  this  chapter  because  of  the  difficulties  in  making  the  joints  owing  to  the  rel- 
ative softness  of  the  wood.  If  one  can  design  a  truss  in  white  pine  he  will  have  no  trouble 
with  the  design  of  trusses  constructed  with  other  kinds  of  wood. 

t  See,  also,  Table  I,  page  449,  and  Table  XVI,  page  647- 

tThe  Borough  of  Manhattan,  New  York,  Building  Code  (1917),  gives  i  200  for  this 
value.     Other  values  are  about  the  same  as  in  the  table. 

Inclined  Surfaces  of  Wood.  The  normal  intensity  of  the  stress  on  inclined 
surfaces  may  be  found  from  the  empirical  formula 

r  =q+{P  -  q){0/^oy 


Design  of  Wooden  Trusses 


1139 


where  r  equals  the  permissible  normal  unit  stress  on  this  inclined  surface,  q 
that  across  the  fibers,  p  that  on  the  end  of  the  fibers  and  Q  the  angle  the  inclined 
surface  makes  with  the  direction  of  the  grain.     For  white  pine  this  gives 

r  =  200  4-  ^^9 

Round  Pins  on  End-Fibers.*  For  all  practical  purposes  the  permissible 
unit  stress  may  be  taken  as  the  mean  of  p  and  5;   or,  for  white  pine 

\^  {p-\-  q)  =  650  lb  per  sq  in 

Wooden  Columns  over  Fifteen  Diameters  Long.  The  formula  f  used  in 
this  chapter  and  considered  amply  conservative  by  many  engineers  is  the 
formula  approved  by  the  American  Railway  Engineering  and  Maintenance  of 
Way  Association  in  1907.     For  white  pine  this  formula  is  '^ 

Si  =  S  (i  —  1/60  d)  =  1 100  (i  —  1/60  d) 

where  5,  =  the  permissible  unit  stress,  5  =  the  permissible  compression  on  the 
end-fibers,  I  =  the  length  of  the  column  in  inches  and  d  the  least  dimension  of 
the  cross-section  of  the  column  in  inches. 

Steel  Columns.  For  the  shapes  used  in  roof-trusses,  the  formula  advocated 
by  C.  E.  Fowler  in  bk  specifications  for  roof-trusses  is  used  in  this  chapter: 

Si  =  12  500—  500  l/r 

where  Si  =  the  permissible  unit  stress,  /  =  the  length  of  the  column  in  feet,  and 
r  =  the  least  radius  of  gyration  of  the  cross-section  of  the  column. 

Example  i.  The  truss  shown  in  Fig.  1,  which  is  the  queen  truss  shown  in 
Figs.  3,  12,  53  and  54  in  Chapter  XXVII,  is  considered  for  this  example.  The 
stresses  given  in  tlie  following  table  are  used.  The  members  RR  are  wrought- 
iron  round  rods,  not  upset  at  the  ends;,  and  all  other  members  are  of  white 
pine.  None  of  the  members  in  this  truss  is  subject  to  transverse  stress,  so 
direct  tension  and  compression  onlj'^,  have  to  be  considered: 


Table  II.     Stresses  and  Dimensions  for  the  Truss  Shown  in  Figure  t 


Member 


A 
B. 
C. 
D. 
E. 

N, 
M 

R. 


^  Stress  in  pounds 


+21  250 
-|-i8  900 
-f  13  200 
+  6450 
+  5  100 

-17  150 
-12  750 


Dimensions 


6  by  6-in  white  pine 
6  by  6-in  white  pine 
6  by  6-in  white  pine 
4  by  6-in  white  pine 
4  by  6-in  white  pine 

i6  by  8-in  white  pine  or 
Three  2  by  8-in  pieces  with  %-in  bolts, 
2  ft  on  centers 
One  iH-in  round  rod 


Vertical  Rods,  Fig.  1.  The  tension  in  each  rod  is  9  100  lb.  If  the  permis- 
sible stress  is  12  000  lb,  the  section-area  of  each  rod  is  9  100 -m  2  000  =  0.76  sq  in. 
The  net  area  of  a  iH-'u\  rod  is  0.694  sq  in;  and  of  a  itl-in  rod,  0.893  sq  in.  The 
iH-in  rod  would  answer  but  the  iH-in  rod  is  preferred. 

*  When  the  same  unit  stresses  are  used  for  flat  and  curved  surfaces,  Tables  VII  and 
VlII,  pages  430  to  431,  of  Chapter  XII  may  be  used. 
I  For  other  formulas  and  Tables  based  upon  them,  sec  Chapter  XIV,  pages  449  to  452. 


1140 


Design  and  Construction  of  Roof-Trusses  Chap.  28 


Rafters,  Fig.  1.  The  stress  in  the  rafter  at  A  is  21  250  lb  and  at  B  18  900  lb; 
but  as  it  will  be  made  of  one  piece,  the  size  is  governed  by  the  greater  stress. 
The  unsupported  length  is  about  9  ft,  and  assuming  the  least  dimension  of  the 

(9  X  I2\ 
I  —  - I  =  770  lb  per  sq  in.  21  250/770  = 
60  X  6/ 
27.6  sq  in  =the  area  of  cross-section  required, which  is  less  than  that  of  a  6  by  6-in 
piece.  A  6  by  6-in  timber  is  actually  sV^  by  s'/^-in,  with  a  cross-sectional  area  of 
30.25  sq  in,  a  little  in  excess  of  the  area  required.  In  general  the  nominal  and 
STANDARD  sizcs  of  timbers  differ  by  about  one-half  an  inch  in  each  cross-dimension. 


Fig.  1.    Queen  Truss.     (See,  also,  Figs.  4a,  10,  13  and  16  and  Chapter  XXVII,  Figs. 
3,  12,  53  and  54) 

Member  C,  Fig.  1.  The  stress  in  this  member  is  13  200  lb  and  its  unsupported 
length,  12  ft.  In  this  case  l/d  =  24,  wheni  =  6  in;  Si  =  660  lb  per  sq  in.  The 
required  section-area  is  13  200/660  =  20  sq  in,  and  hence'  a  6  by  6-in  timber  is 
used.  The  top-chord  should  have  one  dimension  constant  in  order  to  facilitate 
the  making  of  good  connections  at  the  joints. 

Braces,  Fig.  1.  The  stress  in  the  brace  Z)  is  6  450  lb  and  its  unsupported 
length  about  9  ft.  A  4  by  6-in  timber  is  first  tried.  Here  l/d  =  27  and  Si  =  605 
lb  per  sq  in.  The  required  area,  therefore,  is  10.7  sq  in  and  a  4  by  4-in  timber 
answers  the  purpose;  but  for  additional  stifTness  and  convenience  in  making  con- 
nections, a  4  by  6-in  piece  is  used.  Each  brace,  E,  has  a  stress  of  5  100  lb  and  a 
total  length  of  17  ft.  If  the  braces  are  bolted  where  they  cross  the  unsupported 
length  may  be  taken  as  8'/^  ft.  It  is  evident  that  a  4  by  6-in  piece  is  ample  for 
each  brace. 

Bottom  Chord,  or  Tie-Beam,  Fig.  1.  The  maximum  tension  in  the  bottom- 
chord  is  17  150  lb  in  N.  The  permissible  unit  stress  is  700  lb  per  sq  in;  hence 
the  net  section-area  required  is  17  150/700=  24.5  sq  in.  A  2  by  12-in  plank,  if 
continuous  from  end  to  end  of  the  truss  and  without  holes  and  notches,  will  take 
care  of  the  stress  alone  but  will  not  permit  of  proper  connections.  A  6  by  6-in 
piece  is  selected,  but  it  may  be  necessary  to  substitute  for  it  a  6  by  8-in  piece 
when  the  connections  are  made  and  it  is  spliced  in  the  middle.  If  the  member 
is  built  up  of  planks,  three  2  by  8-in  pieces  are  required;   and  they  must  be 


Design  of  Wooden  Trusses 


1141 


thoroughly  bolted  together  by  a  pair  of  bolts  every  2  ft  of  their  length.  If  24- 
ft  and  14-ft  lengths  are  used,  the  joints  of  the  strands  will  be  about  10  ft  apart. 
Example  2.  For  this  example  the  truss  illustrated  in  Fig.  2,  which  is  the 
scissors  truss  shown  in  Figs.  4  and  24,  Chapter  XXVII,  is  considered.  The 
direct  stresses  for  dead  load,  wind  and  snow  were  found  in  Chapter  XXVII  and 
are  given  in  the  following  table.    The  rafters  and  the  bottom  chord  support 


Fig.  2.     Scissors  Truss.     (See,  also,  Chapter  XXVII,  Figs.  4  and  24) 


loads  between  the  joints  and  consequently  must  resist  cross-bending  stresses 
as  well  as  direct  stresses.  The  load  on  each  piece  is  given  in  the  table  under 
the  word  transverse. 

Table  III.     Stresses  and  Dimensions  for  the  Truss  Shown  in  Figure  2 


Member 

Stress,  lb 

Transverse 
load. lb 

Dimensions,  white  pine 

A 

B 

D 

-1-8  000 
-h6  6oo 
+1890 
+    750 
-4350 
-2  530 
-1875 
.  -5400 
-1875 

I  000 
I  320 

Two  2  by  8-in  planks 
Two  2  by  8-in  planks 
One  2  by  lo-in  plank 
One  2  by  lo-in  plank 
Two  I  by  8-in  planks 
Two  I  by  8-in  planks 
One  2  by  lo-in  plank 
One  2  by  lo-in  plank 
One  2  by  lo-in  plank 

E 

F 

H 

5 

470 
384 

T 

Ti 

Rafter  B,  Fig.  2.  The  piece  B  rather  than  the  piece  A  is  considered,  as  it  is 
considerably  longer.  The  total  vertical  load  on  the  piece  acting  as  a  beam  is 
I  320  lb  and  the  horizontal  span  is  about  8  ft.    The  bending  moment  at  the  center 


1142  Design  and  Construction  of  Roof-Trusses         Chap.  28 

is  li  (i  320  X  8X  12)  =  15  840  in-lb.  If  the  depth  of  the  piece  is  assumed  to 
be  8  in,  the  proper  thickness  is  found  from  the  equation,  15  840=  H  Sbd^  = 
M  (700  X  8X  8X  fc),  or  h=  2.12  in.  This  neglects  the  component  of  the  ver- 
tical load  parallel  to  the  rafter.  Considering  now  the  direct  compression  of 
6  600  lb  and  remembering  that  the  sheathing  is  nailed  to  the  rafter,  the  least 
dimension  d  of  the  piece  is  it»  depth,  which  may  be  taken  the  same  as  that 
used  for  the  piece  resisting  the  transverse  stress.  The  unsupported  length 
of  the  piece  is  about  12  ft.  Then  l/d  =  18,  ^i  =  770  lb  per  sq  in  and  the  required 
area  of  cross-section  is  6  600/770  =  8.6  sq  in.  As  the  depth  is  8  in,  the  thickness  is 
about  I.I  in.  Combining  the  two  pieces,  the  total  thickness  is  2.12  +1.1  =  3.22 
in,  and  a  piece  having  the  nominal  size  of  4  by  8  in  is  required.  Since  the 
sheathing  is  nailed  to  the  rafters,  two  2  by  8-in  planks  may  be  used  without  de- 
creasing the  stiffness  of  the  member.  While  the  above  method  of  designing  a 
piece  subject  to  two  kinds  of  stress  is  not  correct  for  all  conditions  which 
occur  in  practice,  the  results  are  on  the  safe  side,  and  the  method  has  the  ad- 
vantage of  being  easily  applied. 

Member  S,  Fig.  2.  Considering  the  transverse  load  first,  the  bending  moment 
at  the  middle  is  found  to  be  %  (470  X  15. 5  X  12)  =  10  930  in-lb.  If  the  depth  is 
assumed  to  be  10  in,  the  required  thickness,  found  from  the  equation  10  930 
=  %  (700  X  10  X  10  X  &),  is  0.94  in;  or,  a  board  i  by  10  in  in  cross-sectional  area 
will  carry  the  transverse  load  if  prevented  from  twisting  sidewise,  which  it  has  a 
tendency  to  do  in  this  case  where  the  ceiling  is  attached  directly  to  the  member. 
The  side-stiffness  will  be  further  increased  when  the  additional  material  for 
resisting  the  tension  is  in  place.  The  net  area  for  the  direct  tension  of  i  875  lb 
is  2.68  sq  in,  which  requires  a  board  10  in  wide  and  only  a  trifle  over  \i  in  thick. 
The  total  thickness  becomes  0.94 -|-  0.27  =  1.21  in,  and  it  will  therefore  be  nec- 
essary to  use  a  2  by  lo-in  plank. 

Member  B,  Fig.  2.  This  is  in  compression,  but  the  stress  is  quite  small, 
being  only  750  lb.  The  possible  extension  of  the  2  by  lo-in  piece  used  for  S  is 
next  considered,  to  find  if  it  can  be  extended  and  used  here.  The  unsupported 
length  *s  about  6  ft,  and  the  least  dimension  2  in;  hence  l/d  =  36,  Sx  =  440  lb 
per  sq  in  and  the  required  area  of  the  cross-section  becomes  less  than  2  sq  in. 
The  2  by  lo-in  piece  is  therefore  ample. 

Members  T  and  Ti,  Fig.  2.  Inspection  shows  that  a  2  by  lo-in  plank  is 
quite  sufficient  for  these  pieces. 

Member  D,  Fig.  2.  The  unsupported  length  is  about  7  ft.  Then,  f or  <f  =  2 
in,  l/d  =  42,  S\  =  330  lb  per  sq  in  and  the  required  section-area  is  1890/330  = 
5.73  sq  in.  A  piece  2  by  10  in  is  more  than  sufficient;  but  as  this  size  allows  of 
a  simple  prolongation  of  the  pieces  T  and  Ti,  a  piece  of  this  dimension  is  used. 

Members  F  and  //,  Fig.  2.  For  the  piece  F  a  net  area  of  4  350/700  =  6.25 
sq  in  is  required;  or  a  board  i  by  8  in  in  cross-section  may  be  used.  For  con- 
venience in  construction,  two  i  by  8-in  boards  are  chosen.  It  is  evident  that  the 
same  arrangement  can  be  made  for  the  piece  //. 

Caution.  Since  this  truss  is  a  scissors  truss,  the  horizontal  deflection  at 
the  supports  should  be  determined,  and,  if  this  is  an  appreciable  quantity,  the 
members  as  designed  above,  should  l)e  increased  in  size  or  their  lengths  changed 
in  framing;  this  is  so  that  the  span,  after  the  truss  is  loaded  and  the  deflection 
has  taken  place,  becomes  the  distance  between  the  supports.  This  is  discus^HI 
m  Chapter  XXVII,  pages  1085  to  1087.  ^| 

Example  3.  For  this  example  the  Howe  truss  shown  in  Fig.  3  is  considered. 
The  vertical  load  is  assumed  to  be  46H  lb  per  sq  ft  on  the  top-chord  and  16  lb 
per  sq  ft  on  the  bottom-chord.     For  trusses  spaced  about  15  ft  8  in  on  centers. 


Design  of  Wooden  Trusses 


1143 


the  loads  and  stresses  are  shown  in  Fig.  4.    The  figures  preceded  by  the  letter 
W  indicate  the  transverse  loading  of  the  pieces. 

Vertical  Rods,  Fig.  3.  These  are  assumed  to  be  wrought  iron  and  not  upset. 
For  the  stress  13  492  lb  (Fig.  4),  using  the  unit  stress  12  000  lb  per  sq  in,  the  net 
section-area  required  is  1.16  sq  in,  which  is  provided  by  a  iH-in  rod  (Table  II, 
page  388) .  For  the  stress  5  804,  the  net  section-area  required  is  0.48  sq  in,  which 
is  provided  by  a  i-in  rod.    The  stress  in  the  middle  rod  is  so  small  that  the  rod 


a'  a     a     a    T    a     H     it--^-2''xl0''    go^oncenteri< 


Fig.  3.    Howe  Truss.     (See,  also,  Figs.  4,  9a,  9b,  14,  15  and  17a) 
5885  5704  57S 


—  43260 
-7'l0- 

19377  1984  1968  1968 

Fig.  4.     Howe-truss  Diagram.     Stresses  in  Truss  Shown  in  Fig.  3 

would  be  but  a  little  over  H-in  in  diameter.  This  would  appear  light  so  a  %-'m 
rod  is  used. 

Top-Chord,  Fig.  3.  As  this  is  to  be  uniform  in  size  from  end  to  end,  a 
middle  section  is  considered  in  determining  its  size.  It  is  assumed  that  the 
depth  is  ID  in.  For  the  transverse  load  the  center  moment  is  H  (5  704  X  7^6  Xi  2) 
=  67  022  in-lb.  From  the  equation,  67  022  =  H  (700  X  10  X  10  X  b),  the  breadth 
6=5.74  in.  For  the  compression,  43260  lb,  the  least  dimension  may  be 
taken  as  10  in,  as  the  rafters  prevent  side  buckling  for  the  unsupported 
length  of  7%  ft.  Then  l/d  =  9.4,  ^i  =  i  100  lb  per  sq  in  (note  that  the  piece  is 
less  than  fifteen  diameters  long)  and  the  required  section-area  becomes  39.3  sq  in. 
For  a  depth  of  10  in,  the  thickness  is  3.93  in.  The  total  thickness  of  the  piece  now 
becomes  5.74  -|-  3.93  =  9.67  in;  and  hence  a  10  by  lo-in  piece  may  be  used.  Since 
the  actual  cross-section  size  of  a  nominal  10  by  lo-in  piece  is  about  gH  by  9H  in, 
a  10  by  1 2 -in  timber  is  used  and  the  12 -in  dimension  is  placed  vertical. 

Bottom-Chord,  Fig.  3.  Considering  the  piece  at  the  middle,  with  a  tensile 
stress  of  48  560  lb,  it  is  found  that  the  net  area  of  the  cross-section  must  be 
69.4  sq  in,  and,  if  the  piece  is  12  in  deep,  the  thickness  is  5.78  in.  The  bendin?? 
moment  at  the  middle  of  the  piece  produced  by  the  load  i  968  lb,  is  H  (i  968  X 
7%  X  12)  =  23  224  in-lb.  This  moment  requires  a  piece  12  in  deep  and  1.28  in 
thick.  The  total  thickness  now  becomes  5.78-1-1.28=  7.06  in.  To  allow  for  holes 
and  notches  it  is  necessary  to  increase  this  to  at  least  10  in,  making  the  bottom 


1144  Design  and  Construction  of  Roof-Trusses         Chap.  28 

chord  I  o  by  12  in.  A  single  piece  of  this  size,  nearly  50  ft  long,  is  difficult  to 
obtain;  so  at  least  one  splice  is  necessary.  If  planks  are  substituted  it  requires 
six  2  by  i2-in  pieces  to  give  an  equivalent  area. 

Inclined  End-Post,  Fig.  3.  The  stress  in  this  post  is  S3  450  lb  and  its  un- 
supported length  about  9.75  ft.  An  8  by  lo-in  piece  is  tried  first,  the  lo-in 
dimension  being  the  same  as  one  dimension  of  the  chords.  Then  l/d  —  14.62, 
Si  =  825  lb  per  sq  in  and  the  required  area  of  cross-section  becomes  33  450/825  = 
40.54  sq  in,  which  is  about  one-half  the  cross-sectional  area  of  an  8  by  lo-in  piece. 
li  d=  6  in,  there  results  l/d  =  19.50,  S\  =  740  lb  per  sq  in  and  the  required  area 
=  45.2  sq  in,  which  is  a  much  smaller  cross- sectional  area  than  that  of  a  6  by 
lo-in  timber. 

Intermediate  Diagonals,  Fig.  3.  For  the  first  diagonal  a  6  by  6-in  piece  is 
tried.  The  required  section-area  is  19  630/740  =  26.5  sq  in,  which  is  well  within 
the  section-area  of  a  6  by  6-in  timber.  A  4  by  4-in  timber  could  be  used  for  the 
next  brace,  but  it  is  better  to  use  either  a  6  by  6-in  timber  or  one  4  by  6  in. 

Purlins,  Figs.  1  and  4a.  While  the  stresses  given  for  the  members  of  the 
truss  shown  in  Fig.  1  are  based  upon  a  vertical  loading  covering  the  effect  of 
dead  load,  snow-load  and  wind-load,  the  wind- 
load  is  separated  from  the  others  in  order  to 
illustrate  the  method  to  be  followed  in  design- 
ing a  purlin  when  the  plane  of  the  load  is  not 
parallel  to  one  of  its  sides.  The  trusses  of  the 
type  illustrated  in  Fig.  1,  are  15  ft  on  centers. 
This  distance,  therefore,  is  the  span  of  the 
purhn.  The  purlin  at  joint  2,  Fig.  1,  has  a 
vertical  loading  of  4  500  lb  and  a  wind-load, 
acting  normal  to  the  roof,  of  2  000  lb.  This 
inclined  loading,  resolved  parallel  to  h  and  </, 
Fig  4a,  and  combined  with   the  vertical  load, 

^J^. ^    gives  for  the  total,  parallel  to  d,  4  500 -f-  i  400 

Fig.  4a.     Purlin-design  for  Joint  2     =  5  9oo  lb;    and  for  that  parallel  to  h,  1400 
of  Truss  Shown  in  Fig.  1  lb.     If  then,  loads  are  assumed  to  act  through 

the  center  of  gravity  of  the  purlin-section,  they 
produce  both  tension  in  the  fiber  at  B  and  compression  diagonally  opposite  B. 
The  bending  moment  at  the  middle  of  the  purlin  due  to  the  vertical  load  is  \i 
(5900X  15  X  12)  =  132  750  in-lb;  and  that  due  to  the  horizontal  load  is  % 
(i  400 X  i5Xi2)  =  3i  500  in-lb.  It  is  assumed  that  6  =  8  in  and  d=  10  in. 
Then  the  fiber-stress  at  B,  due  to  the  first  moment  is 

5"  =  6  X  132  750/W2  =  gg5  lb  per  sq  in 
The  fiber-stress  at  B,  produced  by  the  second  moment  is 

^"  =  6X31  Soo/hH  =  29s  lb  per  sq  in 

The  total  fiber-stress  is  996 -h  295  =  i  291  lb  per  sq  in.  This  is  91  lb  in  excess 
of  the  permissible  fiber-stress  in  the  most  conservative  practice  and  in  many  city 
building  laws  for  long-leaf  yellow  pine  or  white  oak.  If  a  10  by  lo-in  timber 
is  used  the  fiber-stress  is  986  lb  per  sq  in,  and  if  the  piece  is  10  by  12-in,  it  be- 
comes 710  lb  per  sq  in. 

2.   Design  of  Steel  Trusses 

General  Considerations.  The  members  of  the  ordinary  steel  roof- 
TRUSSES  are  composed  of  two  rolled  angles  placed  back  to  back  and  at  the 
joints  each  piece  is  connected  to  gusset-plates  by  rivets.    The  size  of  the 


Design  of  Steel  Trusses 


1145 


smallest  angle  permissible  in  good  practice  is  2 V^  by  2  by  H  in;  and  while  %-'m 
rivets  are  often  used^  it  is  better  to  use  ^l-in  rivets,  which  are  the  largest  that 
can  be  used  in  a  23-^-in  leg  of  an  angle.  As  in  wooden  trusses,  it  is  economical 
to  use  the  same  sizes  for  all  members  which  are  in  the  same  straight  line,  but 
this  is  not  always  done. 

Example  4.     Fig.  5  shows  a  fan  truss  of  the  form  and  dimensions  of  a  truss 
used  for  supporting  the  roof  of  a  machine-shop.    The  loading  is  light  and  con- 


Fig.  5.    Fan-truss  Diagram  with  Stresses 

sequently  the  stresses  are  quite  small  in  many  of  the  members.  For  conven- 
ience the  stresses,  lengths  of  compression-members  and  final  sections  are  arranged 
in  tabular  form. 


Table  IV.     Stresses  and  Dimensions  for  the  Half-Truss  Shown  in  Figure  6 


Member 

Stress, 
lb 

Approxi- 
mate 
length,  in 

Net  area 

required, 

sq  in 

Make-up  of  member 

AD 

—16900 

-13800 

-  9  200 

-  4650 

-  7  700 

-  3070 

-f  20  200 

+  Sooo 
-f  I  900 

72 

144 

72 

1.06 

Two  2y2  by  2  by  14-in   angles 
Net  area=i.7o  sq  in 

Two  2H  by  2V2  by  H-in  angles, 
and  one  10  by  H-in  plate 

Two  2y2  by  2  by  Ki-in  angles 

DF 

FM 

FL 

LK 

DE  and  EL,.. 
AB 

EF..   .    . 

CD 

Member  AD,  Fig.  5.  This  member  has  the  maximum  stress  of  the  bottom- 
chord  and  its  size  will  be  used  up  to  the  joint  F  and  possibly  for  the  entire  length 
of  the  chord.  The  nst  area  required  is  16  900/16  000=  1.06  sq  in,  or  the  net 
section-area  of  one  angle  is  0.53  sq  in.  One  leg  of  the  angle  is  riveted  to  the 
gusset-plate  with  %-m  rivets  which  is  assumed  to  cut  out  a  section  %  in  by  the 


1146  Design  and  Construction  of  Roof-Trusses  Chap.  28 

thickness  of  the  angle.  From  Table  XI,  page  365,  we  find  that  a  2\i  by  2  by 
H-in  angle  has  an  area  of  1.06  sq  in.  The  area  to  be  deducted  on  account  of 
one  rivet-hole  is  %  X  H  =  ^^2  =  0.22  sq  in.  This  leaves  for  the  net  area  of  the 
angle  1.06  —  0.22  =  0.84  sq  in,  which  is  well  above  the  required  area.  As  this 
is  the  smallest  angle  which  can  be  used  and  as  all  the  other  tension-members 
have  less  stress  than  AD,  the  tension-members  will  be  made  uniform  through- 
out. With  the  exception  of  FK,  many  designers  would  use  but  one  angle  for 
the  web-members.  While  the  net  area  is  ample  for  the  stresses,  yet  it  is  poor 
practice,  as  one  angle  produces  a  one-sided  pull  on  the  gusset-plates. 

Member  AB,  Fig.  5.     This  piece  has  the  maximum  stress  of  the  top-chord, 

a  compression  of  20  200  lb  and  a  transverse  load  of  2  000  lb.     The  combined 

EFFECT  OF  THE  TWO  LOADINGS  in  this  case  must  be  determined  in  a  manner 

quite  different  from  that  followed  for  wooden  construction.     The  maximum 

fiber-stress  must  not  exceed   that  found  from  some  column-formula  as,   for 

^^^K^^rr—  example,  5i=  12  500—  500  l/r.     The  maximum  fiber- 

^^^^^-f'^-  stress  S  may  be  found,  approximately,  from  the  expres- 

I  sion    S  =  P/A  -\-  Mc/I.     In    this  equation,   P    is    the 

—\-'Q  direct   compression,   which  is   20  200  lb  in  this  case, 

jr-  A  the  area  of  the  section  of  the  piece,  /  the  moment 

r  of  inertia  of  this  section,  c  the  distance  of  the  outcr- 

I  most  fiber  of  the  section  which  is  in  compression  from 

I       I  its  gravity-axis  and  M  the  maximum  bending  moment 

-t___i_g  produced  by  the  tranverse  load.     The  principal  axis 

Fig   6     Section  through    ^^  ^^^  section  must  lie  in  the  plane  of  the  transverse 

Ratter-member  of  Truss    loading,    if    the    above    formula    is    used.     For    sym- 

Shovvn  in  Fig.  5.     (Axis    metrical   sections,  as  two  angles  back  to  back,  an  I 

at  dx  from  A  B,  through    beam,  or  a  channel,   the  principal  axes  are  axes  of 

c.  g.  of  angles;   axis  at    SYMMETRY,   and    the    values  of   /    and    c   are   readily 

Cg,  through  c.  g.  of  sec-    ^^^^^^  ^^^^  ^^^  properties  of  rolled  shapes  tabulated 

tions;    axis  at  dn  from    j^  Chapter  X.     The  first  trial-section  is  that  shown 

AB,    through    c.    g.    of    .      ^.     ^_.  .    .  ,  ^  ,^  ,         ,^  ,       ,^  .  ,  ^ 

l^j.g )  in  Fig.  6,  consisting  of  two  2K'  by  2i/^  by  H-m  angles 

and  one  10  by  H-'m  plate.  To  find  the  moment  of 
inertia,  /,  and  the  radius  of  gyration,  r,  the  center  of  gravity  of  the  section  is 
found  first.  The  distance  X  of  the  center  of  gravity  from  AB  (Fig.  6)  is  found 
from  Equation  (2),  page  295, 

area  of  plate  Xdn-\-  area  of  angles  X  di 


I 


X- 


area  of  entire  section 


From  the  properties  of  angles,  Table  XII,  page  367,  the  distance  from  the  back 
to  the  center  of  gravity  of  the  angle  is  J  =  0.72  in,  /  =  0.7  and  the  area  of  the 
two  angles  =  2.38  sq  in.  The  plate  does  not  usually  extend  to  the  back  of  the 
angles,  a  clearance  of  from  H  to  H  in  being  allowed.  A  clearance  of  H  in  is 
assumed. 

Then,  di  =  10.25  -  0.72  =  9.53  in,  and  ^u  =  5  in 

TT  V      2-5X5  +  2.38x9-53      ^  ^^  . 

Hence,  X  = =  721  m 

2.50+2.38 

The  value  of  the  moment  of  inertia  /,  about  Cg  as  an  axis,  is  found  as  follows 

(Chapter  X): 

t¥     0.25  X  10* 

For  the  plate  (page  335),  —  = =  20.80 

12  12 

Eq-  (3)  (page  33^),       A  (X-  (/u)-=  2.5  (2.21)2=  12.21 


Design  of  Steel  Trusses  1147 

For  the  two  angles  (page  367)  2  X  0.70  =1.40 

Eq.  (3)  (page  33^),      A  {di  -  Xy-  =  2.38  (2.32)2  =  12.81 
For  the  entire  section,  /  =  47.22 

For  any  section,  I  =  Ar"^  or  r  ^Vl/A,  hence  for  this  section  r  =  v  47.22/4.88 
=  3.11  in.  (See  Equation  (2),  page  33s-)  The  distance  to  the  outermost  fiber 
in  compression  from  the  axis  Cg  is  3.04  in  =  c.  There  is  now  sufficient  data  to 
determine  the  actual  fiber-stresses  due  to  the  loading  and  also  the  permissible 
stress.    The  bending  moment  produced  by  the  transverse  load  is 

M  =  1/^  (2  000  X  6.16  X  12)  =  18  480  in  lb 
5  =  20  200/4.88  +  (18  480  X  3-04)/47.2  2  =  S  330  lb  per  sq  in 
5i=  12  500-  500X6.16/3.11  =  II  510  lb  per  sq  in 

This  shows  that  the  actual  fiber-stress  is  very  much  smaller  than  the  allow- 
able fiber-stress,  but  as  we  have  used  minimum-size  angles  and  a  minimum  thick- 
ness for  the  plate,  the  only  way  to  reduce  this  section  is  to  use  a  smaller  plate. 
This  is  not  feasible  because  of  "the  requirements  for  making  proper  connections 
at  the  joints.  The  above  analysis  assumes  that  the  member  is  prevented  from 
bending  sidewise  by  the  roof-covering.  If  such  is  not  the  case,  r  will  have  to 
be  determined  for  a  vertical  axis  through  the  center  of  gravity  of  the  section. 
First,  finding  the  moment  of  inertia. 
For  the  plate,  ht^/ 12  =  (lo  X  0.253)/! 2  =  0.026 

For  the  angles,  2  X  0.70  =  1.400 

2.38  (0.72 -F  0.125)2  =  1.699 

For  the  entire  section,  /  =  3.125 


r    =  V3. 125/4.88 -0.8  in 

Si=  12  500-  500  X  6.16/0.8  =  8650  lb  per  sq  in 

This  is  also  less  than  the  value  of  Si,  and  hence  this  sections  fulfills  all  the 
requirements,  considering  the  unsupported  length  vertically  and  sidewise  as 
6.16  ft. 

Member  EP,  Fig.  5.  Taking  two  2H  by  2  by  H-m  angles  with  the  2>^in 
legs,  back  to  back,  the  least  value  of  r  =  0.78  in  (Table  XVI,  page  371). 

5i  =  12  500- 500  X  12/0.78  =  4810  lb  per  sq  in 
5  000  ^  4  810  =  1.04  sq  in,  required. 

The  area  of  the  two  angles  used  is  2  X  1.06  =  2.12  sq  in  (Table  XVI,  page  371). 

Member  CD,  Fig.  5.  The  stress  in  this  member  is  very  small  and  one  angle 
will  probably  fulfill  the  requirements.  For  one  angle,  2  H  by  2  by  U  in,  the  least 
r  =  0.42  in  (Table  XI,  page  365)  and  ^i  =  5  300  lb  per  sq  in,  indicating  that  this 
angle  gives  a  large  excess  of  strength.  As  pointed  out  above,  it  is  better  to  use 
two  angles. 

Sienderness-Ratio.  The  best  specifications  Hmit  the  ratio  of  the  least  dimen- 
sion to  the  unsupported  length  of  a  compression-member  to  50,  unless  the  allow- 
able unit  stress  as  given  by  the  column-formula  is  decreased.  The  member  EF 
is  2y2  in  deep  and  about  144  in  long,  so  that  its  length  is  57.6  times  its  least 
dimension.  As  there  is  a  great  excess  of  area,  the  actual  unit  stress  is  much 
below  that  given  by  the  formula. 

Stay-Rivets.  The  compression-members  made  up  of  two  angles  and  designed 
as  described  in  the  preceding  paragraphs,  have  been  considered  as  if  acting  as 
solid  pieces.  It  is  clear  that  the  various  parts  must  be  so  fastened  together  that 
no  individual  piece  will  buckle.    If  /  is  the  unsupported  length  of  the  member 


1148 


Design  and  Construction  of  Roof-Trusses  Chap.  28 


as  a  whole,  r  the  corresponding  least  radius  of  gyration,  r'  the  least  radius  of 
gyration  for  any  part  and  /'  the  unsupported  length  of  the  part,  or  the  distance 
between  stay-rivets,  there  is  the  following  relation: 

I'/r'  =  l/r  or  /'  =  Ir'/r 
For  the  member  EF  I'  =  144  x  0.42/0.78  =-  78  in. 

Practice  reduces  this  to  2  or  3  ft. 

Tension-Members,  also,  should  be  riveted  together  in  a  similar  manner  to 
make  the  parts  pull  together. 

Example  5.  The  next  truss  considered  is  the  Fink  truss  shown  in  Fig.  7, 
in  which  two  angles  are  used  for  ail  members  and  ■>:i-in  rivets  at  the  connec- 
tions. 

Member  AC,  Fig.  7.  For  a  unit  stress  of  16000  lb  per  sq  in,  the  net  area 
required  is  21  800/16  000  =  1.36  sq  in.  Two  2H  by  2M  by  H-in  angles  have  a 
section-area  of  2.38  sq  in  (Tab/e  XII,  page  367).  Deducting  2  {VsX  H)  =  0.41 
sq  in,  the  net  sectio»<  becomes  1.94  sq  in,  while  the  required  area  is  1.36  sq  in. 


a 

H 

u 

0 

•■^1              -21800            C             -18700             E                      - 

12500 

I 


I 


V SlV : H 

'  I 

Fig.  7.    Fink  Truss.     (See,  also,  Figs.  22,  22a,  22b,  22c,  and  22d) 


Members  CB  and  £//,  Fig.  7,  are  composed  of  angles  of  the  same  size. 

Members  CD^  DP^  EF  and  PO,  Fig.  7,  are  made  of  two  2^/^  by  2  by  H-in 
angles  with  a  net  area  of  2.12  sq  in.    This  greatly  exceeds  the  required  area. 

Members  BC,  BP  and  DB,  Fig.  7.  From  the  preceding  example  it  is  evident 
that  a  pair  of  minimum-size  angles  will  be  quite  sufficient.  Two  2H  by  2  by 
H-in  angles,  having  a  section-area  of  2.12  sq  in,  are  used. 

Member  AB,  Fig.  7.  For  this  member  in  which  there  is  a  direct  compres- 
sion of  23  500  lb  and  a  transverse  stress  due  to  a  load  of  2  500  lb,  a  preliminary 
trial  is  made  with  two  5  by  3!/^  by  %-m  angles,  with  the  5 -in  legs  back  to  back  and 
separated  by  a  H-in  gusset-plate.  The  moment  of  inertia  about  an  axis  passing 
through  the  center  of  gravity  of  the  two  angles  and  parallel  to  the  shorter  legs 
is  (Table  XI,  page  363)  7.78*  and  the  corresponding  radius  of  gyration  is  1.6 
in.  About  a  vertical  axis  the  radius  of  gyration  is  (Table  XVI,  page  "371) 
1.42  in,  which  is  the  least  radius  to  be  used  in  the  column-formula.      The 

*  It  will  be  noticed  that  the  values  given  for  the  properties  or  elements  of  the  angles  used 
in  this  example  differ  slightly  from  those  given  in  the  tables  referred  to,  as  the  section-area, 
I,  r,  X,  etc.  This  changes  the  result  very  slightly  and  is  due  to  variations  in  the  decimal 
figures  of  values  in  different  editions  of  manufactures'  handbooks.  Editor-in-chief. 


Joints  of  Wooden  Trusses  1149 

moment  produced  by  the  2  500-lb  load  at  the  center  of  the  member  is  H 
(2  500  X  9.2  X  12)  =  34  500  in  lb.  The  section-area  of  the  two  angles  is  (page 
363)  6.1  sq  in. 

5  =  23  500/6.10+  (34  500  X  1.61)77.78=  10990  lb  per  sq  in 
Si  =  12  500—  (sooX  9.2)/i.42  =  9  260  lb  per  sq  in 

Since  ^i  is  less  than  S,  it  is  seen  that  the  angles  selected  are  a  little  too  light. 

Instead  of  using  angles  of  greater  thickness  it  will  be  better  to  select  a  larger 

size.     If  two  6  by  3]- 2  by  %-m  angles  are  used  (page  363) 

5  =  23  500/6.86  -1-  (34  500  X  2. 04)/ 1 2.86  =  8  890  lb  per  sq  in 
Si  =  12  500 -  (500  X  9.2)/i.34  =  9  070  lb  per  sq  in 

This  shows  that  there  is  ample  strength  and  stiffness  and  that  the  area  is  in- 
creased by  0.76  sq  in.  If  two  5  by  sl^  by  ^le-in  angles  had  been  used,  the  area 
would  have  been  increased  0.96  sq  in  (page  363).  The  least  radius  of  gyration 
used  in  the  expression  for  Si  assumes  that  the  angles  will  be  separated  by  H-in 
gusset-plates.     If  thicker  gusset-plates  are  used^  the  value  of  r  will  increase. 

Practical  Details.  The  use  of  uniform  sizes  for  members  in  the  same  straight 
line  is  economical  and  adds  rigidity  to  the  truss.  The  angles  can  be  furnished 
up  to  lengths  of  60  ft  and  over,  thereby  reducing  the  labor  of  cutting  them  and 
decreasing  the  number  of  rivets  and  the  size  of  the  gusset-plates.  The  portion 
of  the  truss  AEG  shown  by  Fig.  7  would  be  completely  riveted  up  in  the  shops, 
leaving  only  three  joints  to  be  riveted  at  the  building.  In  general,  any  truss 
which  has  one  outside  dimension  not  exceeding  10  ft,  can  be  shipped  by  rail. 
This  governs  the  location  of  the  splices. 

3.    Joints  of  Wooden  Trusses 

The  Joints  of  any  truss  should  be  proportioned  with  as  much  care  as  is  used 
in  determining  the  sizes  of  the  members,  so  that  the  truss  will  be  equally  strong 
in  all  its  parts.  The  general  principles  and  methods  for  designing  joints  are 
explained  in  Chapter  XII  and  illustrated  by  examples.  To  further  explain  the 
subject,  the  methods  of  design  of  some  of  the  joints  for  the  trusses  shown  in 
Figs.  1  and  3  are  added  in  this  chapter. 

Joint  I,  Fig.  1.  This  is  the  most  important  joint  in  the  .truss.  There  are 
many  forms  for  this  joint,  but  only  a  few  of  them  are  illustrated.  Fig.  8  shows  a 
SIMPLE  BOLTED  JOINT.  The  rafter  rests  in  a  notch  in  the  bottom  chord  and  is 
held  in  place  by  one  or  more  rolled-steel  bolts.  These  bolts  are  perpendicular 
to  the  axis  of  the  rafter,  and  the  stresses  in  them  are  found  graphically  by  the 
diagram  abc  (Fig.  8)  in  which  ac  is  perpendicular  to  the  scarf-cut  or  seat  of 
the  rafter.  The  tension  in  the  bolts  is  found  to  be  31  550  lb,  and  with  a  permis- 
sible stress  of  16000  lb  per  sq  in,  the  net  section-area  required  is  1.97  sq  in, 
which  corresponds  to  one  ijg-in  bolt  (Tabic  II,  page  388).  The  washer,  bear- 
ing across  the  grain  of  the  rafter,  will  have  an  area  of  31  550/200=  158  sq  in 
(page  1 1 38).  Since  the  top-chord  is  actually  but  sH  in  wide,  the  length  of  the 
plate  is  about  28  in.  Such  a  plate  would  look  out  of  proportion  with  one  bolt, 
so  five  %-in  bolts  are  substituted,  having  a  net  section-area  of  2.10  sq  in  (Table 
II,  page  388).  Two  bolts  are  placed  near  each  end  of  the  plate  and  one  bolt 
is  placed  in  the  middle.  The  bolts  are  spaced  about  9^/^  in  apart.  The  thick- 
ness of  the  plate  may  be  taken  as  one-fifth  the  distance  from  the  end  of  the 
plate  to  the  nuts  of  the  first  pair  of  bolts.  This  distance  is  about  3.4  in;  hence 
the  thickness  is  0.67  in.  A  %-in  plate  is  used.  The  lower  end  of  each  pair  of 
bolts  is  provided  with  a  plate-washer  bearing  upon  the  inclined  surface  of  the 
white-oak  bolster  as  shown.    The  angle  of  inclination  approximates  45** 


1150 


Design  and  Construction  of  Roof-Trusses  Chap.  28 


and  hence  the  allowable  pressure  on  the  wood  is  500 -f  (i  400—  500)  H  =  725  lb 
per  sq  in.  (Sec  Table  VI,  page  454,  Table  XVI,  page  647,  and  the  equation  on 
page  1138.)  The  pair  of  bolts  carry  a  tension  of  31  550  X  %  =  12  620  lb,  and 
this  stress  requires  a  plate  having  an  area  of  12  620/725=  17.4  sq  in,  which 
will  be  provided  by  a  plate  5H  by  4  by  ^  in.  For  the  single  bolt,  a  4  by  4-in 
CAST-IRON  BEVELED  WASHER  is  used,  having  a  3,4-in  lug  let  into  the  bolster 
to  take  the  horizontal  component  of  the  pull  in  the  bolt.  To  prevent  the  bolster 
slipping  on  the  bottom  chord,  two  oak  keys  are  employed.  (See  Table  VI, 
page  454,  and  Table  I,  page  113S,  for  permissible  unit  stresses.)  The  horizontal 
component  of  the  pull  in  the  bolts  is  about  22  300  lb,  and  for  one  key,  11  150 


^^^f^ 


[{-20^-— H 


4  X  5^x  X"       C.I.  Washer      ^1  x  5><f  x  %' 
rx  4" 


Fig.  8.     Detail  of  Joint  1,  Fig.  1 

lb,  and  taking  the  actual  thickness  of  6  in  to  be  sH  in,  each  inch  in  length  of 
the  key  will  safely  carry  5H  X  200  =  i  100  lb  in  longitudinal  shear  (Table  I, 
page  412).  The  keys  will,  therefore,  be  10  in  long.  The  ends  of  the  keys  push 
against  the  notch  in  the  white-pine  chord,  and  for  end-bearing  each  inch  in 
depth  of  the  notch  carries  sV^X  i  loo  =  6050  lb.  The  depth  of  the  notch, 
therefore,  is  1.8  in  in  the  chord.  In  the  bolster  each  inch  in  depth  of  notch 
carries  5'/iX  i  400  =  7  7oo  lb  (Table  XVI,  page  647),  and  the  depth  of  notch 
is  1.43  in.  This  makes  the  total  thickness  of  the  keys  1.8+  1.43  =  3.23  in,  or, 
say  3'/^  in.  The  size  of  the  keys  is  3^2  by  5H  by  10  in.  The  spacing  of  the 
KEYS  is  governed  by  the  longitudinal  shear  of  the  white-pine  chord.  Each 
inch  in  length  carries  s^/i^X  100=  550  lb  (Table  I,  page  1138),  and  the  clear 
distance  between  keys  is  11150/550=  20  in.  The  various  dimensions  used 
above  will  probaby  appear  large  to  many.  The  large  dimensions  are  due  to 
the  timber  used.  If  long-leaf  yellow  pine  had  been  employed,  many  of  the 
dimensions  would  have  been  materially  smaller.  The  angle-block  detail, 
shown  in  Fig.  9b,  makes  a  much  better  connection  in  this  case.  1%  in 
becomes  iH  in  and  15  in  becomes  13  in.  The  net  area  of  the  bottom  chord 
should  now  be  determined  to  see  if  it  is  sufBcient  to  take  the  tension. 

Wall-Plate.  As  a  rule  it  is  a  good  idea  to  place  the  wall-plate,  which 
receives  the  common  rafters,  just  above  the  bottom  chord  as  shown.  This 
affords  an  opportunity  to  get  at  the  nuts  on  the  bolts  to  tighten  them  as  the 
wood  shrinks.    The  bearing  of  the  truss  on  the  brickwork  should  be  con- 


Joints  of  Wooden  Trusses 


1151 


sidered  and  a  stone  or  metal  plate  provided  to  distribute  the  pressure.  (See 
Chapter  XIII.)  In  this  case  a  i6  by  14  by  iH-in  cast-iron  plate  is  used, 
which  reduces  the  pressure  on  the  briclcwork  to  82I/I2  lb  per  sq  in. 

Joint  I,  Fig.  3.  This  joint  might  be  made  in  the  manner  described  above, 
but  the  type  shown  in  Fig.  9  is  used.  The  thickness  of  the  plate  is  usually 
governed  by  the  thickness  required  at  Y  to  give  the  hook  the  proper  strength. 


„  2-1  boTts^       „,^»      *    .,,» 
M  Plate.       N     9MX3X1X' 


Fig.  9.     Detail  of  Joint  1,  Fig.  3 


Fig.  9a.    Alternate  Detail  of  Joint  1,  Fig.  3 


This  hook  practically  takes  one-half  the  horizontal  component  of  the  stress  in 
the  rafter  (which  is  the  stress  in  the  bottom  chord  in  this  case)  as  the  bolts  are 
assumed  merely  to  keep  the  parts  in  place.  The  metal  bears  against  the  end- 
fibers.  For  each  inch  in  depth  of  the  notch,  the  fibers  carry  9}'^  X  1 100  =  104SO  Ih, 
and  hence  the  notch  is  H  (27  350/10  450)  =  1.31  in  deep,  say  1%  in.  Considering 
the  hook  as  a  wrought-iron  cantilever,  iH  in  long  and  uniformly  loaded 
with  I  100  lb  per  sq  in,  the  thick- 
ness is  found  from  the  expression 
1 100(1.31)2/2  =!'^(l2  000X  I  X/2), 
or,  /  =  0.69  in.  The  nearest 
practical  size  is  a  thickness  of 
%  in.  The  length  of  the  bot- 
tom chord  necessary  to  take 
the  pressure  from  the  hook  in 
longitudinal  .  shear    is    91^12  X  100 

=  950  lb  per  in,  or,   13  675/950 

=  14.4  in  in  all.  The  inclination 
of  the  fibers  at  //  with  the  ver- 
tical cut  is  about  36°,  and  the 
allowable  pressure  on  this  surface 
is  200 +(i  100—  200)  (39^0)^^=  344 
lb.     Then  27  3So/(344  X  9M)  =  8.3 


Fig.  9b.     Alternate  Detail  of  Joint  1,  Fig.  3 


in,  which  is  the  required  depth  of  the  cut. 
As  these  fibers  are  confined  by  the  plate,  one-half  this  value,  or  4H  in,  approx- 
imately, is  used.  The  bolts,  Z,  are  two  li-in  bolts.  There  should  be  two 
bolts  at  Y,  carefully  placed  so  that  the  hook  bears  against  them.  There  is  a 
strong  tendency  for  the  hook  to  straighten  and  hence  i-in  bolts  are  used. 
The  net  section  of  the  plate  in  tension  is  evidently  greatly  in  excess  of  that 
required. 

Joint  I,  Fig.  3.     A  better  detail  at  F,  Fig.  9,  is  shown  in  Fig.  9a.     It  is 
assumed  as  before  that  one-half  the  tension  is  taken  by  the  notch  at  F.    The 


1152 


Design  and  Construction  of  Roof-Trusses         Chap.  28 


Fig.  9c.     Detail  of  Joint  1,  of  Truss  Similar  to  Fig.  1 

iepth  of  the  notch  is  i%  in  and  the  size  of  the  metal  block,  i%  by  3  by  gH  in. 

The  bolts  are  assumed  to  have  a  close  fit  in  the  block  and  in  the  plate  and  hence 

carry  the  stress  in  single  shear, 
At  10  000  lb  per  sq  in. 
the  area  of  the  bolts  is  l>^ 
(27  350/10  000)  =  1.37  sq  in, 
requiring  two  i-in  steel  bolts 
(Table  III,  page  419).  The 
thickness  of  the  steel  plaj^ 
necessary  to  give  sufficient 
bearing  against  the  bolts  is 
V'i  (13  675)  -^  20  000  X  I,  or  ^  = 
.34  in.  A  y2-[n  plate  is  there- 
fore ample. 

Joint  I,  Fig.  3.     An  ordinary 

CAST-IRON     ANGLE-BLOCK     can 

be  used  in  this  particular  case 
as  shown  in  Fig.  9b. 

Other  Details  for  Joint  i. 
Fig.  3.  Another  design  for 
this  joint,  but  for  another 
truss,  is  shown  in  Fig.  9c. 
The  rafter  and  bottom  chord 
are  of  long-leaf  yellow  pine 
and  the  metal  parts  of  steel. 
The  stresses  are  transmitted 
through  3  by  %-in  plates  in 
bearing  against  the  end-fibers 
of  the  v/ood,  and  from  these 
plates  to  the  side  plat] 
through  the  bolts  in  bending.  The  side  plates  should  be  drawn  up  agaii 
the  wood  by  lag-screws,  as  shown,  to  prevent  buckling  when  in  compressioi 


Fig.  9d.     Truss  with  Cast-iron  Angle-block 


Joints  of  Wooden  Trusses 


1153 


Fig.  9d  shows  a  good  application  of  the  cast-iron  angle-block  used  in  the 
trusses  of  a  blacksmith-shop  of  the  Boston  &  Maine  Railroad  Company.  The 
bearing  and  shearing  values  are  provided  for  principally  by  a  tenon  on  the 
back  let  into  the  bottom  chord  as  indicated  by  the  dotted  lines. 

Joint  2,  Fig.  1.  Where  a  brace  abuts  against  a  rafter,  as  in  this  joint,  one  cut 
on  the  end  of  the  brace  should  bisect  the  angle  made  between  the  brace  and  the 
rafter,  and  the  second  cut  should  be  at  right  angles  to  this,  as  shown  iri  Fig.  10. 
The  end  is  then  set  in  a  notch  or  mortise  to  keep  the  brace  in  place  and  to  trans- 
mit the  pressure  to  the  rafter.   The  purhn  may  be  supported  by  a  3 -in  plank,  as 


Fig.   10a.      Purlin-connection. 
Purlins  on  Top  of  Truss-chord 


Fig.   10.     Detail  of  Joint  2,  Fig.  1,  with  Rod  Added 


Fig.  10b.  Purlin-con 
nection  with  Steel- 
Angles 


Fig.  10c.  Purlin-connec- 
tion with  Wooden  Bear- 
ing-block 


Fig.  IOd.     Purlin-connection 
with  Beam-h-anger 


shown  in  Fig.  10.  Some  form  of  metal  hanger,  of  the  Duplex  type  is 
often  preferred.  In  the  truss  shown  in  Fig.  1,  there  is  no  vertical  rod  at  this 
joint;  but  many  trusses  have  a  rod  there,  and  one  is  therefore  shown  in  Fig.  10. 
The  washer  on  top  of  the  rafter  must  have  sufficient  area  to  transmit  the  stress 
ih  the  rod  to  the  rafter.  Other  forms  of  purlin-connections  are  shown  in  Figs. 
10a  to  IOd. 

Apex  of  King-Rod  Truss.  Fig.  11  shows  the  joint  at  the  top  of  a  king- 
rod  TRUSS  with  a  Duplex  hanger  to  support  the  purlin.  The  wrought-iron 
or  steel  plate  for  large  trusses  should  extend  along  the  top  of  each  rafter  a 
sufficient  distance  to  permit  its  being  fastened  by  lag-screws  or  bolts.  Fig  12 
ghows  a  castjng  in  place  of  the  ROLi-PP  plat^. 


1154 


Design  and  Ccnstruction  of  Roof-Trusses         Chap.  28 


Joint  3,  Fig.  1.    This  should  be  made  as  shown  in  Fig.  13.     The  inclined 
cuts  bisect  the  angle  made  between  the  two  6  by  6-in  pieces.     In  place  of  the 

CAST-IRON  WASHER  a  WROUGHT-IRON  OF  STEEL  PLATE  may  be  USCd. 


^  Thick 


Fig.  11.    Detail  of  Apex  of  King-rod  Truss 


Fig.  12.    Alternate  Detail  for  Apex 
of  King-rod  Truss 


pO^'SixOx  5^'* Washer 


Fig.  13.    Detail  of  Joint  3,  Fig.  1 


Fig.  14.    Detail  of  Joint  2,  Fig.  3 


Joint  2,  Fig.  3.     One  method  of  making  the  connections  at  this  joint  is  shown 
in  Fig.  14.     The  end-cut  of  the  main  brace  is  made  as  shown,  the  distance  d 


pJi^L^ Sx  g'x  X  Pla^te 


Fig.  15.     Alternate  Detail  of  Joint  2,  Fig.  3 


being  determined  by  the  necessary  area  of  the  inclined  cut  in  the  top  chord. 
The  permissible  unit  pressure  is  about  525  lb  per  sq  in.  Then  33  450  lb  requires 
64  sq  in,  or  the  distance  d  is  sl  little  greater  than  the  depth  of  the  brace.     This 


Joints  of  Wooden  Trusses 


1155 


form  of  detail  can  only  be  used  for  the  end-brace  by  making  two  notches  as 
shown  by  the  dotted  Hnes.  A  much  better  method  is  shown  in  Fig.  15,  where 
an  ANGLE-BLOCK  is  used.  The  angle-block  is  made  of  very  hard  wood  so  that 
the  bearing  of  the  brace  is  provided  for,  and  it  is  notched  into  the  chord  a  suffi- 
cient amount  to  transfer  the  horizontal  component  of  the  stress  in  the  brace 
to  the  chord.  A  notch  i  in  deep  carries  i  loo  X  9H  =  lo  450  lb  (Table  I,  page 
1 138);  hence  for  a  horizontal  component  of  27350  lb  (Fig.  4),  the  notch  is 
made  2%  in  deep.  This  clearly 
shows  that  braces  should  be  inclined 

at    least   45°    with    the   horizontal, 

unless  awkward  or  weak  details  are  ^ 

to  be  tolerated.     The  vertical  rod 

here  has  a  stress  of  13  492  lb.     The 

WASHER  on  top  of  the  chord  transfers 

this  stress  in  bearing  across  the  grain. 

At  a  unit  stress  of  200  lb  (Table  I, 

page  1 138),  the  area  is  67.4  sq  in, 

requiring    an    8    by    9    by    %-in 

plate. 


6  X  8  X  ^  Washer 
Fig.  16.    Detail  of  Joint  7,  Fig  1 

Joint  7,  Fig.  1.  This  is  shown  in  Fig.  16,  and  the  above  discussions  cover  all 
details  of  its  design. 

Splices.  Since  it  is  not  economical  and  often  impossible  to  procure  timbers 
exceeding  25  or  30  ft  in  length,  it  is  necessary  to  make  one  or  more  splices 
in  the  chords.  The  top-chord  of  a  Howe  truss  is  spliced  by  placing  the  tim- 
bers end  to  end,  and  by  spiking  or  bolting  on  side  planks  to  keep  them  in  place. 
The  bottom  chord  cannot  be  treated  in  this  manner,  as  it  is  in  tension. 

Hook-Splice  or  Tabled  Fish-Plate  of  Wood.  It  is  assumed  that  the 
bottom  chord  of  the  truss  shown  in  Fig.  3  is  to  be  spliced  at  the  middle  of  the 

span.  Fig.  17a  shows 
this  splice.  It  is  as- 
sumed that  the  side 
pieces  are  of  white  pine. 
The  total  depth  of  the 
notches  is  48  5604- 
(iiooXiiH)=(/=3.84 
in  (Table  I,  page  11 38). 
Each  notch,  then,  is 
about  2  in  deep.  The 
length  of  the  table  is 
/=  H  [48560-^(100  X 
1 1  '/^)]  =  2 1  in.  The  net 
thickness  of  each  side 


# 


g  round 


x2^-^12x 


-idl 


k -42^ 


li 

I 


■^ 


zEhL. 


^F- 


Fig.  17.     Splice  of  Bottom  Chord  of  Truss 


piece  is  Vz  (48  560)/ (700  X  nH)  =  3  in,  without  deducting  anything  for  the  two 
bolt-holes.  The  chord-pieces  have  less  than  the  required  area  because  of  the 
deep  notches  required;  hence  a  12X  12-in  timber  is  required  if  this  form  of 
splice  is  used.     The  proper  dimensions  are  shown  in  Fig.  17a. 

Metal  Splice.  Fig.  17  shows  an  old 'and  very  efficient  form  of  splice,  pro- 
portioned to  replace  the  form  shown  in  Fig.  17a. 

Splices  for  Built-up  Chord.  The  top  chord,  when  built  lt  of  2-in  planks, 
requires  thorough  spiking  with  two  H-'m  bolts  at  the  ends  of  each  plank.  The 
bottom  chord,  which  is  in  tension,  should  be  so  arranged  that  the  ends  of 
the  planks  in  one  strand  are  well  removed  from  the  ends  in  other  strands.    Thd 


1156 


Design  and  Construction  of  Roof-TrusSes  Chap.  28 


middle  strand  of  a  built-up  chord  is  completely  cut  away  to  permit  the  passage 
of  the  vertical  rods.  The  strands  should  be  thoroughly  spiked,  and  bolted  every 
2  ft,  care  being  taken  to  see  that  the  bolts  do  not  come  nearer  than  5  in 
from  the  end  of  any  plank.     While  built-up  members  are  in  favor  with  build- 


-21- 


r 


.Table 


12x12: 


-*- 


—21 -H< 21-— ^^t^ 


-21- 


X  bolts 


Fig.  17a-.     Alternate  Detail  for  Splice  of  Bottom  Chord 

ers  because  the  materials  are  readily  obtained,  yet  for  important  structures  the 
writer  believes  it  is  worth  while  to  use  a  little  more  effort  and  pay  a  little  more 
to  get  SOLID  STICKS  for  truss-members. 

Wall- Joint  of  Scissors  Trusses.    In  scissors  trusses  the  joint  over  the 
wall  formed  by  the  rafter  and  tie-beam  should  always  be  carefully  proportioned 


owi  adJ  1- 


-13"  Wall- 


ed. Elate 
14*  long 


J3,  8^"  X  4K'  Lag  Screjya 

Dotted  lines  show  screws 

on,  other  side. 


Fig.  18.     Wall-Joints  for  Scissors  Trusses,  Figs.  24  to  27,  Chapter  XXVI 

to  the  stresses;  otherwise  the  joint  is  liable  to  open  and  the  wall  to  be  pushed 
out.  Much  greater  strength  is  required  in  this  joint  than  in  the  wall-joint  of  a 
KING-ROD  truss  of  thc  same  span,  because  the  stresses  in  a  scissors  truss  are 
usually  at  least  twice  and  sometimes  three  or  four  times  as  great  as  in  a  truss 
with  a  horizontal  tie-beam.    For  a  scissors  truss  built  of  planks,  as  in  Fig.  2, 


Joints  of  Wooden  Trusses 


1157 


a  i-in  bolt  through  the  center  of  each  joint,  with  as  many  spikes  as  can  be 
driven,  will  ordinarily  give  sufficient  strength.  For  trusses  like  those  shown  in 
Figs.  24  to  27  of  Chapter  XXVI,  one  of  the  best  methods  of  making  the  wall- 
joint,  unless  the  roof  is  quite  flat,  is  that  shown  in  Fig.  18,  which  is  the  detail 
of  an  actual  joint  where  the  stress  in  the  tie-beam  was  25  000  lb.  It  should  be 
noticed  that  the  wrought-iron  strap  is  secured  to  the  tie  by  lag-screws  in- 
stead of  BOLTS.  It  is  practically  impossible  to  bolt  a  strap  to  each  side  of  a 
beam  so  as  to  get  a  good  bearing  for  all  of  the  bolts,  owing  to  the  difficulty  in 
boring  the  holes  straight;  and  if  the  holes  are  bored  a  little  large,  some  bolts 
may  bear  on  the  wood  and  some  may  not.  With  lag-screws  each  screw  is 
bound  to  get  a  good  bearing  in  the  wood.  The  holes  in  the  two  sides  of  the 
strap  must,  of  course,  be  staggered,  so  that  they  will  not  come  opposite  each 
other.  The  net  sectional  area  of  the  strap  should  at  least  be  eqiml  to  the  stress 
in  the  tie-beam  divided  by  2  X  12  000  (Table  I,  page  1138).  The  number  of 
lag-screws,  4or  both  sides,  is  found  by  dividing  the  stress  in  the  tie-beam  by 
the  resistance  of  one  screw.  For  the  safe  resistance  of  lag-screws  used  in  this 
way,  the  values  given  in  Table  V  are  recommended.  In  the  joint  shown  in  Fig. 
18,  the  stress  in  the  tie-beam  is  25  000  lb,  and  the  wood  is  Douglas  fir.  The 
above  rules,  therefore,  require  a  sectional  area  in  the  strap  of  H  (25  ooo)/i2  000  = 
1.05  sq  in  and  twenty-three  ^-in  lag-screws.     Only  thirteen  are  shown  in  Fig.  18- 


Table  V.* 

Safe  Resistance  of  Mild-Steel  Lag-Screws  When  Used  as  in  Fig.  18 

Size  of  screw  in 

Safe  resistance  in  pounds 

Minimum 

inches 

thickness 
of  strap  in 

Oak 

White 

Douglas 

Long-leaf 

diam. 

length 

pine 

fir 

pine 

inches 

Vs 

iV2 

288 

255 

267 

288 

M 

Vi 

4 

512 

454 

474 

512 

V4. 

% 

4 

800 

709 

741 

800 

Ka 

% 

AM 

I  153 

I  022 

I  067 

I  153 

Me 

% 

5 

1  569 

I  391 

I  453 

I  569 

H 

*  Based  upon  experiments  made  (1915-1916)  by  Professor  H.  A.  Thomas. 

With  a  thickness  of  %  in,  the  width  of  the  strap  necessary  to  give  a  sectional 
area  of  1.05  sq  in  is  1.05/. 375,  or  about  3  in.  To  this  should  be  added  the  diam- 
eter of  one  lag-screw  to  obtain  the  working  width.  Thus  3  -f-  M  =  3^4  in.  The 
strap  used  is  4  by  Y^  in  in  cross-section,  as  some  additional  strength  is  obtained  by 
the  bolt  at  X,  which  it  is  necessary  to  insert  to  hold  the  timbers  together  while 
the  truss  is  being  raised  into  position,  and  also  to  bring  them  tightly  together 
before  fitting  the  strap.  Fig.  19  shows  another  method  of  making  this  joint 
which  may  be  used  with  advantage  -when  the  inclination  of  the  rafter  is  less 
than  45°.  One  advantage  in  using  this  truss  is  that  if  it  is  erected  one  piece 
AT  A  TIME,  the  tie-beams  may  be  put  up  first,  thus  providing  a  seat  to  receive 
the  rafters.  The  strap  prevents  the  end  of  the  rafter  from  springing  up.  The 
diameter  of  the  bolt  should  be  proportioned  to  the  horizontal  component;  of  the 
stress  in  the  rafter.  Fig.  20  shows  a  good  form  of  joint  to  use  at  joint  5  of  Fig. 
27,  Chapter  XXVI,  when  it  is  desired  to  substitute  a  wooden  tie  for  the  rods 
shown  in  Fig.  27.  The  sectional  area  of  the  strap  and  the  number  of  lag-screws 
should  be  proportioned  by  the  rules  given  for  Fig.  18. 

Washers.  Where  iron  or  steel  rods  are  used  in  wooden  trusses,  wasTiers  are 
necessary  under  the  heads  and  nuts  to  properly  distribute  the  loads  on  the 
wood.    The  dimensions  of  the  washers  are  determined  by  the  allowable  bear- 


1158 


Design  and  Construction  of  Roof-Trusses         Chap.  28 


ing  pressure  on  the  wood  and  the  magnitudes  of  the  loads.  Table  VI  gives  the 
allowable  loads  which  can  be  transmitted  by  standard  round  cast  washers  and 
rectangular  washers  bearing  across  the  wood  fibers.  Table  VII  gives  the  di- 
mension of  standard  round  cast  washers.     The  bearing  areas  of  these  washers 


Casting 


Fig.  19.    Alternate  Detail  for  Fig.  18 

are  too  small  for  use  on  the  softer  woods  and,  therefore,  except  when  the  rods 
are  small,  it  is  better  to  use  rectangular  washers  of  iron  or  steel  plate.  Very- 
large  washers  should  be  cast,  and  should  have  the  form  shown  in  Fig.  20a. 
The  use  of  the  ribs  gives  the  required  strength  and  saves  considerable  material. 


Fig.  20.     Detail  of  Joint  5,  Fig.  27,  Chapter  XXVI  Fig.    20a.      Cast-iron 

Washer  with  Brackets 

Thickness  of  Rectangular  Steel-Plate  Washers.  The  thickness  of  rec- 
tangular steel-plate  washers  can  be  found  from  the  following  formulas  in  which 
/  is  the  distance  from  the  edge  of  the  plate  to  the  nut  and  /  the  thickness  of  the 
plate.     When  used 

On  white  oak /  =  3.4  / 

On  white  pine ^=5.2/ 

On  long-leaf  yellow  pine /  =  3-9  ^ 

On  short-leaf  yellow  pine /  «*  4.6  4 


Joints  of  Wooden  Trusses  1^ 

Table  VI.    Safe  Bearing  Resistance  of  Cast-iron  Washers,  in  Pounds 


Round  wa'ihers 

Size, 

Area,* 

White  pine. 

Short-leaf 

Long-leaf 

White  oak, 

in 

yellow  pine, 
lb 

yellow  pine, 
lb 

lb 

sq  in 

lb 

Vi 

5.16 

I  030 

I  290 

I  810 

2580 

% 

6.69 

I  340 

I  670 

2340 

3350 

% 

7.78 

I  560 

I  950 

2720 

3890 

% 

10.4 

2080 

2  600 

3640 

5  200 

I 

II. 7 

2340 

2930 

4  100 

5850 

\% 

16.6 

3320 

4150 

5810 

8300 

iM 

26.9 

5380 

6730 

9420 

13500 

28.6 

5  720 

7  ISO 
9630 

10  000 

14  300 

38.5 

7  700 

13500 

19300 

2 

49-9 

9980 

12500 

17500 

25  000 

2Vi 

62.8 

12  600 

15700    • 

22  000 

31  400 

2K2 

77.1 

IS  400 

19300 

27  000 

38600 

2% 

92.9 

18600 

23  200 

32500 

46500 

3 

no. 2 

22  000 

27  600 

38600 

55  100 

Rectangular  washers 

4X  6 

24 

4800 

6000 

8  400 

12  000 

8 

32 

6  400 

8000 

II  200 

16  000 

6X  6 

36 

7  200 

9000 

12  600 

18  000 

7 

42 

8  400 

losoo 

14700 

21  OGO 

8 

48 

9600 

12  000 

16800 

24  000 

9 

54 

10  800 

13500 

18  900 

27  000 

10 

60 

12  00b 

15  000 

21  000 

30000 

8X  8 

64 

12800 

16000 

22400 

32000 

9 

72 

14  400 

18  000 

25  200 

36  000 

10 

80 

16  000 

20  000 

28  000 

40  000 

12 

96 

19  200 

24  000 

33600 

48  000 

loXio 

100 

20  000 

25  000 

35  000 

50000 

II 

no 

22  000 

27500 

38500 

55  000 

12 

120 

24  000 

30000 

42  000 

60  000 

14 

140 

28  000 

35  000 

49000 

70  000 

12x12 

144 

28800 

36  000 

SO  400 

72  000 

14 

168 

33600 

42  000 

58  800 

84  000 

16 

192 

38400 

48  000 

67  200 

96  000 

14X14 

196 

39200 

49000 

68600 

98  000 

16 

224 

44800 

56000 

78  400 

112  000 

Unit  values, 

lb  per  sq  in 

200 

250 

350 

500 

*  The  actual  areas  bearing  on  the  wood  are  given  for  round  washers, 
washers  the  total  area  is  given,  no  allowance  being  made  for  holes. 


Details.  Many  other  forms  of  connections  are  in  use  and  their  proper  design 
simply  demands  that  the  methods  explained  in  Chapter  XII  and  in  this  chapter 
be  consistently  followed.  All  details  are  not  suitable  for  all  cases  and  the  de- 
signer must  use  common  sense  in  the  selection  of  the  particular  type  to  b6 
used  and  in  its  design.  Wood  is  very  variable  in  its  properties  and  consequently 
large  factors  of  safety  are  used  for  certain  kinds  of  stress  and  smaller  factors 


1160 


Design  and  Construction  of  Roof-Trusses         Chap.  28 


for  others.  Heavy  trusses,  in  which  the  sizes  of  the  members  are  selected  ac- 
cording to  the  magnitudes  of  the  stresses,  should  be  very  carefully  worked  out 
in  every  detail,  while  small  trusses  with  large  excess  of  material  do  not  demand 
as  much  care. 


Table  VII. 

Proportions  of  Standard  Cast-iron  Washers 

/ 

\ 

(Q)f}'^- 

^ 

;\ 

\            y    1 

'VMm 

7. 

u 

vV_^.J. 

^   -r    .1 

i*^ 

D               V,                            -   •    '1 

Diam  of 
bolt,  d 

D 

d" 

d' 

T 

Weight, 

Bearing 
area, 

in 

in 

in 

in 

lb 

in 

sq  in 

H 

2^ 

^^i 

^9/^6 

% 

1/^ 

S.i6 

% 

3 

m 

11/16 

H 

% 

6.69 

H 

3H 

2% 

13/6 

H 

11/ 

7.78 

Ti 

3H 

2% 

15/6 

% 

ii/ 

10.40 

I 

4 

2% 

1 1/6 

iM 

21/ 

11.70 

iH 

4% 

2% 

1^6 

m 

3 

16.60 

iH 

6 

3 

l5/6 

1% 

5% 

26.90 

iH 

6K 

3H 

1% 

m 

6 

28.60 

iH 

7H 

3% 

1% 

1% 

9H 

38.  SO 

2 

8H 

4H 

2H 

2 

I7H 

49  90 

2H 

m 

4% 

2% 

21/ 

20 

62.80 

2^ 

loH 

sH 

2H     ■ 

2H 

27  H 

77.10 

2V4 

iiH 

S% 

2-^A 

2% 

36 

92.90 

3 

12^4 

6M 

3H 

3 

46 

110.20 

Fc 

r  sizes  not 

given,  D  =  4^  +  M"                   d"=  2d-{-  H 

d'  = 

rf  +  H 

T  '- 

=  d 

4.   Joints  of  Steel  Trusses 

Trusses  with  Riveted  Joints  are  usually  made  with  angles  for  the  web- 
members  and  generally  for  the  chords,  although  the  latter  are  sometimes  made 
of  a  pair  of  channels  or  of  two  angles  and  a  web-plate.  The  members  are 
connected  at  the  joints  by  means  of  gusset-plates,  to  which  all  of  the  members 
are  riveted.  Typical  examples  of  riveted  joints  in  roof-trusses  are  shown  in 
Figs.  22  to  24e.  When  the  rafter  or  chord  has  a  web-plate,  as  in  Fig.  23a, 
the  web-members  are  riveted  to  this  plate  and  a  gusset-plate  is  not  required 
except  at  the  end-joint  and  apex,  as  shown  in  Figs.  23a  and  23e.  In  order  that 
there  shall  be  no  twisting,  it  is  necessary  to  make  the  principal  members  of  the 
truss  double,  so  that  the  gusset-plates  can  be  riveted  between  them.  Where 
single  angles  are  used  for  web-members  and  two  such  members  come  at  one 
joint  they  should  be  riveted  to  opposite  sides  of  the  gusset-plates.  For  equal 
strength  the  thickness  of  the  gusset-plate  should  be  such  that  the  bearing  on 
the  rivets  equals  the  strength  of  the  rivets  in  double  shear,  the  thickness,  how- 
ever, not  exceeding  the  combined  thickness  of  the  two  angles.  Practical  con- 
siderations seldom  make  the  gusset  Qver  H  u^  thick  for  ordinary  construction. 


Joints  of  Steel  Trusses 


1161 


In  laying  out  the  joints,  which  should  be  done  to  a  scale  of  not  less  than  i  in 
to  the  foot,  the  members  should  be  arranged,  when  practicable,  so  that  the  lines 
passing  through  their  centers  of  gravity  will  coincide  with  the  lines  of  the  truss- 
diagram,  and  thus  meet  at  a  single  point,  as  in  Fig.  21.  This  is  not  always  praC' 
ticable,  but  the  prin- 
ciple should  be  followed  --Su„^^  ,  0_,_0_^^0  O  Or. 
as  closely  as  possible. 
For    small    angles  the 

RIVET-LINES    of   the 

members  may  be  con- 
sidered, without  serious 
error,  to  pass  through 
the  centers  of  gravity 
of  the  sections.  The 
number  of  rivets  re- 
quired for  each  mem- 


Fig.  21.     Riveted  Truss-joint  with  Truss-diagram  Lines 


ber  must  be  determined  according  to  the  stress  in  that  member,  the  resistance 
of  the  rivets  being  considered  for  both  shearing  and  bearing.  The  method 
of  determining  the  number  of  rivets  in  a  joint  is  explained  in  Chapter  XII, 
but  to  show  more  clearly  the  application  to  truss-joints,  the  joints  for  the 
truss  shov/n  in  Fig.  7  will  be  designed. 

General  Considerations,  Truss  of  Fig.  7.  It  is  assumed  that  the  truss 
will  be  shipped  in  three  parts,  making  all  the  joints  shop-riveted  except  those 
at  G  and  the  splices  at  each  end  of  the  piece  EH.  All  gusset-plates  are  to  be 
^^-in  thick  and  all  rivets  %-'m,  except  in  the  2-in  legs  of  angles,  where  ^i-in 
rivets  are  to  be  used.  Since  the  bearing  of  a  %-'m  plate  on  a  ^4-in  rivet  at 
20  000  lb  per  sq  in  (Table  I,  page  1138)  is  5  630  lb,  or  at  18  000  lb  per  sq  in 
(Table  III,  page  419)  is  5  060  lb,  and  the  resistance  of  the  rivet  in  double  shear, 
2X4  420  =  8  840  lb  (Table  III,  page  419),  the  number  of  rivets  in  all  the  joints 
is  governed  by  the  bearing  value.     Only  one  leg  of  the  angles  will  be  connected 


10}  [ynh) 


oT  o-L— ■         1 

«->     1 

^^ 

Fig.  22.     Detail  of  Jo'int  A, 
Fink  Truss,  Fig.  7 


Fig.  22a.     Detail  of  Joint  D,  Fink  Truss, 
Fig.  7 


to  the  gusset-plate  as  about  80%  of  the  full  strength  of  the  angle  is  thereby 
developed  if  not  less  than  three  rivets  are  used.  The  use  of  hitch-angles 
for  the  outstanding  leg  has  but  little  influence  in  increasing  the  efficiency  of  the 
connection.  Two  rivets  may  be  considered  the  minimum  number  in  any  con- 
nection, regardless  of  the  unimportance  of  the  member. 

Joint  A,  Fig.  7.     The  top-chord  stress  is  23  500  lb,  and  if  one  rivet  carries 
5  630  lb  into  the  gusset-plate,  five  rivets  will  be  required  to  carry  this  total 


1162 


Design  and  Construction  of  Roof-Trusses         Chap.  28 


stress.  In  like  manner  four  rivets  are  required  for  the  bottom  chord.  The 
supporting  force  or  the  reaction  is  transferred  to  the  gusset  through  the  bottom 
chord  prolonged.  In  this  case  the  reaction  is  about  8  8oo  lb  which  reqdires  two 
rivets.     Fig.  22  shows  the  arrangement  of  this  joint  at  the  e.xpansion-end. 

Joint  D,  Fig.  7.  The  web-members  each  require  less  than  one  rivet,  but  two 
or  three  should  be  used.  Since  the  top-chord  angle  is  continuous,  the  number  of 
rivets  in  it  is  determined  by  the  difference  between  the  two  adjacent  stresses 
and  the  load  of  the  purlin  if  it  rests  on  the  chord.  Here  again  the  number  of 
rivets  required  falls  below  the  minimum  number.     Fig.  22a  shows  this  joint. 

Joint  E,  Fig.  7.  The  piece  CE  requires  four  rivets  and  the  web-members  the 
mioimum  number  permissible.     The  piece  EU  requires,  at  20  000  lb  per  sq  in 


M 

^'pC        I 

lO    0    0  0 

^ i^r^Q?!!*    •    • 

•■  u  o-i — .'    '  ' 

Fig.  22b.     Detail  of  Joint 
E,  Fink  Truss,  Fig.  7 


Fig.  22c.     Detail  of  Joint  E  and  Splice  in 
Ell,  Fink  Truss,  Fig.  7 


bearing  vajue,  12  500/5  630=  2.22  rivets;  but  as  this  connection  is  one  to  be 
made  in  the  field,  it  is  customary  to  increase  the  number  25%.  This  makes 
the  required  number  three.  Sometimes  the  outstanding  legs  are  spliced  to  the 
member  CE  by  a  plate.  Without  doubt  this  increases  the  strength  of  the  joint, 
but  it  is  doubtful  if  the  increase  in  strength  is  enough  to  offset  the  extra  cost. 
Fowler's  specifications  do  not  permit  the  piece  EH  to  be  connected  to  the 
gusset-plate.  They  specify  that  the  connection  shall  be  made  upon  the  right  of 
E.    This  arrangement  allows  the  use  of  a  smaller  gusset-plate  at  E  which  may 

be  counterbalanced  by  the  ad- 
ditional metal  required  for  the 
splice  beyond  E.  (Figs.  22b 
and  22c.) 

Joint  G,  Fig.  7.  The  pieces 
BG  and  EG  are  shop-riveted 
to  the  gusset  on  one  side  and 
FIELD-RIVETED  on  the  Other.  In 
order  to  make  the  joint  sym- 
metrical, the  number  of  shop- 
RiVETS  is  made  the  same  as 
required  for  the  field-connection.  In  this  case  the  top  chord  requires  five 
rivets  and  the  web-member  three.  Two  rivets  may  be  used  in  the  sag-tie. 
(Fig.  22d.) 

Field-Connections.  Bolts  are  often  used  instead  of  rivets  for  making  field- 
connections.  If  the  bolts  fit  the  holes  snugly,  there  is  no  serious  objection  to 
their  use.  In  fact  a  good  bolt  is  better  than  a  poor  rivet.  For  important  work, 
however,  bolts  should  not  be  used  unless  turned  true  to  size  and  driven  into  true 
holes.     Open  holes  or  holes  for  field-rivets  are  indicated  by  black  circles. 

Shop-Drawings.  It  is  not  advisable  for  the  architect  to  make  complete 
drawings  for  the  steelwork.  He  should  make  what  are  usually  designated  as 
general  drawings.    These  are  made  to  scale  and  give  the  general  dimensions 


Fig.  22d.     Detail  of  Joint  G,  Fink  Truss,  Fig.  7 


Joints  of  Steel  Trusses 
G 


1163 


C  E         Span  70' Rise  14'5' 

Fig.  23.     Fink-truss  Diagram.     (See,  also,  Figs.  23a  to  23e)  , 


v^ 

o    o    O    O    O    O    O    1 
o^o   o    o   o    O   O   Oi 

6  X  4  X  yl  Lb. 

'O' 

, 

•    •       • 

•   •       • 

1 

,•/ For  kneebrac6 


Fig.  23a.    Detail  of  Joints  .4,  5  and  C  of  Fig.  23 


^^  Fig.  23b.    Detail  of  Joint  D,  Fig  23. 

?5^ 


l9Jq£xl3 


X    ^ 

^^£^ 

'^y.n.\         . 

6i4iJ«L«. 

tO    o   o    o 

• 

L.!.-.-i»---.. 

E 

^8x%"Pl. 

Fig.  23c.    Detail  of  Joint  £,  Fig.  23 


1164 


l)esign  and  Construction  of  Roof-Trusses  Chap.  28 


and  sizes  of  the  various  members,  and  show  each  rivet  approximately  in  its 
proper  position.  The  manufacturer  who  fabricates  the  structure  prefers  to 
make  his  own  shop-drawings  to  conform  with  his  standards  and  methods. 

Examples  from  Practice.  Figs.  23  to  23e  show  the  details  of  a  modern 
shop-truss.  These  details  were  taken  from  the  shop-drawings  but  with  the 
rivet-spacing  omitted.     No  metal  under  Me  in  thickness,  or  rivets  under  %  in 


Fig.  23d.     Detail  of  Joint 
F,  Fig.  23 


Fig.  23e.     Detail  of  Joint  G,  Fig.  23 


in  diartieter,  are  used.  Another  point  may  be  mentioned  in  connection  with 
this  truss;  very  few  bevel-cuts  are  made.  The  contrary  appears  to  be  the 
case  for  the  details  of  the  very  light  truss  shown  in  Figs.  24  to  24e,  in  which 
BEVEL-cuTS  are  made  on  the  angles  and  more  cuts  than  necessary  on  the  gusset- 
plates.     These  two  trusses  were  designed  by  manufacturers  widely  separated 


2-4'x  3"x  ^i''        ;C   2-3h\2H''xX,i'    jE 
I  I 


2-2K'^  2>i"x  X"i.» 


Fig.  24.    Fink-truss  Diagram.     (See,  also,  Figs.  24a  to  24f) 


and  are  quite  different  in  their  details;    and  the  variations  emphasize  the  fact 
that  the  architect  should  not  attempt  to  make  shop-drawings. 

Trusses  with  Knee-Braces.  Fig.  25  represents  joint  i  of  Fig.  55,  Chapter 
XXVI,  and  was  engraved  from  the  working  drawing  made  by  the  New  Jersey 
Steel  and  Iron  Company,  Trenton,  N.  J.  Another  detail  of  a  truss-connection 
to  a  column  is  shown  in  Fig.  26.  This  was  used  in  the  template-shop  roof-truss, 
Ambridge  plant  of  the  American  Bridge  Company,  Ambridge,  Pa.     Fig.  27 


Joints  of  Steel  Trusses 


1165 


Fig.  24a.    Detail  of  Joint  A,  Fig.  24 


Fig.  24b.    Detail  of  Joint  B,  Fig.  24, 


1166  Design  and  Construction  of  Roof-Trusses         Chap.  28 


li  rivets  U  this  memboi 


Fig.  24c.    Detail  of  Joint  D,  Fig.  24 


Fig.  24d.     Detail  of  Joint  F,  Fig.  24 


Joints  of  Steel  Trusses 


1167 


1  /r 


%  i-Jveta  ia  out  leg  X/"^^^!?^ 

r      l-2"x  Ji"  I.  ^ 


Fig.  24e.     Detail  of  Joint  C,  Fig.  24 


21*x  ^" plate  sVv 
4-2J^x2"ii4''LnO* 
lug"Z"2x  J-^'l  9Jf^ 
17VboUs2Ji'' 
8-%"bolt8  2"i 


'-7'9X 


Kivef8.b 

See  Column  DetiUU' 


Fitr.  1^.     Detail  of  Toint  1.  Fie.  55.  Chapter  XXVI 


1168 


Design  and  Construction  of  Roof-Trusses         Chap.  28 


shows  the  wall-end  of  a  small  truss  supported  by  brick  walls.    The  intersection 
of  the  STRESS-LINES  is  approximately  in  a  point  above  the  center  of  the  support. 


Fig.  26.     Connection  of  Steel  Truss  with  Steel  Columns 


Bed  PI.  12  X  12  X  J^ 
Anchor  Bolts  l"Diani.  13  long 
Anchor  PI.  5"xl0"x%" 


G©) 

^O^O^O^O^ 

on\ 

^^o'^d^d^  ^  i 

&> 

TOP  VIEW  OF  SHOE  PLATE 

SHOWING  ANCHOR    BOLTS 

IN  SLOTTED  HOLES 


[  Fig.  27.    Wall-end  of  Steel  Truss.    Support  and  Anchoring-details 

This  condition  is  seldom  considered  by  architects.  Usually  it  is  possible  without 
any  extra  expense  to  satisfy  tliis  requirement  and  thereby  to  a  great  extent  pre- 
vent unknown  bending-stresses. 


Purlins  and  Purlin-Connections 
5 1   Purlins  and  Purlin- Connections 


1169 


Purlins.  Where  the  roofing  is  supported  directly  on  the  purlins,  as  is  gen- 
erally the  case  in  light  steel  roofs,  the  purlins  and  trusses  are  usually  spaced  so 
close  together  that  simple  rolled  shapes  may  be  used  for  the  purlins.     For 


Fig.  28.    Puriin-connections.    Steel  Clips,  Angles  and  Z  Bars 


.    Fig.  29.    Purlin-connections.    Steel  Sections  with  Wooden  Nailing-strips 

spans  between  trusses  of  from  8  to  lo  ft,  angles  are  commonly  used,  and  for 
greater  spans,  Z  bars,  channels  and  I  beams.  Wooden  Purlins  are  often  used 
with  steel  trusses.  If  steel  purlins  support  wooden  rafters  or  plank  roofing, 
a  nailing-strip  of  wood  is  bolted  to  the  purlin,  as 
shown  in  Fig.  29,  When  the  distance  between  purlins 
is  15  ft  or  more,  a  line  of  ^^-in  rods  should  run  from 
the  ridge  through  the  purlins,  to  prevent  them  from 
sagging  in  the  plane  of  the  roof.  The  purlin  at  the 
ridge  must  be  designed  to  take  the  vertical  com- 
ponent of  the  stress  in  these  rods. 

Purlin-Connections.  Figs.  28,  29  and  30  show  a 
few  of  the  various  methods  of  fastening  the  purUns  to 
the  trusses. 

Design  of  Purlins.  Fig.  31  shows  the  cross- 
sections  of  a  rectangular  wooden  purlin  and  of 
the  usual  rolled  steel  shapes  employed  for  purUns. 
As  stated  on  page  11 70,  when  using  wooden  purlins 
the  formula  for  the  stress  in  the  outer  fiber  is  true 
only  when  used  with  reference  to  the  principal  axes  of  the  section.  Then, 
if  one  principal  axis  does  not  lie  in  the  plane  of  the  loading,  the  loading  must 
be  resolved  into  two  components,  respectively  parallel  to  the  two  principal 
axes.     (See,  also,  pages  573  and  593.) 


Fig.  30.    Purlin-connection, 
Braced  Channel 


1170 


Design  and  Construction  of  Roof-Trusses  Chap.  28 


Let  S'=  the  fiber-stress  with  reference  to  the  principal  axis,  A  A,  for  the  rec- 
tangle, i-i  for  the  I  beam  and  channel,  and  4-4  for  the  angle  and  Z  bar.  M'  =» 
the  bending  moment  of  the  component  of  the  load  which  lies  in  the  plane  per- 
pendicular to  the  above  axis.    /'  =  the  moment  of  inertia  of  the  section  with 


Fig.  31.     Sections  of  Wooden  and  Steel  Purlins 


reference  to  the  above  axis,  c'  =  the  distance  of  any  selected  fiber  from  the 
above  axis.  For  the  other  principal  axis  use  S",  M",  I"  and  C";  then  if  »S  is 
the  resultant  fiber-stress, 

S  ^S'  ^S"  =  We'll'  +  M"c"ll" 
For  the  rectangle, 

5  =  y  -f-  5"  =  6  M'lhd  2  -f  6  W'lhH 
For  the  channel  and  I  beam, 

5=^+5"=  M'dll  /i-i  -f  M"hl2  72-2 

For  the  angle  and  Z  bar, 

S  =S'  ^S"  =  M'c'/h^^-\-M"c"h-z 

The  application  of  these  formulas  offers  no  difficulties  except  in  the  cases 
of  ANGLES  and  Z  bars.  For  the  other  forms,  the  values  of  /  and  c  are  given  in 
the  tables  of  properties  of  the  sections  (Chapter  X).  The  locations  of  the  prin- 
cipal axes  for  the  Z  bars  and  angles  are  also  given  in  the  tables,  but  the  values 
of  c  are  not  given  for  any  of  the  fibers.  The  easiest  way  to  get  the  value  of  c 
in  any  particular  case  is  to  draw  the  section  of  the  angle  or  Z  bar  full  size,  locate 
Uie  principaJ  axes  and  then  measure  the  actual  distances,  c. 


Data  for  Wind-Pressure.     Building  Laws  1171 


CHAPTER  XXIX 

WIND-BRACING  OF  TALL  BUILDINGS 

By 
N.  A.  RICHARDS 

OF 
PURDY  &  HENDERSON,   INC.,   CIVIL   ENGINEERS 

1.   Data  for  Wind-Pressure.     Building  Laws 

Tall  Buildings  of  Modern  Construction,  that  is,  buildings  with  skeleton 
frames  and  light  curtain  walls  or  (iller  walls,  require  that  resistance  to  wind- 
pressure  be  considered  with  care.  The  proportions  of  a  building  and  the  arrange- 
ment and  strength  of  the  walls  determine  to  what  extent  special  bracing  must 
be  provided.  Building  ordinances  in  the  larger  cities  usually  require  consider- 
ation of  a  stated  wind-pressure.  Where  such  ordinances  do  not  definitely  fix 
the  assumed  pressure,  a  unit  force  of  30  lb  per  sq  ft  of  surface  is  generally 
considered  proper  and  adequate.     (See,  also,  page  150.) 

Building  Laws.  The  following  are  extracts  *  from  the  building  ordinances  of 
New  York  City,  Chicago,  Philadelphia  and  Baltimore  with  reference  to  wind- 
pressure: 

New  York  (ipi7) 

"When  Considered.  All  buildings  over  150  ft  in  height  and  all  buildings 
or  parts  of  buildings  in  which  the  height  is  more  than  four  times  the  minimum 
horizontal  dimension,  shall  be  designed  to  resist  a  horizontal  wind  pressure 
of  30  lb  for  every  square  foot  of  exposed  surface  measured  from  the  ground  to 
the  top  of  the  structure,  including  roof,  allowing  for  wind  in  any  direction. 

"Stability.  The  overturning  moment  due  to  wind  pressure  shall  not  exceed 
75  per  cent  of  the  moment  of  stability  of  the  structure,  unless  the  structure  is 
securely  anchored  to  the  foundation.  Anchors  shall  be  of  sufficient  strength 
to  safely  carry  the  excess  overturning  moment,  without  exceeding  the  working 
stress  prescribed. 

"Allowable  Stresses.  When  the  stress  in  any  member  due  to  wind  does 
not  exceed  50  per  cent  of  the  stress  due  to  live  and  dead  loads,  it  may  be  neg- 
lected. When  such  stress  exceeds  50  per  cent  of  the  stress  due  to  live  and  dead 
loads,  the  working  stresses  prescribed  may  be  increased  by  50  per  cent  in  design- 
ing such  members  to  resist  the  combined  stresses." 

Chicago  (191 5) 

"All  buildings  and  structures  shall  be  designed  to  resist  a  horizontal  wind 
pressure  of  twenty  pounds  per  square  foot  for  every  square  foot  of  exposed  sur- 
face. In  no  case  shall  the  overturning  moment  due  to  wind  pressure  exceed 
seventy-five  per  cent  of  the  amount  of  stability  of  the  structure  due  to  the  dead 
load  only. 

"For  stress  produced  by  wind  forces  combined  with  those  from  live  and 
dead  load,  the  unit  stress  may  be  increased  fifty  per  cent  over  those  given  above; 
but  the  section  shall  not  be  less  than  required  if  wind  forces  be  neglected." 

*  Quoted  literally.  Form  in  general  not  edited  or  changed.  Some  paragraph-captions 
added  by  associate  editor. 


1172  Wind-Bracing  of  Tall  Buildings  Chap.  29 

Philadelphia  (191 5) 

Wind  Pressure.  "In  all  buildings  allowances  shall  be  made  for  wind  pres- 
sure, which  shall  not  be  figured  at  less  than  thirty  pounds  per  square  foot  of 
elevation  where  erected  in  open  spaces  or  upon  wharves.  In  high  buildings, 
erected  in  built-up  districts,  the  wind  pressure  shall  not  be  figured  for  less  than 
twenty-five  pounds  at  tenth  story,  two  and  one-half  pounds  less  on  each  succeed- 
ing lower  story,  and  two  and  one-half  pounds  additional  on  each  succeeding 
upper  story,  to  a  maximum  of  thirty-five  pounds  at  fourteenth  story  and  above. 

Wind  Bracing.  "Wind  bracing  may  be  provided  by  making  the  connection 
joint  between  girders  and  columns  sufficient  for  the  vertical  load  as  well  as  the 
bending  due  to  side  pressure;  or  brackets  may  be  placed  at  this  joint,  propor- 
tioned for  the  side  pressure;  or  diagonal  bracing  may  be  placed  between  columns, 
proportioned  to  transfer  the  shear  of  the  side  pressure  to  the  footings. 

Base  of  Column  must  be  Anchored.  Where  buildings  are  narrow  and 
tall,  so  that  the  overturning  due  to  wind  is  more  than  the  down  pressure  of  the 
unloaded  building,  the  base  of  column  must  be  anchored  down  to  a  sufficient 
foundation  to  counteract  this  upward  strain. "  * 

Baltimore  (1914) 

Wind  Pressure.  "AH  new  buildings  exposed  to  wind  shall  be  made  strong 
enough  to  resist  a  horizontal  wind  pressure  in  any  direction  of  thirty  pounds  per 
square  foot  of  exposed  surface,  measuring  the  entire  height  of  the  building. 

Calculation  of.  "The  additional  loads  caused  by  the  wind  pressure  upon 
beams,  girders,  walls  and  columns  must  be  determined  by  calculation  and  added 
to  other  loads  for  such  members,  as  provided  for  in  Section  19  of  this  Article.f 

Special  Bracing.  "Special  bracing  shall  be  employed  wherever  necessary 
to  resist  the  distorting  effect  of  the  wind  pressure. 

Overturning  Moment.  "In  no  case  shall  the  overturning  moment  due  to 
the  wind  pressure  exceed  fifty  per  cent  of  the  moment  of  the  stability  of  the 
structure. " 

Magnitude  of  Unit  Stresses  Used  for  Wind-Pressure.  As  the  above 
extracts  indicate,  it  is  generally  considered  proper  to  use  high  unit  stresses 
when  allowing  for  wind-pressure.  The  practice  is  based  on  the  assumption  that 
the  highest  unit  wind-pressure  will  occur  very  infrequently  and  that  its 
duration  usually  will  be  limited  to  a  very  few  moments.  It  should  be  noted 
that  the  combined  stresses  due  to  wind-loads  and  dead  and  live  loads  should 
not  exceed  ordinary  stresses  by  more  than  50%.  If  stresses  developed  by  the 
wind  alone  do  not  exceed  50%  of  those  due  to  dead  and  live  loads,  they  may  be 
neglected. 

2.    Conditions  Determining  or  Affecting  Wind-Bracing 
Construction  which  Resists  Wind-Pressure.    The  dead  weight  of  a  build- 
ing, the  exterior  walls,  the  interior  partitions  and  the  ordinary  connections  of 
beams  to  columns,  all  aid  in  resisting  wind-pressure,  but  to  a  degree  which  is 
not  determinable  in  any  exact  way;    and  these  factors  vary  greatly,  also,  in 
different  buildings.     Any  allowance  for  these  factors  must  be  largely  a  question 
of  pure  guesswork,  or  it  may  be  judgment,  based  on  the  resistance  which  other 
buildings  have  offered  when  no  special  bracing  was  provided.     It  is  therefore 
best  to  make  special  bracing  take  care  of  all,  or  very  nearly  all,  of  an  assumed 
MAXIMUM  pressure,  when  the  building  under  consideration  is  unusually  light  in 
construction,  or  when  its  proportions  are  such  as  to  make  resistance  to  wind- 
pressure  a  prime  consideration. 
*  Stress  is  meant, 
t  This  refers  to  a  section  of  the  Baltiniore  building  law#. 


Conditions  Determining  Wind-Bracing 


1173 


Height  and  Width  as  Affecting  Wind-Pressure.     It  is  generally  safe  to 
neglect  wind-pressure  in  structural  designs  for  buildings  ten  stories  or  less  in 

height,  where  the  average  width 
Hoot  is  not  less    than  one-third  the 

height.  It  is  also  usual  to  omit 
special  provision  for  wind-brac- 
ing in  higher  buildings  where  the 
width  is  two-thirds  the  height, 
or  more.  The  writer  believes 
the  above  approximations  repre- 
sent conservative  practice,  so  far 
as  general  rules  are  possible. 

Dead  Load  as  Affecting 
Wind-Pressure.  A  building 
should  not  be  so  proportioned 
that  the  overturning  moment 
of  a  wind-pressure  of  30  lb  per 
sq  ft  exceeds  75%  of  the  avail- 
able   RESISTING    MOMENT   of   the 

dead  load.  If  necessary,  the  col- 
umns should  be  anchored  to  the 
foundations. 

3.   General  Theory  of 
Wind-Bracing 
Buildings    Considered     as 
Cantilevers.   Buildings  are  usu- 
ally considered  to  resist  wind  as 

C  1 


Top  of  neighboring 
Building 


-^ 


SECTION 


l'6" 


-4-7'0^ 


I'e'' 


-5G'0- 


PLAN, 


Fig.  1.    Section  and  Plan  of  Wind-braced  Building 

CANTILEVER  GIRDERS  or  trusses,    planted  in  the  earth.     Assuming  a  building 
of  the  general  dimensions  shown  in  section  and  plan  in  Fig.  1.  with  a  wind-^ 


1174 


Wind-Bracing  of  Tall  Buildings 


Chap.  29 


pressure  against  side  yl,  the  walls  A  and  B,  together  with  the  cokimns, 
beams,  etc.,  in  these  walls,  arc  tV't  flanges  of  the  girders.  Walls  C  and  Z>, 
with  their  framing,  together  with  other  intermediate  lines  of  vertical  framing, 
form  the  web  of  the  cantilever  and  transmjt  the  vertical  shears.  Steel  brac- 
ing in  horizontal  planes  is  seldom  necessary,  as  ordinary  floor-constructions 
are  generally  sufficient  to  transmit  wind-loads  to  the  vertical  bracing.  In  some 
cases,  however,  it  is  necessary  to  add  steel  bracing  in  the  floors.  Such  a  case 
is  found  in  the  tower  of  the  new  Custom-House,  in  Boston,  Mass.  The  ele- 
vators and  stairs  are  next  to  the  west  wall  throughout  the  typical  stories.  Under 
this  arrangement  there  is  no  adequate  provision  in  the  ordinary  floor-construc- 
tion for  a  wind-pressure  on  the  north  or  south  face  to  reach  the  resisting  bracing 
in  the  west  face,  as  the  various  open  wells  cut  off  nearly  all  direct  connection 
between  the  floors  and  this  wall.  Flat  plates  were  therefore  added  on  top  of  the 
floor-beams  at  each  floor-level,  running  out  from  the  wall  girders  behind  the 
wells  into  the  main  floor-construction,  and  attached  at  each  end  with  connec- 
tions sufficient  to  transmit  the  horizontal  increment  of  the  wind-ptessure  at 
each  floor  to  the  bracing  which  resists  it. 

4.   Arrangement  of  Wind-Bracing 

Sf  Usual  Position  of  the  Bracing.  As  wind-pressure  is  assumed  to  be  uni- 
formly distributed  over  the  face  of  a  building,  it  is  best  to  arrange  systems  of 
bracing,  as  nearly  as  may  be,  symmetrically  about  the  axis  of  each  face.  It  is 
generally  easier  to  conceal  in  the  exterior  walls  the  required  knees,  gussets,  or 
other  braces,  and  bracing  is  usually  placed  there.  When  the  lines  of  bracing 
have  been  selected,  the  areas  of  wall-surfaces  which  bring  wind-pressure  to  each 
are  readily  determined. 

Bracing  of  Buildings  of  Irregular  Plan.  Some  buildings  are  of  such  shape 
that  it  is  impossible  to  provide  bracing  of  equal  stiffness  in  lines  symmetrical 
about  the  center  of  wind-pressure.  This  is  notably  true  when  the  plan  is 
TRIANGULAR,  as  in  the  so-called  Flatiron  Building  or  in  the  Times  Building, 
New  York  City.  The  result  is  a  tendency  in  such  buildings  to  twist  about  a 
VERTICAL  AXIS.  The  analysis  of  the  resistance  offered  by  a  building  to  a  twist 
of  this  sort  is  unsatisfactory  and  complicated.  The  stresses  produced  in  any 
usual  case,  however,  are  small,  if  not  negligible.  In  the  examples  mentioned 
above,  provision  against  twist  is  made  by  the  use  of  deep  spandrel  girders  all 
around  the  building  at  each  floor-level. 


5.    Types  of  Wind-Bracing 

Ordinary  Beam  and  Girder  Column-Connections.  Wind-bracipg  should 
be  so  proportioned  that  the  joints  between  horizontal  and  vertical  members  are 
sufficient  to  prevent  the  distortion  of  the  frame,  and  the  main  horizontal  and 
vertical  members  sufficient  to  resist  any  bending  moments  produced  throughout 
the  joints,  as  well  as  any  direct  loads  coming  on  them.  The  ordinary  connec- 
tions of  steel  beams  to  steel  columns  (Fig.  2)  provide  considerable  resistance  to 
a  distortion  from  side  thrust.  This  is  also  true,  of  course,  of  connections  between 
beams  and  columns  made  of  cast  iron  or  concrete;  but  as  these  types  are  not  well 
adapted  to  construction  where  wind-bracing  is  required,  they  will  not  be  con- 
sidered. A  usual  connection  for  beams  or  girders  to  columns  consists  of  clip- 
angles  above  and  below  the  beam,  and  perhaps  a  stiffener  below,  if  the  beam 
is  large.  Usually,  in  high  buildings,  four  rivets  are  used  to  connect  either  flange 
to  the  clip-angles  above  and  below,  and  four  to  connect  each  clip  to  the  column. 
The  value  of  four  rivets,  in  single  shear,  multiplied  by  the  depth  of  the  beam. 


Types  of  Wind-Bracing 


1175 


gives  the  resisting  value  of  such  a  connection  against  a  moment  due  to  side 
thrust.  In  lower  buildings  it  is  usual  to  specify  two  rivets  instead  of  four  in 
each  flange,  and  in  the  case  of  very  high  or  narrow  buildings,  six  rivets  are  some- 
times used. 

Resistance  of  Beam  and  Girder-Connections  to  Wind-Pressure.    It  is 

sometimes  assumed  that  the  connections  of  all  beams  or  girders  (running  in  the 


r~~T — ' 

«     )   Oj 
(    )  o 

"ol(  |> 

o 

..      «^:^         O 

o      .^^-^ — —A 

<      > 

Ml' 

(    > 

'V 

^ 

Fig.  2.    Ordinary  Girder  and 
Column-connections 


Fig.  3.    Heavy  Girder  and 
Column -connection 


same  direction  as  the  wind)  to  columns  act  at  their  full  value  to  resist  the  wind. 
This  is  undoubtedly  wrong,  because  the  many  connections  could  probably  not 
be  made  to  work  at  the  same  time,  and  also  because  building-frames  are  seldom 
arranged  so  that  such  a  result  could  be  possible,  under  any  rational  assumption, 
in  regard  to  the  distribution  of  the  vertical  shears.  Side  clips  are  sometimes 
added  to  the  column-connections  to  furnish  additional  stiffness.  They  are  not 
of  great  value,  however,  as  on  most  beams  they  are  not  deep  enough  to  help 
much. 

Heavy  Column-Connections  in  Wind-Resistance.  Column-connections 
are  sometimes  made  very  heavy,  as  shown  in  Fig.  3.  A  connection  of  this  kind 
can  be  arranged  to  resist  a  large  twist.  The  resisting  value  is,  of  course, 
measured  by  the  resisting  moment  of  the  rivets  connecting  the  beam  to  the  cHp- 
angles,  or  by  the  connection  of  the  angles  to  the  column.  This  type  is  used  wher«» 
the  resistance  to  wind  is  provided  for  in  a  very  large  number  of  connections, 
perhaps  in  all  the  column-connections,   throughout   the   building.      Such   an 


1176  Wind-Bracing  of  Tall  Buildings  Chap.  29 

arrangement  was  used  in  the  Hudson  Terminal  Buildings,  New  York  City. 
There  are  several  objections  to  this  type  of  connection.  Double  beams  or 
girders  are  required,  and  the  resulting  finish  is  awkward  in  appearance;  tne 
cost,  also,  of  double,  compared  with  single,  beams  and  girders,  is  high.  The 
additional  fireproofing,  also,  increases  the  expense,  and  on  the  whole,  it  docs  not 
generally  prove  a  satisfactory  method  of  stiffening  a  building. 

The  Gusset-Plate  Type  of  Wind-Bracing.  In  addition  to  ordinary  beam 
and  girder-connections,  as  described  in  the  preceding  paragraphs,  there  are 
several  distinct  types  of  special  wind-bracing  commonly  employed.  Perhaps 
the  most  common  form  is  the  gusset-plate,  shown  in  Fig.  4.  This  is  not 
usually  an  economical  type,  <as  it  requires  much  field-riveting  and  results  in 
large  bending  moments  in  the  columns  and  girders.  It  accommodates  itself 
well,  however,  to  walls  in  which  there  are  openings,  and  is  generally  easily  con- 
cealed by  architectural  treatments. 

The  Knee-Brace  Type  of  Wind-Bracing  shown  in  Fig.  5  is  also  com- 
monly used  where  wind-bracing  is  placed  in  exterior  walls. 

The  Sway-Rod  Type  of  Wind-Bracing  shown  in  Fig.  6  is  theoretically 
the  most  economical  type  of  wind-bracing,  but  is  now  little  used.  It  is  diflficult 
to  arrange  openings  in  walls  or  partitions  in  which  the  sway-rods  are  placed, 
and  they  cut  up  the  masonry  considerably. 

The  Latticed-Girder  Type  of  Wind-Bracing  shown  in  Fig.  7  is  sometimes 
used  where  deep  bracing  is  desirable  for  stiffness,  and  where  the  stresses  are 
light. 

The  Portal  Type  of  Wind-Bracing  shown  in  Fig.  8  is  cumbersome  and 
expensive,  but  is  sometimes  necessary  where  large  openings  are  required  between 
columns. 

6.    Computation  of  Wind-Stresses 

The  Shears  to  be  Transmitted  by  Wind-Bracing  of  any  Type  are  the 

same  in  any  given  case,  but  the  bracing  of  each  type  transmits  these  shears  in  a 
different  hianner,  and  thus  each  must  be  considered  separately.  It  is  as  though 
a  PLATE  GIRDER  with  SOLID  WEB  Were  set  on  end  in  the  ground,  a  side  thrust  ex- 
erted, and  the  web  then  cut  away  at  successive  levels  corresponding  to  the 
stories  in  a  building.  The  amount  of  the  shears  to  be  transmitted  between  the 
flanges  would  not  vary  as  holes  in  the  web  were  made,  but  the  road  by  which  the 
shears  traveled  would  need  to  be  determined  by  the  character  of  the  resulting 
construction  after  the  holes  were  cut;  and  the  exact  character  of  the  secondary 
stresses,  also,  set  up  in  the  remaining  portions  of  the  web,  would  depend  en- 
tirely upon  the  number  and  size  of  holes  and  their  position  in  the  web.  The 
investigation  of  the  shears  and  moments  taken  care  of  by  the  individual  members 
of  a  bracing-system  may  be  likened  to  a  study  of  the  secondary  stresses  in  the 
mutilated  web  in  the  imaginary  plate  girder  described  above.  For  a  building 
it  is  generally  convenient  to  determine  the  vertical-shear  increments  at  each 
level  of  bracing,  and  use  these  increments  in  the  further  analysis  of  the  bending 
moments  and  shears  in  the  individual  members  of  the  system. 


7.    Illustration  of  Method  of  Computing  Wind-Stresses 

Thrusts,  Vertical  Shears  and  Moment-Increments.  If  bracing  is  plaa 
in  the  walls  C  and  D,  Fig.  1,  it  is  assumed  that  one-half  the  length  of  thebuildi; 
contributes  pressure  to  each  line.  Let  it  be  further  assumed,  for  the  presei 
that  these  lines  of  bracing  are  the  only  features  of  the  construction  offering 
resistance  to  wind-bracing  against  side  A.     Then,  assuming  the  wind  to  blo] 


1 


Illustration  of  Method  of  Computing  Wind-Stresses         1177 

at  50-lb  pressure  per  sq  ft,  perpendicular  to  side  A,  there  are  horizontal  thrusts 
in  each  story,  on  each  line  of  bracing,  of  50  by  12  by  30  lb,  or  18  000  lb.  Re- 
ferring to  Table  I,  page  1178,  there  are  found  listed  in  the  second  column  of  the 
table  these  horizontal  thrusts  at  each  floor.  It  is  assumed  that  no  additional 
wind-pressure  reached  the  building  below  the  fourth  floor.  In  the  third  column 
of  the  table  these  horizontal  thrusts,  S//,  are  summarized  from  the  top  down  to 
each  floor-level,  giving  the  total  horizontal  thrusts.  For  example,  202  500  lb 
is  the  total  horizontal  thrust  down  to  and  including  the  tenth  floor.  Each  tier 
of  bracing  must  transmit  a  vertical  shear  equal  to  the  difference  in  flange- 
stress  between  a  point  midway  in  the  story  above  the  tier  in  question,  and  a 
point  midway  in  the  story  below.  This  difference  of  flange-stress  can,  of  course, 
be  found  by  ascertaining  the  difference  in  bending  moments  between  the  two 
points,  and  dividing  by  the  effective  depth  of  the  system,  as  in  a  plate  girder  or 
truss.  It  will  now  appear  that  the  differences  in  moments  applying  to  each  tier 
may  easily  be  found  and  tabulated.  These  will  be  called  the  moment-incre- 
ments. They  have  been  tabulated  for  the  assumed  case  in  the  fifth  column  of 
the  table.  Of  course,  the  sum  of  all  the  moment-increments  must  equal  the 
TOTAL  OVERTURNING  MOMENT  of  the  wind.  The  simplest  way  to  obtain  the 
moment-increment  for  any  tier  is  to  multiply  the  total  horizontal  thrust,  2^, 
down  to  the  level  in  question  by  the  distance  between  points  midway  in  the 
stories  above  and  below  the  tier.  Thus,  for  the  tenth  floor,  202  5cx)  by  12  equals 
2  430  000  f  t-lb 

The  Increments  of  Vertical  Shear  are  found  by  dividing  the  moment- 
increments  by  the  effective  depth  of  the  cantilever,  in  this  case,  47  ft.  The 
VERTICAL  INCREMENTS  are  listed  in  the  sixth  column  of  the  table.  It  is 
usual  to  take  the  full  depth  between  outside  columns  as  the  effective  depth  of 
the  cantilever.  This  is  not  strictly  correct  where  there  are  four  or  more  columns 
in  the  plane  of  the  bracing,  but  the  assumption  is  made  on  the  ground  that  the 
walls  A  and  B  furnish  flanges  which  are  so  many  times  more  effective  than  the 
intermediate  columns  that  the  latter  may  be  neglected.  If  there  are  a  number 
of  columns  in  the  plane  of  the  bracing,  say  six  or  seven,  this  assumption  becomes 
rather  too  inaccurate,  and  the  effective  depth  should  be  reduced.  The  function 
of  the  bracing,  as  heretofore  stated,  is  to  carry  between  the  flanges  at  each  floor- 
level  the  increments  of  vertical  shears  thus  found.  The  summation  of  all  the 
vertical  increments  from  the  top  down  gives  the  total  vertical  load  and  up- 
IJFT  due  to  wind,  on  the  corner-columns,  or  more  correctly,  on  the  outside 
flanges  of  the  girder. 

Excess  Vertical  Shear.  In  this  assumed  case,  the  total  uplift  exceeds  the 
probable  dead  and  live  loads  on  the  corner-columns.  This,  however,  is  not 
serious,  provided  there  are  sufficient  means  furnished  for  transferring  any  excess 
of  load  or  uplift  into  the  walls  A  and  B,  which  act  as  flanges  to  the  wind-resisting 
girder.  As  a  general  rule,  the  side  walls  of  a  city  building  are  not  much  reduced 
by  windows,  and  in  higher  buildings  there  are  usually  spandrel  bearns  in  the 
walls  at  each  floor.  With  such  an  arrangement  a  considerable  amount  of  excess 
shear  can  be  taken  care  of.  In  some  cases  special  bracing  may  be  necessary,  at 
least  in  the  end-panels  of  wafls  A  and  B. 

The  Total  Vertical  or  Flange-Stress.  When  considering  any  question 
regarding  the  vertical  lo.\d  or  uplift,  such  as  the  one  described  in  the  pre- 
ceding paragraphs,  it  should  be  kept  in  mind  that  totals  should  be  used  without 
.  reductions  of  any  sort.  Vertical  forces  forming  couples  to  resist  the  wind  must 
be  the  same  whether  they  are  transmitted  through  the  masonry  walls  or  through 
special  steel  bracing.  Referring  again  to  the  illustration  of  the  plate  girder  set 
up  in  the  earth,  the  vertical  shears  are  dependent  only  on  the  force  of  the  wind 


1178 


Wind-Bracing  of  Tall  Buildings 


Chap.  29 


and  the  effective  depth  of  the  girder.  The  exact  web-stress  will  vary  with  the 
form  and  arrangement  of  the  web,  but  the  total  vertical  or  flange-stress 
must  remain  the  same  in  any  case. 

Indeterminate  Resistance-Factors.  An  analysis  which  makes  no  allowance 
for  the  resistance  of  walls,  ordinary  connections,  etc.,  to  wind  is  fairly  direct 
and  simple,  and  the  bracing  can  be  proportioned  with  as  much  precision  as  any 
structural  feature.  When  the  wind-resistance  of  a  building  is  a  primary  con- 
sideration, as  in  a  tower,  the  analysis  should  be  made  thus,  for  only  in  this  way 
can  a  result  be  obtained,  where  it  is  not  required  to  rely  on  almost  unsupported 
judgment  for  the  value  of  indeterminate  factors  of  resistance.  When, 
however,  ordinary  buildings  of  usual  proportions  are  under  consideration,  it  is 
customary  and  well  to  make  allowance  for  the  intederminate  factors,  to  the 
best  of  one's  judgment.  This  is  necessary  for  economy,  and  is  perfectly  proper 
^o  long  as  usual  cases  are  to  be  dealt  with. 


Table  I.     Thrusts,  Shears,  Moment-Increments,  etc.,  for  the  Building 
Shown  in  Fig,  1 


I 

Floor 

II 

Horizon- 
tal thrust 
at  each 
floor, 
H 

III 
Total  hori- 
zontal 
thrusts 
from  roof 
to  each 
floor, 
2/f 

IV 

Arm, 
A 

'  V 

Moment- 
incre- 
ment, 
M 

VI 

Vertical 
incre- 
ment, 
V 

VII 

Total  ver- 
tical in- 
crements 
from  roof 
down, 

VIII 

Corrected 
vertical 
incre- 
ment, 

Roof 

20 

19 

i8 
17 
i6 
IS 
14 
13 

12 

II 
ID 

9 
8 
7 
6 
S 
4 
3 
2 
I 

lb 

4  500 
i8  ooo 
18000 
18000 
18000 
18  000 
18  000 
18  000 
18000 
18000 
18000 
18  000 
18000 
18  000 
18  000 
18000 
18  000 
■    18000 

lb 

4  Soo 
22500 
40500 
58500 
76500 
94500 
112  500 
130500 
148500 
166  500 
184  500 
202  500 
220  500 
238500 
256500 
274500 
292500 
310  500 
310500 
310500 
310500 

ft 
6 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 

ft-lb 

27  000 

270000 

486000 

702  000 

918  000 

I  134  000 

I  350000 

I  566  000 

I  782000 

1  998000 

2  214  000 
2  430000 

lb 
550 
5750 
10350 
14950 
19500 
24  100 
28700 
33  300 
37900 
42  600 
47  200 
51  800 
56400 
61  000 
65  600 
70  200 
74700 
79300 
79300 
99200 
99200 

lb 

550 

6300 

16  650 

31  600 

51  100 

75200 

103900 

137  200 

175  100 

217700 

264900 

316700 

373  100 

434  100 

lb 

4  600 
9300 
13900 
18  500 
23  100 
27700 

12 
12 
12 
12 
12 
12 
12 
15 
15 

2  646  000 

2  862000 

3  078  000 
3  294  000 
3510000 
3  726000 

3  726000 

4  657  500 
4  657  500 

499700 
569900 
644  600 
723900 
803  200 
902  400 
I  001  600 

32300 
36900 
41  400 
46000 
46  000 
65900 
65900 

Scheme  for  Developing  Special  Bracing.  The  writer  offers  the  following 
as  a  reasonable  and  consistent  scheme  for  developing  special  bracing  when 
such  allowances  are  considered.  Unfortunately,  it  does  not  seem  possible  to 
recommend  any  method  of  determining  the  correct  allowances,  except  such  gen- 
eral guides  as  are  mentioned  in  Subdivision  2,  page  1172.  In  each  instance 
some  one  familiar  with  construction  and  usual  practice  should  decide  how  far 


Analysis  of  Stresses  in  Different  Types  of  Wind-Bracing     1179 

down  from  the  top  it  will  be  safe  to  assume  the  building  rigid  and  secure  against 
wind,  without  special  bracing.  In  this  case,  let  it  be  assumed  that  the  building 
is  capable  of  safely  resisting  the  wind,  without  the  aid  of  special  bracing,  as  fat 
down  as  the  thirteenth  floor.  Then,  assuming  that  the  walls,  beam-connections, 
etc.,  remain  reasonably  the  same  in  the  floors  below,  it  is  fair  to  say  that  the 
amount  of  the  increment  at  the  fourteenth  floor  can  be  deducted  from  the 
moment-increment  at  each  floor  below. 

Corrected  Vertical  Increments.  The  corrected  vertical  increments 
found  in  this  manner  should  be  used  only  in  the  proportioning  of  special  bracing. 
The  full  overturning  moment  of  the  wind,  and  the  full  vertical  shears,  should 
be  used  in  considering  all  other  effects  of  the  wind  and  the  resistance  of  the 
building  to  it.  It  should  also  be  borne  in  mind  that  this  method  of  proportion- 
ing bracing  is,  at  best,  largely  dependent  upon  individual  opinion,  and  in  any 
unusual  case  it  is  far  better  to  err  on  the  safe  side,  even  to  the  extent  of  disre- 
garding altogether  the  uncertain  factors  of  resistance.  The  corrected  vertical 
INCREMENTS  for  the  assumed  case  have  been  listed  in  the  eighth  column  of 
Table  I.  Since  the  flanges  of  the  building,  acting  as  an  upright  cantilever 
girder,  have  been  assumed  concentrated  in  the  outside  walls  A  and  B  (Fig.  1),  it 
follows  that  the  vertical-shear  increments  will  be  constant  from  outside  t6 
outside  of  bracing. 


8.   Analysis  of  Stresses  in  Different  Types  of  Wind-Bracing 

The  Horizontal  Thrusts,  which  must  be  carried  by  the  bracing  at  each  level 
as  struts,  are  small  and  can  usually  be  neglected.  The  maximum  thrust  at 
each  floor-level  can 
not  exceed  the  hori- 
zontal pressure  of  tlite 
wind  for  one  story, 
or,  in  the  example, 
i8  coo  lb. 

The  Total  Hori- 
zontal Shear.  The 
columns  in  the  brac- 
ing-system must  carry 
the  total  horizontal 
shear  in  each  story, 
but  this,  also,  is  usually 
very  small  in  compari- 
son with  the  shearing 
resistance  of  the  col- 
umns and  can  be  neg- 
lected. 

Stresses  in  Gusset- 
Plates.  Fig.  4  repre- 
sents   a  typical  panel 

of      G  U  S  S  E  T-BR  ACING . 

Under  the  influence  of 

a  side   pressure  there 

would  be  a  tendency  to  distort  the  frame,  changing  the  angle  between  the  vertical 

and  horizontal  members;  that  is,  the  columns  and  girders.  For  this  investigation,  a 

girder  at  any  level  is  considered,  with  gusset-plates  at  either  end,  as  shown.    These 

gusset-plates  act  to  prevent  the  distortion,  and  since  they  both,  at  either  end,  re- 


Fig.  4. 


Gusset-plate  Type  of 
Wind-bracing 


Fig.  5.    Knee-brace  Type  of 
Wind-bracing 


1180  Wind-Bracing  of  Tall  Buildings  Chap.  29 

sist  the  same  wind-action,  the  twisting  moment  in  each  has  the  same  sign.  But  if 
they  twist  in  the  same  direction  at  opposite  ends  of  the  girder,  there  is  somewhere 
along  the  girder  and  between  the  gussets  a  point  of  inflection  or  a  point  of  no 
BENDING.  The  position  of  this  point  varies  with  the  relative  strength  of  the  two 
gussets,  but  for  simplicity  it  is  usually  assumed  midway  between  them  and  they 
are  then  proportioned  to  take  care  of  the  resulting  moments.  Let  the  point  of 
inflection  in  the  example  be  thus  taken.  As  there  is  no  bending  moment  at  this 
point,  the  bending  moment  at  any  other  point  on  the  girder  may  be  found  by 
multiplying  V,  the  increment  of  vertical  shear  for  the  level  in  question,  by  the 
distance  from  the  point  of  inflection.  So,  at  the  toe  of  the  gusset-plate,  the 
bending  moment  on  the  girder  equals  V  multiplied  by  e,  and  this  is  the  maximum 
BENDING  MOMENT  ON  THE  GIRDER.  The  flange-stress  having  been  determined 
from  this  bending  moment,  it  is  possible  to  fix  the  number  of  rivets  required 
to  fasten  the  flanges  to  the  gusset.  The  connection  of  the  web  to  the  gusset 
must  provide  for  a  shear  equal  to  V.  V  multiplied  by  /  gives  the  moment  pro- 
duced through  the  gusset  at  the  face  of  the  column.  The  rivets  connecting 
the  gusset  to  the  column  must  be  sufl&cient  to  resist  this  moment. 

Points  of  Inflection  occur  in  the  columns  midway  between  the  gussets,  just 
as  in  the  girders.  The  bending  moment  in  the  column  may  be  obtained  approxi- 
mately by  assuming  the  moment  exerted  through  the  gusset-plates  to  be  applied 
in  the  form  of  a  couple  acting  at  points  two-thirds  of  the  way  out  from  the  center 
of  the  gusset  to  the  tips,  as  indicated.  The  maximum  bending  moment  in  each 
COLUMN  will  then  be  the  horizontal  force  P  multiplied  by  d.  P  is  obtained  by 
multiplying  F  by  /  and  dividing  by  c,  I  being  the  distance  from  the  inflection- 
point  in  the  girder  to  the  axis  of  the  column,  and  c  being  the  distance  between 
the  inflection-points  in  the  column  above  and  below  the  girder. 
^  Gusset-Plates  on  Both  Sides  of  Column.  If  there  are  gusset-plates  on 
TWO  SIDES  of  a  column,  as  is  usual  on  interior  columns,  the  maximum  bending 
moment  in  the  column  will  be  the  sum  of  the  maximum  moments  due  to  each 
gusset.  Gusset-plate  connections  are  easily  arranged  with  plate  girders  or  with 
double  channels,  or  even  with  I  beams. 

Stresses  in  Knee-Braces.  Let  Fig.  5  represent  a  typical  panel  of  knee- 
bracing.  As  described  in  the  preceding  paragraphs  on  gusset-plates,  there  must 
be  POINTS  OF  inflection,  and  consequently  points  of  no  bending,  in  the  girders 
and  also  in  the  columns.  These  points  are  assumed  midway  between  the  ends 
of  the  knee-braces  in  both  the  columns  and  girders.  Let  V  be  the  vertical 
increment  for  the  level  under  investigation. 

Then  P  =  Vl/c 

and  the  reaction  of  the  girder  at  the  column, 
R  =  Va/b 

Since  V  and  R  act  always  in  the  same  direction,  5  must  be  equal  to  their  sum. 
Hence  S^R+V 

Maximum  bending  moment  on  girder  =  Va 

or  the  equivalent 

Maximum  bending  moment  on  girder  =  Rb 
Maximum  bending  moment  on  column  =  Pd 
Stress  in  each  knee-brace  ==  y^S  cosecant  a. 

It  is  evident  that  R  is  the  shear  anywhere  between  the  intersection-point  of 
the  center  line  of  the  knee-braces  and  the  columns,  and  that  V  is  the  shear  any- 


Analysis  of  Stresses  in  Different  Types  of  Wind-Bracing    1181 


where  between  the  braces  at  either  end  of  the  girder.     All  web-splices,  and 
also  the  pitch  of  flange-rivets,  must  be  proportioned  from  these  shears. 

Arrangement  of  Braces  for  No  Bending  Moment  in  Girder  or  Column. 
It  is  apparent  from  the  above  that  the  nearer  a  and  d  approach  zero  the  less  the 
bending  moments  in  the  girder  and  column  become.  If  the  intersections  of  the 
center  lines  of  the  braces  can  be  arranged  so  that  a  and  d  become  zero,  there 
will  be  NO  BENDING  MOMENTS  in  the  girders  or  columns. 

Knee-Braces  on  One  Side,  Only,  of  Girder.    It  is  often  necessary  to 
arrange  knee-braces  on  one  sroE,  only,  of  the  girder,  either  above  or  below. 
In  a  case  of  this  kind  the  girder  itself  serves  as  one  arm  of  tlje  brace,  and 
The  stress  in  the  single  knee  =  S  cosecant  a 

R  and  5  are  as  determined  above,  but  there  must  also  be  taken  into  account 
the  horizontal  stress  in  the  girder,  due  to  its  action  as  one  arm  of  the  brace. 

Horizontal  stress  in  girder  =  Vl/{H c—  d) 

The  connection  between  the  column  and  the  girder  must  provide  for  the  com- 
bined action  of  R  vertical  and  Vl/iVzc  —  d)  horizontal. 

Stresses  in  Sway-Rods.  For  the  correct  analysis  of  sway-bracing  (Fig.  6), 
the  vertical  increments  should  be  found  in  a  manner  slightly  dififerent  from  that 
described  in  Subdivision 
7,  pages  1 176-9.  The 
horizontal  pressures  are 
found  as  before,  except 
that  the  total  pressures 
from  the  top  down  to 
each  floor  include,  in  each 
case,  the  additional  pres- 
sures against  areas  of  one- 
half  the  story  below.  The 
arm,  A,  for  each  level 
should  be  the  story- 
height  below.  (See  sec- 
tion, in  Fig.  1  and  fourth 
column  of  Table  I.)  The 
vertical  increments  are 
found  just  as  for  the  other 
types,  except  for  these 
slight  variations;  and, 
again,  these  vertical  in- 
crements are  constant 
throughout    each    story. 

The  STRESS  IN  ANY  DI- 
AGONAL equals  the  verti- 
cal increment  in  the  story  multiplied  by  the  cosecant  of  the  angle  a  (Fig.  6). 
It  is  assumed  that  the  diagonals  are  used  for  tension  only  and  that,  consequently, 
only  one  system  acts  at  a  time.  Each  horizontal  member  must  take  compression 
equal  to  the  vertical  increment  in  the  story  below,  multiplied  by  the  cotangent 
of  «.  If  the  joints  are  arranged  so  that  axial  lines  of  members  intersect,  there 
will  be  no  bending  either  in  the  columns  or  the  horizontal  members. 

Stresses  in  Latticed  Girders.  Let  V  in  Fig.  7  equal  the  vertical  increment 
for  any  story.  As  in  the  other  types,  V  is  constant  between  the  columns,  and 
the  stress  in  any  diagonal  equals  V  multiplied  by  the  cosecant  of  a.    As  in  the 


Fig.  6.     Sway-rod  Type  of 
Wind-bracing 


Fig.  7.    Latticed-girder  Type 
of  Wind-bracing 


1182 


WInd-BracIng  of  Tall  Buildings 


Chap.  29 


KSH 


fri 


vy 


iJlogr 


J 


Flange  7'!  floor 


OUSSET-TYPE  and  KNEE-BRACE  TYPE,  there  is  no  bending  at  the  middle  section 
of  the  girder-length,  and  consequently  no  stress  in  the  middle  section  of  the 
top  chord.  The  maximum  bending  moment  in  the  girder  is  at  the  column-face, 
and  this 

Maximum  bending  moment  in  the  girder  =  Vf 

The  maximum  chord-stress  is  at  this  same  point,  and  this 
Maximum  chord-stress  =  Vf/h 

The  connections  of  the  chords  to  the  columns  must  provide  against  this  max- 
imum stress. 

P  =  Vl/c 
and  the 

Maximum  bending  moment  in  the  column  =  Pd 

Stresses  in  Portal  Bracing.     It  is  not  possible  to  analyze  exactly  the 
stresses  in  portal  bracing  (Fig.  8),  when  it  is  used  in  connection  with  columns 

of  continuous  section.  The  analysis  here 
given  follows  that  of  C.  T.  Purdy  in  "  Modern 
Framed  Structures."  It  is  considerably  on 
the  safe  side,  and  for  ordinary  cases  can 
well  be  followed.  In  a  large  building,  where 
much  bracing  of  this  type  might  be  used, 
the  exact  form  of  the  portals  should  be 
determined,  and  greater  allowance  made  for 
the  effect  of  continuous  columns. 

Let  SH  equal  the  accumulated  force  of 
horizontal  shear  from  the  wind  at  the  floor 
next  above  floor  M,  applied  half  on  one 
side  and  half  on  the  other.  Let  Hi  equal 
the  force  of  the  wind  or  the  shear  directly 
tributary  to  floor  Al.  Then,  taking  moments 
about  O  (Fig.  8) 

VX2l=(ZH-hHi)c 
or 

F=:  (ZH4-ni)c/2l 
and  the 

Horizontal  reaction  =  J-^  (EH  -\-  Hi) 

To  determine  the  maximum  stress  in  the 
curved  flange  /,  assume  a  point  p  in  the 
flange  r,  horizontally  distant  x  from  the  line  WW,  and  at  the  distance  y,  meas- 
ured normal  to  a  tangent  to  any  point  in  the  flange  /;  then,  taking  the 
center  of  moments  at  the  left  extremity  of  the  distance  x,  the  stress  in  the 
flange  /  multiplied  by  y,  equals  V  multiplied  by  x,  or  Vx/y  equals  the  stress  in 
the  flange  /,  at  the  section  taken,  and  this  is  a  maximum  when  x/y  has  its  great- 
est value. 

Each  leg  of  the  portal,  including  the  column,  may  be  considered  as  a  canti- 
lever with  two  forces  acting  on  it,  the  horizontal  force  H  (ZH  +  Hi)  and  the 
vertical  force  (S//-f  Hi)  c/2  I,  the  flange  /  (of  the  right  leg  for  example)  being 
in  compression  and  the  column  itself  acting  as  a  tension-chord.  Assuming  a 
point  on  the  axial  line  of  the  column,  distant  xi  from  the  bottom  of  the  leg  and 
at  right-angles  to,  and  distant  yi,  measured  normal  to  a  tangent  to  any  jjoint  in 
the  flange  t,  and  taking  moments  about  this  assumed  point,  the  stress  in  the 
flange  t  multiplied  by  yi  equals  >^  (Si^ -{-fl'i)  multiplied  by  xi,  or  the  stress  in 


Fig.  8.     Portal  Type  of  Wind-bracing 


Combination  of  Dead  and  Live  Loads  with  Wind-Loads     1183 

the  flange  t  equals  ^  (EH  +  Hi)  multiplied  by  i^i/ji,  and  this  is  a  maximum 
when  xi/yi.  has  its  greatest  value.  There  is  approximation  in  this  treatment, 
but  it  is  on  the  side  of  safety.  If  the  flange  t  has  a  section  proportioned  to 
these  maximum  stresses  the  requirements  will  be  fulfilled.  The  stress  in,  and 
section-area  required  for,  the  flange  r  can  be  obtained  in  a  similar  manner.  The 
connection  of  the  portal  above  this  flange  to  the  portal  and  column  above  must 
be  such  that  it  will  safely  resist  the  stress  H  2//  at  each  leg. 

9.   Combination  of  Dead  and  Live  Loads  with  Wind-Loads 

General  Principles.  It  usually  happens  that  the  same  girders  that  are  used 
as  wind-bracing  serve  also  to  carry  floors  or  walls.  The  dead  and  live  loads 
should  be  considered  with  the  wind,  and  the  resultant  combined  stresses 


Fig.  9.     Types  of  Columns  Arranged  for  Wind-bracing. 


ascertained.  It  should  be  borne  in  mind  that  the  maximum  bending  moment 
caused  by  the  wind  is  often  at  a  point  on  the  girder  more  or  less  removed  from 
the  point  of  maximum  bending  moment  for  dead  and  live  loads.  When  result- 
ant shears  and  moments  are  considered,  in  which  the  forces  are  the  wind-load 
and  the  live  and  dead  loads,  it  is  generally  deemed  proper  to  use  unit  stresses 
50%  in  excess  of  those  of  common  practice  under  usual  loading.  The  columns 
should  be  investigated  for  direct  live,  dead  and  wind-loads  and  for  the  bending 
due  to  wind.  The  resultant  stress,  again,  should  not  exceed  150%  of  the 
stresses  generally  used  for  live  and  dead  loads  only.  It  is  often  best  to  design 
columns  with  a  special  view  to  proper  connections  for  bracing.     This  aids  in 


1184 


Wind-Bracing  of  Tall  Buildings 


Chap.  29 


both  design  and  detail.     In  Fig.  9  are  shown  a  few  typical  arrangements  of 
column-material  illustrating  this  point. 

10.   Wind-Bracing  of  Water-Towers  and  Similar  Structures 

The  Principles  Involved  in  Water-Tower  Bracing.     In  the  case  of  a 

TOWER  WITHOUT  MASONRY  WALLS,  a  problem  IS  presented  much  simpler  than 

that  of  a  building,  as  the  indeterminate  factors  of  resistance  are  largely 

I  '  "     J  eliminated.    The  bracing  should 

coJncction^oidBuiiing  be   designed   to   resist    the   full 

wind-pressure.  It  should  be 
borne  in  mind  that  in  water- 
towers  the  condition  of  minimum 
stability  obtains  when  the  tank 
is  empty.  The  most  common 
form  for  tower-bracing  is  the 
sway-rod.  The  analysis  of 
stresses  is  the  same  as  described 
on  page  ii8i.  The  application 
of  the  thrust  is  largely  at  the  top 
where  the  tank  stands,  but  this 
does  not  in  any  way  alter  the  an- 
alysis. The  legs  of  water-towers 
are  frequently  sloped  to  give  a 
greater  spread  at  the  bottom. 
In  this  case  the  stresses  are  more 
readily  determined  by  graphic 
methods  than  by  algebraic 
or  trigonometrical  computation. 
(See  Chapter  XXVII.) 

The  Assumed  Unit  Pres- 
sures should  be  somewhat 
greater  for  towers  than  for  build- 
ings. Towers  are  small  in  com- 
parison with  buildings,  and  the 
probability  of  the  full  wind-pres- 
sure being  developed  over  the 
entire  surface  is  greater.  Prob- 
ably 40  lb  per  sq  ft  is  ample. 
Pressure  against  a  cylindrical 
body,  such  as  a  tank,  may  be 
taken  at  about  two-thirds  of  the 
full  pressure  against  the  projec- 
tion on  the  diametrical  plane. 
The  stresses  under  this  assumed 
pressure  should  be  kept  within 
usual  bounds  for  ordinary  dead 
or  live  loads.     The  anchorage  of 


Fig.  10.    Whitehall  Building. 
Lines  of  Bracing 


Plan  and 


each  post  should  exceed,  by  a  safe  margin,  the  full  uplift  due  to  the  assumed 
pressure.  The  weight  of  water  in  the  tank  should  not  be  considered  as  resisting 
the  uplift. 

A  Good  Example  of  a  Steel  Water-Tower  is  described  and  illustrated  in 
the  Engineering  Record  of  June  20,  1903,  the  stress-diagrams  and  details  of  con- 
struction being  given. 


Examples  of  Wind-Bracing  in  Tall  Buildings 


1185 


Fig.  11.    Whitehall  Building.    Wind-bracing  on  Line  I,  Fig.  IQ 


1186 


Wind-Bracing  of  Tall  Buildings 


Chap.  29 


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Fig.  12.    Whitehall  Building.    Wind-bracing  on  Line  II,  Fig.  10 


Examples  of  Wind-Bracing  in  Tall  Buildings 


1187 


11.   Recent  Examples  of  Wind-Bracing  in  Tall  Buildings 

The  Whitehall  Building  f  (Figs.  10 
to  17),  2  to  14  West  Street,  New  \ork 
City,  consists  of  a  thirty-one  story  addi- 
tion to  the  earlier  Battery  Place  Building. 
It  joins  the  older  twenty-story  building 
which  is  on  the  south.  As  the  plan,  Fig.  10, 
indicates,  the  building  is  very  long  and  nar- 
row when  compared  with  its  height  and  it 
represents  a  type  in  which  wind-bracing  must 
be  considered  an  essential  feature.  The  six 
lines  of  bracing  indicated  on  the  plan  (Fig. 
10)  by  the  Roman  numerals  and  the  letters 
W.B.  were  chosen  so  as  to  interfere  as  httle 
as  possible  with  the  requirements  of  the  plan. 
Knee-braces  were  used  as  far  as  practi- 
cable, but  in  several  instances  it  was  neces- 
sary to  use  GUSSETS  because  of  the  limited 
space  available.  It  was  assumed  that  the 
ordinary  connections  of  girders  to  columns, 
and  the  walls,  furnished  sufficient  stiffness 
down  to  the  twenty-fourth  floor-level.  Be- 
low that  level  the  bracing  was  proportioned 
as  described  on  pages  1179-80;  that  is,  al- 
lowance was  made  for  the  indeterminate 
FACTORS  or  RESISTANCE  equal  to  the  wind- 
moment  at  the  twenty-fourth  floor. 

The  United  States  Realty  Building  t 
(Fig.  18),  IIS  Broadway,  New  York  City, 
is  another  example  of  a  building  in  which 
SPECIAL  BRACING  is  quite  essential.  It  is 
twenty-one  stories  high,  and  its  width  is 
small  when  compared  with  its  length  and 
height.  Bracing  was  used,  as  indicated,  in 
the  end-walls,  but  it  was  not  feasible  to  put 
enough  in  these  hnes  to  do  all  the  work. 
Additional  lines  were  therefore  added  be- 
tween some  of  the  elevator-shafts  and  in 
other  places  as  shown  on  the  plan.  No 
special  bracing  was  used  above  the  fifteenth 
floor. 

The  Morton  Building  §  (Fig.  19),  681 
Fifth  Avenue,  New  York  City,  is  but  twelve 
stories  high,  but  is  rather  narrow.  The 
building  is  on 'an  interior  lot,  and  it  was 
necessary  to  keep  the  openings  in  the  ex- 
terior walls  as  large  as  possible,  in  order  to 
properly  light  the  interior.  This,  of  course, 
made  the  exterior  walls  of  but  little  value 


Fig.  13.     Whitehall  Building, 
bracing  on  Line  III,  Fig. 


*  Purdy  &  Henderson  acted  as  designing  engineers  for  these  buildings. 

t  Clinton  &  Russell,  architects. 

X  Francis  H.  Kimball,  architect. 

§  McKim,  Mead  &  White,  architects. 


1188 


Wind-Bracing  of  Tall  Buildings 


Chap.  29 


IV 

Fig.  14.     Whitehall  Building.    Wind- 
bracing  on  Line  IV,  Fig.  10 


Floor 


'19th 


Floor 
18th 


Floor 


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Floor 


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2-15  ][  ••53' 
15.%"rh 


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Fig.  15.    Whitehall  Building.    Wind- 
bracing  on  Line  V  and  VI,  Fig.  10 


Examples  of  Wind-Bracing  in  Tall  Buildings 


1189 


Wind-Bracing  of  Tall  Buildings 


sChap.  29 


Pig!.  16  Fig.  17 

Fig.  17.    Whitehall  Building.    Wind-bracing  Details 


Examples  of  Wind-Bracing  in  Tall  Buildings  1191 

. u'q'/u J 

--■rr.—  — :r-  •  —  — nr-- --J — j— 


W.B.«i 

IH 

I 


fll 


wraT^r' 


h 


'  W.B. 


-irt^^r 


_L 


Fig.  18.    United  States  Realty  Building. 
Plan  and  Lines  of  Braciiig 


-42'0^ 


W.B.  t 

"SY.B. 

t  W,.B, 

ffl 

W.B. 

W.B. 
W.B. 

i  ^ 

1  5" 

bk 

W.B 

Elevator 

Fig.  19.     Morton  Building.    Plan 
and  Lines  of  Bracing 


1192 


Wind-Bracing  of  Tall  Buildings 


-43'6'^ 


I  Stairs 


W.B. 

I  Elevjiitors  |  ' 


f^-24'6'^ 

Coniieotion  to  OU 


Old  Building 


I    S 

!  3 


Ele|*tor 


i  £leV|itors 


Fig.  20.     Masonic  Building.     Plan  and  Lines  of  Bracing 


^n'o" 

lEleratJor 
}EleTat)3r 

]    \ 

! 

', 

> 
> 

oa  4                 . .  .     > 

,      H-  . 

iq 

h 

11" 

Sr--- 

1 

' . 

L J 

1      'I      li      ' 

1          <l          M          ■ 

■  --jL-- Jl.-.] 

K 

Fig.  21.    Everett  Building.    Plan 


Examples  of  Wind-Bracing  in  Tall  Buildings 


1193 


for' bracing.  Small  knee-braces  and  gussets  were  introduced  in  each  end- 
wall,  and  additional  knee-braces  next  to  the  elevator-wells  and  stair-wells.  The 
interior  girder-connections  to  the  columns,  also,  were  made^with  six  rivets  in 
each  flange,  instead  of  with  four  as  is  usual.  These  special  bracing-features  were 
carried  up  to  the  fifth  floor-level. 

The  Masonic  Hall*  (Fig.  20),  24th  Street  Building,  New  York  City,  twenty- 
two  stories  high,  has  virtually  no  special  bracing.  Light  knee-braces  were 
introduced  in  the  two  wings,  but  these  were  rather  to  insure  the  steelwork  against 
getting  out  of  plumb  in  erection,  than  to  assist  in  wind-resistance. 

The  Everett  Building  t  (Fig.  21),  45  East  17th  Street,  New  York  City,  is  a 
sixteen-story  building,  with  no  special  bracing  of  any  kind.  It  is  large  on  the 
ground,  and  the  ordinary  features  of  construction  offer  ample  resistance  to 
wind. 

The  Metropolitan  Tower  |  (Fig.  22),  Madison  Square,  New  York  City,  is 
'  such  an  unusual  case  that  it  is,  perhaps,  out  of  place  to  mention  it  as  an  example 
in  any  wise  typical.     It  is  700  ft  „.„ 

high  and  about  75  by  85  ft  in  plan 
throughout   the   lower  stories. 
Wind-bracing   in    this    case  is    a 
prime  feature  of  the  structural  de-  rfj 
sign  and  received  much  attention.  *^ 
It  is  designed  from  top  to  bottom 
to  resist  a  full  pressure  of  30  lb  per 
sq  ft,  with  no  reduction  for  the 
value  of  walls,  etc.    The  bracing 
consists,    in    general,    of     plate  ^ 
girders  in  the  walls  at  each  level, 
with  knee-braces   and   gussets 
for  the  joints.     The  columns  are 
designed  with  especial  view  to  the 
manner  of  connection  for  the  brae-  d 
ing.    The  dead  weight  of  the  tower  b= 
offers  a  moment  of  resistance  to 
overturning  far  in  excess  of  the 

MOMENT  OF  THE  WIND. 

These  examples,  all  drawn  from 
New  York  City  buildings,  are  per- 
haps as  typical  of  the  most  ap- 




r         stairs        1 

— 

"1 

'"ElermtorB""" 
ElfeTators 

1 
1 

- 

•■- «r„- 

.-- 

\j 

W.B.  W.B.  w.n. 

Fig.  22.    Metropolitan  Tower.    Plan  and 

Lines  of  Bracing 


proved  modern  practice  in  respect  to  wind-bracing  as  could  be  chosen.  There  is 
such  an  infinite  variety  in  the  shape  and  size  of  buildings  that  no  case  is  ever 
quite  like  any  previous  example. 

*  H.  P.  Knowles,  architect. 

t  Goldwin  Starrett  &  Van  Vleck,  architects. 

j  N.  LeBrun  &  Sons,  architects. 


1194      Specifications  for  Structural  Steelwork  of  Buildings      Chap.  30 


CHAPTER  XXX 

SPECIFICATIONS*   FOR    THE   STRUCTURAL   STEELWORK 
OF   BUILDINGS.     DATA   ON  STRUCTURAL  STEEL 

By 
ROBINS  FLEMING 

OF   mE    AMERICAN   BRnXJE    COMPANY,    NEW   YORK,    N.    Y. 

1.  General 

(i)  Drawings.  The  drawings  forming  a  part  of  these  specifications  are 
[give  number,  maker,  title,  and  date  of  each  drawing]. 

(2)  Classification.  For  the  purpose  ]of  classification  buildings  are  divided 
into  two  classes: 

1.   MiLL-BuiLDINGS 

II.  Office-Buildings 

Under  Class  I  are  included  manufacturing  plants,  machine-shops,  power- 
houses, rolling-mills,  foundries,  forge-shops,  pattern  and  template-shops,  train- 
sheds,  pier-sheds,  car-barns,  roundhouses,  electric-light  stations,  armories,  and 
buildings  of  a  similar  character. 

Under  Class  II  are  included  office-buildings,  hotels,  apartment-houses,  dwell- 
ings, public  buildings  (hospitals,  libraries,  schools,  court-houses,  jails),  places  of 
public  assembly  (churches,  theaters,  halls),  stores,  warehouses,  garages,  and 
buildings  of  a  similar  character. 

(3)  Scope  of  Work.  It  is  intended  that  these  specifications  and  drawings 
cover  the  structural  steelwork  complete  for  the  building.  Cast-iron  bases  are 
included  with  the  structural  steel.  The  steel-erector  shall  erect  in  place  the 
steel  framework  on  foundations  furnished  by  others.  Anchor-bolts,  loose  hntels, 
and  material  not  connected  with  main  frame  of  structure,  are  to  be  dehvered  at 
the  site,  but  put  in  place  by  other  contractors. 

(4)  Materials  to  be  Furnished  for  Buildings  of  Class  1.  Unless  specified 
otherwise  in  contract,  the  materials  to  be  furnished  for  buildings  of  Class  I 
include  steel  trusses,  columns,  purHns,  bracing,  floor-framing,  crane-girders  with 
rails,  trolley-beams,  hntels,  girts,  framing  around  door  and  window-openings, 
beams  supporting  tanks,  elevator-framing,  stair-framing,  floor-plates,  bunker- 
framing  and  steel  lining,  stairs  and  railings  unless  of  an  ornamental  character, 
cast-iron  bases,  grillage-beams,  and  anchor-bolts. 

The  materials  jJot  furnished  include  ornamental  ironwork  and  steelwork, 
masons'  anchors,  carpenters'  anchors  and  irons,  elevator  sheave-beams,  switches 
for  trolley -beams,  steel  stacks,  steel  tanks,  and  steel  reinforcement  for  concrete. 

(5)  Materials  to  be  Furnished  for  Buildings  of  Class  II.  Unless  specified 
otherwise  in  contract,  the  materials  to  be  furnished  for  buildings  of  Class  II 
include  steel  columns,  cast-iron  bases,  rolled  and  cast-steel  slabs,  grillage-beams, 
anchor-bolts,  floor-framing,  roof  and  ceiling-framing,  purlins,  cornice-supports, 
supports  for  tanks,  penthouse  framing,  bracing,  and  lintels. 

The  MATERIALS  NOT  FURNISHED  include  ornamental  ironwork  and  steelwork, 
masons'  anchors,  terra-cotta  anchors,  carpenters'  anchors  and  irons,  stair-work, 

*  The  various  values  used  in  these  Specifications  agree  generally  with  those  used 
throughout  the  book.  Any  slight  variations  in  values  are  due  to  recognized  and  allowable 
differences  in  engineering  judgment,  diflEerences  in  Building  Codes,  etc. 

/ 


Material  1195 

elevator-framing,  elevator  sheave-beams,  steel  stacks,  steel  tanks,  light  shapes 
supporting  metal  ceiling-lath,  cast-iron  sills  and  similar  work,  and  steel  rein- 
forcement for  concrete. 

(6)  Rivets  and  bolts  for  fastening  steel  to  steel  (but  not  for  connecting  the 
work  of  other  trades)  shall  be  furnished  by  the  steel-contractor.  Fitting-up 
bolts  for  erection  are  to  be  furnished  by  the  contractor  for  erection  as  a  part  of 
his  equipment. 

(7)  As  soon  as  possible  a  column-footing  plan  shall  be  sent  to  the  pur- 
chaser, showing  the  location,  elevation,  and  dimensions  of  all  column-bases,  with 
the  location,  elevation,  size,  and  length  of  all  anchor-bolts.  The  loads  coming 
upon  the  column-footings  from  the  columns  shall  also  be  given. 

(8)  Crane-clearance  diagrams  showing  the  clearances  assumed  for  traveling 
cranes  shall  be  furnished  the  purchaser  at  an  early  date. 

(9)  Substitution  of  Material.  If  the  contractor  wishes  to  substitute  other 
SHAPES  OR  SIZES  for  those  called  for  on  the  drawings  he  may  do  so,  subject  to  the 
approval  of  the  engineer,  provided  the  architectural  features  are  maintained  and 
proposed  sections  are  sufficient  to  carry  the  required  loads. 

(10)  Work  of  Other  Trades.  Holes  conforming  to  the  usual  standards  of 
fabrication  shall  be  punched  in  the  steel  for  attaching  the  work  of  other  trades, 
provided  their  location  is  given  while  the  working  drawings  are  being  made. 

(11)  Working  Drawings.  Working  or  shop  drawings  shall  be  made  by 
the  steel-contractor,  and  when  requested,  prints  in  duplicate  sent  to  the  pur- 
chaser or  his  engineer  for  approval.  The  engineer's  approval  of  drawings  shall 
cover  general  design,  strength  and  type  of  details.  The  engineer  shall  not  be 
held  responsible  for  the  fit  of  work  at  the  site.  If,  to  expedite  delivery,  or  for  any 
other  reason,  he  waives  the  approval  of  drawings,  the  contractor  will  not  be; 
relieved  of  responsibility  for  errors  or  omissions  due  to  neglect  or  oversight 
on  his  (the  contractor's)  part. 

(12)  All  work  shall  conform  to  local  or  state  ordinances  and  regulations. 

2.  Material* 

(13)  Properties  and  Tests.  All  parts  of  the  metallic  structure  shall  be  of 
ROLLED  steel,  cxccpt  columu-bascs,  bearing  plates,  or  minor  details,  which  may 
be  of  CAST  IRON  or  cast  steel. 

(14)  Structural  steel  may  be  made  by  either  the  Bessemer  process  or  the 
open-hearth  process;  except  that  rivet-steel,  and  steel  for  plates  or  angles  over 
li  in  in  thickness  which  are  to  be  punched,  shall  be  made  by  the  open-hearth 
process. 

(15)  Structural  steel,  if  made  by  the  Bessemer  process,  shall  contain  not  more 
than  0.10%;  and  if  by  the  open-hearth  process,  not  more  than  0.06%  of  phos- 
phorus. Rivet-steel  shall  not  contain  more  than  0.06%  of  phosphorus  nor 
more  than  0.045%  of  sulphur. 

(16)  Structural  steel  shall  have  an  ultimate  tensile  strength  of  from  55  000 
to  65  000  lb,  and  rivet-steel  from  46  000  to  56  000  lb  per  sq  in  of  cross-section.  The 
MINIMUM  YIELD-POINT  as  determined  by  the  drop  of  the  beam  of  the  setting- 
machine  shall  be  one  half  of  the  ultimate  tensile  strength. 

*  The  requirements  for  material  are  taken,  by  permission,  from  the  following  Standard 
Specifications  of  the  American  Society  for  Testing  Materials,  Philadelphia,  Pa.:  Standard 
Specifications  for  Structural  Steel  for  Buildings  (A9-16),  Standard  Specifications  for 
Gray  Iron  Castings  (A48-05),  and  Standard  Specifications  for  Steel  Castings  (A27-16).  ' 


1196        Specifications  for  Structural  Steelwork  of  Buildings    Chap.  30 

(17)  The  MINIMUM  PERCENTAGE  OF  ELONGATION  in  8  in  shall  be  I  400000 
divided  by  the  ultimate  tensile  strength.  For  structural  steel  over  %  in  in  thick- 
ness, a  deduction  of  i  from  the  above  percentage  of  elongation  in  8  in  shall  be 
made  for  each  increase  of  }i,  in  in  thickness  above  %  in,  to  a  minimum  of  18%. 
For  structural  steel  under  ^le.  in  in  thickness,  a  deduction  of  2.5  from  the  above 
percentage  of  elongation  shall  be  made  for  each  decrease  of  Kie  in  in  thickness 
below  ^ie  in. 

(18)  Test-specimens  for  plates,  shapes,  and  bars  shall  bend  cold  through  i8o° 
without  cracking  on  the  outside  of  the  bent  portion,  as  follows:  For  material 
%  in  or  under  in  thickness,  flat  on  itself;  for  material  over  ^  in,  to  and  including 
1 1^  in  in  thickness,  around  a  pin  the  diameter  of  which  is  equal  to  the  thickness 
of  the  specimen;  and  for  material  over  13^:4  in  in  thickness,  around  a  piu  the  diam- 
eter of  which  is  equal  to  twice  the  thickness  of  the  specimen.  The  test-specimen 
for  rivet-steel  shall  bend  cold  through  180°,  flat  on  itself,  without  cracking  on 
the  outside  of  the  bent  portion. 

(19)  Iron  castings  shall  be  of  tough  gray  iron,  true  to  pattern,  free  from 
cracks,  flaws,  and  excessive  shrinkage.  The  sulphur-contents  shall  be  not 
over  0.08%  for  light  castings,  0.10%  for  medium  castings,  and  0.12%  for  heavy 
castings. 

A  test-bar  1 3^^  in  in  diameter  and  1 5  in  long,  placed  upon  supports  1 2  in  apart 
and  tested  under  a  centrally  applied  load,  shall  conform  to  the  following  require- 
ments: 

Minimum  applied  load,  2  500  lb  for  Hght,  2  900  lb  for  medium,  and  3  300  lb 
for  heavy  castings; 

Minimum  deflection  at  center,  o.io  in. 

Light  castings  shall  be  able  to  withstand  an  ultimate  tension  of  18  000,  medium 
castings  21  000,  and  heavy  castings  24000  lb  per  sq  in.  Castings  having  any 
section  less  than  )4  in  thick  shall  be  known  as  light  castings.  Castings  in 
which  no  section  is  less  than  2  in  thick  shall  be  known  as  heavy  castings. 
Medium  castings  are  those  not  included  in  the  above  classification. 

(20)  Steel  castings  for  ordinary  use,  not  annealed,  shall  contain  not  more 
than  0.30%  of  CARBON,  nor  more  than  0.06%  of  phosphorus.  They  shall  sub- 
stantially conform  to  the  sizes  and  shapes  of  the  patterns,  be  made  in  a  work- 
manlike manner,  and  be  free  from  injurious  defects. 

3.  Loads 

(21)  Roof -Loads.  Roof-trusses  and  columns  shall  be  designed  to  carry 
a  uniform  load  per  square  foot  of  exposed  roof-surface,  appHed  vertically.  This 
load  includes  the  weight  of  the  structure,  the  snow,  and  the  wind.  For  spans  up 
to  and  including  90  ft,  and  in  climates  corresponding  to  that  of  New  York,  the 
total  minimum  uniform  load  in  pounds  per  square  foot  of  roof-surface  for  different 
kinds  of  covering  shall  be  taken  as  follows: 

lb  per 
sqft 

Corrugated  metal 40 

Gravel  or  composition  on  wood  sheathing 50 

Slate  on  boards .' 50 

Tile  on  steel  purlins 55 

Gravel  or  composition  on  cinder  concrete 65 

Gravel  or  composition  on  stone  concrete 75 

Slate  or  tile  on  cinder  concrete 70 

Slate  or  tile  on  stone  concrete 80 

Fire-proof  buildings  of  Class  II,  where  slope  is  less  than  2  in  per  ft 90 


•  Loads  1197 

(22)  For  roof-spans  over  90  ft,  the  above-cited  loads  shall  be  increased  1% 
for  every  2-ft  increase  of  span. 

(23)  For  roofs  in  climates  where  snow  is  excessive,  from  5  to  10  lb  per  sq  ft 
shall  be  added,  and  in  climates  where  there  is  not  liable  to  be  snow,  lolb  per  sq  ft 
may  be  deducted  from  the  foregoing  loads. 

(24)  If  a  ceiling  is  carried  by  the  roof-framing,  the  ceihng-load  shall  be  assumed 
at  not  less  than  10  lb  per  sq  ft. 

(25)  If  SHAFTING  is  carried  by  the  bottom  chord,  the  load  at  the  shaft  shall  be 
assumed  at  not  less  than  2  000  lb  for  light  shafting,  4  000  lb  for  ordinary  shafting, 
and  6  000  lb  for  heavy  shafting.  Unless  the  shafting  is  definitely  located  these 
loads  shall  be  considered  as  liable  to  be  concentrated  at  any  point  of  the  bottom 
chord. 

(26)  In  designing  purlins  carrying  roof-covering  only,  the  loads  in  Para- 
graphs (21)  and  (23)  may  be  decreased  5  lb  and  considered  normal  to  the  roof. 
When  the  pitch  of  the  roof  is  more  than  from  2  K  in  to  i  ft,  tie-rods  shall  be  used 
between  the  purlins. 

(27)  Special  loadings,  such  as  tanks  or  elevator-supports  above  the  roof, 
and  hoists  or  trolleys  on  the  bottom  chord,  shall  be  taken  into  consideration. 

(28)  Flat  roofs  used  as  places  of  public  assembly  or  for  storage-purposes 
shall  be  considered  as  floors. 

(29)  Floor  Loads.  Floor  loads  consist  of  dead  loads  and  live  loads.  The 
dead  load  is  composed  of  the  weight  of  the  floor-construction  and  of  any  perma- 
nent wall  resting  upon  it.  In  designing  floor-beams  and  girders  for  fire-proof 
construction  the  dead  load  shall  be  assumed  at  not  less  than  70  lb  per  sq  ft. 
Partitions  of  wooden  studding  or  of  hollow  tile,  not  more  than  4  in  thick,  may  be 
considered  as  part  of  the  live  load. 

(30)  Unless  governed  by  a  local  or  state  building  code,  buildings  of  Class  I 
shall  be  designed  for  minimum  live  loads,  in  pounds  per  square  foot  of  floor- 
area,  as  follows: 

lb  per 
sqft 

Mold-lofts,  pattern  and  template-shops 60 

Machine-shops,  light  machinery 120 

Machine-shops,  heavy  machinery 150  to  200 

Factories 150  to  200 

Foundries,  charging-floor 300  to  800 

Power-houses 200 

(31)  Buildings  for  special  industries  shall  be  designed  for  the  loadings 
incident  to  those  industries. 

(32)  Provision  shafl  be  made  for  the  support  of  machinery,  engines,  boilers, 
tanks,  and  other  concentrated  loads,  when  carried  by  the  steel  construction. 

(33)  Crane-Loads.  Loads  due  to  electric  traveling  cranes  shall  be  in- 
creased 25%  to  provide  for  the  effects  of  impact.  For  hand-power  cranes  the 
impact  may  be  taken  at  10%.  For  two  cranes  in  action  on  the  same  girder,  no 
impact  need  be  added,  provided  the  stress  obtained  is  larger  than  the  stress  due 
to  a  single  crane  with  impact.  In  addition  to  the  vertical  loads  the  top  flanges 
of  crane-girders  shall  be  designed  to  resist  a  transverse  horizontal  thrust  on  each 
carriage,  applied  at  the  wheels,  of  10%  of  the.Hfting  capacity  of  the  crane.  The 
breaking-force  due  to  stopping  the  crane  shall  be  assumed  at  20%  of  each  wheel- 
load  and  may  be  considered  as  distributing  itself  along  the  entire  length  of  the 
runway. 


1198      Specifications  for  Structural  Steelwork  of  Buildings      Chap.  30 

(34)  Coal-Bunkers.  Coal-bunkers  shall  be  assumed  to  be  surcharged 
when  it  is  possible  for  them  to  be  so  loaded.  The  weight  of  anthracite  coal 
shall  be  taken  at  not  less  than  50  lb  per  cu  ft,  and  the  angle  of  tepose  assumed  to 
be  30°. 

(35)  Buildings  of  Class  II  shall  be  designed  for  minimum  live  loads,  in  pounds 
per  square  foot  of  floor-area  as  follows: 

lb  per 
sqin 

Dwellings  (private  residences),  first  floor 40 

Dwellings  (private  residences),  upper  floors 30 

Apartment-houses,  first  floor 50 

Apartment-houses,  upper  floors 40 

Hotels,  first  floor 80 

Hotels,  upper  floors 40 

Office-buildings,  first  floor 100 

Oflice-buiidings,  upper  floors 50 

School-buildings,  class-rooms 50 

School-buildings,  assembly-rooms 75 

Churches  and  theaters 75 

Places  of  public  assembly,  where  floors  are  used  for  drilling  or  dancing 1 20 

Places  of  public  assembly,  where  floors  are  not  used  for  drilling  or  dancing ...  100 

Retail  stores,  ordinary 100 

Warehouses , 200  to  500 

Private  garages,  pleasure  vehicles  only 60 

Public  garages,  pleasure  vehicles  only 90 

Garages,  motor  trucks,  from  i  to  3  tons  capacity 150 

Garages,  motor  trucks,  from  sHto  5  tons  capacity '. 200 

(36)  Concentrated  loads  shall  be  taken  into  consideration.  Every  steel 
beam  in  any  floor  used  for  business  purposes  shafl  be  capable  of  sustaining  a  live 
load,  concentrated  at  the  middle,  of  not  less  than  3  000  lb.  Every  steel  beam  in 
the  floor  of  a  garage  shall  be  capable  of  sustaining  a  concentrated  live  load  of 
2  000  lb,  if  a  private  garage  storing  pleasure  vehicles  only;  of  3  000  lb,  if  a  public 
garage  storing  pleasure  vehicles  only;  of  8  000  lb,  if  motor  trucks  of  from  1  to  3 
tons  capacity  are  stored;  and  of  12  000  lb,  if  motor  trucks  of  from  33^  to  5  tons 
capacity  are  stored.  Structural  members  carrying  elevators  and  elevator- 
machinery  shall  be  proportioned  to  carry  twice  the  actual  moving  dead  and  live 
loads. 

(37)  Reduction  of  Live  Load.  The  full  live  floor  load  shall  be  used  in  pro^ 
portioning  afl  par^  of  buildings  designed  for  warehouses,  and  such  buildings  as 
are  likely  to  be  loaded  on  aH  floors  at  the  same  time.  In  other  buildings  the 
specified  live  load  may  be  reduced  10%  for  girders  carrying  200  sq  ft  or  more  of 
floor.  For  columns  the  load  on  the  top  floor  may  be  assumed  at  90%  of  the 
specified  live  load,  the  live  load  on  the  floor  next  below  the  top  floor  at  85%, 
and  on  each  succeeding  lower  floor  at  correspondingly  decreasing  percentages, 
provided  that  on  no  floor  shall  less  than  50%  of  the  specified  live  load  be  used, 
and  that  for  the  lower  floor  the  fuH  specified  live  load  shall  be  used.  No  reduc- 
tion shall  be  made  for  any  roof  load. 

(38)  In  calculating  column  loads  no  reduction  of  floor-area  shall  be  made  for 
stair- wefls.  Stairways  shall  be  proportioned  for  not  less  than  75  lb  per  sq  ft  of 
horizontal  projection. 

(39)  Wind-Pressure.'  Wind  shall  be  assumed  blowing  horizontally  in  any 
direction.  The  surface  exposed  to  wind-pressure  shall  be  measured  vertically 
from  the  ground  to  the  top  of  the  structure,  incliiding  the  foof. 


Loads 


1199 


(40)  When  the  overturning  moment  due  to  wind-pressure  exceeds  75%  of 
the  moment  of  stability  the  structure  shall  be  securely  anchored. 

(41)  All  steel  buildings  belonging  to  Class  I  shall  be  designed  to  carry  wind- 
pressure  to  the  ground  by  steel  framework.  For  buildings  not  more  than  25  ft 
to  the  eave-line  the  wind-pressure  shall  be  assumed  at  not  less  than  15  lb  per  sq 
ft,  and  the  corresponding  normal  pressure  on  the  roof.  For  buildings  more  than 
25  ft  to  the  eave-hne  the  wind-pressure  shall  be  assumed  at  not  less  than  15  lb  per 
sq  ft  for  the  lower  25  ft  and  20  lb  per  sq  ft  for  the  side  surface  above  25  ft,  and 
the  corresponding  normal  pressure  on  the  roof. 

(42)  The  steel  framework  of  fire-proof  buildings  belonging  to  Class  II,  in 
which  the  height  is  more  than  twice  the  minimum  horizontal  dimension,  shall  be 
designed  to  resist  a  wind-pressure  of  not  less  than  20  lb  per  sq  ft  on  the  sides, 
and  the  corresponding  normal  pressure  on  the  roof. 

(43)  The  normal  pressure,  Pn,  in  pounds  per  square  foot,  on  a  surface  inclined  9 
degrees  to  the  horizontal  for  a  horizontal  wind-pressure,  P,  of  20  lb  per  sq  ft, 
according  to  the  Duchemin  Formula,* 


is  as  follows: 


2  sin  6 
I  -\-  sin2  e 


0 

Pn 

lb  per  sq  ft 

Slope 

9 

Pn 

lb  per  sq  ft 

5° 

3.46 

I  in  to  I  ft 

4°  45'  49'' 

3.30 

10° 

6.76 

2  in  to  I  ft 

9°  27'  45" 

6.39 

15° 

9-63 

3  in  to  I  ft 

14°     2'  10" 

9.14 

20° 

12.25 

4  in  to  I  ft 

18°  26'     6" 

II   SO 

25° 

14-35 

5  in  to  I  ft 

22°  37'  12" 

13.42 

30° 

16.00 

6  in  to  I  ft 

26°  33'  54" 

14.88 

35° 

17.28 

7  in  to  I  ft 

30°  15'  24" 

16.06 

40° 

18.20 

8  in  to  I  ft 

33°  41'  25" 

16.95 

45° 
45 "^  to  90° 

18.88 

20.00 

For  a  pressure  other  than  20  lb  per  sq  ft  these  values  are  to  be  changed  pro- 
portionately. 

Only  the  excess  of  the  wind-stresses,  determined  by  the  data  of  this  paragraph, 
over  the  wind-stresses  according  to  Paragraph  (21),  need  be  considered.  In 
arriving  at  this  excess,  the  wind  included  in  the  total  uniform  roof-loads  desig- 
nated in  Paragraph  (21),  shall  be  assumed  at  5  lb  per  sq  ft  for  slopes  of  3  in  per  ft 
and  less,  and  10  lb  for  si jpes  more  than  3  in  per  ft. 

(44)  Circular  steel  ciiiiineys  and  tanks  shall  be  designed  to  resist  a  wind- 
pressure  of  not  less  than  20  lb  per  sq  ft  on  the  projected  area,  that  is,  the  diam- 
eter multiplied  by  the  height. 

(45)  Sky-signs  on  tops  of  buildings  shall  be  designed,  to  withstand  a  wind- 
pressure  of  not  less  than  30  lb  per  sq  ft  of  surface. 

4.  Stresses  f 

(46)  Working  Stresses.  In  proportioning  structural  steel  for  stresses  due 
to  the  combined  dead  and  li\"e  loads  together  with  impact,  the  working  stresses 

*  See,  also,  page  1053. 

t  For  slight  variations  from  these  values,  see  Table  XVIIl,  page  6t8,  and  Table  I, 
page  1138. 


I  JiK)        Specifications  for  Structural  Steelwork  of  Buildings    Chap.  30 

in  iwuiuls  i^K^r  square  inch  of  sectional  area  shall  be  not  more  than  the  fol- 
lo\vin>;; 

lb  per 
sq  in 

Tension,  net  sociion,  rolled  steel i6  coo 

Oiroct  compression,  rolled  steel  and  steel  castings 16  000 

Rending  on  extreme  fibers  of  rolled  shapes,  built  sections,  tHr.lers,  and 

steel  castings,  net  section 16  000 

Bemliivg,  on  extreme  tibers  of  pins 24  000 

Shear,  on  shop-rivets  and  pins 12  000 

Shear,  on  field-rivets 10  000 

Shear,  on  bolts 9  000 

Shear,  average,  on  webs  of  plate  girders  and  rolled  beams,  gross  section .    10  000 

Bearing  pressure,  on  shop-rivets  and  pins 24  000 

Bearing,  on  field-rivets 20  000 

Bearii\g,  on  Ixilts 1 S  000 

Tension,  in  rivets 7  000 

Tension,  in  field-bolts  (not  anchor-holts) 9  000 

\\>al  compression,  on  gross  section  of  columns  and  struts 16  000  —7c 

where  /  is  the  effective  length  of  the  member,  in  inches,  and  r  is 
the  least  radius  of  gyration  of  section,  in  inches,  with  a  maxi- 
mum of 13  000 

(47)  For  aiMiuNKi)  stresses  due  to  wind  and  other  loads  the  unit  stresses  in 
Paragraph  (46)  may  be  increased  50%,  except  for  Paragraph  (44),  provided 
tiie  section  thus  obtained  is  not  less  than  that  required  if  wind-forces  are 
neglected. 

(48)  When  the  laterally  unsupported  length,  /,  of  the  compression-flange  of 
beams  and  girders  exceetis  12  times  its  width,  b,  the  unit  stress  in  the  cou- 
PRESsiON-FLANGE,  shall  not  cxcccd  19  000  -250//6. 

(49)  CorNTERSi*NK  Ri\TTS  in  platcs  of  thickness  equal  to  or  greater  than 
one  half  the  diameter  of  rivet  shiUl  be  assumed  to  have  three  fourths  the  value  of 
rivets  with  full  heads.  In  plates  of  thickness  less  thim  one  half  the  diameter 
of  rivet  their  values  shall  be  tiiken  as  three  eighths  that  of  full-headed  rivets. 
Rivets  with  fl.\ttened  Ht:ADS  of  height  not  less  than  Hin,  or  one  half  the  diam- 
eter of  the  rivet  for  *i;-in  rivets  and  less,  may  be  assumeti  to  have  the  value  of 
a>rresix>nding  rivets  with  full  heads.  Rivets  with  heads  flattened  to  less  than 
these  heights  shall  have  countersunk  holes  and  be  regarded  as  countersunk 
rivets. 

(50^  The  allowable  pressure  of  column-b.\ses  and  be.\ring-plates  on 
masonry  shall  not  exceed,  in  pounds  per  square  inch,  the  following.  (See,  also, 
pages  205  to  ^6;^,  and  441.) 

lb  per 

sq  in 
On  brickwork,  cement  mortar.  .50 

On  brickwork,  hme  mc^rtar ...  1 50 

On  Portland-cement  concrete,  1:2:4  mixture 500 

On  Portland-cement  ci^ncrete,  1:3:5  mixture S50 

On  rubble  m;is^>nry,  cement  mortar :oo 

On  rubble  masc^iry,  lime  mortar \  :o 

On  first-class  dimension  sandstone 400 

On  first-class  limestone 500 

On  first-class  granite 600 


Design  1201 

5.  Design 

(51)  General  Design-Requirements.  Trusses  shall  be  riveted  structures. 
Tension-members  as  well  as  compkession-members  shall  he  composecl  of  rolled 
shapes  or  built-up  sections.     Flat  bars  with  riveted  ends  shall  not  be  used. 

(52)  In  calculating  tension-members,  net  sections  shall  be  used.  The  diam- 
eters of  rivet-holes  shall  be  assumed  to  be  y^  in  larger  than  the  nominal  size  of 
the  rivet.  In  single  angles  connected  by  one  leg,  the  net  area  of  the  connected 
leg  and  one  half  that  of  the  outstanding  leg  shall  be  considered  eflcctive. 

(53)  The  nominal  sizes  of  rivets  shall  be  used  in  calculations  of  their  values. 

(54)  In  proportioning  columns  provision  shall  be  made  for  eccentric  loading. 

(55)  Columns  AND  struts  with  direct  loads  of  40000  lb  or  less,  when 
spliced,  shall  have  the  entire  load  transmitted  through  splice-plates. 

(56)  Column-splices  shall  be  designed  to  resist  the  bending-stresses,  and  to 
make  the  columns  practically  continuous  for  their  whole  length. 

(57)  Members  subject  to  reversal  of  stress  from  moving  loads  shall  be 
proportioned  for  the  stress  requiring  the  larger  section,  but  their  connections 
shall  be  proportioned  for  the  larger  stress  plus  one  half  the  smaller. 

(58)  The  effective  length  of  main  compression-members  shall  not  exceed 
120  times  th(;ir  least  radius  of  gyration,  and  for  secondary  members  and  lateral 
bracing,  160  times  their  least  radius  of  gyration.  Any  portion  of  the  cross- 
section  of  a  compression-member  may  be  neglected  in  computing  the  radius  of 
gyration,  provided  that  portion  is  neglected  in  the  design  of  the  member. 

(59)  Wheel-loads  of  cranes  shall  be  assumed  to  be  distributed  on  the  top 
flanges  of  runway  girders  over  a  distance  equal  to  the  depth  of  the  girder,  with  a 
maximum  of  30  in. 

(60)  Plate  girders  shall  be  proportioned  either  by  the  moment  of  inertia  of 
their  net  section,  or  upon  the  assumption  that  the  bending-stresses  are  resisted 
by  the  flanges  concentrated  at  their  centers  of  gravity,  and  that  the  shear  is 
resisted  by  the  web.  When  the  second  method  is  used  one  eighth  of  the  gross 
section  of  the  web,  if  properly  spliced,  may  be  used  as  flange-section. 

(61)  Web-plates  of  girders  shall  have  a  thickness  of  not  less  than  Meo  of 
the  unsupported  distance  between  flange-angles. 

(62)  Flange-plates  of  girders  shall  be  limited  in  width,  so  as  to  extend 
not  more  than  6  in  beyond  the  outer  line  of  rivets  connecting  them  to  the  angles. 

(63)  Web-stiffeners,  in  pairs,  shall  be  placed  over  bearings,  at  points  of 
concentrated  loadings  and  at  intermediate  points,  usually  not  farther  apart  than 
the  full  depth  of  the  girder,  when  the  thickness  of  the  web  is  less  than  Ho  of  the 
unsupported  distance  between  flange-angles. 

(64)  Stiffeners  under  concentrated  loads  and  over  bearings  shall  be  designed 
as  columns,  with  a  length  equal  to  one-half  the  depth  of  the  girder,  and  shall 
have  enough  rivets  to  properly  transmit  the  shear.  When  loads  are  transmitted 
through  the  bearing  of  stiffeners,  the  bearing  value  may  be  assumed  at  24  000 
lb  per  sq  in  of  section,  excluding  the  area  of  the  chamfered  portion  over  fillets 
of  flange-angles. 

(65)  The  DEPTH  OF  GIRDERS  AND  ROLLED  BEAMS  in  floors  shall  be  not  less  than 
H4  of  the  span,  and  if  used  as  roof-purlins  shaU  be  not  less  than  ^2  of  the  span. 
In  case  of  floors  subject  to  shocks  and  vibrations  the  depth  shall  be  limited  to 
Mo  of  the  span. 

(66)  Steel  purlins  shall  be  single  rolled  shapes,  plate  girders  or  lattice 
girders. 


1202        Specifications  for  Structural  Steelwork  of  Buildings     Chap,  30 

(67)  Lateral,  longitudinal,  and  transverse  bracing  in  all  structures  shall 
preferably  be  composed  of  rigid  members,  and  shall  be  designed  to  withstand 
wind  and  other  lateral  forces  when  building  is  in  process  of  erection  as  well  as 
after  erection. 

(68)  Wind-bracing  shall  be  provided  for  tall  buildings  by  making  the  con- 
nection-joint between  girders  and  columns  sufficient  for  the  bending  due  to  side 
pressure  as  well  as  for  the  vertical  load;  or  diagonal  bracing  shall  be  placed 
between  columns,  proportioned  to  transfer  the  shear  of  the  side  pressure  to  the 
footings. 

(69)  No  steel  in  any  structural  member  subject  to  stress  shall  be  less  than  ]4, 
in  thick,  except  the  webs  of  rolled  beams  and  channels.  Steel  subject  to  the 
action  of  hamiful  gases  or  severe  atmospheric  conditions  shall  be  not  less  than 
Mo  in  thick. 

6.  Details 

(70)  General  Detail  Requirements.  Details  throughout  shall  conform 
to  first-class  standard  practice. 

(71)  No  connection  except  lattice-bars  shall  have  less  than  two  rivets,  prefer- 
ably three,  for  better  handling  in  fabrication. 

(72)  In  cases  where  it  is  necessary  to  carry  loads  subject  to  shock  by  bolts  in 
tension,  check-nuts  shall  be  used.  When  bolts  go  through  beveled  flanges, 
BEVELED  WASHERS  to  match  shall  be  used  so  that  head  and  nut  are  parallel.  In 
general,  rivets  and  bolts  in  tension  shall  be  avoided  as  far  as  practicable. 

(73)  Abutting  Joints  in  compression-members  faced  for  bearing  shall  be 
spUced  sufficiently  to  hold  the  connecting  members  accurately  in  place. 

(74)  When  two  or  more  rolled  beams  are  used  to  form  a  girder,  they  shall  be 
connected  by  bolts  and  separators  at  intervals  of  not  more  than  6  ft.  All 
beams  having  a  depth  of  12  in  and  more  shall  have  at  least  two  bolts  to  each 
separator. 

(75)  The  minimum  distance  between  centers  of  rivet-holes  shall  be  three 
diameters  of  the  rivet,  and  the  maximum  distance  in  the  line  of  stress  eight  diam- 
eters. 

(76)  The  minimum  distance  from  the  center  of  any  rivet-hole  to  a 
sheared  edge  shall  be  iH  in  for  ;^8-in  rivets,  iM  in  for  ^-in  rivets,  iK  in  for 
5^-in  rivets,  and  i  in  for  H-in  rivets;  and  to  a  rolled  edge,  1%,  ij4,  i,  and  %  in, 
respectively. 

(77)  The  maximum  distance  from  the  center  of  any  rivet-hole  to  any 
edge  shall  be  eight  times  the  thickness  of  the  plate. 

(78)  The  pitch  of  rivets  at  the  ends  of  built  compression-members  shall 
not  exceed  four  diameters  of  the  rivets  for  a  length  equal  to  one-and-one-half 
times  the  maximum  width  of  the  member. 

(79)  The  latticing  of  compression-members  shall  be  proportioned  to  resist 
a  shearing-stress  equal  to  2%  of  the  direct  stress.  Tie-plates  shall  be  provided 
at  each  end  and  at  intermediate  points  where  latticing  is  interrupted.  In  main 
members  carrying  calculated  stresses,  the  end  tie-plates  shall  have  a  length  not 
less  than  the  distance  between  the  Hnes  of  rivets  connecting  them  to  the  flanges, 
and  intermediate  ones  not  less  than  half  this  distance.  Their  thickness  shall  be 
not  less  than  Voo  of  the  same  distance. 

7.  Workmanship 

(80)  General  Requirements.  All  workmanship  shall  be  first-class  in  every 
respect. 


Workmanship,  etc.  1203 

(8i)  Material  shall  be  thoroughly  straightened  before  being  worked,  by 
methods  that  will  not  injure  it. 

(82)  Shearing  shall  be  done  accurately,  and  all  portions  of  the  work  exposed 
to  view  neatly  finished. 

(83)  Abutting  surfaces  of  compression-members,  except  where  joints  are 
fully  spliced,  shall  be  planed  to  an  even  bearing  so  as  to  give  close  contact 
throughout. 

(84)  Punching  shall  be  done  accurately,  but  occasional  inaccuracies  in  match- 
ing of  holes  may  be  corrected  with  a  reamer.  The  diameter  of  the  punch  shall 
be  not  more  than  Vie  in  larger,  i^or  that  of  the  die  3^  in  larger  than  the  diameter 
of  the  rivet.     Rivets  shall  be  driven  by  pressure-tools  wherever  possible. 

(85)  Holes  in  material  of  same  thickness  as  diameter  of  punch  may  be 
punched  full  size. 

(86)  Web-stiffeners  of  plate  girders  under  concentrated  loads  shall  have 
the  ends  milled. 

8.  Painting 

(87)  General  Painting  Requirements.  Cast  iron  need  not  be  painted  at 
the  shop.  Steelwork  for  foundations  to  be  entirely  embedded  in  concrete  shall 
not  be  painted,  but  must  be  free  of  dirt,  grease,  or  other  matter  which  would  impair 
the  bond  of  the  concrete.  .  Other  steelwork  shall  be  thoroughly  cleaned  and  given 
one  coat  of  paint  before  shipment.  One  coat  shall  be  given  to  surfaces  that  are 
inaccessible  after  being  riveted  together. 

(88)  Machine-fmished  surfaces  shall  be  coated  with  white  lead  and  tallow 
before  shipment. 

(89)  After  erection  all  structural  metalwork  shall  be  cleaned  of  dirt  and  rust 
and  given  one  coat  of  paint  of  a  color  or  shade  different  from  that  of  the  shop-coat. 

(90)  All  painting  at  the  shop  and  site  shall  be  done  by  hand  when  the  surface 
of  the  metal  is  perfectly  dry.     Painting  shall  not  be  done  in  freezing  weather. 

(91)  Paint  shall  be  a  good  quality  of  red  lead  or  graphite,  ground  in  pure  Un- 
seed oil  or  their  equivalent. 

9.  Inspection 

(92)  General  Requirements.  All  inspection  and  tests  shall  be  made  at  the 
option  and  expense  of  the  purchaser. 

(93)  If  material  is  tested  at  the  mills,  the  necessary  number  of  test-pieces  and 
the  use  of  a  testing-machine  shall  be  furnished  free  of  charge  by  the  steel-con- 
tractor. 

(94)  The  purchaser  or  his  representative  shall  have  free  access  at  all  times 
to  the  mills  where  material  is  rolled  and  to  the  shops  where  it  is  fabricated.  In 
ample  time  for  his  needs  he  shall  be  given  dates  of  mill  and  shop-operations 
and  furnished  with  complete  working  drawings. 

10.  Erection 

(95)  General  Requirements.  The  structural  steel  and  iron,  except  anchor- 
bolts,  loose  hntels,  and  material  not  connected  with  the  main  frame  of  the  struc- 
ture, shall  be  erected  by  the  steel-contractor  on  foundations  furnished  by  the 
purchaser. 

(96)  Care  shall  be  taken  that  all  steelwork  is  level  and  plumb  before  bolting  or 
riveting 


1204  Data  on  Structural  Steel  Chap.  30 

(97)  Proper  provision  shall  be  made  for  resisting  stresses  due  to  erection  opera- 
tions. 

(98)  In  general,  field-connections  shall  be  riveted,  but  connections  of  the  follow- 
ing classes  may  be  bolted: 

(a)  Light  subordinate  framing,  such  as  purlins,  monitor  and  skylight-framing, 
girts,  platforms,  stair-framing,'  partitions,  ceilings,  and  penthouses; 

{b)  Ordinary  framing  of  beams  to  beams,  and  beams  to  girders; 

(c)  Connections  not  subject  to  direct  shearing-stress. 

All  connections,  however,  affected  by  loads  that  cause  undue  vibration,  shall 
be  riveted.  One-story  buildings,  not  subjected  to  excessive  wind-pressure  or 
not  supporting  heavy  concentrated  loads,  shafting,  or  moving  loads,  may  be 
bolted  throughout.  The  threaded  part  of  a  bolt  shall  not  be  so  long  that  the 
bearing  value  of  the  unthreaded  portion  is  reduced  to  less  than  the  shearing 
value  of  the  bolt.     Washers  shall  be  used  under  nuts  wherever  needed. 

(99)  Drift-pins  shall  be  used  only  to  bring  parts  together.  Unfair  holes  shall 
be  made  to  match  by  reaming. 

(100)  After  finishing  the  work  the  erector  shall  remove  his  equipment  and  all 
rubbish  resulting  from  his  operations. 


DATA  ON   STRUCTURAL  STEEL* 

Estimating  the  Cost  of  Structural  Steel  for  Buildings 

Structural  steel  for  buildings  is  commonly  made  up  of  I  beams,  channels, 
angles,  Z  bars  and  plates,  which  may  be  used  as  single  beams  or  braces,  or  built 
into  riveted  girders,  columns,  or  trusses.  The  Z  bars  are  now  seldom  used  for 
columns  or  other  structural  work  in  buildings.  The  cost  of  the  completed  steel- 
work is  made  up  of  the  following  items: 

(i)  Cost  of  the  plain  steel  at  the  mill,  plus  freight  and  dealers'  profits. 

(2)  Extras  for  cutting,  punching,  fitting  and  assembling  into  girders,  columns, 
or  trusses. 

(3)  Cost  of  the  fittings,  such  as  connection-angles,  gusset-plates,  etc. 

(4)  Shop-painting. 

(5)  Cost  of  erection  at  the  building. 

(6)  Painting  after. erection. 

Base-Price  of  Steel.  For  orders  of  any  considerable  size,  the  cost  of  plain 
steel  is  based  on  the  price  at  the  mills  plus  the  freight  to  the  point  of  delivery. 

The  BASE-PRICE,  free  on  board  cars  at  Pittsburgh,  Pa.  (1920),  is  about 
$2.45  per  100  lb  for  I  beams  and  channels  15  in  and  less,  and  for  angles  and 
zees  from  3  to  6  in. 

I  beams  over  15  in,  cost  10  cts  per  100  lb  extra,  and  tees  over  3  in,  5  cts  extra. 

For  angles,  channels  and  zees  under  3  in,  the  base  is  $2.45  at  Pittsburgh. 

For  angles,  over  6  in,  $2.45  -f  So.io.f 

For  H  beams,  $2.45-!-  $0.10. 

For  deck  beams  and  bulb  angles,  $2.45  -{-  $0.30.  t 

For  corrugated  and  checkered  plates,  $2.65-!-  5i.7S.§ 

For  plates,  structural,  the  base  is  $2.65. 

*  Valuable  data  v/as  contributed  for  this  section  by  Associate  Editor,  Robins  Fleming. 

t  $2.45-|-$o.io  means  a  base-price  of  $2.45  and  an  extra  $0.10. 

t  $2.45-|-$o.3o  means  a  base-price  of  $2.45  and  an  extra  of  $0.30. 

§  2.6s-|-$i.75  means  a  base-price  of  $2.65  and  an  extra  of  $1.75;  the  same  with  $2.65 
-|-$o.i5,  etc.  Corrugated  steel,  painted,  is  usually  quoted  at  a  base-price  plus  an  extra 
for  painting.    At  present  (1920)  it  is  $4.25-!- $0.25. 


Data  on  Structural  Steel  1205 

For  plates,  flange,  the  base  is  $2.65  +  $0.15.* 

For  corrugated  steel,  painted,  No.  22,  $4. 25  -|-  $0.25.* 

For  corrugated  steel,  galvanized.  No,  22,  $5.30. 

For  steel  sheets,  black,  Nos.  10  and  11,  $4.00. 

For  steel  sheets,  galvanized,  Nos.  10  and  11,  $4.70. 

For  steel  sheets,  black.  No.  22,  $4.20. 

For  steel  sheets,  galvanized.  No.  22,  $5.25. 

For  bar-iron,  the  base  is  $4.50. 

For  rivets,  $4.50. 

For  steel  bars,  I2.35. 

Freight-Rates  (March,  1920)  in  car-load  lots  are: 

Pittsburgh  to  Albany,  N.  Y 27 .0  cts 

to  Baltimore 23 ,  o  cts 

to  Boston 29 . 5  cts 

to  Buffalo,  N.  Y 21.0  cts 

to  Chicago 27.0  cts 

to  Cincinnati 23 . 5  cts 

to  Cleveland 17.0  cts 

to  Columbus,  O , 20.0  cts 

to  Denver 99 .  o  cts 

Pittsburgh  to  Louisville 26.5  cts 

to  New  York 27.0  cts 

to  Norfolk,  Va 31.5  cts 

to  Philadelphia 25.0  cts 

to  Richmond,  Va 30 .  o  cts 

to  Rochester,  N.  Y 21.0  cts 

to  St.  Louis 34.0  cts 

to  Washington,  D.  C 24.0  cts 

On  account  of  the  expense  of  carrying  beams  in  stock,  local  dealers  usually 
charge  from  3/2  to  i3/^  ct  a  pound,  extra,  on  orders  supplied  from  stock. f 

Standard  Classification  of  Extras.  These  lists  are  for  steel  bars  and 
SMALL  SHAPES,  and  the  extras  are  added  to  the  base-prices  for  each  100 
pounds.  This  standard  classification  was  adopted  June  15,  19 19,  by  the 
Carnegie  Steel  Company. 

Specification  and  Inspection 

Hull-material,  subject  to  United  States  Navy  Department  specifications 

for  medium  or  soft  steel ,$0.10 

High- tensile  hull-steel  (except  rivet-rods)  subject  to  United  States  Navy 

Department  specifications i.oo 

Charges  for  other  than  mill-inspection,  such  as  Lloyd's  or  American  Bureau 
of  Shipping,  for  buyer's  account. 

Quantity-Differentials 

All  specifications  for  less  than  2  000  lb  of  a  size  will  be  subject  to  the  fol- 
lowing extras,  the  total  weight  of  a  size  ordered  to  determine  the  extra,  regard- 
less of  length  and  regardless  of  exact  quantity  actually  shipped: 

*  $2.65-1- $1.75  means  a  base-price  of  $2.65  and  an  extra  of  $1.75;  the  same  with 
$4.25  -|-$o.25,  etc.  Corrugated  steel,  painted,  is  usually  quoted  at  a  base-price  plus 
an  extra  for  painting.     At  present  (1920)  it  is  $4.25  -[-$0.25. 

t  At  present  (1920)  a  war  tax  of  3%  is  to  be  added  to  the  rates  given. 


1206  Bata  on  Structural  Steel  Chap.  30 

Quantities  less  than  2  000  lb,  but  not  less  than  i  000  lb $0.15 

Quantities  less  than  i  000  lb 0.35 

Straightening 

Machine-straightening $0.10 

Machine-Cutting  to  Specified   Lengths,  Rounds  and  Squares,  i^  Inches  and 

Larger 

Machine-cutting  to  lengths  over  48  in $0.15 

Machine-cutting  to  lengths  over  24  in  to  48  in,  inclusive 0.25 

Machine-cutting  to  lengths  over  12  in  to  24  in,  inclusive 0.35 

Machine-cutting  to  lengths  of  12  in  and  less,  extra  will  be  furnished  on 

application,  but  will  not  be  less  than 0.45 

The  above  extras  apply  only  to  .50  per  cent  carbon  and  under.  Extras  for 
machine-cutting  over  .50  per  cent  carbon  will  be  furnished  on  application. 

Extras  for  machine-cutting  Rounds  and  Squares  under  iH  in,  Flats,  etc., 
will  be  furnished  on  application. 

Cutting  to  Specified  Lengths,  Other  than  Machine-Cuttiag 

Cutting  to  lengths  of  60  in  and  over No  charge 

Cutting  to  lengths  over  48  in  to  59  in,  inclusive ^0.05 

Cutting  to  lengths  over  24  in  to  48  in,  inclusive o.io 

Cutting  to  lengths  over  12  in  to  24  in,  inclusive 0.20 

Cutting  to  lengths  of  12  in  and  less,  extra  will  be  furnished  on  application, 

but  will  not  be  less  than 0.30 

Cost  of  Erecting.  For  erecting  ordinary  beams  and  columns  in  buildings 
having  masonry  walls  the  cost  of  erection  should  not  exceed  $20  per  ton  when 
there  are  bolted  connections,  and  it  will  sometimes  be  as  low  as  $13  per  ton.  For 
erecting  the  steelwork  of  skeleton  buildings  having  riveted  connections  it  is 
customary  to  allow  $18  per  ton. 

Cost  of  Painting.  The  usual  charge  for  shop-painting  is  about  $3  per 
ton,  but  if  done  in  accordance  with  the  specification  on  page  1203  it  would  exceed 
this  amount.  For  painting  one  additional  coat  after  erection,  allow  about  $3.50 
per  ton. 

Roof-Trusses.  In  lots  of  at  least  six,  the  shop-cost  of  ordinary  roof-trusses 
in  which  the  ends  of  the  members  are  cut  off  at  right-angles  is  about  as  follows:* 
Trusses  weighing  i  000  lb  each,  from  $2.00  to  $3.50  per  100  lb;  trusses  weighing 
I  500  lb  each,  from  $2.00  to  $2.50  per  100  lb;  trusses  weighing  2  500  lb  each, 
from  Si. so  to  S2.50  per  100  lb;  and  trusses  weighing  from  3  500  to  7  500  lb, 
from  S1.25  to  $2.00  per  100  lb.  Pin-connected  trusses  cost  from  10  to  30  cts  per 
100  lb  more  than  riveted  trusses.* 

Steel  Mill-Buildings.  The  average  shop-cost  for  the  frames  of  steel  mill- 
buildings,  including  draughting,  is  about  $40  per  ton,  and  the  cost  of  erection 
from  $20  to  $35  per  ton.* 

Cost  of  Drafting.  Details  for  church  and  court-house  roofs  having  hips 
and  valleys  cost  from  $10  to  $20  per  ton;  details  for  ordinary  mill-buildings  cost 
from  $6  to  $12  per  ton.  The  cost  of  making  shop-drawings  varies  greatly  with 
the  character  of  the  construction  of  the  buildings,  and  with  the  accuracy  of  the 

*  If  there  is  little  duplication  or  parts  of  if  manual  labor  enters  into  the  fabrication  to 
any  great  extent  the  costs  given  will  be  increased. 


Data  on  Structural  Steel  1207 

architect's  drawings.    The  average  costs  per  ton  of  steel,  for  making  shop- 
drawings  are  about  as  follows: 

For  entire  skeleton  construction,  in  which  the  loads  are  all  carried  to  the 

foundations  by  the  steel  columns,  $4.00. 
For  the  interior  parts  which  are  supported  on  steel  columns,  when  the  outside 

walls  carry  the  floor-loads  and  their  own  weight,  $3.50. 
For  the  interior  parts  which  are  supported  on  cast-iron  columns,  when  the 

outside  walls  carry  the  floor-loads  and  their  own  weight,  $2.50. 
For  construction  without  columns,  and  in  which  the  floor-beams  rest  on  ma- 
sonry walls,  $2.50. 
For  buildings  in  which  roof-trusses  supported  by  columns  comprise  the  greater 

part  of  the  construction,  $7.00. 
For  buildings  in  which  roof-trusses  on  masonry  walls  comprise  the  greater 

part  of  the  construction,  $4.00. 
For  mill-buildings,  average,  $9.00. 
For  manufacturing  or  shop-buildings,  with  flat  roofs,  and  one  story  in  height, 

$3.00. 
For  alterations,  additions,  remodeling,  which  require  measurements  before 

details  and  shop-drawings  can  be  made,  $12.00.* 

Approximate  Estimates  of  the  Weight  of  Steel  in  Buildings.  Accord- 
ing to  H.  G.  Tyrell,t  the  weight  of  steel  in  any  proposed  new  building  may  be 
roughly  estimated  from  the  following  data,  which  is  a  fair  average  for  buildings 
not  over  eleven  stories  high,  designed  according  to  the  Building  Laws  of  the 
City  of  Boston: 

Per  sq  ft 
of  floor 

Apartment-houses  and  hotels,  with  outside  frame 14  lb 

Apartment-houses,  without  outside  frame 9  lb 

Office-JDuildings,  with  outside  frame 23  lb 

Office-buildings,  without  outside  frame 15  lb 

Warehouses,  with  outside  frame 28  lb 

Warehouses,  without  outside  frame 18  lb 

For  buildings  higher  than  eleven  stories,  the  weight  of  floors  will  increase  in 
direct  proportion  to  the  number  of  stories,  while  the  weight  of  columns  will 
increase  more  rapidly. 

For  the  approximate  weight  of  roof-trusses,  see  Chapter  XXVII,  pages  1050 
to  1052*. 

Weights  of  Steel  in  Buildings  | 

Factors  Affecting  the  Weights  of  Steel  Structures  are  many  and  varied. 
The  weight  per  square  foot  of  area  or  per  cubic  foot  of  volume  of  a  structure 
already  built  should  not  be  assumed  as  the  weight  of  a  proposed  structure 
unless  all  the  conditions  which  govern  the  one  are  found  in  the  other.  Munici- 
pal building  codes  specify  floor-loads  and  these  vary  greatly.  The  prescribed 
wind-pressure,  working  stresses  and  column-loads,  affect  the  weight.  The 
architectural  features  to  be  followed  also  play  an  important  part.  In  mill- 
buildings  the  weight  is  affected  by  the  kind  of  roofing  and  siding  used,  capacity 

*  This  cost  of  $12.00  includes  the  cost  of  taking  measurements.  This  generally  has  to 
be  done  by  the  contractor. 

t  Estimating  Structural  Steel,  in  Architects  &  Builders'  Magazine,  Jan.,  1903. 
t  From  Notes  by  Robins  Fleming. 


1208 


Data  on  Structural  Steel 


Chap.  30 


of  cranes,  spacing  of  trusses  and  columns,  shafting,  special  loadings  and  the 
allowable  minimum  thickness  of  metal. 

Weights  of  Steel  in  a  Number  of  Structures  are  given  in  the  following 
table  and  notes.  The  caution  regarding  such  weights  being  taken  as  prece- 
dents should  be  emphasized.  The  office-building  heading  the  list  is  the 
Equitable  building,  the  largest  office-building  in  the  world. 


Average  dimensions  in  feet 

Weight  in 

Weight  in 

Tiers 

pounds  per 

pounds  per 

of 

square  foot 

cubic  foot 

Width 

Length 

Height 

beams 

of  framed 
area 

of 
volume 

Office-buildings 

159 

308 

542 

41 

37-00 

2.55 

43 

79 

217 

17 

26.10 

2.20 

90 

90 

258 

22 

28.92 

2.41 

81 

139 

225 

19 

21.90 

1.83 

43 

104 

149 

13 

33.40 

2.99 

48 

III 

115 

9 

17.34 

1.51 

Hotels 

97 

119 

244 

20 

26.02 

1.92 

84 

143 

270 

24 

26.95 

2.39 

96 

lOI 

232 

18 

25.40 

2.02 

108 

120 

"S 

9 

14.00 

1. 01 

Department-stores 

133 

219 

150 

II 

23.87 

1.77 

62 

211 

130 

8 

29-44 

1.83 

103 

132 

89 

7 

18.30 

1.45 

Warehouses 

100 

los 

131 

10 

22.83 

1.76 

88 

121 

121 

9 

20.60 

1.85 

145 

357 

102 

7 

30.80 

2.13 

58 

72 

52 

3 

31.3s 

1.87 

Among  prominent  New  York  buildings  the  55-story  Wool  worth  Building 
with  a  ground-area  of  31  000  sq  ft  weighs  3.0  lb  per  cu  ft.;  the  39-story  Bankers' 
Trust  Building  with  an  area  of  9  000  sq  ft,  3.1  lb.;  the  2S-story  Municipal 
Building  with  an  area  of  42  700  sq  ft,  3.6  lb;  the  25-story  Hotel  McAlpin 
with  an  area  of  31  000  sq  ft,  2.0  lb.  The  lo-story  Curtis  Building  oi  Phila- 
delphia with  an  area  of  94000  sq  ft  weighs  3.0  lb.  The  structural  steel  in 
four  buildings  of  Pittsburgh,  the  Arrott,  the  Farmers'  Bank,  the  Empire  and 
the  Oliver,  is  quoted  as  weighing  respectively  2.8,  2.3,  2.1  and  1.8  lb  per  cu  ft. 
For  buildings  of  from  8  to  12  stories  in  which  the  exterior  walls  are  carried  by 
steel  framing  the  weight  per  cubic  foot  of  volume  may  be  assumed  at  1.9  lb 
for  office-buildings  and  1.5  for  hotels. 

Armories.  The  three-hinged  arches  with  roof-framing  of  an  armory  in 
Brooklyn,  191  by  300  ft  in  area,  weighs  15.5  lb  per  sq  ft  of  ground  area.  An 
armory  in  BufTalo,  233  by  335.  ft,  weighs  18.3  lb.  The  steelwork  of  the  Kings- 
bridge  Armory,  New  York  City,  289  by  590  ft,  said  to  cover  the  largest  drill- 
hall  in  the  world,  weighs  about  90  lb  per  sq  ft,  of  which  one  half  is  roof  and 
one  half  floor  and  miscellaneous  framing. 

Boiler-Shops.  Sizes  and  weights  per  square  foot  of  a  few  boiler-shops  are 
as  follows:  167  by  336  ft,  three  aisles,  floor  in  center  and  cranes  in  outer  aisles, 
concrete  roof  and  sides,  steel  purlins  and  girts,  23.9  lb;    124  by  300  ft,  three 


Data  on   Structural  Steel  1209 

aisles  with  15,  25  and  50- ton  cranes  respectively,  steel  purlins  and  brick  walls 
between  columns,  36  lb;  74  by  160  ft,  lo-ton  crane  in  center  aisle,  single  beams 
over  side  aisles  to  carry  roof,  galvanized  corrugated-steel  covering  and  siding, 
16,15  lb;  85  by  140  ft,  two  aisles,  one  with  crane,  20.8  lb;  94  by  97  ft,  two  aisles, 
one  with  crane,  26.3  lb. 

Car-Barns.  The  steel  roof-trusses  and  bracing  of  a  car-barn  100  by  154  ft, 
wood  purHns,  brick  walls,  weighs  6.2  lb  per  sq  ft.  Another  car-barn,  44  by  270  ft, 
corrugated-steel  roof,  and  sides  on  steel  purlins  and  girts,  9.15  lb.  Another, 
100  by  154  ft,  four  aisles,  concrete  roof  on  steel  purlins,  11.8  lb. 

Cement-Plants.  Four  cement-plants  with  ground-areas  of  58  000,  73  000, 
83000  and  128000  sq  ft  respectively,  weigh  respectively,  23.6,  22.0,  23.5,  and 
17.5  lb.  These  weights  are  the  averages  of  the  buildings  that  usually  form  a 
cement-plant.  The  individual  buildings  vary  from  10  lb  for  an  engine-room 
to  36.7  lb  for  a  clinker-grinding  room. 

Coal-Bunkers.  The  weights  of  six  coal-bunkers  of  the  suspended  type  and 
with  capacities  of  from  350  to  i  000  tons,  range  from  128  to  234  lb  per  ton  of 
capacity,  the  average  being  204  lb.  A  system  of  rectangular  pockets  to  store 
7  500  tons  (10  ft  6  in  from  ground  to  valves)  weighs  158.3  lb  per  ton  of  capacity. 
In  all  cases  the  weights  of  supports  but  not  of  roofs  are  included.  A  35  by  70-ft 
coal-bin  supported  on  plate  girders  with  a  capacity  of  i  000  tons  weighs  240  lb 
per  ton  of  capacity,  including  the  roof-trusses  that  carried  the  conveyor. 

Forge-Shops.  The  steel  framing  for  the  roof  of  a  forge-shop  83  by  126  ft, 
with  no  columns  and  no  cranes,  covered  with  corrugated  steel  on  steel  purlins, 
weighs  I  I.I  lb  per  sq  ft  of  ground-area.  A  forge-shop  220  by  240  ft,  four  aisles, 
each  with  crane-runways,  composition  roofing,  concrete  sides,  steel  purlins  and 
girts,  weighs  24.6  lb.  A  forge-shop  no  by  425  ft  for  heavy  work,  47  ft  6  in  to 
bottom  chord,  two  aisles  each  with  a  50-ton  crane,  tile  roof,  glass  and  brick 
sides,  weighs  40  lb. 

Foundries.  A  pipe-foundry,  50  by  150  ft,  slate  covering,  wooden  purlins, 
brick  walls,  15-ton  crane,  weighs  11.35  lb  per  sq  ft.  A  similar  one  for  the 
same  company,  45  by  82  ft,  with  a  30-ton  crane,  weighs  17.23  lb.  A  foundry, 
71  by  180  ft,  one  center  aisle,  with  light  crane,  lean-to  each  side,  corrugated- 
steel  roof  and  sides,  weighs  14.8  lb.  A  foundry,  150  by  290  ft,  for  a  pump- 
company,  four  aisles  with  20-ton  crane  in  one  aisle,  wooden  purHns,  two 
40  by  50-ft  charging-floors  of  concrete  on  steel  beams,  weighs  13.9  lb.  A 
foundry,  116  by  252  ft,  equipped  for  heavy  work,  60-ft  center  aisle,  two  side 
aisles,  28-ft  charging-floor,  storage-platform,  weighs  38.9  lb. 

Machine-Shops.  A  machine-shop,  90  by  328  ft,  for  heavy  work,  one 
center  aisle  40  ft  wide  with  25-ton  crane,  each  side  aisle  25  ft  wide  with  gallery- 
floor  and  5-ton  crane  underneath,  tile  roof  on  steel  purHns,  brick  and  glass 
sides,  weighs  43  lb  per  sq  ft  of  ground-area.  A  two-story  machine-shop, 
69  by  422  ft,  three  aisles,  light  cranes  in  lower  story,  composition  roof,  steel 
purHns,  concrete  sides,  weighs  35.15  lb.  A  one-story  building,  75  by  300  ft, 
20  ft  to  bottom  chord,  shafting,  corrugated-steel  roofing  and  siding,  weighs 
13.0  lb.  Another  one-story  building,  70  by  100  ft,  18  ft  to  bottom  chord, 
shafting,  concrete  roof  on  trusses  10  ft  apart,  no  purHns,  weighs  13.88  lb.  In 
addition,  the  steel  framing  for  the  Hy-rib  sides  of  this  building  weighs  3.44  lb 
per  sq  ft  of  vertical  surface.  A  machine-shop,  116  by  252  ft,  60  ft  center  aisle, 
with  upper  lo-ton-crane  runway  and  lower  25-ton-crane  runway,  two  side 
aisles  28  ft  wide  with  traveling  jib-cranes,  weighs  ss  lb. 

RoUing-Mills.  A  rolHng-miU,  93  by  186  ft,  corrugated-steel  roof  and 
sides,  weighs  17.6  lb  per  sq  ft.    Another,  170  by  384  ft,  two  aisles  each  with 


1210  Data  on  Structural  Steel  Chap.   30 

5-ton  cranes,  saw-tooth  roof-trusses  on  longitudinal  girders,  concrete  slabs  on 
steel  purlins,  brick  walls  between  columns,  weighs  17-5  Ih.  A  similar  building 
for  shop-purposes  weighs  18.62  lb. 

Paper-Mills.  The  entire  structural  steel  for  three  paper-mills  weighs 
respectively  18.4,  20.6  and  21.4  lb  per  sq  ft  of  area.  All  roof-trusses  are  of 
the  flat  type,  spaced  8  ft  apart  in  the  first  and  third,  and  i6  ft  in  the  second. 

Power-Houses.  A  power-house,  44  hy  186  ft,  49  ^  to  Iwttom  chord,  60- 
ton  crane  tile  roof  on  steel  purlins,  brick  walls  between  columns,  weighs  50  lb 
per  sq  ft.  Another,  53  by  270  ft,  33  ft  to  bottom  chord,  20-ton  crane,  tile  roof 
on  steel  purlins,  brick  walls  and  sash  between  columns,  weighs  39-6  lb.  Another, 
120  by  96  ft,  one  aisle  for  boiler-room  and  one  with  lo-ton  crane  for  engine- 
room,  steel  purlins  for  concrete  roof-covering,  brick  walls  between  columns, 
weighs  17.8  lb. 

Train-Sheds.  The  train-shed  of  the  Pennsylvania  Raihoad  in  Phila- 
delpliia,  598  ft  long  and  with  arches  300  ft  8  in  from  center  to  center  of  pins, 
weighs  39.1  Vb  per  sq  ft  of  ground-area;  the  train-shed  of  the  same , railroad  at 
Jersey  City,  777  ft  long  and  with  arches  252  ft  8  in,  weighs  27.9  lb;  and  that  of 
the  Philadelphia  &  Reading  Railroad  in  Philadelphia,  506  ft  8  in  long  and 
with  arches  259  ft  8  in,  weighs  31.5  Ih.  The  train-shed,  390  by  8x5  ft,  of  the 
Central  Railroad  of  New  Jersey  in  Jersey  City,  is  a  series  of  concrete  and  steel 
umljrellas,  of  the  Bush-type.    The  structural  steel  weighs  17  lb  per  sq  ft  of  area. 

Three  Industrial  Plants.  In  one  of  the  plants  of  a  great  industrial  cor- 
poration a  two-story  shop,  51  by  380  ft,  weighs  28  lb  per  sq  ft  of  ground-area; 
a  three-story  shop,  80  by  420  ft,  37-9  Ih I  a  three-story  shop,  80  by  300  ft,  46.3  lb; 
a  three-story  shop,  80  by  630  ft,  67.5  Ih;  a  four-story  shop,  77  by  140  ft, 
66.6  lb;  a  foundry,  121  by  150  ft,  40.5  lb.  In  another  plant  of  the  same  cor- 
poration, a  three-story  machine-shop,  80  by  51c  ft,  weighs  84.3  lb;  a  five-story 
office-building,  49  by  243  ft,  70.3  lb;  a  power-house,  55  by  120  ft,  37-5  lb; 
a  bkicksraith-shop,  81  by  200  ft,  15.6  lb.  In  a  plant  of  another  corporation, 
a  boiler-house,  50  by  94  ft,  weighs  23.3  lb;  a  furnace-building,  60  by  160  ft, 
25.1  lb;   a  roUing-mill,  80  by  80  ft,  24.4  ft;   a  rod-mill,  243  by  220  ft,  28.1  lb. 

Cost  of  Merchant  Steel.  The  cost  of  merchant  iron  and  steel  of  all  kinds 
is  based  on  a  certain  size  of  each  particular  shape,  which  is  taken  as  the  base, 
and  the  price  of  all  other  sizes  is  figured  at  a  certain  extra  rate  above  the  base 
according  to  a  standard  card  of  mill-extras.  The  base-price  may  fluc- 
tuate and  be  changed  without  notice,  but  the  extras  remain  constant,  and  arc 
the  same  in  all  localities.  The  following  tables  include  the  standard  classification 
of  extras  on  iron  and  steel  bars. 


Data  on  Structural  Steel 


mi 


standard  Classification*  of  Extras  oh  Iron  and  Steel  Bars 

Adopted  July  15,  igig. 


Rounds  and  squares 


Sizes 


%  to  3Hg  in 
^to  ii'io  irt 
3^  to  ^le  in 
Ms  in 

%  in 

H2  in 

Mo  in 

Yzz  in 

Va,  in. 

564  in, 


Extra  per 
100  lb 


Base 

$0.05 
o.io 
0.20 
0.25 
0.30 
0.3s 
0.40 
0.50 
0.75 


Sizes 


Vii  in 

M  6  in 

3H  tos^e  in 
iYi  t0  4M6  in 
4!/^  to  49^0  in 
4/^  to  5 Ho  in 
SH  to  5^6  in 
5^  to  6H6  in 
6)^  to  6H6  in 
SY^  to  7^^    in 


Flats 


Sizes 


to  6 

mX 

r% 

to  I 

in 

to  6 

inX 

M 

to  Me 

in 

1  J-i  6  to  1  •)!  8 

inX 

y. 

to    % 

in 

iMf 

to  1^6 

inX 

% 

to  Me 

in 

9l6 

toH 

inX 

% 

to   1^ 

in 

91  G  to  5^ 

inX 

H 

to    Me 

in 

3^ 

inX 

% 

to   Me 

m 

K2 

inX 

M 

to   Me 

in 

Me 

inX 

y^ 

in 

Me 

inX 

H 

to  Me 

m 

% 

inX 

Vx 

to  Me 

m 

K 

to  6 

inX 

tHe 

to  iMe 

in 

K 

to  6 

inX 

c^ 

toiH 

m 

M 

to  6 

inX 

[5/8 

to  2^ 

in 

H 

to  6 

inX3 

to  4 

in 

Standard  Classification  t  of  Angles,  Channels  and  Tees 


Angles 


Sizes 


t}/2  X  I  li  in  and  wider,  but  under  3  in  X  M e  in  and  over . 

I H  X  1 3^  in  and  wider,  but  under  3  in  X  3^  in 

I      X  I  to  1 3'i  X  I H  in  X  ^1  e  in  and  over 

I      X  I  to  13/4  X  i3i  in  X  3^  in 

VsXVs  ■         in  X  Mo  in 

KXVs  ■  in  X  3^  in 

HXH  in  X  Me  in 

HXK  in  X  3^  in 

YsXYs  inX3^in 

YgXYs  inXHain 

3^X3^  inX3^in 

H  XH  in  X  less  than  3/^  in 

3  in  on  one  or  both  legs  X  less  than  34  in , 


Unequal-leg  angles  are  subject  to  special  prices,  which  will  be  furnished  on  application 


*  Intermediate  sizes  take  the  next  higher  extra.     It  is  not  customary  to  enforce  more 
than  one  half  the  "standard-card  extras"  for  round  and  square  bars, 
t  Intermediate  sizes  take  the  next  higher  extra. 


1212  Data  on  Structural  Steel  Chap.  30 

Standard  Classification  *  of  Angles,  Channels  and  Tees     (Concluded) 


Channels 


I  ^2  in  and  wider,  but  under  3  in  X  M  6  in  and  over 

1 3^^  in  and  wider,  but  under  3  in  X  H  in 

I  to  1 34  in  X  M  6  in  and  over 

I  to  iM  in  X  H  in 

I  to  1 34  in  X  %4  in 

%  and  K  in  X  Me  in  and  over 

3^  and  3^^  in  X  3^  in 

3^  and  ^^  in  X  %4  in 

^  in  X  3^  in  and  over 

s^g  in  X  ^^2  in 

3/^  in  X  ^^4  in  and  over ". 

3^  in  X  ^64  in 


Extra  per 

100  lb 

$0 

15 

0 

25 

0 

25 

0 

35 

0 

50 

0 

30 

0 

40 

0 

55 

1 

20 

I 

40 

I 

80 

Tees 


I H  X  1 3^  in  and  wider,  but  under  3  in  X  M  6  in  and  over 

I  X  I  to  iJ4  X  i34  in  X  Me  in  and  over 

I  X  I  to  i>^  X  1^4  in  X  K  in 

3^  X>8  inXMe  in 

K  X  ^  in  X  3^  in 

M  X  M  in  X  ^i  6  in 

MX^inX3^in 

^X^in  X^in 

H  X  )i  in  X  3-8  in 

Unequal- leg  tees    are  subject  to  special  prices,  which  will  be  fur- 
nished on  application. 


Extra  per 

IOC 

lb 

$0 

20 

0 

40 

0 

50 

0 

50 

0 

60 

0 

60 

0 

70 

z 

30 

I 

80 

*  Intermediate  sizes  take  the  next  higher  extra. 

The  base  for  car-load  lots  for  any  city  may  be  obtained  by  adding  the  freight- 
rates  given  on  page  1524  to  the  base  prevailing  at  the  mills. 


Domes  1213 


1  CHAPTER  XXXI 

DOMICAL    AND    VAULTED    STRUCTURES* 

J  I  By 

I  ■  : 

I  EDWARD    F.   RIES 

•  CONSULTING   ENGINEER,    SAN   ANTONIO,    TEXAS 

1.    Domes  * 

Classification:  Domical  structures  may  be  considered  under  two  main 
divisions:  (i)  Smooth-shell  domes,  and  (2)  ribbed  domes.  The  first  division 
may  again  be  divided  into  (a)  domes  with  shells  of  uniform  thickness,  and  (b) 
domes  with  shells  of  uniformly  varying  thickness.  The  materials  of  con- 
struction of  division  (i)  are  brick,  stone,  concrete,  and  tile;  and  of  division  (2), 
steel,  concrete,  and  wood.  A  dome  may  be  constructed  with  or  without  a 
LANTERN,  or  with  or  without  an  occulus  or  eye;  and  in  the  case  of  ribbed 
domes,  they  may  have  either  circular  or  polygonal  bases. 

(i)  Smooth-Shell  Domes 

Mechanical  Principles.  Under  this  heading  are  considered  both  (a)  domes 
with  shells  of  uniform  thickness,  and  (b)  domes  with  shells  of  uniformly  vary- 
ing thickness,  and  also  domes  with  or  without  lanterns  and  eyes.  A  dome 
whose  shell  tapers  toward  the  top  is  the  more  stable  dome.  It  is  evident  that 
the  upper  part,  or  crown,  tends  to  fall  in  and  thereby  push  out  the  lower  por- 
tion; hence  the  lighter  the  upp)er  part  is  in  relation  to  the  lower  part,  the 
more  stable  the  dome.  The  exact  actions  of  the  internal  stresses  in  a  dome 
are  difficult  to  determine,  but  a  very  practical  solution  can,  however,  be  developed 
after  assuming  that  the  stresses  are  parallel  to  a  surface  midway  between  the 
outer  and  inner  surfaces  of  the  dome. 

General  Analysin.  A  dome  may  be  imagined  to  consist  of  a  number  of 
horizontal  rings  of  decreasing  diameter,  each  one  laid  on  top  of  another. 
Since  the  upper  part  tends  to  fall  in  and  push  out  the  lower  part,  there  must  be  a 
tendency  to  contract  each  ring  in  the  upper  part  and  to  expand  each  ring  in  the 
lower  part.  That  is,  there  must  be  end-compression  on  all  stones  (imaginary 
divisions  in  concrete)  of  the  upper  part,  and  end-tension  on  all  stones  of  the 
lower  part.  The  dividing  line  or  horizontal  joint  between  these  upper  and  lower 
parts  of  the  dome  is  called  the  joint  of  rupture.  The  angle  made  by  the 
joint  of  rupture  with  the  vertical  (center  of  dome  as  apex  of  angle)  is  known 
as  the  critical  angle.  It  is  evident,  then,  that  the  determination  of  the 
joint  of  rupture  and  the  critical  angle  determines  also  the  points  below 
which  there  is  tension  in  the  rings.  By  reinforcing  the  lower  part  with  steel 
bands  or  rods  to  resist  this  tension,  the  dome  can  be  made  secure.  If  the  dome 
is  a  FLAT  DOME,  that  is,  one  in  which  the  angle  the  base  makes  with  the  vertical 
is  less  than  the  critical  angle,  the  tension-steel  must  be  placed  at  the  base 
of  the  dome  to  resist  the  outward  push  or  thrust, 

*  See,  also,  Chapters  VII  and  VIII. 


1214 


Domical  and  Vaulted  Structures 


Chap.  31 


Notation  and  Theory  (See  Fig.  1): 

r  =  mean  radius  of  dome; 

a  =  thickness  of  shell  at 
crown; 

/  =  thickness  of  shell  or  of 
ring  at  any  point; 

a = angle  made  with  the  ver- 
tical by  radius  to  lan- 
tern-ring. Center  of 
dome  is  the  apex  of 
angle.  In  a  dome 
without  lantern,  a  =o; 

0=  angle  made  with  the  ver- 
tical by  radius  passing 
through  any  point  in 
shell  (in  equations 
angles  are  in  radians); 

c  =  constant  of  variation  of  / 
with  respect  to  arc  6; 

cr 

—  =»  a    constant    (based    on 
a 

above  notation)  for 
any  dome; 
0=  critical  angle,  that  is, 
the  angle  made  with 
the  vertical  by  the 
joint  of  rupture; 
w  =  weight  of  cubic  unit  of 

masonry; 
V  =  volume  of  shell  of  com- 
plete dome  above  any 
ring; 
Wd='U^V  =  total  weight  of  complete  shell  above  any  ring  (including  the  part 

removed  for  eye) ; 
Wi-o  =  weight  of  lantern  minus  weight  of  shell  removed  for  occulus  or  eye 

{Wi-o  may  be  either  positive  or  negative); 
W^Wa-\-Wi-o; 

n  =  — — - ,  a  constant  for  any  dome; 
2  T  war  2 

P  —  total  tangential  pressure   for   any  ring,  due   to   lantern  and   shell  above 

that  ring; 
U  =  tangential  pressure  per  unit-length  of  ring; 
H  =  total   radial    horizontal    pressure   on   any  ring,  due  to  outward  push  or 

thrust  of  shell  above  that  ring; 
T  =  hoop-tension  or  hoop-compression  in  ring,  due  to  77; 

Using  this  analysis  and  notation,  the  following  equations  are  developed: 

Equation  (i)     t  =  a  ■\-  crO 

Equation  (2)     F=  27rf2[a(i  —  cos  0)  -\-  cr  (sin  0—  d  cos  0)] 


Fig.  1.     Smooth-shell  Concrete  Dome.     Analysis 


Equation  (3)    Wa  =  wV  =^  2'k war 


[- 


cos  6)  4-  —  (sin  O—dcosd)     =war'^z. 


].. 


Domes  1215 


in  which 


Equation  (5)     U  =  war 

=  war  (Si  +  S),    in  which 
Si  =  -T-y^    and 


27r     (i  —  cos  e)+~  (sin  d—  6  cos  6) 

"[(wc 

[cr  -t 

cosec  6—  cotan  0-\ — (i  —  d  cotan  ^) 
-^+ ^^ 
sin2^                               sin^  J 


Equation  (4)     P  =  2ir  war-  \  (n  cosec  d  -\-  cosec  0—  cotan  ^)  +  — (i  —^  cotan  0) 


cosec  0  —  cotan  0  -| —  (i  —  0  cotan  0) 
a 

sin  0 


Equation  (6)     T=  —  =  war^    n  cotan  0  +  (i  —  cos  ^)  cotan  6 
27r  L 


4-  —  (sin  0—  ^  cos  0)  cotan  0 


=  war'^  (Fi+  F),  in  which 
Y\=  n  cotan  0     and 


[,.-. 


F  =  I  (i  —  cos  0)  cotan  0+-  (sin  0—  0  cos  0)  cotan  0  I 

„        .      ,  ^    cr  „^     COS0— sin^^ 

Equation  (7)    —=  n  cosec^  0 ^-- 

a  I  +  cos  0 

Design  and  Investigation  of  Smooth-Shell  Circular  Domes.     By  the  use 

of  the  foregoing  equations  any  circular  dome  can  be  designed  or  investigated. 
The  computations,  however,  connected  with  some  of  these  equations  are  long 
and  tedious,  and  are  simpHfied  by  using  curves  plotted  from  the  solutions 
found,  after  giving  different  values  to  some  of  their  elements  or  factors.  (See 
Plates  I,  II,  III,  and  IV.) 

Equation  (7)  is  represented  by  the  curves  in*Plate  I.     By  the  use  of  these 
curves  the  position  of  the  joint  of  rupture  for  any  dome  is  found  by  inspection 

when  the  values  of  —  and  n  are  known.     The  value  of  —  is  easily  determined,  as  c 

a  a 

can  be  found  by  using  Equation  (i)  after  determining  or  assuming  a,  the  thick- 
ness at  the  crown,  and  t,  the  thickness  at  the  base;  and  the  value  of  n  is   found 

from  the  ratio  n  = ;. 

2Trwar^ 

Equation  (3)  is  represented  by  the  curves  in  Plate  II.     From  these  curves  the 
weight  of  any  shell  is  determined. 
Equation  (5)  is  represented  by  the  curves  in  Plate  III.     Knowing  the  values 

of  n  and  — ,  the  values  of  Si  and  S  are  found  by  inspection,  and  hence  U  is  easily 

a 
computed. 


1216 


Domical  and  Vaulted  Structures 


Ciiap.  31 


Values  of  -^ 

Plate  I.     Curves  for  Determination  of  Joint  of  Rupture  of  Domes.    Based  on  Equation  (7) 


Equation  (6)  is  represented  by  the  curves  in  Plate  IV. 


Knowing  the  values  oi 
When 


n  and  — ,  the  values  of  Yx  and  Y  are  found,  and  T  computed  for  any  ring. 

n  equals  zero,  Fi  equals  zero,  and  the  value  of  T  depends  upon  Y  as  given  in  the 
lower  curves.  It  will  be  noticed  that  F  increases  as  Q  increases  until  the  crit- 
^  ICAL  ANGLE  for  a  dome  without  lantern,  or  eye  (w  =  o),  is  reached;  that  is,  each 
successive  ring  increases  the  outward  thrust,  and  at  the  critical  angle  there  is 
a  maximum  value  of  F,  and  hence  a  maximum  hoop-tension  T.  After  the 
CRITICAL  angle  is  passcd  the  rings  are  in  tension,  and  therefore  T  and  F  are 
reduced  by  the  tension  required  of  the  ring  or  masonry. 

The  curves  also  indicate  that  the  stability  of  a  dome  with  a  shell  of  imiform 


Domes 


Values  of  z 

Plate.  II.     Curves  for  Determination  of  \yeight  of  Shell  of  Domes.  Based  on  Equation  (3) 

thickness  and  with  no  lantern  is  not   affected  by  the  thickness  of  the  shell, 

since  c  =  o,  and  therefore  —  =  o,  regardless  of  the  value  of  a. 
a 

Example.  It  is  required  to  design  a  smooth-shell  reinforced  concrete 
DOME  of  45-ft  radius,  and  with  a  lantern  of  lo-ft  radius,  weighing  50  000  lb.  The 
shell  within  the  lantern  is  to  be  removed,  forming  an  eye.     (Fig.  2.) 

Solution.  Assume  a  crown-thickness,  a,  of  5  in,  and  a  thickness,  /,  at  the  base 
of  8  in. 

From  Equation  (i) 

cr     t—a 
t^  a+  crd,  or  -  =  — — 


1218 


Domical  and  Vaulted  Stnictures 


Chap.  31 


+0.5 

\     \.A 

y s._|...s ^A- -     - 

; s,..4r:^.  t t...  . 

0 

\     xj'^s..  m __    .  

.- -:|^^. -J --.==-----^-=---;:::;;;:--^^^^=    - 

o 

ilo           '  ■ + .-t-:"":    ■ :  : 

^ 

-0.6 

j                           

'd 

im+ntTnTlt  |Jji4l4+llllllll  liiliitro            \\m 

;> 

.%'-'        '-''    ,.'"' 

7  "w" 'y'" -'"      " ":  :::::::::  : 

-1.0 

^     /'    /'  S''"                              1 

i      y'<^'' 

/   t'  \                         i 

1      ^    ' 

u.iL              \\4u 

;-a-r.)(S 

+<;'» 

2.0 

r^>' ? 

IJol^  . 

t          1&-  * 

: :  :                 :                                                ;iF ' 

'WV  ' 

....        "  " "                    " '    ■ '"'"         ±"";l/ .' 

" """ X""'  Y'A    ' 

1    ., '',^1?   '\ 

. /^/ Aa^  - 

, /.X  '  i  y. , 

1.0 

t   .'  .'K  '  t4f . 

cn 

:     .:         :'^'^'' :'  >  '^ 

«M 

o 

,''  /'','' ''  '''  'dSi'' 

«> 

f'' ,''  i^'  ^'  ,''    ,'T  \'      ,  ' 

n 

^,,>^>'f>'f   A'xL'^        ■<     \  ^"^ 

'.^ 

-._  u            '" > ' ^P^SJ-^  -^^'Li>^^^ ' ' '  i - ' ' '    1  j> •" ' T 

r^ 

r                             '<*;^  ""Jk^^-^^  ■'^'^^^^-^^                  --f        -(!-i*T^ 

::t::::;:  i|^^^^ 

-^^  ;^1<^"Tj1— -^  "^  !j_--r|^       -H''^        "',--'" 

g:::±;h::;;:::;;;:;::::::::::::  ::::: 

! ffllffr 

^--.-.- 

r-^ L_ 

— 

riiiiiiiiiiiiiiiiiiiiiiii 

0 

1 

::::::::: 

1 

1 

^            1|0           20           30           4|0           50            60           70           80 

Angle  d 

Plate  III.     Curves  for  Determination   of  Tangential    Stress  per  Unit-length  of  Dome- 
ring.     Based  on  Equation  (s) 

For  the  dome  without  wind-loads  or  snow-loads 

Cr  12         12 

a 


©'-«■ 


•  =  o.^i 


lO 


The  angle  a  =  sin~^  —  =  i2~  so'. 

45 
From  Plate  II  the  weight  of  the  shell  removed  for  the  eye  is 


•fe) 


150    -- )  (45)'(o.i6s)  =  20  883  lb 


Domes 


1219 


+0.5 

¥                 1   T 

-\1  X i .^-             : " 

..T..\.!s.^_ !_..__ : ::   

__  1  LA.-'s-  v.-l - 

..lA     \  '-,  \t 

0 

\^\     \\-^.<:lt                   

I  ^    '!;•,:+:. ^^.                     :      ' 

*>^ 

1            '"■-...      " ! - 

;  .  :■      ,  :  ,  .     '  .  .._^— . 

mtiiiiiiiiii     1 

o 

1         ^  =  0    1rT...t:::+-ff+fr:^ 

^&i..i.... 

i 

-0.5 

-  ;;:::^- ::"-----"::::=-:^^=''''^^^ ^" 

rf 

I       .''''  fit'""  .-■■'"---'•'""       Till 

> 

t     ''    ^'    .--'''.--■''' 

T  /     /TT/'' T''-'' 

-1.0 

'Ti:':'""m''' 

4i  J  ^'  ¥ 

t'../_/  % 

\._i  _  sr^-- 

4'.:.!|:::T 

(wj-a* 

r^)(Y,+ 

yilillli^iB 

> 

J5 

.6 
.5 
.4 
.3 

4j-r±f^!^-— hi 

|;  i  i  1  i 

P 

i 

4i| 

.2 

.1 

0 

1 

,             10 

20 

3 

40 

50 

rtT±FFF 

60 

70 

1 

80 

1 

Plate  IV. 


Angled 

Curves  for  Determination  of  Hoop-tension  or  Hoop-compression  in  Dome- 
ring.     Based  on  Equation  (6) 
Therefore 

PFi-o  =  50  cx)o— 20  883  =  29  117  lb 
For  wind  bads  and  snow-loads  a  simple  and  safe  method  of  procedure  is  tx> 
allow  a  uiiif  jrm  load  over  the  surface  of  the  dome,  since  this  load  can  be  trans- 
lated int  >  its  equivalent  in  inches  of  masonry  and  hence  the  same  equations  and 
curves  used.  A  wind  l)ad,  for  example,  of  25  lb  per  sq  ft,  is  equivalent  to  2  in 
of  concrete  weighing  150  lb  per  cu  ft  Hence  the  new  a  and  /  equal  7  and  10  in, 
respectively.     Hence  from  Equation  (i) 

10       7 

cr  12      12 

=  0.307 


fe)- 


396 


1220 


Domical  and  Vaulted  Structures 


Chap.  31 


and 


Wi- 


29  117 


27rwaf2 


27r(iso) 


(a 


•  0.026  ^ 


(45)2 


Weight  of 
Lantern,  60,000  lb 


From  Plate  I,  with  —  =  0.307, 
a 

and  n  =0.026,  the  critical  angle 
is  found  to  be  52°  35'. 

From  Plate  IV,  at  the  critical 
ANGLE  for  the  dome  with  snow- 
load  and  wind- load 


'& 


T=  i5o\  —  )  (45)'(o.o20-|- 0.352) 

=  65  914  lb  tens' 3n 

This  must  be  resisted  by  steel 
reinforcing  rods.  Allowing  a  unit 
tensional  stress  of  16  ceo  lb  per 
sq  in     in    the    steel,    a   total    of 

6s9M  •  .       , 

-^ =  4.12  sq  in   sectional  area  . 

16  000 

of  steel  is  required.     At  the  base 

({?=8c°) 

T  =  150  (~\  (45)^(0.005  +  0.186) 

=  33  843  lb 

The  total  cross-sectional  area  of 
steel  in  tension    at    the  base    is 

33843  .  .  ,  r 

— =  2.12  sq  in,  given  by  five 

16  000 

round  rods,  each  %  in  in  diameter. 

'The  remaining  required  sectional  area  of  steel,  4.12—  2.12  =  2  sq  in,  must 

be  spaced  in  the  lower  part  of  the  dome  over  an  angular  distance  of  (80°— 52°  35') 

=  27°  25' =  0.4785  radian,  or  0.4785X45=  21.53  ft    up  the  surface  of    the 

dome. 

The  assumed  thickness  of  shell  at  the  base  was  8  in,  and  the  thickness  at  the 

lantern-ring  will  be,  from  Equation  (i), 

cr  ^ 

t  =a-^  crd  =  a-\-a  —  d 


Fig.  2.     Smooth-shell    Concrete    Dome 
Lantern  and  Eye.     See  Example 


5+5  (0.43) (0.2 239)  =  5.48  in 

Allowing  0.2  per  cent  of  steel  cross-section,  horizontally  and  meridionally,  for 
secondary  stresses  caused  by  temperature-changes  and  possible  unequal 
snow-loads  and  wind-loads,  there  should  be  8  X12  X  0.002  =  0.19  sq  in  of  steel 
cross-section  per  running  foot  at  the  base,  and  5.48  X  12  X0.002  =  0.13  sq  in 
per  running  foot  at  the  lantern-ring.     The  spacing  of  the  horizontal  reinforcing 

*  The  snow-load  on  the  top  of  the  lantern  is  taken  care  of  because  snow-loads  and  wind- 
loads  over  the  entire  dome  were  included,  and  only  the  actual  masonry  of  the  eye  was 
subtracted. 


Domes 


1221 


is  best  found  as  indicated  in  Fig.  3.  Curve  A  gives  the  total  amount  of  steel 
necessary  for  secondary  stresses  above  any  point  in  the  cross-section  of  the 
shell.     Curve  B  gives  the  necessary  tensional  resistance,  using  Curve  .4  as  a 


10  15  20  25  30  35  10 

Distance  in  Feet  Jleasured  up  the  Sliell 

Fig.  3.     Diagram  for  Determination  of  Amount  of  Horizontal  Steel  Reinforcing  in 
Concrete  Domes 

starting-point  for  the  ordinates.     Various  points  on  the  curve  are  easily  deter- 
mined.    For  example,  for  6  =  70° 

^  =  5  +  5(o.43)(i-22i7)  =7.63  in 

The  cross-section  of  temperature-steel  per  foot  at  70**  is 

7.63  X  12  X  0.002  =  0.18  sq  in 

The  total  cross-section  of  temperature-steel  above  70°  is  then 

0.18  -+-  0.13 

X  (1.2217  —  0.2239)45  =  6.96  sq  in 


The  tension-steel  cross-section  (Plate  IV)  above  70°  is 

(150)  (7/12)  (45)2(0,298^-0.009) 


4.12  —  - 


:  0.72  sq  in 


16  000 

With  points  determined  in  this  manner  the  curves  are  developed. 
The  total  cross-section  of  horizontal  steel  in  the  entire  cross-section  of  the 
shell  is 

8.45  -f  2.00  =  10.45  sq  in 

with  an  additional  2.12  sq  in  of  tension-steel  at  the  base.     If  ^-in  round  rods 

are  used,  there  will  be  — '——  =  54,  required  in  the  shell.    By  dividing  the  area 
0.1963 


1222  Domical  and  Vaulted  Structures  Chap.  31 

below  the  curve  (Fig.  3)  into  54  parts,  the  distance  up  from  the  base,  where  each 
rod  should  be  placed,  is  determined.  The  meridional  steel  should  be  such  that 
there  will  be  0.19  sq  in  of  cross-section  per  foot  of  circumference  at  the  base, 
and  0.13  sqin  per  foot  of  circumference  at  the  lantern-ring;  that  is,  if  3^-in  round 

rods  are  used,  they  should  be  spaced  — — —  =  i  .03  ft  at  the  base,  and  — — —   = 

0.19  0.13 

1.51  ft  at  the  lantern-ring.    The  punching-shear  at  the  lantern-ring  is  equal  to 

=  12. 1  lb  per  sq  in 


.(5.48)  (27rioX  12) 
This  is  well  within  the  limit  of  40  lb  per  sq  in. 

(2)  Ribbed  Domes 

General  Principles.  The  following  discussion  applies  to  domes  of  either 
circular  or  polygonal  horizontal  cross- sections.  All  steel  doiiies  are  ribbed 
domes,  and  usually  have  from  six  to  twenty-four  ribs  resting  against  a  lantern- 
ring  or  SPIDER  at  the  top.  The  ribs  may  have  solid  webs,  perforated  v.el  f,  or 
latticed  webs,  with  angle  or  channel-flanges.  The  latticed  angle-ribs  are  prefer- 
able because  of  their  Ughtness.  The  tension-rings  and  compression-rings  may 
be  built  similar  to  the  main  ribs,  and  should  brace  the  latter  throigh  rigid 
gusset-connections.  The  diagonals  are  usually  rods  with  turnbuckles  fcr  adjust- 
ment. Concrete-ribbed  domes  or  wooden-ribbed  domes  may  be  designed 
according  to  the  same  general  principles  followed  for  steel  domes,  but  the  diag- 
onals are  omitted  and  dependence  for  rigidity  is,  placed  on  the  slab-f.llings 
between  the  ribs. 

The  Schwed.er  Method  for  the  Design  of  Steel  Domes.  W.  Schv^edler 
has  by  simple  resolution  of  the  forces  derived  equations  for  domes,  based  on  the 
forms  of  SURFACES  OF  revolution.  These  equations  are  easily  checked  vhen 
the  forces  acting  through  a  rib  (the  rib  acting  as  a  strut  between  the  joints) 
and  through  a  ring  at  a  joint  are  considered.  The  following  laws  may  be 
stated: 

(i)  The  ribs  are  in  maximum  stress  when  the  whole  dome  is  loaded; 

(2)  A  ring  is  in  maximum  tension  when  all  of  the  dome  above  the  ring  is  fully 
loaded,  and  in  maximum  compression  when  all  of  the  dome  below  the  ring  and 
the  ring  itself  is  fully  loaded; 

(3)  The  diagonals  are  not  stressed  when  the  dome  is  symmetrically  loaded. 
The  diagonals  in  a  panel  are  in  maximum  stress  when  the  dome  on  one  side  of  a 
meridional  plane  passed  through  the  center  of  that  panel  is  fully  loaded  and 
the  other  side  unloaded. 

In  Fig.  4  let 

ai,  a.1,  ca,  etc.  =  angles  made  by  rib-sections  with  the  horizontal; 
/3i,  ^2,  ^3,  etc.  =  angles  made  by  diagonals  with  the  ribs; 
Pi,  Pa,  Pz,  etc.  =  dead  loads  at  ends  of  rib-sections; 
Li,  L2,  L3,  etc.  =  live  loads  at  ends  of  rib-sections; 
Di,  D2,  D3  etc.  =  stresses  in  rib-sections; 
T\,  Ti,  Ti,  etc.  =  stresses  in  rings; 
A""!,  iV?,  N-i,  etc.  =  stresses  in  diagonals; 
n  —  number  of  ribs. 


Domes 


1223 


\        X      Tr. 


ELEVATION 


SECTION 


Fig.  4.     Schwedler  Ribbed  Dome 


L/2  =    — 


sin  ai  sin  az 

sin  as 
(Pi  +  7.1 )  cot  ai  Dicosai 


,  etc. 


2  sin  -  2  sin  - 

n  w 

(when  the  result  is  negative  the  stress  is  compressive). 


1224  Domical  and  Vaulted  Structures 

Maximum  J.  =  (^■  + ^O  cot  «i- (P. +  /..  +  />,)  cot  g. 


Chap.  31 


Minimum  T,  =  ^- ^"t  «,  -  (A  +  P.  +  £,)  cot  a, 

.       TT 

z  Sin  - 
n 

Maximum  T>  =  (-P'  +  ^-  +  A  +  Z.,)  cot «,-  (f .  +  £.  +  ^8+  £,  +  f .)  cot  g, 


Minimum  T,  =  (^■  +  -P')  '^"ta^-  (f  ■  +  Pa  +  Pa  +  i.3)  cot  a^ 


etc. 


i\ri. 


2  sin  ai  cos  /3i 


i\r2=  ■ 


X1  +  1.2 

2  sin  oro  cos  / 


,-        Z,i  +  Z2  4-  jl3 

^3  =  — : -,  etc. 

2  sin  as  cos  ^3 


Fig,  4a.     Graphical    Determination   of 
Stresses  in  Ribbed  Domes 


For  the  stresses  in  the  diagonals  the 
factor  2  is  introduced  because  Muller- 
Breslau  found,  by  exact  analysis, 
stresses  only  one  half  as  large  as  those 
determined  by  the  simple  resolution  of 
forces.  The  diagonals  are  stressed  under 
a  wind-load,  and  this  is  resisted  by 
assuming  a  vertical  live  load  equal  to 
from  20  to  30  lb  per  sq  ft  of  horizontal 

PROJECTION. 

A  GRAPHICAL  METHOD,  developed  by 
E.  Schmidt,  for  determining  the  stresses 
A,  A,  A,  Ti.  Ta,  n,  etc.,  is  shown  in 
Fig.  4a. 

Weights  of  Steei  Domes.    It  was 

found  by  Scharowsky,  from  calculations 
made  for  a  large  number  of  Schwedler 
FLAT  DOMES  Varying  in  span  from  60  to 
180  ft,  that  the  weight  of  the  lantern 
and  steel  skeleton  per  sq  ft  of  projected 
(covered)  area  is 

w=  0.01565+4 

where  w  =  pounds  per  square  foot  of 
projected  area,  and  S  =  the  span,  in  feet. 
For  preliminary  calculations  on  full 
HEMISPHERICAL  DOMES,  the  weight 
found  by  this  equation  should  be  in- 
creased from  two  and  a  half  to  three 
times. 


Domes  1225 

Steel  Dome  of  the  Horticulture  Palace,  San  Francisdd,  Cal.*  This  is  a 
SCHWEDLER  HEMISPHERICAL  DOME  of  iS2-ft  Span,  with  twenty-fouF  latticed  ribs, 
36  in  deep,  carrying  a  lantern-ring  or  spider  at  the  top,  and  connected  by  eleven 
horizontal  rings.  The  lantern-ring  is  6  ft  in  diameter,  36  in  deep,  with  a  solid 
web,  and  braced  twice  diametrically.  The  ribs  are  constructed  of  two  4  by  4 
by  Me-in  angles  at  the  top,  two  3  by  3  by  Me-in  angles  at  the  bottom,  and  a  2  3^ 
by  23^  by  J^-in  angle  single-lattice  web.  The  dome-steel  weighs  about  17  lb 
per  sq  ft  of  projected  area. 

Concrete  Ribbed  Domes.  In  a  reinforced-concrete  ribbed  dome 
the  number  of  ribs,  varying  from  eight  upward,  is  determined  by  the  substruc- 
ture and  the  size  of  the  dome.  The  different  steps  in  designing  a  ribbed  rein- 
forced-concrete  dome  are:  (i)  the  determination  of  the  number  of  ribs  and  rings; 
(2)  the  determination  of  the  loading,  per  rib,  using  the  required  shell-thickness 
and  the  assumed  rib-sizes  and  ring-sizes  for  preliminary  calculations;  (3)  the 
finding  of  the  forces  acting  on  the  ribs  by  the  use  of  Schwedler's  formulas; 
(4)  the  drawing  of  the  elastic  curve  for  the  ribs;  (5)  the  determination  of  the 
stresses  and  necessary  reinforcement  in  the  ribs,  rings,  and  slabs;  (6)  the  adjust- 
ment of  sizes  and  loads,  so  as  to  be  on  the  side  of  safety;  and  (7)  the  reworking 
of  the  preliminary  computations  for  the  final  design.  The  elastic  curve 
should  always  remain  in  the  middle  half  f  of  the  rib,  and  should  never  be 
so  far  away  from  the  center  of  gravity  of  the  rib-section  that  the  maximum  com- 
pressive stress  of  500  lb  per  sq  in  in  the  outer  fiber  of  the  rib  is  exceeded.  The 
reinforcement  in  the  ribs  should  be  sulhcient  to  resist  the  flexural  stresses  due 
to  the  eccentricity  of  the  elastic  curve.  The  reinforcement  in  the  rings 
should  be  sufficient  to  resist  the  tensile  stresses,  and  should  be  as  straight  as 
possible  in  order  to  avoid  a  sidewise  stress  or  movement.  The  rings  must  be 
reinforced  to  resist  their  flexure,  as  beams.  The  panel-slabs,  if  domical  (see 
Smooth-Shell  Domes),  should  be  reinforced  for  shrinkage -stresses  and  tem-^ 
perature-stresses,  in  addition  to  the  reinforcement  for  tension  below  the 
critical  angle.  If  the  slabs  are  straight  they  should  be  designed  as  floor-slabs, 
and  by  similar  methods. 

Example.  J  It  is  required  to  build  a  dome  (Fig.  5)  with  a  span  of  132  ft  and  a 
rise  of  31  ft  6  in.  This  makes  the  radius  85  ft.  The  eye  is  to  be  12  ft  in  diam- 
eter. The  outer  surface  of  the  dome  is  to  be  a  domical  slab  on  ribs,  carrying  a 
suspended  plastered  ceihng  forming  the  inner  surface. 

Solution.  §  To  obviate  the  necessity  of  building  a  complete  domical  form, 
supported  from  the  floor  below,  the  decision  is  to  build  a  ribbed  dome  as  follows: 
It  is  decided  to  build  a  central  tower  to  temporarily  carry  the  upper  ends  of  the 
ribs,  to  precast  these  ribs,  raise  them  into  position,  cast  the  ring  of  the  eye,  sus- 
pend the  ring-forms  from  the  ribs,  pour  the  rings  in  place,  and  then  fill  in  the 
slab-panels  on  forms  supported  from  the  rings  and  ribs. 

Since  the  span  of  the  dome  is  132  ft,  the  circumference  at  the  base  is  41 4-7 
ft.     Because  of  the  suspension  of  the  panel-forms,  it  is  well  to  keep  the  panel- 

*  A.  W.  Earl  and  T.  F.  Chase,  Engineering  Record,  Oct.  24,  1914. 

t  The  usual  practice  has  been  to  keep  the  resistance-line  within  the  middle  third  in 
arches  generally.  In  reinforced-concrete  arches  and  domes  it  may  depart  a  small  dis- 
tance outside  the  middle  third,  but  there  should  be  sufficient  steel  to  resist  any  tension 
developed.  The  ribs  of  domes  differ  from  ordinary  arches  as  they  are  rigidly  braced 
by  the  rings  and  the  slab-panels. 

t  The  dome  of  this  example  is  similar  to  the  dome  over  the  Hippodrome  at  Copen- 
hagen, Denmark,  by  Christiani  and  Nielsen.  See  the  periodical,  Concrete,  for  December, 
1917. 

§  In  the  solution  of  this  example  all  calculations  have  been  made  with  the  slide-rule. 


1226 


Domical  and  Vaulted  Structures 


Chap.  31 


\ 


\  \  \  \  \ 


^   \,  \  \  \  \ 

\ 


\    \ 


.,\  \\  \  \  1  , 

-  -^ \-  -66 ':=^'85  sin  5^56^ \ V \ \- 


\ 


'0 


\ 


\ 


DIAGRA.M  A^ 


D.I4GRAM  0 

CROSS-SECTION  OF  EYE-RINQ 


Fig.  5.     Segmental  Concrete  Ribbed  Dome 


Domes  1227 

WIDTHS  within  about  a  20-ft  limit.  Hence  twenty  ribs  are  necessary.  With 
three  intermediate  rings,  the  lower  panels  are  approximately  square.  The 
rings  are  not  to  show  below  the  cciUng,  and  hence  a  narrower  spacing  toward 
the  top  is  unnecessary  for  appearance.  For  preliminary  calculations,  allowing 
1 1 00  lb  per  lin  ft  for  the  eye-ring  and  the  load  due  to  a  glass  covering  over 
the  eye,  250  lb  per  ft  for  the  weight  of  the  ribs,  and  150  lb  per  ft  for  the  weight 
of  the  intermediate  rings;  and  assuming  a  slab-thickness  of  3H  in,  a  suspended 
plaster  ceiling  ^i  in  thick,  and  25  lb  per  sq  ft  of  surface  for  snow-loads  and  wind- 
loads  (or  an  equivalent  of  a  2-in  thickness  of  concrete),  the  loading  on  the  ribs  is 
as  shown  in  Diagram  A  of  Fig.  5.  To  illustrate  the  method  of  determining 
THE  LOADS,  the  Calculations  for  the  loading  at  the  lower  intermediate  ring  are 
given.     The  weight  of  the  rib  is  250X17.39  =  4347  lb.     The  weight  of" 

2X7rX8sXsin39°  14'  ,,       ^, 

the    ring   is    150 =2534   lb.     The  weight    of   the 

20 

shell  and  ceiling  between  6  =  33°  21'  and  0=  45°  5'  is,  from  the  curves  in 

Plate  II,  with  -  =0, 
a 


(85)2(1.84)- 150  (^'■^^':^-^)  (85)^(1.03) 

=  15  570  lb 


The  total  dead  load  is 

4  347+ 2534 -f- 15  570=  22  451  lb 
The  total  live  load  is 

15  570  X  2 


sH-^ 


■■  7  330  lb 


The  stress  D4  (see  method  in  Fig.  4a),  in  the  lower  section  of  the  rib  is  the 
largest,  and  according  to  Schwedler's  formulas,  page  1223,  is 

6  6cxD+ 15  301  +  22  908-I- 29  781 

■ :; a — ; =  io5  4°°  lb 

sin  45    5 

The  eccentricity  of  the  stress  Di  is 

85—  (85  cos  5°  51')  =  0.445  ft 

The*  moment  due  to  the  eccentricity  of  Dt  is 

105  400  lb  X  0.445  ft  =  46  903  ft-lb,  or  562  836  in-lb 

To  resist  the  column-like  compression  of  Di  there  is  required  a  cross-sec- 
tional area  of  rib  of 

105  400  '      e  ^ 

■ =  211  sq  m  of  concrete 

500 

To  resist  the  effect  of  the  eccentricity  of  the  stress  A,  it  is  necessary  to 
insert  enough  steel  so  that  the  total  stress  in  it,  multiplied  by  the  distance 
between  the  top  and  bottom  steel  reinforcements,  is  equal  to  the  moment,  562  836 
in-lb,  already  found. 

Since  the  eccentricity  of  Z>4  is  0.445  ft,  and  the  line  of  action  of  the  thrust 
is  to  be  kept  within  the  middle  half  of  the  rib,*  the  rib  will  be 

4  X  0.445  =  1.78  ft  =  21 H  in  in  depth 
*  See  foot-note  on  page  1225. 


i22S  Domical  and  Vaulted  Structures  Chap.  31 

Allowing  iH  in  of  concrete  for  steel-protection  at  the  top  and  bottom  of  the 
rib,  the  distance  between  the  inner  and  outer  reinforcements  is 

2iK  — 3  =  183^  in 
Therefore  a  stress  of 

562  836  • 

-^^  =  30  424  lb 

is  to  be  resisted  by  the  steel  at  the  top  and  bottom.     Since  there  is  steel  in  both 
COMPRESSION  and  tension,  the  allowable  unit  stress  in  it  is 


/65oXi8H\,  ^  Q      ,u 

I —  I  (15— i)  =  7  83olbper  sqi 

\       2ii^      / 


This  is  because  the  allowable  compressive  unit  stress  in  the  outer  fibers  of  con- 
crete beams  is  650  lb  per  sq  in;  the  ratio  of  the  modulus  of  elasticity  of  the 
steel  and  of  concrete,  15;  and  the  distance  between  the  inner  and  outer  steel 
'reinforcements,  and  the  distance  of  the  rib-depth,  18K  and  21K  in  respectively. 
The  I  in  the  expression  (15  —  1)  is  to  take  care  of  the  stress  carried  by  the 
concrete  replaced  by  the  steel. 

The  TOTAL  cross-section  of  steel  necessary  at  both  the  top  and  bottom  of  the 
rib  is,  therefore, 

30424  Q 

— -—   =  3.89  sq  m 
7830 

furnished  by  four  i^-in  round  rods.  The  best  arrangement  of  the  211  sq  in 
of  concrete,  and  the  steel,  results  in  a  cross-sectional  shape  shown  in  Diagram  B 
of  Fig.  5.  The  stirrups  should  be  spaced  not  more  than  three  fourths  of  the 
distance  between  lines  of  longitudinal  steel,  or  54  X  18H  =  12  in  (approximately), 
and  they  should  be  made  from  ^-in  round  rods.  Because  of  the  ties  in  the 
flanges,  it  is  advisable  to  use  small  J^-in  rods  as  stiffeners  at  the  inter- 
sections of  the  ties  and  stirrups.  Projecting  loops  should  be  left  for  fastening 
the  panel-slabs.     The  actual  weight  per  linear  foot  of  the  ribs  is 

211 

—  X  150  =  220  lb 

144 

for  the  concrete,  plus 

(4  +  3.38)+ II  =  25  lb 

for  the  steel,  equal  to  a  total  of  245  lb,  as  against  250  lb  per  lin  ft  previously 
allowed  in  the  calculations. 

As  the  ribs  are  to  be  precast  and  raised  into  place,  it  is  necessary  to  determine 
whether  they  are  of  sufficient  strength  for  this,  and  whether  they  will  stand,  un- 
supported by  the  rings,  without  breaking  under  their  own  weight.  By  consider- 
ing the  ribs  to  be  simple  arches,  and  testing  them  by  determining  the  line  of 
thrust,  it  is  found  that  they  are  amply  safe.  In  order  to  resist  the  thrusts  or 
stresses  developed  by  raising  the  ribs  into  place,  it  is  necessary  to  tie  the  ends 
together  with  bow-string  rods. 

The  stresses  in  all  of  the  rings,  except  the  footing-ring,  are  compressive. 
This  is  because  they  are  all  above  the  critical  angle.  (See  Smooth-Shell 
Domes.)  Therefore,  in  determining  the  stresses  by  Schwedler's  formulas,  only 
the  equations  for  the  minimum  values  of  Ti,  Ti,  Ti,  and  Ti  need  be  used. 

The  stress  in  the  eye-ring  is 

(5750+850)  cot  9°  55' 


- 1 20  600  Jb 


2  sm  — 
20 


Domes  1229 

The  stress  in  the  first  intermediate  ring  is 

(S  750  cot  9°  55O—  (5  750+  12  146+3  155)  cot  21°  38' 

=  —  65  000  lb 

■T 

2  sin  — 

20 

The  stress  in  the  second  intermediate  ring  is 

(5  750+  12  146)  cot  2i°38'— (s  750+  12  146+  17  573  +  5  335)  cot  33"  21' 


=  —  53  900  lb 
The  stress  in  the  third  intermediate  ring  is 

(5  750+12  146  +  17  573)  cot  33°  21^ -(5  750+12  146+17  573+22  451  +  7330)  cot  45°  5^ 


^  —  35  600  lb 

The  stress  in  the  footing-ring  is  tensile,  and  hence  the  equation  for  the  max- 
imum VALUE  of  Ts  gives 

(5  750+850  +12  146+  3  155+  17  573  +  5  335+  22451  +  7330)  cot  45°  5^ 

2  sin  — 

20  =  238  000  lb 

1 20  600 
The  EYE -ring  should  have =  242  sq  in  of  concrete,  but  for  appearance  it 

should  be  as  wide  as  or  wider  than  the  ribs;  hence  it  is  made  21H  in  high  and  16 
in  wide.  This  size  allows,  also,  a  firm  anchorage  for  the  rib-reinforcing.  With 
1%  of  reinforcing  it  requires  four  iH-in  round  rods.  (See  Diagram  C,  Fig.  5.) 
The  first  intermediate  ring  should  be 

65  000 

=  130  sq  m 

500 

in  cross-section,  requiring  a  7-in  width  and  a  18  J^-in  height,  to  resist  the  load,  as  a 
column.  As  the  ring  must  also  act  as  a  beam,  carrying  its  own  weight,  the 
weight  of  half  the  slab,  and  the  live  load  (the  forms  taking  the  place  of  the  live 
load  during  construction),  steel  must  be  added  to  resist  the  bending  moment 

2x85  sin  15°  47'^ 


/130      ^     \    /27r85  sin  15°  47^^       /6710+3  i55\    /^ 


=  3  570  ft-lb  =  42  840  in-lb 

SuflScient  steel,  in  tension  and  compression,  must  be  added  to  keep  the  addi- 
tional stress  in  the  concrete,  due  to  this  moment,  down  to  150  lb  per  sq  in,  since 
500+  150  =  650  lb  per  sq  in  is  the  maximum  allowable  compressive  stress 
in  the  concrete  of  the  beam.     From  Formula  (i)  page  925,  or  Formula  (5)  page 

931. 

42  840 


7X(i7)' 
From  .Formulas  (2),  (3)   and  (4),  (pages  925-6),  when  K  =  21.2  and  St  =  16000 
lb  per  sq  in;  Sc  =  245  lb  per  sq  in,  p  =  0.0014,  and  x  =  0.185.     Since  Sc  must 


1230  Domical  and  Vaulted  Structures  Chap.  31 

not  exceed  150  lb  per  sq  in,  it  is  necessary  to  add  comfression-steel  to  resist  a 
stress  of 


/24S_2S^\  ^7)(q  J85  X  17)  =  I  040 


lb 


The  allowable  stress  in  the  compression-steel  (page  1228),  less  the  stress  already 
allowed  for  the  concrete  which  lA  replaced  by  the  steel,  if  placed  i  H  in  from 
the  outside,  is 

(— ^^ — I  ( (0.185  X  17)  — 1.5)  (15- i)  =  4  770  lb  per  sq  in 
\0.185  X  17/   \  / 

The  amount  of  compression-steel  is,  therefore, 

I  040 

=  0.22  sq  in,  cross-section 

4770 

The  tensile-steel  necessary  is 

0.0014  X  7  X  17  =  0.16  sq  in 

but  because  of  the  negative  moment  at  the  ribs,  the  same  cross-sectional  area  is 
used  as  for  compression,  that  is,  0.22  sq  in,  furnished  by  two  3^-in  round  rods. 
The  unit-shear  is 


/130  \   /27r85  sin  15°  47'\        /6710+3  i55\ 


18.6  lb  per  sq  in 
7  X  17  X  I  I ^^1  X  2 


No  stirrups  are  necessary  to  resist  shear,  but  stirrups  made  from  K-in  round 
rods  should  be  spaced  about  18  in  on  centers,  to  tie  the  panel-slabs  securely  to 
the  ring. 

The  second  intermediate  ring,  if  made  the  same  size  as  the  first,  will  have 
a  stress  of 

53900 


7X.8H    '4i61bpersqin 


The  moment  will  be 


/130  \   (2lr85  sin  27°  31^  ,     /n  375  + 5  335\   /^TrSs  sin  27°  31^ 

\i44  ^  '^7   \  20  /         \  2  /   \  20  / 

12 

=  10  300  ft-lb  =123  600  in-lb 

From  Formulas  (i),  u),  (3), and  (4),  (pages  925-6),  A'  =  6i.2,5f  =  455  lb  per  sq  in, 
p  =  0.0043,  and  X  =  0.3.  Since  Sc  cannot  exceed  650—  416  =  234  lb  per  sq  in, 
the  compression-steel  must  resist 


(^'^-^')(r)(o.3Xi7)^-^3  930 


lb 


The  section-area  of  the  compression -steel  is,  therefore, 
3930 


=  0.62  sq  in 


furnished  by  two  %-in  round  rods  at  top  and  bottom.    The  unit  shear  is 


Vaults 


1231 


/130      ^     \   /27r85  sin27°3iY       /ii375+5  335\ 


7  X17  X 


(-t) 


=  46.9  in  per  sq  in 


X  2 


It  is  therefore  necessary  to  resist  46.9  —  40  =  6.9  lb  per  sq  in  of  shear,  with 
STIRRUPS,  that  is,  with  two  ^-in  round-rod  stirrups,  spaced  12  in  apart  at  the 
ends,  and  the  others  18  in  apart  through  the  remaining  distances. 

The  THIRD  INTERMEDIATE  RING  is  7  by  1 83^  in  in  section,  with  two  J4-m 
round  rods  at  top  and  bottom,  and  with  two  3/^-in  round-rod  stirrups,  spaced 
9  in  apart  at  the  ends,  two  more,  spaced  12  in,  and  the  rest  spaced  18  in. 

The  MOMENT  due  to  the  eccentricity  of  the  column-like  thrust,  that  is, 
the  longitudinal  horizontal  compressive  stress,  in  the  rings  is  resisted  by  the  slabs. 
A  more  exact  analysis  may  be  made  by  considering  only  the  normal  components 
OF  THE  LOADS  on  the  rings  in  determining  these  moments. 

The  FOOTING-RING  must  have  enough  tensile-steel  to  resist  the  outward  push 


or  THRUST  of  the  ribs,  that  is 


238000 


=  14.9  sq  in  of  steel  cross- section.    In 


16  000 

addition  to  this,  if  the  ring  acts  as  a  beam,  there  must  be  sufficient  steel  to  resist 
the  moment  due  to  the  combined  weights  of  the  dome  and  the  ring  itself. 

The  PANEL-SLABS  being  domical  and  above  the  critical  angle,  are  in  com- 
pression, and  should  be  designed  as  illustrated  in  the  discussion  of  Smooth- 
Shell  Domes. 

2.     Vaults  * 

Classification.  Vaults  may  be  conveniently  considered  under  the  following 
divisions:  (i)  Barrel  vaults,  (2)  Groined  vaults,  and  (3)  Ribbed  vaults  (Masonry, 
Tile,  or  Framed). 

General  Considerations.  A  knowledge  of  the  elastic  theory  of  arches 
and  the  stability  of  buttresses  is  necessary  in  a  rigid  investigation  of  vaults,  since 
their  design  involves  the  application  of  the  principles  of  that  theory.  (See,  also, 
Chapters  VII  and  VIII.)  In  any  vault,  lines  of  action  of  the  stresses  or  thrusts 
must  pass  through  the  material  between  certain  limiting  lines;  otherwise  the 
vault  may  fail.  These  thrusts  are  brought  to  the  grade-line,  or  to  foundations, 
by  walls,  often  buttressed  in  the  case  of  barrel  vaults,  and  by  piers  and  but- 
tresses in  the  case  of  groined  and  ribbed  vaults.  By  building  vaults  of  light 
materials,  such  as  hollow  bricks  or  hollow  tiles,  the  magnitude  of  the  thrusts  are 
decreased,  and  lighter  walls,  piers,  or  buttresses  can  be  used. 


(a)  «-)  <*> 

Fig.  1.   Three  Methods  of  Building  Barrel  Vaults 

Barrel  Vaults.     Fig.  1,  (a),  (b),  and  (c),  illustrates  three  methods  of  building 
barrel  vaults.    In  {c)  the  longitudinal  ribs  are  merely  for  appearance,  as 

•    •  A  full  treatment  of  this  subject  may  be  found  in  the  Handbuch  der  Architektur, 
.and  Breyman's  Baukonstructious  Lehre. 


1232 


Domical  and  Vaulted  Structures 


Chap.  31 


(a) 

Fig.  2, 


(c)      (d)  (6) 

Methods  of  Joining  Barrel  Vaults  to  Walls 


they  do  not  strengthen  the  vault.    The  diagrams  (a)  and  (b),  Fig.  2,  illustrate  two 
methods  of  disengaging  the  masonry  of  barrel  .vaults  from  the  walls.     Diagram 

(6)  is  the  better  method, 
and  improves  the  appear- 
ance of  the  vault  on  the 
inside.  Diagrams  (c)  and 
(d)  illustrate  the  use  of 
stone  skewbacks  for  seg- 
mental vaults. 

Strength  of  Barrel 
Vau'ts.  Barrel  vaults  may 
be  considered  as  a  series 
OF  ARCHES  set  next  to  each 
other;  and  hence  if  a  sec- 
tion one  unit  long  is  found 
safe  when  investigated  as 
an  arch,  the  vault  itself  is 
considered  safe.  By  build- 
ing the  wall  and  the  vault 
together    as   a   unit,  to  a 

point  on  the  arc  6o°  from  the  vertical  or  crown,  that  is,  to  a  point  on  the  in- 

trados  one  third  of  the  distance  from  the  horizontal  spring-hne,  the  actual  span 

is  materially  decreased.    With  the  spring-line  at  6o°,  the  line  of  thrust  in  an 

unloaded    arch   or    barrel 

vault  of  an  equal  thickness 

throughout,    will     remain 

within  a  strip  whose  radial 

thickness  or  width  is  about 

one    forty-second    of    the 

radius.      If    the    line   of 

thrust  is  to  remain  within 

the  middle    third    of  the 

arch-ring  or   vault-ring,   / 

should    be    (f/42)  X  3  = 

r/14.     If  it  is  to  remain 

within    the    middle    half, 

/  should  be   (r/42)  X  2  = 

f/21.      In    the    following 

example,     the     theory  of 

the  middle  half  will  be  fol- 
lowed, in  which  /  =  r/2i. 

If   it  were  assumed   that 

/  =  r/14,  the  line  of  thrust 

being     kept    within     the 

middle  third,  the  span  of 

the  vault  In   the  example 

would  have  to  be  changed 

from  21  to  14  ft. 

If  built,  then,  as  described  (Fig.  3),  the  minimum  thickness  of  the  unloaded 

vault-shell  is  about  one  twenty-first  of  the  vault-radius,  that  is, 

t=r/2i 

The  VE-RTICAL  COMPONENT  Pv  of  the  thrust  P  is  equal  to  the  weight  of  half  the 

free  vault,  that  is,  of  the  section  A  BCD.   It  can  be  shown  that  the  horizontal 


Ftg.  3.    Analysis  of  Barrel  Vault 


Vaults 


1233 


COMPONENT  Ph  of  the  thrust  is  0.79  of  the  vertical  component,  and  that  the 
thrust  is  not  at  right-angles  with  the  spring-line  AB;   that  is, 

P/i=o.79^ 
Example.     It  is  required  to  construct  a  barrel  vault  over  a  corridor  21  ft 
wide.     The  vault-radius  is  loVz  ft,  and  the  minimum  thickness  of  the  shell  is 
10.5/2 1  =  0.5  f t  =  6  in.     If  built  of  brick  it  is  cheaper  to  build  a  ribbed  vault,  as  . 
the  unit-dimensions  of  bricks  are  approximately  4  in,  8  in,  12  in,  etc.     Referring 
to  Fig.  4,  it  is  found  that  a  4-in  vault  with  ribs  4  by  8  in  every  3  ft  3  in,  is  equiva- 


10                                                                    jr 

it                               \ 

% 

--    -    -            \    -         -                 -                 -    --- 

\ 

Q                                                                "                                                                    S 

8                                 __                          _            _                   A                          _            _                   __      ___ 

^                                                            ^ 

OJ                                                                                                                                   S 

ta               :     --                                     :                         ---  -- 

c                            \                                                                                    ^ 

St                          r                      ^                      _             - 

4  ^              ~K                   --   \--         -          -^^ |J 

2           i         "      .                 ?K'^ 

0            ^          -    ^                ""^iM   -   ------ 

,S                                                       J^WfArP                                       5                                                                            ^    ' 

0                                          \.  \Mh\  '                              ^                                    *     '              \ 

^ijh  \                                   \// M  ^  "                                       k. 

^-^                         Xsiti^                      -      -I         -      - 

\                                         J^^.-                               -             s^         _         - 

5                               ^^"                                       ^^ 

Q                                                                              -S                                                                   ^V.              _                                                                   -^S 

2-     it             \                ^v                   -  \ 

^^                  s                     \ 

s                    :^  ^s.                          \ 

s                  _      ^v  _               _     _  5i 

Ny, 

4                    6                    8                   10                  12                   14 
Equivalent  Thickness  in  Inches 

Fig.  4.    Barrel  Vaults,  Ribbed  and  Non-ribbed.     Equivalent  Thicknesses 

lent  to  a  6-in  vault,  and  hence  would  be  used.    The   brick   masonry  weighs 
125  lb  per  cu  ft. 
The  VERTICAL  COMPONENT  Po  of  the  thrust  is 

I4/12X3MX  i/37rXio.5X  125] -f  [4/12  X  8/12  X  i/37r(io.5  +  0-33)  X  125I 

=  5  595  lb  per  lin  ft 

The  HORIZONTAL  COMPONENT  Ph  of  the  thrust  is  0.79  X  5  595  =  4  420  lb  per  lin  ft. 
The  supporting  wall  must  be  thick  enough,  buttressed  enough,  or  loaded  suf- 
ficiently from  above,  to  take  care  of  this  horizontal  component  of  the  thrust. 
Fig.  5  is  a  graphical  analysis  of  the  stresses  in  this  vault.  It  will  be  noticed 
in  Fig.  5  that  the  line  of  pressure  remains  in  the  middle  half  of  the  vault- thick- 
ness.    Scheffler,  after  numerous  tests  of  vaults,  stated  *  that  if  one  fourth  the 

*  Theorie  der  Gewolbe. 


1234 


Domical  and  Vaulted  Structures 


Chap.  31 


vault-thickness  is  deducted  at  the  extrados,  and  one  fourth  at  the  intrados,  and 
that  if  the  line  of  pressure  found  according  to  the  elastic  theory  of  arches  is 


Fig.  5.     Graphical  Determination  of  Stresses  in  a  Barrel  Vault 

confined  to  the  remaining  portion,  that  is,  the  middle  half,  then  the  vault  may 
be  considered  safe.     Fig.  6  shows  the  resistance-line  passing  slightly  outside  the 


Fig.  6.     Line  of  Pressure  through  Vault-thickness 

middle  third.*  It  illustrates  tho  hss  conservative  theory  that  the  resistance- 
Hne  might  in  some  cases  pass  near  the  outside  of  the  middle  half.  The  arch  or 
vault  in  Diagram  (6)  of  Fig.  (3  would  have  a  greater  tendency  to  fail  according 
to  the  middle-third  theory,  because  the  line  of  pressure  or  resist ance-Une 
passes  outside  of  the  middle  third.  Diagram  (a)  of  Fig.  6  shows  the  same  arch 
or  vault  with  the  shell  cut  so  that  the  line  of  pressure  passes  down  the  exact  center 
of  the  uncut  portion.     This  results  in  a  sort  of  theoretical  or  ideal  arch-form. 

*  See  foot-note  relating  to  Concrete  Ribbetl  Domes,  page  1225. 


Vaults 


1235 


Of  course  the  thickness  of  part  c  must  be  sufficient  to  develop  a  safe  compres- 
sive resistance  in  the  material,  and  it  is  advisable  to  add  sufficient  steel  to  take 
care  of  any  tension  in  the  parts  farthest  from  the  resistance-line.  Vaulted  con- 
struction is  often  relatively  protected  and  free  from  the  live  loads  and  moving 
loads  to  which  arches  are  generally  subjected;  and  for  such  construction 
Scheffler's  conclusions  are  considered  valid. 

Groined  Vaults.    A   groined  vault  is  formed  by  the  intersection  of  two 
BARREL  VAULTS.     (Scc  (a),  Fig.  7.)     By  using  groined,  vaults  it  is  possible  to 


Perspective,  Showing  Penetrations  and 
Intersections 


Intersecting  Vaults  of  Different 
Widths 


Fig.  7.     Groined  Vault 


bring  the  tops  of  windows  and  doors  above  the  spring-lines  of  the  vaults,  and  to 
concentrate  the  pressures  or  thrusts  on  piers  or  columns. 

Groins.  The  intersections  of  two  vaults,  called  groins,  are  straight  lines  in 
horizontal  projection,  only  when  they  are  of  the  same  curvature  and  height. 
If  the  vaults  are  of  different  widths,  it  is  best  to  make  one  semicircular,  draw 
the  horizontal  projections  of  the  groins  as  straight  Hues,  and  then  determine  the 
contour  of  the  other  vault.  This  is  illustrated  in  Fig.  7  {h).  Vault  A  is  semi- 
circular and  has  a  span  ^.  Vault  B  has  a  span  B.  CC  are  the  groins,  and  D  is 
the  circular  contour  of  the  narrow  vault.  Any  points,  a,  b,  c,  etc.,  are  chosen  at 
random,  and  lines  a-az,  h-hi,  c-oi,  etc.,  and  a-ai,  b-bi,  c-a,  etc.,  drawn  parallel  to 
the  axes  of  the  respective  vaults.  The  line  as-ai  is  laid  off  equal  to  ai-a^;  br-btf 
equal  to  61-&2,  etc.  The  smooth  curve  connecting  ai,  bi,  a,  etc.,  is  the  contour  E 
of  the  vault  B.  In  like  manner  the  contour  F  of  the  groins  is  found  by  similarly 
laying  off  a-,-a^,  b^-b^,  etc.,  equal  to  ai-as,  bx-bi,  etc. 

The  VAULT-SHELLS,  at  the  intersections  or  groins,  should  never  have  what 
might  be  called  miter- joints.  The  vaults  should  be  monohthic  or  there  should 
be  concealed  ribs  to  carry  the  vault-shells  and  transmit  the  thrusts  to  the  piers. 
If  the  intersecting  vaults  are  of  stone,  and  of  the  same  diameter,  the  groins  may 
be  built  as  shown  in  Fig.  8  (a)  for  small  vaults,  or  as  in  Fig.  8  {b)  for  larger 
vaults.  In  Fig.  8  (a)  the  groin-stones  are  L-shaped  and  are  cut  so  as  to  carry 
the  stone  courses  of  one  vault  around  to  the  other  vault.  The  stone  shown  in 
Diagram  {a)  of  Fig.  8  is  shown  in  plan  at  b,  with  two  views  at  c  and  d.  A  better 
method  is  shown  in  Fig.  8  {b).     Here  the  groin-stones  are  cut  so  that  the  joints 


1236 


Domical  and  Vaulted  Structures 


Chap,  31 


are  normal  to  the  groins,  thus  forming  concealed  ribs.  This  bearing-surface 
is  obtained  as  follows.  Point  a,  the  intersection  of  an  extended  vault-joint  and 
the  groin-edge,  is  projected  down  to  a'  and  h\  the  intersections  of  the  projecting 
line  and  the  assumed  side  and  center  hnes  of  the  rib.     Point  b'  is  projected- up  to 


Fig.  8.     Groiri'details  for  Stone  Vaults  of  the  Same  Diameter 


6",  a  point  on  the  center  line  or  edge  of  the  rib.  From  6"  a  horizontal  line  interr 
sects  with  a  Hne  projected  up  from  a'  to  give  c"  a  point  on  the  joint,  which  is 
drawn  normal  to  the  groin.  The  intersection  d''  of  this  joint  with  the  groin- 
e4ge  is  projected  down  to  d'  on  the  center  line  of  the  rib.    By  connecting 


Vaults 


1237 


a'  and  d' ,  and  d'  and  e"  (the  point  opposite  a'  on  the  other  side  of  the  rib)  with 
a  curved  line,  the  lower  edge  of  the  bearing-surface  is  determined. 

Points  d'  and  e'  projected  up  determine  d  and  e,  the  same  points  in  elevation. 


Fig.  9.     Groin-details  for  Stone  Vaults  of  Different  Diameters 


Other  points  on  these  curved  lines  can  be  found  by  choosing  points  between  a 
and  d  and  projecting  them  in  the  same  way  as  in  the  method  used  to  find  the 
projections  of  /.     The  procedure  is  as  follows.     The  point  /  is  projected  down 


1238  Domical  and  Vaulted  Structures  Chap.  31 

to  the  center  line  of  the  rib,  locating  g' .  Then  g'  is  projected  up  to  g" ,  the  inter- 
section with  the  line  representing  the  joining  of  the  upper  surfaces  of  the  vaults. 
A  horizontal  Une  is  projected  over  from  g"  to/",  the  point  of  intersection  with  the 
normal  joint.  The  point  i"  is  projected  down  to/',  on  the  projecting  Une  from/. 
By  connecting/'  and  h'  {h!  is  opposite/'  and  equidistant  from  the  center  Hne  of 
the  rib)  with  a  straight  line,  the  upper  edge  of  the  bearing-surface  is  determined. 
The  point  h  is  found  by  projecting  up  from  h' .  By  connecting  a!  and  /',  and  e' 
and  h'\  also  a  and  /,  and  e  and  h,  the  side  edges  of  the  bearing-joint  are  located. 
The  lower  bearing- surface  of  a  stone,  or  the  upper  bearing-surface  of  the  next 
lower  stone,  is  found  in  a  similar  manner. 

If  the  vaults  are  not  of  the  same  diameter,  either  of  two  methods  may  be  used. 
The  number  of  stone  courses  in  both  vaults  may  be  made  the  same,  thus  making 
the  courses  in  the  wide  vault  wider  than  those  in  the  narrow  vault,  and  the 
method  of  finding  the  shape  of  the  groin-stones  is  similar  to  that  shown  in  Fig.  8(6) ; 
or  the  stones  may  be  the  same  width,  thus  making  a  greater  number  of  courses  in 
the  wide  vault  than  in  the  narrow  vault.  In  the  latter  case  the  groin-stones  are  de- 
termined as  in  Fig.  9.  To  take  care' of  the  different  number  of  courses  in  the  two 
vaults,  one  course  in  the  narro^y  vault  is  sometimes  made  to  receive  two  courses 
in  the  wide  vault,  as  shown  by  stone  A  in  Fig.  9.  Because  the  joint  a  is  higher 
than  the  joint  h,  there  results  a  peak  toward  the  side  of  the  groin-Hne.  This  is 
cut  ofif  at  right-angles  to  the  groin,  thus  making  the  bearing-surface  c.  This 
surface  is  determined  as  follows.  The  intersection  of  the  joint-planes  d  and  e 
is  at/.  The  vertical  projection /i,  of/,  is  drawn  through  h\,  found  by  projecting 
up  h  and  g,  and  a  horizontal  line  from  g\.  The  intersection  of  /i  and  a  line 
through  gi,  normal  to  the  groin-curve  gives  ii,  which,  projected  to  i,  gives  the 
intersection  of  the  sides  of  the  bearing-surface  c. 
The  point  /  is  found  .  by  projecting  up  k,  the 
intersection  of  a  and  the  diagonal,  to  ^1;  then 
projecting  k\  to  j\,  the  intersection  with  the 
normal  Hne;  and  then  projecting  j\  to  /.  By 
connecting  g  and  /  with  a  curved  line  (other 
points  of  which  are  determined  by  drawing 
lines  parallel  to  a  and  proceeding  by  the  method 
used  in  finding/);  and  g  and  i,  and/  and  /,  with 
straight  lines;  the  sides  of  c  are  determined. 

If  the  vaults  are  built  of  brick,  it  is  better  to 
run  the  courses  at  right-angles  to  the  groins, 
thus  giving  a  chance  for  the  bricks  to  overlap, 
as  shown  in  Fig.  10.  If  the  brick  courses  are 
to  run  parallel  to  the  center  line  of  the  vaults,  it 
is  necessary  to  use  stone  ribs  to  carry  the  shell. 

Determination  of  the  Stresses  in  Groined 
Vaults.    The  problem  of  a  groined  vault  span- 
,  (ci)  ning  a  rectangular  area  which  is  not  square, 

Fig.  10.  Groins  of  Brick  Vaults  ^^  ^^^^  considered,  as  a  vault  spanning  a 
SQUARE  AREA  ofTcrs  fewer  difficulties  and  can  be 
worked  out  on  the  same  principles.  The  problem  is  to  span  an  area,  whose 
half-length  of  the  short  diameter  is  a,  and  whose  half-length  of  the  long  diameter 
is  h.  Fig.  11  (a).  In  order  to  obtain  a  more  stable  construction,  the  point  of  inter- 
section of  the  crowns  of  the  vault  is  raised  a  distance  cd  =  c'd,  thus  giving  the 
crown  of  the  long-span  vault  a  slope  cc  and  the  crown  of  the  short-span  vault 
a  slope  c'J.  The  vault  is  divided  into  strips  ^,  B,  C,  etc.,  and  A',  B' ,  C,  etc., 
from  the  rib  R,  as  shown  in  the  projected  area  in  Fig.  11  {a).     The  rib  R  is 


Vaults 


1239 


Fig.  11.     Determination  of  Stresses  in  Groined  Vaults 


1240  Domical  and  Vaulted  Structures  Chap.  31 

given  a  width  equal  to  the  assumed  width  of  the  supporting  diagonal  concealed 
arch,  and  the  widths  A,  B,  C,  etc.,  and  A',  B',  C,  etc.,  are  obtained  by  dividing 
the  two  vaults  into  the  same  number  of  equal  parts.  These  strips  are  considered 
as  adjacent  arches  resting  on  the  rib  R.  For  simphfication  the  hne  of  pressure 
or  resistance-line  of  each  strip  is  placed  in  the  center  of  that  strip  as  gk  in  A 
and  g'k'  in  A'.     The  error  in  this  is  on  the  side  of  safety. 

Even  though  the  projected  areas  of  the  two  intersecting  vaults  are  the  same, 
the  actual  surface-area  of  the  smaller-span  vault  is  slightly  larger  than  that  of 
the  longer-span  vault.  Therefore,  if  the  vaults  are  of  the  same  thickness,  the 
shorter-span  vault  is  slightly  heavier  than  the  larger- span  vault.  In  order  to 
have  the  resultants  of  the  horizontal  components  of  the  thrusts  from  strip  A 
and  strip  A\  strip  B  and  strip  B\  etc.,  parallel  to  the  direction  of  the  rib  R, 
the  procedure  is  as  follows. 

The  thrusts  of  the  strips  on  the  heavier  side,  that  is  of  strips  A,  B,  C,  D,  E, 
and  F,  are  determined  as.  shown  in  Fig.  1 1  (6)  and  (c) .  The  curvature  of  the 
strips  being  the  same,  the  work  can  be  considerably  lessened  by  dividing  the 
arch  into  sections  of  unequal  lengths  for  weight-determinations.  The  dividing 
line  for  the  sections  is  found,  by  projecting  up  the  point  of  intersection  of  the  line 
of  pressure  of  each  strip  and  the  side  of  the  rib  R,  as  g  to  g',  h  to  h\  etc.  The 
weights  w\,  W2,  wz,  etc.,  of  each  section  are  then  determined  and  the  composite 
load-Une  drawn  as  in  Fig.  11  (c).  The  positions  of  W a,  Wb,  Wc,  etc.,  in 
Diagram  (b)  are  determined  by  the  usual  stress-polygon.  H  is  then  drawn  so 
as  to  be  at  the  upper  limit,  and  the  dififerent  thrusts  so  as  to  act  near  the  lower 
limit  of  the  middle  half  of  the  vault-thickness.  *  Lines  drawn  in  Fig.  1 1  (c) 
parallel  to  these  thrusts,  determine  their  values,  and  the  values  of  the  hori- 
zontal components  Ha,  Hb,  He,  etc.  The  weights  w'l,  w'i,  w'z,  etc.,  in  Diagram 
{d),  are  found  in  the  same  way,  the  load-line  in  Diagram  (/)  drawn,  and  the 
positions  of  W  \',  Wb',  Wc\  etc.,  found  as  before.  H'  in  Fig.  11  {d)  is  drawn, 
at  the  upper  limit  of  the  middle  half  in  this  demonstration.*  Ha\  Hb\  He', 
etc.,  however,  must  have  such  values  that  the  resultants  of  Ha,  and  Ha',  Hb 
and  Hb',  etc.,  are  parallel  to  R.  The  required  values  of  Ha',  Hb',  He',  etc., 
are  found  as  in  Fig.  11  (e),  by  laying  off  Ha,  Hb,  He,  etc.,  and  drawing 
Ti,  Ti,  Ts,  etc.,  parallel  to  R.  The  resulting  values  of  Ha',  Hb',  He',  etc., 
are  then  laid  ofif  in  Fig.  1 1  (/)  and  the  thrusts  drawn.  When  drawing  the 
thrusts  in  Fig.  11  (d)  through  the  intersection,  of  H'.  and  Wa',  H'  and  Wb', 
etc.,  parallel  to  their  directions  in  Fig.  11  CO,  it  is  found  that  they  act  very 
slightly  above  the  lower  edge  of  the  middle  half. 

The  rib  R  is  then  drawn  as  in  Fig.  1 1  [h)  and  the  points  of  application  of  the 
loads  located.  The  load-polygon  is  drawn  as  in  Fig.  11  {g).  The  resultants 
R\,  R-i,  etc.,  are  drawn  in  both  Diagrams  {h)  and  {g)  of  Fig.ll,  the  position  of  X 
in  Diagram  {h)  found  by  the  usual  stress-polygon,  and  the  thrusts  Z  and  Y 
determined.  The  point  through  which  Z,  Diagram  (A),  passes  at  the  spring  of 
the  rib,  should  be  so  chosen  that  the  line  of  pressure  remains  at  least  within 
the  middle  half  of  the  rib;  or  the  more  usual  and  conservative  limits  of  the 
middle  third  may  be  used.  In  the  case  of  brick  vaults  the  strips  A,  B,  C, 
etc.,  are  taken  at  right-angles  to  the  groin,  resulting  in  vertical  loads,  only,  on 
the  assumed  rib. 

Ribbed  Vaults.  In  ribbed  vaults  the  ribs  are  designed  to  be  built  first, 
to  be  free-standing,  and  of  sufficient  strength  to  support  the  shell  when  it  is 
placed  over  them.  To  simplify  the  construction,  all  the  rib-arcs  are  ordinarily 
•  made  with  the  same  radius,  thus  making  all  the  ribs  disengage  each  other  at  the 

*  The  theory  of  the  middle  third  is  the  one  usually  followed,  as  it  is  the  most  conserva- 
tive and  results  in  a  larger  factor  of  safety.     See,  also,  foot-note  on  page  1225. 


Vaults 


1241 


same  height.  This  makes  the  narrower  rib-arches  pointed,  and  the  diagonal 
rib-arches  semicircular,  but  they  are  all  constructed  of  similar  stones  with  cross- 
sections  of  the  same  shape.  To  determine  the  points  A  and  B  (Fig.  12),  at  which 
the  ribs  become  independent  of  each  other  and  of  the  wall,  the  proceeding  is  as 
follows.  In  plan  the  clustered  ribs  are  shown  just  above  the  column- capitals, 
with  the  diagonal  ribs  extending  into  the  wall  a  distance  ab.  To  find  the  height 
at  A ,  draw  an  arc  through  a  with  the  same  curvature  as  that  of  the  diagonal  rib, 
and  draw  at  right-angles  to  the  ribs,  in  plan,  a  line  from  h,  until  it  cuts  this  arc  at 
c.  The  height  ch  is  the  height  at  A .  The  height  at  B,  equal  tofe,  is  found  in  the 
same  way.    The  webs,  or  parts  of  the  vault-shell  supported  by  t'le  ribs,  are 


Fig.  12.     Vault-rib  Construction 


usually  shallow  arches  in  cross-section,  and  are  spherical  triangles,  that  is, 
they  are  domical. 

In  order  to  use  to  the  fullest  advantage  the  finished  lower  portions  of  the  vault 
as  supports  for  the  upper  courses  as  laid,  the  courses  of  the  vault-shell,  or  web 
are  laid  in  planes  normal  to  the  wall  and  the  transverse  ribs.  This  is  shown  in 
horizontal  projection  in  Fig.  13  I.  The  web  being  arched  in  both  directions,  the 
thrusts  act  in  two  directions,  as  in  domes.  From  the  study  of  the  theory  of 
domes  it  is  found  that  the  thickness  of  the  shell  in  a  dome  has  no  effect  on 
ITS  stability.  The  web  in  ribbed  vaults  being  domical,  can  be  made  relatively 
thin,  but  for  stone  or  brick  vaults  it  should  not  be  less  than  about  4  in  thick 
for  spans  up  to  35  ft. 

■  The  ribs  are  designed  as  arches,  loaded  with  the  thrusts  of  the  web  supported. 
These  thrusts  are  determined  as  illustrated  in  Fig.  13  II.  The  vaulting 
resting  on  the  half -wall,  or  transverse  rib  A,  and  the  half-diagonal  rib  B,  is 
divided  into  any  number  of  equal  lunes,  or  figures  bounded  by  the  two  inter- 
secting arcs,  and  radiating  from  the  axis  of  the  dome  of  which  that  part  of  the 
vaulting  is  a  spherical  triangle.  This  axis  is  found  by  projecting,  at  right- 
angles  from  the  rib§  A  and  B,  lines  starting  at  the  center  of  curvature  of  the  ril?§ 


tm 


Domical  and  Vaulted  Structures 


Chap.  31 


and  intersecting  at  the  point  e,  which  is  the  projection  of  the  axis  of  the  dome. 
The  RADIUS  OF  THE  DOME  is  then  Ri  in  Fig.  13 II,  equal  to  the  distance  from  e  to 


Fig.  13.     Determination  of  Stresses  in  Vault-ribs 

the  spring  of  the  diagonal  rib  B.  The  thrust  of  each  lune  on  the  ribs  is  then 
found  as  shown  for  lune  L. 

Example.  Let  the  radius  -Ri,  Fig.  13  II,  be  25  fee:,  and  let  the  shell  be  4  in 
ihick,  constructed  of  stone,  and  weighing  125  lb  per  cu  ft.  The  angle  0  (by  meas- 
urement) is  54°  30',  and  the  angle  a  is  18°  30'.  These  are  found  by  projecting 
up  from  the  point  of  intersection  /  of  the  center  line  of  the  lune  L  and  the  center 
of  the  rib  B,  and  the  intersection  g  of  the  center  line  of  the  lune  L  and  the  crown- 
line  of  the  vault,  to /x  and  gi,  respectively,  on  the  vertical  projection  £1  of  the 
lune  L. 

Using  the  same  notation,  equations,  and  curves  as  were  derived  for  smooth- 
shell  domes  (page  1214),  it  is  found  from  Plate  II,  with  -  =  o  and  a  =  18°  30', 

a 

that 

Wi-o=  -125(4/12)  (25)2(0.33)=  -85941b 
and  that 


-8594 


27r(i25)(4/i2)(25)' 


=  —0.0525 


From  Plate  I  it  is  found  that  the  critical  angle,  for  values  of  —  =  o    and 

a 


Vaults  1243 

n  =  —0.0525,  is  55°  30',  and  the  vaulting  should  be  back-filled  as  high  as  this, 
as  shown. 

From  Plate  III,  with  —  =  o.  and  w  =  —  0.0525,  it  is  found  that  at  0  =  54°  30' 

U  =  (125  X  4/12  X  25)(-^.o79  +  0.63)  =  573  lb 

By  measurement,  the  width  of  lune  L  at  /  is  2  ft;  hence  the  total  tangential 
PRESSURE  C  (Fig.  13),  is  2  X  573  =  i  146  lb.  The  horizontal  component  D 
of  this  is  6  655  lb,  and  the  component  F  (along  the  rib  B)  of  Z)  is  5  750  lb.  The 
vertical  component  E  of  C  is  9  339  lb. 

The  value  of  T  is  found  from  Plate  IV  to  be  125  X 4/1 2  X  (25) ^  x  (—0.004 
+  0.295)  =  7  570  lb,  and  the  component  //  (along  the  rib  B)  of  T  is  3  630  lb. 

The  THRUSTS  acting  on  the  rib  B  of  the  other  lunes  above  L  are  found  in  the 
same  way,  and  the  portion  of  rib  above  the  back  fill  investigated  as  an  arch. 
In  Fig.  13  that  portion  of  the  rib  below  the  web  is  not  indicated. 

For  vaults  with  semicircular  diagonals  of  about  33-ft  span,  the  ribs  should  be 
from  7  to  10  in  wide  and  from  "ro  to  14  in  in  total  height,  and  the  minimum 
dimensions  of  the  projecting  portions  of  the  ribs  below  the  webs,  for  smaller 
vaults,  should  be  3  3^  in  width  and  6  in  in  height.* 

Tile  Vaults.  Tile  vaults,  as  built  by  the  R.  Guastavino  Company,  are 
constructed  of  tiles,  from  6  by  12  to  24  in  in  plan,  and  i  in  in  thickness,  and 
laid  in  several  layers  so  as  to  make  a  solid,  thin  shell  that  is  both  light  and 
strong.  Because  of  the  overlapping  of  the  tiles,  the  shell  has  considerable 
tensile  resistance,  and  the  vaults  are  practically  monolithic.  It  is  due  to 
this  and  to  the  lightness  of  the  construction  that  the  thrusts  and  the  weight  of 
the  entire  structure  are  materially  reduced.  Ordinarily  a  finished  acoustic  tile, 
backed  by  rough  constructional  tile,  is  used  for  the  exposed  surfaces. 

Framed  Vaults.  Vaulting  in  buildings  of  moderate  cost  is  frequently 
constructed  by  suspending  from  the  roof-trusses  steel  or  wooden  frames 
carrying  lath  and  plaster.  The  roof-trusses  must  in  this  case  be  designed  to 
carry  the  direct  loads  of  the  framed  vaulting,  which  must  be  of  the  required 
strength  and  shape  to  carry  and  fit  the  plastered  surfaces. 

*  Handbuch  der  Architektur. 


PART  III 


USEFUL  INFORMATION 


ARCHITECTS,    DRAUGHTSMEN,   BUILDERS,   AND 
SUPERINTENDENTS 

AND   ALL   WHO  HAVE   TO   DO   WITH    THE    BUILDING   TRADES 

Note.  The  editor  has  arranged  the  information  in  Part  III  in  the  following 
order : 

Heating  and  Ventilation. 

Chimneys. 

Hydraulics,  Plumbing  and  Drainage,  Gas  and  Gas-Piping. 

Lighting  and  Illumination  of  Buildings. 

Electric  Work  for  Buildings. 

Architectural  Acoustics. 

Weights,  Quantities,  and  Miscellaneous  Data  on  Building  Materials. 

Dimensions  and  Data  Useful  in  the  Preparation  of  Drawings  and  Specifica- 
tions. 

Miscellaneous  Information  for  Architects  and  Builders, 

Glossary  of  Architectural  and  Technical  Terms. 

Legal  Definitions  of  Architectural  Terms. 


Ill   THA4 


Heating  and  Ventilation  of  Buildings  1247 

HEATING  AND  VENTILATTON  OF  BUILDINGS* 

By 
LOUIS  A.  HARDING 

©'FORMERLY  PROFESSOR   OF  MECHANICAL  ENGINEERING,   PENNSYLVANIA  STATE 

COLLEGE 

Physical  Units  and  the  Measurement  of  Heat 

System  of  Units.  In  this  country  the  system  of  units  in  general  use  by 
engineers  is  known  as  the  foot-pound-second  system,  and  the  following  defini- 
tions and  examples  will  show  the  significance  of  each. 

Defiinition  of  Units  Employed.    The  unit  of  time  is  the  second,  which  is 

equal  to  — part  of  the  mean  solar  day.   /  =  time.    Time  is  also  expressed  in 

86  400 

minutes  and  hours. 

L  =  length.    The  unit  of  length  is  the  foot  =  0.3048  meter. 

W  =  weight.    The  unit  of  weight  is  the  pound  =  0.4532  kilogram. 

A  =  area.     The  unit  of  area  is  the  square  foot.    The  unit  often  used  is  the 

square  inch. 
V  =  volume.     The  unit  of  volume  is  the  cubic  foot.     Volume  =  area  X 
length  =  A  XL. 
In  calculations  involving  the  quantity  of  air  required  Q  is  often  used  for  cubic 
foot. 

Example.  The  volume  displaced  per  stroke  by  the  plunger  of  a  pump,  if  the 
diameter  is  6  in  and  the  stroke  is  12  in,  is  J^i  X  6^  X  12  =  339.29  cu  in,  or  0.196 
cu  ft. 

If  the  plunger  makes  30  working  strokes  (not  revolutions)  per  minute,  then 
the  plunger-DisPLACEMENT  per  minute  is  0.196  X  30  -  5.88  cu  ft.  One  United 
States  gallon  =231  cu  in  =  0.1336  cu  ft.  This  pump  will  therefore  theoret- 
ically dehver  5.88/0.1336,  or  44  gal  per  minute.  The  actual  delivery  of  the 
pump  will  be  10  to  15%  less,  owing  to  the  slip,  which  is  the  leakajge  back  through 
the  pump-valves,  around  the  plunger,  and  that  due  to  imperfect  fiUing  of  the 
pump-cylinder  on  the  suction-stroke. 

Density.  D  =  density.  The  weight  of  a  unit  volume  (i  cu  ft)  of  a  sub- 
stance is  called  its  density.  The  density  of  water  at  70°  F.  is  62.3  lb  per  cubic 
foot.  The  density  of  air  at  70°  is  .075  lb  per  cubic  foot.  The  pump  in  the  pre- 
ceding example  would,  therefore,  handle  5.88  X  62.3  or  366  lb  of  water  per 
minute. 

If  the  water-end  of  the  pump  is  operated  by  a  steam-cylinder-  having  a  dis- 
placement of  0.349  cu  ft  per  stroke,  and  takes  steam  at  the  same  pressure  for 
the  full  stroke  as  in  the  direct-acting  type  and  if  we  assume  that  the  steam- 
pressure  is  loo-lb  gauge,  we  find  from  the  steam-table  (Table  I),  that  the 
density  of  steam  at  this  pressure  is  0.2565  lb.  The  steam-consumptjon  of  the 
pump,  therefore,  would  be  0.2565  X  0.349  X  30  X  60  =  161. 6  lb  per  hour, 
theoretically.  A  fan  handling  10  000  cu  ft  per  minute  of  air  at  70°  F,  delivers 
10  000  X  .075  =  100  lb  per  minute. 

Velocity,  v  =  velocity.  The  rate  of  motion  of  a  body  is  measured  by  the 
distance  passed  over  in  a  unit  time.     Velocity  is  expressed  in  feet  per  second. 

*  Much  of  the  data  of  this  section  has  been  condensed    from  Vol.  I  of  Mechanical 

Eailinmenf  of  Til1llfHnP'<i    hv  HnrHmcr  nnrl  WJllnrrl     nnhlJcViPrl  »w   Tnlin  Wi'Ipv  Rj  «;r,n<:     Tnr 


1248 


Heating  and  Ventilation  of  Buildings 


Part  3 


Energy  or  Work.  U  =  energy  or  work.  The  unit  of  work  is  the  foot- 
pound, and  is  the  quantity  of  energy  expended  or  the  work  performed  by  a  force 
of  I  lb  moving  through  a  distance  of  i  ft  in  the  line  of  action  of  the  force. 

Power  is  the  rate  of  doing  work.  Note  that  power  involves  the  factor 
TIME  and  is  equal  to  the  amount  of  work  done  divided  by  the  time  required  to 
do  this  work. 

Horse-Power,  h.p.  =  horse-power.  The  unit  of  power  is  the  horse- 
power and  is  the  performance  of  work  at  the  rate  of  550  ft-lb  per  second,  or 
S3  000  ft-Ib  per  minute. 

Example.  Required  the  theoretical  work  and  horse-power  developed  by  the 
water-end  of  the  pump  in  the  preceding  example,  assuming  that  the  head  or  the 
height  pumped  against  is  200  ft,  and  that  no  frictional  resistance  is  to  be  over- 
come. 

The  work  Um  performed  per  minute  is  the  lifting  of  the  weight  of  water,  W, 
366  lb  per  min,  through  a  height  of  200  ft  and  is  Um  =  366  X  200  =  73  200  ft-lb 
per  min.     The  h.p.  =  Um/ss  000  =  73  200/33  000  =  2.22. 

The  actual  power  required  will  be  somewhat  greater,  as  the  force  required 
to  overcome  frictional  resistance,  etc.,  has  been  neglected. 

Equivalent  Values  of  Electrical  and  Mechanical  Units 


I  horse-power . . 

f  746  watts 

0.746  kilowatt 
1  33  000  ft-lb  per  min 

550  ft-lb  per  sec 
i  2  546  Btu  per  hr 

I   kilowatt 

1  000  watts 
1.34  h.p. 

2  654  200  ft-lb  per  hr 
44  240  ft-lb  per  min 
737-6  ft-lb  per  sec 

3  414-5  Btu  per  hr 

Measurement  of  Pressure.  It  is  customary  to  measure  pressure  by  means 
of  GAUGES  which,  in  reahty,  only  indicate  the  difference  between  the  pressure 
being  measured  and  the  pressure  of  the  atmosphere,  barometric  pressure, 
at  the  same  time  and  place.  These  gauges  may  indicate  either  a  higher  or  lower 
pressure  than  that  of  the  atmosphere;  in  the  former  case  they  are  known  as 
pressure-gauges  and  in  the  latter  as  vacuum-gauges  or  draft-gauges. 

Pressure-Gauges  and  Vacuum-Gauges.  The  most  common  type  of  pres- 
sure-gauge (Fig.  1)  is  provided  with  a  flexible  hollow  brass  tube  of  oval  cross- 
section  known  as  bourdon  tube.  When  sub- 
jected to  pressure,  this  tube  tends  to  straighten 
out;  and  this  causes  a  sector  of  a  gear  to  mesh 
with  a  small  pinion,  which  is  on  the  same  shaft 
with  the  indicating  hand  or  pointer,  and  rotate 
the  latter  a  corresix)nding  amount.  The  pointer 
is  placed  just  in  front  of  a  graduated  dial,  not 
shown  in  the  figure,  from  which  the  pressure 
may  be  read  in  suitable  pressure-units,  such  as 
pounds  per  square  inch.  These  gauges  may  also 
be  used  for  indicating  vacuum,  or  a  pressure  less 
than  that  of  the  atmosphere. 

Draft-Gauges.  The  measurement  of  pressures 
but  slightly  above  or  below  the  atmospheric 
pressure,  barometric  pressure,  is  usually  accomplished  by  the  use  of  a  draft- 
gauge.  This  is  essentially  a  U  tube,  containing  either  water,  kerosene,  alco- 
hol, or  mercury,  mounted  upon  a  graduated  scale,  and  reading  either  in  inches 
of  fluid  or  in  pounds  or  ounces  per  square  inch.     Since  the  pressure  indicated 


Fig.  1.     Single-spring  Pressure- 
gauge.     Interior  View 


Physical  Units  and  the  Measurement  of  Heat 


1249 


is  a  differential  one,  due  to  the  left-hand  leg  being  open  to  the  air,  the  reading 
must  be  ol)tained  by  adding  the  depression  in  the  left-hand  leg  to  the  elevation 
in  the  right-hand  leg,  using  zero  as  the  reference-point  in  both  cases. 

Barometers.  The  pressure  of  the  atmosphere  is  usually  measured  by  a 
MERCURIAL  BAROMETER  (Fig.  2),  wMch,  in  its  simplest  form,  consists  of  a  glass 
tube  about  3  ft  long,  closed  at  one  end.  After 
being  filled  with  mercury  it  is  inverted  in  a  shallow 
bath  of  mercury.  The  pressure  of  the  atmosphere 
at  sea-level  maintains  the  mercury-column  in  the 
tube  about  30  in  above  the  level  in  the  bath  or 
cistern.  The  barometric  height  or  length  of  this 
column  of  mercury  varies  with  the  altitude  above 
or  below  sea-level.  When  the  mercury  in  the  tube 
falls,  that  in  the  cistern  rises  in  corresponding  pro- 
portion, and  vice  versa,  so  that  there  is  an  ever- 
varying  relation  between  the  level  of  the  mercury 
in  the  tube  and  the  mercury  in  the  cistern,  which 
affects  the  accuracy  of  the  readings.  It  is,  there- 
fore, necessary,  before  *  reading  the  height  of  the 
mercury-column  on  the  stem  of  the  barometer  by- 
means  of  a  movable  vernier,  to  adjust  the  level  of 
the  mercury  in  the  cistern.  All  standard  or  observ- 
atory-barometers of  the  mercurial  type  have  this 
adjustment.  Barometers  of  other  types,  such  as 
the  ANEROID  BAROMETER,  must  be  frequently 
compared  with  a  standard  mercurial  barometer  in 
order  to  check  the  accuracy  of  their  readings. 

Barometric  Pressure.  By  barometric  height  is  meant  the  height  of  a 
column  of  pure  mercury  at  32°  F.  which  just  balances  the  pressure  of  the  atmos- 
phere at  the  time  and  place  of  the  observation.  The  standard  or  normal 
barometric  pressure  is  defined  as  the  pressure  of  a  column  of  pure  mercury 
760  mm  (29.92  in)  high  at  32°  F.  This  is  the  normal  barometric  pressure  at 
latitude  45°  and  at  sea-level.  Since  the  weight  of  i  cu  in  of  mercury  under 
these  same  conditions  is  0.491  lb,  the  normal  barometric  pressure  =  height  of 
mercury-column  X  weight  per  cubic  inch  =29.92  X  0.491,  or  14.7  lb  per 
sq  in.  This  pressure  of  14.7  lb  per  sq  in  is  known  as  the  absolute  pressure 
of  the  atmosphere  at  latitude  45°  and  at  sea-level.  Now,  since  the  ordinary 
pressure-gauge  measures  only  pressures  above  or  below  that  of  the  atmosphere, 
it  is  necessary  to  add  the  barometric  pressure  at  the  place  in  question  to 
the  gauge-reading  to  obtain  the  total  absolute  pressure  corresponding 
to  the  pressure  indicated  by  the  gauge.  That  is,  absolute  pressure  =  barometric 
pressure  -f  gauge -pressure. 

Heat 

Definition  of  Heat.  Heat  is  a  form  of  energy.  It  is,  in  fact,  the  kinetic 
and  potential  energ}^  of  the  molecules  of  which  all  substances,  whether  solid, 
liquid,  or  gaseous,  are  composed.  Whenever  the  vibratory  motion  of  the  mole- 
cules composing  a  body  of  given  mass  is  increased  from  any  cause  the  thermal 
kinetic  energy  is  increased.  The  temperature  of  the  bod}'-  rises,  its  sensible 
HEAT  increases,  and  the  body  feels  warmer. 

Measurement  of  Temperature.  Thermometry.  Intensity  of  heat  is 
measured  by  thermometers  and  pyrometers,  the  latter  being  used  for  high 
temperatures?  above  from  400°  to  500°  F.     In  engineering  work  mercurial 


Fig.  2.    Simple  Barometer 


1250 


Heating  and  Ventilation  of  Buildings 


Tarts 


70 -§ 

.Cm 


32l 


P5 


II  21.1  I 


160 


-492 


theiiuometers  are  very  largely  employed.  These  depend  upon  the  uniform 
expansion  of  mercury  to  indicate  changes  in  temperature.  The  unit  of  measure- 
ment is  called  a  degree,  and  is  capable  of  very  exact  determination,  provided 
that  two  points,  at  which  the  heat-intensity  is  always  constant,  can  be  used  as 
bases  or  references  for  calibration.  The  melting-point  of  ice  and  boiling-point 
of  water  at  atmospheric  pressure  are  usually  selected  as  bases,  and  the  uniform 
expansion  of  the  mercury  between  these  two  points  is  indicated  on  a  scale 
divided  into  i8o,  loo,  or  8o  divisions.  (Fig.  3.)  Each  of  these  divisions  is 
known  as  a  degree  and  the  scales  used  are  known  re- 
spectively as  Fahrenheit,  Centigrade  or  Celsius, 
and  Reaumur.  The  Fahrenheit  is  used  almost  exclu- 
sively in  engineering  in  this  country. 
Absolute  Temperature.  In  addition  to  the  three 
g  temperature-scales  already  described,  physicists  employ 

oi  what  is  known  as  the  absolute  scale  of  tempera* 
h  tures,  based  on  the  so-called  absolute  zero  of  tem- 
l  perature,  at  which  point  no  molecular  vibration  exists. 

I"  This  zero  is  conceived  as  491.6°  F.  below  the  melting- 
point  of  ice  (32°  F.),  it  having  been  discovered  that  an 
ideal  perfect  gas  would  change  in  volume  by  1/49 1.6 
of  its  volume  at  32°  F.  for  each  1°  change  in  its  tem- 
"~"  perature,  at  constant  pressure.  Thus,  if  491.6  cu  ft 
of  gas,  measured  at  32°  F.,  is  cooled  20°  F.  at  constant 
pressure,  the  new  volume  will  be  471.6  cu  ft.  It  is 
only  necessary  to  add  491.6  —  32,  or  459.6,  to  the 
actual  thermometer-reading  to  get  the  absolute  tem- 
perature. That  is,  T  =  /-{- 459.6,  where  T  =  absolute 
278"  temperature,   and  /  =  actual  thermometer-reading  on 

Absolute    Scalgg  the  Fahrenheit-scale.     For  engineering- work,   460°  is 
used  rather  than  459.6".     For  the  Centigrade  scale  the 
relation  is  T  =/  -f-  273.1. 
~"  Measurement    of  Heat-Quantity.     Calorimetry. 

I  1  Q  Heat  may  be  measured,  since  it  is  a  form  of  energy, 

Fig  3  Fahrenheit  and  ^^  ^^^  ^^  ^^^  ^^^^^  energy-units,  as  the  joule,  foot- 
Centigrade  Thermometers  POUND,  or  horse-power  hour.  It  is  the  custom,  how- 
ever, to  use  for  this  purpose  a  special  unit  more  readily 
applicable  to  heat-changes.  This  unit  in  the  English  system  is  known  as  the 
British  thermal  unit  (Btu),  and  is  the  amount  of  heat  required  to  raise  i  lb  of 
water  from  63°  to  64°  F.  For  all  practical  purposes  in  ordinary  calculations,  a 
Btu  is  the  amount  of  heat  required  to  raise  i  lb  of  water  i"  F. 

Specific  Heat.  It  is  a  well-known  fact  that  equal  quantities  of  heat  will 
raise  equal  weights  of  different  substances  a  different  number  of  degrees,  depend- 
ing on  the  nature  of  the  substances.  This  property  of  matter  is  known  as 
SPECIFIC  HEAT,  and  for  any  substance  can  be  expressed  as  the  number  of  Btu 
required  to  raise  or  lower  the  temperature  of  i  lb  1°  F.,  at  some  given  tem- 
perature. It  is  also  customary  to  make  use  of  the  mean  or  average  value  for 
a  certain  temperature-interval.  Two  specific  heats  are  recognized,  one  known 
as  the  TRUE  specific  heat,  measured  at  the  temperature  stated,  and  the  other 
as  the  mean  specific  heat,  which  is  the  average  value  between  the  temperatures 
under  consideration.     The  specific  heat  of  air  at  constant  pressure  is  0.24. 

Relation  between  Units  of  Energy  and  Power.  Since  the  various  forms  of 
energy,  heat,  mechanical  energy,  electrical  energy,  etc.,  are  mutually  convert- 
ible, there  must  be  definite  numerical  relations  between  the  various  units  used 


Steam  1251 

to  express  energy.  As  determined  by  various  physicists  the  relation  between 
the  Btu  and  the  ft-lb  is 

I  Btu  =  777.64  ft-lb 

The  number  777.64  is  called  the  mechanical  equivalent  of  heat  and  is 
denoted  by  /.  For  ordinary  use  the  value  778  may  be  taken.  Another  con- 
venient relation  is, 

I  h.p.    =   2  564  Btu  per  hr 

Steam 

Properties  of  Steam.  Steam  is  water-vapor,  which  exists  in  the  vaporous 
condition  because  sufficient  heat  has  been  added  to  the  water,  from  which  the 
steam  has  licjn  formed,  to  supply  the  latent  heat  of  evaporation,  and  to  change 
the  liquid  into  a  vapor.  This  change  of  state  takes  place  at  a  definite  and 
constant  temperature,  which  is  determined  solely  by  the  pressure  of  the  steam. 
A  change  in  pressure  will  always  be  accompanied  by  a  change  in  the  tempera- 
ture at  which  ebulUtion  or  boiling  will  occur,  and  there  will  be  a  corresponding 
change  in  the  latent  heat.  The  properties  of  steam,  together  with  other  char- 
acteristics, are  tabulated  in  the  steam-tables.  (See  Table  I.)  Steam  in  con- 
tact with  the  water  from  which  it  has  been  generated  is  known  as  saturated 
BTEAM,  and  may  be  known  as  dry  saturated  steam,  or  as  wet  saturated 
steam.  The  latter  contains  more  or  less  actual  water  in  the  form  of  mist  or 
PRIMING,  as  it  is  called.  If  dry,  saturated  steam  be  heated,  and  the  pressure 
maintained  the  same  as  when  it  was  vaporized,  its  temperature  will  increase 
and  it  will  become  superheated;  that  is,  its  temperature  will  be  higher  than 
that  of  saturated  steam  at  the  same  pressure. 

Sensible  and  Latent  Heat.  Whenever  heat  is  added  to  a  substance,  without 
change  of  state,  its  temperature  is  raised,  and  the  heat  thus  added  is  known  as 
SENSIBLE  heat,  as,  for  example,  the  heat  added  to  water  the  temperature  of 
which  is  between  50°  and  140°  F.  Sensible-heat  changes,  as  already  stated,  are 
measured  by  the  thermometer.  Heat  may  be  added  to  a  body  without  any 
change  of  temperature  provided  a  change  of  state  from  solid  to  liquid  or  from 
liquid  to  vapor  takes  place,  and  the  heat  thus  added  is  known  as  latent  heat. 
When  the  change  is  from  solid  to  liquid,  as  from  ice  to  water,  this  heat  is  known 
as  the  latent  heat  of  fusion.  At  atmospheric  pressure  ice  melts  at  32°  F., 
and  the  latent  heat  is  144  Btu  per  lb.  When  the  change  is  from  liquid  to  vapor, 
as  from  water  to  steam,  the  heat  required  to  effect  the  change  is  known  as  the 
latent  heat  of  evaporation.  At  atmospheric  pressure  water  evaporates  at 
212°  F.,  and  the  latent  heat  is  971.7  Btu  per  lb.  A  conception  of  the  relation 
between  the  properties  or  characteristics  of  steam,  and  the  manner  in  which  the 
changes  of  state,  temperature  and  pressure  are  brought  about,  is  described  in  the 
following  paragraphs. 

Generation  of  Steam.  Consider  a  frictionless  cylinder  (Fig.  4),  containing 
I  lb  of  water  at  32°  F.  Also  consider  the  pressure  of  the  atmosphere  to  be  14.7 
lb  per  sq  in  and  to  be  replaced  by  that  of  the  piston  B.  When  heat  is  applied 
to  the  cylinder  the  temperature  of  the  water  rises  until  the  boiling-point,  212°  F., 
is  reached.  The  heat  necessary  to  raise  the  temperature  from  32°  F.  to  the 
boiUng-point  is  known  as  the  heat  of  the  liquid  or  sensible  heat,  and  is  de- 
noted by  the  symbol  Q.  This  condition  is  denoted  in  Fig.  8  by  the  point  C. 
The  average  specific  heat  of  water  between  32°  F.  and  212°  F.  is  i;  hence  the 
number  of  British  thermal  units  (Btu)  necessary  to  raise  the  temperature  of 
the  water  this  amount  is  212  —  32  or  180  Btu. 

When  more  heat  is  added  the  water  begins  to  evaporate  and  expand  at  con- 


1252 


Heating  and  Ventilation  of  Buildings 


Part  3 


stant  temperature  until,  as  in  Fig.  5,  the  water  is  entirely  changed  into  steam. 
This  condition  is  also  shown  in  Fig.  8,  by  the  point  D.  The  heat  thus  added  is 
known  as  the  latent  iucat  of  evaporation  and  is  denoted  by  the  symbol  r. 
This  heat  r  is  subdivided  into  two  parts.  (See  Fig.  7.)  First  the  attraction 
between  the  molecules  must  be  broken  down.  This  is  known  as  tlie  internal 
latent  heat  and  is  denoted  by  the  symbol  p.  Next  the  external  resistance 
must  be  overcome,  the  weight  P  being  raised  against  gravity.  The  heat  thus 
added  is  known  as  EXTEimAL  latent  iikat  and  is  designated  by  the  symbols 
APu,  where  u  is  the  change  in  volume,  in  cu  ft  of  i  lb  of  water,  A  is  1/778,  and 


r-i-T 


EM 


ififkii 


_\ t  _f 


-f- 


'Fjd._4      Fig".  5      J\L  6 


I    i     I  Lbs. 

I"  "iiiiir 


Diagram  Showing 
Relatiorib  between 
"the  Liquid  and  Saturated 
and  Superheated  Vapor 

^iJci 


'^•'-'¥k 


'^ 


-H«- 


E  .  D 


h-^- 


Ileat  added  B.t.u 


-Ha:- 


^PiBton    , 
arca-c:  ID 


.Fig.  8 

External  Work  of  Evaporation  «  P  (v-d),»Pa 

or  in  B.t.n  .=  AP  (v-d)  =  APu  &  A  =  ^g  " 

Since  r=  total  Heat  of  Evaporation,  then  r-.APu -Internal 


T 

;i    I  J,       Since  rs  total  Heat  ot  £Jvaporation  tbenr-.APu- Internal 

I    1  LiqViid  1  >      Heat  of  Evaporation  a  p  necebsary  to  oy.excome  Molecular  attrasfiaft 

Fig:.  7 

Figs.  4  to  8.    Diagrams  Explaining  the  Generation  of  Steam 

P  is  the  pressure  of  the  atmosphere  in  pounds  per  square  feet  (barometric 
pressure).     It  is  evident  then  that  the  latent  heat 

r  =  p  -\-  APu,  or  p  -r  —  APu 

The  term  APu  is  the  heat-equivalent  of  the  work  performed  for  the  change  in 
volume  from  water  to  steam. 

The  heat  added  from  the  starting-point  (32°  F.),  is  known  as  total  heat 
(//),  or  q  -i-r  =  H.  If  more  heat  is  added,  the  pressure  remaining  constant, 
the  temperature  of  the  steam  rises  and  the  steam  becomes  what  is  known  as 
superheated  steam.  The  heat  added  is  equal  to  the  meaij  specific  heat 
{Cp)  of  the  steam,  times  the  change  in  temperature  (ts  —  212).  The  specific 
heat  of  steam  is  the  Btu,  or  heat,  required  to  raise  the  temperature  of  i  lb  of  the 
steam  1°  F.  Since  the  specific  heat  of  steam  is  less  than  that  of  water,  the 
slope  of  this  line  becomes  greater  than  that  of  the  water-line  The  point  is 
now  located  at  h  (Fig.  8),  and  the  steam  has  increased  in  volume  in  the  cylinder 
(Fig.  5),  until  the  piston  occupies  the  dotted  position  B'. 

If  instead  of  the  above  condition  of  pressure,  additional  pressure  is  added, 


Steam 


m 


Table  I.    Properties  of  Saturated  Steam.  ' 
G.  A.  Goodenough 


Absolute  pressure 


Inches  of 
mercury 


Lb  per 
sq  in 


Tem- 
pera- 
ture, 
deg. 
F. 


Vol- 
ume, 
cu  ft 
per  lb 


Weight, 
lb  per 
cuft 


Heat-content 
in  Btu 


of 
liquid 


of 
vapor 


Latent  heat 
in  Btu 


of 

vapor- 
ization 


t 


H 


4.072 
8.144 
12. 216 
16.  29 
20.36 
24-43 
30 


14.74 

16 

18 


24 
26 
28 
30 
32 
34 
36 
38 
40 
50 
54 
60 
64 
70 
74 
80 
84 
90 
94 
100 
104 
no 
114 
120 
124 
130 
134 
140 
144 
ISO 
154 
160 
164 
170 
174 
180 
190 
200 


126.10 

152.99 

170.07 

182.87 

193-21 

201 .96 

212.13 

216.3 

222.4 

228.0 

233 -I 

237.8 

242.2 

246.4 

250.3 

254-0 

257.6 

260.9 

264.2 

267.2 

281.0 

285 

292 

296 

302 

306 

312 

31S 

320 

323 

327.8 

330.7 

334.8 

337.4 

341.3 

343.7 

347.4 

349.7 

353.1 

355.3 

358.5 

360.5 

363.6 

365.6 

368.5 

370.4 

373.1 

377.6 

381.9 


173.6 
90.6 
62.0 
47.35 
38.43 
32.41 
26.7s 
24.76 
22.18 
20. 10 
18.38 
16.9s 
15.73 
14-67 
13.76 
12.95 
12.24 
11.60 
11.03 
10.51 

8.53 

7.93 

7.18 

6.76 

6.22 

5 

5 

5 

4 

4 

4 

4 

4 

3 

3 

3 

3 

3 

3 

3 

3 

2 


90 

48 

23 

905 

709 

442 

279 

057 

921 

735 

620 

461 

363 

226 

140 

020 

945 
2.839 
2.773 
2.679 
2.620 
2.536 
2.4o8|o 
2 .  292I0 


00576 
01104 
01614 

02112 
02602 
03086 
03739 
04038 
04508 
04976 
0544 
0590 
0636 
0681 
0727 
0772 
0818 
0862 
.0907 

09SI 
.1173 
.  1261 
.1392 
.  1479 
.  1609 
.1695 
.1824 
.  1910 
,2039 
.  2124 
.  2251 
■  2337 
.2465 
.2550 
.2678 
.2762 
.2889 
.2973 
.3100 
.3184 
.3311 
.3396 
.3522 
.3606 
.3733 
.3817 

3943 
.4154 
.4364 


94.02 
120.9 
137.9 
150.8 
161 . 1 
169.9 
180. 1 
184.3 
190. 5 
196.0 
201.2 
206.0 
210.4 
214.6 
218.6 
222.4 
225.9 
229.4 
232.6 
235.8 
249.8 
254-7 
261 .7 
266.1 
272.2 
276. 1 
281.6 
285.1 
290.1 
293.3 
297.9 
300.9 
305. 1 
307.9 
311. 9 
314.4 
318.2 
320,.  6 
324.2 
326. 5 
329.8 
332.0 
335.2 
337-3 
340.3 
342.3 
345.2 
350. 0 
354-5 


116. 2 
127.9 
135.0 
140.3 
144.4 
147.9 
151. 8 
153.4 
155.7 
157-7 
159.6 

161. 3 
162.8 
164-3 
165.7 
166.9 
168. 1 
169.2 
170.3 
171. 3 
175. 6 
177. 1 
179-I 
180.3 
182.0 
183.0 
184.4 
185.3 
186.5 
187.3 
188.4 
189.0 
190.0 
190.6 
191.4 
191-9 
192.6 
193. 1 
193-7 
194. 1 
194-7 
195-I 
195-7 
196.0 
196.5 
196.8 
197.2 
197.9 
198. 5 


I  022.2 
I  007.0 
997.1 
989.5 
983.3 
978.0 
971.7 
969.1 
965 
961 
958 
955 
952 
949 
947 
944 
942 
939-9 
937-7 
935-5 
925.9 
922.4 
917-4 
914-3 
909.8 
906.9 
902.8 
900.  2 
986.4 
894.0 
890.5 
888.2 
884.8 
882.7 
879-5 
877.5 
874-4 
872 
869 
867 
864 
863 
860 
858 
856 
854 
852 
847 
844 


*  Condensed  from  original  tables  published  by  John  Wiley  &  Sons,  Inc, 


1254  Heating  and  Ventilation  of  Buildings  Part  3 

as  shown  by  the  weight  W  in  Fig.  6,  the  temperature  of  the  boiling-point  will  be 
raised  from  the  temperature  of  212°  F.  to  some  other  point,  as  ti  (Fig.  8).  As 
may  be  seen  by  this  figure,  the  sensible  heat  g  has  been  increased  to  qi.  When 
more  heat  is  added  the  water  is  evaporated  at  the  temperature  h,  and  if  heat 
again  be  added  the  saturated  steam  will  become  superheated  steam. 

Quality  of  Steam.  The  proportion  of  the  dry  steam,  per  pound  of  steam 
delivered  by  the  boiler,  is  known  as  the  quality  of  the  steam  and  is  repre- 
sented by  the  symbol  x,  and  the  heat  (Hx)  contained  in  the  steam  above  32°  F. 
is  g  +  xr;    the  state-point  is  located  at  E  (Fig.  8). 

Specific  Volume  and  Density.  The  volume  of  a  pound  of  steam  is  known 
as  the  SPECIFIC  volume  v,  and  as  may  be  seen  by  comparing  Figs.  5  and  6,  de- 
creases as  the  pressure  increases.  The  reciprocal  of  this,  or  the  weight  of  steam 
per  cubic  foot,  is  known  as  the  density,  and  is  denoted  by  d  or  i/v. 

Entropy.  Another  quantity  known  as  entropy  is  made  use  of  in  calcula- 
tions relating  to  steam-engines  and  turbines,  and  is  defined  as  the  ratio  obtained 
by  dividing  the  quantity  of  heat  added  to  a  substance  by  the  absolute  tempera- 
ture at  which  it  is  added. 

The  Total  Heat,  //,  of  a  dry,  saturated  vapor  for  any  pressure  and  tem- 
perature is  the  sum  of  the  heats  required  to  raise  the  temperature  of  one  pound 
of  the  liquid  from  the  freezing-point  to  the  given  temperature  and  corresponding 
pressure  and  entirely  vaporize  it  at  this  pressure.  For  this  case  x  =  i, 
and  consequently 

II  ^{p  +  APu)  +  g  =  y  -f  g 

The  total  heat  {Hx)  of  wet  vapor  at  any  pressure  and  temperature  is 

II X  =  xr  +  q 

It  is  manifestly  incorrect  to  say  that  this  is  the  heat  in  the  vapor,  as  the  APu 
is  not  the  heat  in  the  vapor,  but  the  external  work  performed  by  the  vapor  while 
evaporating. 

Superheated  Steam  or  Vapor.  Superheated  steam  is  defined  as  water- vapor 
which  has  been  heated  out  of  contact  with  its  hquid,  until  its  temperature  is 
higher  than  that  of  saturated  vapor  at  the  same  pressure. 

The  heat-content  of  superheated  steam  or  vapor  may  be  expressed  by  the 
equation 

Hs  =q  -^f  -{■  Cp{ts  -t)  =11  +Cp  its  -  /) 

where  ts  is  the  temperature  of  superheated  vapor,  /  the  temperature  of  saturated 
vapor  at  the  corresptmding  pressure,  q  the  heat  of  the  hquid  at  /,  and  r 
the  heat  of  vajxirization  at  temperature  /.  Cp  is  the  mean  specific  heat  of 
superheated  vapor  (approximately  0.50),  //  the  total  heat  of  i  lb  of  dry  sat- 
urated steam,  and  lis  the  total  heat  of  i  lb  of  superheated  steam. 

Properties  of  Air 

Charles*  Law.  Charles'  Law  refers  to  the  relation  between  pressure,  volume 
and  temperature  of  a  gas,  and  may  be  stated  as  follows.  The  volume  of  a 
given  weight  of  gas  varies  directly  as  the  absolute  temperature  at  constant 
pressure,  and  the  pressure  varies  directly  as  the  absolute  temperature  at  constant 
volume.  Hence,  when  heat  is  added  at  constant  volume  Vc*  this  equation  results: 

P2      Ts 
Pi  ~  Tx 


Properties  of  Air  1255 

or  for  the  same  temperature-range,  at  constant  pressure  Pc,  the  relation  is 


Tx 


In  general,  for  any  weight  of  gas  M,  since  volume  is  proportional  to  weight  at 
any  given  volume  and  temperature, 

PV  =  MRT  JBmitaa 

which  is  the  characteristic  equation  for  a  perfect  gas.     In  this  formula 

P  =  the  absolute  pressure  of  the  gas  in  pounds  per  square  foot  «  21 16.8 

(atmospheric  pressure)  ; 
V  5=  the  volume  of  the  weight  M  in  cubic  feet; 
M  ==  the  weight  in  pounds  of  the  gas  taken; 

R  =  a  constant  depending  on  the  nature  of  the  gas  =  53.37  for  air; 
T  =  the  absolute  temperature  in  degrees  Fahrenheit  (/  -f-  459.6). 

Table  II.     Properties  of  Dry  Air 

Barometric  pressure,  29.921  in.     Specific  heat,  0.24 


Btu  absorbed 

Cubic  feet 

Temperature 

Weight  per 

Per  cent  of 

by  one  cubic 

of  dry  air 

in  degrees 

cubic  foot 

volume  at 

foot  dry  air 

warmed  one 

Fahrenheit 

in  pounds 

70°  Fahrenheit 

per  degree 
Fahrenheit 

degree  per 
Btu 

0 

0.08636 

0.8680 

0.02080 

48.08 

10 

0.08453 

0.8867 

0.02039 

49-05 

20 

0.08276 

0.9057 

0.01998 

50.05 

30 

0.08107 

0.9246 

0.0I9S7 

5J.JQ 

40 

0.07945 

0.9434 

0.01919 

52.11 

50 

0.07788 

0.9624 

0.01881 

53.17 

60 

0.07640 

0.9811 

0.01846 

54.18 

70 

0.07495 

I .0000 

0.01812 

55.19 

80 

0.07356 

I .0190 

0.P1779 

56.21 

90 

0.07222 

1.0380 

0.01747 

57.25 

100 

0.07093 

1.0570 

0.01716 

58.28 

no 

0.06968 

1.0756 

0.01687 

59-28 

120 

0.06848 

1-0945 

0.01659 

60.28 

130 

0.06732 

I.1133 

0.01631 

61.32 

140 

0.06620 

I. 1320 

0.01605 

62.31 

150 

0.06510 

1.1512 

0.01578 

63-37 

160 

0.06406 

I. 1700 

0.0ISS4 

64.35 

170 

0.06304 

I. 1890 

0.01530 

65.36 

180 

0.06205 

I .2080 

0,01506 

66.40 

190 

0.06110 

1.2270 
I -2455 

0.01484 
0.01462 

67.40 
68.41 

200 

0 . OdOI 0 

240 

0.05673 

I. 3212 

0.01380 

72.46 

300 

0.05225 

1.4345 

0.01274 

78.50 

350 

0.04903 

1.5288 

0.01197 

83.5s 

400 

0.04618 

1.6230 

0.01130 

88.50 

450 

0.04364 

1. 7177 

0.01070 

93.46 

500 

0.04138 

I.8113 

0.01018 

98.24 

5S0 

0.03934 

I . 9060 

0.00967 

103.42 

600 

0.03746 

2.0010 

0.00923 

108.35 

700 

0.03423 

2.1900 

0.00847 

118.07 

1256 


Heating  and  Ventilation  of  Buildings 


Parts 


A  PERFECT  GAS  conforms  exactly  to  the  above  equation,  and  while  no  gases  are 
PERFECT  in  this  sense,  they  conform  so  nearly  that  the  above  equation  applies 
to  most  engineering-computations.  The  volume  of  i  lb  of  air,  known  as  the 
SPECIFIC  VOLUME,  at  any  temperature  and  pressure,  can  be  found  at  once  by 
the  equation 

V  =  (53-37  X  T)/P 


Estimating  Heating  Requirements  of  Buildings 

Heat  Required  and  Supplied.  The  amount  of  heat,  measured  in  Btu  to  be 
SuppUed  by  the  heating-apparatus  to  a  building  to  maintain  the  inside  tempera- 
ture above  that  of  the  outside,  commonly  termed  heat-losses,  is: 

(a)  The  heat  required  to  offset  the  heat- transmission  of  the  walls,  ceiling  or 
roof,  and  floor.  This  loss  of  heat  depends  upon  the  type  and  materials  of  con- 
struction used  and  the  temperature-difference  to  be  maintained  between  the 
inside  and  the  outside  of  the  building. 

(b)  The  heat  required  to  warm  the  air  entering  the  building  from  the  outside, 
either  by  infiltration  or  purposely  introduced  for  ventilation. 

(c)  The  heat  supplied  by  {persons,  lights,  machinery  and  motors,  which  may 
be  deducted  from  the  sum  of  items  (a)  and  (b)  to  obtain  the  net  amount  of  heat 
to  be  supplied  by  the  heating-apparatus.     (Item  (c)  is  usually  not  considered.) 

It  is  customary  in  all  calculations  connected  with  the  design  of  heating- 
installations  to  base  the  estimate  on  the  amount  of  heat  per  hour  to  be  supplied 
by  the  apparatus.  The  total  heat  to  be  supplied  per  hour  is  //  =  [(item  a)  -|- 
(item  b)  —  (item  c)]  Btu.  The  method  in  use  for  the  calculation  of  the  various 
items  above  mentioned  will  now  be  taken  up  and  discussed  in  the  order  given. 

Temperatures.  The  inside  temperature  to  be  maintained  and  the  air  re- 
quired for  ventilation  for  various  classes  of  work  are  discussed  under  Ventilation, 
to  which  the  reader  is  referred.  The  outside  temperature  for  which  the  heating- 
installation  should  be  designed  is  fixed  by  the  lowest  outside  temperature  that 
is  liable  to  continue  for  several  days  during  the  heating-season. 

Usual  Inside  Temperature  Specified 


Kind  of  buildings 

Public  buildings.  . 

Factories 

Machine-shops. 

Foundries,  boiler-shops,  etc 

Residences 

Bath-rooms 

Schools 

Hospitals 

Paint-shops V'.V'i  .1 . . 

0-S.S  .  T 


Degrees  P. 


68-72 

65 
6o-6s 
50-60 

70 

85 

70 
72-75 

80 


In  designing  the  heating-system  a  temperature  of  from  10*'  to  15°  F.  higher 
than  the  lowest  recorded  temperature  is  recommended  to  be  used  for  the  out- 
side temperature. 

Heat-Transmission  of  Walls,  Ceilings,  Roofs,  Floors,  etc.  (a)  The  heat- 
loss  through  building-construction  is  dependent  upon  the  character  of  the 
material,  thickness  and  character  of  the  surfaces,  and  the  velocity  of  the  air 
over  the  surfaces.  Numerous  tests  have  been  conducted  by  various  experi- 
menters to  determine  accurately  the  heat-transmission  of  various  types  of 


Estimating  Heating  Requirements  of  Buildings 


Table  HI.    Outside  Temperatures 

Lowest  and  Average  Temperatures   in  the  United   States.     All  stated  in  Fahrenheit 
degrees  and  compiled  from  United  States  Weather  Bureau  Records 


State 


Ala  .  . 

Ariz.  . 

Ark.. 

Cal.  . 

Col.  . 

Conn. 
D.  C. 
Fla... 

Ga... 

Idaho 

111..  . 

Ind.. 

la.... 

Kan.. 

Ky... 
La... 

Me... 

Md.  . 
Mass. 
Mich. 

Minn. 

Miss  . 

Mo.  . 

Mont, 


City 


Mobile 

Montgomery . . 

Flagstaff 

Phoenix 

Fort  Smith 

Little  Rock .  .  . 
San  Diego .... 
Independence.. 

Denver 

Grand  Junction 
Southington. .  . 
Washington.  .  . 

Jupiter 

Jacksonville. .  . 

Savannah 

Atlanta 

Boise 

Lewiston 

Chicago 

Springfield .... 
Indianapolis. .  . 
Evans  ville .... 
Sioux  City .... 

Keokuk 

Dodge  City .  .  . 

Wichita 

Louisville 

New  Orleans .  . 
Shreveport. .  .  . 

Eastport 

Portland 

Baltimore 

Boston 

Alpena 

Detroit 

Duluth 

Minneapolis. .  . 

Meridian 

Vicksburg 

Springfield .... 

Hannibal 

Havre 

Helena 


Lowest 


-25 
-15 
-31 
-26 
-26 


7 

-  5 
-21 
-17 

-  7 
-13 
-27 
-24 
-41 
-33 

-  6 

-  I 
-29 
-20 
-55 
-42 


Aver- 
age.* 


57-7 
56.1 
34.8 
58.9 
49. 5 
52.0 
57.2 
48.7 
38.4 
39-2 
36.3 
42.9 
69.8 
60.9 
57.2 
51.4 
39.6 
42.5 
35.9 
39.0 
40.4 
44.1 
32.1 
37.6 

42.9 
45.0 
60.5 
55.7 
31. 1 
33.5 
43.3 
37.2 
29.1 
35. 3 
25.5 
28.4 
53-9 
56.0 
43.0 
39.7 
27.7 
30.9 


State 


Neb.  . 

Nev.  . 

N.  H 
N.  J.. 
N.  Y. 

N.  M. 

N.  C. 

N.  D. 

Ohio  . 

Okla  . 
Ore.  . 

Pa... 

R.  I.  . 

S.  C.  . 

S.  D.. 

Tenn. 

Tex.  . 

Utah. 
Vt.  .. 
Va... 

Wash. 

W.Va. 

Wis.  . 

Wyo  . 


City 


North  Platte.. 

Lincoln 

Carson  City. .  . 
Winnemucca.  . 

Concord 

Atlantic  City.  . 
Saranac  Lake.. 
New  York  City 

Roswell 

Santa  Fe 

Hatteras 

Charlotte 

Devil's  Lake.  . 

Bismarck 

Toledo 

Columbus 

Oklahoma 

Baker  City. . . . 

Portland 

Pittsburgh .... 
Philadelphia. . . 
Providence. .  . . 
Rock  Island. .  . 
Charleston .... 

Columbia 

Huron 

Yankton 

Knoxville 

Memphis 

Corpus  Christi. 
Fort  Worth .  .  . 
Salt  Lake  City. 

Northfield 

Cape  Henry. .  . 
Lynchburg. .  .  . 

Seattle 

Spokane 

Parkersburg. .  . 

Elkins 

La  Crosse 

Milwaukee .... 

Cheyenne 

Lander 


Lowest 


-35 
-29 

-  22 
-28 
-35 

-  7 
-38 

-  6 
-14 
-13 

8 

-  S 
-51 
-44 
~i6 
—20 
-17 
—20 

-  2 
—20 

-  6 

-  9 

-  4 
7 
2 

-43 
-32 
-16 

-  9 
II 

-  8 
20 

-32 
5 

-  5 
3 

-30 
-27 

-  21 
-43 
-25 
-38 
-36 


*  Average  is  taken  from  October  i  to  May  i. 


construction.  The  following  table  represents  the  results  of  the  experiments 
(1914-15)  by  Harding  and  Willard  in  this  connection,  based  on  an  average 
outside  wind-movement  of  approximately  15  miles  per  hour; 


1258  Heating  and  Ventilation  of  Buildings 

Table  IV.     Heat-Tiransmission  of  Building-Construction 


Parts 


Construction 


Thick- 
ness, 


Btu  transmitted  per  square  foot  per  hour 


Temperature-difference 


20 


40" 


6o° 


70° 


8o° 


Blain  bilckr-nU 


9 
13 

I8 

24 


.363 
.281 

.220 

.174 


7.3 

5.6 

4.4 
3.5 


14-5 

II. 2 

8.8 

7.0 


21.8 
16.9 
13.2 
10.4 


25.4 
19.7 
IS. 4 
12.2 


29.0 
22.5 
17.6 
13.9 


.217 
.185 
.156 
.132 


4-3 

3.7 

.  3.1 

2.6 


8.7 
7.4 
6.2 
5.3 


13.0 

II. I 

9.4 

7.9 


IS. 2 

13.0 

10.9 

9.2 


17.4 
14.8 
12.4 

10.6 


.20 


4.0 


8.0 


12.0 


14.0 


16.0 


i^m$^wm^ 


•  547 
.370 
.279 


10.9 
7.4 
5.6 


21 .9 
14.8 
II. 2 


32.8 
22.2 
16.7 


38.3 
25.9 

19-5 


43.8 
29.6 
22.3 


.409 
.325 
.281 


8.2 

6.5 

5.6 


16.4 
13-0 
II. 2 


24.5 
19-5 
16.9 


28.6 
22.8 
19.7 


32.7 
26.0 
22. S 


.784 
.714 
.655 
.563 


IS. 7 
14.3 
13.1 
II. 3 


31.4 
24.6 
26.  2 
22.5 


47.0 
42.8 
39-3 
33.8 


54-9 
So.o 

45-9 
39-4 


62.7 
57.0 
52.4 
45.0 


For  3-in  concrete  covered  with  slag  roofing,  de- 
duct approximately  iO%  from  values  stated. 


Single 

Double 

Triple 


1. 126 

22.5 

45-0 

67.6 

78.8 

.450 

9-0 

18.0 

27.0 

31.5 

.281 

5.6 

II. 2 

16.9 

197 

.018 

.360 

.720 

1.08 

1.26 

90.0 
36.0 

22.5 


One  air-change  per  hr  cu  ft 


1.44 


Btu  loss  per  foot  of  sash  perimeter  per  hour 


Wooden  sash 

Wooden  sash,  metal  strip. .  .  . 

Hollow  metal  sash 

Hollow  metal  sash,  stripped. . 


2.05 

41.0 

82.0 

123 

144 

0.43 

8.6 

17.2 

26 

30 

4.5 

90 

180 

270 

315 

1.6 

32 

64 

96 

112 

164 

34 
360 
128 


•  For  lath-and-plaster  ceiling  with  no  floor  above,  double  the  values  given  for  wooden 
floor  with  plaster  ceiling. 


Estimating  Heating  Requirements  of  Buildings  1259 

The  following  data  on  the  heat-transmission  of  various  types  of  roofs  were 
taken  from  the  test-results  of  C.  L.  Norton: 


Table  V.     Heat-Transmission  through  Roofs 

Construction 

Btu  per  sq  ft 
per  hour  per  i  ° 

difference  in 
temperature  of 
still  air  inside 

and  outside 

APM  gypsum  slab  roof  4  in  thick  with  S-ply  tar  and  felts.  . 
APM  gypsum  slab  roof  3  /^  in  thick  with  5-ply  tar  and  felts 
APM  gypsum  slab  roof  3  in  thick  with  5-ply  tar  and  felts. 
Spruce  planks  3  in  thick  with  5-ply  tar  and  felts 

0.134 
0.149 
0.170 
0.192 
0.282 
0.348 
0.488 
0.508 
0.575 
0.633 

Hard-pine  plank  3  in  thick  with  5-ply  tar  and  felts 

Hollow  terra-cotta  tile  3  in  thick  with  5-ply  tar  and  felts. .  . 
Stone  concrete  6  in  thick  with  5-ply  tar  and  felts 

Cinder  concrete  4  in  thick  with  5-ply  tar  and  felts 

Stone  concrete  4  in  thick  with  5-ply  tar  and  felts 

Stone  concrete  3  in  thick  with  5-ply  tar  and  felts 

The  heat-transmission  of  stone  walls  is  approximately  50%  greater  than  that 
of  brick  of  equal  thickness.  The  Btu-loss  per  foot  of  sash-perimeter  is  based  on 
the  leakage-determinations  by  Voorhees  and  Meyer,  Trans.  Am.  Soc.  H.  and 
V.  E.,  1916. 

Heat-Transmission  of  Roofs  and  Floors.  The  temperature  of  the  air  in 
contact  with  the  under  side  of  a  ceiling  or  roof  is  found  to  be  higher  than  the 
temperature  maintained  at  the  breathing-line,  at  which  point  the  temperature 
is  usually  measured;  and  this  is  due  to  the  natural  tendency  of  the  warmer  or 
less  dense  air  to  rise.  It  is  recommended  that  an  increase  of  approximately 
15%  be  made  to  the  specified  inside  temperature  for  the  temperature  at  the 
ceiUng  for  ceiling  or  wall-heights  not  exceeding  15  ft,  and  30%  for  ceiling-heights 
of  20  ft  or  more,  in  estimating  the  heat-loss  of  roofs.  Thus,  if  65°  F.  is  the  spe- 
cified inside  temperature  to  be  maintained  in  a  room  the  height  of  which  is 
20  ft,  the  temperature  of  the  air  in  contact  with  the  under  side  of  the  roof  may 
be  assumed  to  be  65°  -|-  30%,  or  85°  F.  The  loss  of  heat  through  the  ceiling 
of  a  room  over  which  a  large  air-space  exists,  through  partitions  between  a 
heated  and  a  cold  room,  or  through  the  first  floor  to  the  cellar,  may  be  estimated 
on  the  assumption  that  the  warmed  rooms  give  off  sufficient  heat  tc  maintain 
the  temperature  of  these  colder  spaces  according  to  the  following  schedule: 

Closed  attics  under  metal  or  slate  roofs 14°  F. 

Closed  attics  under  tile,  cement,  tar,  or  gravel  roofs 23 '^  F. 

Cellars  and  rooms  kept  closed 35°  F. 

The  heat-transmission  of  floors  that  are  laid  directly  upon  the  ground  may  be 
estimated  on  the  assumption  that  the  ground  in  contact  with  the  under  side  of 
the  floor  has  an  approximate  temperature  of  50°  F.  Thus  the  estimated  heat- 
loss  through  a  6-in  concrete  floor  laid  directly  upon  the  ground,  assuming  an 
inside  temperature  of  65°  F.,  is 

0-563  (65  —  50)  or  8.4  Btu  per  square  foot  per  hour 

Heat-Loss  by  Infiltration,     (b)  The  heat  required  to  warm  the  outside  air 


1260 


Heating  and  Ventilation  of  Buildings 


Parts 


which  may  enter  by  leakage  through  the  cracks  or  clearances  around  windows 
and  doors  is  that  required  to  raise  the  temperature  of  the  weight  of  incoming 
air  per  hour  from  the  outside  to  the  inside  temperature. 
Let      b  =Btu  required  per  hour  to  heat  the  incoming  air; 
/  =inside  room-temperature  in  degrees  Fahrenheit; 
to  =  outside  temperature; 
Cp  =  specific  heat  of  air  at  constant  pressure  =0.24; 
d  =  density  of  the  air  at  temperature  /; 
=0.075  for  70°  inside  temperature; 
=0.076  for  60°  inside  temperature; 
Q  =  cubic  feet  of  air  per  hour  entering  building  by  infiltration,  measured 

at  temperature  /; 
W  =  weight  of  air  per  hour  entering  building  by  infiltration  =  d  XQ; 
Then   b  =Cp  (t  -  k)  Q  X  d  =  0.24  XW  X{t  -  /o); 
=  1.26  Q  for  70°  inside  temperature; 
=  1.08  Q  for  60°  inside  temperature. 

There  are  two  assumptions  made  by  engineers  in  practice  for  obtaining  the 
value  of  Q.  The  common  method  in  vogue  is  to  assume  a  certain  number  of 
air-changes  n,  per  hour  in  the  cubical  contents  C,  of  the  room  in  accordance 
with  the  following  table: 

Table  VI.     Number  of  Air-Changes  per  Hour 


Halls 

Rooms  on  ist  floor 

Rooms  on  2nd  floor 

Offices  and  stores,  ist  floor 

Offices  and  stores,  2nd  floor 

Churches  and  public  assembly-rooms, 
Large  rooms  with  small  exposure .  ,  .  . 
Factory -buildings 


n  =  2  to  3 

n  —  I H  to  2 

n  =  ^  to  2 

n  =  H  to  I 

n  =  M  to  I 


Example.  Required  the  heat-loss,  by  infiltration,  from  a  room  containing 
20  000  cu  ft,  the  temperature  of  which  is  maintained  at  70°  F.  in  zero  weather, 
the  estimated  number  of  air-changes  n,  being  two  per  hoiu:. 

Solution.  Q  =  2  X  20  000  =  40  000  cu  ft  of  air  entering  per  hour  measured 
at  70.°  F. 

b  =  0.018  X40  000  X   (70  —  o)  =50  400  Btu  per  hour. 

The  other  method  is  to  use  the  estimated  amount  of  air-leaking  in  the  build- 
ing through  the  cracks  around  the  sash-perimeter  and  meeting-rail.  The  fol- 
lowing data  may  be  used  in  this  connection  and  is  based  on  a  wind-movement  of 
approximately  20  miles  per  hour  (Voorhees  and  Meyer  Tests). 


Plain  wooden  sash 

Plain  wooden  sash,  weather- 
stripped 

Hollow  metal  sash 

Hollow  metal  sash,  weather- 
stripped 

Copper-covered  sash 


24 
216  to  268 


72  to  150 

132 


cu  ft  air  per  hour  per  foot  perimeter 

cu  ft  air  per  hour  per  foot  perimeter 
cu  ft  air  per  hour  per  foot  perimeter 

cu  ft  air  per  hour  per  foot  perimeter 
cu  ft  air  per  hour  per  foot  perimeter 


For  a  room  with  more  than  one  outside  wall  use  only  the  sum  of  the  per- 
imeters of  the  windows,  in  the  side  having  the  greater  number. 


Estimating  Heating  Requirements  of  Buildings  1261 

Example.  An  office  14  by  16  by  lo-ft-high  ceiling,  has  two  3  by  7-ft  wooden- 
sash  windows.  The  maintained  inside  temperature  is  70°,  and  the  outside 
temperature  0°  F.     Required  the  heat-loss  by  infiltration. 

Solution.  By  the  first  method,  assuming  two  air-changes  per  hour,  the  loss 
is 

b  =  1.26  X  2  X  (14  X  16  X  10)  =  5  645  Btu  per  hr 

By  the  second  method  this  loss  is:  ry 

b  =  1.26  X2(3  +3  +3+7  +7  perimeter)  X  114  =6  607  Btu  per  hir 

Increase  in  Heat-Losses  for  Tall  Buildings.     It  is  advisable  to  increase  the 

calculated  heat-losses  above  the  tenth  floor  by  approximately  15%  for  walls 
that  are  exposed  to  the  prevailing  winds. 

Heat  Supplied  by  Persons,  Lights,  Motors,  Machinery,  etc.     (c)  The 

quantity  of  heat  emitted  by  persons  is  ordinarily  not  of  sufficient  importance 
to  be  taken  into  account,  except  in  cases  of  assembly-halls  and  theaters.  The 
following  allowances  may  be  made  when  required: 

(i)  Persons: 

Man  at  rest 400  Btu  per  hour 

Man  at  work 500  Btu  per  hour 

The  heat  introduced  by  lights  is  as  follows: 

■  ;r  t  • 

,(2)  Lights: 

Electric  lamps: 

Btu  per  hour  equals  watts  per  lamp  X  number  of  lamps  X  3415 

Gas-lighting: 

I  cu  ft  producer  gas 150  Btu 

I  cu  ft  illuminating  gas 700  Btu 

I  cu  ft  natural  gas i  000  Btu 

'A  Welsbach  burner  averages  3  cu  ft  of  gas  per  hour  and  a   fish-tail  burner 
cu  ft  per  hour. 

(3)  Motors.  Motors  and  the  machinery  which  they  drive,  if  both  are  located 
in  the  room,  convert  all  of  the  electrical  energy  supplied  into  heat,  which  is 
retained  in  the  room  if  the  product  being  manufactured  is  not  removed  until  its 
temperature  is  the  same  as  the  room-temperature. 

(4)  Machinery.  If  power  is  transmitted  to  the  machinery  from  the  outside, 
then  only  the  heat-equivalent  of  the  brake  horse-power,  d.h.p.,  supplied  is  used. 

In  the  first  case  the 

^  ,.    ,         ,  motor  horse-power  ^ 

Btu  supplied  per  liour  =  --,  . . X  2  546 

elnciency  of  motor 

and  in  the  second  case 

Btu  per  hour  =  d.h.p.  X  2  546 

in  which  2  546  is  the  Btu  equivalent  of  i  horse-power  hour.  In  high-powered 
mills  this  is  the  chief  source  of  heating  and  is  sometimes  sufficient  to  overheat 
the  building  even  in  zero  weather,  thus  requiring  cooling  by  ventilation  the  year 
round. 

Short  Rules  for  Estimating  the  Heat-Loss  of  Buildings.  There  is 
a  great  variety  of  ruli:-of-thumb  methods  for  estimating  the  heat-loss  // 
for  proportioning  the  heating-surface  required  when  direct  radiation  is  to  be 


1262 


Heating  and  Ventilation  of  Buildings 


Parts 


used.  These  so-called  practical  rules  are  intended  to  be  based  on  average 
building-construction  and  on  the  ratio  of  wall  and  glass-surface  to  the  cubical 
contents  as  found  in  buildings  of  the  class  to  which  they  refer.  These  rules 
when  modified  for  unusual  conditions  and  appHed  by  engineers  of  long  experi- 
ence in  the  proportioning  and  design  of  heating  systems  produce  satisfactory 
results.  They  are,  however,  rapidly  being  discarded  except  as  rough  checks 
on  the  more  refined  methods  of  calculation. 

Carpenter's  Rule.     The  following  formula,  or  rule,  which  has  been  widely 
used  for  many  years  in  this  country,  was  proposed  by  R.  C.  Carpenter.    It  is 


SECOND  FLOOR 
Fig.  9.  Floor-plans  and  Section  of  Building  Explained  in  Table  VII.    (See,  also,  Fig.  34) 

not  intended  to  be  applied  to  buildings  covered  with  corrugated  sheet  steel  or 
metal  lath  and  plaster  walls,  unless  the  wall-constant  is  changed  to  suit  the  con- 
dition. 

By  reference  to  Table  IV,  it  will  be  noted  that  a  fair  average  value  for  the 
heat-transmission  of  the  usual  well-constructed  building-wall  is  approximately 


Estimating  Heating  Requirements  of  Buildings  1263 

Table  VII.     Tabulation  of  Heat-Losses  for  Building  Shown  in  Fig.  9. 


Room- 
designation 

Net  volume, 
cu  ft 

Net  wall-area, 
sq  ft 

Floor  or 

ceiling, 

sq  ft 

Glass-area, 
sq  ft 

I 

2 

3 

4 

5 

First  floor: 
Sample-room. 

Hall 

Laboratory.  . 

Office 

Toilet 

Second  floor: 
Mgr's  office.  . 

Hall 

Gen'l  office .  . 
Sup't's  office.. 

10  o8o 

2  595 
4  320 

2  520 

900 

4320 

2  595 

10  080 

4320 

852 

99 
378 
288 

90 

393 
119 

852 
393 

864 
216 
360 
210 
75 

360 
216 
864 
360 

180         ' 
45        "' 
90 
60 
30 

75 

25 

150 

75  :  jii  1  • 

Totals 

41  730 

3464 

730 

Room- 
designation 

Transmission-loss, 
Btu  per  hour 

Infiltration  loss, 
Btu  per  hour 

Total 
heat- 
loss, 
Btu  per 
hour 

a 

Wall-loss 

19.7  X 

col.  3 

Floor  or 
ceiling- 
loss, 
13.  X  col.  4 
18.8  X  col.  4 

Glass- 
loss, 
78.8  X 
col.  5 

Assumed 
no.  air- 
changes 
per  hour 

Infiltra- 
tion-loss, 
1.26  Xcol. 
2  Xcol.  9 

I 

6 

7 

8 

9 

10 

II 

First  floor: 
Sample-room. 

Hall 

Laboratory.  . 

Office 

Toilet 

Second  floor: 
Mgr's  office.  . 

Hall 

Genl.  office.  . 
Sup't's  office. 

16  784 
I  950 
7  446 
5  674 

1  773 

7  742 

2  344 
16  784 

7  742 

II  232 

2  808 

4  680 

2  730 

975 

6768 
4  061 
16  243 

6  768 

14  184 
3  556 
7  112 
4728 
2  364 

5  910 

I  970 

II  820 

5  910 

I 
3 
2 
2 
2 

2 
3 

•      2 

12  700 

10  809 

10  886 

6350 

2  268 

10  886 
10  809 
25  400 
10  886 

54900 
19  123 
27358 
19  482 
7380 

31  306 

19  224 
70  247 
31  306 

Totals 

100  OQA 

280  326 

0.25  Btu  and  for  glass  i.o  Btu  per  degree  difference  between  the  inside  and  out- 
side temperature  per  hour. 

Professor  Carpenter  states  that  usually  we  may,  with  sufficient  accuracy, 
neglect  all  inside  walls,  floors  and  ceilings  and  consider  only  the  outside  walls. 

The  estimated  number  of  air-changes  per  hour,  by  infiltration,  has  already 
I  been  given  in  Table  VI. 


1264  Heating  and  Ventilation  of  Buildings  Part  3 

Let  C  =  cubical  contents  of  room  in  cubic  feet; 

n  =  number  of  air-changes  per  hour  (see  Table  VI) ; 
0.02  =  Btu  to  raise  i  cu  ft  of  entering  air  i°  F.; 
W  =  net  wall-surface  in  square  feet; 
G  =  glass-surface  in  square  feet; 
(/  —  h)  =  temperature-difference  between  inside  and  outside; 
H  =  total  heat  to  be  supplied  per  hour  in  Btu; 
11  =  (o.o2«C  +G  -\-  }iW)  it  -  /o). 

Calculating  the  Heat-Loss  of  a  Building.  The  following  example  (Table 
VII)  will  serve  to  illustrate  the  method  employed  in  calculating  and  tabulating 
the  heat-loss  of  a  typical  building,  the  floor-plans  and  section  being  shown  in  Fig. 
9.  (See,  also,  Fig.  34.)  The  heating  requirements  are  for  a  temp)erature  of  70°  F. 
in  zero  weather.  The  heat-transmission  for  the  outside  walls  per  square  foot 
is  taken  from  Table  IV  for  a  temperature-dilTerence  of  70°.  The  heat-loss 
through  the  first  floor  is  based  on  a  temperature-difference  of  70—35  or  35°. 
The  heat-transmission  per  square  foot  per  1°  difference  in  temperature  per 
hour  for  i^^-in  wood  is  0.37;  hence  for  35°  it  is  0.37  X  35  =  13  Btu  per  hour. 
The  heat-loss  through  the  ceihng  of  the  second  floor  is  based  on  a  temperature- 
difference  of  70  —  23  =  47°,  23°  being  the  assumed  temperature  of  the  attic 
in  zero  weather.  The  heat-transmission  per  square  foot  per  hour  is  therefore 
47  X  0.40  =  18.8  Btu.  The  infiltration-loss  is,  in  this  example,  based  on  an 
estimated  number  of  air-changes  per  hour  as  indicated  in  Table  VII. 

By  Carpenter's  rule  the  heat-loss  of  this  building  based  on  two  air-changes 
per  hour,  is 

[0.02  X  2  X  41  730  +  (3  464/4)  +  730]  X  70  =  228  564  Btu  per  hour 

Radiation 

Direct  Radiation.  Steam  or  hot-water  radiators  placed  in  the  room  to  be 
heated  are  termed  direct  radiators  or  direct  radiation.  Common  types 
of  direct  radiators  are  shown  in  Figs.  10,  11,  12  and  13. 

Indirect  Radiation.  Radiators  used  to  warm  the  air  passed  over  them,  the 
heating  of  the  building  being  accomplished  by  hot  air,  are  termed  indirect 
radiators  or  indirect  radiation.  (See  Figs.  45  and  46.)  This  type  of 
radiation  is  frequently  used  for  installations  in  which  provision  must  be  made 
for  ventilation  as  well  as  heating,  as  in  the  case  of  schools,  public  buildings,  etc. 
Indirect  radiation  is  also  used  to  some  extent  in  high-grade  residence-heating 
where  direct  radiation  may  be  thought  unsightly,  particularly  for  the  first  floor. 
Direct  radiation  is  ordinarily  employed  for  the  floors  above  the  first  floor.  The 
principal  use  of  indirect  radiators  is  in  connection  with  the  hot-blast  system 
of  heating,  described  later,  in  which  a  fan  is  used  to  circulate  the  air  over  the 
radiator  and  through  the  duct  system. 

Direct-Indirect  Radiation.  Direct-indirect  radiators  (Fig.  14)  arc 
radiators  placed  in  the  rooms  to  be  heated  and  furnished  with  a  cold-air  con- 
nection through  the  outside  wall.  It  serves  the  purpose  of  providing  tem- 
pcred-air  ventilation. 

Materials  and  Connections  of  Radiators.  Radiators  are  constructed  of 
cast  iron,  pressed  steel  or  pipe-coils.  The  sections  for  one-pipe  steam  systems 
are  connected  only  at  the  bottom.  The  sections  for  hot-water  radiators  and 
two-pipe  steam  systems  are  connected  at  both  top  and  bottom.  The  latter 
is  known  to  the  trade  as  hot- water  radiation. 


Radiation 


12G5 


Pressure  in  Radiation.  Cast-iron  radiators  should  not  be  operated  above 
15  Ib-per-sq-in  pressure.  Standard  pipe-coil  direct  radiation  may  be  operated 
up  to  a  125-lb  pressure. 

Rating  of  Radiators.  Radiators  are  rated  according  to  the  square-foot  area 
of  external  heating-surface.  Cast-iron  and  prcsscd-steel  direct  radiators  are 
built  up  of  sections.  The  amount  of  heating-surface  per  section  of  cast-iron 
radiators  for  the  various  standard  heights  manufactured  is  given  in  Table  VIII. 


r*^^ 

r^ 

1  ' 

hi  ^ 

1  riM 

3) 

^. 

Fig.  10.     Rococo  Three-column  Radiator        Fig.  1 1.     Peerless  Three-column  Radiator 

New  Type  of  Direct  Cast-iron  Radiator.  The  American  Radiator  Com- 
pany has  recently  placed  on  the  market  a  new  type  of  direct  cast-iron  radiator 
termed  Corto.  Approximately  30%  more  heating-surface  for  a  given  floor-area  is 
obtainable  with  this  than  with  other  types  of  direct  radiation.  The  length  of 
each  section  is  2  in  and  the  width  8  in  for  all  heights. 

The  heating-surface  per  section  is  as  follows: 


42-in,  5  sq  ft 
2  7 -in,  3  sq  ft 


38-in,  4H  sq  ft 
23-in,  2M  sq  ft 


34H-in,  4  sq  ft 
193^-in,  2  sq  ft 


31-in,  33^  sq  ft 


Wall-radiation  (Fig.  12)  is  largely  used  in  bath-rooms,  and  also  for  factory- 
heating  where  the  width  of  column-type  radiation  is  objectionable.  (See 
Table  IX  for  rating  and  dimensions.) 

Pressed-Metal  Radiators.  These  radiators  have  been  developed  in  recent 
years,  and  are  most  ingeniously  fabricated  of  No.  20  United  States  standard- 
gauge  soft-iron  sheets  made  into  shapes,  widths  and  heights  which  correspond 
almost  exactly  with  the  cast-iron  column-radiators.  Each  section  is  made  up 
of  two  pressed  sheets  joined  by  a  double-lapped  seam  and  the  separate  sections 
are  connected  by  single-lapped  seams.  The  pipe-connection  is  made  into  a 
threaded   malleable-iron  ring  secured  to  the  end-section  by  rolling  the  sheet 


1266 


Heating  and  Ventilation- of  Buildings 

Table  VIII.     American  Direct  Radiators 

Heights,  widths,  lengths  and  heating-surfaces 


Parts 


Height  in  inches 


45 


38 


26 


23 


Peerless,  single-column,  steam  and  water. . 
Rococo,  single-column,  steam  and  water.  . 
Peerless,  two-column,  steam  and  water.  .  . 
Rococo,  two  column,  steam  and  water. .  .  . 

Verona,  steam  and  water 

Peerless,  three-column,  steam  and  water.  . 
Rococo,  three-column,  steam  and  water. .  . 
Peerless,  four-column,  steam  or  water.  .  .  . 

Rococo,  four-column,  steam  or  water 

Aetna  flue,  steam  or  water 

Italian  flue,  steam  or  water 

Rococo  window,  steam  or  water 


sH 


4H 


3 
3 


Height  in  inches 


16 


Length 
per 

section 

in 
inches 


Width 

of 
section 

in 
inches 


Peerless,  single-column,  steam  and  water. . 
Rococo,  single-column,  steam  and  water.  . 
Peerless,  two-column,  steam  and  water.  .  . 
Rococo,  two-column,  steam  and  water. .  .  , 

Verona,  steam  and  water , 

Peerless,  three-column,  steam  and  water.  . 
Rococo,  three-column,  steam  and  water. .  , 
Peerless,  four-column,  steam  or  water.  .  .  . 

Rococo,  four-column,  steam  or  water 

Aetna  flue,  steam  or  water 

Italian  flue,  steam  or  water.  .  .  . » 

Rococo  window,  steam  or  water 


iH^ 


4M 
3M 


2H 


2^ 
2K 

3 
3 
3 
3 

3 


4V2 
4K2 
TVs 
7H 
8 
9 
9 
loH 
10  H 
12H 
8H 


*  Peerless  15-in  in  steam  only. 

The  location  of  the  figures  in  the  above  columns  in  line  with  the  names  of  patterns 
of  radiators  indicates  the  heights  in  which  the  various  patterns  are  made.  The  figures 
themselves  represent  the  amount ;of  heating-surface  contained  in  each  section. 

To  obtain  the  total  length  of  the  radiator,  multiply  the  length  per  section  by  the  num- 
ber of  sections. 


Table  IX.     American  Rococo  Wall-Radiators 

Ratings  and  measurements  of  sections 


Section-numbers 

Length, 
in 

Width, 

in 

Thickness, 
in 

Thickness 
(with 

bracket), 
in 

Heating- 
surface. 

sq  ft 

S-A 

16^ 

213^ 
20  Mg 

13  Me 
13  Mo 

13  -yia 

2^ 
2Vs 

3^ 

3H 

5 
7 
9 

7-A  and  7-B .... 
9-A  and  9-B .... 

Radiation 


1267 


metal  snugly  over  a  suitable  flange  on  the  inner  face  of  the  ring.     Air-valve 
connections  are  made  in  a  similar  manner.    See  Fig.  13  and  Table  X.    These 


Fig.  12.     Typical  Installation  of  Rococo  Wall-radiators  in  Single  Tier  on  Adjustable 

Brackets 

radiators  are  light  in  weight  and  therefore  easy  to  handle  and  install,  and  cost 
less  for  freight  and  shipping  charges.     For  the  same  height,  width  and  area  of 


Fig.  13.     Presto  Single-column  Pressed  Metal  Radiator 

heating-surface  these  radiators  are  shorter  than  cast-iron  radiators,  being 
spaced  iH  instead  of  2H  in,  center  to  center  of  sections. 

Direct  Pipe-Coil  Radiation  is  largely  used  in  manufacturing  establishments 
and  is  usually  made  up  of  iM  or  i^-in  pipe  screwed  into  cast-iron  manifolds 
as  shown  in  Fig.  15. 

Heat-Emission  of  Direct  Radiation.  The  unit  heat-transmission  K,  or  the 
Btu  transmitted  by  one  square  foot  of  direct  radiation  per  hour  per  degree  dif- 


1268 


Heating  and  Ventilation  of  Buildings 


Pari  3 


Table  X.    Presto  Single-Column  Floor  or  Wall-Radiators  for  Steam  or  Water 
Each  section  is  4  H  in  wide.     Legs  spread  sH  in 


Number 

of 
sections 

Length  * 
iy2  in 

per 
section 

j-surface  i 

Heating 

n  square  feet 

32  in 
high 

26  in 
high 

23  in 
high 

20  in 
high 

17  in 
high 

14  in 
high 

2  sq  ft 

per 
section 

I  5  sq  f  t 

per 
section 

l.3sqft 

per 
section 

I.I  sqft 

per 
section 

0.9  sq  ft 

per 

section 

0.7  sq  ft 

per 
section 

4 
5 
6 
7 
8 
9 
10 

6 

7H 

9 

10  H 
12 

13  H 
15 

8 
10 
12 
14 
16 
18 
20 

6.0 
7.5 
9.0 
10.5 
12.0 
13. 5 
ISO 

5.2 

6.5 

7.8 

9.1 

10.4 

II. 7 

13.0 

4.4 
5. 5 
6.6 
7.7 
8.8 
9.9 
II  .0 

3.6 
4.5 
5-4 
6.3 
7.2 
8.1 
9.0 

2 
3 

4 
4 
5 
6 

7 

8 
5 
2 
9 
6 
3 

0 

*  Length  of  radiator  over  all,  including  malleable-iron  hubs.    Add  %  in  for  each  bushing. 
Legs  are  detachable  and  can  be  applied  to  any  section. 
These  radiators  are  tapped  i  H  in  and  bushed  as  specified. 

ference  between  the  heating-medium  and  the  temperature  of  the  air  in  the  room, 
varies  somewhat  with  the  type  of  radiator,  height,  temperature,  etc. 


Fig.  14.    Direct-indirect  Radiator-installation 

Coefficients  of  Transmission  for  Direct  Steam-Radiators.  Tatle  XI 
is  based  on  the  average  performance  of  direct  steam-radiators  standing  exposed 
in  still  air  at  70°  F.  with  steam  at  220°  F.,  or  2 -lb  pressure,  with  a  standard 


Radiation 


1269 


temperature-difference  of   150°.     In  order  to  apply  the  coertidents  given  in 
Table  XI  to  conditions  other  than  standard,  it  is  only  necessary  to  know  the 


Pipe-Coil  Radiators  and  Connections 


Air-Valve  CSteam) 

[jBushinff 


Air-Vial  ye 
for  Watei  \ 


Branch-Tee 


A.V.CAlter- 
native^ 

Union 

Check-Valve 


^^iC 


-  Expansion-Bolts  - 


Steel  or  W.I.  Pipes 


— Hook-Platea  ~ 


fastened  to  Walls 


R.  *n(]  I 


^  Jb 


■/ 


I 
I 

I  Reducing- 
I  I  Elbow         R. 

?  I  Union^- 


Dirt-Pocket 
(Capped)       Radiator  for  Two-Pipe  Low-Pressure 

Steam-System.  Air-Valve  her© 

I       Plug    yfo*-  Water 


Radiator  for  Two-Pipe 
Vacuum  Steam-System,  Divided  Surface. 
Table 


/ 


Branch-Tees 
(Crane  Co.) 


Run 
Open 


Inlet 
Open 


Run 
Open 


N0.2  For  Circulation     I  Closea,' 


Outlet  Open 

Closed  \\       No.  r.  for  Bos_Colls_Jl  Cloned 
Inlet  Open  f.^ 

Order  bj  Size  and  Numbet 

Linear  Feet  oflPipe  perP'KS. 
2.9'  of  1  -^  Pipe=l=^'n.S. 
2.3'      of.      Vj"   "    =  1°'II.S. 

2.0'    of    iV/  "  ■=  i°'n.s. 

1.6'     of      2"      "    ^  1^'H.S. 


1"  Branch-Tees 

1J4"  Branch-Tecs, 
3"c-c 

IH"  Branch-Tees, 

3H"c-c 

2"  Branch-Tees, 
VA"  c-c 

RUDB 

Runs 

Runs 

Runs 

\"-vA"\m" 

2" 

i 
1K"-1M"|  2"  2J^" 

VA"-2" 

2H" 

3" 

2" 

2H"-3" 

VA" 

No.  of  Branches 

No.  of  Branches 

No.  of  Branches 

No.  of  Branches 

2  to 
9 

2to  2to 
16     16 

3  to 
16 

3  to 
16 

3to 
16 

3to 
12 

3to 
12 

3to 
12 

3  to 
10 

3to 
10 

3to 
10 

Inside  Diama. 

Inside  Diams. 

Inside  Diams. 

Inside  Diams. 

m' 

2%" 

2y," 

2H'"' 

2H" 

2y/' 

2Ji"-  |2>/i" 

2%" 

m" 

3J4" 

3H" 

Notes.  Ail  openings  in  Branch-Tees  for  circulation  are  tupped 
right  hand. 

Branch-Tees  for  Box  Coils  are  always  tapped  left  hand  in 
branches  and  right  hand  in  back  inlet. 

The  run  and  back  opouiuKa  of  Branch-Tees  are  tapped  the 
same  siie  as  branches,  imless  otherwise  ordered. 


Fig.  15.     Pipe-coil  Radiation-data 

Variation  in  K  for  a  given  increase  or  decrease  in  the  temperature-range  above 
or  below  150°,  the  standard  range.     An  examination  of  test-data  so  far  avail- 


1270 


Heating  and  Ventilation  of  Buildings 


Parts 


able  seems  to  indicate,  that  this  variation  Is  nearly  0.2%  per  degree  above  or 
below  the  standard  range  of  150°.  Thus,  if  a  three-column,  38-in  high,  direct 
radiator  is  to  be  used  in  a  room  kept  at  60°  F.,  with  steam  at  230°,  we  would 
have  a  temperature-range  of  170°  or  20°  above  standard,  and  the  value  of  K 
would  become 

K  =  (1.55  +  0.002  X  20  X  1.5s)  =  i-6i 
and  each  square  foot  of  radiation  would  give  off  1.61  X  170  =  274  Btu  per  hr. 

Table  XI.     Values  of  K  for  Direct  Radiators 


Type  of  radiator 

Height  of  radiator 

32  in 

38  in 

20  and 
22  in 

26  in 

1.9s 
1.80 
1.70 
1 .60 

1.85 
1.9s 
1.90 
2.00 

1.90 
I. 75 
1.65      . 
I. 55 

1. 85 
1.70 
1.60 
1.50 

1.80 
1.6s 
1.55 
1.4s 
1.57* 

Two  columns                 

Four  columns                  .   . 

Flue,  42  sq  ft 

Window                                .    .  . 

Wall  (horizontal) 

Wall  (vertical) 

Pipe-coils 

•  Air  entering  flues  at  70°  F.  and  leaving  same  at  152°  F.     Allen, 
/([■increases   (i)  as  height  of   radiator   is  reduced   and  (2)  as  number  of  columns  or 
width  of  radiator  decreases. 

Coefficients  of  Transmission  for  Direct  Hot- Water  Radiators.  Table  XI 
may  be  used  for  values  of  K  for  hot-water  radiators  of  the  same  type  as  there 
listed,  but  allowance  should  be  made  for  the  lower  temperature-range  in  hot- 
water  heating.  Thus,  with  a  room  usually  at  70°  F.,  and  water  at  180°  entering 
and  at  160°  leaving  the  radiator,  the  temperature-range  is  only  100°,  or  50°  less 
than  the  standard  range.  Then  for  a  two-column  26-in  high  direct  radiator,! 
the  value  of  K  becomes 

K  =  (1.75  -  0-002  X  50  X  1.75)  =  1-58 
and  each  square  foot  of  this  radiation  gives  off,  1.58  X  100  =  158  Btu  per  hr. 

Concealed  Radiators.  The  effect  of  placing  a  grill  in  front  of  a  direct 
radiator,  with  a  cover  over  the  top,  reduces  the  heat-emission  by  approximately 
20%.  A  clear  space  between  the  radiator,  wall  and  enclosure  should  not  be 
less  than  2H  in.  Concealed  radiators  are  not  looked  upon  with  favor  from  a 
strictly  sanitary  point  of  view. 

The  Usual  Assumptions  Made  for  the  He?.t-Transmission  of  Direct 
Radiation  is  250  Btu  per  sq  ft  per  hr  for  low-pressure  steam  (2  lb)  cast-iron  tadi- 
ators,  and  150  Btu  per  sq  ft  per  hr  for  cast-iron  hot-water  radiators  with  the 
water  at  180°.  The  square-foot  rating  of  heating-boilers  is  based  on  the  above 
figures.  For  more  exact  values  use  the  data  given  in  Table  XI.  Accordingly, 
a  hot- water  installation  requires  66%%  more  radiation  than  a  low  pressure 
steam  system. 

Example.  It  is  required  to  determine  the  amount  (R)  of  direct  cast-iron 
radiation,  low-pressure  steam  and  hot  water,  to  supply  a  heat-loss  of 

//  =  10  000  Btu  per  hr 

I 


Fuels  and  Combustion 


1271 


Solution.    For  the  direct  steam  system 


R  -  11/250  =  40  sq  ft 

and  for  a  direct  hot-water  system 

R  =  n/150  =  66M  sq  ft 

If  a  three-column  cast-iron  radiator,  38  in  high,  is  to  be. used,  the  heating-surface 
of  which  is  5  sq  ft  per  section,  it  will  require  40/5  =  8  sections  for  the  steam-job, 
making  the  length  of  radiator  equal  to  8  X  2  3^^  =  20  in. 

Fuels  and  Combustion 

Classification  of  Fuels.  Fuels  are  generally  classified  as  solid,  liquid,  and 
gaseous.  Solid  fuels  are  coal,  wood,  and  wastes.  Liquid  fuels  are  petroleum 
and  its  products.     Gaseous  fuels  are  natural  and  artificial  gas. 

Coal-Fields  in  the  United  States.  Most  of  the  anthracite  is  found  in  beds 
of  less  than  500  sq  miles  in  area  located  in  eastern  Pennsylvania.  The  prin- 
cipal deposit  of  semibituminous  coal  is  about  300  miles  long  by  20  miles  wide 
and  lies  along  the  eastern  edge  of  the  Northern  Appalachian  field.  The  bitumi- 
nous coals  extend  from  this  deposit  westward.  A  little  graphitic  coal  is  found 
in  Rhode  Island. 

Composition  of  Coal.  The  uncombined  carbon  in  coal  is  known  as  fixed 
CARBON.  Some  of  the  carbon-constituent  is  combined  with  hydrogen,  and  this, 
together  with  other  gaseous  substances  driven  off  by  the  application  of  heat, 
form  that  portion  of  the  coal  known  as  the  volatile  matter.  The  fixed  carbon 
and  the  volatile  matter  constitute  the  combustible.  The  oxygen  and  nitrogen 
contained  in  the  volatile  matter  are  not  combustible,  but  custom  has  applied 
this  term  to  that  portion  of  the  coal  which  is  dry  and  free  from  ash,  thus  includ- 
ing the  oxygen  and  nitrogen  in  the  combustible. 

Classification  of  Coals.  Coals  may  be  classified  according  to  the  percentages 
of  fixed  carbon  and  volatile  matter  contained  in  the  combustible. 

Table  XII.     Classification  of  Coals  (Kent) 


Name  of  coal 

Percentages  of  combustible 

Btu  per  pound 

of  combustible 

Fixed  carbon 

Volatile  matter 

Anthracite 

97.0  to  92.5 
92.5  to  87. 5 
87. 5  to  75.0 
75.0  to  60.0 
65.0  to  50.0 
50.0  and  under 

3.0  to    7.5 
7.5  to  12. s 
12. 5  to  25.0 
25.0  to  40.0 
350  to  50.0 
So.o  and  over 

14  600  to  14  800 

14  700  to  IS  500 

15  500  to  16  000 
14  800  to  15  300 
13  500  to  14  800 
II  000  to  13  500 

Semianthracite   .... 
Semibituminous  .  .  . 
Bituminous,  East. .  . 
Bituminous  West. .  . 
Lignite. 

Calorimetric  Determinations.  The  only  accurate  and  reliable  way  to  deter- 
mine the  heating- value  of  a  fuel  is  to  do  so  experimentally  with  a  calorimeter. 
For  soUd  fuels,  the  bomb-calorimeter  is  the  most  practical.  The  various  types 
On  the  market  include  the  Mahler,  the  Hempel,  the  Atwater  and  the  Emerson. 
These  consist  essentially  of  a  tight  vessel  containing  a  weighed  sample  and  oxygen 
Under  pressure.  This  receptacle  is  placed  within  another  vessel  containing  a 
known  weight  of  water  and  surrounded  by  heat-insulating  material  to  minimize 


1272 


Heating  and  Ventilation  of  Buildings 


Parts 


radiation  The  sample  is  exploded  electrically,  and  the  heat  absorbed  by  the 
surrounding  water  is  determined  by  means  of  a  very  accurate  thermometer 
reading  hundredths  of  a  degree.  Correction  has  to  be  made  for  the  heat  ab- 
sorbed by  the  instrument  itself,  and  for  radiation. 

For  a  complete  description  of  calorimeters  and  their  use,  see  Carpenter  and 
Diederichs'  Experimental  Engineering. 

Calorific  Value  by  Formula.  The  following  expression,  known  as  Du  Long's 
FORMALA  for  hcating-value  per  pound  of  coal,  can  be  used  if  the  ultimate 
chemical  analysis  of  the  fuel  is  known: 

F  =  14  600  C  +  62  GOO  (5  -  VsO)  +  4  000  5 

where  C,  H,  0,  and  S  represent  the  proportionate  parts  of  each  element  per  i  lb 
of  fuel,  and  F  denotes  the  heat- value  in  Btu  per  pound  due  to  combustion. 
This  formula  does  not  apply  when  the  fuel  contains  carbon  monoxide,  CO,  but 
can  be  made  to  apply  by  adding  a  term,  10  150  C,  in  which  C  is  the  proportionate 
part  of  carbon  burned  to  the  monoxide. 

Example.  The  application  of  the  formula  to  a  coal  of  ultimate  analysis  as 
here  given  follows: 

Analysis  (based  on  fuel  as  received) 


c 

74-79% 

H 

4.98 

0 

6.42 

N 

1.20 

S 

3-24 

H2O 

1.55 

Ash 

7.82 

100.00% 

Then  by  Du  Long's  formula,  14  600  X  0.7479  +  62  000  (0.0498  —  0.0642/8) 
H-  4  000  X  0.0324  =  13  650  Btu  per  i  lb  of  coal. 

A  bomb-calorimeter  test  showed  13  480  Btu  for  this  coal.  The  formula  fails 
to  allow  for  evaporating  and  superheating  the  moisture  present  in  the  fuel. 

Combustion  of  Fuel.  Combustion,  as  used  in  steam-engineering,  signifies  a 
rapid  chemical  combination  between  oxygen,  and  the  carbon,  hydrogen,  and 
sulphur  composing  the  various  fuels.     This  combination  takes  place  usually  at 

Table  XIII.    Theoretical  Amount  of  Air  Required  for  Combustion 


Fuel 

Composition  by  weight 

Lb  of 

air  per 

lb  of 

fuel 

%c 

%H 

%o 

Wood-charcoal 

93.0 
80. 0 
94-0 
91.5 
87.0 
70.0 
58.0 
So.o 
85.0 

3.5 
so 
SO 
6.0 
6.0 
13.0 

2!6"' 

4.0 
20.0 
31.0 
43-5 
i.o 

II. 16 

9.6 

10.8 

II. 7 

II. 6 

8.9 

7.68 

6.00 

14.30 

Peat-char  oal 

Coke 

Anthracite  coal. 

Bituminous  coal,  dry..  ..... 

Lignite. 

Peat,  dry 

Wood,  dry 

Mineral  oil 

Steam-Heating  Boilers  and  Hot- Water  Heaters 


1273 


high  temperature  with  the  evolution  of  light  and  heat.  The  substance  com- 
bining with  the  oxygen  is  known  as  the  combustible,  and  if  it  is  completely 
burned  or  oxidized  the  combustion  is  perfect,  that  is,  no  more  oxygen  can  be 
taken  up  by  the  products  of  the  reaction.  The  combustion  is  imperfect  or 
incomplete  when  carbon  burns  to  form  carbon  monoxide,  CO,  instead  of  the 
dioxide,  CO2,  since  the  former  may  be  further  burned  to  form  carbon  dioxide  if 
the  necessary  oxygen  is  supplied.  It  is  necessary  to  provide  for  an  excess  of  air 
when  burning  coal  under  either  natural  or  forced  draft,  amounting  to  approxi- 
mately 50  to  100%  of  the  net  calculated  amount,  or  about  18  to  24  lb  per  lb  of 
coal.  Less  air  results  in  imperfect  combustion  and  smoke,  while  an  excess  cools 
the  fire  and  setting  and  carries  away  a  large  percentage  of  the  heat  in  the  flue- 
gases. 

Table  XIV.     Weight  and  Calorific  Value  of  Various  Gases  at  32  Degrees  Fahren- 

heit  and  Atmospheric  Pressure,  with  Theoretical  Amount  of  Air 

Required  for  Combustion 


Gas 

Symbol 

Cubic  feet 

of  gas 
per  pound 

Btu 

Cubic  feet 

of  air 

required 

per  cubic 

foot  of  gas 

Per 
pound 

Per  cubic 
foot 

Hydrogen 

Carbon  monoxide. .  . 

Methane 

Ethane 

Ethylene .  ,    .  . 

H 

CO 

CH4 

C2H6 

C2H4 

C2H2 

178.0 
12.81 
22.4 
12.0 
12.8 

13.79 

62  000 
4380 
23  842 
22  400 
21  430 
21  430 

348 
342 
I  065 
I  86s 
I  67s 
I  555 

2 .  408 

2.388 

9. 57 

16.74 

14.33 

11.93 

Acetylene 

Fuel-Storage.  Space  for  fuel-storage  must  be  based  on  fuel -consumption  per 
season  as  estimated  under  Fuel-Consumption,  page  1278,  and  in  government 
buildings  it  is  customary  to  proportion  the  storage-space  on  the  basis  of  8  sq  ft 
of  floor-area  per  ton,  the  storage-space  being  made  ample  to  hold  an  entire 
season's  supply. 

The  following  volumes  per  ton  of  2240  lb  of  coal  are  given  for  proportioning 
storage-space:  bituminous  coal,  41  to  45  cu  ft,  and  may  run  as  high  as  49  cu  ft; 
anthracite  coal,  34  to  41  cu  ft;  charcoal,  123  cu  ft;  coke,  70.9  cu  ft. 

This  is  based  on  fuel  broken  down  ready  for  market.  Also  i  bushel  hard 
coal  =  86  lb  and  i  bushel  soft  coal  =  76  lb. 


Steam-Heating  Boilers  and  Hot- Water  Heaters 

Pressures,  Attention,  and  Materials.  Heating-boilers  usually  operate  under 
much  lower  pressure  than  do  power-boilers,  and  in  most  cases  receive  far  less 
attention.  The  steam-boilers  are  usually  designed  to  operate  on  from  2  to  5  LB 
steam-pressure,  and  the  water-boilers  or  hot-water  heaters  are  seldom  sub- 
jected to  a  hydrostatic  head  in  excess  of  100  ft  when  in  operation.  The  atten- 
tion given  these  boilers  is  of  such  an  intermittent  characti^.r  that  they  must 
carry  the  heating-load  for  comparatively  long  periods  without  firing.  These 
periods  may  range  from  6  to  10  hrs  and  in  consequence  the  combustion-rate  is 
low,  and  relatively  large  grates  and  fire-pots  are  necessary.  The  materials 
employed  for  constructing  heating-boilers  are  cast  iron,  especially  for  the 
smaller  sizes,  although  boilers  of  nearly  100  equivalent  steam-boiler  horse- 
power (see  Rating  of  Heating-Boilers)  are  made  of  this  same  material;    and 


1274  Heating  and  Ventilation  of  Buildings  Part  3 

STEEL  or  WROUGHT  IRON,  which  are  more  generally  used  in  the  larger  sizes.  The 
government  departments  usually  specify  steel  heating-boilers,  and  they  are  used 
extensively  in  oflSce  and  loft-buildings  as  well. 

Boiler  Heating-Surface.  The  capacity  of  any  boiler  or  water-heater  depends 
on  the  amount  of,  and  the  temperatures  on  the  opposite  sides  of,  the  heat- 
transmitting  surfaces  in  contact  with  the  water  in  the  boiier  on  one  side,  and  the 
fire  or  hot  gases  on  the  other.  It  is  most  important  that  a  rapid  circulation  of 
water  and  the  hot  gases  shall  take  place  over  these  surfaces,  and  preferably  in 
opposite  directions.  Two  kinds  of  surface  are  distinguished  in  boiler-practice, 
and  known  as  direct  and  indirect  surface.  Direct  surface  is  that  on  which 
the  fire  shines,  and  indirect  that  in  contact  with  the  flue-gases  only.  All  such 
surface  must  have  water  on  the  opposite  side.  In  some  boilers  the  hot  gases 
are  allowed  to  come  in  contact  with  the  boiler-surface  above  the  water-line 
so  that  there  is  only  steam  in  contact  with  this  surface  on  the  inner  side.  Such 
surface  is  known  as  superheating-surface  in  order  to  distinguish  it  from 
ordinary  heating-surface.  Direct  surface  is  the  more  valuable  of  the  two,  per 
square  foot,  as  it  is  usually  subjected  to  a  higher  temperature,  and  furthermore 
because  the  intensity  of  radiation  from  an  incandescent  surface  appears  to  vary 
as  some  power  of  the  temperature  of  that  surface,  either  the  third  or  fourth. 

Equivalent  Evaporation.  The  equivalent  evaporation  of  a  boiler  is  the 
pounds  of  water  the  boiler  would  evaporate  per  pound  of  coal  burned  if  it 
received  the  feed-water  at  212°,  and  evaporated  it  into  steam  at  this  same  tem- 
perature and  pressure,  so  that  the  evaporation  would  take  place  from  and  at 
212°  F.  In  practice  the  feed- water  is  usually  below  this  temperature  and 
evaporation  actually  takes  place  at  some  higher  temperatrue  than  212°.  Hence, 
to  find  the  equivalent  evaporation  it  is  always  necessary  to  make  use  of  the 
following  relation: 

(X2r2  -\-  Qi  —  q\) 


.971-7 


X  P 


where  the  fractional  part  of  the  expression  is  known  as  the  factor  of  evap- 
oration;  so  that 

E  =  factor  of  evaporation  X  P 

E  =  equivalent  evaporation  from  and  at  212  **  F.,  in  pounds; 
X2  =  quality  of  steam  as  actually  evaporated; 
r2  =  latent  heat  of  steam  as  actually  evaporated; 
52  =  heat  of  the  liquid  as  actually  evaporated; 
^1  =  heat  of  the  Hquid  as  actually  fed  to  boiler; 
P  =  actual  evaporation  in  pounds  per  pound  of  fuel  burned; 
971 . 7    =  latent  heat  of  steam  at  212°  F. 

Boiler  Horse-Power.  A  boiler  horse-power  is  the  energy  required  to  evap- 
orate 34.5  lb  of  water  at  212°  F.  into  dry  steam  of  212°  F.,  or 

971-7  X  34-5  =  33  S24  Btu 
The  horse-power  rating  of  a  boiler  is  always  measured  in  terms  of  the  equivar  I 
lent  evaporation.     Thus,  if  we  divide  the  equivlaent  evaporation  of  a  boiler  I 
by  34-5  we  get  the  boiler  horse-power  developed. 

Boiler-Efficiencies.  Heating-boilers,  operate  i  at  their  rated  capacity,  will  | 
show  an  efficiency  of  from  55  to  65%.  This  efficiency  is  the  ratio  of  heat  I 
absorl^ed  per  pound  of  dry  coal  by  the  water  and  SLcam  in  the  boiler  to  the  actuaJ 
heat-value  of  one  pound  of  the  coal,  and  is  the  combined  efficiency  of  the 
boiler  and  furnace. 


Steam-Heating  Boilers  and  Hot-Water  Heaters 


1275 


Rates  of  Combustion  for  Heating-Boilers.     Combustion-rates  for  varying 
sizes  of  grates  are  given  in  Table  XV: 

Table  XV.    Combustion-Rates 


Grate-areas 

Coal  per  square 

foot  per  hour,  in 

pounds 

Remarks 

6  sq  ft  or  less 

(small), 

6-10  sq  ft 

(medium), 

10  sq  ft  or  larger 

(large), 

5 

6.6 

A  variation  of  io%  up  or  down 
from  these  rates  is  perfectly  safe. 
The  higher  values  are  for  full-sized 
chimneys  with  lined  flues  and  the 
lower  for  unlined  flues  or  long 
breeching-connections. 

4  to     8  sq  ft 
10  to  i8  sq  ft 
20  to  30  sq  ft 

4 
6 

10 

(Am.  Soc.  H.  and  V.  E.  Com.  1909.) 
Rates  of  combustion  reported  for 
anthracite  coal,  as  fired  in  inter- 
nally fired  heating-boilers.  See 
Transactions  for  further  details. 

Rating  of  Heating-Boilers.  Standard  Conditions.  It  is  the  general  cus- 
tom of  American  manufacturers  of  heating-boilers  to  rate  their  boilers  in  terms 
of  the  number  of  square  feet  of  standard  direct  cast-iron  radiating-surface  which 
the  boiler  is  capable  of  supplying  under  the  following  conditions: 

(i)  Steam  boilers;   steam-pressure  2-lb  gauge  at  boiler. 

(2)  Hot- water  boilers;  water- temperatures:  180°  F.  leaving,  and  i6o**  F, 
entering  boiler. 

(3)  Fuel;   anthracite  coal  of  stove-size. 

The  RATE  OF  COMBUSTION,  or  amount  of  coal  necessary  per  hour  for  the  boiler 
to  develop  its  rating  has,  until  recently,  seldom  been  given;  and  the  method  of 
determining  the  rating  has  varied  with  different  makers  and  is  seldom  stated. 
Moreover,  it  is  possible  for  a  boiler  to  be  placed  on  the  market  and  assigned  a 
certain  rating  although  such  rating  has  never  been  actually  checked  by  test. 
It  therefore  becomes  most  important  to  not  only  establish  standard  conditions 
FOR  rating-tests,  but  to  require  the  manufacturer  to  be  in  a  position  to  pro- 
duce certified  test-sheets  of  such  tests  for  his  line  of  boilers.  The  standard 
conditions  under  which  a  boiler  should  be  tested  to  develop  its  rating  are  gen- 
erally understood  by  the  manufacturers  at  the  present  time  to  be  as  follows: 

(i)  Pressure,  temperature  and  fuel  as  stated  above. 

(2)  Fuel-capacity  to  be  sufficient  to  carry  the  boiler  from  6  to  8  hr  on  one 
charge  and  leave  20%  reserve  for  igniting  fresh  charge. 

(3)  Draft  of  sufficient  intensity  to  burn  the  fuel  at  the  required  rate.  A 
chimney  n^t  less  than  40  ft  in  height  is  recommended. 

(4)  Each  square  foot  of  direct  cast-iron  radiation  has  a  transmission-value  of 
250  Btu,  and  150  Btu  per  hour  for  steam  and  water-radiators  respectively. 

(5)  The  condensation  from  steam-radiators  returns  to  the  boiler  at  the  same 
temperature  as  the  steam,  or  without  loss  of  heat,  so  that  the  boiler  simply  sup- 
plies the  latent  heat  of  evaporation  at  2  lb  pressure,  or  967  Btu  per  lb  evaporated. 

(6)  The  water  from  hot-water  radiators  returns  to  the  boiler  at  160°,  allowing 
a  20°  drop  in  the  radiators,  so  that  there  is  no  loss  in  temperature  allowed  in 
the  return-main. 

(7)  Suitable  heat-allowance  must  be  made  for  all  connecting  piping  and  boiler- 
surface,  and  such  surface  must  be  figured  as  radiating-surface  or  its  equivalent. 


1276  Heating  and  Ventilation  of  Buildings  Part  3 

A  general  rule  is  to  add,  for  an  ordinary  installation,  about  50%  of  the  sq  ft  of 
radiation  installed,  in  calculating  the  total  load  on  the  boiler,  with  anthracite 
fuel  and  65%  with  l)ituminous  fuel,  to  allow  for  radiation-loss  of  piping  and  boiler 
and  the  additional  tax  on  the  boiler  due  to  starting  up  with  cold  radiation. 

Equivalent  Boiler  Horse-Power  Rating  of  Heating-Boilers.  The 
capacities  of  heating-boilers  may  be  stated  in  boiler  horse-power,  and  the  equiva- 
lent of  same  in  square  feet  of  standard  radiation  may  be  easily  determined  as 
follows: 

Since  i  boiler  horse-power  is  equal  to  34.5  lb  of  water  evaporated  per  hour, 
from  and  at  212°  F.,  the  boiler  must  dehver 

34-5  X  971.7  (latent  heat  at  212°  F.)  =  33  524  Btu  per  hr 

Now  since  i  sq  ft  of  standard  cast-iron  steam-radiation  transmits  250  Btu 
per  hour, 

I  boiler  horse-power  =  33  524/250  =  134. i  sq  ft  of  this  radiation,  or 

I  sq  ft  of  direct  cast-iron  steam-radiation  =  0.00756  boiler  horse-power 

It  also  follows  that  the  equivalent  boiler  horse-power  rating  of  a  hot-water 
heater  is 

33  524/150  =  223.5  sq  ft  of  direct  cast-iron  hot-water  radiation,  or 

I  sq  ft  of  direct  cast-iron  hot-water  radiation  =  0.00447  boiler  horse-power 

Grate-Surface.  It  is  always  advisable  to  check  the  grate-area  required 
/or  heating-boilers,  especially  if  the  total  heat-loss  to  be  suppHed  by  the  boiler 
Is  known.  This  total  heat-loss  must  include  not  only  the  calculated  loss,  due 
to  transmission  through  walls  and  glass,  for  which  the  radiation  is  proportioned, 
but  also  about  50%  additional  for  heat-losses  from  the  piping  system,  boiler, 
etc.     So  that,  if  ^  is  the  building-loss  in  Btu,  1.5  //  =  total  Btu-loss. 

Then 

G  =  1.5/// (C  XF  XE) 

where  C  =  rate  of  combustion  in  pounds  of  dry  coal  per  square  foot  of  grate- 
area  per  hour,  F  =  calorific  value  of  fuel  in  Btu  per  pound  of  dry  coal  (12  000 
is  the  usual  assumption  for  anthracite  coal),  and  E  =  the  combined  efficiency  of 
boiler  and  grate  (60%  is  the  usual  assumption).  G  is  in  sq  ft  and  the  boiler 
selected  should  have  not  less  than  this  grate-area.  Special  attention  is  called 
to  the  distinction  between  grate-area  and  fire-box  or  fuel-pot  area  as 
explained  below  under  Depth  of  Fuel-Pot. 

Depth  of  Fuel-Pot.  The  average  of  the  fire-box  area  is  usually  somewhat 
larger  than  the  grate-area  in  sectional  boilers,  while  it  may  be  less  than  the 
grate-area  in  certain  types  of  round  boilers.  In  any  event  the  capacity  of  the 
fire-box  or  fuel-pot  from  grate  to  middle  of  fire-door  should  alwtiys  be  suf- 
ficient to  hold  all  the  coal  required  for  an  8-hr  firing-period,  plus  at  least  20% 
reserve  to  be  used  for  igniting  a  fresh  charge. 

The  following  method  is  used  to  determine  the  depth  of  pot  or  the  firing-period 
as  the  case  may  be.  Let  G  =  grate-area  in  sq  ft,  C  =  rate  of  coml)Ustion,  A 
average  area  of  fire-pot,  h  =  firing-period  in  hours,  W  =  weight  of  fuel  per  cu  ft 
(50  lb  for  anthracite  and  40  lb  for  bituminous),  D  =  depth  of  fuel -bed  in  ft. 
Then  (GC  Jt}  -f  20%  (allowance  to  ignite  fresh  charge)  =  total  weight  of  one 
charge;  also,  AWD  =  total  weight  of  one  charge.     Hence 

D  =  i.2GCh/AW,  or  A  =  AWD/1.2GC 


Steam-Heating  Boilers  and  Hot- Water  Heaters  1277 

As  noted  above  D  is  measured  from  grate  to  center  of  fire-door,  which  varies 
from  8  X  14  in  in  small,  to  11  X  19  in  in  large  boilers.  This  formula  allows 
for  the  greater  bulk  of  soft  coal. 

Example.  Given  a  boiler  with  grate-area  of  8  sq  ft,  average  area  fire-pot 
9  sq  ft,  height  to  center  of  fire-door  =  18  in,  rate  of  combustion  =  6  lb  per  sq  ft 
of  grate  for  anthracite  coal.  Required  the  number  of  hours  this  boiler  will 
carry  its  load  on  one  charging. 

Solution. 

^  =  (9  X  50  X  i.s)/(i-2  X  8  X  6)  =  II. 7  hours 

Effects  of  Fuels  on  Ratings.  All  ratings  are  based  on  anthracite  coal  of 
STOVE-SIZE  unless  otherwise  stated.  In  case  bituminous  coal  is  used  and  the 
boiler  is  selected  by  catalogue-rating,  a  boiler  with  fire-pot  having  at  least  25% 
greater  capacity  should  be  selected,  for  the  same  weight  of  coal  occupies  25% 
more  space.  With  soft  coal  additional  heating-surface  is  also  required  as  the 
accumulation  of  soot  from  such  coal  renders  the  heating-surfaces  less  effective 
than  when  hard  coal  is  used.  Boilers  for  pea-coal  should  also  have  a  larger 
fire-pot  than  those  for  stove  or  furnace-coal.  The  small  sizes  of  anthracite 
contain  far  more  ash  than  the  larger  sizes,  and  hence  have  a  greater  bulk  for  the 
same  heating  effect;  so  that  larger  fuel-pots  for  the  same  capacity  are  required. 
Firing-periods,  differing  from  the  one  on  which  the  boiler  is  rated,  will  also  affect 
the  fuel-holding  capacity.  For  example,  if  it  is  required  to  operate  a  certain  line 
of  boilers  designed  for  an  8-hr  period  on  a  12-hr  basis,  at  least  50%  greater  fuel- 
holding  capacity  will  be  necessary  and  a  larger  boiler  must  be  selected,  as  shown 
by  the  formula  already  given  for  the  depth  of  the  fuel-pot. 

Equivalent  Rating  for  Conditions  Other  than  Standard.  If  often  happens 
that  the  load  connected  to  a  steam- or  hot-water  boiler  may  not  be  operated  under 
the  standard  conditions  previously  assumed  as  a  basis  of  rating.  In  this  case 
tables  of  ratings  cannot  be  used  until  the  equivalent  value  of  this  load  in 
terms  of  square  feet  of  standard  cast-iron  radiation  has  been  determined. 

The  following  relations  show  a  method  for  finding  such  equivalent  values: 

Let  i?  =  sq  ft  standard  cast-iron  radiation  =  250  Btu  per  sq  ft  for  steam,  and 
150  Btu  per  sq  ft  for  water.    Also  let 

r  =  actual  sq  ft  of  radiation  to  be  supplied; 
K  =  coefficient  of  transmission  for  this  radiation; 
ts  or  tw  =  temperature  of  steam  or  average  temperature  of  hot  water  in 
the  radiator; 
ta  =  temperature  of  air  surrounding  radiator; 
K{ts  —  ta)  =  radiation-factor  or  Btu  given  off  per  sq  ft  per  hr; 

Then 

Rs  =  ri  X  Ki{ts  —  ta) /2S0,  and  Rw  =  rz  X  K^itw  —  /a)/i5o 

Example.  (Steam-heating.)  Required  the  size  of  boiler  (rating  in  sq  ft  of 
standard  cast-iron  radiation)  to  supply  i  000  sq  ft  of  direct  pipe-coil  radiation. 
Steam-pressure  =  5-lb  gauge.  Air  =  65°  F.  K  (by  test)  =  2.42  Btu.  From 
steam-tables,  ts  =  227.14,  R  =  1000  X  2.42(227.14  —  65)7250  =  1000  X 
(2.42  X  162.14)7250  =  I  570  sq  ft.  To  this  add  50%  for  pipe  and  boiler- 
radiation  and  the  additional  tax  for  starting  up  with  cold  radiation,  or,  1.5  X 
I  570  =  2  355  sq  ft,  or  practically  a  2  400-sq-ft-capacity  boiler  will  be  required. 
The  grate  should  be  checked  by  calculation  previously  given  to  ascertain 
minimum  size. 

G  =i.5H/{C  XF  XE) 


1278  Heating  and  Ventilation  of  Buildings  Part  3 

Example.  (Water-heating.)  Let  Q  =  total  number  of  gal  of  water  to  be 
heated  in  h  hours. 

W  =  (SH  XQ)/h  =  weight  of  water  to  be  heated  per  hour 
^1  =  initial  temperature  of  water,  k  =   final  temperature  of  water 

Then  Wih  -  ti)  =  Btu  to  be  supplied  per  hour.  Hence  Wik  -  /i)/iSo  =hot- 
water-heater  rating  required.     W{k  -  h)/2So  =  steam-boiler  rating  required. 

Example.  A  swimming  pool  contains  50  000  gal  of  water,  and  this  water  is 
heated  by  being  passed  through  a  hot-water  heater  in  four  hours.  Entering- 
temperature  =  50°  F.  and  final  temperature  =75°  F.  Hot-water  radiation 
reduced  to  equivalent  standard  value  =[(50000  X  8H)/(4  X  150)]  X 
(75  —  50)  =17  350  sq  ft  =  rating  of  hot- water  heater,  to  which  must  be  added 
50%  for  losses  from  piping,  etc. 

Fuel-Consumption.  The  estimated  fuel-consumption  for  heating- 
boilers  per  heating-season  may  be  based  on  grate-areas,  square  feet  of  radiation 
installed,  or  culjic  contents  of  building  to  be  heated.  The  United  States  Treasury 
Department  allows  5  tons  of  coal  per  sq  ft  of  grate-area  per  season  of  240  days, 
or  I  lb  of  coal  per  cu  ft  of  contents  of  building  for  the  same  period.  This 
applies  to  government  buildings.  The  district  steam-heating  companies  estimate 
500  lb  of  steam  per  sq  ft  of  direct  steam-radiation  per  season,  which  is  practically 
the  same  as  70  lb  of  coal  of  good  quality.  This  is  approximately  equivalent  to 
assuming  that  one-third  of  the  radiation  installed  is  in  operation  continuously  for 
240  days.  In  other  words,  the  coal  required  for  a  heating-season  is  about  one- 
third  the  quantity  that  would  be  used  if  all  the  radiation  were  in  constant  use 
every  hour  of  the  day  and  night.  The  amount  of  coal  for  maximum  conditions 
is  determined  as  follows: 

Since  each  foot  of  direct  steam-radiation  or  its  equivalent  will  give  ofif  250 
Btu  per  hour  under  conditions  of  2  lb  (220°)  pressure  at  boiler,  and  70°  air  sur- 
rounding the  direct  radiators  (the  piping  on  the  average  job  may  be  roughly 
taken  as  25%  of  the  direct  radiation);  and  since  for  approximation  we  may 
assume  8  000  Btu  per  pound  of  anthracite  coal  burned;  we  can  readily  estimate 
the  amount  of  coal  per  hour  li  R  —  amount  of  direct  radiation  iii  square  feet: 

(1.25  xR  X  2.5o)/8ocx3  =  C  =  coal  per  hour  in  pounds 

In  a  heating-season  of  7  months  or  210  days  of  24  hours  each,  there  would  be 
burned  under  maximum  conditions  during  the  entire  period 

(1.25  XR  X  250  X  210  X  24)/(8  000  X  2  000)   =  0.0984^  tons  of  coal 

the  actual  consumption  being. about  one-third  of  the  maximum  possible,  or 
0.0328  R  tons  of  coal  for  the  heating-season.  For  hot- water  heating  the  fuel- 
consumption  for  the  entire  season  is  approximately  0.0197  R  tons. 
'  Types  of  Heating-Boilers.  Cast-iron  steam-heating  boilers  are  designed  to 
be  operated  at  a  maximum  pressure  of  15  lb  per  sq  in,  and  the  sections  are  tested 
by  the  manufacturer  to  about  100  lb  per  sq  in,  hydrostatic  pressure.  Cast-iron 
boilers  are  constructed  of  sections,  which  are  connected  by  means  of  nipples  of 
either  the  push  or  screw-type.  The  sections  are  held  in  place  by  means  of  long 
bolts.  Round -type  boilers  have  horizontal  sections  surrounding  the  fire-pot, 
and  in  the  sectional  type  the  sections  are  placed  vertically.  (See  Figs.  16,  17, 
and  18.)  The  maximum  size  of  round-type  boilers  manufactured  is  rated  at 
about  I  400  ft.  Sectional  boilers  are  ol)tainable  up  to  a  10  000-sq-ft-rating. 
See  manufacturers'  catalogues  for  capacities,  dimensions,  etc.) 


Steam-Heating  Boilers  and  Hot- Water  Heaters 


1279 


Smokeless  or  Down-Draft  Cast-iron  Boilers.  Boilers  having  a  water-grate 
are  now  being  made  for  use  with  free-burning  soft  coal,  where  local  smoke- 
ordinances  would  not  permit  the  use  of  such  fuel  on  ordinary  gratesu 


ft 


Fig.  16.     Sectional  Type  of  Cast-iron  Boiler 


Drain  to  Seweo 


Fig.  1 7.    Tfiinniings  and  Connections  for  Sectional  Steam-heating-boiler 


1280 


Heating  and  Ventilation  of  Buildings 


Pait3 


Selection  of  Cast-iron  Boilers.  The  selection  of  cast-iron  boilers  should 
not  be  influenced  too  largely  by  considerations  of  price,  and  the  ease  with 
which  they  may  be  carried  into  a  building  where  structural  conditions  interfere 

with  the  introduction  of  a  steel  boiler.  In 
many  cases  the  character  of  the  service  or 
attendance,  or  both,  especially  in  govern- 
ment and  other  pubHc  building  work,  may 
be  such  that  steel  equipment,  which  is  cap- 
able of  withstanding  more  abuse,  should  be 
used.  This  is  particularly  true  when  the 
returns  are  handled  by  a  pump.  If  cast- 
iron  boilers  are  to  be  installed,  the  grate- 
area  necessary  should  be  carefully  computed 
as  already  indicated,  using  an  average  rate 
of  combustion,  and  a  fuel-pot  depth  based 
on  the  firing-period  required.  The  United 
States  Treasurj'  Department  selects  cast- 
iron  boilers  by  proportioning  them  to  carry 
25%  more  radiation  than  actually  installed 
if  anthracite  coal  is  used,  and  35%  more  if 
bituminous  coal  is  used.  In  addition  to 
this,  suitable  allowance  must  be  made  for 
mains  and  other  piping,  and  in  most  cases 
two  boilers  are  installed,  each  capable  of 
supplying  two-thirds  of  the  radiation  in 
order  to  provide  for  units  which  can  be 
operated  with  a  high-load  factor,  and  also 
^.  ^„  _  .  ,  _,  ,^  ^  .,  act  as  a  reserve  for  each  other  in  case  of  a 
Fig.  18.  Section  of  Round-type  Boiler  breakdown. 

Steel  Heating-Boilers.  There  are  two  general  types  of  all-steel  boilers  used 
for  heating  work,  the  fire-box  type  and  the  return  tubular  type. 

In  the  fire-box  type  the  grate  and  combustion-chamber  are  surrounded  by  an 
extension  of  the  steel  shell  which  is  water-jacketted.  The  products  of  com- 
bustion pass  directly  through  the  tubes  to  the  smoke-flue  located  in  the  rear. 
In  the  return  tubular  type,  the  boiler  consists  of  a  shell  with  tubes  set  in  a 
brick  setting,  the  grate  and  combustion-chamber  being  directly  under  the 
front  portion  of  the  shell.  The  products  of  combustion  in  this  case  pass  under 
and  around  the  shell  to  the  rear  of  the  boiler,  and  then  through  the  tubes  to 
the  front  into  the  smoke-box. 

Fire-box  type  boilers  may  be  obtained  in  capacities  ranging  from  500  to  13  000 
sq  ft  of  direct  radiation.  The  most  common  of  these  boilers  are  the  Dunning, 
Gorton,  and  Kewanee.  Detailed  information  as  to  capacities,  dimensions,  etc., 
may  be  obtained  from  the  makers'  catalogues.  As  usually  constructed,  these 
boilers  are  designed  for  a  working  pressure  of  60  lb  per  sq  in  and  are  so  insured 
by  the  boiler-insurance  companies.  This  type  may  be  obtained  with  or  without 
(portable  type)  brick-setting.  The  return  tubular  boiler  is  erected  with  a 
brick  setting  and  as  ordinarily  constructed,  is  designed  for  a  working  pressure 
of  100  lb  per  sq  in,  but  may  be  obtained  for  a  working  pressure  of  150  lb  per  sq  in 
if  desired.  It  is  primarily  a  power-typ)e  boiler,  but  is  commonly  used  in  con- 
junction with  large  heating  systems  having  10  000  sq  ft  or  more  of  direct  radia- 
tion. These  boilers  are  rated  on  a  basis  of  10  sq  ft  of  boiler  heating-surface  per 
boiler  horse-power.  A  special  design  of  setting  is  required  for  smokeless  com- 
bustion when  bituminous  coal  is  to  be  used  as  fuel.  The  so-called  standard 
setting  should  not  be  used  in  this  connection.     (See  Boilers  and  Rules  for  Con- 


Chimneys  for  Heating-Boilers 


1281 


structlon  in  Mechanical  Equipment  of  Buildings,   Vol.  II,  by  Harding  and 

Willard.) 

Chimneys  for  Heating-Boilers.  (See  also,  under  Chimneys,  page  1364.) 
In  order  to  produce  an  intensity  of  draft  sufficient  to  properly  operate  low- 
pressure  heating-boilers,  hot-water  boilers,  and  hot-air  furnaces  up  to  their 
rated  capacity,  the  chimney  should  not  be  less  than  40  ft  in  height,  measured 
from  the  grate.  No  flue  should  be  less  than  8  X  8  in.  The  failure  of  many 
heating-installations  may  be  traced  to  insufficient  draft  to  burn  the  fuel  at  the 
rate  required  to  run  the  boiler  or  furnace  to  rated  capacity.  The  tempera- 
ture of  flue-gases  leaving  the  boiler  should  range  between  400°  and  500°  F.  when 
the  apparatus  is  worked  at  its  rated  capacity.  The  chimney  should  be  so 
located  with  reference  to  any  higher  buildings  nearby  that  wind-currents  will 
not  form  eddies  and  force  the  air  downward  in  the  shaft,  as  shown  in  Fig.  19. 
The  flue  should  run  as  nearly 
straight  as  possible  from  the  base 
to  the  top  outlet.  The  outlet 
must  not  be  capped  so  that  its 
area  is  less  than  the  area  of  the 
flue.  The  flue  should  have  no 
opening  into  it  other  than  the 
boiler  smoke-pipe.  Sharp  bends 
and  ofl^sets  in  the  flue  often  reduce 
the  area  and  choke  the  draft,  and 

the  flue  must  be  free  of  any  Fig.  19.Relation  of  Height  of  Chimney  to  Draft 
feature   which    prevents  the  full 

area  for  the  passage  of  smoke.  If  the  flue  is  made  of  tile,  the  joints  must  be 
well  cemented,  or  all  space  between  the  tile  and  brickwork  fiUed  in  tightly. 
There  must  be  no  open  crevices  into  the  flue  where  the  tile  sections  meet,  other- 
wise the  draft  will  be  checked.  If  the  flue  is  made  of  brick,  the  stack  should 
have  outside  walls  at  least  8  in  thick  to  insure  safety.  The  inside  joints  should 
be  well  struck,  and  each  course  should  be  well  bedded  and  free  from  surplus 
mortar  at  the  joints.    The  exposed  bricks  at  the  top  of  a  brick  chimney  should 


Table  XVI.    Fire-Clay  Flue-Linings 

Robinson  Clay  Product  Co.,  Akron,  Ohio 


Rectangular 

Round 

Nominal 

Actual  size 

Actual  size 

Inside 

Outside 

size, 

outside. 

inside, 

diameter, 

diameter, 

m 

m 

m 

m 

m 

4HX   81^ 

4HX   SVs 

3M   X   7 

6 

7M 

4HX13 

4HX13H 

3M6X11M 

7 

sy2 

4KX18 

4HX17 

3^^^   XIS}^ 

8 

9 

6      X12 

6      X12 

4H   XioM 

9 

loH 

7      X   7 

7MX   7H 

55^  X  5^ 

10 

12 

8HX   SH 

8HX   8M    , 

7H   X   7H 

12 

14 

8HX13 

8V2X13 

6%  Xii^ 

IS 

17  K 

8HX18 

8HX18 

eVi  X16 

18 

20  K 

13      X13 

13      X13 

iiH  XiiM 

20 

23 

13      X18 

13      X18 

10  M  X15M 

24 

27 

18      X18 

18      X18 

isH  XisH 

30 

35 

1282 


Heating  and  Ventilation  of  Buildings 


Parts 


be  laid  in  cement  mortar  to  prevent  the  acid  fumes  and  rain  from  cutting  out 
the  joints.  This  will  happen  if  lime  mortar  is  used.  The  most  desirable  loca- 
tion for  a  chimney  is  near  the  center  of  the  building,  as  all  walls  are  then  kept 
warm.  If  there  is  a  soot-pocket  in  the  Hue  below  the  smoke-pipe  opening,  the 
clean-out  door  should  always  be  tightly  closed.  If  this  soot-pocket  has  other 
openings  into  it  from  fireplaces  or  other  connections,  these  openings  check  the 
draft  and  prevent  the  best  results.  The  smoke-pipe  should  not  extend  into  the 
flue  beyond  the  inside  surface  of  the  latter.  If  it  does  extend  beyond,  its  end 
cuts  down  the  area  of  the  flue.  The  joints,  where  the  smoke-pipe  fits  the 
smoke-hood  of  the  boiler,  or  where  the  pipe  enters  the  chimney,  should  be  made 
tight  with  boiler-putty  or  asbestos  cement.  Fire-clay  flue-linings  are  used  in 
the  best  practice  for  small  and  medium-sized  flues.  Rectangular  flue-hnings 
are  rated  by  outside  dimensions^  and  round  Hiiings  by  inside  dimensions. 

Flues  for  Elitchen  Ranges  and  Fireplaces.  (See  also,  under  Chimneys, 
page  1364.)  For  a  kitchen  range  an  8H  by  8H-in  tile  flue  is  ordinarily  sufficient, 
but  an  8H  by  13-in  is  better.  For  fireplaces  the  sectional  area  of  the  flue  for 
burning  wood  or  bituminous  coal  should  be  from  Mo  to  14  the  area  of  the  fire- 
place-opening for  a  rectangular  flue,  and  H2  for  a  circular  flue.  For  burning 
anthracite  coal  the  areas  may  be  reduced  to  H2  and  Me  respectively. 

Selection  of  Chimney-Flues.  (See  also,  under  Chimneys,  page  1364.)  The 
selection  of  chimney-flues  for  heating-boilers  must  depend  upon  the  judgment  of 
the  heating-engineer,  but  it  is  believed  that  Table  XVII,  by  R.  C.  Carpenter,  will 
very  much  assist  the  engineer  in  selecting  flues.     It  is  necessary  that  area  and 

HEIGHT,  THICKNESS  OF  WALLS,  GENERAL  STRUCTURE,   and  the  POSITION  OF  THE 

TOP  OUTLET  with  reference  to  the  building  and  other  buildings  near  by  should  be 
carefully  noted  and  observed  in  the  selecting  or  building  of  a  flue.  The  figures 
given  under  the  varying  heights  of  chimneys  are  diameter-measurements  in 
inches,  or,  the  side  of  a  square,  the  theory  being  that  the  spirally  ascending 
column  of  smoke  and  gases  will  make  a  12  by  12 -in  flue  no  more  "eff"ective  in 
practical  working-area  than  a  twelve-inch  round  flue.  Rectangular  shapes  may 
be  used  if  the  area  is  equal  and  the  difference  in  width  and  breadth  is  not 
extreme.  •  A  maximum  ratio  of  2  :  i  for  the  internal  dimensions  should  not  be. 
exceeded. 

Table  XVII.     Chimneys  for  Steam  and  Hot- Water  Boilers 


Direct  radiation 

Height  of  chimney-flue 

Steam, 
sqft 

Water, 
sq  ft 

30  ft 

40  ft 

50  ft 

60  ft 

Soft 

250 

375 

7.0 

6.7 

6.4 

6.2 

6.0 

500 

750 

9-2 

8.8 

8.2 

8.0 

7.6 

750 

I  150 

10.8 

10.2 

9.6 

9.3 

8.8 

I  000 

I  500 

12.0 

II. 4 

10.8 

10. s 

10. 0 

I  500 

2  250 

14.4 

13.4 

12.8 

12.4 

II. S 

2  000 

3  000 

16.3 

15.2 

14. 5 

14.0 

13.2 

3  000 

4  500 

18.5 

18.2 

17.2 

16.6 

15.8 

4  000 

6000 

22.2 

20.8 

19.6 

19  0 

17.8 

5  000 

7  500 

24.6 

23.0 

21.6 

21.0 

19.4 

6  000 

9  000 

.26.8 

25.0 

23-4 

22.8 

21 .2 

7  000 

10  500 

28.8 

27.0 

25  5 

24.4 

23  0 

8  000 

12  000 

3®. 6 

28.6 

26.8 

26.0 

2.;   2 

9  000 

13  500 

32.4 

30.4 

28.4 

27.4 

r-  6 

10  000 

IS  000 

34  0 

32.0 

30.0 

28.6 

27.0 

Direct  Steam-Heating  1283 

Rules  for  Grate-Areas  and  Stack-Dimensions.  For  return  tubular 
type  of  boilers  N.  S.  Thompson  gives  tlie  following  rules  for  grate-areas  and 
stack-dimen  sions : 

R  =  total  direct  radiation  in  building;  B.  II.  S.  =  heating-surface  in  boiler; 
G  =  area  of  grate;    (all  in  sq  ft) 

B.  H.  S.  =  R  ^  7  for  steam;  R  -=-  ii  for  water.  G  =  B.  II.  S.  -r-  25  (anthra- 
cite, pea,  or  rice  coal);  G  =  B.  H.  S.  -j-  30  to  B.  H.  S.  -;-  35  (bituminous  coal, 
plain  grate);  G  =  B.  H.  S.  -^  45  (lower  grate  of  down-draft  furnace). 

H  =  height  of^stack,  ft.     A  =  area  of  grate,  sq  ft.     S  =  area  of  stack,  sq  ft. 

S  =  A  -j-  V  H  (anthracite  coal,  lump  coal,  oil,  and  gas). 

S  =  (A  X  1.25)  -~  V  H  (bituminous  and  small  anthracite). 

For  anthracite,  pea,  or  rice  coal,  tube-area  must  be  not  less  than  }4  grate,  and 
always  larger  than  stack. 

For  boilers  with  down-draft  furnace,  tube-area  must  be  not  less  than  }4  of 
lower  grate,  and  always  larger  than  stack. 

Maximum  length  of  tube  must  not  exceed  48  diameters. 

Maximum  length  of  boilers,  54-in  diameter  and  under,  must  not  exceed  3 
diameters;   over  S4-in,  2V2  diameters. 

Tubes,  an  odd  number  of  feet  in  length,  are  not  used. 

Stacks  for  Tall  Buildings  are  special  cases  and  may  be  designed  by  methods 
used  in  the  design  of  chimneys  for  power-boilers.  (See  Power  Plants  and 
Refrigeration,  by  Harding  and  Willard.  See  also.  List  of  Tall  Brick  Chimneys, 
page  I379-) 

Direct  Steam  Heating 

Systems  of  Direct  Steam  Heating  in  Use.  Systems  for  heating  with  direct 
steam  radiators  are   broadly  divided  into  two  general  classes,  known  as:    (i) 

GRAVITY    CIRCULATING    SYSTEMS,    and    (2)    MECHANICAL    CIRCULATING    SYSTEMS. 

The  distinguishing  characteristic  is  the  manner  in  which  the  water  of  condensa- 
tion from  the  radiators  is  returned  to  the  boiler.  In  the  first  type  the  condensate 
enters  the  boiler  by  gravity,  due  entirely  to  the  static  head  existing  in  the 
returns,  and  the  sytem  is  a  closed  circuit.  The  steam-pressure  existing  in  the 
boiler,  mains,  and  radiators  is  the  same,  except  for  friction-pressure  losses  due 
to  the  flow  of  steam  to  the  heating-surfaces.  In  the  second  type  the  condensate 
is  allowed  to  return  to  a  receiver  or  feed-water  heater  and  is  then  forced  into  the 
boiler  by  a  pump,  or  return-traps,  or  both.  This  is  not  a  closed  system,  and 
the  pressure  in  the  boiler  may  be  much  higher  than  that  in  the  mains  and  radi- 
ators. The  receiver  is  usually  vented  to  the  atmosphere,  and  in  the  case  of 
vacuum  systems  an  additional  pump  is  attached  directly  to  the  returns  and 
arranged  to  discharge  the  condensation  into  the  receiver  or  heater.  Gravity  cir- 
culating systems  are  further  divided  into  the  one -pipe  system  and  the  two-pipe 
system  with  basement-mains  supplying  risers  to  the  various  floors  above  (Figs. 
20,  21  and  22),  or  with  overhead  mains  supplying  drop-risers  to  the  floors  below. 
In  the  latter  system  the  steam  and  water  of  condensation  in  the  risers  flow  in 
the  same  direction;  so  that  less  friction  is  produced  as  countercurrents  do  not 
occur  and  smaller  pipe-sizes  may  be  used.  The  overhead  system  is  very  com- 
monly spoken  of  as  the  mill's  system. 

One-Pipe  Gravity  Systems.  The  one -pipe  circuit  system  (Fig.  20)  with 
basement-mains  is  probably  the  simplest,  and  most  common  gravity  system  in 
use.  The  steam-main  rises  close  to  the  basement-ceiling,  just  above  the  boiler, 
and  then  grades  down  uniformly  from  this  high  point  with  a  fall  of  i  or  ^  in  in 
10  ft.     When  the  last  radiator  has  been  ?'jrved  the  main  drops  below  the  boiler 


1284 


Heating  and  Ventilation  of  Buildings 


Parts 


water-line  and  its  size  is  reduced,  as  on  the  run  back  to  the  boiler  it  carries  only 
condensation  and  is  known  as  a  wet  return.  This  return  may  be  run  above  the 
boiler  water-line  if  necessary,  and  is  then  called  a  dry  return.  Return-mains 
are  graded  i  in  in  30  ft  in  gravity  work.    In  either  case  an  automatic  air-valve 


Note ;  Separate  branched 
to  all  first-lloor  radiators 


Not  less  t 
18  "above  boiler 
water-line 
/  DETAIL  OF  FIRST-FLOOJl 
RADIATOR- CONNECTIO.NS 


DETAIL  AT  END 
OF    MAIN 


Fig.  20.    Low-pressure  Gravity  System.    One-pipe  Basement-main 

must  be  installed  on  the  end  of  the  main  at  the  drop,  as  shown,  to  vent  the  same 
when  air  collects  in  the  piping.  The  elevation  of  the  end  of  the  steam-main  with 
respect  to  the  boiler  water-line  must  be  carefully  determined,  in  order  that  water 
may  not  back  up  from  the  boiler  and  flood  the  main,  including  the  air-valve  and 


KaJiator 
Braneh-ruus  at  cleiling  below- 


PLAN  OF  2ND  FLOOR  CONNECTIONS 
Riser 


Fig.  21.     One-pipe  Relief  Easement-main 

branches.  It  is  customary  to  maintain  at  least  18  in  between  the  under  side  of 
main  at  the  drop  and  the  normal  water-line  of  the  boiler  to  provide  for  contin- 
gencies. In  operation  it  will  be  noted  that  steam  and  water  flow  in  the  same 
direction  through  the  one-pipe  steam-main,  and  in  opposite  directions  through 
the  basement-branches,  risers,  and  radiator-branches.  This  necessitates  larger 
piping  and  valves  than  in  any  other  steam  system,  and  especially  is  this  true 
of  the  main,  which  must  be  run  fuU  size  from  boiler  to  drop,  unless  dripped  as 
shown  under  piping -details. 


Direct  Steam-Heating 


1285 


The  ONE -PIPE  RELIEF  SYSTEM  (Fig.  21)  is  Very  similar  to  the  one-pipe  circuit 
system  except  that  the  risers  are  dripped  individually  into  the  return,  and  the 
steam-main  carries  no  radiator-condensation,  and  is  itself  dripped  at  intervals 
into  the  return-main,  which  may  run  dry  or  wet.  This  makes  it  possible  (i) 
to  reduce  the  size  of  main  as  radiation  is  taken  off,  (2)  to  use  smaller  branches, 
and  (3)  to  run  the  main  much  closer  to  the  basement-ceiling,  a  very  important 
.consideration  where  basement-space  is  valuable.  A  combination  or  the  one- 
pipe  relief  and  the  two-pipe  system  is  frequently  used  in  large  installations, 
the  latter  being  used  for  the  first  and  second  floors,  and  the  former  for  the 
upper  floors  of  high  buildings.  In  this  way  the  amount  of  condensation  flowing 
down  the  one-pipe  risers  against  the  steam  is  much  reduced  and  smaller  risers 
may  be  used.  The  application  of  the  one-pipe  sj^stem,  with  gravity-circulation 
and  basement-mains  to  tall  buildings,  is  not  at  all  unusual,  and  if  the  piping  is 
properly  designed  for  the  circulation  of  steam  and  the  return  of  the  water  of 
condensation  it  will  be  found  satisfactory.  In  the  case  of  long  narrow  buildings 
heated  by  a  gravity  system  it  may  be  necessary  to  provide  a  deep  boiler-pit  so 
that  the  elevation  of  water  in  the  return-connections  will  not  flood  the  far  end 
of  the  steam-mains. 

Two-Pipe  Gravity  Systems.  The  two-pipe  system  with  basement-mains 
(Fig.  22)  is  often  used  in  large  buildings,  and  in  all  work  where  indirect 


Fig.  22.     Two-pipe  Basement-main 


fa|se  wat^r-une  J 


radiation  is  installed.  This  system  can  be  readily  adapted  to  mechanical 
vacuum  systems,  and  is  very  extensively  used  in  this  connection.  It  will  be 
noted,  however,  that  when  apphed  to  a  gravity  system  the  return  from  each 
radiator  is  separately  sealed,  either  by  dropping  below  the  water-line  to  a 
wet  return  or  else  by  using  drip-loops,  as  shown  at  the  left,  before  connecting  to 
a  dry  return.  Even  in  one-pipe  work  all  drips  or  reliefs  are  sealed  as  shown  in 
Fig.  22.  If  this  precaution  is  not  taken  steam  may  enter  a  drip  or  return  from 
the  outlet-end  and  cause  knocking  in  the  system  due  to  countercurrents  of  steam 
and  water  of  condensation.  Any  drip,  relief,  return-riser,  or  connection  from  the 
steam  to  the  return-side  of  the  system  must  be  sealed.  This  may  be  done  by 
connecting  below  the  water-line,  or  efse  by  using  a  running  trap  or  a  return-trap 
somewhere  on  this  connecting  line.  Neglect  of  this  precaution  will  cause  an 
unsatisfactory  operation  of  the  System. 

Automatic  Radiator  Air-Valves  for  Gravity  Systems.  The  automatic 
REMOVAL  OF  AIR  from  steam-radiators  must  be  provided  for  if  the  highest  effi- 
ciency of  the  radiating-surfaces  is  to  be  realized  in  gravity  circulating  systems. 


1286 


Heating  and  Ventilation  of  Buildings 


Parts 


Manually  controlled  air-valves  or  cocks  are  usually  neglected,  and  are  seldom 
used  for  steam-radiators  although  their  use  is  quite  general  for  hot-water  radi- 
ators. Fig.  23  shows  a  float-type  of  automatic  air- valve.  Thermostatic  air- 
valves  are  finding  favor  in  this  field.  The  proper  location  of  the  air-valve 
on  a  steam-radiator  is  at  the  end  of  the  radiator  opposite  the  steam-inlet,  and  as 
near  the  bottom  of  the  radiator  as  possible,  since  air  is  heavier  than  steam  at 
the  same  temperature.    In  practice,  however,  the  manufacturer  of  radiators 


VALVE  CLOSED  VALVE  OPEiS 

Fig.  2^.    Norwall  Automatic  Air-valve 

usually  places  the  air-valve  tapping  about  two-thirds  the  height  of  the  radiator 
from  the  floor  in  order  to  prevent  possible  flooding  of  the  valve. 

Special  Gravity  Systems.     In  addition  to  the  low-pressure  gravity  systems 
already  described  there  are  many  special  steam  heating  systems  known  as  air- 


Steam  25  ^  or  above 
HIGH-PRESSURE     EXHAUSTER-STEAM 
Fig.  24.    The  Paul  Air-line  System 


TWO-PIPE 
SYSTEM 


LINE,  VAPOR,  and  vacuttm  systems,  also  operating  with  gravity-return  of  the 
water  of  condensation.  The  air-ltne  .system  may  be  attached  to  any  one  or 
two-pipe  gravity  system,  and  is  applied  by  connecting  the  automatic  air- valve 
of  each  radiator  with  small-size  piping  to  'an  exhauster  which  maintains  a  slight 
vacuum  in  the  air-piping  and  effectually  removes  the  accumulation  of  air  in 
the  radiators.  As  this  scheme  is  a  positive  means  of  air-removal  its  application 
to  the  ordinary  one  or  two-pipe  gravity  system  will  improve  its  operation. 
The  original  air-line  system  is  known  as  the  Paul  systkm  (Fig.  24).  The  ex- 
haustion used  for  less  t|ipji  j^gp^f|^is, a  water-driven  vacuum-pump^,}vitjia^^ 


Direct  Steam-Heating 


1287 


sure  of  at  least  20  lb  per  sq  in.  Larger  systems  use  a  high-pressui-e  steam-jet 
(see  above),  or  if  steam  is  not  available,  a  motor-driven  vacuum  pump  of  about 
H  horse-power,  i  in  air-mains  in  basement,  and  a  gate  valve  on  each  air-riser 
are  used.  The  steam  used  varies  from  i  to  5%  of  the  total  condensation.  All 
radiator-connections  are  made  as  shown.    The  Bishop-Babcock-Becker  Com-j 


"^  ^"Air-Liue  Main 


Automatic 
Electric  Switch  ^5  o 
and  Vacuum- 
Controller 


Foundation' 


Fig.  25.    The  Bishop-Babcock-Becker  Air-Iinc  System 

pany  manufacture  the  following  line  of  air-pumps  that  are  used  for  exhausters 
in  air-line  systems  (Fig.  25) : 


Table  XVIII. 

Hydraulic  Exhausters 

Diam 

Diam 

.  City 

Max. 

Number 

City 

Max. 

Length 

Number 

motor- 

suction- 

of 

stroke, 

of 

pump 

water- 

cap. 

of 
pump 

water- 

cap. 

cylin- 

dep-, 

in 

cylin- 
der, 
in 

pres- 
sure, 
lb 

direct 
rad., 
sq  ft 

pres- 

direct 
rad., 
sq  ft 

in 

Ib 

2 

2y2 

4 

lOI 

20 

700 

104 

40 

4  000 

2 

2Y, 

4 

lOI 

40 

8oo 

io6 

20 

6  600 

2^ 

4 

6 

102 

20 

900 

io6 

40 

9  600 

2% 

S^-Mg 

10 

102 

40 

I  100 

2-106 

20 

14000 

104 

20 

2  500 

2-106 

40 

20  000 

Mechanical  Vacuum  Systems.  The  so-called  mechanical  Vacuum  Systems 
are  of  the  two-pipe  type,  and  have  a  vacuum-pump  attached  directly  to  the 
returns.  This  pump  may  be  steam  or  motor-driven,  but  must  be  capable  of 
handling  both  air  and  water,  as  no  air-valves  can  be  used  on  the  radiators  in  the 
vacuum  system.     The  return-end  of  each  radiator  is  equipped  with  a  radiator- 


12S8 


Heating  and  Ventilation  of  Buildings 
Table  XIX,     Motor-Driven  Exhausters 


Parts 


Number 

of 

pump 

Max. 
capacity, 

direct 
radiation, 

sqft 

Cylinder-sizes 

Size  of 
connection 

Strokes 
per 

minute 

Horse- 
power 

Bore, 
in 

Stroke, 

Disch'e- 
pipe. 

Suction- 
pipe, 
in 

m 

I  279 

112 

113 

114 
115 

4  ooo 
10  ooo 
i8  ooo 
28  ooo 
35  000 

2}i 

3 

4 
4 
5 

3 

3H 

S 

5 

I 
I 

2 

I 
I 

2 

150 
70 
70 
68 
60 

I 
2 

^                   1 

trap,  usually  of  the  thermostatic  type  and  commonly  termed  a  vacuum-valve, 
such  as  the  Dunham  (Table  XX),  Webster,  lUinois,  Monash,  etc.  A  volatile 
liquid  is  employed  in  the  thermostatic  element  or  bellows.  This  liquid  is  vapor- 
ized immediately  as  steam  is  brought  in  contact  with  the  bellows,  and  causes 
the  latter  to  expand  and  thus  close  the  valve.  The  temperature  of  the  con- 
densate from  the  radiator  is  slightly  below  the  temperature  of  the  steam  but  is 
not  sufficiently  high  to  vaporize  the  liquid.  The  valve  therefore  remains  open 
and  will  pass  the  water  of  condensation 
and  air  until  the  steam  fetarts  to  flow, 
when  it  immediately  closes.  These 
valves  are  very  sensitive,  and  when  prop- 
erly adjusted  and  in  order  will  not  blow 
steam.  One  type  of  thermostatic 
VALVE  is  shown  in  Fig.  26.  It  is  cus- 
tomary practice  to  connect  a  K-in  cold- 
water  line  to  the  main  return  at  the 
pump,  which  serves  to  condense  any 
steam  that   may  leak   by  the  vacuum- 


Connected  to  Return-Pipo 


Fig.  26.    Thermostatic  Valve  or  Vacuum- 
trap 


Fig.  27.  Detail  Showing  Method  of 
Draining  Bottom  of  Steam-riser  in  an 
Overhead  System 


valves  due  to  dirt  getting  under  the  seat  and  preventing  the  valve  from 
closing  tight.  Figs.  27,  28  and  29  show  clearly  the  application  of  vacuum- 
traps  to  the  two-pipe  system.  It  will  be  observed  by  inspection  of  Table 
XXVII  that  the  return-connections  for  a  vacuum  system  are  much  smaller 
than  ar^  used  in  the  ordinary  two-pipe  system,  Table  XXVI.    The  vacuum 


Direct  Steam -Heating 


1289 


Punham  Air-Tra 


system  is  largely  employed  In  connection  with  exhaust  steam-heating,  where 
it  is  important  to  keep  down  the  back-pressure  on  the  steam-engines  or  tur- 
bines to  approximately  5  lb  per  sq  in. 
A  by-pass  with  reducing-valve  is  used 
to  cross-connect  the  live-steam  main 
with  the  heating  system.  This  valve 
automatically  opens  and  allows  Hve 
steam  at  a  reduced  pressure  (usually 
from  2  to  5  lb)  to  flow  into  the  heating 


Discharge  to 
Open  Drain 
Ail-Trap  not 
^  necessary 
|if  BoilerTEeed 
oPump  ia  usedl 


Fig.  28.     Detail  Showing  Method  of  Drip- 
ping Rise  in  Steam-main 


Fig.  29.  Detail  Showing  Method  of  Con- 
necting Rotary  Vacuum-pump  when 
Return-line  is  Below  Vacuum-pump 


system  whenever  the  demand  is  greater  than  the  supply  from  the  engines,  or 
when  the  engines  are  not  in  operation.     (See  Fig.  30.) 


Exhaust  from  Engine 

Fig.  30.    Exhaust  Steam-heating  Vacuum  System 

The  vacuum  maintained  by  the  pump  on  the  main-return  line  is  ordinarily 
about  10  in  of  mercury.  This  pump  is  placed  under  automatic  control.  The 
controller  being  operated  by  the  pressure  in  the  return-line. 


1290  Heating  and  Ventilation  of  Buildings 

Table  XX.     Capacities  of  Dunham  Vacuum-Traps 


Part  3 


Capacity, 

Pipe- 

Diameter 

Number 

Size. 

direct 
radiation, 

connec- 
tion, 

Weight, 

of 
port. 

Lift, 

in 

sq  ft 

m 

lb 

in 

m 

I 

Vi 

100 

Vi 

i>^ 

2 

H 

350 

Vi 

2  3-2 

% 

H 

3 

4S0 

H 

B.T. 

% 

I  500 

% 

13 

% 

3/16 

B.T. 

I 

3  000 

I 

21 

I 

These  traps  are  designed  for  steam-pressures  not  in  excess  of  lo-lb  gauge.  For  main 
and  riser-drips,  use  no  smaller  trap  than  the  No.  3,  and  install  trap  as  per  details. 

Care  must  be  exercised  in  selecting  a  trap  or  traps  of  the  proper  size  for  hot-blast 
heating-coils.  The  capacity-ratings  for  all  traps  are  in  terms  of  direct  cast-iron  radia- 
tion, on  a  condensation-basis  of  approximately  0.25  lb  per  sq  ft  per  hr.  Every  unit  of 
blast-coil  must  be  reduced  to  that  basis  before  trap-sizes  are  chosen  and  specified.  (See 
Hot-Blast  Heating  for  further  details  in  reference  to  rating  of  vacuum-traps  for  hot- 
blast  coils.) 

Size  of  Vacuum-Pump  Required.  The  following  table  by  the  Warren 
Webster  Co.  may  be  used  in  determining  the  size  of  steam-driven  vacuum-pump 
necessary.  To  determine  the  size  of  pump  required  the  following  empirical 
formula  is  used: 

Square  feet  of  direct  radiation  +  (number  of  units  X  100)  =  F.  Choose 
the  nearest  size  corresponding  to  the  value  of  F  given  in  the  table.  The  steam- 
cylinders  are  proportioned  on  a  basis  of  80-lb  pressure  and  for  lower  pressures 
the  steam-cylinder  must  be  proportioned  accordingly. 

Example.  Required  the  size  of  pump  for  5  000  sq  ft  of  direct  radiation  in  150 
radiators.     5  000  +  (150  X  100)  =  20  000.     Use  a  5  X  6  X  lo-in  pump. 


Table  XXI.     Sizes  and  Capacities  of  Vacuum-Pumps 

Size 

Steam, 
in 

Exhaust, 
in 

Suction, 
in 

Dis- 
charge, 
in 

F 

Floor- 
space 

4      XS 

4      X4      X   6. 

4  X4      X   8. 

5  XS 

4      XS      X  6. 

4  XS      X  8. 
4MXSMX  8. 

6  XS 

6  X7 

4MX6      X  8. 

5  X6      Xio. 

7  X7HX10. 

6  X7MX12. 

7  X8      Xi6. 
6      X8      X12. 

% 
Vs 

H 
I 

H 

I 

'"y 
I 

iM 
I 

I 

2H 

2M 

3 
3 
3 

3 

4 
S 

s 
s 
s 

2 
2 

'  2  K  * 

2Vi 
2H 

3 

S 
4 
4 
4 

6  830 

7  270 

8  000 

10  680 

11  3S3 

12  500 

IS  125 
IS  990 

17  215 

18  000 

19  390 
28  256 
30  60s 
34  470 
36  620 

11X34 
II  X34 

13X36 
13X38 
13X38 

13X38 
18X50 
18X52 
19X54 
18X52 
19X54 

This  table  may  also  be  employed  in  determining  the  size  of  motor-driven 
reciprocating  vacuum-pumps,  the  last  two  figures  under  Size  being  the  diameter 


Design  of  Low-Pressure  Steam-Heating 


1291 


and  stroke,  respectively,  of  the  pump.  A  vacuum-pump  should  be  specified  to 
have  a  displacement  of  at  least  from  lo  to  15  times  the  volume  of  the  con- 
densate when  operating  at  its  normal  rated  speed. 


Table  XXII.     Capacity  and  Size  of  Steam-Driven  Vacuum-Pumps 

Drain-     Drain- 

Steam- 
cylinder 
diam- 
eter. 

Water- 
cylinder 
diam- 
eter. 

Stroke, 

Steam- 
pipe, 

Ex- 
haust- 
pipe, 

Suc- 
tion- 
pipe, 

Dis- 
charge- 
pipe, 

ing           ing 

capacity  capacity 

direct        con- 

radia-     densed 

Floor- 
space, 

in 

in 

in 

in 

in 

in 

in 

sq  ft 

lb 

in 

3 

2^ 

4 

H 

H 

!}-€ 

iM 

2  700 

810 

30  X   6 

4 

4 

6 

Vi 

M 

2 

iH 

7  000 

2  \QQ 

4  8d^ 

40  Xio 

6 

6 

10 

I 

iM 

4 

3 

16  000 

59X14 

10 

ID 

12 

iM 

2 

6 

5 

40  800 

12  240 

72X20 

10 

12 

12 

iJ4 

2 

8 

7 

62  000 

18  600 

72X20 

10 

14 

12 

iM 

2 

10 

8 

85  000 

25  500 

10 

16 

18 

iH 

2 

12 

10 

92  000 

27  600 

10 

18 

18 

i^ 

2 

12 

10 

128  000 

38  400 

*  Condensation  figured  at  0.3  lb  per  sq  ft  radiating-surface  per  hour. 

Vacuum-pumps  with  belted  electric  motors  are  made  by  the  Bjshop-Babcock- 
Becker  Co.,  with  capacities  of  2000,  5000,  10  000,  17000  and  25000  sq  ft  of  direct 
radiation.  This  pump  should  be  under  the  control  of  a  reliable  vacuum-pump  governor 
so  that  when  the  requured  vacuum  has  been  produced  the  pump  will  stop. 


Design  of  Low-Pressure  Steam-Heating  Systems 

Amount  of  Radiation  Required.  The  heat-loss,  //,  of  the  various  rooms  is 
calculated  as  previously  indicated,  and  //  is  divided  by  250.  The  result  is  the 
amount  of  direct  radiation  in  square  feet  required.  The  heat-emission  of  cast- 
iron  radiation  for  pressures  up  to  5  lb  per  sq  in  may  be  assumed  as  250  Btu  for 
all  practical  purposes  of  calculation. 

Rating  of  Boiler  Required.  If  anthracite  coal  is  to  be  used  for  fuel  add  not 
less  than  50%  to  the  total  amount  of  direct  radiation  to  be  installed  and  65% 
if  bituminous  coal  is  to  be  used,  to  allow  for  radiation-loss  of  boiler,  mains, 
returns,  etc.    The  steam-mains  and  risers  should  always  be  covered. 

Size  of  Mains,  Branches  and  Return-Pipes.  Steam-mains  in  low-pressure 
gravity  systems  should  be  so  proportioned  that  the  loss  in  pressure,  due  to  pipe- 
friction,  does  not  exceed  approximately  i  oz  or  0.062  lb  per  sq  in,  per  100  ft  of 
run.  The  reason  for  thus  limiting  the  pressure-loss  is  apparent  from  an  inspec- 
tion of  Fig.  31.  Owing  to  the  fact  that  the  steahi  is  losing  pressure  as  it  flows 
through  the  main,  it  follows  that  1  he  pressure  at  the  last  riser  will  be  lower  than 
in  the  boiler.  The  difference  in  pressure,  or  pressure-loss,  P,  causes  the  water 
in  the  return-main  to  stand  higher  than  the  water-line  of  the  boiler.  The 
added  height  Z  is  equal  to  the  height  of  a  column  of  water  which  pressure  P 
will  support.  Thus,  if  the  boiler-pressure  is  2  lb  per  sq  in  and  the  pressure  at 
the  far  end  of  the  main  is,  say  i>^  lb,  with  water  weighing  61  lb  per  cu  ft,  or  0.035 
lb  per  cu  in,  the  water  in  the  return  will  stand  (2  —1.50)  -h  0.035,  or  -^  =14  in 
above  the  water-line  of  the  boiler  for  a  >^-lb  loss  in  pressure  between  the  boiler 
and  the  end  of  main.    It  is  apparent  in  this  instance  that  unless  the  water-line 


1292 


Heating  and  Ventilation  of  Buildings 


Parts 


of  the  boiler  is  about  1 8  in  or  more  below  the  last  riser,  or  radiatoi*-connectioa, 
water  is  quite  likely  to  flood  the  steam-main  and  to  be  accompanied  by  a  ham- 
mering and  a  poor  circulation  in  the  radiators  located  at  or  near  the  end  of  the 
run.     Steam-mains  are  graded  in  the  direction  of  flow  approximately  i  in  in  lo  ft. 


Fig.  31.    Location  of  Boiler  and  Arrangement  of  Pipes  for  Low-pressure  Steam-heating 

Systems 

Referring  to  Fig.  31,  and  assuming  a  7  ft-6  in,  or  90  in,  clear  height  of  base- 
ment, and  a  boiler  having  a  7 2-in  water-line  and  a  length  of  steam-main  of  icx)  ft, 
it  is  evident  that  the  boiler  must  be  located  in  a  pit,  the  depth,  A',  of  which  is 


6  4-  10  -f  18  -1-  72 


.90 


16  in 


in  order  to  maintain  t8  in  between  the  water-line  in  the  boiler  and  the  end  of 
steam-main.  The  distance  in  practice  should  not  be  made  less  than  from  18 
to  24  in.  The  extreme  pressure-load  stated,  ^  lb,  in  this  illustration,  is  never 
approached  in  normal  operation,  when  the  mains  are  designed  for  i-oz  drop 
per  100  ft,  but  may  approach  the  value  stated  when  the  system  is  being  started 
up  with  cold  radiators,  when  the  rate  of  condensation  is  very  much  higher.  The 
pressure-loss  in  a  pipe  flowing  full  of  steam  may  be  approximated  by 
Babcock's  formula 


IF  =87.5 


i, 


ypd^ 


h'i) 


in  which  W  is  the  weight  of  steam  flowing  per  minute  in  pounds,  L  the  length  of 
pipe  in  feet,  d  the  diameter  of  pipe  in  inches,  y  the  density  of  the  steam  and  p 
the  loss  in  pressure  in  pounds  per  square  inch. 

One  square  foot  of  direct  radiation  will  condense,  under  nonnal  conditions  of 
operation,  0.25  lb  per  hr,  and  the  density  of  steam,  y,  is  0.043  lb  for  a  2.3-lb 
pressure.  The  sizes  of  steam-mains  given  in  the  tables  were  calculated  by  the 
above  formula,  the  pressure-loss,  p,  being  limited  to  i  oz,  or  0.062  lb  per  sq  in 
per  100  ft  of  straight  pipe.  To  allow  for  the  fittings  approximately  twice  this, 
or  }4  lb  per  sq  in  per  100  ft  of  pii^e  may  be  assumed.  The  pipe-sizes  for  the  one- 
pipe  system  are  given  in  Table  XX III,  corresponding  to  the  amounts  of  direct 
radiation  stated  in  the  last  column.  Branches  and  risers  may  l)e  taken  from 
Table  XXIV,  and  reliefs  for  risers  from  Table  XXV.  For  the  two-pipe  and  also 
the  one-pipe  relief  system  the  steam-main  may  be  reduced  in  size  as  rapidly  as 
the  radiation  carried  will  permit.  The  steam-main  should  not,  however,  be 
of  any  smaller  size  than  risers  called  for  in  Table  XXIV. 

For  one-pipe  circuit  systems,  unless  the  steam-main  is  frequently  dripped, 


p' 


Design  of  Low-Pressure  Steam  -Heating 


1093 


THE  MAIN  MUST  BE  RUN  FULL  SIZE  to  the  end,  at  which  point  an  automatic  air- 
yalve  should  be  installed  and  the  main  dripped  into  the  return.  This  system 
is  generally  used  for  the  heating  of  residences  not  exceeding  two  stories  in 
height.    For  buildings  two  stories  or  more  in  height  the  one-pipe  relief  system 


<^   2nd 


SECOND  AND  T^|llRD  FLOOR  RADIATORS 


1)^' 


riir 


Main-J^l>^^    '{^^  I'Relief  or  Drip 

Branch    ^^t^^  j^^^^^^  ^^^^^  j,j^^^) 


^ 


1st  Y 


I  ,i&«lH 


FIRST-FLOOR  RADIATOR 
Fig.  32.    One-pipe  Relief  System 


X  •>[crGT 


Cable  XXm.     Pipe-Sizes  for  One-Pipe  Low-Pressure  Gravity  Heating  Systems. 
Main-Table 


Steam-main, 

Dry  return,* 

Radiation, 

m 

m 

sq  ft 

I 

I 

40 

iH 

I 

75 

I  }4 

iH 

126 

2 

iH 

286 

2y2 

2 

535 

3 

2M 

890 

3H 

2^4 

I  360 

4 

3 

I  950 

5 

3 

3  600 

6 

4 

5  900 

8 

4 

12  700 

10 

s 

22  900 

12 

6 

37  000 

*  For  wet  returns  reduce  one  size,  with  iK  in  as  a  minimum  size 


1294 


Heating  and  Ventilation  of  Buildings 


Parts 


may  be  employed,  in  which  case  the  risers  supplying  the  radiation  for  the  second 
floor  and  above  are  dripped  into  the  return  as  shown  in  Fig.  32.  The  minimum 
size  for  a  wet  return  should  not  be  less  than  i  J<  in,  as  a  smaller  pipe  is  Hkely  to 
become  plugged  with  an  accumulation  of  dirt  and  scale. 


Table  XXIV. 


Pipe-Sizes  for  One-Pipe  Low-Pressure  Gravity  Heating  Systems, 
Branch  and  Riser-Table 


Radiation, 
sq  ft 

Radiator- 
tapping, 

in 

Branch- 
riser, 

radiator- 
arm, 
in 

0  to     20 

I 

I 

21  to      24 

I 

i>i 

25  to    40 
41  to     6o 
6i to     8o 
8i to  100 

lOI  to   200 
201    to  300 

2 

2 
3 

For  risers  carrying  more  radiation  than  given  by  the  table,  use  the  table  fo 
Steam-mains  and  increase  one  size. 


Table  XXV.     Pipe-Sizes  for  One-Pipe  Low-Pressure  Gravity   Heating  Systems 
Reliefs  for  Risers  (One-Pipe  Relief  System) 

Riser,  in i 

Relief,  in H 

I 

I 

2 

2H 

i?/2 

3         3^ 
2         2 

4 

2H 

4^ 
3 

5 
3 

Table  XXVI.     Pipe-Sizes  for  Two-Pipe  Gravity  Systems 


msH'tr^.  '^ni 


Direct 

Diameter 

Diameter  of 

radiation- 

of  supply. 

dry  return,* 

surface 

-Ul-OitiM 

supplied. 

m 

m 

sq  ft 

H 

H 

20 

I 

% 

36 

i}4 

I 

72 

iK 

iH 

120 

2 

I'A 

280 

2V2 

2 

530 

3 

2^ 

900 

3M 

2K 

I  320 

4 

3 

I  920 

4M 

3 

2  760 

S 

3H 

3  720 

6 

33^ 

6  000 

8 

4 

12  800 

9 

4K 

17  800 

10 

5 

23  200 

12 

6 

31  000 

*  For  wet  returns,  reduce  one  pipe-size,  with  1)^  in  as  a  nunimtUti. 


Design  of  Low-Pressure  Steam-Heating 


1295 


Pipe-Sizes    for    Two-Pipe    Low-Pressure    Gravity    Heating    Systems. 

Table  XXVI  may  be  used  in  determining  the  sizes  of  mains,  branches  and  risers 
for  a  two-pipe  gravity  system. 


i^'"        Fig.  33.     Riser-diagram  for  Down-feed  Mechanical  Vacuum  System 


1296 


Heating  and  Ventilation  of  Buildings 


Part  3 


Pipe-Sizes  for  Two-Pipe  Mechanical  Vacuum  Systems.  The  sizes 
of  branch-supplies  to  radiators,  risers,  steam-mains,  radiator-returns  with  ther- 
mostatic valves  and  main-returns  may  be  taken  from  Table  XXVII.  (See 
Example,  Fig.  33.) 

Table  XXVII.     Two-Pipe  Mechanical  Vacuum  Systems 


Size  of 
pipe. 

in 

Rating  direct  radiation 

Radiator-connections 

Steam- 
mains  and 
risers, 

sq  ft 

Return- 
mains  and 
return-risers, 

sq  ft 

Size  of 
radiator, 

sqft 

Size  of 
steam- 
connection, 

in 

Size  of 
return- 
connection 
and  valve, 
in 

I 
iK 

2 

2H 

3 

3H 

4 

4H 

S 

6 

8 

9 

10 
12 

14 

5 

20 

40 

75 
150 
300 
500 
900 

1  500 

2  000 

2  800 

3  600 
6  000 

13  000 
18  Qbo 
23  obo 
37  000 

40 

160 
320 

600 

1  200 

2  400 
4000 
7  200 

12  000 
16  000 
22  400 
28  800 
48  000 

i     72  000 

1 

30 

50 
.75 
100 
125 
150 
200 
300 

I 

iH 

2 

2 

H 
K 
K 

'A 

A 

' 

55  000 

Table  XXVIII. 


Direct  Radiation  Required  for  the  Factory  OflBce-Building  Shown 
in  Figs.  9  and  34. 


Room-designation 

Btu- 

loss 
per  hr 

Direct 

rad'n 

required, 

column 

2-7-250 

Ra 

diation  to  be  installed 

No. 
radiators 

No.  cols. 

and 

height 

No.  sect's 

each 
radiator 

•'Total, 
sq  ft 

I 

2 

3 

4 

"   S       \ 

6 

7 

Sample  rm 

Hall 

54  900 
19  123 
27  358 
19  482 
7  380 
31  306 
19  224 
70  247 
31  306 

219 
77 
95 
77 
29 

125 

78 
281 

125 

4 

I 
2 

I 
I 
2 
I 
4 
2 

Z-Z2" 
3-38" 
3-32" 
3-32" 
3-32" 
3-32" 
3-38'' 
3-32" 
3-32" 

12 
15 
II 
17 
7 
14 
16 
16 
14 

216 

75 

99 

76K 

31M 
126 

80 
288 
r26 

Laboratory 

Storage 

Toilet 

Mgr's  office 

Hall         

Gen'l  office 

Sup*t's  office  .  .-.  . 

Totals 



I  108 

Design  of  Low-Pressure  Steam-Heating  1297 

Pipe-Sizes  for  Indirect  Gravity  Radiation.  Multiply  square  feet  of 
indirect  radiation  by  2  and  use  Table  XXVI. 

Design  of  One-Pipe  Low-Pressure  Gravity  Heating  System.  Direct 
Radiation.     Let   it    be   required    to    design  a  heating  system  of  this  type 


Flanges 
NOTE:- All  Radiators  2-Col. 
32"  high  unless  otherwise 
noted. 

Fig.  34.     Single-pipe  Low-pressure  Steam-heating  System  for  Factory  Office-building. 
(See,  also,  Fig.  9.) 


for  the  factory  office-building  shown  in  Figs.  9  and  34,  the  heat-losses  being  as 
previously  calculated  and  given  by  Table  VII.  The  location  of  the  radiators 
are  as  indicated  on  the  floor-plans,  Fig.  9. 


1298 


Heating  and  Ventilation  of  Buildings 


Part  3 


Direct  Radiation  Required.  The  total  Btu-loss  for  each  room  is  repeated 
in  column  2  of  Taljle  XXVI IT.  The  amounts  of  radiation  required  for  these  losses 
is  given  in  column  3  and  were  obtained  l^y  dividing  the  Btu-loss  in  each  case  by 
250,  the  average  heat-emission  of  direct  radialion  (Btu)  per  square  foot  per 
hour  for  a  room- temperature  of  70°  and  2  lb  steam-pressure. 

Boiler-Capacity  Required.  The  boiler-capacity  must  be  such  that  it  will 
carry  the  radiation  installed  plus  the  extra  heat-loss  from  the  steam-mains 
return-mains  and  boiler.  The  steam-mains  are  to  be  covered  and  anthracite 
fuel  is  to  be  used.  The  fuel-capacity  of  the  fire-pot  is  to  be  sufficient  for  an  8- 
hi  firing-period.  Adding  50%  to  the  sq  ft  of  radiation  installed,  1.5  X  1.108 
=  I  662  sq  ft,  the  boiler-rating  required.  The  fuel-holding  capacity  of  the 
fire-pot  should  be  checked  for  the  boiler  proposed  as  previously  stated  under 
Boilers. 

Chimney-Size.  The  size  of  chimney  may  be  taken  from  Table  XVn,  and, 
in  this  case,  is  12  X  12-in  inside  dimensions,  by  a  40-ft  height.  The  nearest 
size,  for  Hue-lining,  Table  XVI,  is  13  X  18  in. 

Design  of  Piping  System.  The  layout  of  the  basement-mains  and  risers 
for  a  ONE -PIPE  CIRCUIT  SYSTEM  is  given  in  Fig.  34.  The  risers  are  not  dripped 
in  this  case.  Steam-main  A  supplies  623  sq  ft  of  radiation,  and,  according  to 
Table  XXIII  must  be  3  in  in  diameter.  The  diameter  must  be  carried  to  the 
end  where  it  is  dipped  into  the  return-main  by  a  i  ^-m  relief,  as  indicated  in 
Table  XXIII,  for  a  dry  return-pipe.  In  order  to  keep  the  steam-main  as  close 
to  basement-ceiling  as  possible,  where  it  passes  beneath  the  floor-girder,  a  rise 
is  made,  and  consequently  a  i  M-in  drip  must  be  provided  to  take  care  of  234 
sq  ft  of  radiation.  The  main  wet  return  takes  care  of  1108  sq  ft  of  radiation 
and  is  therefore  made  2-in  diameter.  The  risers  and  branches  are  proportioned 
by  Table  XXIV, 

Gravity  Indirect  Heating 

General  Description.  A  satisfactory  means  of  providing  for  the  heat-loss 
in  a  room,  and,  at  the  same  time,  supplying  air-ventilation,  is  accomplished  by 
this  system.     The  radiators  properly  encased  with  a  sheet-metal  casing,  cov- 


Table  XXIX.  Final  Temperature  of  Air  Passing  Over  Indirect  Radiation.  Ex- 
tended-Surface Type.  Initial  Temperature  of  Air,  0°  F.  Heater,  One 
Stack  in  Depth.    Four-Inch  Spacing  of  Sections 


Velocity  of  air 
through  free 
area  of  heater, 

in  ft  per  min,  v* 

Final  temperature,  /2,  in 
degrees  Fahrenheit 

Steam  at 
2-lb  pressure 

Hot  water, 
180°  F. 

SO 

100 
125 
150 
175 
200 

122 
100 
95 
90 
86 
82 

147 
127 
120 
113 
106 
102 

♦Measured  At  70"  F.    For  first-floor  registers  a  velocity  of  150  ft  per  min  through 
ree  area  and  150  ft  per  min  for  second-floor  registers  is  the  usual  assumption. 


Gravity  Indirect  Heating 


1299 


ered  with  insulation,  are  ordinarily  hung  from  the  basement  ceiling  by  means  of 
light  angle-iron  or  strap-iron,  as  shown  in  Fig.  35.    Each  radiator  is  ordinarily 


1  Clean-Out> 

or  T  Iron  belaw^ 

Casing  -^ 
Fig.  35.     Indirect  Radiators,  Casings,  Connections,  etc. 


ibove  W.L.  for  V.Clean--Out  I  Clean-Ontl 

aravitj-Steain  Systems  Ciean-UUt       „  , 

i ^ ELEVATION.  INDIRECT  RADIATOR  WITH   ^Tlfon  bSS 

G.I.  CASING  AND  DUCTS 


provided  with  a  fresh-air  inlet  and  hot-air  duct  connecting  the  radiator  with  the 
room-register.  A  recirculating  duct  may  be  provided,  as  indicated,  in  order  to 
economize  on  the  heating  in  ex- 
tremely cold  weather  if  desired. 
There  should  be  a  separate  ver- 
tical hot-air  duct  for  each  register 
to  be  supplied,  connected  with 
its  own  indirect  radiator.  At- 
tempting to  supply  more  than 
one  register  from  an  indirect 
radiator  is  not  usually  success- 
ful, or  recommended,  unless  a 
fan  system  is  employed  to  give 
a  positive  air-flow  as  with  the 
hot-blast  system,  described 
later.  The  hot-air  ducts  for 
the  upper  floors,  for  best  results, 
should  be  double  pipe  as  later 
shown  under  furnace-heating. 
The  indirect  radiator  is  designed 
to  present  a  maximum  of  heating-surface  to  the  air  passing  over  same. 
Among  the  various  standard  types  for  gravity  indirect  heating  rriay  be  men- 
tioned the  Indirect  Pin  Radiator  (Fig.  36),  Excelsior,  Sterling  and  Vento. 
Indirect  radiators  are  now  rated  according  to  the  temperature-increment,  or 


Fig.  36. 


School  Pin  Indirect  Radiator  for  Steam 
or  Water 


1300 


Heating  and  Ventilation  of  Buildings 


Parts 


rise,  which  they  are  capable  of  giving  to  the  air  passing  between  and  over  the 
sections  of  the  heater  for  various  velocities  of  air,  initial  temperature,  and  tem- 
perature or  pressure  of  the  steam,  or  temperature  of  the  hot  water.  The  veloc- 
ities stated  are,  for  convenience  in  rating,  based  on  air  at  70°.  The  free  or  unob- 
structed area  means  the  net  area  between  heater-sections  after  deducting  the 
area  of  the  projecting  surfaces  from  the  gross  area.  Limitations  of  space  pre- 
vent giving  more  than  these  data  for  one  type  of  indirect  radiator. 


rjyjr\ 


-+t4 


HI 


7M 


an 


xjmj- 


ipct 


1+  +  + 


2  Pipe  Tap, 


Fig.  37.    Vento  Thirty-inch  Indirect  Heater-section 


Tables  XXIX  and  XXX  give  the  results  of  tests  made  on  Vento,  indirect 
radiation,  American  Radiator  Company.     (See  Fig.  37.) 

Table  XXX.     Dimensions,  etc.,  Vento  Indirect  Radiation 


Size 

Heating- 
surface,  5, 

sqft 

Height, 
in 

Width, 
in 

Free  area 

between 

sections,  (a), 

sqft 

30-in  section 

40-in  section 

50-in  section 

60-in  section 

8.00 
10.75 
13.50 
16.00 

29  J'S 
SO  2042 

601H6 

9H 
9M 
9K 
9K 

0.256 
0.3S 
0.428 
0.511 

Spacing  of  sections,  4  in  on  centers  for  gravity  air-circulation. 

Weight  of  Air  to  be  Circulated  per  Minute,  W.  U  =  temperature  of  air 
leaving  register.  /  =  temperature  of  room.  0.24  =  sp  heat  of  air.  H  —  heat- 
loss  of  room  to  be  warmed  in  Btu  i^er  hour.  V  =  volume  of  air  in  cubic  feet 
per  minute  measured  at  70°. 


Then 


W  =  ///[60  X  o.24(/i  —  /)],  lb  of  air  per  min 
Y  =  IF/ (0.075  =  the  density  of  the  air  at  70**) 


Gravity  Indirect  Heating  1301 

Area  of  Indirect  Heating-Surface  Required,  S.  k  =  initial  temperature  of 
air  entering  indirect  heater,  ti  =  final  temperature  air  leaving  heater  =  ti  +5° 
(assumed  temperature-loss  in  hot-air  duct).  V  =  velocity  through  free  area  of 
heater  in  feet  per  minute,  measured  at  a  temperature  of  70°.  F  =  total  fire- 
area  required  in  heater,  in  square  feet,  a  =  free  area  for  one  section  of  heater 
in  square  feet,    n  =  number  of  sections  required. 

Then  F  =  V/v  =  W /0.75V,  n  =  F/a  and  5  =  n  X  5 

Example.  Required  the  amount  of  indirect  low-pressure  steam-surface  of 
the  extended-surface  type,  the  number  and  size  of  sections,  and  the  over-all 
dimensions  of  an  indirect  radiator  to  supply  the  necessary  heat  to  warm  a 
first-floor  room,  the  heat-loss  of  which  is  ^  =20  000  Btu  per  hour.  All  the  air 
is  to  be  taken  from  the  outside,  the  temperature  of  which  is  /  0  =  0°  F.  The 
inside  temperature  to  be  maintained  is  /  =  70°  F. 

Solution.  It  is  first  necessary  to  assume  a  temperature,  h,  for  the  air  entering 
the  room,  in  order  to  calculate  the  amount  or  weight,  W,  of  air  required  to  be 
circulated  to  convey  the  heat  required  to  make  up  the  heat-loss  //. 

Assume  h  =95°  and  ^2  =  /i  +  5  (loss)  =  100°;  and  v  =  100  ft  per  min, 
from  Table  XXIX. 

Then  W  =  20  oco/[6o  X  0.24(100  —  70)]  =  46.3  lb  per  min 

and  V  =  46.3/0.75  =  617  cu  ft  per  min,  measured  at  70°  F. 

Assume  40  in  as  the  length  of  section  desired  in  this  installation, 

a  =0.35  (Table  XXX); 

F  =  617/100  =  6.17,  the  total  square  feet  of  free  area  required; 

n  =  617/0.35  =  i3,  the  number  of  sections  of  40  in. 

Vento  is,  therefore,  required,  giving  a  total  heating-surface  of 

S  =  10.75  X  18  =  193.5  sq  ft 

Dividing  this  equally  between  two  indirect  radiators  the  width  of  each  heater 
is  equal  to  nine  (sections)  X  4  (spacing-sections)  =  36  in. 
Low-Pressure  Boiler-Rating  Required  for  Gravity  Indirect  Radiation. 

The  amount  of  heat  given  up  to  the  radiator  is 

h  =  o.24W{l2  -  to)  X  60  Btu  per  hr 

The  equivalent  rating  in  square  feet  of  direct  radiation  is  therefore  R  = 
h/250,  plus  25%  for  radiation  of  mains,  returns,  etc. 

Example.     Required  the  equivalent  low-pressure  boiler-rating  to  supply  the 
indirect  radiation  in  preceding  example. 
Solution. 

h  =  0.24  X  46.3  (100  —  o)  X  60  =66  672  Btu  per  hr 
R  =  (66  672/250)  X  1.5  =  399  sq  ft 

In  other  words,  i  sq  ft  of  low-pressure  steam  indirect  radiator  with  gravity- 
circulation  is  practically  equivalent  to  2  sq  ft  of  direct  radiation;  or  the  amount 
of  indirect  surface  is  approximately  0.4  of  the  amount  of  direct  radiation 
required. 

Area  of  Hot-Air  Ducts  for  Gravity-Circulation.  A  velocity  of  approxi- 
mately one  third  of  the  theoretical  velocity  attainable  by  natural  draft,  due  to 


1302 


Heating  and  Ventilation  of  Buildings 


Part  3 


the  smaller  density  of  the  heated  air,  is  assumed  in  practice  in  proportioning 
the  area  of  the  hot-air  ducts. 

Table  XXXI.    Theoretical  Velocity  (V)  of  Air,  in  Feet  per  Second,  Due  to  Natural 

Draft 


Height 
of  flue 

Excess  of  temperature 

in  flue  above  external  air 

in  feet.  E 

1 

10" 

15° 

20" 

25° 

30° 

50° 

100° 

150" 

I 

I .  I 

1.4 

1.6 

1.8 

2.0 

2.5 

3.6 

4.4 

5 

2.5 

3-1 

3.6 

4.0 

4-5 

5.6 

8.1 

9.^^; 

ID 

3.6 

4-4 

5.1 

5.7 

6.6 

8.1 

II. 4 

14.0     ? 

IS 

4-4 

5.4 

6.3 

7.0 

7.7 

9-9 

14.0 

17.1 

20 

5.1 

6.3 

7.2 

8.1 

8.8 

11.4 

16. 1 

19.8 

25 

5.7 

7.1 

8.1 

9  0 

9-9 

12.8 

18.0 

22.1 

30 

6.3 

7.8 

8.8 

9-9 

I0.8 

14.0 

19.8 

24.2r;.t 

35 

6.8 

8.4 

9-5 

10.7 

IT. 7 

15. 1 

22.3 

26.1.1 

40 

7.3 

8.9 

10.2 

II.4 

12.5 

16. 1 

22.8 

27.9 

Example.  Required  the  size  of  hot-air  duct  for  each  of  the  indirect  radiators 
in  the  preceding  examples  for  a  first-floor  installation,  the  effective  height  E  being 
5  ft. 

Solution.  The  excess  of  temperature  in  the  flue  above  the  external  air  is 
100  —  o  =  100°.  The  theoretical  velocity  in  the  duct,  from  Table  XXXI,  is 
8.1  X  60  =  486  ft  per  min.  The  actual  velocity  is  approximately  one  third  of 
this,  or  162  ft  per  min.  The  weight  of  air  per  minute  passing  through  the  flue  is 
23  lb,  or 

23/(0.07 1  (density  at  ioo°)]  =  324  cu  ft 

The  required  area  of  the  flue  is  therefore 

324/162  =  2  sq  f t  =   288  sq  in 

The  gross  area  of  the  register-face  must  be  approximately  1.8  this  amount 
or  518  sq  in,  to  obtain  the  same  free  area  through  the  register-grill  as  exists  in 
the  flue  or  duct.  Sizes  of  standard  registers  are  given  in  the  section  on  Fur- 
nace-Heating. 

Direct  Hot- Water  Heating 

Systems  in  Use.  Systems  for  heating  with  direct  hot-water  radiators,  like 
the  direct  steam  heating  systems,  may  be  divided  into  two  general  classes,  the 
first  of  which  includes  all  those  systems  operating  by  gravity  only,  depending 
on  the  difference  in  density  of  the  water-columns  in  the  flow  and  return-lines  to 
cause  circulation.  The  second  class  includes  those  systems  in  which  a  forced 
circulation  is  maintained  by  means  of  a  pump  placed  on  the  return-line  just 
before  it  enters  the  boiler  or  heater.  These  latter  systems  are  employed  usually 
only  in  large  installations  or  in  district-heating  service. 

Gravity  Hot-Water  Heating  Systems.  The  gravity  systems  are  divided 
into  the  upfeed  systems^  using  basement-mains,  and  the  downfeed  systems, 
using  overhead  or  attic-mains.  The  upfeed  systems  may  have  either  a  one-pipe 
basement-main  or  two-pip>e  basement-mains,  and  the  latter  type  may  have 
either  a  direct  or  a  reversed  retuni-mahi.     (See  Figs  38  and  39  for  reversed 


Direct  Hot- Water  Heating 


1303 


return.)  The  downfeed  systems  may  have  either  SINGLE  OR  double  risers; 
Either  system  may  be  operated  with  an  open  or  closed  expansion-tank, 
as  shown  in  Figs.  42  to  46.  In  general,  the  downfeed  or  overhead  systems  are 
more  positive,  permit  the  use  of  smaller  mains  and  risers,  and  provide  for  the 
automatic  removal  of  air  from  the  radiators  and  piping.  It  is  necessary,  how- 
ever, that  the  headroom  or  clear  space  in  the  attic  should  be  at  least  4  or  s  ft  if 
the  overhead  mains  and  branches  are  to  be  properly  installed.  It  is  sometimes 
possible  to  run  the  overhead  mains  at  the  ceiling  of  the  top  floor,  and  in  such 
cases  the  above  restriction  does  not  apply.  Mains  run  in  attics  must  be 
well  insulated  to  prevent  freezing.    The  underfeed  systems  are  used  where 

fote:-  First-floor-supply  riser-connections 
;o  be  taken  from  top  of  main,  and  risers 
ibovo  first  at  45.     All  z-eturns  into  side 
»f  main,  (or  bottom).  3ee  below. 


Fig.  38 
BASEMENT  HEATING  PLAN 

Figs.  38,  39,  40  and  41.    Hot-water  Heating.    Two-pipe  Up-feed  System 


basement-space  is  available,  and  of  little  or  no  value,  and  the  radiation  is 
located  on  two  or  more  floors;  or  where  attic-space  is  so  limited  that  it  would 
not  be  possible  to  install  overhead  mains  and  branches.  Underfeed  systems 
are  liable  to  prove  unsatisfactory  in  buildings  less  than  two  stories  in  height,  as 
the  motive  head  with  radiators  on  the  first  floor  only  is  so  slight  that  faulty  or 
deficient  circulation  is  quite  likely  to  result. 

The  Upfeed  One-Pipe  System.  The  upfeed  one-pipe  system  is  in  very 
general  use  today,  and  is  employed  almost  exclusively  by  the  United  States 
Treasury  and  War  Departments  whenever  upfeed  hot-water  systems  are  to  be 
installed.  In  this  system,  as  shown  in  Figs.  43  and  45,  the  supply-main  rises 
close  to  the  basement-ceiling  just  above  the  boiler  and  grades  down  in  the  direc- 
tion of  flow,  with  a  uniform  grade  of  %  in  in  lo  ft.  Branches  are  taken  from  the 
top  of  this  main  for  supplying  flow-risers  and  the  return-branches  are  made  into 


1304 


Heating  and  Ventilation  of  Buildings 


Parts 


the  side  or  bottom.     (Fig.  40.)     Flow-connections  should  always  be  made  from 
the  top,  or  at  an  angle  of  45**  in  the  case  of  branches  near  the  boiler,  or  for  branches 

HOT-WATER   HEATING  -  EXPANSION  TANKS 
(OPEN  AND  CLOSED  SYSTEMS) 


_     S.A.O.  Connection 
f        for  Cold  Climateff 

^'■^  CJbeck-Valvo 


TableV.,. 
Expansion-Tanlcs 


Size 

in 

Inches 


10x20 


22  X  CO 


Capa- 
citjr 
Gal. 


100 


Sq.  ft  of 
Rad- 
iation 


250 


6000 


l^ote.- Galvanized  Steel,  Tested 
at  100  lb.  Tapped  lX"Top  and 
Bottom,  and  for  Gauge- 
Glass 


Runs  full  Size,  drop  after 
Serving  last  Radiator 


^ 


^ 


Grade  ^Si^in  lo'-O"  jij^l' 


Fig.  43 

ONE-PIPE  UNDERFEED 

SYSTEM, OPEN  TANK 

For-Piping-Si^es  See 

Tables  3cXXIl-and  XXXIII 


n 
H 


K—  2^0* -H  Grade  Dowa 
^       at  least 

5  Figr.  45 

1  PLAN 

^  Fig.  46 

:^~f  USUAL  METHOD 

2  3*   FOR  SMALL  SYSTEMS 


From  system^ 

Fig.  4r, 

HONEYWELL  GENERAT6R, 
FOR  USE  WITH  A  CLOSED- 
TANK  SYSTEM 


Figs.  42,  43,  44,  45  and  46.    Hot-water  Heating.    Expansion-tanks.    One-pipe 
Underfeed  System 

suppl5ang  only  upper-floor  radiators.     It  will  be  seen  that  in  the  case  of  branches 
supplying  radiators  on  all  floors  the  upper-floor  radiators  may  be  made  to  pull 


Direct  Hot-Water  Heating 


1305 


or  augment  the  circulation  of  the  first-floor  radiators  by  taking  the  basement- 
branch  for  the  former  from  the  side  of  the  branch  running  to  the  latter  radiator. 
The  first-floor  branch  is  usually  run  full  size  all  the  way  to  favor  the  lowest 
radiator,  as  shown  in  Fig.  45.  After  having  served  all  the  radiator-branches 
the  main  drops  and  returns  to  the  boiler,  continuing  the  same  size  for  the 
entire  circuit.  Connections  (Fig.  43)  to  radiators  should  be  made  at  the  top 
on  the  supply-end,  using  a  union  elbow,  and  at  the  bottom  on  the  return-end, 
using  a  quick-opening  hot-water  radiator-valve  with  union  connection.  By 
this  arrangement  only  one  valve  is  required  to  control  the  radiator.  Since  the 
temperature  of  the  water  in  the  one-pipe  main  gradually  drops,  due  to  the  return 
of  water  at  a  lower  temperature  from  the  radiators  served  in  the  course  of  the 
main  around  the  building,  it  is  advisable  to  increase  the  last  radiators  on  the 
main  from  5  to  10%  in  area  and  to  increase  the  size  of  branch  and  riser-connec- 
tions at  the  end  of  the  main  by  a  one-pipe  size.  Pipe-sizes  may  be  taken  from 
Tables  XXXH  and  XXXIII.  In  using  the  tables  all  mains  must  be  measured 
back  to  the  boiler,  and  risers  to  any  floor  are  proportioned  to  supply  all  the 
radiation  above  that  floor  as  well  as  the  radiator  actually  installed  on  that 
floor,  as  shown  in  Figs.  43  and  45. 


Table  XXXII.     Hot-Water    Heating.     Piping-Sizes. 
Basement-Mains 

Mains  up  to  100  ft 


Open-Tank    (Upfeed    with 


Pipe-size 
in  inches 

Direct 
radiation 

Indirect 
radiation 

in  square  feet 

in  square  feet 

iK 

135 

100 

iH 

220 

135 

2 

350 

225 

2H 

460 

320 

3 

67s 

500 

3V2 

850 

650 

4 

I  100 

850 

4H 

I  350 

I  050 

S 

I  700 

I  3SO 

6 

3  600 

2  900 

7 

4  800 

3  900 

8 

6  200 

5  000 

9 

7  700 

6  300 

10 

9  800 

7  900 

12 

14000 

II  400 

Table  XXXII  was  compiled  by  J.  J.  Hogan,  and  is  to  be  used  for  either  one  or  two- 
pipe  work. 

Length  of  main  must  be  measured  back  to  boiler. 


For  mains  over  100  ft,  reduce  capacity  in  the  ratio 


The  Upfeed  Two-Pipe  System.  The  upfeed  two-pipe  system  is  also  in 
very  general  use,  and  if  installed  with  a  reversed  return,  as  shown  in  Figs. 
38  and  39,  will  give  good  results.  It  a  direct  return  is  used  so  that  the  water 
circulates  first  through  the  radiators  nearest  the  boiler,  and  then  through  each 
succeeding  group  in  turn,  the  ends  of  mains  will  be  slow  in  warming  up,  the  last 
radiators  may  be  cold,  and  the  system  prove  unsatisfactory.     With    the    re- 


1306 


Heating  and  Ventilation  of  Buildings 


Parts 


Table  XXXIII.    Hot-Water  Heating.    Piping-Sizes.    Open-Tank    (Upfeed  with 
Basement-Mains) 

Branches  and  Risers 


Pipe-size 

Floor 

First 

Second 

Third 

Fourth 

in  inches 

Direct  radiation  in  square  feet 

% 

30 

45 

55 

70 

I 

6o 

75 

85 

95 

iM 

no 

120 

135 

150 

i3^ 

i8o 

195 

210 

230 

2 

290 

320 

350 

370 

23^ 

400 

490 

52s 

550 

3 

620 

650 

690 

730 

2>y^ 

820 

870 

920 

970 

4 

I  050 

I  120 

I  185 

I  250 

4^ 

.1  32s 

I  400 

1485 

I  560 

Table  XXXIII  was  compiled  by  J.  J.  Hogan,  and  is  to  be  used  for  either  one  or  two- 
pipe  work. 

VERSED-RETURN  SYSTEM  cach  group  of  radiators  has  exactly  the  same  length  of 
water-travel,  and  hence  the  resistance  to  be  overcome  is  practically  the  same, 
irrespective  of  the  distance  of  the  radiator-group  from  the  boiler.  It  will  be 
noted  that  the  return  begins  at  the  first  radiator  served  and  flows  in  the  same 
DIRECTION  as  the  flow-main,  increasing  in  size  while  the  latter  decreases.  The 
flow-main  grades  up  uniformly  ^  in  in  10  ft,  and  the  return  grades  down  toward 
the  boiler^with  the  same  pitch.  Pipe-sizes  may  be  taken  from  Tables  XXXII 
and  XXXIII  as  in  one-pipe  work,  and  the  main-size  reduced  or  increased  as 
rapidly  as  the  change  in  radiation  supplied  will  permit.  It  is  also  customary 
in  government  work  to  install  a  starting-pipe  (Fig.  38),  between  the  main  flow 
anci  return  at  the  boiler,  in  underfeed  systems.  This  pipe  ranges  from  i  M  to 
2K  in  in  size,  depending  upon  the  capacity  of  the  boiler,  and  is  intended  to  assist 
in  the  estabhshment  of  an  initial  circulation  between  flow  and  return-headers, 
even  before  the  water  in  the  mains  is  moving. 

Equalization-Table.  In  Federal-building  work  N.  S.  Thompson  makes  use 
of  the  following  Equalization-Table  in  proportioning  mains  and  risers  serving 
more  than  one  radiator  in  both  upfeed  and  downfeed  systems.  The  equal- 
izing-numbers represent  the  relative  capacities  of  the  different  sizes  of  pipes  for 

Table  XXXIV.     Equalization-Table  for  Mains  and  Risers 


=  2 
=  60 
=  650 


in 

y^ 

= 

5 

2^2 

= 

no 

6 

= 

I  050 

m 

I  =  10 
3  =  175 
7=1  600 


m 

i\i  =■  20 
3  M  =  260 
8        =2  250 


iH  =     30 
4       =  380 


Example.      A  iM-in,  iH-in  and  2-in  pipe  have  a  total  value  of  no  units,  and  hence 
are  equivalent  in  carrying  capacity  to  a  2  yi-\xi  main. 


Direct  Hot- Water  Heating  1307 

the  same  friction-pressure  loss  per  loo  ft  of  run,  and  are  proportional  to  the  5/2 
powers  of  the  diameters.  Thus  the  weight  of  water  flowing  varies  as  shown  by 
the  relation,  W  =  Kdy^^,  in  which  W  =  weight,  /  =  a  constant,  and  d  =  pipe- 
diameter. 

Details  of  Piping  Systems  and  •  Connections  for  Direct  Hot-Water 
Heating.  The  distinctive  piping-details  of  each  system  of  hot-water  heating 
have  been  discussed  under  that  system,  as  described  in  the  preceding  para- 
graphs. In  general  all  main  piping  and  branches  must  be  uniformly  graded, 
as  already  indicated,  and  ample  provision  made  for  expansion  and  contraction, 
and  the  ready  removal  of  air  from  all  parts  of  the  system.  Air-traps  or  pockets 
in  a  hot-water  system  are  fully  as  serious  as  water-pockets  in  a  steam  system. 
Hence  a  hot-water  main  grading  down  in  the  direction  of  flow  cannot  be  relayed 
unless  an  air-outlet  is  provided  at  the  top  of  the  relay.  If  the  main  is  reduced 
in  size  at  any  point  an  eccentric  fitting  must  be  used  to  keep  the  top  of  the 
large  and  small  main  in  the  same  plane  and  avoid  an  air-pocket.  Not  only 
must  all  the  piping  be  designed  to  permit  the  removal  of  air,  but  free  and  com- 
plete drainage  of  water  must  be  provided  for  as  well,  so  that  when  the  drain 
or  blow-off  cock  is  opened  at  the  boiler  the  entire  system  can  be  emptied  of  water. 
If  branch-mains  are  taken  from  a  header  at  the  boiler  they  must  all  rise  to  the 
same  elevation  so  that  the  tops  of  all  the  branches  will  lie  in  the  same  plane 
as  they  start  away  from  the  boiler.  The  fittings  on  all  main  piping  and  branches 
must  be  of  the  long-sweep  pattern,  and  all  pipe  should  be  carefully  reamed  to 
remove  burrs  and  sharp  edges.  Where  the  same  riser  supplies  radiators  on  two 
or  more  floors  the  branches  to  the  radiators  on  the  intermediate  floors  may  be 
connected  with  special  tees  (Fig.  41)  known  as  O.  S.  fittings,  with  a  deflector 
arranged  to  divert  the  current  of  flow  into  the  outlet  of  the  tee,  and  thus  favor 
the  radiators  on  the  intermediate  or  lower  floors.  By  using  top-flow  and 
bottom-return  connections  at  each  radiator  it  is  possible  to  positively  control 
each  unit  by  a  single  valve,  except  for  the  slight  circulation  intended  to  prevent 
freezing,  which  takes  place  through  the  I'ie-in-diameter  hole  drilled  in  the  valve- 
disc  or  sleeve,  when  the  valve  is  closed.  If  both  connections  are  made  at  the 
bottom  tappings,  and  only  one  valve  is  used,  it  is  entirely  possible  that  the 
radiator  may  still  be  supplied  with  hot  water  through  the  unvalved  connection 
even  when  the  valve  is  closed. 

Air-Removal  in  Hot- Water  Systems.  Suitable  provision  must  be  made  for 
the  removal  of  air  from  all  hot-water  radiators,  wherever  an  upfeed  system  is 
installed.  Usually  small  air-cocks  are  attached  to  the  highest  point  of  each 
radiator  and  are  periodically  opened  to  relieve  any  accumulation  of  air.  If 
these  cocks  are  forgotten  a  radiator  may  become  air-bound  and  fail  to  heat 
because  of  faulty  circulation;  hence  automatic  air- valves  are  sometimes  installed 
for  this  purpose.  The  automatic  air-valve  for  hot-water  radiators  is  not  very 
generally  used,  due  to  its  HabiUty  to  pass  water  as  weU  as  air;  but  a  standard 
type,  made  by  the  Monash-Younker  Company,  may  be  mentioned. 

Expansion-Tanks  for  Hot- Water  Heating.  Open-Tank  Systems.  The 
low-pressure  system  of  hot-water  heating  is  not  a  closed  system,  as  provision 
must  be  made  for  expansion  and  contraction  of  the  water  within  the  system. 
An  open  tank  is  provided  at  a  suitable  elevation,  not  less  than  3  ft  above  the 
highest  radiator,  and  connection  made  to  the  nearest  return-riser;  or  preferably 
a  separate  expansion-Hne  is  run  to  the  flow  or  return-main  in  the  basement. 
The  size  of  the  expansion-tank  varies  with  the  amount  of  water  in  the  system, 
and  also  with  the  range  in  temperature  of  same,  and  its  capacity  is  determined 
as  follows: 

The  increase  in  volume  of  a  given  weight  of  water  heated  from  32°  to  212°  ig 


1308  Heating  and  Ventilation  of  Buildings  Part  3 

about  Hs,  or  approximately  4.33%;  so  that  for  every  23  gal  in  the  system  at 
32°,  an  allowance  of  i  gal  must  be  made  in  the  expansion-tank  when  the  water 
in  the  system  is  raised  to  212°.  Cast-iron  radiators  have  an  internal  volume  of 
ij^  pints  per  sq  ft,  while  steel  radiators  and  i-in  pipe  hold  about  i  pint  per  sq  ft. 
Assuming  the  internal  volume  of  the  radiators  to  be  about  50%  of  the  entire 
system,  we  have  for  3  000  sq  ft  of  actual  radiation,  3000  X  2  X  H  gal  =  750 
gal  of  water.  This  water  will  increase  Hs  X  7So  =  33  gal  on  being  heated 
from  32°  to  212°.  Hence  an  expansion-tank  of  2  X  33  =  66-gal  capacity  is 
necessary,  the  tank  being  made  double  the  theoretical  volume  for  practical 
considerations. 

A  list  of  expansion-tank  capacities  and  dimensions  is  given  in  a  table 
(included  with  Figs.  42  to  46),  from  which  a  commercial  tank  may  be  readily 
selected  for  systems  under  6  000  sq  ft.  For  larger  systems  the  size  of  tank 
should  be  separately  determined  and  the  nearest  commercial  tank-size,  as  taken 
from  the  manufacturer's  list,  should  be  specified.  These  tanks  should  have  i 
or  i34-in  top  and  bottom  tappings  with  J^-in  water-gauge  tappings,  for  con- 
necting a  gauge-glass,  at  least  12 -in  long,  on  the  side  of  the  tank  as  shown  in 
Fig.  43.  The  tank  must  be  securely  supported  well  above  the  highest  radiator 
in  the  system,  and  in  the  larger  installations  special  framing  must  often  be 
designed  to  carry  the  weight  of  tank  and  water.  Automatic  expansion-tanks 
equipped  with  a  ball-cock  and  overflow  are  sometimes  installed,  and  the  altitude- 
gauge  on  boiler,  and  the  gauge-glass  and  fittings  on  tank  omitted.  These  tanks 
may  be  covered  with  hardwood  and  varnished  if  it  is  necessary  to  place  them  in  a 
finished  room  or  apartment. 

Expansion-Tank  Connections.  The  most  approved  method  of  connecting 
an  expansion-tank  to  a  low-pressure  one-pipe  system  is  shown  in  Fig.  43,  where 
an  expansion-and-vent  line  is  run  from  the  top  of  the  main,  at  the  high  point 
just  above  the  boiler,  and  connected  to  a  return-bend  just  beneath  the  tank. 
A  return  circulating-line  is  taken  from  the  other  side  of  this  bend  and  connected 
with  the  return-main  at  the  boiler.  The  circulation  of  water  in  this  loop  will 
prevent  freezing  at  the  tank.  From  the  top  of  the  tank  a  iJi-in  vent-line  is 
taken  through  the  roof,  and  a  iM-in  overflow  is  taken  out  of  this  vent-line  at  a 
tee  just  above  the  tank.  This  overflow  should  discharge  into  an  open  sink  or 
drain  near  the  boiler  so  that  it  will  be  immediately  evident  to  a  person  in  the 
boiler-room,  filling  the  system,  just  when  the  water  has  risen  to  the  overflow 
above  the  tank.  The  movable  hand  on  the  boiler  altitude-gauge  can  then  be  set 
to  correspond  with  the  middle  of  the  gauge-glass,  and  the  water-level  brought 
to  this  point  with  the  system  cold.  No  valves  should  ever  be  installed  on  either 
the  expansion  or  the  overflow-lines,  and  in  case  the  system  is  valved  at  the  boiler 
the  expansion-line  must  be  connected  on  the  boiler-side  of  this  valve;  and  where 
two  boilers  are  installed  this  line  must  be  carried  to  a  point  above  the  water- 
line  in  the  expansion-tank  to  prevent  siphoning  the  water  out  of  the  entire 
system  in  case  it  is  necessary  to  drain  OHly  one  boiler.  Expansion  or  vent-pipe 
connections  must  always  be  so  made  to  main-piping  in  basement  so  that  all  air 
will  be  automatically  removed  from  high  points.  Wherever  possible  risers  or 
branches  to  risers  may  be  used  for  reUeving  any  accumulation  of  air  in  the  main- 
piping.  In  SMALL  INSTALLATIONS  the  expansion-Une  may  be  connected  to  the 
return-riser  of  one  of  the  highest  radiators,  and  no  overflow  other  than  the  vent 
need  be  provided  for,  as  shown  in  Fig.  46.  This  is  a  cheap  method,  and  should 
not  be  resorted  to  unless  extreme  economy  must  be  practised.  The  tank  must 
be  in  the  same  room  with  the  radiator  to  prevent  freezing,  as  no  circulation  is 
provided  for,  and  the  overflow  is  simply  discharged  out  of  doors  and  usually 
upon  the  roof.     The  usual  result  is  that  an  unsightly  appearance  is  soon  created. 

The  United  States  Treasury  Department  employs  a  special  vent  and  overflow- 


Direct  Hot-Water  Heating 


1300 


connection  (Fig.  42)  in  cold  climates,  where  there  is  liability  of  the  vent-line  freez- 
ing up  if  run  out  through  the  roof,  due  to  the  condensation  and  freezing  of  vapor 
passing  out  through  this  line.  The  vent-line  is  made  only  2  ft  high  above  the 
tank  so  that  it  is  kept  within  the  building,  and  it  is  equipped  with  a  check-valve 
to  prevent  the  escape  of  water  through  the  same  in  case  the  tank  should  sud- 
denly overflow.  The  closing  of  the  check-valve  will  compel  the  excess  water  to 
pass  down  the  overflow,  and  prevent  the  flooding  of  the  building. 

Closed-Tank  Systems.  The  permissible  temperatures  in  any  hot-water 
system  are  limited  by  the  pressure  on  the  system,  which  latter  factor  determines 
the  point  at  which  boiling  will  take  place.  The  pressure  at  any  elevation  in  an 
open-tank  hot-water  system  will  vary  directly  with  the  distance  below  the  level 
of  the  water  in  the  expansion-tank,  and  hence  it  will  be  possible  theoretically  to 
carry  the  water  in  the  boiler  at  a  temperature  corresponding  to  the  hydrostatic 
pressure  at  the  boiler  before  boiling  would  occur.  The  relation  between  hydro- 
static head,  pressure  and  boiling-point  are  given  in  the  following  table: 


Table  XXXV.     Relation  between  Hydrostatic  Head,  Pressure  and  Boiling-Point 


Hydrostatic  head  in 
feet 

Pressure  in  pounds 
per  square  in 

Boiling-point 


0 

12 

24 

37 

49 

61 

74 

87 

100 

113 

125 

0 

5 

ID 

15 

20 

25 

30 

35 

40 

45 

SO 

212 

227 

239 

250 

259 

268 

274 

281 

287 

292 

298 

Practically  it  would  be  quite  impossible  to  carry  temperatures  in  excess  of  2 1 2  ° 
in  any  part  of  an  open-tank  system,  as  the  high-temperature  water  would  imme- 
diately rise  into  the  open  tank  and  boil.  In  order  to  overcome  the  hmitations 
of  the  open-tank  system,  in  which  water  will  always  boil  as  soon  as  a  tempera- 
ture of  212°  F.  is  reached,  various  means  of  increasing  the  pressure  in  these 
systems  have  been  resorted  to  in  the  attempt  to  carry  a  higher  water-tempera- 
ture in  the  radiators  in  very  cold  weather  than  would  be  possible  with  an  open- 
tank  system.  These  devices  have  usually  been  installed  on  the  expansion-line, 
either  at  the  boiler  or  else  just  below  the  expansion-tank  and  the  static  head 
increased  by  interposing  a  column  of  mercury  in  the  path  of  the  expanding 
water  as  it  flows  into  the  expansion-tank. 

A  common  form  of  the  apparatus,  known  as  the  Honeywell  Heat-Genera- 
tor, is  shown  in  Fig.  44,  in  which  it  is  seen  that  water  entering  the  generator 
from  the  system  wiU  force  the  mercury  up  the  inner  tube  A  until  a  head  of  20  in 
or  10  lb  is  established,  at  which  time  the  entrance  to  this  tube  will  be  uncovered 
by  the  mercury  and  water  or  air  may  enter  it  and  pass  to  the  expansion-tank. 
Any  excess  of  mercury  above  that  required  to  just  fill  tube  A  is  returned  by  tube 
B  to  the  reservoir  in  the  base.  When  the  system  cools  off  water  can  flow  back 
down  tube  A  as  soon  as  the  mercury-column  drops  in  it,  and  the  slight  head  of 
mercury  then  existing  at  the  outlet  of  this  tube  is  easily  overcome  by  the  head 
of  water  in  the  expansion-tank  above  this  point.  This  increase  of  10  lb  in  static 
pressure  makes  it  possible  to  carry  a  maximum  water-temperature  of  240**, 
nearly  30°  higher  than  would  be  possible  in  an  open-tank  system.  While  a 
temperature  as  high  as  this  could  theoretically  be  carried  at  the  boiler  in  an 
open-tank  system  with  a  static  head  of  24  ft,  just  as  soon  as  this  water  rose  in  the 
system  it  would  boil,  and  escape  from  the  expansion-tank,  at  the  same  time 
emptying  the  system  of  water.  In  fact  with  the  open-tank  system  the  water 
is  liable  to  be  driven  out  at  a  temperature  of  212°  F.  The  use  of  pressure-gene- 
rators similar  to  the  above  makes  it  possible  to  use  smaller  radiators  in  the 


1310r 


Heating  and  Ventilation  of  Buildings 


Part  3 


heated  rooms,  as  it  is  entirely  possible  to  maintain  steam-temperatures  in  the 
radiators  whenever  desired.  Since  higher  temperatures  are  used,  the  difference 
between  flow  and  return-riser  temperatures  becomes  greater  than  in  the  open- 
tank  system,  and  hence  a  greater  motive  head  exists  and  smaller  mains  and 
risers  may  be  used  with  this  system.  The  Honeywell  Company  recommends 
the  following  schedule  of  radiator-tappings: 

Table  XXXVI.     Riser- Sizes  for  Honeywell  System 


Pipe-size 
in  inches 

Capacity  in  square  feet  of  hot- 
water  radiation 

1st  floor* 

2nd  floor 

3rd  floor 

I 

30 

75 
75  up 

40 

100 

100  up 

50 

125 

125  up 

It  should  be  remembered  that  since  radiators  and  pipes  are  smaller  in  this 
system  there  is  much  less  water  than  in  the  open-tank  system,  making  it  more 
sensitive  in  warming  up  and  also  in  cooling  off.  The  generator  should  not  be 
placed  close  under  the  expansion-tank.  Otherwise  than  this  its  location  may  be 
anywhere  in  the  expansion-line,  as  the  same  hydrostatic  head  is  always  acting 
in  addition  to  the  head  of  mercury-column. 


Furnace-Heating 

The  Furnace  and  Its  Location.  The  method  of  warming  or  heating  a 
building  by  what  is  generally  known  as  a  warm-air  furnace  is  termed  furnace - 
HEATING.  The  furnace  consists  briefly  of  a  cast-iron  or  steel  heater,  containing 
a  combustion-chamber,  fire-pot  and  grate.  The  heater  is  usually  set  in  or 
encased  by  a  double-wall  galvanized  sheet  steel  jacket  (Fig.  47),  although  brick 
is  sometimes  used  instead  of  the  steel  jacket  for  this  purpose.  Furnaces  for 
soft  coal  are  usually  designed  with  a  secondary  air-supply  or  overdraft  for 
admitting  heated  air  just  at  the  surface  of  the  fire  in  order  to  produce  a  more 
perfect  combustion  of  the  volatile  combustible  gases  which  are  liberated  from 
this  fuel  immediately  after  firing.  This  overdraft  should  be  under  positive  con- 
trol so  that  it  may  be  checked  or  closed  after  the  fuel  has  been  coked.  Soft  coal 
may  also  be  burned  efficiently  in  the  underf eed-type  of  furnace  in  which  coal  is  fed 
from  below  by  means  of  a  plunger  operating  in  a  feed-chute  discharging  through 
the  center  of  the  grate.  The  furnace  should  be  located  in  the  basement  in  an 
approximately  central  position  with  reference  to  the  rooms  to  be  heated,  and 
preferably  toward  the  side  or  sides  from  which  the  prevailing  winds  blow  in  the 
winter-time.  This  arrangement  not  only  favors  the  more  exposed  rooms  on  the 
floors  above  by  shortening  the  leaders  to  these  rooms,  but  also  makes  it  possible 
to  reduce  the  length  of  the  cold-air  duct,  which  should  always  be  run  from  the 
exposed  side  of  the  building  to  the  cold-air  pit  below  the  furnace.  (Figs.  53  and 
54.)  In  operation  cold  air  is  drawn  from  the  outside  through  the  cold-air 
DUCT,  passed  through  the  space  between  the  heater  and  its  jacket,  and  warmed 
by  coming  in  contact  with  the  outside  heated  surface  of  the  combustion-chamber 
and  the  radiator,  which  is  usualUy  just  above  the  combustion-chamber.     It  is 


Furnace-Heating 


1311 


then  discharged  through  flues  connected  at  the  top  of  the  jacket,  Ftfki^AGE-GAi, 
or  BONNET  to  the  rooms  to  be  warmed. 


Collar' 


Fig.  47.     Warm-air  Furnace  with  Galvanized  Sheet  Steel  Jacket 

Leaders  and  Stacks.  These  connecting  flues  are  made  up  of  two  sections, 
(i)  the  nearly  horizontal  round  pipes  in  the  basement,  known  as  leaders  (Figs. 
48  and  49),  which  connect  to  the  collars  on  the  top  or  conical  sides  of  the 


r 


Piping-Plan.  AH 

Collars  lined  from 
Center  of  Furnace 


Same  Piping-PIan.  As  for  Fig.48.  All  Collarfl 
lined  from  Regl8t«r-0utleta 


Tig.  48.     Warm-air  Furnace-leaders  with    Fig.  49. 
Elbows 


Warm-air  Furnace-leaders  with- 
out Elbows 


bonnet,  and  (2)  the  vertical  rectangular  pipes  called  stacks  (Fig.  50),  which 
connect  the  boot  at  the  outer  end  of  the  leader,  with  the  double- walled  register- 
box  (Fig.  51)  into  which  the  register-grille  covering  the  opening  into  the  room, 
is  fitted.    The  leaders  should  have  an  upward  pitch  toward  the  base  of  the 


1312 


Heating  and  Ventilation  of  Buildings 


Parts 


stack  of  at  least  i  in  per  foot,  and  for  the  best  results  they  should  not  be  more 
than  from  1 2  to  15  ft  in  length.  The  boots  are  made  in  a  great  variety  of  shapes 
to  suit  actual  conditions,  and  are  simply  adapters  for  the  purpose  of  changing 

from  round  leaders  to  rect- 
angular stacks.  The  stacks 
are  usually  run  between  the 
studding  of  interior  walls  or 
partitions  (Figs.  50  and  51), 
since  if  they  are  placed  in 
outside  walls  the  cooling  effect 
reduces  their  efficiency  not 
only  in  temperature  of  air, 
but  also  in  velocity  of  flow. 
The  METAI,  used  for  leaders 
and  stacks  is  usually  bright 
Ai^  wmmr '  p7tr:''y/r)iMm  ■^tr2iz:j^^_'rT'";'Wt±iq       IX  tin,  although  for  leaders 

1  Iflll        "    llll  IP  |||==        larger  than  12  in,  galvanized 

\  P    -^ III  I         j  fli —        st^^^  o^  N^-  26  United  States 

llinilil  Standard    gauge     is    usually 

employed.  The  covering  of 
all  leaders,  boots  and  stacks, 
as  well  as  the  furnace  itself,  is 
mast  important,  and  either  a 
heavy  grade  of  asbestos  paper 
is  pasted  on  the  outside,  or, 
as  in  the  case  of  leaders  .and 
the  furnace  itself,  asbestos 
air-cell  covering,  about  %'in 
thick  may  be  used  and  secured 
with  brass  bands  or  wire. 
Since  the  stacks  must  run, 
generally,  in  a  4-in  studding- 
space,  with  a  net  depth  of 
about  z%  in,  every  effort 
must  be  made  to  keep  them 
as  deep  as  possible;  and  steel 
lathing  or  expanded  metal 
should  be  used  in  front  of  all 
such  stacks,  which  ordinarily 
have  only  a  single  layer  of  asbestos-paper  covering.  A  more  effective  insulation 
may  be  provided  by  using  a  double-wall  stack,  in  which  there  is  an  air-space 
between  the  inside  and  outside  pipes,  and  no  asbestos  covering  is  used.  See 
Table  XLII  for  this  equipment,  as  made  by  the  Excelsior  Steel  Furnace 
Company.  Attention  of  the  architect  is  here  called  to  the  fact  that  in  the  case 
of  large  second-floor  rooms  to  be  warmed  by  one  register,  6-in  stud  partitions 
are  generally  required  for  the  first  floor. 


Fig.  50.     Vertical  Stack  with  Side-wall  Register 


The  Design  of  a  Burnace  Heating  System. 

Heat-Loss  and  Air  Required.  Tlie  determination  of  the  size  of  the  furnace, 
and  the  connecting  leaders,  stacks,  registers,  ducts,  etc.,  is  based  on:  (i)  The 
actual  heat-loss  from  each  room  in  the  biiilding,  including  wall  and  glass-trans- 
mission losses,  as  wefl  as  loss  due  to  infiltration;  and  (2)  the  amount  of  air  to  be 
circulated  per  hour,  wliich  in  turn  is  based  on  this  heat-loss,     A  building  is 


The  Design  of  a  Furnace-Heating  System 


1313 


warmed  or  heated  by  hot  air  by  introducing  the  air  into  the  rooms  at  a  higher 
temperature  than  that  required  to  be  maintained  in  the  rooms  at  the  breathing- 
line  (approximately  70°  F.)  The  air  in  cooling  gives  up  per  pound,  0.24  Btii 
(specific  heat  of  air  at  con- 
stant pressure)  for  each 
degree  drop  in  tempera- 
ture, and  in  this  way  sup- 
plies the  iveat  necessary  to 
offset  the  heat-transmis- 
sion of  the  walls,  etc.,  and 
at  the  same  time  provides 
a  supply  of  fresh  air  for 
ventilation.  The  maxi- 
mum temperature  of  the 
air  leaving  the  heater-cap 
is  approximately  190°  F., 
and  it  leaves  the  registers 
at  175°  F.,  allowing  a  drop 
in  temperature  of  15°  be- 
tween the  furnace-bonnet 
and  the  registers.  These 
figures  are  maximum 
values  not  to  be  exceeded, 
outside    temperature    is    1 


Fig.  51,    Vertical  Stack  and  Register-box 


If  the  air  is  all  drawn  from  the  outside,  and  the 
°,  then  the  air  is  heated  from  0°  to  190°,  and 
cooled,  in  entering  the  room,  from  175°  to  70°,  or  105°.  In  other  words,  0.24 
Xios  or  25  Btu  is  apparently  thrown  away,  for  every  pound  of  air  circulated. 
If  all  the  air  must  be  brought  in  from  the  outside  in  order  to  supply  a  sufficient 
amount  for  ventilation,  then  this  is  the  price  which  must  be  paid  for  ventilation, 
and  it  would  be  the  same,  no  matter  what  system  of  heating  is  employed,  for 
equally  good  ventilation.  It  is  almost  invariably  the  case,  however,  that  a  con- 
siderable portion  of  the  air  may,  if  desired,  be  recirculated,  in  which  event,  for 
equal  ventilation  effect,  the  furnace  system  of  heating  requires  no  more  expendi- 
ture of  heat  in  the  form  of  fuel  burned  than  a  direct  steam  or  hot- water  system, 
and  is  therefore  just  as  economical  to  operate  when  correctly  designed,  installed 
and  operated.  The  head  producing  the  flow  or  circulation  is  due  to  the  differ- 
ence in  weight  between  the  ascending  column  of  heated  air  and  the  weight  of  an 
imaginary  column  of  the  colder  intake  air.  The  system  may  be  proportioned 
for  recirculating  all  of  the  air  during  the  extreme  cold  weather. 

Weight  of  Air  to  be  Circulated  per  Hour.     It  is  first  necessary  to  deter- 
mine the  weight  of  air  required  per  hour  which  must  be  suppUed  to  each  room. 
Let  W  =  pounds  of  air  to  be  circulated  per  hour; 

/  =  inside  temperature  to  be  maintained; 
td  =  temperature  of  air  leaving  the  registers  (assumed  15"  lower  than 

the  temperature  leaving  the  furnace-cap  or  bonnet); 
H  =  Btu  to  be  supplied  to  room  per  hour  as  determined  by  heat-loss 
calculations; 
0.24  (Jd  —  0  "=  Btu  given  up  per  pound  of  air  circulated. 
Then        W  =  U/[o.2^{td  -  t)]. 
The  maximum  value  for  td  is  175°  F.,  and  t  =  70°  F. 

Then      W  =H/2S', 

d  =  density  of  air,  entering  at  temperature  175°  =.063; 
Q  =  cubic  feet  of  warm  air  entering  room  per  hour 
=  PF/.063  =  H/1.5S, 


1314 


Heating  and  Ventilation  of  Buildings 


Parts 


Heat  Required  from  Heater  per  Hour,  Based  on  Recirculation.  The 
heat  required  per  hour  from  the  heater  will  depend  on  the  temperature  of  the 
entering  air  and  will  be  a  maximum  when  all  the  air  circulated  is  taken  from 
the  outside  and  a  minimum  when  all  of  the  air  is  recirculated. 

Let        h  =Btu  required  from  heater  per  hour; 

te  =  temperature  of  dr  entering  heater  =  65°; 
tji  te  temperature  of  air  leaving  heater  =  190°. 

Then     h  =  0.24  W{ih  -  h)^ 

Substituting  the  values  given  above  for  W,  tn,  and  te, 

h  =  1.2  //. 

Size  of  Furnace.  The  capacity  of  a  furnace  for  heating  air  depends  primarily 
upon  the  amount  of  coal  that  may  be  burned  per  hour,  which  is  the  product  of 
the  RATE  OF  COMBUSTION  by  the  grate-area.  With  an  assumed  or  fixed  rate  of 
combustion,  the  capacity  of  the  furnace  is  dependent  upon  the  grate-area.  The 
grate-area  is  therefore  used  as  a  basis  for  the  rating  and  comparison  of  warm-air 
furnaces.  The  average  rate  of  combustion  usual  in  furnace-heating  ranges 
from  3  to  4  lb  per  sq  ft  of  grate-surface  per  hour,  but  in  zero  weather  this  rate 
may  run  as  high  as  6  lb,  and  is  readily  obtainable  with  the  ordinary  height  of 
residence-chimney;  that  is,  at  least  35  ft.  A  properly  designed  furnace  will 
have  a  combined  furnace  and  grate-efficiency  of  from  55  to  60%.  Higher  effi- 
ciencies have  been  obtained  in  tests. 

Commercial  Ratings  of  Furnaces.  Manufacturers  rate  their  furnaces 
according  to  the  amount  of  space,  cubical  contents,  in  the  ordinary  residence- 
construction  they  will  heat  to  70°  F.  in  zero  weather.  Maximum  temperature 
of  air  leaving  registers  =  175°  F.  The  detailed  dimension  and  capacity-data, 
other  than  grate-area  and  space  heated,  of  most  furnaces  are  seldom  published 
by  the  manufacturer,  although  there  are  a  few  notable  exceptions.  The  actual 
size  of  the  furnace  naturally  depends  upon  the  heat-transmission  of  the  walls, 
floors  and  roofs,  plus  the  infiltration-losses,  as  already  explained.  The  claim, 
however,  is  made  that  these  "in  turn  bear  a  reasonably  uniform  relation  to  the 
cubical  contents  of  the  ordinary  house,"  with  the  usual  proportions  and  ratios 
of  wall  to  glass-surface,  and  that  therefore  the  rating,  as  given,  is  justifiable. 
Tables  XXXVH  and  XXXVHI  were  taken  from  the  Warm  Air  Furnace  Hand- 


Table  XXXVII.     Capacity  of  Warm-Air  Furnaces  of  Ordinary  Construction  in 
Cubic  Feet  of  Space  Heated 


Divided 

space  in  cubic  feet 

Fire-pot 

Undivided  space  in  cubic  feet 

-f  10° 

0° 

—  10° 

Diam- 
eter, 

in 

Area, 
sq  ft 

H-io'' 

0° 

—10° 

12  000 

10  000 

8  000 

18 

1.8 

17  000 

14  000 

12  000 

14000 

12  000 

10  OOQ 

20 

2.2 

22  000 

17  000 

14  000 

17  000 

14000 

12  000 

22 

2.6 

26000 

22  000 

17  000 

22  000 

18  000 

14  000 

24 

3.1 

30  000 

26  000 

22  000 

26  000 
30  000 

22  000 
26  000 

18  000 
22  000 

26 
28 

3.7 
4.3 

35  000 
40  000 

30  000 
35  000 

26  000 
30  000 

35  000 

30  000 

26  000 

30 

4-9 

SO  000 

40  000 

35  000 

The  Design  of  a  Furnace-Heating  System 
Table  XXXVIII.    Air-Heating  Capacity  of  Warm-Air  Furnaces 


1315 


Fire-pot 

Casing  * 

Total  cross- 
sectional 

area  of  heat- 
pipes,  a, 
sq  in 

Number  and  size  of  heat- 
pipes  that  may  be  supplied 

Diameter, 
in 

Area, 
sq  ft 

Diameter, 
in 

i8 

20 
22 
24 
26 
28 
30 

1.8 
2.2 

2.6 

3.1 
3-7 

4-3 

30-32 
34-36 

36-40 

40-44 

44-50 

48-56 

180 
280 

360 

470 

565 

650 

730 

3-9"  or  4-8" 
f  2-10  and  2-9" 
\  2-9"  and  2-8" 
1 3-  10"  and  2-9" 
I  4-9"  and  2-8" 
r3-io"  and  1-9" 
I  2-10"  and  5-8" 
f 5-10",  3-9" 
1 3-10",  4-9"  and  2-8" 
f  2-1 2",  3-10"  and  3-9" 
I  5-10",  3-9"  and  2-8" 
f  3- 1 2",  3-10"  and  3-8" 
\  5-10",  5-9"  and  1-8" 

4.9 

52-60 

*  The  casing-diameter  should  be  such  that  the  minimum  cross-sectional  area  M, 
between  casing  and  radiator,  will  be  at  least  20%  greater  than  the  total  cross-sectional 
^rea  of  all  the  heat-pipes,  a,ox  M  =  1.2  X  a  sq  in. 

book,  published  by  the  Federal  Furnace  League,  an  association  of  United  States 
furntace-manufacturers.  This  association  is  no  longer  in  existence.  If  the 
majority  of  the  basement  or  leader-pipes  exceed  12  ft  in  length  or  have  less  than 
1  in  rise  to  the  foot,  or  if  more  than  one  sixth  of  the  outside  surface  of  the  building 
is  glass,  then  the  furnace  should  be  increased  one  or  more  sizes.  The  size  of  the 
furnace  required  can  also  be  determined  by  the  combined  area  of  the  cross- 
sections  of  the  warm-air  pipes. 

Furnace-Rating  Based  on  Efficiency  and  Rate  of  Combustion.  The 
Btu  per  hour  that  a  furnace  is  capable  of  imparting  to  the  air  (not  the  room) 
may  also  be  estimated  from  the  grate-area  by  assuming  that  the  average  coal 
used  will  contain  approximately  12  000  Btu  per  lb.  A  combined  furnace-and- 
grate  efl&ciency  of  55%,  and  a  maximum  c©mbustion-rate  of  6  lb  per  sq  ft  of 
grate  per  hour  for  maximum  conditions  (coldest  weather)  are  also  usually 
assumed. 

Grate-Surface  Required,  Based  on  Recirculation.  The  area  of  the 
grate  is  readily  calculated  as  soon  as  the  heat  to  be  supplied  to  the  building  per 
hour  has  been  determined. 

H  =  Btu  to  be  supplied  building  per  hour; 

h  =  Btu  required  from  furnace  per  hour  for  heating  the  air  =  .12  H; 
C  =  heating  value  Btu  of  coal  per  lb; 
E  =  combined  furnace-and-grate  efficiency; 
R  =  rate  of  combustion,  pounds  of  coal  per  square  foot  of  grate-surf^-ce 

per  hr; 
G  =  grate-area  in  square  feet; 
h  =G  XC  XE  XR  =i.2n. 
Then     h  =  area  of  grate  in  square  feet  X  12  000  X  0.5 5  X  5-5 

=  36  300  X  G,  which  is  Btu  transmitted  to  the  air  passing  the  fur- 
nace; 
G  =  (1.2  X^)/36  300. 


J  316 


Heating  and  Ventilation  of  Buildings 


Parts 


Measurements 

of  galv. 

casings  and 

tops,  series 

A.  B.  C. 

.5 

::^     :^     :^ 

m  O  fO  O  <N      <£)           cr. 
fo  rf  T}- lo  lo      lo          lo      ' 

ll 

"o  S 

N    O 

c/3  ^ 

Chestnut 

Chestnut  or  stove 

Stove 

Stove  or  egg 

Stove  or  egg 

Egg 

Egg 

o 

■f 
a 

Q 

o 

_c 

'+3 

a 

bo 

to 

a 
o 

'd    . 

o  o  o  o  o  o 

o  o  o  o  o  o 
o  o  o  o  o  o 

O  "^O  lOiO  o  o 

O    M    OJ    fO  -^O   CTi 

o 

o  o  o  o  o  o 

«3  O  O  O  O  O  O 

o  o  o  o  o  o 

OO  to  to  o  o 
H  M  n  comr- 

_d 

T7-  lo  to  to  »0       O               ^O 

"o 

N  (M  N  ro  ro  't 

o  o  o  o  o  o 

M    M    M    M    M    M    W 

c 

00  M<0  rovo       O            -^ 

bO 
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O  O  O  IT)  O  li^  o 

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«  ro  '^  iOvD  00  a^ 

1 

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3 

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c^ 

c 

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XXXXXX^XX^X 

OOOMTtrl-OOMOOrj- 

-d    ► 

11 1 

(3S 

0  o  o  o  o  o  o 

vD  O  ^  ■^  ^^  f^  I'i 

M  M  c^  ro  rt  ir; 

1  1     1     1     1     1     ! 
O  O  O  O  O  O  O 
O  O  O  O  O  O  O 
O  O  O  O  O  O  O 
■rj-KD   N  00  Tt  ir>  lA 

M  M  M  rc  -^ 

c 

Tro<r)Oootr>      wo      o 

<N  CO  ro  •^  ■^  lO^-x  rovo  U  '^ 

XXXXXX^XXojX 

(NMNTtTl-'itO'st-^'^Tt 
MMMHMH           MMOM 

Vh  'T  P 

X>  be  »-< 

l|R 

P. 

TfvD  00  ►-•  fO  «n  O^ 
O  O  O  O  O  O  O 

+J  4J  +J   +J  4J  4J   -U 

CO  -"tvO  C7>0  M  T^ 

H    M    M 

?i  o  SI 
•-5  0.52 

c 

fO  CO  -^-^tO         lO              VD 

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•^'noo  M  "d-r-  O 

M    M    M    (N    M    M    fO 

^    0)    Oj 

M  M  M  N  <>»        N             ro 

The  Design  of  a  Furnace-Heating  System  1317 

The  usual  assumptions,  with  anthracite  fuel  are: 
j  C  =  12  ooo  Btu  per  lb; 

^  2?  =  4  lb  ordinary  rate  and  5.5  lb  for  maximum  conditions  in  coldest 

weather; 
£=0.55; 
Then    G  =  h/{i2  000  X  5-5  X  0.55)  =  h/s6  300  =  i. 2/7/36  300. 

Size  of  Leaders  and  Stacks.  The  area  of  the  air-pipes  (leaders  and  stacks) 
required  for  a  room  depends  upon  the  quantity  of  air  to  be  indroduced  per  min- 
ute and  the  velocity  with  which  the  air  will  flow  with  natural  circulation. 

Q/60  =  cubic  feet  of  warm  air  to  be  introduced  into  the  room  per  minute; 

V  =  velocity  of  air  in  feet  per  minute  attainable; 

H  =  heat-loss  of  room; 

A  =  area  of  pipe  in  square  feet; 
Q/60  ==  AV,  and  substituting  value  of  ^  =  H/1.5S; 

A   =H/(95XV). 

The  following  velocities  are  approximately  obtained  in  the  leaders  and  stacks 
for  the  floors  as  stated: 

First  floor,  175  ft  per  min; 

Second  floor,  240  ft  per  min; 

Third  floor,  310  ft  per  min. 

The  above  velocities  have  been  observed  in  practice  in  well-designed  systems. 
Then  for  various  floors,  substituting  in  the  above  equation,  in  square  inches: 

Ai  =  ///115  for  first-floor  pipes,  leaders  and  stacks; 
A2  =  H/160  for  second-floor  pipes,  leaders  and  stacks; 
An  =  H/206  for  third-floor  pipes,  leaders  and  stacks. 

See  Bulletin  No.  112,  Engineering  Experiment  Station,  University  of  Illinois, 
1919- 

Actual  leader  and  stack-sizes  are  based  on  the  above  areas,  using  the  nearest 
half-inch  for  leader  the  diameter  (Table  XL),  and  keeping  the  stacks  of  such 
proportions  that  the  cross-sectional  dimensions  are  never  in  a  greater  ratio 
than  3  to  I .  For  example,  a  stack  4  by  20  in  is  seldom  effective  over  its  full  area, 
as  it  is  too  narrow,  and  as  its  large  rubbing-surface  causes  excessive  friction. 
The  actual  velocities  obtained,  however,  will  depend  upon  the  head  or  pressure 
causing  the  flow  and  the  friction-head,  and  will  seldom  exceed  50%  of  the  theoret- 
ical velocities.  Table  XL  has  been  recommended  by  the  Federal  Furnace 
League  and  gives  the  sizes  of  round  pipe  for  leaders,  the  size  of  wall-pipe  for 
stacks,  and  free  areas  of  registers  to  connect  with  same.  Leaders  over  12  ft  in 
length  should  be  increased  i  in  in  diameter  for  each  5  ft  beyond  12  ft. 

Registers.  The  free  area  through  the  ordinary  register-grille  is  only  ap- 
proximately 55%  of  the  gross  area,  and  consequently  a  register  must  be  selected 
that  has  a  gross  area  of  double  the  area  of  the  pipe  with  which  it  connects,  in 
order  that  the  air-passage  may  not  be  contracted  and  the  capacity  reduced. 
Commercial  register-sizes  are  based  on  the  actual  inside  dimensions  of  the  grilled 
opening  and  are  made  either  of  pressed  steel  or  cast  iron,  with  a  variety  of  fancy 
or  plain  grilles.  The  plain  rectangular  grille  is  to  be  preferred,  finished  to  suit 
the  decorative  scheme,  in  black  japan  or  electro-plated  in  brass,  bronze  or 
copper  finish.  Warm-air  registers  may  be  placed  in  the  floor,  but  preferably 
in  inside  partitions,  for  first-floor  rooms.  By  using  the  modern  base-board 
REGISTER,  Fig.  52,  it  is  usually  possible  to  secure  the  required  capacity  without 


1318  Heating  and  Ventilation  of  Buildings  Part  3 

Table  XL.     Capacities  and  Dimensions  of  Warm-Air  Piping  and  Registers 


Diameter  of 
round  cellar 

Proper  size  of 
rectangular 

Area  of 
riser-pipe. 

Required  area 
of  register-face, 

or  riser-pipe, 

riser-pipe, 

in* 

in* 

sq  in 

sq  in  * 

6 

3       X    9H 

28 

52 

6M 

3H  X    9H 

33 

62 

7 

3M  X  II 

38 

72 

iVi 

ZVl    X  I2M 

44 

84 

8 

3H  X  14 

50 

96 

8M 

4       Xi4 

57 

108 

9 

4       X  i6 

64 

120 

9H 

4       X  i8 

71 

134 

10 

4       X  20 

78 

142 

10  H 

6       X  iaYi 

86 

158 

II 

6       X  i6 

95 

176 

11^ 

6       XI7H 

104 

194 

12 

6       X  19 

113 

204 

12^ 

6       X  2oH 

122 

222 

13 

6         X  22 

132 

242 

13  H 

8       Xi8 

143 

254 

14 

8       X  19 

154 

276 

14  H 

8       X20^ 

i6s 

298 

15 

8          X  22 

176 

320 

i6 

8       X  25 

201 

358 

17 

10       X22H 

227 

410 

i8 

10       X25  3^ 

254 

450 

19 

12       X233^ 

283 

508 

20 

12       X  26 

314 

554 

21 

12     y.2^yi 

346 

618 

22 

14       X  27 

380 

686 

23 

14     X29M 

415 

707 

24 

14       X  32 

452 

770 

*  When  the  required  size  of  pipe  falls  on  the  odd  half -inch  (as  7H,  8H,  9H,  etc.), 
the  size  may  be  increased  to  the  even  inch  (as  8  instead  of  7H,  9  instead  of  8.1^,  etc.), 
for  the  first-floor  rooms  and  bath-rooms;  provided  that  the  pipes  for  upper-floor  rooms, 
other  than  bath-rooms,  be  decreased  by  Vi  in  when  the  required  sizes  fall  on  the  odd 
half-inch.  It  is  better,  however,  to  use  pipes  of  the  sizes  given  in  the  above  table,  with 
proper  allowances  for  length  of  pipe,  extra  bends,  etc.,  beyond  straight  runs  12  ft  long. 

resorting  to  floor-registers.  These  base-board  registers  can  be  connected  to  a 
flue  from  3  to  4  H  in  deeper  than  the  studding.  This  has  been  accomplished  by 
making  the  special  base-board  register  so  that  it  projects  2  in  into  the  room  at 
the  floor-line,  necessitating  the  cutting  out  of  the  floor,  and  also  utilizing  the 
space  of  about  i  in  occupied  by  the  lath  and  plaster,  or  a  total  increase  in  depth 
of  flue  of  about  3  in.  For  upper-floor  rooms  registers  should  be  placed  in  inside 
partition  walls,  using  convex  registers  for  shallow  stacks.  As  a  general  rule 
warm-air  registers  should  be  so  placed  as  to  shorten  leader  and  stack-connections 
as  much  as  possible.  The  use  of  a  floor-register  may  be  permitted  in  an  entrance- 
hall  for  drying  shoes  and  garments,  but  it  is  unsanitary  and  cannot  fail  to  collect 
dirt  and  filth  of  all  kinds.  In  case  such  registers  are  used,  however,  suitable 
REGISTER-BOXES  must  be  provided,  and  they  are  preferably  constructed  with 
double  walls. 

Example  in  Furnace- Heating.  A  gravity  furnace-heating  system  is  to  be 
designed  for  the  two-story  frame  building  shown  in  Fig.  55,  with  inside  and  out- 


The  Design  of  a  Furnace-Heating  System 


1319 


Base-board  Register 

used  on  First  Floor 

takes  the  supply 

from  a  Flue?  in. 

Deep  or  3  in. Deeper 

than  Studding 


COLD-AIR    DUCTS 
Fig.  53.     Cold-aid  Ducts  for  Warm-air  Furnaces 


FRESH  -  AIR  ROOM 
WITH   DUST-COLLECTOR 


1320 


Heating  and  Ventilation  of  Buildings 


Parts 


Table  XLI.    Table  of  Sizes   of   Floor-Registers,   Base-Board   Registers   and 
Register-Boxes 


Size  of 

Size  of 

register-box 

Size  of 

Size  of 

Size  of 

Size  of 

register- 
box  to 

Size  of 
base-board 

to  base- 
board 

base-board 
register 

round 
cellar- 

round 
floor- 

rectangular 
floor- 

base-board 
where  studs 

register 
where  studs 

register 
where  there 
is  no  limit 
to  depth  of 

where  there 
is  no  limit 

pipe, 

register. 

register. 

are  not 
more  than 

are  not 
more  than 

to  depth  of 
register- 

4  in  deep, 

4  in  deep, 

register- 
box, 

box. 

in 

in 

in 

in 

in 

in 

in 

6 

9 

8X8 

2%  Xio 

7  X  10 

2H    X   10 

7  X  10 

6H 

9 

8X8 

3M  X  10 

7  X  10 

SH  Xio 

7  X  10 

7 

10 

8  X  10 

ZH  X  10 

7  X  10 

3M  X  10 

7  X  10 

7^ 

12 

8  X  12 

4H  X  10 

7  X  10 

4H  X  10 

7  X  10 

8 

12 

8  X  12 

4H  X  12 

7  X  12 

4H  X  12 

7  X  12 

8H 

12 

9  X  12 

4H  X  12 

7  X  12 

4H  X  12 

7  X  12 

9 

14 

10    X   12 

S       X  13 

8  X  13 

5       X  13 

8  X  13 

9H 

10 

14 

14 

10  X  14 
10  X  i6 

6       X  12 
6^^  X  12 

10    X   12 

6       X  12 

10    X   12 
10    X    12 

10    X   12 

6H  X  12 

loH 

i6 

10  X  i6 

ey2  X  13 

^0  X  13 

ey2  X  13 

10  X  13 

II 

i6 

12    X  IS 

6M  Xi4 

12  X  14 

en  X  14 

12  X  14 

iiM 

i6 

12  X  i8 

7        X  IS 

12    X  IS 

7M  X  14 

12  X  14 

12 

i8 

12    X  20 

6H  X  i8 

12  X  i8 

7H  X  IS 

12    X   IS 

I2H 

i8 

14  X  i6 

6^  X  i8 

12  X  i8 

eu  X  i8 

12  X  i8 

13 

i8 

14  X  i8 

7H  X  i8 

12  X  i8 

13  J^ 

i8 

14  X  20 

8       X  i8 

12  X  i8 

Table  XLII.     Dimensions  of  Excelsior  Double  Wall-Pipe 

Excelsior  Steel  Furnace  Company 


Number 

Measurements 

Area  of 
stack, 

sqMn 

Nominal, 
in 

Inside, 

in 

Outside, 
in 

4 
6 
7 
8 
9 

12 

.  14 

3      Xio 

3  Xi2 

4  Xii 

2HXI0 
lHXl2 

i      Xio 

5      X12 

X13 

X12 

HX13 

3      XioH 
3      Xi2ys 
3^X10^ 
3^Xi2H 
3^Xi3H 
S^^Xi2H 
6KX13H 

24 

28H 

30 

36 

39 

60 

72 

4      Xi3 
4      Xi4 
6      Xi3 
6HXI4 

5 

Number 

Collar-diameter, 
in 

Area  of  collar, 
sq  in 

Register-size, 

convex  or  wafer, 

sq  in 

4 
6 
7 
8 
9 

12 

14 

7 
8  and     9 

8  and     9 
8,  9  and  10 

9  and  10 
9  and  10 

10  and  12 

39 
SI  and  63 
61  and  53 
SI  and  78H 
63  and  78  H 
63  and  78  M 

78H 

6X8—   SXio 

8X10—   0X12 

8X10—   9X12 

8  Xio— 10X14 

10X12— 10X14 

10  X12 — 10X14 

10X14 — 12X14 

The  Design  of  a  Furnace-Heating  System 


1321 


side  temperatures  of  70°  and  0°  F.  respectively,  and  the  air  all  recirculated  in 
zero  weather.     Transmission  and  infiltration-losses  are  as  computed  in  Table 


Fig.  55.    Furnace-heating  Layout.     (See  data  in  Table  XL VI) 

XL VI,  which  'also  gives  the  size  of  heat-pipes,  leaders  and  stacks,  and  register- 
sizes. 

Size  of  Furnace  and  Grate.  The  size  of  the  furnace  is  calculated  on  the 
assumption  that  all  the  air  is  taken  from  the  outside.  The  total  calculated  heat- 
loss  from  building  per  hour  is  124  558  Btu.  which,  multiplied  bj^  1.2,  and  divided 


1322  Heating  and  Ventilation  of  Buildings 

Table  XLIII.     Dimensions  of  Excelsior  Single  Furaace-Pipe 

Excelsior  Steel  Furnace  Company 


Parts 


Measurement 

Size  of  boot- 

Capacity  of 

Capacity  of 

in  inches 

collars,  diameter, 

collars, 

pipe, 

in 

sq  m 

sq  m 

3      Xio 

8 

51 

30 

3HX10 

8 

SI 

35 

3      X12 

8  and    9 

51  and    63 

36 

3HX12 

9 

63 

42 

3MX13 

9  and  10 

63  and     78 

45 

SMX12 

10 

78 

66 

SHX14 

12 

114 

77 

sJ^xie 

12  and  14 

114  and  154 

88 

7HX16 

14 

154 

112 

Note.  Stacks  sH  in  deep,  made  to  order  only.  With  frictionless  boots,  collars  in 
same  can  be  made  with  a  diameter  equal  to  width  of  stack.  Collars  11  in  in  diameter 
furnished  when  so  ordered.  -> 


Table  XLIV.     Capacities  and  Dimensions  of  Fresh-Air  Ducts,  Rooms,  Etc. 


Size  of  hori- 

Size of  hori- 

Cross-section 
area  of  hori- 
zontal portion 
of  fresh-air 
duct. 

Size  of  fresh- 
air-room ; 

Size  of  fresh- 
air  intake 

zontal  portion 

zontal  portion 

•length  and 

(area  of 

of  rectangular 
fresh-air  duct. 

of  round  fresh- 
air  duct. 

width  (height 

same  as  depth 

of  cellar). 

woven-wire 

netting,  not 

including 

frame) , 

in 

in 

in 

in 

in 

8X18 

1-14 

144 

18  X48 

12X16 

8X21 

1-15 

168 

21X48 

14X16 

8X24 

1-16 

192 

24X48 

16X16 

10X21 

1-16 

210 

21  X60 

14X20 

10X24 

1-18 

240 

24X60 

16X20 

10X27 

2-13 

270 

27X60 

18X20 

10X30 

2-14 

300 

30X60 

20X20 

12X27 

2-14 

324 

27X72 

18X24 

12X30 

2-15 

360 

30X72 

20X24 

12X33 

2-16 

396 

33X72 

22X24 

12X36 

2-17 

432 

36X72 

24X24 

12X39 

2-17 

468 

39X72 

24X26 

14X36 

2-18 

504 

36X84 

24X28 

14X39 

2-19 

546 

39X84 

26X28 

14X42 

2-19 

588 

42X84 

28X28 

14X45 

2-20 

630 

45X84 

28X30 

14X48 

2-21 

672 

48X84 

28X32 

14X51 

2-21 

714 

51X84 

28X34 

16X48 

2-22 

768 

48X96 

32X32 

16X51 

2-23 

816 

51X96 

32X34'' 

16X54 

2-24 

864 

54X96 

32X36 

16X57 

2-24 

912 

57X96 

32X38 

16X60 

2-25 

960 

60X96 

32X40 

The  Design  of  a  Furnace-Heating  Surface  1323 

Table  XLV.     Sizes  and  Capacities  of  Wooden  Register-Faces  for  Cold-Air  Ducts 


Nearest  size 

Nearest  size 

Size 

Net  area 
of  air-space, 

of  round 

pipe  of 

equivalent 

area, 

Size, 

Net  area 
of  air-space. 

of  round 

pipe  of 

equivalent 

area. 

sq  m 

m 

in 

sq  in 

in 

12X20 

135 

12 

24X24 

323 

20 

12X24 

161 

14 

24X26 

349 

20 

12  X30 

202 

16 

24X30 

403      ■ 

22 

,      14X20 

157 

14 

28X28 

439 

22 

14X26 

203 

16 

30X30 

504 

26 

16X20 

179 

14 

36X20 

403 

22 

16X24 

215 

16 

36X24 

484 

24 

16X30 

269 

18 

36X30 

60s 

28 

18X24 

242 

18 

36X36 

72s 

30 

18X30 

303 

20 

72X18 

726 

■ 

20X20 
20  X24 

224 
269 

16 
18 

72X20 
72  X24 

806 
968 

20X26 

291 

18 

72X30 

I  210 

20  X30 

336 

20 

72  X36 

I  450 

Table  XL VI.     Furnace-Heating  Example  (See  Fig.  65) 


First  floor 

Parlor 

Hall 

Dining- 
room 

Library 

Kitchen 

Cubic  feet 

Heat-loss,     H,     in 

Btu  per  hour. .  .  . 

Area  of  heat-pipe, 

H 

■  sq  in 

115 
Diameter  of  leader 

in  inches 

Size  of  register  in 
inches 

2  280 
14855 

127 

13 
12X18 

2  170 
13  400 

116 

12 
12X18 

2  400 
II  655 

lOI 

II 
12X15 

2  280 
II  S15 

100 

11 
12X1S 

3  600 
II  127 

96 

II 
12X1S 

Heat-loss 
of  kitchen 
is  based  on 
kitchen- . 
range    ' 
supplying 
one^half 

the 
required 
amount. 

Second  floor 

Chamber 
No.  I 

Chamber 

No.  2 

Chamber 
No.  3 

Chamber 

No.  4 

Chamber 
No.  5 

Bath- 
room 

Contents  in  cubic 
feet 

2  052 
14  370 

89 

loH 
5^X16 
12  X14 

I  458 
12  000 

75 
10 

SHX14 
10X13 

I  746 
10  413 

65 

9 
53^X12 
10X12 

I  206 
9  070 

56 

9 

5HX12 

9X12 

I  242 
10  883 

68 

9 
5HX12 
10X12 

5,6 

5  400 

34 

8 

5  H  X.IO 

10X12 

Heat-loss    in    Btu 

per  hour. . 

Area  of  heat-pipe, 
// 
160 
Diameter  of  leader 
in  inches 

Stack,  in  inches .  .  . 
Size  of  register  in 
inches  *. .  .  . 

The  net  area  of  register-faces  is  assumed  to  be  55%  of  the  gross  area.     The  gross 
area  equals  1.8  times  the  area  of  the  leader-pipe. 


1324  Heating  and  Ventilation  of  Buildings  Part  ^ 

by  36  300,  the  heat  available  from  1  sq  ft  of  grate  when  burning  5.5  lb  of  coal, 
of  12  000  Btu  heat-value  per  pound,  at  55%  efficiency,  gives  4.1  sq  ft  as  the 
grate-area.  This  will  require  a  grate  of  28-in  diameter.  This  building  has  a 
net  volume  of  26  000  cu  ft,  and  by  reference  to  Table  XXXVII  it  is  seen  that  a 
28-in  grate  is  recommended  for  this  amount  of  divided  space.  The  furnace,  in 
this  problem,  has  been  located  practically  in  the  center  of  the  house,  but  on  the 
north  side  of  its  east  and  west  axis,  giving  a  direct  cold-air  connection  from  the 
north  wall  and  short  direct  runs  for  most  of  the  leaders. 

Leader-Layout.  The  leaders  may  be  laid  off.  as  shown  in  Fig.  55  and  in  Fig. 
48,  by  dividing  up  the  circumference  of  the  bonnet  into  areas  proportional  to 
the  amount  of  air  to  be  distributed  by  each  leader,  and  then  connecting  collar 
and  leader  radially  to  furnace-cap,  making  one  or  more  elbows  in  the  leader,  if 
necessary  to  connect  with  stack.  Another  method  is  to  run  practically  all 
leaders  direct  from  furnace  to  foot  of  stack  (Fig.  49)  and  cut  the  collars  in  on  the 
angles  at  which  they  intersect  the  casing.  The  former  method  is  recommended, 
and  requires  less  skill  in  installation.  The  basement  heating-plan  is  shown  on 
the  first-floor  plan,  which  also  shows  all  stack-sizes  to  both  floors.  Floor- 
registers  have  been  shown  on  the  first-floor  plan  in  order  to  simplify  the  layout 
and  make  the  plan  clearer.  In  general,  base-board  registers  are  to  be  preferred. 
The  sum  of  the  areas  of  leader-pipes  is  927  sq  in. 


Hot-Blast  Heating 

General  Features.  The  mechanical  indirect  method  of  heating,  commonly 
known  as  the  blower  system  or  hot-blast  system,  particularly  adapted  to  the 
warming  and  ventilating  of  large  structures,  is  made  up  of  three  units:  (i)  A 
heater  constructed  of  pipes,  tubes,  or  cast-iron  sections,  through  which  steam, 
hot  water  or  hot  gas  may  be  passed.  (2)  A  fan  or  blower  to  circulate  air  over 
the  heater-surfaces,  the  air  acting  as  a  heat-carrier  or  medium  of  heat- transfer. 
(3)  A  system  of  ducts  or  pipes  to  convey  the  heated  air  from  the  heater  to 
points  where  heat  may  be  required.  When  the  heater  is  located  between  the 
fan  and  main  duct,  the  combination  is  termed  blow-through,  and  when  the 
fan  is  installed  between  the  heater  and  the  duct,  the  arrangement  is  known  as 
draw-through.  These  two  arrangements  are  shown  in  Fig.  57.  The  draw- 
through  combination  is  more  often  used  for  shop  and  factory-installations 
where  compactness  is  desirable,  the  blow-through  combination  being  used 
principally  for  hot-and-cold  systems  as  installed  in  schools  and  public  buildings. 
^"  Advantages  of  the  Blower  or  Hot-Blast  System.  The  advantages  of  the 
blower  or  hot-blast  system  over  those  of  direct  radiation,  briefly  summarized, 
are:  • 

(i)  When  ventilation  is  a  requirement  in  order  to  maintain  a  healthful  atmos- 
phere, this  method  affords  a  positive  means  of  accomplishing  this  particularly 
desirable  result,  which  is  entirely  independent  of  the  changing  climatic  con- 
ditions. 

(2)  When  a  standard  humidity  of  the  air  is  to  be  maintained,  a  feature  which 
is  becoming  to  be  more  generally  recognized  as  desirable  in  any  heating-and- 
ventilating  installation,  and  quite  essential  to  the  successful  manufacture  of 
some  materials,  the  humidifying-apparatus  may  readily  be  made  an  integral 
part  of  the  system. 

(3)  A  much  smaller  amount  of  radiating-surface  is  required  to  perform  an 
equal  heating-duty,  with  a  consequent  reduction  in  the  number  of  steam-tight 
joints,  unions  and  valves  to  keep  in  repair. 

(4)  The  air-leakage  being  mostly  outward,  the  building  will  in  general  be  freer 


Hot-Blast  Heating  1325 

from  drafts  and  more  uniformly  heated.  If  the  air  is  simply  recirculated,  no 
fresh  air  being  taken  into  the  heating  system  from  the  outside,  the  above  state- 
ment does  not  apply.  The  pressure  of  the  air  in  the  building,  even  when  all  of 
the  air  is  taken  into  the  heating  system  from  the  outside,  is  comparatively  feeble, 
and  some  air  will  enter  by  infiltration  through  the  window  and  door-cracks  on 
the  windward  side  of  the  building,  although  the  statement  is  often  made  that 
the  leakage  being  all  outward,  prevents  the  infiltration  of  cold  air  from  the 
outside. 

(5)  This  system  is  more  easily  regulated,  and  readily  responds  to  changing 
outside  temperatures. 

(6)  The  air  entering  for  ventilation  may  be  conveniently  cooled  in  summer, 
either  by  the  circulation  through  the  heater  of  cold  water  or  of  brine  previously 
cooled  by  mechanical  refrigeration, 

(7)  Simply  running  the  fan  will  in  itself  greatly  relieve  the  oppressiveness  in  hot 
sultry  weather,  and  when  cold  water  is  circulated  through  the  coils  the  difference 
is  very  noticeable. 

Typical  Arrangements.  When  ventilation  is  not  a  requirement,  or  when  it  is 
relatively  unimportant,  as  is  frequently  the  case  in  shop  or  factory-heating  where 
the  number  of  persons  vitiating  the  air  is  small  compared  with  the  cubical  con- 
tents of  the  building,  the  air  may  be  simply  recirculated,  sufficient  fresh  air 
for  ventilation  being  supplied  l:)y  infiltration.  The  amount  of  heat  to  be  sup- 
pUed  the  heater  in  this  case  is  the  same  as  would  be  required  for  a  direct-radiation 
installation.  When  ventilation  is  a  requirement  to  be  met  a  cold-air  intake 
is  provided.  Since  the  amount  of  air  necessar}''  for  heating  is  generally  in  excess 
of  the  amount  required  for  ventilation  considerable  economy  may  be  effected  by 
recirculating  a  portion  of  the  air.  In  this  case  only  sufficient  fresh  air  is  drawn 
into  the  system  from  the  outside  to  meet  the  ventilation  requirement  and  the 
remainder  of  the  air  necessary  for  heating,  is  recirculated.  This  may  be  readily 
effected  by  an  arrangement  of  ducts  and  dampers  on  the  suction-side  of  the  fan. 
If  the  fresh  air  introduced  is  to  be  washed  or  conditioned  the  washer  or  humid- 
ifier and  tempering-coil  may  be  added  between  the  inlet  for  the  recirculated  air 
and  the  fresh-air  intake. 

Amount  of  Air  to  be  Circulated  for  Heating.  The  weight  of  air  to  be  cir- 
culated per  hour  for  heating  a  room  or  building  is  found  by  dividing  the  heat- 
loss  (//)  by  the  amounts  of  heat  given  up  by  i  lb  of  air  in  cooling  from  the  tem- 
perature at  the  duct-outlets  to  the  mean  room-temperature. 

Let   //  =  heat-loss  of  room,  Btu  per  hr; 

M  =  weight  of  air  to  be  introduced  in  room  per  hour; 
/  =  mean  inside  temperature; 
td  =  temperature  of  air  leaving  duct-outlets.  • 

Then  M  =  II/[o.24(ta  -  t)] 

The  temperature  fd  depends  upon  the  temperature  of  the  air  entering  the 
heater,  the  velocity  through  the  clear  area,  the  amount  of  heating-surface  and 
the  temperature  of  the  steam.  This  temperature  in  practice  ordinarily  ranges 
from  125°  to  150°  F.  and  may  be  readily  determined  for  any  specified  condition 
by  the  data  given  later  under  Hot-Blast  Heaters.  The  temperature  of  the  air 
leaving  the  duct-outlets  for  ordinary  installations,  when  the  ducts  are  not  run 
underground  or  in  outside  walls,  may  be  assumed  to  be  the  same  as  the  tempera- 
ture (h)  of  the  air  leaving  the  heater.  Any  loss  in  temperature  in  this  case 
goes  toward  heating  the  building  and  is  therefore  not  a  direct  loss.  If,  how- 
ever, the  ducts  are  run  underground  or  in  outside  walls,  a  considerable  loss  in 


1326  Heating  and  Ventilation  of  Buildings  Part  3 

temperature  may  occur,  which  is  a  direct  loss,  and  must  be  provided  for  by 

INCREASING  THE  TEMPERATURE  OF  THE  AIR  LEAVING  THE  HEATER  by  an  amount 

equal  to  the  estimated  temperature-drop  in  the  ducts. 
Temperature  of  Air  Entering  Heater. 
Let  h  =  temperature  of  air  entering  heater; 
/2  =  outside  temperature; 
t  =  mean  inside  temperature; 
tz  —  temperature  of  air  leaving  heater; 
(«)  When  the  air  is  all  recirculated,  k  =  t;  ' 

{h)  When  fresh  air  only  is  circulated,  h  =  to] 

(c)  W^hen  a  ix)rtion  of  the  air  is  recirculated  the  resulting  temperature  of  the 
mixture  of  fresh  and  recirculated  air  may  be  found  by  the  method  of  mixtures. 
Let  Mv  =  weight  of  fresh  air,  pounds  required  per  hour  for  ventilation  (30 
cu  ft  per  min  per  person) ; 
=  0.075  X  I  800  X  number  of  persons  (usual  requirements); 
Mr  =  weight  of  air  that  may  be  recirculated; 
M  =Mv  -{-Mt 
H  =  0.24  {Mt  +  Mr)  {td  -  /). 
Having  assumed  or  fixed  the  value  of  tdt  the  only  unknown  quantity  is  Mr. 

Jl/r-///[o.24(/rf  -0]  -Mv 

The  temperature  h  may  then  be  found  as  follows: 

Mv  X  {to  +  460)  =  A 

Mr  X{t  -\-  460)  =  B 

{Mv  +  Mr)  {h  +  460)  =  A  i-B 

or  <i  =  (^  +  B)/{Mv  +  Mr)  -  460 

Example.  The  heat-loss  //  for  a  certain  factory-building  is  70  600  Btu  per  hr. 
The  number  of  men  employed  is  50.  Mean  inside  temperature  /  =  65^*  F. 
Outside  temperature  to  =  0°  F.  Ventilation  is  to  be  provided  at  the  rate  of 
1800  cu  ft  of  fresh  air  per  hour  per  person.  Assumed  temperature  of  air  leaving 
duct-outlets  is  135°  F. 

Solution.  Mv  =  0.075  X  1800  X  50  =  6  750  lb  per  hr  fresh  air  for  ventila- 
tion.    The  weight  of  air  that  may  l)e  recirculated  is 

Mr  =  706  ooo/[o.24(i35  -  65)]  -  6  750  =  35  273  lb  per  hr 

The  temperature  of  the  air  entering  the  heater  will  be: 

6  750  X  (  o  -f-  460)  =    3  105  000 
35  273  X  (65  4-  460)  =  18  516  750 

/i  =  (21  621  750/42  023)  -  460  =55°  F. 

If  FRESH  air  only  is  to  be  used,  as  in  school-house  and  public-building  heating^ 
the  weight  of  air  to  be  circulated  is  determined  directly  by  the  ventilation 
requirement. 

Then         M  =  Mv  =  ///[o.24(/rf  -  t)],  or  la  =  {H  +  0.24  if  ,0/0.24  Mv 

Temperature  of  Air  at  Duct-Outlets.     When  heating,  by  the  hot-bla 
system,  a  building  containing  a  number  of  room^  having  different  heat-losses 
and  ventilation  requirements,  it  is  obviously  irPipossible  to  maintain  the  desired 


-iS' 


Hot-Blast  Heating 


1327 


temperature  by  controlling  the  temperature  (^2)  of  the  air  leaving  the  heater  at 
one  point.  The  temperature  td  of  the  air  leaving  the  duct-outlets  will  ordinarily 
be  didercnt  for  each  room  in  the  building,  as  shown  in  the  following  example. 
This  result  is  accomplished  by  the  double  plenum-chamber  system  described 
later. 

Example.  Let  it  be  required  to  determine  the  temperature  of  the  entering 
air  {td)  to  offset  the  heat-loss  and  provide  ventilation  for  the  several  rooms  as 
given  in  Table  XL VII.    Inside  temperature  {t)  to  be  maintained  is  70°, 


Table  XL VII.     Data  for  Example 


Room- 
number 

Number 

of 

occupants, 

n 

Ventilation 

Heat-loss, 
H 

Tempera- 
ture of 
entering 
air,  td 
(see  formula) 

Cubic  feet 

per  hour 

at  70**, 

I  800  x« 

Weight 
per  hour, 

Mv 

A-i 

A-2 

Hall 

50 
S3 

90  GOO 

95  400 
30  000 

6  750 

7  I2S 
2  250 

32  GOG 

21  GOO 

4  000 

89. 5 
82.2 

57.4 

Temperature  of  Air  Leaving  Heater.  If  all  of  the  air  is  first  warmed  by  the 
TEMPE RING-COIL  to  70°  F.,  and  a  mixture  of  approximately  {i  —  x)  parts  of 
tempered  air  and  x  parts  of  hot  air  is  to  be  used,  then  the  required  temperature  of 
the  hot  air  leaving  the  heater  may  be  determined,  for  any  particular  case,  by 
the  METHOD  OF  MIXTURES  previously  given;  or,  assuming  this  temperature,  the 
proportions  of  hot  and  tempered  air  may  be  determined. 

Example.  Required  the  temperature  of  the  hot  air  (//?)  leaving  the  heater  for 
room  A  —  2,  (Table  XL VII)  if  the  mixture  entering  the  room  is  made  up  of 
one  half  tempered  air  at  70°  and  one  half  hot  air.  The  total  weight  of  air 
entering  the  room  is  7  125  lb  per  hr,  or  3562.5  lb  of  tempered  air  and  3562.5  lb 
of  hot  air. 

Solution.  3  562.5  X  (70-1-460)  ■\-  3  562.5  X  {th  +160)  =  7  125  X  (82.2  -I-460). 
Hence  th  =  94- 

Assuming  a  temperature  of  tn  =  120°,  it  is  required  to  determine  the  relative 
proportions,  by  weight,  of  the  mixture  required. 

Let  X  =  parts  of  hot  air  in  mixture.     Then  (i  —  x)  =  parts  of  tempered  air. 

.i;(i2o  -f  460)  -f  (i  —  x)  X  (70  +  460)  =  (82.2  -f-  460) 
Then 

X  =  0.244  and  (i  —  x)  =  0.756 

Air  Supplied  for  Ventilating  Purposes  Only.  A  combination  of  direct  radia- 
tion, to  offset  the  heat-loss  H,  and  a  hot-blast  system,  to  supply  the  fresh  air 
needed  for  ventilation,  is  sometimes  installed.  In  this  case  it  is  customary  to 
install  a  heater  of  sufficient  capacity  to  warm  the  air  for  ventilation  to  about  80°. 
The  heater  used  for  this  purpose  is  made  three  sections  deep  and  is  often  termed  a 

TEMPERING-COIL. 

Hot-and-Cold  Systems.  In  order  to  accomplish  the  results  required  in  the 
preceding  example,  the  so-called  iiot-and-cold  system  or  double-plenum- 
GH  AMBER  SYSTEM  is  uscd.     All  of  the  air  drawn  into  the  system  from  the  outside 


1328 


Heating  and  Ventilation  of  Buildings 


Parts 


is  first  passed  through  a  tempering-coil,  which  is  designed  to  heat  the  air  to 
approximately  70°.  A  portion  of  the  tempered  air  is  then  passed  through  a 
heater  and  raised  to  125°  to  150°.     Then  if  varying  proportions  of  the  hot  and 


Fig.  58.  Single-duct  System 


Cold  Air  Beneath  Cold  Air  AboT« 

Fig.  57.  Types  of  Heater-jackets  ' 


Fig.  59.   Deflecting-damper 
for  Branch-duct 


Fig.  60.    Thermostaticallj-controled 
Mixing-damper 


Figs.  56  to  60.    Details  of  Ducts  for  Hot-and-cold  Heating  Systems 

tempered  air  are  correctly  mixed  the  resulting  temperature  (td)  is  readily  con- 
trolled without  var\'ing  the  quantity  of  air  discharged,  which  evidently  must 
remain  constant  on  account  of  the  ventilation  requirement.     There  are  two 


Hot-Blast  Heater^ 


132^ 


methods  of  distribution  used,  as  shown  in  Figs.  56  and  58.  Referring  to  Fig.  58 
it  is  seen  that  the  hot  and  tempered  air  meet  at  the  end  of  the  plenum-chamber 
at  the  entrance  to  the  ducts,  and  the  temperature  of  the  mixture  is  controlled 
by  the  mixing-dampers,  which  may  either  be  hand-operated  or  placed  under 
automatic  thermostatic  control.  It  will  be  observed  that  the  plenum-chamber 
is  divided,  and  that  each  duct  serving  a  room  has  its  own  independent  set  of 
mixing-dampers.  This  method  of  distribution  is  known  as  the  singi.e-duct 
SYSTEM  and  is  frequently  employed  where  the  installation  of  the  double -duct 
SYSTEM,  as  described  below,  is  not  feasible  or  is  undesirable.  Fig.  56  shows  a 
double  set  of  ducts  run  from  the  plenum-chamber  to  the  base  of  each  vertical 
flue,  one  carrying  the  hot  air  and  the  other  the  tempered  air,  the  mixing  being 
done  at  the  base  of  the  flue  as  shown.  The  mixing-dampers  (Fig.  60)  may  be 
controlled  by  hand  by  means  of  a  chain  carried  up  the  flue  and  run  into  the 
room  at  a  point  several  feet  above  the  floor-line,  or  placed  under  automatic 
thermostatic  control  through  the  medium  of  a  compressed-air-operated  damper. 

Hot-Blast  Heaters 

Pipe-CoU  Heaters.     The  type  of  heater  that  has  been  a  standard  for  a 
number  of  years,  for  hot-blast  work,  is  made  up  of  four  or  eight  vertical  rows. 


Fig.  61.    Pipe-coil  Heater-base 


depending  on  the  manufacturer,  of  i-in  pipe  screwed  ihto  a  cast-iron  base  and 
spaced  from  2  3^  to  2  3^  in  on  centers,  the  pipes  in  each  row  being  cross-connected 
at  the  top  by  the  use  of  nipples  and  ells.  The  arrangement  of  coils  and  the 
method  of  dividing  the  base  by  a  vertical  pa^rtition,  running  longitudinally,  in 
order  to  separate  the  supply  and  return  as  used  by  the  American  Blower  Com- 
pany, are  shown  in  Fig.  61.    A  base  with  its  accompanying  pipes  is  termed  a 


1330 


Heating  and  Ventilation  of  Buildings 


Parts 


SECTION.     The  heater  is  made  up  of  a  number  of  such  sections  enclosed  by  a 
SHEET-STEEL  JACKET,  usually  No.  22  gauge. 

Cast-iron  Indirect  Heaters.  Special  cast-iron  sections  for  indirect  heaters 
are  often  used,  and  Fig.  62  shows  a  cast-iron  heating-unit  or  section,  named 
Vento,  manufactured  by  the  American  Radiator  Company,  which  is  quite  widely 
used  in  this  class  of  work.  A  stack  made  up  of  several  sections  has  a  smaller 
number  of  joints  than  a  pipe-coil  section  of  equal  heating-surface.  The  deteri- 
oration of  the  cast-iron  sectional  type  of  heater  is  practically  nothing  except  for 
the  right-hand  and  left-hand  hexagonal  nipples  connecting  the  units  which  go 
to  make  up  a  stack.    There  are  three  standard  lengths  of  Vento  heater-sections 


Fig.  62.    Plan  of  the  Assembly  of  a  Vento  Heater 

as  indicated  in  Table  XL VIII,  which  also  includes  other  data  required  by  the 
designer. 

Table  XL VIII.     Vento  Hot-Blast  Heater-Data 


Length  of 

section  in 

inches 

Heating- 
surface,  regular 
sections,  in 
square  feet 

Free  area  in  square  feet, 

per  section, 

inches  on  centers 

Ratio,  square 
feet  heating- 
surface  to  free 
area  for  5  in 
on  centers 

4^8 

5 

S% 

40 
SO 
60 

10.75 
13.50 
16.00 

0.52 

0.65 
0.78 

0.62 
0.77 
0.92 

0.72 
0.91 
1.08 

17.34 
17.53 
17.39 

Selection  of  Hot-Blast  Heaters.  General  Conditions.  In  selecting 
the  size  of  a  heater  for. any  particular  service  the  choice  is  based  on  the  final 
temperature  desired  and  the  free  area  required  for  a  certain  allowable  velocity. 
That  is,  for  any  specified  initial  and  final  temperature  desired,  and  a  certain 
number  of  sections,  a  final  temperature  results  when  the  velocity  has  been  fixed 
in  advance.  Good  practice  limits  the  velocity  to  the  values  given  by  the  fol- 
lowing tables.     High  velocities  are  objectionable  in  public-building  work  on 


Hot-Blast  Heaters 


1331 


account  of  the  resulting  noise.  The  resistance  through  the  heater  increases 
in  proportion  to  the  square  of  the  velocity,  which  adds  to  the  power  required 
to  move  the  air  as  the  velocity  is  increased,  as  will  be  noted  later. 

Rating  of  Hot-Blast  Heaters.  The  rating  of  an  assembled  heater  of  sev- 
eral sections  (pipe-coil  type)  or  stacks  (Vento  type)  is  based  on  the  temperature- 
rise  of  the  air  passing  over  the  heating-surface  for  certain  velocities  through  the 
free  or  unobstructed  area  of  the  heater-face.  The  velocity  is  based  on  the 
volume  of  air  at  an  assumed  temperature  of  70°  for  convenience  in  rating. 

Let  M  =  weight  of  air  to  be  circulated  through  heater  per  hour; 

0.075  =  density  of  air  at  70°; 

A  =  free  area  of  heater  in  square  feet; 

V  =  velocity  of  air  in  feet  per  minute  through  free  area  based  on  70** 
temperature. 
Then 

A  =  M/(6o  X  0.075  X  F)  =  M/4.5F  sq  ft. 

The  following  tables  will  serve  as  guides  in  selecting  the  velocity  V  and  the 
NUMBER  OF  SECTIONS  OR  STACKS  for  various  purposes. 

Table  XLIX.     Allowable  Velocities  of  Air  through  Vento  Heaters 

Referred  to  a  temperature  of  70°  F. 


Number  of 

stacks  deep, 

regular  5  in 

on  centers 

Public-building 
work,  velocity  in 
feet  per  minute 

Factory  work, 

velocity  in  feet 

per  minute 

*4 
5 
6 
7 
8 

I  000  to  I  500 

I  000  to  I  300 

I  000  to  I  200 

900  to  I  100 

800  to  I  000 

I  200  to  I  600 
I  200  to  I  600 
I  200  to  I  600 
I  200  to  I  500 
I  200  to  I  400 

Table  L. 


Number  of  Heater-Sections  for  Pipe-Coil  Heaters  or  Stacks  of  Ventd 
Ordinarily  Required 


Service 


Public  buildings,  fresh  air,  exhaust-steam. .  .  . 
Industrial  buildings,  fresh  air,  4-lb  gauge .... 
Industrial  buildings,  fresh  air,  exhaust-steam. 
Industrial  buildings,  recirculation,  S-lb  steam 
Temperin^-coils,  fresh  air,  exhaust-steam .... 


Number  of 
seccions 
or  stacks 


Number  of 
rows  of 
i-in  pipe 


20 
24 
28 


Temperature-Rise.  The  temperature -rise  of  the  air  passing  through  hot- 
blast  heaters  of  various  types  has  been  well  established  by  experiment,  the 
various  manufacturers  having  published  the  results  in  the  form  of  bulletins  and 
catalogues. 

Example.  It  is  required  to  determine  the  size  of  a  Vento  hot-blast  heater  to 
supply  the  necessary  heat  for  a  public  building,  the  calculated  heat-loss  of  which 


1332 


Heating  and  Ventilation  of  Buildings 


Parts 


is  //  =  I  420  000  Btu  per  hr  for  70°  inside  and  0°  outside  temperature.  The 
temperature  of  the  air  entering  the  rooms,  ta,  is  to  be  approximately  1 20°.  The 
steam-pressure  is  5-lb  gauge.  The  temperature  of  the  air  entering  the  heater 
is  0°. 

Solution'.  First  determine  from  Table  LI  the  number  of  stacks  deep  required 
for  F.T.  at  120°  and  entering  air  at  0°,  using  a  velocity  of  1000  ft  per  min. 
This  condition  calls  for  a  5-stack-deep  heater.  Then  determine  the  weight  of 
the  air  to  be  circulated  per  hour. 

M  =H/[o.2^{td  ~ /)]  =1  420ooo/[o.24(i2o  —  70)]  =  118  333  lb 
The  free  area  required  is 

^  =  118  333/(4-5  X  I  000)  =  25.1  sq  ft 

Table  LI.     Final  Temperatures  and  Condensations,  Vento  Heaters 

Regular  section,  Standard  spacing,  5-in  center  to  center,  of  loops.  Steam,  s-lb  gauge. 
C  is  the  condensation  in  pounds  per  hour  per  square  foot  of  heating-surface.  F.  T. 
is  the  final  temperature  of  air  leaving  heater. 


Velocity  through  heater  in  feet  per  minute,  measured  at 

70° 

Number 
of 

Temperature 
of  entering 

I 

300 

I 

200 

I 

^00 

I 

600 

stacks 

deep 

air 

F.T. 

C. 

F.T. 

C. 

F.T. 

c. 

F.T. 

C. 

f 

20 

SI 

1.99 

49 

2.23 

47 

2.42 

45 

2.S6 

30 

60 

1.92 

58 

2.17 

56 

2.33 

54 

2.46 

I 

40 

68 

1.80 

66 

2.00 

64 

2.16 

62 

2.26 

60 

84 

I.S4 

82 

1 .  69 

81 

1.89 

80 

2  .05 

70 

92 

1. 41 

90 

I.  54 

89 

1. 71 

88 

1.85 

20 

76 

1.80 

72 

2.00 

69 

2.20 

66 

2.36 

30 

83 

1.70 

79 

1.89 

76 

2.06 

73 

2.21 

2   -1 

40 

90 

1.60 

86 

1.77 

83 

1.93 

81 

2.10 

60 

103 

1.38 

100 

1.54 

98 

1. 71 

96 

1.85 

70 

no 

1.28 

107 

1.42 

los 

1.57 

103 

1.69 

20 

97 

1.6S 

92 

I. 85 

88 

2.06 

8S 

2.22 

30 

103 

i.S6 

98 

1.75 

94 

1-91 

91 

2.08 

3  \ 

40 

109 

1.47 

104 

1.64 

100 

1.79 

97 

1.9s 

60 

120 

1.28 

116 

1-44 

113 

1.S8 

no 

I. 71 

70 

126 

1.20 

122 

1.34 

119 

1.46 

n6 

1.57 

20 

IIS 

1.52 

no 

1.73 

los 

1. 91 

lOI 

2.08 

30 

120 

1.44 

IIS 

1.63 

no 

1.80 

106 

1-95 

4   ■ 

40 

124 

I.3S 

119 

I.S2 

IIS 

1.68 

III 

1.82 

60 

134 

1. 19 

129 

1.33 

I2S 

1.46 

122 

I.  59 

70 

138 

1.09 

134 

T.23 

131 

1.37 

128 

1.49 

20 

130 

1. 41 

124 

1.60 

119 

1.78 

114 

1.93 

JO 

134 

1.33 

128 

I. 51 

123 

1.67 

n8 

1.80 

S 

40 

138 

1.26 

132 

1.42 

127 

1.56 

123 

1.70 

60 

14s 

1.09 

140 

1.23 

136 

1.36 

133 

I.  SO 

70 

149 

1 .01 

144 

1. 14 

141 

1.27 

138 

1 .40 

20 

142 

1.30 

136 

1.49 

130 

1.6s 
1.S6 

126 
130 

1. 81 
I. 71 

30 

14s 

1.23 

139 

1.40 

134 

6 

40 

148 

LIS 

143 

1.32 

138 

1.47 

134 

1.60 

60 

ISS 

1.02 

ISO 

I. IS 

146 

1.29 

142 

1.40 

70 

20 

IS2 

I. 21 

^46 

1.39 

141 

I. 55 

^36 

1.70 

7 

30 

ISS 

LIS 

149 

1. 31 

144 

1.46 

139 

1.60 

40 

IS8 

1.08 

153 

1.24 

148 

1.39 

143 

1. 51 

Design  of  Air-Ducts  l33^ 

Table  LI  (Continued).     Final  Temperatures  and  Condensations,  Vento  Heaters 


Velocity  through  heater  in  feet  per 

minute 

,  measured  at 

70° 

Number 

of 
stacks" 

Temperature 

I  OOO 

I 

200 

I  400 

I 

5oo 

of  entering 

deep 

air 

F.T. 

C. 

F.T. 

C. 

F.T. 

C. 

F.T. 

C. 

.   1 

—  20 

—  10 

I 

0 

35 

2.24 

32 

2.46 

.  ! 

-20 

49 

2.22 

44 

2.46 

40 

2.69 

37 

2.92 

-10 

56 

2.12 

SI 

2.35 

47 

2.56 

44 

2.77 

i 

0 

62 

1.99 

58 

2.23 

54 

2.42 

51 

2.62 

—  20 

75 

2.03 

69 

2.28 

64 

2.51 

59 

2.70 

3 

—  10 

8o 

1.92 

75 

2.18 

70 

2.39 

66 

2.60 

0 

86 

1.84 

81 

2.08 

76 

2.27 

72 

2.46 

—  20 

96 

1.86 

90 

2. 12 

84 

2.34 

78 

2.51 

4   ^ 

—  10 

lOI 

1.78 

95 

2.02 

89 

2.22 

84 

2.41 

0 

io6 

1.70 

100 

1.92 

95 

2.13 

90 

2.31 

f. 

—  20 

114 

1.72 

107 

1.95 

100 

2.15 

94 

2.34 

5  { 

-10 

iiS 

1.64 

III 

1.86 

105 

2.06 

99 

2.24 

[ 

0 

122 

1.56 

115 

1.77 

109 

1.96 

104 

2.14 

i 

—  20 

129 

1.59 

121 

1. 81 

115 

2.02 

no 

2.22 

' ! 

—  10 

132 

1. 52 

125 

1.73 

119 

1.93 

114 

2.12 

0 

135 

1.44 

129 

1.65 

123 

1.84 

118 

2.02 

[ 

-20 

MI 

1.47 

134 

1.69 

128 

1.90 

122 

2.08 

' 

—  10 

144 

1. 41 

137 

1.62 

131 

1. 81 

126 

1.99 

1 

0 

147 

1.35 

140 

1. 54 

135 

1.73 

130 

1.90 

f 

-20 

151 

1.37 

144 

1.58 

138 

1.77 

•133 

1.96 

8 

—  10 

153 

1. 31 

147 

1. 51 

141 

1.69 

136 

1.87 

i 

0 

156 

I.  25 

150 

1.44 

144 

1.62 

139 

1.78 

Referring  to  Table  XL VIII  and  choosing  a  60-in  length  of  units,  5  in  on  centers, 
it  is  found  that  the  free  area  per  section  is  0.92  sq  ft.  The  number  of  sections 
required  across  the  face  of  the  heater  is 

A/o.g2,  or  25.1/0.92  =  27 

The  heating-surface  per  section  is  16  sq  ft.  The  total  heating-surface  is  there- 
fore 

5  =  5  X  27  X  16  =  2  160  sq  ft 

and  the  condensation  per  hour  is 

2  160  X  1.56  (Table  LI)  =  3  370  lb 
to  be  supplied  by  the  boiler,  or  by  exhaust-steam,  at  s-lb  pressure. 

Design  of  Air-Ducts 

Pressure-Loss.  The  frictional  resistance  of  air  flowing  through  smooth 
sheet-metal  ducts,  commonly  termed  pressure-loss,  measured  in  inches  of 
water,  for  70°  air  and  for  a  length  of  duct  equal  to  100  ft,  is  given  by  the' follow- 
ing formula: 

h  =  0.000136  X  (R/A)  X  v^ 

in  which  i?  is  the  perimeter  of  the  duct  in  feet,  A  the  area  of  duct  in  square 
feet,  V  the  velocity  of  the  air  in  feet  per  second,  and  h   the   pressure-loss 


1^4 


Heating  and  Ventilation  of  Buildings 


I'artS 


measured  in  inches  of  water-column.    For  round  ducts  the  above  formula 
reduces  to 

h  =  o.ooos<,v'^/D 

in  which  D  is  the  diameter  of  the  duct  in  feet. 

The  diagrams  in  Figs.  63  and  64  are  based  on  this  formula,  from  which  the 

Cubic  Feet  of  Air  per  Minute ,  Q 


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c 

\ 

^ 

\ 

^ 

.^' 

^ 

^ 

^ 

^  v^ 

V 

\ 

\ 

vA' 

n  " 

^ 

^ 

\\ 

\ 

\ 

c\ 

\^ 

%<^  \ 

^  \ 

r. 

^ 

^ 

V 

\\^ 

V 

^ 

\ 

3^ 

V^ 

n^ 

:^ 

^ 

^ 

^ 

> 

\\l 

\ 

^ 

\ 

\ 

V 

■.^ 

L/ 

, 

^ 

^ 

^ 

'\^ 

\ 

V 

X 

^ 

^V 

^ 

^ 

^ 

■^ 

-^ 

^ 

^ 

w\ 

^ 

^ 

A  * 

'A 

Diameter  of  Tipe 
Fig.  63.    Diagram  of  Friction-pressure  Loss 


Design  of  Air-Ducts 


1335 


DIAMETER  OF  A  ROUND  DUCT  for  various  velocitics,  and  the  pressure-loss  or 
RESISTANCE  foF  various  quantities  of  air  flowing,  may  be  found  without  solving 
the  above  equation. 

Cubic  Feet  of  Air  per  Minute,  Q 

||.§8§§         i§         §§8S8g         go        2 


Diameter  of  Pipe 
Fig.  64.    Diagram  of  Friction-pressure  Loss 

Example.  What  should  be  the  size  of  a  round  duct  required  to  convey  i  500 
cu  ft  of  air  per  minute  with  a  velocity  of  i  800  ft  per  min;  and  what  is  the  pres- 
sure-Joss per  100  ft  of  duct. 


1336 


Heating  and  Ventilation  of  Buildings 


Parts 


Solution.  Locate  i  500  on  the  upper  side  of  the  pipe-diagram  in  Fig.  64,  and 
pass  horizontally  downward  until  the  i  800-ft-velocity  diagonal  line  is  inter- 
sected. The  duct  which  comes  nearest  to  the  required  size  has  a  diameter  of 
12  in.  At  this  intersection  pass  to  the  right  side  to  the  base-hne  and  read  0.48- 
in  water-pressure  loss. 

Allowable  Velocity  of  Air  in  Ducts  and  Flues.  In  order  to  limit  the  resist- 
ance or  pressure-loss  in  the  duct  system  the  designer  should,  in  general,  keep  the 
velocities  within  the  Umits  stated  in  Table  LII.  In  pubHc-building  work  the 
air  should  be  delivered  to  a  room  at  a  velocity  that  will  insure  its  movement 
to  the  desired  points  in  the  room  without  objectionable  draft  or  noise  in  passing 
through  the  register-grills. 

Table  LIT.    Allowable  Velocities  in  Hot-Blast  Systems 


4 

Types  of  buildings 

Allowable 

velocity  in  feet 

per  minute 

Public  buildings 
Throuffh  free  area  of  wall-registers                                              .  . 

400-    500 
200-    300 
600-    750 
800-1  000 
I  500-2  500 

I  200-1  500 
600-    900 

I  500-2  400 
900-1  500 

Through  free  area  of  floor-registers 

Vertical  flues  to  registers 

Connections  to  base  of  flues.                                                     .    .  . 

Main  horizontal  distributing  ducts 

Manufacturing  plants 
In  plants  where  the  occupation  is  more  or  less  sedentary  and 
the  employe  sits -ell  day  feeding  automatic  machinery: 
Main  ducts '. 

Branches 

In  plants  where  the  employe  stands  all  day,  as  in  machine- 
shops,  foundries,  etc.: 

Branches                                                                               

The  velocity  through  the  fan-outlet,  under  the  ordinary  conditions  that  obtain  in  heating 
work,  varies  from  i  500  to  2  500  ft  per  min. 

Table  LIU.     Metal  Gauges  for  Ducts 

American  Blower  Company 


Heating  and  ventilating 

Thickness  and  weight 

Blowpiping  and 
exhaust  work 

«  Diameter 
in  inches 

United 
States 
standard 
gauge- 
number 

Thickness  in  inches 

and  weight  in  pounds 

per  square  foot 

Diameter 
in  inches 

United 
States 
stanaard 
gauge- 
number 

6-18 
19-36 
38-48 
SO-60 
63-72 

26 
24 
22 
20 
18 

in           lb  per  sq  ft 
0.1087            0.91 
0.025               i.i6 
0.0312            I. 41 
0.0375            1-66 
0.05                2.16 

3-    5 

6-  8 

y-15 

16-24 

26-30 

26 
24 
22 
20 
18 

Design  of  Air-Ducts 


1337 


Sheet-Metal  Pipes  and  Ducts.  The  recommended  gauge  (United  States 
sheet-metal  gauge)  for  various  sizes  of  galvanized  sheet-steel  pipes  for  heating 
and  ventilating  work,  blowpiping  and  exhaust  work,  is  given  in  Table  LIII. 

Pressure-Loss  of  Rectangular  Ducts.  The  simplest  method  of  determining 
this  is  to. proportion  the  system  for  round  ducts  throughout,  and  then  transfer 
to  RECTANGULAR  SIZES  giving  equal  pressure-losses  (not  equal  areas)  by  means  of 
Table  LIV. 


Table  LIV. 

Round  and  Rectangular  Ducts  of  Equal  Pressure-Losses 

Side  of 

rectangular 

duct  in 

inches 

4 

6 

8 

10 

12 

14 

15 

16 

18 

20 

22 

24 

Equivalent  diameters  in  inches 

4 
5 
6 
7 
8 
9 

10 

II 

12 

13 

14 
15 
i6 
17 
I8 
19 

20 
22 
24 
26 
28 

30 

32 

34 
36 
38 
40 

42 

44 
46 
48 
50 
52 
54 
56 
58 
6o 

62 

64 
66 
68 

4-4 
4-9 
5-4 
5.8 
6.1 
6.5 
6.8 
7.1 
7.4 
7.6 
7.6 

8.2 

8.4 
8.6 
8.9 
9-1 
9-3 
9.7 

10. 0 

10.4 
10.8 

II  .0 

II. 3 
II. 6 
II. 9 

12.2 
12.5 
12.7 

13.0 
13. 3 
13.5 
13.7 
13-9 

14. 1 
14-3 
14.6 
14-7 
15.0 
15. 1 
15-3 
IS. 5 

6.6 
7.0 
7.6 
8.0 

8.4 
8.8 

9-2 

9.6 
9.9 

10.  2 

10. 5 
10.8 

11.  I 
II. 4 

11. 6 
12. 1 
12.6 
13-1 
13.5 
13.9 
14.3 
147 
15. 1 
15.4 
15.7 
16. 1 
16.4 
16.7 
17.0 
17.3 
17.6 
17.9 
18.2 
18.4 
18.7 
19-0 
19.2 
19.5 
19.7 

8.8 
9.3 
9.8 
10.2 
10.7 
II. I 
II. 5 
II. 9 
12.3 
12.6 
13.0 
13.3 
13.6 
14.2 
14.8 
15.4 
15.9 
16.4 
16.9 
17.3 
17.7 
18.2 
18.6 
19.0 
19.4 
19.8 
20.1 
20.4 
20.8 
21. 1 
21.5 
21.8 
22.1 
22.4 
22.7 
23.0 
23-3 

II. 0 
II. 5 
12.0 
12.5 
12.9 
13.4 
T^    8 

13.2 
13.7 
14-3 
14.7 
15.2 

15.4 
16.0 
16.5 
17.0 
17.4 
17.9 
18.4 
19.2 
20.0 
20.8 
21.5 
22.2 
22.9 
23.5 
24.2 
24.8 
25.4 
25.9 
26.5 
27.0 
27.5 
28.0 
28.5 
29.0 
29-5 
30.0 
30.5 
30.9 
^1.3 

le^s 
17. 1 
17.6 
18. 1 
18.6 
19.0 

19-9 
20.8 
21.6 
22.4 
23.1 
23.8 
24.4 
25.1 
25.8 
26.4 
26.9 
27.5 
28.1 
28.6 
29.2 
29.6 
30.1 
30.6 
31. 1 
31.6 
32.1 
32.6 
33.0 
33.4 

17*6 
18.2 
18.7 
19.2 
19-7 
20.6 
21.5 
22.3 
23.1 
23.9 
24.6 
26.3 
26.0 
26.7 
27.3 
27.9 
28.5 
29.1 
29.6 
30.3 
30.7 
31.2 
31.7 
32.2 
32.7 
33.2 
33.7 
34-2 
34.7 

19^8 
20.4 
20.9 
21.9 
22.8 
23.8 
24.6 
25.4 
26.2 
26.9 
27.7 
28.4 
29. 1 
29.8 
30.3 
31.0 
31.6 
32.2 
32.9 
33.4 
33.9 
34-4 
34-9 
35.4 
35.9 
36.4 
36.9 

22.0 
23.1 
24.0 
25.1 
26.0 
26.8 
27.7 
28. s 
29-3 
30.0 

24.2 
25.2 
26.3 
27.3 
28.2 
29.1 
30.0 
30.8 
31.5 

26.4 
27.5 
28.5 
29.5 
30.5 
31.3 
32.2 
33.1 
33.9 
34.5 
35.3 
36.2 
37.0 
37.6 
38.3 
38.9 
39-6 
40.3 
40.9 
41.6 
42.2 
42.8 
43.4 

14.2 
14.6 
15.0 
15.4 
16. 1 
16.8 
17.3 
18.0 
18. 5 
19. 1 
19.6 
20.1 
20.  6 
21. 1 
21.6 
22.0 
22.4 
22.8 
23.2 
23.6 
24.0 
24.4 
24.7 
25.1 
25.5 
25.9 
26.  2 
26. 5 

15.7 
16. 1 
16. S 
17.0 
17.8 
18.5 
19.2 
19.8 
20.5 
21. 1 
21.6 
22.2 
22.8 
2-3.3 
23.8 
24.3 
24.8 
25.2 
25.7 
26.2 
26.6 
27.0 
27.4 
27.8 
28.2 
23.6 

31-4 
31.2 
32.8 
33.4 
34-1 
34.7 
35.3 
35.9 
36.4 
37.1 
37.7 
38.2 
38.7 
39-2 

32.4 

33  0 
33-7 
34.6 
35.2 
35.9 
36.5 
37.2 
37.8 
38.4 
39.1 
39.6 
40.2 
40.8 
41.4 

29.0 
29-4 

31.7 
33.1 

1338 


Heating  and  Ventilation  of  Buildings 


Parts 


Example.     What  is  the  width  of  a  rectangular  duct  6  in  high  equivalent  to 
the  pressure-loss  for  a  duct  12-in  in  diameter? 
Solution.     22  in. 


Table  LV.     Friction  Pressure-Loss  of  90°  Elbows 


Radius  of  throat  in  diam- 
eters of  pipe 

M 

H 

% 

I 

iM 

13-^ 

2 

3 

4 

5 

Number  of  diameters  of 
straight  pipe  of  equiva- 
lent pressure-loss 

67 

30 

16 

10 

7-5 

6 

4-3 

4.8 

5-2 

5.8 

Example.  A  duct  12  in  in  diameter  and  120  ft  long  contains  two  90°  elbows. 
The  ratio  of  the  radius  of  throat  to  pipe-diameter  is  3.  The  amount  of  air  flow- 
ing is  I  500  cu  ft  per  min  and  the  velocity  i  800  ft  per  min. 

Solution.    The  total  equivalent  length  of  duct  is 

120  H-  (2X4.8)=  129.6  ft 

The  pressure-loss,  from  the  diagram  of  Fig.  64  is  0.48  in  per  100  ft.    The  loss  is 
therefore 

0.43  X  (i  29.6/100)  =  0.62  in  of  water 

The  pressure-loss  for  square  elbows  is  o.85z>2/2^  in  of  water  for  round  pipes  and 
i.2sv'^/2g  for  square  pipes,  v  is  the  velocity  in  feet  per  second.  The  pressure- 
loss  through  register-grills  may  be  taken  at  0.023  in  for  a  velocity  of  400  ft  per 
min  through  free  area.  The  gross  area  of  registers  is  twice  the  free  area.  The 
pressure-loss  in  air-washers  and  humidifiers  for  a  velocity  of  400  ft  per  min 
through  free  area  is  0.15  in  of  water.  The  pressure-loss  through  hot-blast 
heaters  may  be  taken  from  Table  LVI. 

Table  LVI.    Friction  of  Air  through  Vento  Heaters 

Friction-loss,  in  inches  of  water,  due  to  air  passing  through  Vento  stacks.     Regular  sec- 
tion.    Standard  5-in  spacing  of  loops.     Air-temperature  70°  F. 


Velocity 

in  feet 

per  minute 

One 

Two 

Three 

Four 

Five 

Six 

Seven 

stack 

stacks 

stacks 

stacks 

stacks 

stacks 

stacks 

800 

0.037 

0.070 

0.103 

0.135 

0.167 

0.200 

0.  232 

900 

0.047 

0.088 

0.129 

0.170 

0.211 

0.252 

0.293 

I  000 

0.059 

0, 109 

0.160 

0.211 

0.262 

0.313 

0.364 

I  100 

0.071 

0.132 

0.193 

0.255 

0.316 

0.377 

0.438 

I  200 

0.084 

0.IS7 

0.230 

0.303 

0.376 

0.449 

0.522 

I  300 

0.099 

0.18s 

0.271 

0.356 

0.442 

0.528 

0.614 

I  400 

0.115 

0.214 

0.314 

0.414 

0.513 

0.612 

0.712 

I  500 

0. 132 

0.246 

0.360 

0.474 

0.588 

0.702 

0.816 

I  600 

0.150 

0.280 

0.410 

0.540 

0.670 

0.800 

0.930 

I  700 

0. 169 

0.316 

0.463 

0.609 

0.756 

0.903 

1.049 

I  800 

0.190 

0.354 

0.518 

0.683 

0.848 

1. 012 

1. 177 

Effect  of  Temperature  on  Pressure-Losses.    The  preceding  data  on  pres- 
sure-losses in  ducts,  registers  and  heaters  are  based  on  an  air-temperature  of  70°. 


Design  of  Air-Ducts 


1339 


For  other  temperatures,  the  pressure-losses  are  to  be  multiplied  by  the  ratio, 
density  of-  air  at  actual  temperature  to  density  at  70**.  These  ratios  are  given 
in  Table  LVII.  For  heaters  use  the  average  temperature  of  the  air  passing 
through  the  heater. 


Table  LVII.     Ratios  of  Density  of  Air  at  Actual  Temperature  to  Density  at  70°  F. 


Temperature 

Factor 

Temperature 

Factor 

100 
120 
130 

0.945 
0*.  910 
0.890 

140 
ISO 
160 

0.880 
0.865 
0.850 

Design  of  Duct  Systems.    There  are  two  schemes  used  in  proportioning 

air-ducts:  (i)  the  velocity  method,  and  (2)  the  method  of  equal  friction  pres- 
sure-loss per  foot  of  length.  The  first  method  involves  the  fixing  of  the  veloci- 
ties (see  Table  LII)  in  the  various  sections,  and  the  gradual  reduction  of  the 
velocity  from  the  beginning  of  duct  to  the  point  of  discharge.  In  this  case  the 
pressure-loss  is  computed  separately  for  each  section  having  a  different  velocity 
and  the  various  pressure-losses  added  together  to  obtain  the  total  loss  in  pres- 
sure. The  second  method  is  used  principally  in  the  design  of  duct  systems  for 
factory- heating.  The  velocity  in  the  outlet  farthest  from  the  fan  is  fixed  and 
the  area  and  diameter  of  this  branch  are  determined  by  the  volume  of  air  to 
be  delivered.  The  friction  pressure-loss  per  100  ft  of  a  duct  of  this  size  is  deter- 
mined by  the  diagrams  in  Figs.  63  and  64.  The  remainder  of  the  main  duct  is 
then  proportioned  for  this  same  pressure-loss  per  100  ft. 

Example.     The  first  method  is  illustrated  in  Fig.  65,  showing  a  single-duct 
system.     The  risers  are  figured  for  a  velocity  of  600  ft  per  min,  or  10  ft  per  sec; 


<PIeqniB-Chamb«r 


w 

I 200 -____y  , 


V=900ft.perinin. 
12' 


-  Mixing-Dampers 
.3a "LP.  in  Plenum-Chamber 


Slngle-Duct  System 


Motor 


^orizontal  Run 


Fig.  65.     Single-duct  System 


and  400  ft  per  min,  or  6.6  ft  per  sec;    through  free  area  of  register-grill.     The 
velocity  in  the  longest  main,  B,  is  900  ft  per  min,  the  volume  of  air  to  be  delivered 
2  000  cu  ft  per  min,  and  the  temperature  120°, 
Solution.     The  area  of  the  riser  required  is 

2  000/600  =  3H  sq  ft,  or  480  sq  in 
An  18  by  27-in  riser,  giving  486  sq  in  area,  is  used.     The  area  of  main,  B,  is 

2  000/900  =  2.22  sq  ft,  or  320  sq  in 


1340 


Heating  and  Ventilation  of  Buildings 


The  size  of  the  duct  is  12  by  27  in.  The  diameter  of  a  round  duct  for  the  same 
friction-loss  for  the  riser,  from  Table  LIV,  is  24  in,  and  for  the  main,  B,  19.5  in. 
Referring  to  the  diagram  in  Fig.  G4,  the  pressure-loss  for  the  riser  is  0.032  in 
per  100  ft.  For  the  main  the  pressure-loss  is  0.09  in  per  100  ft.  The  main  has 
one  elbow  and  the  riser  one  elbow,  and  the  ratio  of  radius  at  throat  to  diameter 


'^,y/yy/^j^^^^A^A-i/^-l^/y:;7rf^ 


will  be  assumed  to  be  3,  in  both  cases.    The  equivalent  length  of  main,  B,  is 
therefore 

200  4-  (4.8  X  20/12)  =  208  ft 
and  the  pressure-loss  is 

0.09  X  (208/100)  =  0.187  in 
The  equivalent  length  of  riser  is 

34  -f  (4.8  X  24/12)  =44  ft 
and  the  pressure-loss  is 

0.032  X  (44/100)  =  0.014  ^^ 


Ventilating  Fans 


1341 


The  pressure-loss  through  the  register-grill  is  0.023  in.     The  total  resistance 
of  the  duct  system  is  therefore 

0.0187  +  0.014  +  0.023  =  0.224  in 

Assuming  that  a  five-section  Vento  heater  is  employed,  with  a  velocity  (fig- 
ured through  free  area)  of  i  200  ft  per  min,  the  pressure-loss  through  the  heater 
is  0.376  in  (Table  LVI).     The  total  resistance  against  which  the  fan  must  • 
operate  is 

0.224  in  -f  0.376  in  =  0.60  in 

based  on  70°  air.     Assuming  the  temperature  of  the  air  to  be  120°,  the  resist- 
ance is 

0.60  X  0.91  (Table.LVII)  =  0.55  in 

The  second  method  of  duct-design  is  illustrated  by  the  example  given  under 
Application  of  Hot-Blast  Heating-Data,  page  1342. 


Ventilating  Fans 

Steel-Plate  Fan.  The  standard  type  of  fan  that  has  been  used  for  a  number  of 
years  in  hot-blast  work  is  known  as  the  steel-plate  fan,  the  construction  of  the 
wheel  being  shown  in  Fig.  67.     As  the  name  implies,  the  wheel  and  casing  of  this 
fan  are  constructed  of  steel  plate 
and  light  structural   sections,  the 
wheel    having    eight    to    twelve 
blades,  straight  or  slightly  curved 
at  the  periphery,  and  in  a  direc- 
tion   opposite     to    the    rotation. 
Steel-plate  fans  are  designated  by 
number,    this   number   being  the 
approximate   height   of   the   fan- 
casing  in  inches. 

Multibladed  Fan.   A  new  type 
of   fan,    known    as   the    sirocco 

WHEEL  or  TURBINE-TYPE  IMPEL- 
LER, Fig.  68,  has  recently  entered 
the  field  of  heating  and  ventilat- 
ing, and  on  account  of  its  higher 
efficiency,  quieter  running,  and 
relatively  smaller  size  for  the  same 
capacity  than  the  steel-plate  fan, 
it  is  rapidly  supplanting  the  latter. 
The  higher  efficiency  is  accounted  for  by  the  material  reduction  of  the  air- 
resistance  or  pressure-head  loss  by  friction  through  the  fan,  due  to  the  shorter 
blades  and  the  larger  inlet,  which  is  of  practically  the  same  diameter  as  the 
wheel  itself.  This  fan  deserves  more  than  passing  mention  as  it  represents 
perhaps  the  greatest  single  improvement  ever  made  in  the  design  of  a  centrif- 
ugal fan. 

Rating  of  Fans.  The  volume  of  air  at  70°  which  a  fan  will  deliver  (cubic  feet 
per  minute)  varies  with  the  resistance  against  which  it  operates.  In  order  to 
choose  a  fan  from  Table  LIX,  the  resistance  (static  pressure)  must  first  be 
determined  by  the  duct-design,  and  after  the  size  of  the  heater  has  been  chosen 
and  its  resistance  determined.     The  speed  and  brake  horse-power  required  to 


Fig.  67.     Standard  Steel-plate  Fan-wheel 


1342 


Heating  and  Ventilation  of  Buildings 


Parts 


drive  the  fan  are  also  stated  in  the  tables.  The  temperature  of  the  air  handled 
by  the  fan  with  draw-through  apparatus  is  higher  than  70°,  except  for  a  fan 
which  is  connected  ahead  of  a  tempering-coil,  usually  a  two-scction-deep  heater. 
The  tabulated  speed,  volume  and  brake  horse-power  to  maintain  the  pressure 

must  be  multiphed  by  the  factors 
given  in  Table  LVIII  for  temperatures 
other  than  70°.  The  above  factors 
in  this  table  are  the  square  roots  of 
the  ratios  of  the  density  of  the  air  at 
70°  F.  to  its  density  at  the  tempera- 
ture stated. 


Table  LVIII.    Factors  for  Speed,  Vol- 
ume and  Brake  Horse-Power 


Fig.  68. 


Sirocco  Wheel  or  Turbine-type  Im- 
peller 


Temperature  in 

degrees 

Fahrenheit 

Factors 

0 
100 
120 
130 
140 
150 

0.932 
1.028 
1.046 
1.055 
1 .064 
1.073 

Application  of  Hot-Blast  Heating-Data 

The  Application  of  the  Foregoing  Data  on  lu)t-l)last  heating  to  a  factory- 
building  follows  (see  Fig.  69).     The  calculated  heat-loss  is  i  423  920  Btu  per  hr. 

Conditions.  Air  recirculated  and  inside  temperature  maintained  at  60°. 
Velocity  of  air  through  heater,  from  i  000  to  i  200  ft  per  min.  Velocity  of  air 
at  last  outlet  in  duct  system,  i  275  ft  per  min.  Temperature  of  air  delivered 
by  heater,  145°. 

Weight  of  Air  to  be  Circulated  per  Minute.    This  is 

I  423  920/(0.24(145  —  60)160]  =  I  163  lb 

Size  of  Heater.  This  condition,  60°  initial  and  145°  final  temperature, 
requires  a  heater  five  stacks  deep  (Table  LI),  and  a  velocity  of  i  000  ft  per  min 
through  free  area  at  a  temperature  of  70°.  The  volume  of  air  per  minute 
measured  at  70",  to  be  handled  by  the  heater  and  fan  is 


I  163/0.075  =  15  506  cu  ft 


The  FREE  AREA  required  is: 

15  S06/1  000  =  15.5  sq  ft 

Assuming  a  60-in  length  of  section  with  loops  5  in  on  centers,  the  free  area  per 
section  is  0.92  sq  ft  (Table  XLVIII).     The  number  of  sections  per  stack  is 

15-5/0.92  =  17 
The  total  number  of  sections  required  is 

5  X  17  =  85 


Application  of  Hot-Blast  Heating-Data  1343 


[3  Concrete  Roof 
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Fie.  69.     Hot-blast  HeatiriK  for  a  Factory-buildinc.     (See  Example  for  Computations) 


1344 


* 

Heating  and  Ventilation  of  Buildings 

1 

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1346 


Heat'mg  and  Ventilation  of  Buildings 


Part  3 


The  total  heating-surface  is 

8s  X  i6  =  I  360  sq  ft 

Weight  of  Steam  or  Condensation  per  Hour.    This  is 

I  360  X  1.09  (Table  LI)  =  i  482  lb 

The  equivalent  amount  of  direct  radiation  is 

I  482/0.25  =  5  929  sq  ft 

Design  of  Duct  System.  The  round  ducts  will  be  designed  for  equal-friction 
pressure-loss  per  foot  of  length.  The  final  velocity  at  the  last  or  most  remote 
outlet  from  fan  will  be  taken  at  1275  ft  per  min.  The  friction  pressure-loss  for 
this  velocity,  as  read  from  the  diagram  in  Fig.  64,  is  0.25  in  of  water  per  100  ft 
of  length.  There  are  to  be  eighteen  outlets.  The  total  volum'^  of  air  to  be  dis- 
charged, measured  at  145°  F.,  is 

I  163/0.065  =18  000  cu  ft  per  min 
or 

18  000/18  =  I  000  cu  ft  per  min  per  outlet 

The  cross-sectional  area  of  the  outlet  or  last  section  is  i  000/ 1  275  sq  ft,  cor- 
responding to  a  circular  section  with  a  diameter  of  12  in.  The  branch-outlets 
may  all  be  made  the  same  size  and  provided  with  dampers  to  adjust  or  equalize 
the  flow.     The  friction  pressure-loss  in  the  duct  system  is  therefore 

(212/100)  X  0.25  =  0.53  in  of  water 

The  siT^e  of  each  section  of  duct  is  determined  by  locating  the  quantity  of  air 
at  the  right  of  the  diagram  and  passing  horizontally  to  the  intersection  with  the 
o.2S-in  pressure-loss  Hue. 


Table  LX. 

Data  for  Design  of  Ducts  in 

Fig.  69 

Section 

Quantity 
of  air  in 
cubic  feet 

Duct- 
diameter  in 

Velocity 
in  feet  per 

Measured  length 
plus  allowance  for 

per  minute 
145°  F. 

inches 

minute 

ells,  in  feet 

A 
B 
C 
D 
E 
F 
G 
H 
I 
J 

1  000 

2  000 

3  000 

4  000 

5  000 

6  000 

7  000 

8  000 

9  000 
18  000 

12 

16 

i8J4 

21 

23 

25 

26 
28 
29 
38 

I  275 

25+[iX(6+3)]-34 

15 

IS 

15 

15 

IS 

IS 

IS 

3S+[2.4(6-fio)l-73 

2  285 

Total  length  =212 

Selection  of  Fan  for  Draw-Through  Arrangement.     The  statir  pressure 
rating  required,  referred  to  a  temperature  of  70°,  is: 

Pressure-loss  in  heater  (data  from  Table  I.VT)  —  0.26  in 
Pressure-loss  in  duct  (data  from  chart,  Fig.  04)  =  0.53  in 


Total  =  0.79  in 


Application  of  Hot-Blast  Heating-Data  1347 

The  actual  pressure-loss  wHI  be  somewhat  less,  owing  to  the  fact  that  the  air- 
temperature  is  higher  (145°  F.)  and  the  density  less  than  for  air  at  70°  F.  The 
actual  estimated  pressure-loss  is  therefore  assumed  to  be  %  in. 

The  volume  of  air  the  fan  must  handle  in  this  example  is  18  000  cu  ft  per  min, 
measured  at  145°  F.  As  stated  under  Rating  of  Fans,  to  maintain  a  constant 
pressure  the  tabulated  speed,  volume  and  horse-power  must  be  multiplied  by 
the  square  root  of  the  ratio  of  densities,  or 

Vo.075/0.066  =  1.07  (nearly)  (Table  IT) 

We  therefore  select  from  Table  LIX  a  fan  having  a  capacity,  measured  at 
70°  F.,  equal  to 

18  000/1.07  =  16  822  cu  ft  per  min  (approximately  17  000) 

when  operating  with  a  static  pressure  of  %  in.  A  No.  8  Sirocco  fan  fulfills  this 
requirement.  The  tabulated  speed  and  horse-power  when  multiplied  by  the 
factor  1.07  gives 

196  X  1.07  =210  R.P.M. 
and 

3.76  X  1.07  =  4.02  brake  horse-powei: 

Selection  of  Fan  for  Blow-Through  Arrangement.  In  this  case  fhe 
fan  may  be  called  upon  to  handle  air  at  a  temperature  of  0°  F.,  or  lower.  Assum- 
ing the  same  weight  of  air,  or  70  000  lb  per  hr,  to  be  handled  by  the  fan  at  a  static- 
pressure  of  %  in,  the  volume  at  0°  is 

70  000/(0.086  X  60)  =  13  566  cu  ft  per  min 

Referring  to  Table  LVIII,  the  ratio  between  the  speed,  volume  and  power  neces- 
sary to  produce  the  same  pressure  for  air  at  0°  and  air  at  70°,  is  found  to  be 
0.932.     We  therefore  choose  a  fan  with  a  capacity  of 

13  566/0.932  =  14  557  cu  ft  of  air  at  70° 
and  with  a  static  pressure  of  %  in. 

Fan-Engine.  When  high-pressure  steam  is  available  an  automatic  high- 
speed engine  is  frequently  employed  for  fan-driving,  and  the  exhaust  from  the 
engine  is  used  in  the  first  section  of  the  heater. 

Selection  of  Motor  for  Fan-Driving.  It  is  considered  good  practice  to  add 
from  10  to  15%  to  the  brake  horse-power,  as  determined  from  the  fan -tables, 
for  the  rating  of  the  motor,  to  allow  for  a  possible  overload  due  to  the  fact  that 
the  fan  may  not  be  operated  under  exactly  the  same  conditions  as  to  pressure 
and  speed  as  those  under  which  it  was  originally  rated.  For  the  preceding  exam- 
ple (D  raw-Thro ugli  Arrangement)  a  5 -horse-power  motor  would  be  selected. 

Additional  Heating  Requirement.  It  is  frequently  desirable  to  proportion 
the  heating- apparatus  large  enough  so  that  the  fan  may  be  shut  down  at  night 
and  started  up  about  two  hours  before  the  shop  or  factory  is  opened  in  the 
morning.  In  this  event  it  may  be  safely  assumed  that  the  temperature  of  the 
air  in  the  building  will  not  be  below  30°  F.  when  the  fan  is  started,  and  that 
the  air  is  all  recirculated.  The  fan  and  heater  must  be  of  sufficient  capacity 
to  take  care  of  the  heat-loss  from  the  building,  including  the  infiltration,  and 
in  addition  to  warm  up  the  contained  air  f^om  30°  to  60°  in  two  hours.  Assum- 
ing the  same  data  as  given  in  the  preceding  example,  the  additional  heat  re- 
quired will  be,  if  the  cubic  contents  of  the  building  are  328  000  cu  ft, 

(328  000  X  0.08  X  0.24  X  Zo)/2  =  94  464  Btu  per  hr 


1348 


Heating  and  Ventilation  of  Buildings 


Parts 


This  amounts  to  an  increase  of  approximately  7%  in  the  heating  requirements 
as  previously  calculated  and  is  readily  provided  for  by  increashig  ?he  steam 
pressure  carried  m  the  heater  to  approximately  lo-lb  gauge.  Catalogue,  bul- 
letins etc  on  the  subject  of  hot-blast  heating,  air-washing  and  humfd  fiction 
may  be  obtamec^  from  the  American  Blower  Company,  the  B  F.  SturtTvant  Com 
pany,  the  Buttalo  Forge  Company,  and  the  Carrier  Air  Conditioning  Company. 

Ventilation 
Natural  and  Mechanical  Ventilation.     Ventilation,  whether  naturai.  or 
MECHANiGA.,  consists  m  the  displacement  of  vitiated  air  from  an  apartm^and 


S^JmCl 


Ventilation 


13^ 


its  replacement  by  fresh  aif.  To  state  that  the  air  in  an  apartment  is  renewed 
any  given  number  of  times  per  hour  is  not  strictly  accurate,  as  a  positive  change 
does  not  actually  occur;  the  incoming  air  mixes  with  and  dilutes  the  foul  air  to  a 
point  suitable  for  healthful  respiration.  In  natural-ventilation  systems  the 
movement  of  the  air  in  flues,  ducts,  etc.,  is  induced  solely  by  the  thermal  head 
produced  by  the  difference  between  the  density  of  the  column  of  air  in  the 
ducts  and  that  of  the  outside  atmosphere;  the  higher  the  temperature  in  the 
ducts  the  more  powerful  the  draft.  The  direction  and  velocity  of  the  wind 
materially  affect  the  natural  ventilation,  retarding  or  accelerating  the  move- 
ment of  the  air  through  ducts  and  flues,  according  to  the  exposure  of  the  building 
and  the  position  of  inlets  and  outlets.  In  mechanical  ventilation  the  move- 
ment of  air  is  maintained  by  means  of  various  types  of  fans,  driven  by  a  steam- 
engine,  electric  motor,  or  other  prime  mover.  With  fans  of  known  efficiencies ' 
the  results  can  be  accurately  estimated.  The  principal  advantages  of  the  use 
of  mechanical  systems  of  heating  and  ventilation  have  already  been  stated 
under  Hot-Blast  Heating. 

Systems  of  Ventilation.  Ventilation  systems  are  also  broadly  divided  into 
two  general  classes  known  as  the  upward  system  and  the  downward  system."" 
The  UPWARD  system  (Fig.  70)  is  generally  used  for  audience-rooms  where  there  is 
strong  natural  tendency  for  the  heat  given  off  by  the  large  number  of  occupants  to 
rise  and  take  with  it  the  vitiation-products  due  to  respiration.  The  air  is  sup- 
plied NEAR  THE  FLOOR-LINE  through  mushroom  ventilators  in  the  floor,  or 
through  the  hollow  pedestals  of  the  chairs  themselves,  or  through  low  registers. 
The  viTiATED-AiR  OUTLETS  ARE  IN  OR  NEAR  THE  CEILING.  This  systcm  makes  it 
rather  difficult  to  heat  the  room  in  advance  of  the  arrival  of  the  audience  as  the 
outlets  allow  the  warmed  air  to  escape  almost 
as  rapidly  as  it  can  be.  introduced.  The 
DOWNWARD  SYSTEM  is  Very  generally  used 
in  school-rooms,  hospitals,  institutions,  etc. 
The  occupants  are  not  as  closely  placed  as 
in  the  former  case,  and  a  more  even  distri- 
bution of  air  and  more  uniform  heating  can 
be  secured  when  the  air  is  supplied  eight 

FEET  OR  more    ABOVE    THE   FLOOR,  and  the 
vitiated     air    REMOVED    AT    OR    NEAR    THE 

FLOOR-LINE.  On  account  of  the  elevation 
of  the  inlets  abovethe  headsof  the  occupants 
there  is  little  liability  of  drafts,  and  if  the 
outlets  are  on  the  same  side  wall  as  the  in- 
lets there  is  very  little  opportunity  for 
short-circuiting  between  inlet  and  outlet, 
since  the  incoming  air  must  flow  out  across 
the  room  to  the  cold  outside  wall  before  it 
can  cool  and  drop  to  the  floor-level.  It  is, 
however,  necessary  in  the  downward  system, 
to  overcome  the  natural   tendency  of  the 

heated  air  from  the  bodies  of  the  occupants  to  rise  and  oppose  the  uniform 
downward  tendency  of  the  incoming  fresh  air.  The  selection  of  either  system 
must  depend  entirely  on  the  conditions  to  be  met.  These  have  been  outhned 
in  the  above  paragraphs. 

Distribution  of  the  Air.  In  general,  it  should  be  observed  that  whether 
upward  or  downward  ventilation  is  employed  there  should  always  be  a  definite 
system  of  vitiated-air  removal,  designed  to  provide  for  uniform  distribution  and 


SIZES  OP  "ABC"  MUSHROOM  VENTILATOR. 


Size. 

Approximate 
Inside  Diameter. 

Approximate 
Weight 

.    4 

6 
6 

0% 

61b. 
10  lb. 
15  1b. 

Fig.  71.     Section  through  ABC 
Mushroom  Ventilator 


1350 


Heating  and  Ventilation  of  Buildings 


Parts 


prevent  short-circuiting  between  inlets  and  outlets.  A  practically  complete 
diffusion  can  only  be  attained  when  inlet  and  outlet  are  placed  in  the  same 
inside  wall,  with  the  former  at  least  from  7  to  8  ft  above  the  latter.    Multiple 


Flanges  (Bolted) 


Return-Main, 
Steam  and  Water 

f 

Union  (Screwed) 


Hot-Water  Main, (Flow) 


J-^         .1      .1 


Tee  and  Ell,  Long  Sweep 
(  Same  Plane) 


Tee  and  Ell,  Close 
(Same  Plane) 


Drop 


■+0- 


Plan 

Oast -Iron  Boiler 
and  Conuoctious 


Deflecting  and  Mixing  Damper* 


Heat  and  Vent-Flues 
with  Regifcters 


^ 

\ 

Two-Piw 

- 

5  AQ 


Elbows  in  Rounds  Duct  i 

Fig,  72.    Heating  and  Ventilating  Symbols 

INLETS  and  MUSHROOM  VENTILATORS,  in  Order  to  secure  a  better  mechanical 
distribution  of  the  air,  are  being  made  useof  in  many  systems  of  upward  ventila- 
tion for  audience-rooms  with  fixed  seats.     In  this  case  a  false  flojr  or  plenum 

CHAMBER  must  be  constructed  iiist  bc'Iow  the  mnin  flexor  throiifirh  wbuh  the  Mir 


Ventilation 


1351 


is  to  be  supplied.  Mushroom  ventilator-heads  (Fig.  71)  are  then  located  under 
every  second  or  third  seat  and  adjusted  to  give  a  uniform  discharge  of  tempered 
air  over  the  entire  seating-area.     These  heads  are  either  mounted  on  an  ad- 

I 


k 


$1 — K) 
Boiler 


r  itii( 


'2^ 
Blow-off  or 
Drain 


H> 

Boiler 
t-i 


I  (Alternate) 


coner 


^Expansion-arm 


Typical  Elow-Connections.  Plan 
Header  JRelurn  -/ 


r- 


1,    \^ 


Boiler 
C» — 


F" 


ii  I 


4 


leometric-Perspective 
Sectional  C.  I.  Type. 


Steam.or  FloW  ' 


Blow-  , 

l0j 


ri: 


n 


Boiler 
— O 


\i 


u 


Header^ 

Twin-Boiler  Connections.  Plan 


Hound  d.  I.  Type 


Elevation. 
Fig.  73.     Heating-boiler  Connections  . 


instable  spindle  (Fig.  70),  which  is  supported  centrally  in  the  cast-iron  floor- 
sleeve  (^r  flange,  or  else  they  have  a  non-adjustable  spindle  similarly  supported, 
and  are  cauipped  with  a  control-damper.     In  either  case  the  adjustable  h«a4  or 


1352  Heating  and  Ventilation  of  Buildings  Part  3 

damper  must  be  locked  positively  in  the  finally  adjusted  position.  In  the  case 
of  concrete  floors  it  is  very  desirable  to  use  a  cast-iron  sleeve  and  flange  (Fig. 
70)  rather  than  a  galvanized  sleeve  and  cast-iron  flange. 

The  Effect  of  Vitiated  Air.  The  amount  of  carbon  dioxide  present  in 
vitiated  air  has  been,  until  recently,  quite  generally  understood  to  be  the  element 
of  danger  that  should  be  kept  within  safe  Umits.  Dr.  Ira  Remsen  has  pointed  out 
that  the  presence  of  carbon  dioxide  in  itself  is  not  dangerous  to  health  except 
that  it  reduces  the  supply  of  oxygen  by  displacing  it.  Carbon  dioxide  is  not 
poisonous,  but  the  organic  impurities  that  are  exhaled  at  the  same  time  with 
other  gases  that  are  given  off  may  prove  a  menace  to  health.  The  ill  effects  of 
breathing  air  in  a  poorly  ventilated  room  are  due  to  the  small  quantities  of 
decomposing  organic  matter  and  unhealthful  gases.  The  carbon  dioxide  gen- 
erated by  the  lungs  and  given  off  at  the  same  time  as  the  other  impurities  serves 
more  or  less  as  an  indicator  of  the  presence  of  the  real  danger.  Any  lowering 
of  the  oxygen-supply  that  is  actually  required  for  the  proper  and  necessary 
transformation  of  the  potential  heat-value  of  the  food  into  the  physical  and 
nervous  energy  required  to  keep  the  human  machine  running,  and  to  readily 
supply  the  additional  demand  made  upon  that  machine  to  perform  external 
work,  means  that  industrial  workers  who  perform  their  duties  in  a  vitiated 
atmosphere  do  so  at  the  expense  of  a  lowered  vitahty,  and  are  naturally  less 
productive.  Satisfactory  ventilation  consists  not  only  in  constantly  supplying, 
in  a  pure  condition,  fresh  air  free  from  dust  and  other  impurities,  at  the 
proper  temperature  and  with  the  proper  amount  of  moisture  present,  but 
also  in  efficiently  removing  the  vitiated  air.  This  cannot  be  positively  accom- 
pHshed  during  the  heating-season  by  simply  opening  the  doors  and  windows. 
Some  mechanical  means  must  be  employed.  Many  physicians,  however,  do 
not  believe  in  mechanical  ventilation  for  hospitals,  and  advocate  ventilation 
by  the  open- window  method;  and  many  hospitals  are  now  constructed  without 
any  provision  for  mechanical  ventilation  except  for  the  toilets  and  operating- 
rooms  for  which  exhaust-fans  are  provided. 

Relation  between  Humidity  and  Temperature.  The  proper  and  healthful 
RELATIVE  HUMIDITY  OF  THE  AIR  in  buildings  has  only  in  recent  years  been  given 
the  thought  and  attention  it  rightfully  deserves.  Heated  or  warmed  air, 
whether  purposely  introduced  into  a  building  for  warming,  or  naturally  entering 
by  infiltration,  on  being  expanded  by  heat,  has  its  percentage  of  moisture  or  rela- 
tive humidity  lowered,  and  consequently  its  capacity  for  absorbing  moisture 
greatly  increased.  There  is,  therefore,  experienced  the  sensation  due  to  so-called 
DRY  HEAT.  This  causes  an  excessive  and  unnatural  evaporation  of  moisture 
from  the  skin  and  from  the  membranes  of  the  respiratory  organs.  Evaporation 
takes  place  by  the  direct  application  of  heat  and  is  essentially  a  refrigerating  or 
cooling  process.  The  abstraction  of  heat  from  the  body  for  this  purpose,  nat- 
urally tends  to  lower  the  surface-temperature,  and  one  feels  several  degrees 
cooler  than  the  temperature  recorded  by  the  thermometer  in  the  room.  Dr. 
H.  M.  Smith's  many  observations  and  experiments  upon  the  sensations  produced 
by  different  percentages  of  satltiation,  led  him  to  make  the  following  state- 
ment: "It  may  be  accepted  as  a  cardinal  rule  that  if  a  room  is  at  68°  and  is  not 
warm  enough  for  any  healthy  person,  it  is  because  the  relative  humidity  is 
too  low."  A  standard  relative  humidity  may  be  obtained  when  mechanical 
ventilation  is  used  by  the  addition  of  a  humidifier  to  the  system.  The  subject 
of  air-conditioning  is  fully  treated  in  Heating  and  Ventilating,  Vol.  I,  by 
Harding  and  Willard. 

Requirements  for  Good  Ventilation.  There  is  quite  a  diversity  of  opinion 
among  various  authorities  as  to  what  constitutes  good  ventilation  in  many 


Ventilation  1353 

instances.     The  following  data  by  G.  D.  Small  represent  good  practice  in  this 
respect: 

Types  of  Buildings.     Air-Changes  to  be  Allowed 

f  Portions  above  grade One  change  per  hour. 

Office -Buildings  j  Basement,  general Four  changes  per  hour. 

[  Mechanical  plant Ten  changes  per  hour. 

Factory-Buildings  which  have  no  mechanical  or  natural   ventilation,  one 

change  per  hour.     For  factories  in  which  large  doors  from  the  outside  are 

frequently  opened,  about  four  air-changes  per  hour. 
Residences  which  have  loose  windows,  two  changes  per  hour. 
Churches.    Four  changes  per  hour,  except  small  rooms,  which  should  have  five 

or  six  changes  per  hour.     These  data  for  churches  contemplate  mechanical 

ventilation.     The  majority  of  public  buildings  and  many  of  the  factories 

require  ventilation  or  the  fan  system  of  heating.  . 

The  Usual  Requirements  for  Air  Supplied  per  Person  are  as  Follows 

Hospitals  (O'"'^^''^ from  35  to  40  cu  ft  per  min 

I  Epidemic 80  cu  ft  per  mm 

Air-change 

Detention-rooms 6  min 

Toilet-rooms 6  min 

Bath-rooms  and  duty-rooms 8  min 

Kitchens 3  min 

Serving-rooms 10  min 

Fumigating-rooms 10  min 

Workshops 25  cu  ft  per  min 

Prisons 30  cu  ft  per  min 

Theaters from  20  to  30  cu  ft  per  min 

Meeting-Halls 20  cu  ft  per  min 

Schools 30  cu  ft  per  min  per  child  and  40  cu  ft  per  min  per  adult 

The  Usual  Time-Intervals  for  One  Air-Change  are  as  Follows 

Hotels 

Room  Air-change  Room  Air-change 

Engine-room 6  min  Cafe 8  min 

Kitchen 1^-5  min  Lobby  under  balcony. .  8  min 

Restaurant 6  min  Main  lobby 20  min 

Base-toilet 5  min  Banquet-hall 15  min 

Billiard 10  min  Retiring-room 10  min 

Barber-shop 8  min  Kitchens 8  min 

Dining-room 15  min  All  others 15  min 

Palm-room 12  min  Toilets 6  min 

Buffet 8  min 

Libraries 

Corridors 15  min  Inside  rooms 8  min 

Basement-rooms 15  min  Corner  rooms *  .  . .     7  min 

Reading-rooms 12  min  Toilet-rooms 5  min 

Laundries  should  have  an  air-change  every  4  to  6  min. 

Note.     Radiation  on  sides  of  buildings  subjected  to  prevailing  and  cold  winds  should 
be  increased  10%  up  to  the  loth  floor  and  15%  above  that  floor. 


1354  Heating  and  Ventilation  of  Buildings  Part  3 

Ventilation-Laws.  The  number  of  ventilation-laws  has  increased  very 
rapidly  in  the  last  few  years,  not  only  as  regards  the  number  of  states  which 
nave  added  such  laws  to  their  codes,  but  also  as  to  the  scope  and  effectiveness  of 
these  statutes.  In  many  cases  a  special  ventilation-officer  or  commission  has 
been  appointed  to  see  to  the  enforcement  and  extension  of  the  requirements  for 
compulsory  ventilation,  so  that  it  behooves  the  architect  or  engineer  to  become 
thoroughly  famiHar  with  the  law  of  the  state  or  states  wherein  he  practices. 
A  summary  of  the  law  recently  enacted  by  the  legislature  of  the  state  of  Ohio 
is  given  in  the  following  paragraphs  as  an  example  of  the  regulations  with 
which  architects  and  engineers  must  conform  in  preparing  plans  and  specifica- 
tions. This  law  as  well  as  the  law  of  Massachusetts,  attempts  to  provide  very 
definite  regulations  for  heating  and  ventilating  all  classes  of  buildings.  Future 
legislation  in  other  states  will  undoubtedly  take  a  more  specific  form,  establishing 
complete  and  definite  codes  for  the  heating  and  ventilation  not  only  of  public 
buildings  but  of  workshops,  factories  and  mercantile  establishments  as  well. 


Requirements  of  the  Department  of  Inspection  of  the  Industrial 

Commission  of  Ohio  for  the  Heating  and  Ventilation 

of  Public  Buildings,  Hospitals,  Asylums  and 

Homes 

Temperature 

A  heating  system  shall  be  installed  which  will  uniformly  heat  the  various 
parts  of  the  building  to  the  following  temperatures  in  zero  weather. 

Theaters  and  Assembly-Halls.  All  parts  of  the  buildings,  except  storage- 
rooms,  65°  F. 

Churches.  Auditorium,  social  and  assembly-rooms,  65°  F.  All  other 
parts  of  the  building,  except  storage-rooms,  70°  F. 

School-Buildings.  Corridors,  hallways,  play-rooms,  toilets,  assembly- 
rooms,  gymnasiums  and  manual-training  rooms,  65°  F.  All  other  parts  of  the 
buildings,  70°  F. 

Hospitals,  Asylums  and  Homes.  Operating-rooms,  85°  F.  All  other  parts 
of  the  buildings,  except  storage-rooms,  70°  F. 


Change  of  Air 

The  heating  system  shall  be  coml)ined  with  a  system  of  ventilation  which  at 
normal  temperature  will  change  the  air  the  following  number  of  times,  or  supply 
to  each  person  the  following  number  of  cubic  feet  of  air  per  hour. 

Theaters.    Parlors,  retiring,  toilet  and  check-rooms,  six  changes  per  hour. 

Auditoriums,     i  200  cu  ft  of  air  per  person  per  hour. 

Assembly-Halls.  When  used  in  connection  with  a  school-building,  lodge- 
building,  club-house,  hospital  or  hotel,  six  changes  per  hour;  and  in  all  other 
assembly-halls,  i  200  cu  ft  of  air  per  hour  per  person. 

Churches.  Auditoriums,  assembly-rooms  and  social  rooms,  six  changes  per 
hour. 

School-Buildings.  All  parts  of  the  buildings,  except  corridors,  halls  and 
storage-rooms,  six  changes  per  hour. 


Requirements  for  Heating  and  Ventilation  of  Buildings       1355 
Asylums,  Hospitals  and  Homes,    (i)  Rooms  with  fixed  capacity: 

Adults  Children         Babies 

Hospitals,  contagious  and  epidemic 6  ooo  4  000            3  000 

Hospitals,  surgical  and  medical 3  000  2  400            i  500 

Penal  institutions i  800  i  800 

All  other  buildings i  800  i  500 

(2)  Rooms  with  variable  capacities: 

Hospitals,  contagious  and  epidemic 12  times  per  hour 

Hospitals,  surgical  and  medical 12  times  per  hour 

All  other  buildings 6  times  per  hour 

Rooms  accommodating  four  or  less  persons  need  not  be  provided  with  a  system 

of  ventilation. 

Radiators 

No  radiator  shall  be  placed  m  any  aisle,  foyer  or  passageway  of  a  new  theater, 
assembly-hall  or  church,  but  such  radiators  may  be  placed  in  recesses  in  the 
walls. 

Registers 

No  floor-registers  shall  be  used  in  theaters,  assembly-halls,  or  hospitals. 

No  floor-registers,  except  foot-warmers,  shall  be  used  in  a  school-building. 

Floor-registers  may  be  used  in  churches. 

Otherwise  all  vent-registers  shall  be  placed  not  more  than  2  in  above  the  floor^ 
line,  and  warm-air  registers  not  less  than  8  ft  above  the  floor-line  (except  when 
such  registers  are  used  when  a  change  of  air  is  not  prescribed). 

Systems  to  be  Installed  Where  a  Change  of  Air  is  Required 

The  system  to  be  installed  when  a  change  of  air  is  required  shall  be  either  a 
gravity  or  mechanical  furnace  system,  gravity  indirect  steam  system,  or  hot- water 
system;  mechanical  indirect  steam  or  hot-water  system,  or  split  steam  or  hot- 
water  system;  except  in  hospitals,  where  a  direct-indirect  system  may  be  used 
in  connection  with  an  exhaust-fan.  The  fresh-air  supply  shall  be  taken  from 
outside  the  building  and  no  vitiated  air  shall  be  reheated.  All  vitiated  air  shall 
be  conducted  through  flues  or  ducts  and  be  discharged  above  the  roof  of  the 
building. 

Exceptions.  Standard  ventilating  stoves  may  be  used  in  the  following 
buildings: 

Assembly -halls  seating  less  than  100  persons. 

Churches  seating  less  than  100  persons. 

All  school-buildings,  hospitals,  asylums  and  homes. 

Furnaces 
Furnaces  may  be  used  in  all  classes  of  buildings. 

Gravity  Indirect  Hot-Water  or  Steam-Radiator  Systems 

Indirect  hot-water  or  steam-radiators  shall  be  located  in  basement  fresh-air 
rooms  ■  directly  at  the  base  of  masonry  hot-air  flues,  and  shall  be  properly  con- 
nected to  same  with  galvanized-iron  housing. 


1356  Heating  and  Ventilation  of  Buildings  Part  3 

Indirect  Radiating-Surface  for  Heating  and  Ventilating  Purposes 

One  square  foot  of  radiating-surface  shall  be  provided  to  heat  not  more  than 
the  following  number  of  cubic  feet  of  air  per  hour: 

Hot 

Height  Steam     water 

First  story 200         125 

Second  story 250         160 

Third  story 300         200 

Fourth  story 250         235 

For  Heating  Wall- Surfaces  and  Glass-Surfaces.  The  amount  of 
radiating-surface  for  the  heating  of  the  glass-surface  and  wall-surface  shall  not 
be  less  than  that  obtained  by  adding  together  the  glass-surface  and  one  fourth 
the  exposed  wall-surface,  both  in  square  feet,  and  multiplying  by  the  following 
factors: 

Hot 

Height  Steam     water 

First  story 0.7        i .  05 

Second  story 0.6       0.9 

Third  story 0.5        0.75 

Fourth  story 0.4       0.5 

Accelerating  or  Aspirating  Coils  for  Vent-Flues.  Vent-flues  used  in 
connection  with  a  gravity  indirect  steam  or  hot-water  system  shall  be  provided 
with  accelerating  coils  placed  i  ft  above  the  vent-openings. 

Mechanical  Fan  Plenum  System 

This  system  shall  be  designed  with  furnaces,  tempering  coils  or  blast-coils 
so  as  to  furnish  heated  air,  and  is  to  have  cleaning-screens,  fan  plenum  chamber, 
galvanized-iron  or  masonry  horizontal  ducts,  masonry  hot-air  flues,  electric 
motor,  gas  or  gasoline  engine,  or  a  low-pressure  steam-engine  operating  on  a 
steam-pressure  not  to  exceed  35-lb  gauge  to  operate  fan  and  such  other  device  as 
is  necessary  to  make  this  a  complete  working  system.  All  parts  and  apparatus 
in  connection  with  the  installation  are  to  be  of  ample  size  to  make  a  perfectly 
free  and  easily  working  system,  which  must  thoroughly  heat  all  portions  of  the 
building  without  forcing. 

Velocity  of  Air 

The  velocity  of  the  air  traveling  through  ducts,  flues,  etc.,  shall  never  exceed 
the  following  number  of  feet  per  minute: 

Feet  per 
Ducts,  Flues,  etc.  minute 

Fresh-air  screens,  small  mesh 600 

Fresh-air  ducts,  gravity  system 300 

Fresh-air  ducts,  mechanical  system 850 

Tempering  coils,  gravity  system 300 

Tempjering  coils,  mechanical  system i  000 

Furnaces,  gravity  system 400 

Furnaces,  mechanical  system 900 

Trunk-ducts,  mechanical  system i  000 

Laterals,  branches  and  single  ducts,  mechanical  system •  75° 

Vertical  flues,  mechanical  system 500 


Specifications  for   Furnace-Work  1357 

Vertical  warm-air  flues,  gravity  system,  first  story 300 

Vertical  warm-air  flues,  gravity  system,  second  story 350 

Vertical  warm-air  flues,  gravity  system,  third  story 390 

Vertical  vent-flues  less  than  20  ft  high 300 

Vertical  vent-flues  from  20  to  ss  ft  high 350 

Vertical  vent-flues  from  33  to  46  ft  high 390 

Vertical  vent-flues  from  46  to  60  feet  high 440 

Warm-air  registers 300 

Vent-registers 300 

Maximum  Speed  of  Fans 

The  maximum  speed  of  fans  used  in  connection  with  either  an  exhaust  or 
plenum  system  of  heating  or  ventilating,  under  normal  conditions,  shall  never 
exceed  the  following: 

Diameter  of  fan  in  inches. .. .     18       24      36      48      60      72       96     120     180 
Revolutions  per  minute 700     550    400    300     225     175     150     125       75 

Location  of  Heater-Room 

No  heater-room  shall  be  located  under  the  auditorium,  stage,  lobby,  passage- 
way, stairway  or  exit  of  a  theater;  noF,  under  any  exit,  passageway,  public  halJ 
or  lobby  of  an  assembly-hall,  church,  school-building,  asylum,  hospital  or  home. 
This  applies  to  new  buildings,  and  a  changed  location  of  a  heater-room  in  an 
existing  building.  No  cast-iron  boiler  carrying  more  than  lo-lb  pressure  or 
steel  boiler  carrying  more  than  30-lb  pressure  shaU  be  located  within  the  main 
walls  of  any  school-building. 

Standard  Fire-Proof  Heater-Room  for  New  Buildings 

All  furnaces  and  boilers,  including  the  breeching,  fuel-rooms  and  firing-spaces 
shall  be  enclosed  by  brick  walls  not  less  than  1 2  in  thick,  or  by  monolithic  con- 
crete walls  not  less  than  8  in  thick.  The  ceiUng  over  the  same  shall  not  be  less 
than  the  following:  reinforced-concrete  slab,  4  in  thick;  brick  arches,  4  in  thick, 
covered  with  i  in  of  cement  mortar  and  supported  by  fire-proof  steel  with  the 
necessary  tie-rods;  or  hollow-tile  arches,  6  in  thick,  covered  with  2  in  of  concrete, 
plastered  on  the  under  side  and  supported  by  fire-proof  steel  with  the  necessary 
tie-rods. 

Specifications  for  Furnace-Work 

The  following  form  is  given  as  a  guide  to  architects  in  preparing  the  specifi- 
cations for  furnace-work : 

Specifications  for  Furnace -Work  in  Residence  for  Mr to  bb 

BUILT  AT 

Architect 

Furnace.  Furnish  and  set  up  complete,  where  shown  on  basement-plan,  one 
(.  . .  name  . .  .)  furnace,  or  approved  equal,  portable-pattern,  with  double  casings. 
Connect  the  furnace  with  the  chimney  with  a  No.  22  galvanized-iron  smoke-pipe 
of  the  same  size  as  the  collar  on  the  furnace;  all  bends. or  turns  to  be  made  with 
three-piece  elbows;  the  pipe  to  be  strongly  supported  by  wire,  and  to  be  kept 
12  in  below  the  ceiling. 

Air-Pit.  Excavate  for  and  build  a  cold-air  chamber  under  the  furnace  not 
less  than  18  in  deep,  with  8-in  brick  walls,  laid  and  plastered  with  cement;  also 


1358 


Heating  and  Ventilation  of  Buildings 


Parts 


cement  the  bottom  of  the  chamber.  Build  the  cold-air  duct  under  cellar-floor, 
where  shown  on  plan,  —  ft  long,  14  in  deep  in  the  clear,  and  —  in  wide,  with 
sides  of  hard  brick  in  cement,  and  with  the  sides  and  bottom  smoothly  plastered 
with  cement.  Cover  the  duct  with  3-in  flagstones  with  tight  joints,  leaving 
opening  of  proper  side  for  the  wooden  box  to  be  built  by  the  carpenter  (wooden 
box  should  be  included  in  carpenter's  specifications). 

Hot-Air  Pipes.  Furnish  and  properly  connect  with  furnace  and  register-boxes, 
leaders  and  stacks  of  the  following  sizes,  all  to  be  made  of  bright  IX  tin,  and  the 
stacks  are  to  be  double  with  an  air-space.  All  turns  in  leaders  to  be  made  by 
three-piece  or  four-piece  elbows,  and  the  stacks  to  have  boots  or  starters  of 
approved  pattern. 


Sizes  of  Pipes  and  Registers 


Hall 11"      leader,     no  stack 

Parlor 11  y^"  leader, 

Dining-room 12"      leader. 

Library loV^"  leader, 

Chamber  No.  i 10"      leader, 

Chamber  No.  2 9"      leader, 

Chamber  No.  3 8H"  leader: 


12"  X  14"  register. 
no  stack  12"  X  15"  register 

no  stack  12"  X  15"  register 

no  stack  12"  X  14"  register 

4"  X  15"  stack,  10"  X  14"  register 
4"  X  13"  stack,  10"  X  12"  register 
4"  X  13"  stack,  10"  X  12"  register 


Registers.  All  registers  are  to  be  of  sizes  given  in  the  foregoing  list,  of  the 
(. .  .name. . .)  or  approved  equal,  manufacture;  japanned,  except  those  in  the 
first  story,  which  are  to  be  electro-bronze-plated.  All  floor-registers  are  to 
be  set  in  iron  borders  corresponding  with  the  registers. 

Register-Boxes.  All  register-boxes  to  be  made  double;  for  first-story  boxes 
the  JOISTS  ARE  TO  BE  LINED  WITH  TIN  and  provided  with  ceiling-plates  the 
full  size  of  the  registers,  with  plaster-collars  attached,  so  that  pipes  and  boxes 
can  be  removed  without  disturbing  the  plastering  or  defacing  the  ceiHng. 

Miscellaneous.  All  horizontal  pipes  in  the  basement  are  to  be  round,  and 
where  they  pass  through  partitions  they  are  to  be  provided  with  collars,  so  that 
the  pipes  can  be  removed  without  disturbing  the  plastering.  All  leaders  are  to 
be  provided  with  dampers  and  tin  tags  designating  the  different  rooms  they 
supply;  and  whenever  pipes  run  near  woodwork  the  same  is  to  be  properly 
covered  with  tin  and  protected  from  any  danger  from  fire.  The  contractor  is 
to  remove  afl  rubbish  made  by  him,  clean  up  all  ironwork,  leave  the  whole 
apparatus  in  complete  working  order,  and  furnish  a  poker  of  proper  size. 

Guarantee.  The  contractor  is  to  guarantee,  if  he  furnishes  the  heating- 
drawings,  that  the  furnace  shall,  under  proper  management,  heat  all  rooms 
with  registers  connected  with  the  furnace,  to  70°  F.,  when  the  temperature 
outside  indicates  0°.  In  the  event  of  the  failure  of  the  furnace  to  do  this, 
the  contractor,  at  his  own  expense  and  without  unnecessary  delay,  is  either 
to  make  the  furnace  heat  said  rooms  or  substitute  another  furnace  that  will 
heat  them. 


Hot-Air-and- Water  Combination-Furnaces 

Combination-Furnaces.  It  is  quite  difficult,  if  not  impossible,  to  heat 
dwellings  covering  throughout,  more  than  i  400  sq  ft  with  warm  air  alone. 
On  account  of  the  much  larger  exposure  and  the  increased  length  of  leaders, 
it  becomes  necessary  to  supplement  the  warm  air  with  an  auxiliary  heat  which 


Specifications  for  Furnace-Work  135W 

can  be  carried  to  remote  and  exposed  parts  of  the  house,  and  which  will  not 
be  affected  by  pressure  of  wind  or  long  and  crooked  pipes.  For  supplying  this 
auxiliary  heat,  hot  water  has  been  found  best  adapted  as  a  rule,  and  a  variety 
of  COMBINATION-FURNACES  are  now  made  which  contain  provisions  for  heating 
water  which  may  be  carried  by  pipes  to  radiators  located  in  those  parts  of  the 
house  most  difficult  to  heat  by  warm  air.  Such  combination-systems  have 
been  used  with  success.  The  construction  of  the  parts  for  heating  the  water 
varies  with  different  makes  of  furnaces.  Some  furnaces  have  a  portion  of  the 
fire-pot  hollow,  and  the  water  is  heated  there;  others  have  a  separate  heater 
suspended  over  the  fire-pot.  As  a  rule,  the  parts  of  the  house  which  should 
be  heated  by  the  hot  water  afe  the  halls,  bath-rooms,  and  pferhaps  the 
rooms  on  the  north  or  west  sides  of  the 'house.  The  same  rules  govern  the 
size  of  the  radiators  and  piping  and  the  manner  of  installing  as  in  an  entire 
hot-water  plant. 

Specification  for  Hot- Water  Heating-Apparatus  in  a  Residence 

This  specification  contemplates  a  complete  upfeed  two-pipe  gravity  hot-water 
heating  system,  to  be  installed  in  accordance  with  the  drawings  covering  the 
same. 

Heater.  Furnish  and  set  up  in  cellar,  where  shown  on  plan,  one  ( . . .  name . . . ) 
water-boiler,  or  approved  equal,  guaranteed  free  from  all  flaws  and  defects. 
The  heater  to  be  set  on  a  substantial  foundation  of  hard  brick  laid  in  cement 
mortar  and  put  in  by  the  heating-contractor.  Furnish  and  deliver  one  set  of 
fire-tools,  consisting  of  one  poker,  one  sUce-bar  and  one  fine  brush  and  handle. 

Smoke-Pipe.  Connect  the  boiler  to  the  chimney  by  means  of  smoke-pipe 
made  of  No.  22  galvanized  iron,  the  diameter  of  the  pipe  to  be  equal  to  the 
outlet  on  the  heater. 

Trimmings.  The  boiler  is  to  be  provided  with  one  thermometer  registering 
from  80°  F.  to  250°  F.,  and  one  Standard  altitude  gauge.* 

Water-Connections  and  Blow-off.  Feed-water  with  its  supply-pipe  will  be 
brought  within  6  ft  of  the  boiler  by  the  plumber  and  left  with  one  54-in  cast-iron 
fitting  for  boiler-connection,  which  is  to  be  made  by  this  contractor,  with  suit- 
able cock.  Draw-off  cock  to  be  placed  on  lowest  point  of  system  and  to  be 
fitted  for  hose-attachment. 

Pipes.  Furnish  and  run  all  necessary  flow  and  return-mains  of  ample  size, 
connecting  them  to  radiators  with  risers  of  ample  size  to  insure  the  free  flow 
of  hot  water  to  and  from  the  radiators.  All  connections  from  risers  to  radiators 
to  be  made  below  floors. 

Quality  of  Materials.  All  materials  used  in  the  construction  of  this  apparatus 
are  to  be  the  best  of  their  respective  kinds,  all  fittings  to  be  heavily  beaded  and 
made  of  the  best  gray  iron  with  clean-cut  threads,  and,  when  practicable,  Y's 
and  45°  L's  are  to  be  used. 

Reaming.  The  ends  of  all  pipes  used  in  the  construction  of  this  apparatus 
are  to  be  reamed  and  all  obstructions  removed  before  pipes  are  placed  in  position. 
All  flow  and  return-mains  in  the  basement  are  to  be  supported  by  neat,  strong, 
adjustable  hangers,  arranged  to  suit  expansion  and  contraction,  and  properly 
secured  to  timbers  overhead.  *  At  all  points  where  pipes  pass  through  ceilings, 

*  An  altitude-gauge  indicates  the  amount  of  water  in  the  system  and  is  a  convenient 
attachment  which  avoids  the  necessity  of  consulting  the  gauge-glass  in  the  tank.  It 
can  be  dispensed  with  if  desired. 


1360 


Heating  and  Ventilation  of  Buildings 


Parts 


floors,  or  partitions,  tin  thimbles  are  to  be  provided  and  the  holes  protected 
with  floor  or  ceiling-plates. 

Expansion-Tank.  The  expansion-tank  is  to  be  constructed  of  galvanized  iron, 
and  is  to  be  furnished  with  a  proper  gauge-glass  with  brass  mountings  complete. 
It  is  to  be  placed  at  least  3  ft  above  the  highest  radiator  in  a  suitable  place 
and  supported  on  a  proper  shelf.  From  this  tank  an  overflow-pipe  will  be 
run  to  the  basement  or  other  suitable  place  with  a  vent-pipe  through  the  roof, 
properly  flashed. 

Radiators.     Furnish,  set  up,  and  pipe  the  following  radiators: 


Rooms 


Number 
of  radiators 

Radiating- 
surface. 

sq  ft 

I  indirect  radiator 

108 

I  indirect  radiator 

120 

I  direct  radiator 

40 

I  direct  radiator 

60 

I  direct  radiator 

40 

I  direct  radiator 

44 

I  direct  radiator 

36 

I  direct  radiator 

32 

I  direct  radiator 

32 

Main  hall 

Sitting-roon 

Library 

Dining-room 

Sitting-room  chamber. 

Library  chamber 

Dining-room  chamber, 

Kitchen  chamber 

Bath-room 


9  radiators 


In  all  there  are  to  be  284  sq  ft  of  direct  surface  and  228  sq  ft  of  indirect;  total 
surface,  512  sq  ft.  The  direct  radiators  to  be  (. .  .name. . .)  hot-water  pattern, 
or  approved  equal,  38  in  high. 

Air-Valves.  Each  radiator  is  to  be  provided  with  a  nickel-plated  key-type 
air-valve. 

Radiator-Valves.  Each  direct  radiator  is  to  be  promptly  connected  to  the 
system  of  piping  with  a  quick-opening  nickel-plated  radiator-valve  and  union 
elbow. 

Indirect  Radiation.  The  indirect  radiators  are  to  consist  of  two  stacks  of 
( . . .  name . . . )  hot- water  radiation,  or  approved  equal,  connected  together 
with  tight  joints  and  firmly  suspended  from  the  basement-ceiling  by  suitable 
wrought-iron  hangers.  The  stacks  are  to  be  so  piped  and  hung  as  to  permit 
a  noiseless  and  constant  flow  throughout  of  the  heated  water.  Each  stack 
is  to  be  enclosed  in  a  galvanized-iron  chamber  with  proper  fresh-air  inlet-duct 
and  a  corresponding  outlet-duct  for  warm  air,  connected  to  the  register  in  the 
room  which  the  stack  is  intended  to  heat.  The  registers  are  to  be  of  the 
(. .  .name.  .  .)  pattern,  electro-bronze-plated,  and  of  the  following  sizes:  hall, 
12  by  19;  sitting-room,  14  by  22  in.  Registers  are  to  have  floor-borders  and 
to  be  set  in  register-boxes.  The  duct  connecting  the  stack  and  register  is  to 
be  so  arranged  that  all  fresh  air  coming  in  wiU  be  properly  heated  and  con- 
veyed, with  least  loss,  to  its  destination.  In  arranging  indirect  boxes,  care 
is  to  be  exercised  in  getting  ample  space  for  cold  air  under  the  stack,  and  a 
corresponding  space  for  warm  air  over  the  stack. 

Covering  of  Pipe.  All  flow  and  return-pipes  and  fittings  in  cellar  above  the 
floor  are  to  be  properly  covered  with  i-in  hair-felt  neatly  sewed  up  in  canvas 


specifications  for  Furnace-Work  1361 

and  painted  one  coat  of  good  white  lead,  or  covered  with  asbestos  or  magnesia 
sectional  covering,  with  canvas  cover,  and  secured  by  lacquered-brass  bands. 

Boiler-Covering.  All  exposed  parts  of  the  boiler,  except  the  front,  are  to 
be  covered  with  plastic  asbestos,  i  ^  in  thick,  neatly  applied  and  troweled, 
smooth. 

Workmanship.  All  work  is  to  be  done  in  a  neat,  substantial  and  workman- 
like manner,  and  the  apparatus,  when  completed,  is  to  be  thoroughly  tested 
and  left  in  good  working  order. 

Guarantee.  The  contractor  is  to  guarantee,  if  he  is  to  furnish  the  heating- 
drawings,  that  the  apparatus  he  installs  will  be  of  ample  capacity  to  evenly 
maintain  a  temperature  of  70°  F.  in  the  rooms  in  which  radiators  are  located, 
when  the  outside  temperature  is  at  zero,  and  that  the  apparatus  throughout 
will  have  a  free  circulation  when  in  operation. 

Steam-Heating  for  Residences 

General  Requirements.  For  very  large  residences,  the  author  would 
recommend  steam-heat,  all  of  the  principal  rooms  to  be  heated  by  indirect 
radiation,  and  only  the  bath-room,  halls,  and  perhaps  the  attic  and  one  or  two 
rooms  on  the  north  side,  which  generally  includes  the  dining-room,  by  direct 
radiation.  For  dining-rooms  a  special  direct  radiator,  containing  a  warming- 
closet,  is  made.  The  air-supply  to  the  indirect  stacks  should  be  very  large 
and  provided  with  a  damper,  so  that  the  supply  may  be  regulated  according 
to  the  weather.  The  boilers  used  in  residence-heating  are  generally  of  the  cast- 
iron  sectional  type  described  on  page  1278.  The  single-pipe  system  is  com- 
monly used  in  dwellings,  all  indirect  radiators,  however,  being  two-pipe. 

Specification  for  a  Low-Pressure  Steam-Heating  Apparatus  for 
Heating  by  Direct  Radiation 

Intention.  This  specification  is  intended  to  cover  everything  necessary  to 
fully  finish  and  install  in  the  above-mentioned  building  a  complete  steam-heat- 
ing system  in  strict  accordance  with  the  plans  and  this  specification,  as  prepared 
by ,  architect. 

Plans.  The  drawings  herewith  are  intended  to  show  only  the  location  of  the 
boiler,  piping  and  radiators;  the  arrangement  of  the  piping  will  be  left  largely 
to  the  contractor,  subject  to  the  approval  of  the  architect. 

General  Requirements.  This  contractor  is  to  provide  all  necessary  tools  and 
appliances  for  the  erection  and  completion  of  the  work,  and  when  completed, 
is  to  remove  all  apparatus,  refuse  and  debris  from  the  building  and  grounds, 
leaving  the  work  in  a  clean,  uninjured  and  perfect  condition.  No  cutting  of 
any  description  tending  to  weaken  the  building  structurally  is  to  be  undertaken" 
without  consulting  the  architect.  This  contractor  is  to  be  fully  responsible  for 
the  safety  and  good  condition  of  the  work  and  material  embraced  in  this  contract 
until  the  completion  and  acceptance  of  the  same.  All  work  is  to  be  of  the  best 
quality,  and  should  at  any  time  improper,  imperfect,  or  unsound  material  or 
faulty  workmanship  be  observed,  whether  before  or  after  same  has  been  built 
into  the  structure,  this  contractor,  upon  notice  from  the  architect,  is  to  remove 
same  and  substitute  good  and  proper  material  and  workmanship  without  delay 
in  place  thereof,  in  default  of  which  the  architect  is  to  effect  same  by  other 
means  as  may  be  deemed  best,  and  is  to  deduct  the  cost  of  such  alterations  from 
the  sura  due  the  contractor  under  this  contract. 


13G2  Heating  and  Ventilation  of  Buildings  Part  3 

System.  The  heating  is  to  be  effected  by  direct  radiation  distributed  through- 
out as  shown  on  the  drawings,  and  the  circulation  of  the  steam  is  to  be  by  the 
one-pipe  circuit  system. 

Boiler.  This  contractor  is  to  build  the  foundation  for  the  boiler,  where 
shown,  12  in  deep,  of  common  hard  brick  laid  in  cement  mortar.  He  is  to 
leave  an  ash-pit  for  the  boiler  of  proper  size,  12  in  deep,  cemented,  and  made 
water-tight.  He  is  to  furnish  and  set  up  one  (. .  .name. . .)  cast-iron  sectional, 
or  approved  equal,  boiler,  provided  with  6-in  low-pressure  brass-cased  steam- 
gauge,  water-gauge,  and  glass,  gauge-cocks,  combination-column,  safety-valves 
and  blow-off  valves,  and  all  other  usual  and  necessary  trimmings  to  complete 
the  boiler,*  and  a  full  set  of  fire-tools,  consisting  of  one  slicing-bar,  one  hoe, 
one  poker,  and  a  cleaning-brush.  He  is  to  cover  the  boiler  with  i  M-in  of  asbestos 
cement,  neatly  troweled  to  a  smooth  finish. 

Water-Supply.  The  plumber  is  to  bring  the  water-supply  to  within  6  ft  of 
boiler,  but  this  contractor  is  to  make  connection  with  boiler  with  ^-in  iron 
pipe,  stop-cock  and  check- valve. 

Smoke-Pipe.  Contractor  is  to  connect  the  boiler  with  the  chimney  with  a 
round  smoke-pipe  made  of  No.  22  galvanized  iron  with  suitable  balance-damper. 
This  connection  to  be  of  same  size  as  left  for  this  purpose  by  maker  of  boiler. 

Main  Pipes  and  Risers.  The  steam-main  is  to  be  run  full  size  for  the  entire 
length  and  provided  with  an  automatic  air-vent  at  the  end  of  the  run.  It  is 
to  be  of  ample  size  to  carry  all  the  risers  and  radiators  attached  to  the  system, 
and  is  to  be  graded  i  in  in  10  ft  in  the  direction  of  the  flow.  From  the  top  of 
this  main  the  various  branches  are  to  be  taken  to  radiators  and  risers,  the 
connections  for  which  are  to  be  so  made  that  no  traps  are  formed.  If  a  trap 
cannot  be  avoided,  a  drip  connected  with  the  return-main  is  to  be  installed. 
Radiators  on  first  story  are  to  be  connected  direct  to  steam-main.  Radiators 
for  the  second  and  third  floors  may  be  taken  off  the  same  riser.  The  main, 
after  serving  the  last  radiator,  is  to  drop  below  the  water-line  of  the  boiler, 
and  its  size  reduced,  and  it  is  to  run  back  to  the  boiler  as  a  wet-return-main. 
The  steam-main  at  the  end  of  the  run  is  to  be  24  in  or  more  above  the  water-line 
of  the  boiler.  The  boiler  is  to  be  installed  in  a  pit  if  necessary  to  accomplish 
this. 

Pipes  and  Fittings.  All  pipe  used  throughout  is  to  be  of  the  best  quality 
wrought-iron  or  steel  pipe  of  standard  weight  and  thickness,  with  the  ends 
reamed,  free  from  imperfections,  and  true  to  shape.  All  threads  are  to  be 
clean-cut,  straight  and  true.  All  fittings  are  to  be  of  the  best  heavy  gray  iron, 
with  taper-threads,  and  are  to  be  heavily  beaded.  No  inferior  pipe  or  fittings 
will  be  allowed. 

Supports.  AH  piping  is  to  be  supported  by  approved  expansion-hangers  or 
rollers,  not  to  exceed  10  ft  apart.  Neat  cast-iron  floor  and  ceiling-plates  are 
to  be  used  where  pipes  pass  through  floors,  ceilings  and  partitions. 

Radiators.  Direct  radiation  is  to  be  furnished  to  the  amount  enumerated  on 
the  drawings  of  the  ( . . .  name . . . )  rnake,  or  approved  equal. 

Radiator-Valves.  The  radiators  are  to  be  furnished  with  removable  disk- 
type  union  valves,  rough  nickel-plated,  and  are  to  have  hard-wood  hand-wheels. 

Air-Valves.  Radiators  throughout  the  entire  building  are  to  be  furnished 
with  ( .  . .  name . . . )  automatic  air- valves,  or  approved  equal. 

*  For  house-heating  plants  it  is  well  to  specify  also  "one  automatic  damper-regulator 
of  approved  pattern,  with  connection  for  operating  draft-door  and  cold-air  check." 


Specifications  for  Furnace- Work  1363 

Pipe-Covering.  All  pipes  in  the  cellar  above  the  floor  are  to  be  covered 
with  I -in  asbestos  (or  magnesia)  sectional  covering  with  canvas  cover  and 
secured  by  lacquered-brass  bands. 

Painting  and  Bronzing.  AH  radiators  and  exposed  pipes  in  rooms  or  halls 
are  to  be  neatly  painted  two  coats  of  best  radiator-enamel,  or  bronzed  in  desired 
colors. 

Finally.  When  completed,  the  apparatus  is  to  be  tested  to  lo-lb  steam- 
pressure  and  made  tight  at  that  pressure,  said  test  to  be  conducted  under  the 
supervision  of  the  architect.  Fuel  for  the  test  is  to  be  furnished  by  the  owner, 
and  when  accepted,  the  apparatus  is  to  be  turned  over  to  the  owner  in  com- 
plete working  order.  All  valves  and  stuffing-boxes  are  to  be  properly  packed 
and  the  plant  completed  in  all  its  parts,  it  being  understood  that  this  contractor ' 
is  to  furnish  all  miscellaneous  material,  tools,  labor,  etc.,  necessary  to  complete 
the  work  in  a  first-class  and  workmanlike  manner. 

Guarantee.  This  contractor  is  to  guarantee  that  when  the  apparatus  is 
completed  it  will  be  free  from  all  mechanical  defects  and,  if  he  is  to  furnish 
the  design  and  layout,  that  the  installation  shall  be  of  ample  capacity  to  heat 
all  rooms  where  radiation  is  placed  to  a  temperature  of  70°  F.  when  the  outside 
temperature  is  0°  Fo 


1364  Chimneys  Part  3 


CHIMNEYS* 

By 
L.  A.  HARDING 

FORMERLY    PROFESSOR    OF     MECHANICAL    ENGTNEERING,    PENNSYLVANIA    STATE 

COLLEGE 

Draft.  To  burn  a  fuel  at  a  given  rate  (pounds  per  square  foot  of  grate-surface 
per  hour)  requires  a  definite  weight  of  air  to  be  supplied  for  combustion.  The 
air  passes  under  the  grate  and  through  the  fuel-bed  and  meets  with  considerable 
resistance  in  its  flow,  not  only  through  the  fuel-bed,  but  through  or  around  the 
boiler-tubes  and  smoke-flue  or  breeching.  The  motive  force  causing  the  air-flow 
in  a  natural-draft  plant  is  suppHed  by  the  chimney.  The  difference  between 
the  atmospheric  pressure  and  the  pressure  existing  at  any  point  in  the  furnace 
or  in  the  flue  is  termed  the  draft  at  that  particular  point.  This  pressure  is 
ordinarily  measured  by  means  of  a  U  tube  filled  with  water,  the  draft  being 
recorded  in  inches  of  water,  and  is  the  difference  in  the  heights  of  the  water- 
columns  in  the  two  legs  of  the  U  tube. 

Height.  The  intensity  of  draft  that  a  chimney  is  capable  of  producing  at 
the  base  is  a  fimction  of  its  height,  the  temperature  of  the  flue-gases,  and  the 
temperature  of  the  outside  air,  which  is  generally  assumed  to  be  60°.  The  tem- 
perature of  the  flue-gas  is  ordinarily  assumed  to  be  550°.  The  intensity  of 
draft  produced,  per  foot  height,  measured  in  inches  of  water  is 

H  =  0.0071  L 

L  =  height  of  chimney  above  grate,  in  feet.  The  flue-gas  temperature  is  taken 
at  550°  and  the  outside  temperature  at  60°.  Ordinarily  0.8//  is  taken  as  rep- 
resenting the  available  draft,  in  order  to  allow  for  the  cooling  of  the  chimney- 
gases.  Then  o.&H  must  be  equal  to  or  greater  than  the  sum  of  the  expected 
draft-losses  as  given  in  the  following  paragraphs. 

Draft-Losses.  The  draft-losses  through  the  fuel-bed  depends  upon  the 
rate  of  combustion  required  and  the  kind  of  fuel.  This  loss  may  be  approxi- 
mated by  using  the  data  in  Table  I. 

The  loss  of  draft  between  the  grate  or  furnace  and  a  point  just  beyond  the 
damper-box  of  a  boiler  is  about  as  shown  in  Table  II  when  the  boilers  are  oper- 
ated at  normal  rating;  bituminous  coal  burned  at  the  rate  of  from  25  to  30 
lb  per  sq  ft  of  grate-surface  per  hour. 

The  loss  of  draft  through  the  boiler  will  depend  largely  upon  the  method  of 
baffling  employed,  and  increases  with  the  per-cent  rating  at  which  the  bpiler  is 
operated.  The  precipitating-figures  should  be  increased  by  approximately 
55%  when  the  boiler  is  operated  at  150%  of  its  rated  capacity,  and  by  75% 
when  it  is  run  at  200%  rating. 

Velocity  of  Gases  through  Flue  and  Chimney.  In  preliminary  estimates 
5  lb  coal  per  boiler  horse-power  developed,  and  24  lb  air  per  lb  of  coal  is  usually 

*  See,  also,  Chimneys  for  Heating  Boilers,  page  1281;  Flues  for  Kitchen  Ranges  an4 
F'replace§,  page  1282,  and  Selection  of  Chimney  Flues,  page  1282. 


Velocity  of  Gases  through  Flue  and  Chimney  1365 

Table  I.     Loss  of  Draft  between  Furnace  and  Ash-Pit  to  Burn  Coal 


Kind  of  coal 


111.,  Ind.,  Kan.,  bituminous.  .  . 
Ala.,  Ky.,  Pa.,  Tenn..  bituminous 
Md.,  Pa.,  Va.,  W.  Va.,  semibitu 

minous 

Anthracite  pea 

Anthracite  buckwheat  No.  i .  .  . 


Combustion-rate,  R,  in  pounds  of  dry  coal 
per  square  foot  of  grate  per  hour 


15         20         25         30         35         40         45 


Force  of  draft  in  inches  of  water 


14 

.20 

.26 

.33 

.40 

.48 

16 

.23 

.31 

.40 

.49 

.60 

18 

.26 

.35 

.45 

.57 

.71 

30 

.45 

.64 

.88 

1.23 

43 

.68 

1. 00 

I.  SO 

.57 
.72 


.87 


Table  II. 


Loss  of  Draft  between  Grate  •r  Furnace  and  a  Point  Just  beyond 
Damper-Box 


Horizontal  return  tubular 

Babcock  &  Wilcox 

Stirling 

Vertical  tubular 


.  25  to  .30  in  of  water 
.  20  to  .35  in  of  water 
.51  in  of  water 
.43  in  of  water 


assumed.  The  customary  allowable  velocities  of  gases  in  chimneys,  when 
the  design  is  based  on  1 20  lb  of  the  flue-gas  per  hour  per  rated  boiler  horse-power, 
varies  from  17  ft  per  sec  for  a  diameter  of  stack  equal  to  24  in,  to  31  ft  per  sec 
for  a  72-in  or  larger  diameter.  These  figures  correspond  to  a  weight  of  0.68 
and  1. 10  lb  per  sq  ft  of  area.  The  formula  that  is  supposed  to  give  the  most 
economical  diameter  for  an  unlined  steel  chimney  or  stack,  and  used  by  many 
engineers  in  this  country  isd  =  4 .68/(h.p.) ;  in  which  d  is  the  diameter  in  inches 
and  h.p.  is  the  rated  capacity  of  the  boilers  served. 

The  following  figures  are  frequently  used  by  engineers  for  approximating  the 
loss  of  draft  in  flues  or  breechings: 

(i)  Horizontal  flues,  square  or  rectangular,  from  0.13  to  0.15  in  of  water  per 
100  ft.  Increase  these  values  50%  for  brick-lined  flues.  Loss  of  draft  for  easy 
right-angle  bends,  0.05  in  of  water. 

(2)  When  economizers  are  to  be  installed  the  temperature  of  the  flue-gas  is 
reduced  to  from  250°  to  325°,  and  the  total  head,  //,  should  be  calculated  on  a 
basis  of  these  temperatures. 

(3)  The  loss  of  draft  through  the  economizers  should  not  be  figured  less 
than  0.3  in  of  water. 

(4)  The  turns  which  the  flue  makes  in  leaving  the  damper-box  of  the  boiler, 
where  it  enters  the  main  flue  and  at  the  stack,  should  be  considered  and  allowed 
for. 

(5)  It  is  customary  to  make  the  flue  or  breeching  approximately  from  10  to 
15%  greater  in  area  than  the  stack  to  which  it  connects.  The  cross-section  is  re- 
duced in  proportion  to  the  volume  of  gas  to  be  handled  as  the  flue  passes  the 
boilers  in  succession.     The  width  of  the  flue  or  breeching,  where  it  enters  the 


1366  Chimneys  t'art  3 

chimney,  should  never  exceed  one  third  the  outside  diameter  of  the  chimney  at 
its  base. 

Example.  The  method  of  procedure  in  determining  the  dimensions  of  a 
chimney  and  breeching  is  explained  in  the  following  example. 

Three  150-1  h.p.  return  tubular  boilers  with  a  total  of  i  500  sq  ft  of  heating-' 
surface  are  to  be  served.  The  total  area  of  the  grate-surface  is  90  sq  ft.  The 
measured  length  of  the  breeching  is  40  ft.  The  gas  makes  two  right-angle  turns, 
one  at  the  entrance  to  the  breeching,  and  one  on  entering  the  chimney.  The 
.  fuel  assumed  is  Pennsylvania  bituminous  coal.  If  5  lb  of  coal  per  boiler  horse- 
power per  hour  is  assumed  as  the  fuel-consUmption,  the  rate  of  combustion  is 
(3  X  150  X  5)/9o  =  25  lb  per  sq  ft  of  grate-surface  per  hour. 

The  weight  of  flue-gas  per  second  is 

(3  X  120  X  i5o)/(6o  X  60)  =  IS  lb 

Assuming  a  temperature  of  550°,  the  volume  of  the  flue-gas  per  second  is 
iS/0.0393  =  382  cu  ft.  Assuming  an  allowable  velocity  through  the  chimney- 
area  of  25  ft  per  sec,  the  required  area  is, 

382/25  =  15.3  sq  ft 

corresponding  to  S4-in  diam,  approximately  The  area  of  the  flue  is  to  be 
15%  greater,  or 

15.3  X  1.15  =  17-6  sqft 

at  the  last  boiler  next  to  the  chimney.     The  chimney  must  produce  sufficient  * 
draft  to  overcome  the  following  resistance.     The  loss  of  draft  through  fuel-btd 
based  on  a  rate  of  combustion  of  25  lb  per  sq  ft  per  hr  (Table  I)  is  0.31  in.     The 
loss  of  draft  through  return  tubular  boilers  (Table  II)  is  0.27  in.     The  loss  of 
draft  through  the  breeching  is 

0.15  X  40/100  =  0.06  in 

The  loss  of  draft  occasioned  by  two  turns  is 

2  X  0.05  =  0.10  in 
The  total  loss  is 

.    0.31  4-0.27  +0.06  +0.10  =  0.74  in 
Then 

//  =  0.74/0.8  =  0.92  in 

or  approximately  i  in. 

Substituting  this  value  of  //  in  the  equation 
//  =  0.007  iL 
the  height,  L,  of  the  stack  is 

1/.0071  =  140  ft 
-measured  above  the  grate. 

Kent's  Chimney-Formulas.  The  following  chimney-formulas  by  William 
Kent  are  largely  used  by  engineers  in  this  country:  The  formula  is  based  on 
the  assumption  that  the  friction-head  in  the  chimney  is  considered  equivalent 
to  a  diminution  of  the  area  by  an  amount  equal  to  a  lining  of  inert  gas,  2  in  in 
thickness.  ^ 


Size  of  Chimneys  for  Steam-Boilers 


1367 


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1368  Chimneys  Part  3 

If  A  =  the  actual  area  in  square  feet; 

E  =  the  effective  area  in  square  feet; 
D  =  the  diameter  in  feet; 
Then  E  =  A  -o.6oV^. 

The  draft-power  of  a  chimney  varies  directly  as  the  effective  area,  E,  and  as 
the  square  root  of  the  height,  L.  The  formula  for  the  horse-power  of  a  chimney 
will  take  the  form,  h.p.  =  CE^ L,  in  which  C  is  a  constant.  The  value  of  C 
as  obtained  by  Kent  from  an  examination  of  a  large  number  of  chimneys  is 
2,.:s:s  when  5  lb  of  coal  is  burned  per  boiler  horse-power  per  hour. 

The  formula  for  the  horse-power  rating  of  a  chimney  is,  therefore, 

h.p.  =  2>.2>2>^^1^  =  2>-2>Z  {A  -  o.WJWT 

or  

E  =  0.3  h.p./VL 

The  Babcock  &  Wilcox  Company  recommend  that  when  the  fuel  used  is  low- 
grade  bituminous  coal  of  the  Middle  or  Western  States,  the  sizes  given  in  Table 
III  be  increased  from  25  to  60%,  depending  upon  the  nature  of  the  coal  and  the 
capacity  desired.  If  the  gas  makes  more  than  two  turns  it  is  advisable  to  increase 
the  diameter  given  in  the  table  by  one  size.  The  height  must  be  increased  at 
least  30%  if  economizers  are  used.  Table  III  may  be  applied  to  heating-boilers, 
the  equivalent  rating  in  square  feet  of  direct  radiation  being  approximately  equal 
to  the  horse-power  rating  X  100. 

Chimneys  for  Tall  Office  and  Loft-Buildings.  The  chimney  or  stack  for  a 
tall  building  is  a  special  case  in  which  the  height  is  frequently  fixed  by  the  height 
of  the  structure  itself  or  the  height  of  the  adjoining  buildings.  In  this  case  a 
diameter  is  assumed  and  the  method  outlined  in  the  preceding  example  apphed. 

General  Formulas  for  the   Design  of  Brick   Chimneys.       See  Fig.  1. 

Let         P  =  horizontal  wind-pressure  in  pounds  per  square  foot,  ordinarily 
assumed  as  25  lb  per  sq  ft  for  round  chimneys 
:  any  section  distant  z  from  top  of  chimney 


(d  -f  dA 


■■  projected  area  above  xx 
■■  horizontal  wind-load  in  pounds 
Pz 


m 


y  =  distance  from  xx  to  center  of  gravity  of  portion  above  xx 
M  =  wind-moment  in  foot-poimds 


=  Pzy 


m 


Properties  of  Section 
di  =  outside  diameter 
di  =  inside  diameter 
c  =  di/2 

I  =  moment  of  inertia  of  section 
A  =  area  of  section  in  square  feet 
=  0.7854  {di^  -  d2^) 

—  =  section-modulus 


General  Formulas  for  the  Design  of  Brick  Chimneys       1369 

/      0.0982  {di^  -  ^2") 

c  di 

W  =  weight  of  chimney  above  xx,  in  tons 

Si  =  compressive  stress  at  edge  on  leeward  side  due  to  W,  in  tons  per 

square  foot 
52  =  compressive  stress  at  edge  on  leeward  side  due  to  M,  in  tons  per 

square  foot 


W  Mc 

W 

Windward  side,  Sw  =  ~  — 
A 

W 
Leeward  side,        5/  =~  + 
A 


Mc  ^       .     X 
— -  (tension) 


-— —  (compression) 


] 
] 


/ 

Sw  and  Si  should  not  exceed  tlie  following  values,  in  tons  per  square  foot,  for 
Radial  Brick  Chimneys: 

Maximum  tension  Maximum  compression 

Below  150  ft 2  to  2  H  200  ft  and  below 19 

From  150  to  200  ft. . .   i  to  i  J/2  Above  200  ft 21 

Above  200  ft o 

Foundations.     Calculate  wind-moment,  M\  for  chimney  above  groun*d-line. 


Ml  =  Phyi 


(--:-•) 


/  =  length  of  side  of  square  base  in  feet 
Ai  =  P  =  area  of  base  in  square  feet 

/       P 

—  =  —  =  section-modulus  of  base 
c       6 

Wi  =  combined  weight  of  chimney  and  foundation 

Example.  It  is  required  to  determine  the  maximum  compression,  in  tons  per 
sq  ft  at  the  base  of  the  column,  for  the  chimney  shown  in  Fig.  2,  and  also  the 
maximum  soil-pressure  in  tons  per  sq  ft.  The  assumed  wind-pressure  is  25  lb 
per  sq  ft.     (See  General  Formulas  for  the  Design  of  Brick  Chimneys,  and  Fig.  1.) 

The  area  of  section  at  base,  A   =  0.7854  (162  —  12.32)  =  80.9  sq  ft. 

The  section-modulus  at  base,  I/c  =  [0.0982 (16*  —  i2.30]/i6  =  257. 

The  total  weight  of  brick  column  (Table  Y)  isW  =  495  tons  (interp  olated). 

The  projected  area  of  column  is  H  X  (8.75  -f  16)   X  180  =  2  228  sqft. 

The  horizontal  wind-load,  i^  =  2  228  X  25  =  55  700  lb  =  27.8  tons. 

The  moment-arm  of  i^  is  y  =  1^  X  i8o[(2  X  8.75)  +  i6]/(8.75  +  16)  =  81  ft. 

The  wind-moment,  M  =  81  X  27.8  =  2  252  ft  tons. 

•S*!  =  495/80.9  =  6.2  tons  per  sq  ft. 

52  =  ±  2  252/257  =  8.7  tons  per  sq  ft. 

The  maximum  compression  on  the  leeward  side,  5i  -1-52  =6.2  -[-8.7  =  14.9 
tons  per  sq  ft.  The  maximum  tension  on  the  windward  side,  5i  —  52  =  —  2.2 
tons  per  sq  ft.     The  following  computations  are  for  a  square  base: 

Foundation.  The  length  of  base,  I  =25.5  ft,  Ai  =  /2  =  650  sq  ft,  I/c  = 
255^/6  =  814.  The  weight  of  foundation,  based  on  1.9  tons  per  cu  yd,  is  266 
tons.  The  weight  of  the  4,V^-in  lining  is  36  X  n  X  0.063  =  25  tons.  The  total 
weight  of  column,  lining  and  foundation,  is  Wi  =   495  -|-  25  -f-  266  =  786  tons. 

The  moment-arm  for  R  may  be  assumed  the  same  as  before,  or  81  ft. .  Then 
M  =  2  252  ft-tons.     The  section-modulus  of  the  base,  I/c  =  l^/&  =  814. 

Si  =  786/650  =1.2  tons  per  sq  ft.     52  =  2  252/814  =  2.8  tons  per  sq  ft, 

The  maximum  soil-pressure,' 5i  -j-  52  =  1.2  4-2.8  =4  tons  per  sq  ft. 


1370 


Chimneys 


Resultant  Soil-pressure  ia 
Tons  per  square  foot 


Si  =  — -  =  compression  per  sq  ft  due  to  Wi 

S2  =  —r-  =  compression  por  sq  ft  due  to  Mi 
Fig.  1.     Details  of  Construction  of  Tall  Bnck  Chimney 


General  Formulas  for  the  Design  of  Brick  Chimneys       1371 


^Cement  Cap,  1-3  mix. 


7M-?- 


11^^:^*- 


i3K-»"^*- 


16^H 


Is       18)<->>N: 


i  p  2034'-> 


5^   X  3  W.I.  Retaining- 
ring  set  ih  Cull  Bed 
of  Cement  Mortar 


yEAD  OF  CHIMNEY  (ENLARGED) 


Outsiilo  Filler-wall  to 

prot«'C't  Bti.iras  from 

Atmosphere 


l''Ri8e  to  Arch  for^T 
eaoli  2  ft.  of  Fiue-  U 
opening  Width 


Solid  Concrete 
1-3  mix. 


<.  4)^"  Lining 

"  Five  6  I  Beams 
over  Fluo-opening  * 
•with  Ji,"Bearipg-plat€ 


VERTICAL  SECTION  THROUGH 
FLUE-OPENING  (ENLARGED) 


,22K-^ 


Minimum  Air-space 

of  ii  between  Lining 

and  Main  Wall 


I  Beams  over  Flue- 
opening  sufficient 
to  carry  Weight 


Add  2"  to  thickness^ 
of  Pilaster  for  each 
Foot  of  Flue-opening 
Width,  starting  with  12^1       !*— ^'^^ 
Pilaster  to  3-ft.  Opening^ 

CROSS-SECTION  A'A  (ENLARGED) 

Fig.  2.     Details  of  Tall  Radial-brick  Chimney 


1372 


Chimneys 


Parts 


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Radial-Brick  Chimneys  1373 

Table  V.     Dead-Load  of  Radial-Brick  Chimneys  in  Tons  of  2  000  Pounds  * 


Inside  diameter  at  top, 

in  feet 

Height 
in  feet 

3 

4 

5 

6 

7 

8 

9 

10 

90 

90 

98 

no 

122 

100 

no 

120 

131 

143 

161 

180 

no 

138 

143 

155 

167 

188 

206 

120 

160 

170 

.185 

198 

218 

237 

130 

202 

218 

231 

252 

273 

29s 

318 

140 

237 

256 

270 

290 

310 

337 

357 

ISO 

277 

296 

311 

330 

353 

375 

400 

160 

317 

340 

357 

375 

402 

423 

447 

170 

362 

388 

410 

425 

454 

475 

Soo 

180 

480 

510 

537 

555 

190 

535 

570 

592 

617 

200 

600 

632.. 

657 

685 

210 

727 

760 

220 

804 

843 

*  These  values  are  interpolated  from  curves  by  the  M.  W.  Kellogg  Company,  and  are 
for  round  radial-brick  chimneys  exclusive  of  the  weight  of  the  foundation. 

Table  VI.     Width  of  Foundations  at  Base  for  Radial-Brick  Chimneys  * 


Height 
in  feet 


Inside  diameter  at  top,  in  feet 


90 
100 
no . 
120 
130 
140 
ISO 
160 
170 
t8o 
190 
200 
210 
220 
250 


ft    in 
n   6 

12  6 

13  6 

14  6 

15  6 


ft    Jn 


13  o 

14  3 

15  3 

16  6 

17  9 

19  o 

20  6 


ft    in 

13  9 

14  8 

15  6 

16  6 

17  8 

18  10 

20  o 

21  6 


ft    in 


ft    in 


16  o 

17  o 


ft    in 


ft    in 


19 


*  These  values  are  interpolated  from  curves  by  the  M.  W.  Kellogg  Company.  The 
maximum  unit  soil-pressure  at  the  outer  edge  of  the  foundation,  due  to  dead  and  wind- 
loads,  does  not  exceed  2  tons  per  square  foot. 

Reinforced-Concrete  Chimneys.  Area  of  Steel  Reinforcement  Re- 
quired. The  following  formulas  are  used  by  one  concern  in  the  design  of  rein- 
forced-concrete  chimneys: 

M  =  wind-moment  at  section  considered,  in  inch-pounds; 
W  =  weight  of  shell  above  section  considered,  in  pounds; 


1374 


Chimneys 


Parts 


D  =  outside  diameter  of  shell,  in  feet; 
d  =  inside  diameter  of  shell,  in  feet; 
R .  =  radius  of  steel  circle,  in  inches; 
r  =  radius  of  neutral  core  =  ]/iD[i  -}-  {d/DY]  feet; 
WR  =  moment  of  stabiUty  from  weight  of  shell,  in  inch-pounds; 

5  =  i6  ooo,  the  allowable  fiber-stress  in  the  steel  in  pounds  per  square  inch; 
A  =  total  cross-sectional  area  of  steel  rods  required  at  section  considered,  in 

square  inches; 
A  =  2{M  —  Wr)/SR  =  number  of  barsX  cross-sectional  area  of  one  bar. 
The  bars  used  are  ordinarily  ^l-in  square,  twisted  bars,  each  with  a  cross- 
Sectional  area  of  0.5625  sq  in.  The  thickness  of  the  shell,  if  made  without  a 
taper,  is  ordinarily  6  in,  and  if  constructed  with  a  taper  the  shell  is  made  5  in 
in  thickness  at  the  top  and  increased  H  in  in  thickness  for  each  5  ft  in  height. 
The  maximum  compression  due  to  the  wind-moment  and  dead  load  in  the 
concrete,  at  the  base,  is  ordinarily  hmited  to  350  lb  per  sq  in.  The  same  formulas 
apply  in  this  case  as  in  the  design  of  brick  chimneys  (Fig.  1). 

Example.  A  reinforced-concrete  chimney  has  the  following  dimensions: 
150  ft  high;  no  taper;  9  ft  inside  diameter;  thickness  of  shell  6  in;  outside 
diameter  10  ft;  weight  of  shell  335  250  lb.  It  is  required  to  determine  the  total 
cross-sectional  area  of  reinforcement. 

Af  =  25  X  10  X  150  X  150/2  =  2  812  500  ft-lb  =  7,2,  750000  in-lb; 

r  =  10/8  X  [i  +  (9/10)21  =  2.3  ft  =  27.6  in; 
R  =  58  in; 

^   =  2I33  750  000  -  (335  250  X  27.6)1/16  000  X  58)   =  53  sq  in; 
If  ^-in  square  bars  are  used,  it  requires  53/0.5625  =  94  bars. 


Table  VII.     Reinforced-Concrete  Chimneys. 

Dimensions.     (Fig.  3) 

Maxi- 

Width 

Height 

Inside 

Depth 

Height 

Height 

Ttoal 

mum 

of 

above 

diam- 

below 

double 

single 

height 

outside 

square 

grade 

eter 

grade 

shell 

shell 

A^B+C 

diam- 
eter 

founda- 
tion 

ft 

ft 

ft 

ft 

ft 

ft 

ft       in 

ft 

H 

C 

A 

B 

C 

D 

E 

F 

100 

4 

S 

33 

67 

105 

6       4 

12 

100 

5 

5 

33 

67 

105 

7        4 

12 

125 

5 

S 

42 

83 

130 

7        4 

15 

125 

6 

s 

42 

83 

130 

8       4 

16 

ISO 

6 

6 

48 

102 

156 

8       4 

18 

150 

7 

6 

48 

102 

IS6 

9       4 

18 

150 

8 

6 

48 

102 

156 

10       4 

i      19 

175 

8 

7 

57 

118 

182 

10       6 

22 

175 

9 

7 

57 

1x8 

182 

II        6 

22 

175 

10 

7 

57 

118 

182 

12        6 

23 

200 

10 

7 

66 

134 

207 

12        6 

25 

200 

II 

7 

66 

134 

207 

13       6 

25 

200 

12 

7 

66 

134 

207 

14       6 

26. 

225 

12 

8 

69 

IS6 

233 

14        8 

29 

225 

13 

8 

69 

156 

233 

IS        8 

29 

325 

14 

8 

69 

IS6 

233 

16        8 

30 

250 

14 

8 

81 

169 

258 

16       8 

32 

250 

IS 

8 

81 

169 

258 

17        8 

33 

250 

16 

8 

81 

169 

258 

18        8 

34 

Reinforced-Concrcte  Chimneys 


1375 


mm\ 

>A. 

BASE 


Fig.  3.     Details  of  Tall  Reinforced-concrete  Chimney 


The  Weber  Chimney  Company,  Chicago,  111.,  designed  and  constructed, 
among  other  tall  chimneys,  the  great  reinforced-concrete  chimney  at  Saganoseki, 
Japan,  for  the  Oriental  Compressol  Company,  for  the  copper  smelter.  It  was 
completed  in  January,  19 17,  and  ranks  with  the  highest  in  the  world,  being 
570  ft  above  the  foundations  and  261^  ft  in  internal  diameter  at  the  top. 


1376 


Chimneys 


Part  3 


Self-Sustaining  Steel  Chimneys*  are  largely  used,  especially  for  tall  chimneys 
of  iron-works  and  power-houses  from  150  to  300  ft  in  height. 

"The  advantages  claimed  are:  Greater  strength  and  safety;  smaller  space 
required;  smaller  cost  by  30  to  50%  as  compared  with  brick  chimneys;  avoid- 
ance of  infiltration  of  air  and  consequent  checking  of  the  draught,  common 
in  brick  chimneys.  They  are  usually  made  cylindrical  in  shape,  with  a  wide 
curved  flare  for  10  to  25  ft  at  the  bottom.  A  heavy  cast-iron  base-plate  is 
provided,  to  which  the  chimney  is  riveted,  and  the  plate  is  secured  to  a  massive 
foundation  by  holding-down  bolts.     No  guys  are  used.".t 

The  largest  self-sustaining  steel  chimney  in  the  world  (19 19)  is  that  built 
by  the  Chicago  Bridge  and  Iron  Works  at  the  plant  of  the  United  Verde  Copper 
Company,  Clarkdale,  Arizona.  It  is  30  ft  93/2  in  in  diameter  and  400  ft  in 
height.  The  thickness  of  plates  varies  from  %  in  at  the  top  to  Hie  in  for  the 
bell-shaped  portion  at  the  bottom.  The  weight  of  steel  is  800  cxx)  lb.  The 
stack  is  anchored  to  the  foundation  by  thirty-six  bolts,  each  4  in  in  diameter, 
upset,  and  spaced  equidistant  in  a  bolt-circle  of  25  ft  4H  in  radius. 


Table  VHI. 


Sizes  of  Foundations  for  Self-Sustaining  Steel  Chimneys,   Half- 
Lined  t 


Diameter,  clear,  in  feet.  .  . 

3 

4 

S 

6 

7 

9 

II 

Height 

ft     in 

ft     in 

ft     in 

ft     in 

ft     in 

ft     in 

ft     in 

100 
IS   9 
6  6 

100 
IS   3 

7 
125 
17   6 
7   6 

150 

20  4 
9 
200 

23   8 

10 

ISO 
21     10 

8 

200 

25  0 

10 

150 

22   7 
9 
250 

29  8 

12 

175 
25   9 
10 

27s 
33   6 
12 

225 

29   II 

13 
300 

36  0 

14 

Least  diam.  of  foundation 
Least  depth  of  foundation 
Height 

Least  diam.  of  foundation 
Least  depth  of  foundation 

The  governing  feature  in  the  design  of  a  self-sustaining  steel  chimney  or 
STACK  is  the  force  of  the  wind.  The  cylinder  above  any  horizontal  plane  section 
may  be  assumed  to  act  as  a  cantilever  beam  in  which  the  bending  moment,  in 
foot-pounds,  is 

M  =HD  XP  Xy2H  =  ViHWP 

in  which  H  is  the  height  in  feet  above  the  section  considered,  D  the  diameter  in 
feet  and  P  the  assumed  pressure  of  the  wind  in  pounds  per  square  foot  on  a  ver- 
tical cross-section.  The  fiber-stress  S,  in  pounds  per  square  inch,  according  to 
the  formula  for  flexure,  is  5  =  Mc/I.  For  hollow  cyHnders  of  large  diameter 
and  small  thickness,  the  moment  of  inertia  I  =  irR'^t,  in  which  R  =  mean 
radius  in  feet  (equivalent  to  c  in  the  flexure  formula)  and  /  =  thickness  of  shell 
in  inches.     Hence 

S  =  MR/httRH  =  o.ioUI/DH,    and  /  =  o.io6M/SD'^. 
The  stress  S  is  tensile  on  the  windward  side  and  compressive  on  the  leeward  side. 


*  Compiled  from  data  furnished  by  Robins  Fleming, 
t  Mechanical  Engineers'  Pocket  Book.     Kent. 

X  These  dimensions  were  taken  from  a  pamphlet  published  by  the  Philadelphia  Engineer- 
IDK  Works. 


Radial  Brick  Chimney  1377 

There  is  also  a  small  compressive  stress  due  to  the  weight  of  the  stack.  The 
value  of  P  may  be  taken  at  25  lb  per  sq  ft  and  of  5  at  16  000  lb  per  sq  in,  as  given 
in  the  Specifications  for  the  Structural  Steel  Work  for  Buildings,  Chapter  XXX. 
As  stacks  are  built  for  durability  as  well  as  strength  it  is  often  advisable  to 
increase  the  theoretical  thickness  of  the  shell.  No  plate  should  be  used  with  a 
thickness  less  than  ]i  in.  It  is  important  that  the  stack  be  securely  anchored 
to  the  foundation.  Many  methods  have  been  proposed  for  determining  stresses 
in  anchor-bolts.  As  the  problem  depends  for  its  solution  on  the  physical  con- 
ditions of  stack,  base  and  bolts,  no  exact  analysis  is  possible.  (See  editorial  dis- 
cussion after  article,  Anchor-Bolt  Tension,  in  Engineering  News,  April  30,  19 14.) 
The  most  severe  assumption  is  that  the  bolts  are  screwed  up  with  a  high  initial 
tension.  The  anchor-bolt  ring  can  then  be  considered  in  the  same  way  as  a  ring 
of  the  cylinder.  The  maximum  stress  at  any  point  of  the  bolt-circle  is  devel- 
oped when  the  wind  is  blowing  parallel  to  the  radius  through  that  point.  The 
stress  for  each  circumferential  inch  is  0.106M / {iRi)'^,  2R1  being  the  diameter 
of  the  bolt-circle.  Let  b  be  the  circumferential  distance  in  inches  between 
adjacent  anchor-bolts,  N  the  number  of  bolts  equidistant  on  the  bolt-circle  and 
W  the  weight  of  the  stack.  For  the  anchor-bolt  on  the  windward  side  there  is  a 
tensile  stress,  Sw,  due  to  the  wind, 

Sw    =0.I06Wf/(2i?l)2] 

Since  b  =  (2R1  X  12  X  7r)/iV 

Sw  =  2M/R1N 

Deducting  the  weight  of  the  portion  of  the  stack  between  adjacent  bolts,  the 
maximum  tensile  stress  in  any  anchor-bolt  may  be  expressed  by  the  equation 

Sw  =  {2M/RyN)  -W/N 

Radial-Brick  Chimneys.  These  chimneys  are  built  with  special  blocks 
formed  to  suit  the  circular  and  radial  lines  of  each  section  of  the  chimney  so 
that  the  finished  brickwork  has  joints  of  an  even  thickness  throughout  and  a 
perfectly  smooth  surface.  The  blocks  being  much  larger  than  common  bricks, 
there  are  only  from  one  third  to  one  half  as  many  joints.  Radial-brick  chim- 
neys are  always  circular  in  plan  above  the  base.  The  best  form  of  base  is  octag- 
onal in  cross-section  so  as  to  permit  the  breeching  to  enter  the  chimney  at  a 
flat  surface  and  at  the  same  time  comply  best  with  the  rules  of  stability. 
Except  for  chemical-works,  refineries,  furnaces,  etc.,  radial-brick  chimneys  are 
built  with  a  single  shell,  a  lining  only  being  provided  in  the  immediate  vicinity 
of  the  flue-entrance.  All  radial  bricks  are  perforated  vertically  and  this  insures 
thorough  burning  and  allows  the  mortar  to  enter  the  perforations,  thus  forming 
a  vertical  anchorage. 

Radial  blocks  for  chimney-construction  have  been  used  extensively  in 
England,  Germany,  France  and  Russia  since  1870.  They  were  not  introduced 
into  this  country,  however,  until  1898.  About  forty-five  years  ago  (1869  or 
1870)  Alphons  Custodis,  of  Diisseldorf,  Germany,  originated  a  method  of  building 
tall  chimneys  of  perforated  radial  blocks,  made  from  selected  clays  and  burned 
at  a  very  high  temperature,  and  in  1898  an  American  company  *  was  formed 
for  the  purpose  of  erecting  chimneys  by  this  method  of  construction.     Since 

*  Alnhons  Custodis  Chimnev  Construction  Comnanv.  New  York  Citv. 


1378  Chimneys  Part  3 

that  time  the  company  through  various  agencies  has  built  more  than  six 
thousand  chimneys  in  all  parts  of  the  world.  The  tallest  chimney  in  the 
world  (1919),  585  feet  high  and  60  ft  in  internal  diameter  at  the  top,  was 
built  by  this  company  in  19 18  for  the  Anaconda  Copper  Company,  at  Ana- 
conda, Mont. 

Mr.  H.  R.  Heinicke,*  of  Chemnitz,  Germany,  builder  of  the  460-ft  stack  at 
Halsbriicke,  Germany,  has  employed  radial  bricks  made  especially  for  each 
chimney.  This  firm  through  long  and  costly  research  has  done  much  to  make 
chimney-building  a  science.  The  chimney  at  Halsbriicke  is  a  very  remarkable 
one  on  account  of  its  proportions.  In  a  height  of  460  ft,  the  diameter  at  the 
top  is  only  8  ft,  whereas  the  585-ft  stack  at  Anaconda,  Mont.,  has  a  diameter 
of  60  ft  at  the  top. 

The  Heine  Chimney  Company  f  has  erected  many  important  high  chimneys. 
The  essential  difference  in  the  methods  of  construction  used  by  this  company 
from  those  of  the  other  chimney-constructors  is  that  the  Heine  Chimney  Com- 
pany uses  perforated,  interlocking,  radial  bricks.  It  is  claimed  that  this 
interlocking-fcature  has  an  advantage  over  the  straight-sided  bricks  in  acting 
as  a  preventive  of  deep  weathering  of  the  joints  and  of  air-leaks.  In  addition 
to  this  it  is  claimed  that  the  circumferential  strength  of  the  walls  when  built 
of  this  type  of  brick  is  considerably  greater  than  when  built  with  plain-sided 
or  corrugated  bricks.  The  perforations  in  these  bricks  arc  fewer  but  larger  than 
those  of  some  of  the  other  constructors.  The  brickwork  is  laid  on  full-mortar 
beds  with  shoved  joints.  These  large  perforations  allow  the  mortar  to  rise 
in  them,  thus  forming  pins  which  give  the  walls  great  strength  and  enable  them 
to  withstand  the  stresses  due  to  expansion  caused  by  the  high  temperature  of 
the  flue-gases.  In  walls  more  than  one  brick  thick,  the  bricks  are  laid  up  in 
English  bond,  that  is,  with  alternate  header  and  stretcher-courses.  This  com- 
pany advocates  this  method  of  construction  even  in  chimneys  built  with  the 
ordinary  straight-sided  common  building-bricks.  Among  the  many  important 
chimneys  constructed  by  the  Heine  Chimney  Company  is  the  one  erected 
at  the  St.  Joseph  Lead  Company's  plant,  at  Herculaneum,  Mo.  The  height 
of  this  chimney  is  350  ft  and  the  inside  diameter  at  the  top  20  ft.  (Seepage 
1706.) 

The  W.  M.  Kellogg  Company  J  has  designed  and  built  many  radial-brick 
chimneys  for  power-plants,  chemical-works  and  other  purposes.  Several  of  the 
iniportant  chimneys  put  up  by  them  are  mentioned  in  the  hst  of  tall  chimneys 
(page  1379).  Some  of  the  details  of  construction  differ  from  those  of  the  other 
companies  mentioned.  One  of  the  points  of  difference  is  the  detail  relating  to 
the  corrugations  on  their  bricks.  These  corrugations  are  3i  in  wide  and  }4  in 
deep  and  are  placed  along  the  vertical  sides  of  the  bricks  as  they  lie  in  the  wall. 
The  adhesion  between  the  bricks  and  mortar  is  increased  by  this  increased  area, 
It  is  claimed  that  tests  made  show  that  this  is  the  case.  On  account  of  these 
corrugations  it  is  not  considered  necessary  to  embed  any  ironwork  in  these 
chimneys  to  prevent  the  development  of  cracks  due  to  heat-expansion.  Iron- 
work has  sometimes  been  inserted  when  plain-sided  bricks  have  been  used.  It 
is  claimed  that  this  design  is  somewhat  heavier  than  that  employed  by  some 
other  constructors,  this  company  holding  that  it  is  not  safe  to  figure  on  wind- 
pressure  of  less  than  25  lb  per  sq  ft  of  projected  area.  Among  the  many 
tall    chimneys   erected   by   this   company  may  be   mentioned   especiall}'   the 

*  H.  R.  Heinicke,  Incorporated,  New  York  City, 
t  The  Heine  Chimney  Company,  Chicago,  111. 


Partial  List  of  Tall  Chimneys  1379 

chimney  at  Douglas,  Ariz.,  erected  for  the  Copper  Queea  Consolidated  Mining 
Company, 

There  are  other  reliable  companies  which  design  anfl  construct  tall  chimneys. 
Those  mentioned  here  were  the  pioneers  in  this  work. 

Partial  List  of  Tall  Chimneys   Over  300  Feet  in  Height 

It  is  to  be  noted  that  this  list  is  constantly  added  to  from  year  to  year. ' 

Diam. 
Height,    inside 
ft         at  top, 
ft 

*Anaconda,  Mont.,  Anaconda  Copper  Co.  (19 18) 585        60 

*Tacoma,  Wash.,  American  Smelting  &  Refining  Co.  (1917)  . .  .  573         25 

t  Saganoseki,  Japan,  Oriental  Compressol  Co.  (1917) 570        263^ 

*Great    Falls,  Mont.,  Boston  &  Montana  Consolidated  Copper 

and  Silver  Mining  Co.  (1907) 506         50 

X  Freiberg,  Saxony,  Germany,  Halsbriicke  Foundry 460  8 

Glasgow,  Port  Dundas,  Scotland,  F.  Townsend 454 

Glasgow,  St.  Rollox,  Scotland,  Tenant  &  Co 436  3^ 

*Jerome,  Ariz.,  United  Verde  Extension  Mining  Co.  (191 8) 425         30 

Creusot,  France,  Messrs.  Musprath  Chemical  Works 406 

§Clarkdale,  Ariz.,  United  Verde  Copper  Co 400         ^0% 

*E1  Paso,  Tex.,  Consolidated  Kansas  City  Smelting  &  Refining 

Co.  (1916) 400        30 

*Hayden,  Ariz.,  American  Smelting  &  Refining  Co.  (191 1) 400         25 

*East  Helena,  Mont.,  American  Smelting  &  Refining  Co.  (1917).  400         16 

Hahfax,  Dean  Clough  Mill,  Scotland,  Messrs.  Crossley's 381 

*Easton,  Pa.,  C.  K.  Williams  &  Co.  (191 1) 375  7 

Lancashire,  Bolton,  England,  DolDson  &  Barlow 367 

♦Rochester,  N.  Y.,  Eastman  Kodak  Co.  (two)  (1906,  191 1) 366,  9  and  13 

♦Constable  Ilook,  N.  J.,  Orford  Copper  Co.  (two)  (1900,  1910). .  365         10 

♦Garfield,  Utah,  Garfield  Smelting  Co.  (1913) 350         22 

iJHerculaneum,  Mo.,  St.  Joseph,  Lead  Co 350         20 

Boston,  Mass.,  Fall  River  Iron  Co 350         n 

*Newark,  N.  J.,  Heller  Merz  Co  (1904) 350  8 

East  Newark,  N.  J.,  Clark  Thread  Co 335 

Barmen,  Prussia,  Germany,  Wessenfield  &  Co 331 

Edinburgh,  Scotland,  Gas-Works 329 

JCopper  Hill,  Tenn.,  Tennessee  Copper  Co 325         20 

JIndianapohs,  Ind.,  Indianapolis  Traction  Co 320         13 

Huddersfield,  England,  Brook  &  Son,  Fire-clay  Works 315 

Smethwick,  England,  Adams  Soap- Works 312 

♦Providence,  R.  I.,  Rhode  Island  Suburban  Railway  Co 308         16 

♦New  York  City,  N.  Y.,  New  York  Steam  Co.  (1904) 308         15 

Carhsle,  England,  P.  Dickon  &  Son 300 

Bradford,  England,  Mitchell  Brothers 300 

*  Constructed  by  the  Alphons  Custodis  Chimney  Construction  Company,  New  York 
City. 

t  Reinforced  concrete,  The  Weber  Chimney  Company,  Chicago,  111. 

i  Constructed  by  H.  R.  Heinicke,  Incorporated,  New  York  City. 

§  Self-sustaining  steel  chimney,  the  largest  (of  this  type)  in  the  world  (1919). 

II  Constructed  by  The  Heine  Chimney  Company,  Chicago,  111. 


1380  Chimneys  Part  3 

Partial  List  of  Tall  Chimneys  over  300  Feet  in  Height  (Continued) 

Diam. 
Height     inside 
ft  at  top    ■ 

ft 

♦Garfield,  Utah,  American  Smelting  and  Refining  Co.  (1905) 300  30 

*Hayden,  Ariz.,  American  Smelting  and  Refining  Co 300  25 

t  Douglas,  Ariz.  Copper  Queen  Consolidated  Mining  Co 300  22 

ITacoma,  Wash.,  Tacoma  Smelting  Co 300  18 

§McGill,  Nev.,  Steptoe  Valley  Traction  Co 300  15 

♦Brooklyn,  N.  Y.,  Nichols  Chemical  Co.  (1905) 300  12 

*Claymont,  Del.,  General  Chemical  Co.  (1912) 300  8 

*  Constructed  by  the  Alphons  Custodis  Chimney  Construction  Company,  New  York 
City. 

t  Constructed  by  The  M.  W.  Kellogg,  Company,  New  York  City. 
X  Reinforced  concrete,  The  Weber  Chimney  Company,  Chicago,  III. 
§  Constructed  by  H.  R.  Heinicke,  Incorporated,  New  York  City. 


Hydraulics 


1381 


HYDRAULICS,  PLUMBING  AND  DRAINAGE,  ILLUMI- 
NATING-GAS AND   GAS-PIPING 

By 
J.  J.  COSGROVE 

CONSULTING    SANITARY    ENGINEER 

(i)    HYDRAULICS 

Water  is  practically  an  incompressible  liquid,  weighing,  at  the  average  temper- 
ature of  62°  F.,  62.355  lb  to  the  cu  ft  and  8.335  lb  to  the  gallon.  These  figures 
change  slightly  with  changes  in  temperature  and  atmospheric  pressure,  and  a 
sUght  variation  for  the  same  temperature  will  be  found  in  different  works. 

Pressure  of  Water.  The  pressure  of  still  water  in  pounds  per  square  inch 
against  the  sides  of  any  pipe  or  vessel  of  any  shape  whatever  is  due  alone  to  the 
HEAD,  or  height  of  the  surface  of  the  water  above  the  point  considered  pressed 
upon,  and  is  equal  to  0.433  lb  per  sq  in  for  every  foot  of  head  at  62°  F.  The 
fluid-pressure  per  square  inch  is  equal  in  all  directions.  To  find  the  total  pres- 
sure of  quiet  water  against  and  perpendicular  to  any  surface,  whether  vertical, 
horizontal,  or  inclined  at  any  angle,  whether  it  be  flat  or  curved,  multiply 
together  the  area  in  square  feet  of  the  surface  pressed,  the  vertical  depth  of  its 
center  of  gravity  below  the  surface  of  the  water,  and  the  constant  62.4.  The 
product  will  be  the  required  pressure  in  pounds.  This  may  be  expressed  by 
formula  as  follows: 

P  =  62.4.AD 
in  which 

P  =  the  pressure  in  pounds  of  quiescent  water  on  the  surface  considered; 

A  =  the  area  pressed  upon  in  square  feet;  and 

D  =  the  vertical  depth  in  feet  of  center  of  gravity  of  surface  considered. 


Table  A.     Pressure  in  Pounds  per  Square  Inch  for  Different  Heads  of 
Water  in  Feet 


Head, 
ft 

0 

I 

2 

3 

4 

S 

6 

7 

8 

9 

0 

0.433 

0.866 

1.299 

1.732 

2.165 

2.598 

3.031 

3.464 

3.897 

10 

4  330 

4.763 

5.196 

5.629 

6.062 

6.495 

6.928 

7.361 

7.794 

8.227 

20 

8.660 

9.093 

9.526 

9.959 

10.392 

10.825 

11.258 

II. 691 

12.124 

12.557 

30 

12.990 

13.423 

13.856 

14.289 

14.722 

15.155 

15.58S 

16.021 

16.454 

16.887 

40 

17.320 

17.753 

18.186 

18.619 

19.052 

19.485 

19.918 

20.351 

20.784 

21.217 

50 

21.650 

22.083 

22.516 

22.949 

23.382 

23.815 

24.248 

24.681 

25.114 

25.547 

60 

25.980 

26.413 

26.846 

27.279 

27.712 

28.145 

28.578 

29.011 

29.444 

29.877 

70 

30.310 

30.743 

31.176 

31.609 

32.042 

32.475 

32.908 

33.341 

33.774 

34.207 

80 

34.640 

35.073 

35.506 

35-939 

36.372 

36.805 

37.238 

37.671 

38.104 

38.537 

90 

38.970 

39.403 

39.836 

40.269 

40.702 

41 . 135 

41.568 

42.001 

42.436 

42.867 

The  pressure  for  greater  heads  can  be  readily  found  by  multiplication  or  addi- 
tion; thus,  the  pressure  for  a  head  of  1 10  ft  is  ten  times  that  for- 11  ft.  The  presc» 
sure  for  118  ft  is  equal  to  the  pressure  for  no  ft  plus  that  for  8  ft. 


1382      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 

Flow  of  Water  in  Pipes.  Owing  to  the-  many  practical  and  variable  con- 
ditions which  affect  the  flow  of  water  in  pipes,  such  as  the  smoothness  of  the 
pipe,  number  and  character  of  the  joints,  bends  and  valves  in  the  pipe,  to  say 
nothing  of  the  size  and  length  of  the  pipe,  all  formulas  for  the  velocity  and 
discharge  of  water  in  and  through  pipes  can  only  be  considered  as  approximate. 
The  following  formulas  and  data  are  taken  largely  from  the  National  Tube 
Company's  Book  of  Standards,  1902  edition.  They  agree  fairly  well  with 
similar  tables  by  Kent  and  Trautwine,  both  of  whom  devote  much  space  to  this 
subject.  The  quantity  of  water  pmssing  through  a  given  pipe  is  governed  by 
the  sectional  area  of  the  pipe  or  outlet  and  the  mean  velocity.  The  velocity 
depends  primarily  upon  the  pressure  or  head,  and  is  greatly  affected  by 
FRICTION,  which  again  varies  with  the  smoothness  of  the  bore,  the  diameter 
and  length  of  the  pipe,  and  whatever  obstructions  there  may  be  in  the  pipe. 
The  head  is  the  vertical  distance  from  the  surface  of  the  water  in  the  reservoir 
to  the  center  of  gravity  of  the  lower  end  of  the  pipe  when  the  discharge  is  into 
the  air,  or  to  the  level  surface  of  the  lower  reservoir  when  the  discharge  is  under 
water.  When  the  pressure  is  produced  by  mechanical  means,  the  head  of  water 
in  feet  may  be  readily  determined  by  the  following  table: 


Table  B.* 


For  Converting  Pressure  in  Pounds  per  Square  Inch  into  Head  of 
Water  in  Feet 


Pres- 
sure 

0 

I 

2 

3 

4 

5 

6 

7 

8 
18.476 

9 

0 



2.309 

4.619 

6.928 

9-238 

11.547 

13.857 

16.166 

20.785 

10 

23.0947 

25.404 

27.714 

30.023 

32.. 333 

34.642 

36  952 

39.261 

41.570 

43.880 

20 

46.1894 

48.499 

50.808 

53.118 

55.427 

57. 737 

60.046 

62.356 

64.665 

66.975 

30 

69.2841 

71.594 

73.903 

76.213 

78.522 

80.831 

83.141 

85.450 

87.760 

90.069 

40 

92.3788 

94.688 

96.998 

99.307 

101.62 

103.93 

106 . 24 

108.55 

110.85 

113  16 

50 

115.4735 

117.78 

120.09 

122.40 

124.71 

126.02 

129.33 

131.64 

133.95 

136.26 

60 

138.5682 

140.88 

143.19 

145.50 

147.81 

150.12 

152.42 

154.73 

157.04 

159  35 

70 

161.6629 

163.97 

166.28 

168.59 

170.90 

173.21 

175.52 

177.83 

180.14 

182.45 

80 

184.7576 

187.07 

189.38 

191.69 

194.00 

196.. 31 

198.61 

200.92 

203.23 

205.54 

90 

207.8523 

210.16 

212.47 

214.78 

217.09 

219.40 

221.71 

224 . 02 

226.33 

228.64 

*  Tables  A  and  B  are  exact  for  water  at  62°  F.  ^nd  for  atmospheric  pressure  at  14.7 
lb  per  sq  in. 


To  find  the  velocity  of  water  discharged  from  a  pipe-line  longer  than 
four  times  its  diameter,  knowing  the  head,  length  and  inside  diameter,  use  the 
following  formula: 


J     hd 

V  z  -I-  54  £ 


in  which 

V  =  approximate  mean  velocity  in  feet  per  second; 

m  =  coefficient  from  the  table  below; 

d  =  diameter  of  pipe  in  feet; 

h  =  total  head  in  feet; 

L  =  total  length  of  hne  in  feet. 

The  following  coefficients  are  averages  deduced  from  a  large  number  of  experi- 
ments. In  most-cases  of  pipes  carefully  laid  and  in  fair  condition,  tbey  should 
give  results  varying  not  more  than  from  5  to  xo%, 


Hydraulics 
Values  of  Coefficient  m 


1383 


Diameter  of  pipe  in  feet 

J   hd 

▼  L  +  54  ^/ 

0.05 

O.IO 

0.50 

I 

1.5 

2 

3 

4 

m 

m 

m 

m 

m 

m 

m 

m 

0.005 

29 

31 

33 

35 

37 

40 

44 

47 

O.OI 

34 

35 

37 

39 

42 

45 

49 

S3 

0.02 

39 

40 

42 

45 

49 

52 

56 

59 

0.03 

41 

43 

47 

50 

54 

57 

60 

63 

0.05 

44 

47 

52 

54 

56 

60 

64 

67 

O.IO 

47 

50 

54 

56 

58 

62 

66 

70 

0.20 

48 

51 

55 

58 

60 

64 

67 

70 

Example.     Given  the  head,  h=  50  ft;    the  length,  L=  s  280  ft  and  the  diam- 
eter, d=  2  it;   to  find  the  velocity  and  quantity  of  discharge. 
Substituting  these  values  in  the  foregoing  formula,  we  get 


A/dxh     _  4  /     2  X  50       _  4  /  100   _ 

V  LTs4~d  ~  V  5280+108  "  V  ^388  ~  °"'^ 


In  column  headed 


find  O.IO,  which  is  the  value  nearest  to  0.136, 

and  look  along  this  line  until  column  headed  2  is  reached;   then  read  62  as 
the  value  of  coefficient  m. 

Then  z)  =  62  x  0.136  =  8.432  ft  per  sec,  the  velocity  required. 

To  find  the  discharge  in  cubic  feet  per  second,  multiply  this  velocity  by 
area  of  cross-section  of  pipe  in  square  feet. 

Thus,  3.1416  X  (i)^  X  8.432  =-  26.49  cu  ft  per  sec. 

Since  there  are  7.48  gal  in  a  cubic  foot,  the  discharge  in  gallons  per  second  == 
26.49  X  748=  198.2. 

The  above  formula  is  only  an  approximation,  since  the  flow  is  modified  by 
bends,  joints,  incrustations,  etc. 

To  find  the  head  in  feet  necessary  to  give  a  stated  discharge  in  cubic  feet, 
use  the  formula 

0.000704  Q2  (L  -^  54  d) 


h- 


d^ 


in  which 

h  =  total  head  in  feet; 

L  =  total  length  of  line  in  feet; 

d  =  diameter  of  pipe  in  feet; 

Q  =  quantity  of  water  in  cu  ft  per  second. 

Example.  Given  the  diameter  of  pipe,  d=  0.5  ft;  the  length  of  pipe,  L  =» 
20  ft;  and  the  quantity  of  water  to  be  discharged,  q=  3.07  cu  ft  per  sec;  to 
find  the  necessary  head. 

Substituting  these  values  in  the  above  formula,  we  get 
0.000704  X  9.4  X  (20+ 27) 


(0.5)^ 
0.000704  X  9.4  X  47 

0.03125 


=  9-95  ft,  the  required  head. 


1384     Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 

The  following  fonnula  is  simpler  and  can  be  used  when  54  d  in  relation  to 
L  is  so  small  as  to  be  negligible: 

0.000704  Q^x  L 

* d^ — 

If  the  pipe  instead  of  being  straight  has  easy  curves  (say  with  radius  not  less 
than  five  diameters  of  the  pipe)  either  horizontal  or  vertical,  the  discharge  will 
not  be  materially  diminished  so  long  as  the  total  heads  and  total  actual  lengths 
of  pipe  remain  the  same,  but  it  is  advisable  to  make  the  radius  as  much  more 
than  five  diameters  as  can  conveniently  be  done. 

To  find  the  diameter  of  a  pipe  of  given  length  to  deliver  a  given  quantity  of 
water  under  a  given  head  use  the  following, 


d  =  0.234 


'  fQ^L 


in  which 


d  =  diameter  of  pipe  in  feet; 

Q  =  cubic  feet  per  second  delivered; 

L  =  length  of  line  in  feet; 

h  =  head  in  feet. 

Example.  Given  the  head,  h=  700  ft;  the  length  of  pipe,  L=  3000  ft; 
the  quantity  to  be  delivered,  Q  =  4  cu  ft  per  sec;  required  the  diameter  of  pipe 
necessary. 

Substituting  these  values  in  the  foregoing  formula,  we  get  : 


\A 


6  X  3  000  5 /— — 

=  0.234  V  68.57  =  0.545  ft  =  6.54  m 

700 


To  find  the  diameter  of  pipe  required  to  deliver  a  given  quantity  of  water 
with  a  given  head. 

Rule,  (i)  Reduce  the  head  to  feet  per  100  ft;  (2)  from  Table  C,  page  1385, 
find  the  discharge  for  the  head  thus  obtained  through  a  pipe  i  ft  in  diameter; 
(3)  divide  the  required  discharge  by  that  obtained  from  Table  C;  look  for  the 
quotient  in  the  column  of  Table  D,  page  1386,  headed  Ratio  of  Discharge,  etc., 
and  opposite  it,  in  the  adjoining  columns  of  the  table,  will  be  found  the  re- 
quired diameter. 

Note.  The  use  of  Tables  C  and  D  gives  results  sufficiently  correct  for  pipes 
less  than  700  diameters  in  length. 

Example.  If  the  head  of  water  from  a  reservoir  to  the  point  of  delivery  is  20 
ft  in  a  distance  of  i  860  ft,  what  is  the  diameter  of  a  pipe  required  to  deliver  6 
cu  ft  of  water  per  second? 

20  ft  head  in  i  860  ft  =  20/18.60  ft  in  100  ft,  or  1.075  ft  in  100 
From  Table  C  we  find  that  the  discharge  per  second  with  a  head  of  1.136  is 
3.989  cu  ft;  for  a  head  of  1.075  it  would  be  about  3.8  cu  ft.  Dividing  the  re- 
quired discharge  6,  by  3.8  cu  ft  per  sec,  we  have  1.58.  From  Table  D  the 
diameter  of  pipe  having  a  ratio  of  discharge  equal  to  1.58  is  found  to  be  about 
14H  in;  therefore  we  must  use  a  15-in  pipe  to  obtain  the  required  discharge.  If 
the  required  discharge  is  in  gallons,  divide  by  7.5  to  reduce  to  cubic  feet.  If  in 
cubic  feet  per  minute,  divide  by  60  to  reduce  to  feet  per  second, 


Hydraulics 


1385 


Table  C.    Velocities  and  Discharges  Through  a  Straight,  Smooth  Pipe  One 
Foot  in  Diameter  and  One  Mile,  or  s  280  Diameters,  in  Length 


Head  in  feet 
per  100  ft 

Head  in  feet 
per  mile 

Velocity  in 
feet  per  sec 

Discharge  in 

cubic  feet 

per  sec 

Discharge  in 
cubic  feet 
per  24  hours 

0.0568 

3 

1. 13 

0.8914 

76982 

O.Q758 

4 

1.31 

1.028 

88  862 

0.0947 

5 

I  47 

1. 150 

99403 

0.1136 

6 

1. 61 

1.264 

109209 

0.1325 

7 

1.74 

1.366 

118  022 

0.1514 

8 

1.86 

1-455 

125  740 

0.1703 

9 

1.96 

1-539 

132  969 

0. 1894 

10 

2.08 

1-633 

141  145 

0.2273 

12 

2.27 

1.782 

153  964 

0.2652 

14 

2.45 

1.924 

166  233 

0.3030 

16 

2.62 

2.057 

177  724 

0.3409 

18 

2.78 

2.183 

188  611 

0.3788 

20 

.  2.93 

2.301 

198806 

0.4735 

25 

3.28 

2.572 

222  156 

0.5682 

30 

3  59 

2.819 

243  604 

0.6629 

35 

3.88 

3.047 

263260 

0.7576 

40 

415 

3.267 

282  288 

0.8523 

45 

4.40 

3  451 

298  209 

0.9470 

50 

4.64 

3.638 

314  352 

1. 136 

60 

5. 08 

3-989 

344  649 

1.326 

70 

5.49 

4  311 

372  470 

1. 515 

80 

5.85 

4.602 

397  613 

1.704 

90 

6.23 

4.900 

423  435 

1.894 

100 

6.56 

5.144 

444  312 

2.083 

no 

6.87 

5.395 

466  128 

2.272 

120 

7.18 

5  639 

487  209 

2.462 

130 

7.47 

5866 

506822 

2.652 

140 

7.76 

6.094 

526  521 

2.841 

150 

8.05 

6.322 

546  048 

3.030 

■  160 

8.30 

6.534 

564  576 

3.219 

170 

8.55 

6.715 

580  176 

3408 

180 

8.80 

6.903 

596  418 

3.596 

190 

9.04 

7.100 

613  440 

3.788 

200 

9.28 

7.276 

628  704 

4.261 

225 

9-84 

7.696 

664848 

4.735 

250 

10.4 

8.168 

705  728 

5.208 

275 

10.8 

8.482 

732  844 

5. 682 

300 

II. 3 

8.914 

769  824 

6.629 

350 

12.3 

9.621 

831  168 

7.576 

400 

13  I 

10.28 

888  624 

8.532 

450 

13.9 

10.91 

943  056 

9-47 

500 

14.7 

11.50 

994  032 

10.41 

550 

15.4 

12.09 

I  044  576 

11.36 

600 

16. 1 

12.64 

I  092  096 

12.30 

650 

16.7 

13. II 

I  132  704 

13-25 

700 

17-4 

13.66 

I  180  224 

14.20 

750 

18.0 

14.13 

I  220  832 

15.15 

800 

18.6 

14.55 

I  257  408 

16.09 

850 

19. 1 

15  00 

I  296  000 

17.04 

9CO 

19.6 

15  39 

I  329  696 

17-99 

950 

20.3 

15  94 

I  377  216 

18.94 

I  000 

20.8 

16.33 

I  411  456 

22.73 

I  200 

22.7 

17.82 

I  539  648 

26.52 

I  400 

24.5 

19.24 

I  662  336 

30.30 

I  600 

26.2 

20.57 

I  777  248 

34  08 

I  800 

27.8 

21.83 

I  886  112 

37.87 

2  000 

29-3 

23.01 

I  988  064 

47.35 

2  500 

32.8 

25.72 

2  221  560 

56.81 

3000 

35.9 

28.19 

2  436  040 

1386      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 
Table  D.    Diameters  of  Pipes  and  Ratio  of  Discharge 


Ratio  of  dis- 

Ratio of  dis- 

Diameter 

of  pipe, 

in 

Diameter 

of  pipe, 

ft 

charge  to  that 

through  a 

i-ft  pipe 

with  the  same 

head  per  mile 

Diameter 

of  pipe, 

in 

Diameter 

of  pipe, 

ft 

charge  to  that 

through  a 

i-ft  pipe 

with  the  same 

head  per  mile 

I 

0.0833 

0.0020 

12H 

1.042 

1. 106 

i\^ 

0.1250 

0.005s 

13 

1.083 

1. 221 

2 

0.1667 

0.0113 

14 

1. 167 

I  470 

2H 

0.2083 

0.0198 

15 

1.250 

1.746 

3 

0.2500 

0.0310 

16 

1.333 

2.053 

3H 

0.2917 

0.0458 

17 

1. 417 

2.388 

4 

0.3333 

0.0643 

18 

1.5 

2.754 

4^2 

0.3750 

0.0857 

.19 

1.583 

3  153 

S 

0.4167 

0.1119 

20 

1.667 

3.585 

sVi 

0.4583 

0.1422 

21 

1.75 

4.051 

6 

0.5 

0.1767 

22 

1.833 

4.551 

6\i 

0.5417 

0.2159 

23 

1.917 

5.084 

7 

0.5833 

0.2600 

24 

2 

5. 649 

7H 

0.6250 

0.3090 

24H 

2.052 

6.000 

8 

0.6667 

0.3631 

26 

2.167 

6.912 

m 

0.7083 

0.4220 

28 

2.333 

8.319 

9 

0.75 

0.4871 

30 

2.5 

9.822 

9M 

0.7917 

0.5575 

30j<4 

2.521 

10. 0 

10 

0.8333 

0.6337 

32 

2.667 

II. 6 

10K2 

0.8750 

0.7157 

34 

2.833 

13.5 

II 

0.9167 

0 . 8044 

36 

3 

15. 5 

11'/^ 

0.9583 

0.8987 

38 

3.167 

17.8 

12 

I 

I 

40 

3.333 

20.2 

This  table  shows,  also,  the  relative  discharging  capacities  of  long  pipes.  Thus, 
one  i2-in  pipe  is  equal  to  two  9-in  pipes,  to  nearly  six  6-in  pipes,  or  to  thirty- 
three  3-iii  pipes. 


Hydraulics 

Table  E.    Flow  of  Water  in  House  Service-Pipes 

Thomson  Meter  Company 
To  find  the  discharge  in  gallons,  multiply  by  7.47 


1387 


Condition  of 
discharge 

Pres- 
sure in 
main, 
lb  per 
sq  in 

Discha 

rge  in 

cubic  feet  per  minute  from  the  pipe 

Nominal  diameters  of  iron  or  lead  service-pipe  in  inches 

Yz 

% 

¥i 

I 

iVi 

2 

3 

4 

6 

Through 
35  ft  of 
service- 

30 

1. 10 

1.92 

3.01 

6.13 

16.58 

33.34 

88.16 

173.85 

444.63 

40 

1.27 

2.22 

3.48 

7.08 

19.14 

38.50 

101.80 

200.75 

513.42 

50 

1.42 

2.48 

3.89 

7.92 

21.40 

43.04 

113.82 

224.44 

574.02 

pipe;  no 

60 

1.56 

2.7.1 

4.26 

8.67 

23.44 

47.15 

124.68 

245.87 

628.81 

back- 

75 

1.74 

3.03 

4.77 

9.70 

26.21 

52.71 

139.39 

274.89 

703.03 

pressure 

100 

2.01 

3  50 

5.50 

11. 20 

30.27 

60.87 

160.96 

317.41 

811.79 

130 

2.29 

3.99 

6.28 

12.77 

34.51 

69.40 

183.52 

361.91 

925.58 

Through 
100  ft  of 

30 

0.66 

1. 16 

1.84 

3.78 

10.40 

21.30 

58.19 

118. 13 

317.23 

40 

0.77 

1.34 

2.12 

4.36 

12.01 

24.59 

67.19 

136.41 

366.30 

service- 
pipe;  no 
back- 

50 

0.86 

I. SO 

2.37 

4.88 

13.43 

27.50 

75.13 

152.51 

409.54 

60 

0.94 

1.65 

2.60 

5. 34 

14.71 

30.12 

82.30 

167.06 

448.63 

75 

1.05 

1.84 

2.91 

5.97 

16.45 

33.68 

92.01 

186.78 

501.58 

pressure 

100 

1.22 

2.13 

3.36 

6.90 

18.99 

38.89 

106.24 

215.68 

579-18 

130 

1.39 

2.42 

3.83 

7.86 

21.66 

44.34 

121. 14 

245.91 

660. 3<> 

Through 
100  ft  of 
service- 
pipe  and 
IS-ft  ver- 
tical rise 

30 

0.55 

0.96 

1.52 

3.11 

8.57 

17.55 

47.90 

97.17 

260.56 

40 

0.66 

1.15 

1. 81 

3.72 

10.24 

20.95 

57.20 

I 16. 01 

311.09 

50 

0.75 

I-3I 

2.06 

4.24 

11.67 

23.87 

65.18 

132.20 

354.49 

60 

0.83 

1-45 

2.29 

4.70 

12.94 

26.48 

72.28 

146.61 

393  13 

75 

0.94 

1.64 

2.59 

5.32 

14.64 

29.96 

81.79 

165.90 

444.85 

100 

1. 10 

1.92 

3  02 

6.21 

17.10 

35.00 

95.55 

193.82 

519-72 

130 

1.26 

2.20 

3.48 

7.14 

19.66 

40.23 

109.82 

222.75 

597-31 

Through 
100  ft  of 

30 

0.44 

0.77 

1.22 

2.50 

6.80 

14. II 

38.63 

78.54 

211  54 

40 

0.55 

0.97 

1-53 

3.15 

8.68 

17.79 

48.68 

98.98 

266.59 

50 

0.65 

1. 14 

1.79 

3.69 

10.16 

20.82 

56.98 

115.87 

312.08 

service- 
pipe  and 
30-ft  ver- 
tical rise 

60 

0.73 

1.28 

2.02 

4.15 

11.45 

23.47 

64.22 

130.59 

351-73 

75 

0.84 

1.47 

2.32 

4.77 

13.15 

26.95 

73.76 

149.99 

403.98 

100 

1.00 

1.74 

2. 75 

5.65 

15.58 

31.93 

87.38 

177.67 

478.55 

130 

1. 15 

2.02 

3.19 

6.55 

18.07 

37.02 

101.33206.04 

554.96 

Table  E  may  also  be  used  when  the  pressure  is  In  feet-head  of  water  by  reducing 
the  head  in  feet  to  pounds  per  square  inch  by  Table  A.  Thus,  if  we  wish  the 
discharge  per  minute  through  a  %-in  pipe  100  ft  long  with  a  head  of  70  ft,  we 
find  from  Table  A  that  a  head  of  70  ft  corresponds  to  a  pressure  of  30  lb  per  sq 
in,  and  from  Table  E  we  find  the  discharge  through  a  %-in  pipe  100  ft  long  with 
a  pressure  of  30  lb  to  be  1.84  cu  ft  per  minute. 


1388      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 

Table  F.     Friction  of  Water  in  Pipes  Based  on  Ellis  and  Rowland's 
Experiments 

The  following  table  gives  the  friction-loss  in  pounds-pressure  per  square  inch 
for  EACH  loo  ft  of  length  in  clean  iron  pipes  of  different  sizes,  discharging  given 
quantities  of  water  per  minute.  This  friction-loss  is  greatly  increased  by  bends 
or  irregularities  in  the  pipe. 

To  find  the  friction-head  in  feet,  multiply  by  2.3 


Gallons 
per  minute 


Sizes  of  pipes,  inside  diameter 


%  in         I  in        i'/4  in      ij'i  in        2  in        2y2  in        3  in         4  in 


IS 

20 
25 
30 
35 
40 
45 
50 
75 

IOC 
125 

150 
175 
200 
250 
300 
350 
400 
450 
500 
600 
700 


3.3 
13.0 
28.7 
50.4 
78.8 


0.84 
3.16 
6.98 
12.3 
19.0 
27.5 
37.0 
48.0 


0.31 
1.05 
2.38 
4.07 
6.40 
915 
12.4 
16. 1 


24.9 
56.1 


0.12 
0.47 
0.97 
1.66 
2.62 
3.75 
5. 05 
6.52 
8.15 
10.  o 
22.4 
390 


0.12 
0.26 
0.42 
0.64 
0.91 
1.22 
1.60 
2.02 
2.44 
5.32 
946 
14.9 
21.2 

28.1 

37.5 


0 

21 

0 

I 

3 
4 
7 
9 
12 
19 
28 

81 
80 
20 
89 
00 
46 
47 
66 
06 

0.20 

0.35 
0.74 

1. 31 
1-99 
2.85 
3.85 
5.02 
7.76 
II. 2 
15.2 
19  5 
25.0 
30.8 


0.09 
0.23 
0.33 
0.49 
0.69 
0.94 
1.22 
1.89 
2.66 
•^.65 
4.73 
6.01 
7.43 
9-54 
14.32 


Water-Pipe  is  usually  tested  to  300  lb  pressure  per  square  inch  before  delivery, 
and  a  hammer-test  should  be  made  while  the  pipe  is  under  pressure.  The  usual 
length  for  each  section  of  cast-iron  water-pipe  is  from  12  ft  4  in  to  12  ft  6  in,  de- 
pending upon  the  depth  of  the  socket,  each  length  making  approximately  12  ft 
of  pipe  when  laid.  Pipes  from  2  to  4  in  diameter  are  sometimes  made  in  8  or 
9-ft  lengths. 


Hydraulics 


1389 


Safe  Pressures  and  Equivalent  Heads  of  Water  for  Cast-Iron  Pipes  of 

Different  Sizes  and  Thicknesses 

Calculated  by  F.  H.  Lewis  from  Fanning's  Formula 


Thick- 

Size of  pipe,  in 

4 

6 

3 

10 

12 

14 

ness, 
in 

2? 

1- 

ia 

ia 

1 

1"^ 

ta 

Mr. 

112 

258 

49 

112 

18 

42 

Vi 

224 

516 

124 

280 

74 

171 

44 

lOI 

24 

55 

9/i6 

336 

774 

199 

458 

130 

300 

89 

205 

62 

143 

42 

97 

% 

274 

631 

186 

429 

132 

304 

99 

228 

74 

170 

iHe 

177 

.  408 

137 

316 

106 

244 

% 

224 

S16 

174 

401 

138 

316 

^U 

212 

488 

170 

392 

H 

249 

574 

202 

465 

1^6 

234 

538 

I 

266 

612 

i6 

18 

20 

24 

30 

36     - 

H 

56 

129 

41 

95 

^VlQ 

84 

194 

66 

152 

SI 

118 

30 

69 

3/4 

112 

258 

91 

210 

74 

170 

49 

113 

24 

55 

13/16 

140 

323 

116 

267 

96 

221 

68 

157 

39 

90 

% 

168 

387 

141 

325 

119 

274 

86 

198 

54 

124 

32 

74 

1^6 

196 

452 

ibb 

382 

141 

32s 

105 

242 

69 

159 

44 

lOI 

I 

224 

516 

191 

440 

164 

378 

124 

286 

84 

194 

57 

131 

iH 

216 

497 

209 

481 

161 

371 

114 

263 

82 

189 

iH 

256 

589 

199 

458 

144 

332 

107 

247 

iH 

237 

546 

174 

401 

132 

304 

i^A 

204 

470 

157 

362 

iH 

234 

538 

182 

419 

iH 

207 

477 

Weights  of  Lead  and  Gaskets  for  Pipe- Joints 
Dennis  Long  &  Company 


Diameter 

Lead, 

Gasket, 

Diameter 

Lead, 

Gasket, 

of  pipe. 

lb 

lb 

of  pipe. 

lb 

lb 

in 

m 

2 

2.5 

0.I2S 

12 

15 

0.250 

3 

3  5 

0.170 

14 

18 

0.375 

4 

4-5 

0.170 

16 

22 

0.500 

6 

6.5 

0.200 

18 

26 

0.500 

8 

90 

0.200 

20 

33 

0.62s 

10 

130 

0.250 

1390     Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping   .  Part  3 

Weights,  per  Foot,  of  Cast-iron  Pipes  in  General  Use,  Including  Socket-Ends 

and  Spigot-ends 

Dennis  Long  &  Company,  Inc.,  Louisville,  Ky. 


Diam- 

Thick- 

Weight 

Diam- 

Thick- 

Weight 

Diam- 

Thick- 

Weight 

eter, 

ness, 

per  ft, 

eter, 

ness, 

per  ft. 

eter, 

ness, 

per  ft, 

in 

in 

lb 

in 
16 

in 

lb 

in 

in 

lb 

3 

H 

12'/^ 

% 

129 

2 

66e 

30 

Vu 

15 

U 

152 

36 

% 

334 

H 

i8 

I 

175 

I 

382 

Ha 

2oyi. 

18 

H 

120 

1% 

432' 

H 

23 

H 

146 

iH 

482 

4 

H 

17 

% 

171 

iH 

532 

Vie 

20 

I 

197 

iH 

587 

H 

2ZVl 

iKs 

223 

iH 

632 

«/|6 

26^4 

iK 

249 

iH 

683 

H 

30 

20 

iHe 

148 

1% 

734 

6 

M6  + 

30 

M 

161 

2 

786 

H 

34 

% 

190 

42 

I 

445 

»/l6 

38H 

I 

216 

iH 

471 

H 

42?.^ 

iH 

247 

iH 

560 

H 

52 

iK 

276 

iH 

629 

8 

Vie 

40 

iH 

305 

iH 

675 

Vi 

43K2 

i].i 

334 

iH 

734 

Vie 

49% 

24 

H 

191 

iH 

794 

H 

56 

li 

225 

1% 

853 

H 

68 

I 

258 

2 

912 

10 

lU 

50 

1% 

293 

48 

iH 

572 

\h 

54 

iH 

327 

iH 

637 

«/i6 

60 

iH 

361 

r)i 

701 

% 

68 

iH 

395 

iH 

768 

% 

82 

1% 

430 

1% 

835 

12 

H 

70 

1% 

465 

iH 

901 

Me 

76 

30 

1^6 

258 

1% 

967 

H 

82 

% 

278 

2 

1034 

Vi. 

99 

I 

319 

60 

iH 

797 

% 

117 

1% 

360 

iH 

880 

14 

9l6 

85 

m 

405 

iH 

964 

H 

94 

1% 

448 

iH 

1049 

% 

113 

m 

489 

iH 

I  133 

i6 

9l6 

137 
100 

1% 

532 

575 

2 

I  216 
1300 

1% 

^^ 

108 

1% 

619 

2H 

1470 

There  is  no  standard  weight  of  pipe  for  any  given  pressure. 


Private  Water-Supply.     Pumps 

Private  Water-Supplies.  The  architect  is  frequently  required  to  furnish 
a  water-supply  for  isolated  buildings,  and  even  in  cities  it  is  becoming  quite 
common  for  manufacturing  establishments  and  large  buildings  to  have  their  " 
own  water-supply;  so  that  some  knowledge  of  the  various  methods  of  sup- 
plying water  is  requisite.  Power-pumps  are  of  so  many  kinds  and  so  intri- 
cate in  construction  that  no  attempt  will  be  made  to  describe  them. 

The  Hydraulic  Ram.     Where  a  small  stream  of  water  having  a  fall  of  2  ft 
or  more  flows  near  the  premises,  an  hydraulic  ram  may  be  used  to  great  advan^ 


Private  Water-Supply.    Pumps 


1391 


tage  to  furnish  water  for  domestic  purposes,  or  even  for  irrigation.  The  ram 
is  operated  by  the  momentum  of  the  water  flowing  through  the  drive-pipe  and 
dehvers  water  into  an  open  tank.  Wate^;  can  be  conveyed  by  a  ram  13  000  ft 
when  elevated  500  ft,  provided  there  is  sufficient  fall.  The  drive-pipe  supplying 
the  ram  should  be  30  or  40  ft  long  to  give  the  necessary  momentum.  The  use 
of  the  ram  is  the  most  economical  method  of  pumping  water,  as  there  is  no 
expense  for  maintenance  except  for  repairs,  and  the  cost  of  installation,  also,  is 
small. 

The  Capacities  of  the  Rife  Rams  are  given  in  the  following  table.  The 
capacities  are  determined  from  the  table  by  multiplying  the  available  supply  of 
water  per  minute,  or  the  rated  amount  of  water  a  Rife  ram  will  use,  by  the  factor 
found  in  the  table  at  the  intersection  of  the  line  giving  the  fall  available,  for  the 
drive-pipe,  and  the  column  showing  the  height  the  water  is  to  be  elevated.  The 
factor  for  a  lo-ft  fall  and  50-ft  discharge  is  192,  and  this  multiplied  by  the  supply 

of  water  per  minute  will  give-  the  delivery  per  day.     This  is 

shown  by  the  example  worked  out  in  the  corner  of  the  table. 

These  capacities  are  based  on  efficiencies  dependent  on  the 

ratio  of  fall  to  lift.     A  fall  of  10  ft  and  a  lift  of  50  ft  give  a 

ratio  of  i  to  5,  and  an  efficiency  of  66%%.     The  efficiencies 

of  Rife  rams  based  on  various  ratios,  are  also  given  in  the 

table. 

Deep  "Wells  and  Plunger-Pumps.    The  common  method 

of  obtaining  a  private  water-supply  is  to  drive  a  deep  well 

until  a    sufficient    supply   of 

water  is  obtained.     The  depth 

to  which  a  well  must  be  driven 

will,   of  course,  depend  upon 

the  locahty,  and  can  only  be 

determined    by   drillings.     As 

the    well    is    driven,    a   large 

wrought-iron  pipe  is  sunk  to 

form  the  casing.     Casings  are 

seldom   less   than   6   or  more 

than  10  in  inside  diameter,  8 

in    being    the    common    size. 

When   the   water-pocket    has 

been  reached,  the  water  will 

usually  rise  and  stand  in  the 

pipe  several  hundred  feet  above 

its  bottom,  and  the  amount  of 

water    that    can    usually    be 

pumped  from  such  wells,  with- 
out lowering  the  water,  is  prac- 
tically   unHmited.     The    cost 

of  drilling  deep  wells,  per  foot 
of  depth,  INCLUDING  THE  CASING,  differs,  of  course,  with  the  strata,  location  and 
other  local  conditions.  As  a  rule,  however,  it  will  average  about  $5  per  foot  for  a 
well  driven  through  rock  and  $6  per  foot  for  a  well  through  sand.  For  raising 
the  water  into  an  open  tank  a  single-acting  pump  consisting  of  a  working- 
head,  (Fig.  1),  which  operates  a  cylinder  placed  in  a  smaller  pipe  lowered  into 
the  well  through  which  the  water  is  raised,  is  commonly  employed.  The 
cylinder  should  preferably  be  placed  below  the  water-line  in  the  well,  and  is 
usually  connected  with  the  working-head  by  wooden  sucker-rods.    The  working- 


Fig.  1.  Working- 
head  for  Deep- 
well  Pump 


Fig.  2.     Deep-well  Working- 
head  for  Belt-attachment 


1392      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 
Table  of  Water  Required  for  Rife  Rams 


Dimensions 

Size  of 

Size  of 

Gallons  per 
minute 

Least  no. 
of  feet  of 

Num- 

drive- 

deliv- 

required 

fall 

Weight, 

ber 

Height, 
ft  in 

Length, 
ft  in 

Width, 
ft  in 

pipe, 
in 

ery- 
pipe, 
in 

to  operate 

engine, 

gal 

recom- 
mended, 
ft 

lb 

10 

2 

I 

3  2 

I  8 

iM 

% 

3  to    6 

3 

150 

IS 

2 

I 

3  4 

I  8 

i\^ 

% 

5  to   12 

3 

175 

*20 

2 

3 

3  8 

I  9 

2 

I 

10  to   18 

2 

225 

25 

2 

3 

3  9 

I  9 

2I/2 

I 

II  to   24 

2 

250 

30 

2 

7 

3  10 

I  10 

3 

iM 

IS  to   3S 

2 

275 

40 

3 

3 

4  4 

2  O 

4 

2 

30  to   7S 

2 

600 

8o 

7 

4 

8  4 

2  8 

8 

4 

ISO  to  3SO 

2 

2500 

*I20 

12 

5 
6 

375  to  750 
750  to  I  500 

2 

3  000 

tl20 

8 

9 

9  6 

3  8 

12  (two) 

2 

5500 

•  Singl« 

'• 

t  Dupl 

ex. 

Table  of  Capacities  of  Rife  Rams 


Power- 
head 

or  fall 
in  ft 

Height  or  head  in  feet  the  water  is  to  be  delivered 

4 

10 

15 

20 

30 

40 

*So 

60 

70 

80 

90 

100 

120 

140 

160 

180 

200 

2 
3 
4 
S 
6 
7 
8 
9 

*I0 

12 
14 
16 
18 
20 
22 
24 
26 
28 
30 

540 

J  02 
301 
432 

540 

128 
192 
256 
345 
432 
505 

96 

144 
192 
240 
302 
378 
432 
485 
540 

64 
96 
128 
160 
192 
235 
270 
300 
360 
430 
505 

43 
72 
96 
120 
144 
168 
192 
216 
252 
301 
353 
432 
486 
540 

29 
58 
77 
96 
115 
134 
154 
173 

*I92 

230 
270 
323 
390 
430 
475 
520 

24 
43 
64 
80 
96 
112 
128 
144 
160 
192 
224 
257 
303 
336 
370 
405 
470 
505 
540 

37 
55 
69 
82 
96 
no 
124 
137 
165 
192 
220 
247 
288 
303 
346 
375 
430 
465 

27 
43 
60 
72 
84 
96 
108 
120 
144 
168 
192 
2:6 
24c 
264 
288 
328 
354 
405 

24 

38 

53 

64 

75 

86 

96 

107 

128 

150 

171 

192 

214 

235 

256 

278 

300 

336 

29 
43 
57 
67 
77 
86 
96 
115 
135 
154 
173 
192 

2X2 
230 
250 
269 
288 

24 
30 
43 
50 
64 
72 
So 
96 
112 
128 
144 
160 
176 
192 
208 
224 
24c 

26 
31 
36 
55 
62 
68 
82 
96 
no 
124 
137 
151 
164 
178 
192 
206 

27 
31 
43 
54 
60 
72 
84 
96 
108 
120 
132 
144 
156 
168 
180 

24 
28 
38 

64 
75 
85 
96 
IC7 
118 
128 
139 
149 
160 

25 
29 

39 
43 
57 
67 
77 
86 
96 
IC5 
lis 
125 
134 
144 

Example 

With  a  supply  of 
I  400  gal  per  min, 
lo-ft  fall,  50-ft  ele- 
vation. No.  120  en- 
gine will  deliver 
268  800  gal  per  day . 

140 

0X1 

92  = 

268 

800 

*  Multiply  factor  opposite  power-head  and  under  pumping-head  by  the  number  of 
gallons  per  minute  used  by  the  engine;  the  result  will  be  the  number  of  gallons  deliV' 
ERED  per  day. 

The  efficiency  developed  is  governed  by  the  ratio  of  fall  to  pumping-head. 

75%      for  a  ratio  of  i  to  2  3'4 


The  efficiency  of  rife  rams  is  based  on. . . . 


70%      for  a  ratio  of  i  to  3 

66?^%  for  a  ratio  up  to  i  to  18 

60%     for  a  ratio  up  to  i  to  23 

.  <o%     for  a  ratio  up  to  x  to  30 


Private  Water-Supply.     Pumps 


1393 


head  may  be  operated  by  hand,  or  by  a  crank  rod  attached  to  a  pumping-jack, 
windmill  or  engine.  With  a  single-acting  pump  the  plunger  is  raised  and 
lowered  once  with  every  revolution  of  the  driving-wheel,  the  principle  of  oper- 
ation being  the  same  as  in  an  ordinary  hand  suction-pump.  Fig.  2  shows  a 
simple  arrangement  for  operating  a  working-head  by  belt-power.  This  is 
known  as  a  deep-well  power  working-head.  A  deep-well  pump  (Fig.  2)  differs 
from  a  suction-pump  in  that  it  will  raise  water  from  any  depth,  whereas  a  suc- 
tion-pump in  practice  will  raise  water  only  about  20  ft.  A  suction-pump  may 
be  placed  at  any  point  in  relation  to  the  well,  and  will  draw  the  water  any 
reasonable  horizontal  distance.  The  deep-well  pump,  on  the  other  hand,  must 
be  set  directly  over  the  well,  but  it  will  then  deliver  the  water  at  any  desired 
point.  The  amount  of  water  pumped  in  a  minute  by  any  single-acting  pump 
is  determined  by  the  diameter  of  the  suction-cylinder,  the  length  of  stroke,  and 
the  number  of  strokes  per  minute.  The  table  following  gives  the  capacity  per 
stroke  for  cylinders  of  different  diameters,  and  for  .strokes  of  different  lengths. 
To  fmd  the  capacity  per  minute,  multiply  the  values  given  in  the  table  by  the 
revolutions  per  minute.  The  usual  speed  of  single-acting  working-heads  and 
pumping-jacks  is  from  25  to  30  revolutions  per  minute.  Cylinders  over  2%  in  in. 
diameter  should  have  a  substantial  iron  working-head. 


Table 

Showing  Capacity  of  Single-Acting  Pumps  of  Given  Diameter  and 
Length  of  Stroke 

Diam. 

of 
cylin- 
der in 
inches 

Length  of  stroke  in  inches 

6 

« 

10 

12 

14 

16 

18 

20 

24 

• 

Capacity  per  stro 

ke  in  gallons 

0.0319 
0.0385 
0.0459 
0.0625 

0.0425 
0.0513 
0.0612 
0.0833 

0.0531 
0.0642 
0.0765 
0.1041 

0.0637 
0.0770 
0.0918 
0.1249 

0.0743 
0.0890 
0.1071 
0.1457 

0.0848 
0.1027 
0.1224 
0.1666 

0.095s 
0.1156 
0.1377 
0.1874 

0.1062 
0.1280 
0.1530 
0.2082 

0.1274 
0.1541 
0.1836 
0.2499 

2 

2H 

2V2 

2% 

0.0816 
0.1033 
0.1275 
0.1543 

0.1088 
0.1377 
0.1700 
0.2057 

0.1360 
0.1721 

0.2I2S 

0.2571 

0.1632 
0.2063 
0.2550 
0.3085 

0.1904 
0.2410 
0.2975 
0.3598 

0.2176 
0.2754 
0.3400 
0.4114 

0.2448 
0.3096 
0.3825 
0.4626 

0.2720 
0.3442 
0.4250 
0.5142 

0.3264 
0.4128 
0.5100 
0.6170 

3 

3V2 
3% 

0.1836 
0.2154 
0.2499 
0.2868 

0.2448 
0.2872 
0.3332 
0.3824 

0.3060 
0.3594 
0.4165 
0.4780 

0.3672 
0.4312 
0.4998 
0.5736 

0.4284 
0 . 5030 
0.5831 
0.6692 

0.4896 
0.5748 
0.6664 
0.7648 

0.5508 
0.6466 
0.7497 
0.8605 

0.6120 
0.7182 
0.8330 
0.9561 

0.7344 
0.8624 
0.9996 
I. 1470 

4 

4H 
4^ 
4% 

0.3264 
0.3684 
0.4131 
0.4602 

0.4352 
0.4912 

0.5440 
0.6141 

0.6528 
0.7368 
0.8262 
0.9204 

0.7616 
0.8596 
0.9639 
1.0730 

0.8704 
0 . 9824 
1.1016 
1.2270 

0.9792 
I . 1050 
1.2393 
1.3800 

1.0880 
I . 2280 
1.3770 
1.5340 

1.3056 
1.4730 
1.6524 
1.8400 

0.5508 
0.6136 

0.6885 
0.7671 

Hot-Air  Engines.  These  are  very  extensively  used  for  pumping  water  for 
country  houses,  as  they  are  absolutely  safe,  require  little  attention,  and  hav6 
no  valves,  springs  or  gauges  to  get  out  of  order.  They  are  also  adapted  to  al- 
most any  kind  of  fuel,  such  as  coal,  coke,  wood,  gas,  or  kerosene  oil.  They 
will  pump  from  either  a  shallow  or  a  deep  well,  but  are  best  adapted  to  wells 


1394     Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part. 3 

in  which  the  surface  of  the  water  is  within  20  ft  of  the  top  of  the  well.  The 
best  known  hot-air  engines  are  the  Rider-Ericsson,  which  have  been  in  success- 
ful operation  for  many  years.  These  engines  have  capacities  ranging  from  150 
to  3  5cx>  gal  per  hour  and  will  deliver  water  from  50  to  350  ft  above  the 
surface  of  water  in  the  well,  although  the  higher  the  water  is  raised  the  less 
will  be  the  quantity  delivered.  The  cost  of  these  engines,  with  pump  at- 
tached, varies  from  $110  for  the  smallest  size,  having  a  capacity  of  150  gal  per 
hour  raised  50  ft,  to  $540  for  the  largest  size,  having  a  capacity  of  3  500  gal  per 
hour  raised  50  ft.  The  smaller  size  requires  about  i  quart  of  kerosene  or  3  lb 
of  anthracite  coal  per  hour.  Hot-air  engines  should  be  placed  close  to  the 
source  of  supply,  and  when  the  latter  is  a  deep  well  the  engine  must  be 
placed  so  that  the  pump-rod  will,  be  in  a  vertical  line  above  the  cylinder  in 
the  well,  the  operation  of  pumping  being  the  same  as  that  of  the  ordinary 
single-acting  deep-well  pump.  It  is  not  practicable  to  draw  water  more  than 
from  20  to  25  ft,  in  height,  with  any  form  of  suction-pump,  because  of  the 
difficulty  of  keeping  the  pipe,  valve  and  fittings  absolutely  air-tight.  For 
further  information,  see  the  catalogue  of  the  Rider-Ericsson  Engine  Company. 

Action  of  Wind  and  Capacities  of  Pumping  Windmills 


Velocity 
per  hour 
in  miles 


25 
30 

40 
50 
60 

80 
100 


Pressure  * 

per  square 

foot  in 

pounds 


0.045 

0.125 

0.33 

0.5 

1 .  125 

2 

3.125 

45 

8 

12.5 
18 

32 

50 


Description  of  wind 


Just  perceptible. .  .  . 

Pleasant  wind 

Fresh  breeze 

Average  wind 

Good  working  wind 

Strong  wind 

Very  strong  wind. . . 

Gale 

Storm 

Severe  storm 

Violent  storm ...... 

Hurricane 

Tornado  


Action  of  wind  and  windmills 


Windmills  will  not  run 
Might  start  if  lightly  loaded 
Will  start  pumping 
Pumps  nicely  if  properly  loaded 
Does  excellent  work  • 
Gives  best  service 
Maximum  results  secured 
Should  be  furled  out  of  wind 
I  Well-constructed    mills    and 
I      towers  safe  if  properly  erected 
i  Buildings,  trees,  etc.,  might  be 
[      injured 

[  Buildings,  trees,  etc.,  would 
'      be  injured 
Ruin 


Froi  1  the  above  table  it  will  be  seen  that  the  only  available  winds  are  those  blowing 
with  a  velocity  of  from  8  to  25  miles  per  hour,  and  that  a  15-milc  wind  can  be  utilized 
to  the  best  advantage.  It  is  therefore  advisable  to  load  a  windmill  for  a  15-mile  wind. 
It  then  starts  pumping  in  an  8-mile  wind,  does  excsllent  work  in  a  is-mile  wind  and 
reaches  the  maximum  results  in  a  25-mile  wind. 

*  The  pressures  per  square  foot  in  pounds  will  vary  slightly  from  the  values  given 
according  to  the  formula  which  is  used  to  obtain  such  pressures.  See,  also,  Chapter 
XXVII,  pages  1052-3,  Chapter  XXX,  page  1199,  and  page  1717. 


Windmills.  In  the  country  and  on  large  suburban  estates,  windmills  are 
extensively  used  for  pumping  water.  Aside  from  the  noise  of  operation,  the 
only  objection  to  the  windmill,  where  it  can  be  used,  is  the  irregularity  of  its 
supply,  but  with  a  large  storage-tank  this  is  not  a  serious  objection  when  used 
for  domestic  purposes  only.  Professor  Thurston  says,  regarding  windmills: 
*'In  estimating  the  capacity,  a  working-day  of  eight  hours  is  assumed,  but  the 


Private  Water-Supply.     Windmills 


1395 


machine,  when  used  for  pumping,  may  actually  do  its  work  twenty-four  hours  a 
day  for  days,  weeks,  and  even  months  together,  whenever  the  wind  is  stiff  enough 
to  turn  it.  It  costs  for  work  done  only  one-half  or  one-third  as  much  as  steam, 
hot-air,  or  gas-engines  of  similar  power."  The  action  of  wind  of  different, 
velocities,  the  pressure  per  square  foot  of  sail-s*irfacc  and  its  relation  to  the 
pumping  capacity  of  pumps  can  be  found  in  the  following  table,  compiled  by 
Fairbanks,  Morse  &  Company. 

The  windmill  operates  the  plunger  in  the  well,  the  process  of  pumping  being 
the  same  as  that  of  the  single-acting  pumps  described  above.  The  following 
table  of  capacity  was  prepared  by  Alfred  R.  Wolff,  and  is  sufficiently  accurate 
for  all  practical  purposes: 


Capacity  of  the  Windmill 

Desig- 

Veloc- 

Gallons of  water  raised  per  minute 

Equiva- 

nation 

ity  of 

Revolu- 

to an  elevation  of 

lent     • 

of  mill 

wheel, 

ft 

wind  in 

miles 
per  hour 

tions  of 

actual 

wheel  per 
minute 

25 

ft 

50 
ft 

75 
ft 

100 
ft 

150 

ft 

200 

ft 

useful 

h.p. 

developed 

SH 

i6 

40  to  50 

6.192 

3.016 

0.04 

10 

i6 

.35  to  40 

19.179 

9.563 

6^638 

4.750 

0.12 

12 

i6 

30  to  35 

33.941 

17.952 

II. 851 

8.435 

5.680 

0.21 

14 

i6 

28  to  35 

45.139 

22.569 

15.304 

11.246 

7.807 

4.998 

0.28    "^ 

i6 

i6 

25  to  30 

64.600 

31.654 

19.542 

16.150 

9  771 

8.075 

0.41 

i8 

i6 

22  to  25 

97.682 

52.165 

32.513 

24.421 

17.485 

12. 211 

0.61 

20 

i6 

20  to  22 

124.950 

63.750 

40.800 

31  248 

19.284 

15.938 

0.78 

25 

i6 

16  to  18 

212.381 

106.964 

71.604 

49.725 

37.349 

26.741 

1.34 

The  horse-power  of  windmills  of  the  best  construction  is  proportional  to  the 
squares  of  their  diameters  and  inversely  as  their  velocities;  for  example,  a  10-ft 
mill  in  a  16-mile  breeze  will  develop  0.15  horse-power  at  65  revolutions  per  min- 
ute; and  with  the  same  breeze: 

a  20-ft  mill,  at  40  revolutions  per  minute,  i  horse-power; 

a  25-ft  mill,  at  35  revolutions  per  minute,  1%  horse-power; 

a  30-ft  mill,  at  28  revolutions  per  minute,  3H  horse-power". 

The  wheels  of  very  few  windmills  are  larger  than  25  ft  in  diameter.  There 
are  no  pumps  which  will  enable  the  user  of  a  wihdmill  to  utilize  the  increased 
power  obtained  from  winds  of  high  velocity,  so  that  in  practice  the  amount  of 
water  pumped  by  windmills  in  high  winds  is  but  little  more  than  is  pumped  by 
the  same  mills  in  winds  having  velocities  of  from  12  to  18  miles  per  hour.  For 
this  reason  it  is  customary  to  regulate  windmills  to  govern  at  about  25  miles  an 
hour.  Theoretically  the  increase  in  power  from  increased  velocity  of  wind  is  equal 
to  the  square  of  its  proportional  velocity;  as,  for  example,  the  25-ft  mill  rated 
above  for  a  16-mile  wind  will,  with  a  32-mile  wind,  have  its  horse-power  increased 
to  4  X  1%  =  7  horse-power.  A  windmill  "will  run  and  produce  work  in  an  8- 
mile  breeze."  Windmills  have  also  been  used  for  the  generating  and  storage 
of  electricity  for  small  lighting-plants.* 

Air-Lift  Process.  Compressed  air  is  now  being  used  to  an  increasing  extent 
for  raising  water  from  artesian  wells.  The  process  in  general  consists  of  sub- 
merging a  discharge-pipe  in  a  closed  well,  with  a  smaller  pipe  inside  delivering 

*  See  Kent's  Mechanical  Engineers'  Pocket-Book. 


1396      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 

compressed  air  into  it  at  the  bottom.  The  compressed  air  by  its  inherent  ex~ 
pansive  force  lifts  a  column  of  mingled  air  and  water  which  is  conveyed  to  an 
open  tank,  to  permit  of  the  escape  of  the  air.  If  desired  the  water  may  then  be 
conveyed  by  gravity  into  a  series  of  closed  tanks,  and  forced  by  air-pressure  to 
different  parts  of  a  building,  ^the  only  machinery  required  being  an  air-com- 
pressor and  power  for  driving  it  The  slip  of  the  bubl)le  constitutes  the  chief 
loss  of  energy  in  the  air-lift.  The  method  of  piping  a  well  differs  according  to 
its  general  conditions  and  the  quantity  of  water  to  be  pumped.  "No  two  wells 
are  alike,  and  consequently  the  method  of  piping  which  might  be  applied  to 
one  would  be  unsuited  to  another."  Information  as  to  the  best  method  of 
piping  any  particular  well  may  be  obtained  from  the  Ingersoll-Sergeant  Drill 
Company. 

Advantages  of  the  Air-Lift  Process.  From  two  to  six  times  as  much  water 
may  be  obtained  from  a  given  diameter  of  well  as  with  any  other  known  system, 
because  there  are  no  valves,  cylinders,  or  rods  to  hinder  the  rapid  discharge  of 
water.  One  air-compressor  operates  any  number  of  wells,  which  may  be  any 
distance  apart  so  as  not  to  affect  one  another.  There  is  nothing  outside  the 
engine-room  to  look  after  or  wear  out.  Nothing  but  common  pipe  in  the  wells. 
Sand  or  gravel  does  no  harm.  The  cost  of  raising  i  ooo  gal  of  water  by  this 
method,  including  fuel,  labor,  oil,  interest  on  cost  of  well,  boiler,  compressor, 
foundations,  pipes,  real  estate,  erection  and  taxes,  including  15%  for  depre- 
ciation, runs  from  2H  cts  down  to  H  ct,  according  to  the  size  of  the  plant, 
height  of  lift,  and  other  local  conditions.  With  the  average  outfit  of  medium 
or  small  size,  it  is  usually  under  lYi  cts.*  The  air-lift  process  is  now  exten- 
sively used  in  ice-works,  breweries,  cold-storage  houses,  textile  mills,  dye-works, . 
etc.,  and  a  great  variety  of  industrial  plants,  and  for  the  water-supply  of' 
quite  a  number  of  the  smaller  cities.  In  Newark,  N.  J.,  pumps  of  this  type 
are  at  work  having  a  total  capacity  of  i  000  ocx>  gal  daily,  lifting  water  from 
three  8-in  artesian  wells. f 

Pneumatic  Water-Supply  Systems.  The  pneumatic  system  of  supplying 
water  to  buildings  is  used  extensively  in  buildings  and  institutions  remote  from 
public  water-supplies.  With  the  pneumatic  system,  instead  of  an  open  ele- 
vated tank,  a  closed  water-tight  tank  of  iron  or  steel  is  used,  and  this  tank  may 
be  located  at  any  level,  for  the  water  is  forced  from  it  by  means  of  compressed 
air  confined  in  the  top  of  the  tank.  This  fact  makes  it  possible  to  bury  the  tank 
in  the  ground  below  the  frost-line,  away  from  the  heat  of  the  sun,  and  where  the 
water  will  have  an  almost  uniform  temperature  the  year  round.  The  water  is 
protected  from  possible  contamination  from  insects,  rats,  birds,  dust,  or  other 
agencies,  while  the  tank  takes  up  no  valuable  space  above  ground,  imposes  no 
weight  upon  the  attic-floor  of  a  building,  and  does  not  disfigure  the  landscape. 
The  principle  of  operation  is  this:  Air  is  compressible,  while  water  is  not.  If 
then,  water  is  pumped  into  a  closed  tank  at  the  bottom,  it  will  trap  the  air 
within,  and  the  more  water  pumped  in,  the  greater  the  compression,  of  the  air. 
The  elasticity  of  the  air,  then,  will  force  the  water  out  again,  whenever  a  faucet  is 
opened,  and  the  water  will  continue  to  flow  as  long  as  the  air  is  under  sufficient  pres- 
sure in  the  tank.  In  practice  the  air  would  become  absorbed  by  the  water  in  the 
tank,  and  in  a  short  time  become  exhausted,  if  it  were  not  supplied  as  fast  as  used. 
This  is  accomplished  by  injecting  a  proportionate  amount  of  air  with  each  stroke 
of  the  pump,  by  means  of  a  snifter-valve  air-compressor,  or  other  device.  All 
connections  to  the  tank  are  taken  from  the  bottom,  to  prevent  the  escape  of  air 
which  would  occur  if  the  connections  were  taken  from  the  top  of  the  tank. 

*  InKersoll-Sergeant  Drill  Company.  t  Kent. 


Fire-Streams 


1397 


Horse-Power  Required  to  Raise  Water  to  Different  Heights 

General  Principles.  The  power  required  to  raise  a  certain  quantity  of  water  to 
a  certain  height  varies  directly  with  the  quantity  to  be  raised,  and  also  with  the 
height.  For  instance,  it  requires  twice  as  much  power  to  raise  200  gal  per  minute 
10  ft  high  as  it  does  to  raise  100  gal  to  the  same  height  and  in  the  same  time;  and  to 
raise  100  gal  20  ft  high  requires  twice  as  much  power  as  it  does  to  raise  100  gal  10 
ft  high.  To  find  the  theoretical  horse-power  necessary  to  elevate  water  to  a  given 
height,  multiply  the  number  of  gallons  per  minute  by  8.335,  the  weight  of  i  gal, 
and  this  result  by  the  total  number  of  feet  the  water  is  raised,  that  is,  from  the 
surface  of  the  water  to  the  highest  point  to  which  the  water  is  raised,  and  the 
result  gives  the  power  in  foot-pounds;  divide  by  33  000,  and  the  quotient  is 
the  horse-power.  To  the  theoretical  power  a  liberal  allowance  must  be  made 
for  the  inefficiency  of  the  pump.  For  a  cylinder-pump  add  from  75  to  100%. 
To  the  actual  height  to  which  the  water  is  to  be  raised  add  the  friction-loss  in 
feet,  given  in  Table  F,  page  1388,  when  the  discharge  is  to  be  piped  any  distance. 

Example.  Find  the  theoretical  horse-power  required  to  raise  100  gal  per 
minute  120  ft  high,  through  a  3-in  pipe,  200  ft  leng. 

Solution.  From  Table  F,  the  friction-head  for  100  gal  per  min  in  a  3-in  pipe, 
100  ft  long,  is  1.3 1  X  2.3  or  3  ft.  For  200  ft  it  will  be  6  ft,  which,  added  to  120, 
gives  126  ft  for  the  height.  Then  theoretical  horse-power  =  100  x  8.35  x  126/ 
33000=  3.2  h.p.  The  actual  horse-power  required  will  probably  vary  from 
5  to  6,  according  to  the  efficiency  of  the  pump.  The  mistake  of  using  too 
small  a  discharge-pipe  can  easily  be  seen  from  Table  F.  For  instance,  if 
one  attempted  to  force  100  gal  per  minute  through  100  ft  of  2-in  pip'ep- 
the  back-pressure  would  be  equivalent  to  raising  the  water  22  ft  high.  The 
fuel  used  would  be  correspondingly  increased.  Right-angle  turns  are  to  be 
avoided,  as  the  friction  is  verj^  materially  increased,  being  practically  equal  to 
the  friction  of  25  ft  of  straight  pipe. 


Table  of  Effective  Fire-Streams 

Using  100  ft  of  2y2-\n  ordinary  best-quality  rubber-lined  hose  between  nozzle  and 
hydrant  or  pump 


Smooth  nozzle 


%\n      , 

^^in 

32 

54 

65 

75 

86 

34 

57 

69 

80 

30 

50 

60 

70 

80 

30 

50 

60 

70 

48 

67 

72 

76 

79 

49 

71 

77 

81 

37 

50 

54 

68 

62 

42 

55 

61 

(i^ 

90 

116 

127 

137 

147 

123 

159 

174. 

188 

Pressure  at  hydrant,  lb . . 

Pressure  at  nozzle,  lb 

Vertical  height,  ft 

Horizontal  distance,  ft.  . 
Gal  discharged  per  min. . 

Smooth  nozzle 

Pressure  at  hydrant,  lb. . 
Pressure  at  nozzle,  lb. . . . 

Vertical  height,  ft 

Horizontal  distance,  ft.  . 
Gal  discharged  per  min. . 


I  in 

ij'^in 

37 

62 

75 

87 

100 

42 

70 

84 

98 

30 

50 

60 

70 

80 

30 

SO 

60 

70 

51 

73 

79 

85 

89 

52 

75 

83 

88 

47 

61 

67 

72 

76 

50 

66 

72 

77 

161 

208 

228 

246 

263 

206 

266 

291 

314 

Fire-Streams.  The  following  is  an  extract  from  a  paper  read  by  John 
R.  Freeman  at  a  meeting  of  the  New  England  Waterworks  Association, 
entitled  Some  Experiments  and  Practical  Tables  Relating  to  Fire-Streams,  1 


loUS      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 

*'When  unlined  liiieii  hose  is  used  the  friction  or  pressure-loss  is  from  8  to 
60%,  increasing  with  the  pressure.  This  kind  of  hose  is  best  for  inside  use  in 
short  lengths.  Mill-hose  is  better  than  unlined  Hnen  hose  for  long  lengths, 
but  ordinarily  the  best  quality  of  smooth  rubber-lined  hose  is  superior  to  the 
mill-hose,  having  less  frictional  resistance.  The  ring-nozzle  is  inferior  to  the 
smooth  nozzle  and  actually  delivers  less  water  than  the  smooth  nozzle.  For 
instance,  the  J6-in  ring-nozzle  discharges  the  same  quantity  of  water  as  a 
94-in  smooth  nozzle,  and  a  i-in  ring-nozzle  the  same  as  a  ^^-in  smooth  nozzle. 
Two  hundred  and  fifty  gallons  per  minute  is  a  good  standard  fire-stream  at 
80-lb  pressure  at  the  hydrant;  loo-lb  pressure  should  not  be  exceeded  except 
for  very  high  buildings  or  lengths  of  hose  exceeding  300  ft." 

Notes  on  the  Construction  of  Cylindrical  Wooden  Tanks* 

Material  should  be  either  cedar,  cypress,  juniper,  fir,  yellow  pine,  or  white 
pine,  free  from  imperfections  and  thoroughly  air-dry.  Clear  Louisiana  red, 
Gulf  cypress  makes  the  most  durable  tanks. 

Staves  and  Bottom  of  tanks  of  greater  capacities  than  15  000  gal  should  be 
made  of  2y>-'m,  dressed  to  about  2^  in,  stock  for  tanks  12  ft  and  not  exceeding 
16  ft  diameter  or  16  ft  deep.  For  larger  tanks  3-iR,  dressed  to  about  2%  in, 
stock  should  be  used.  For  smaller  tanks  2-in  stock  may  be  used.  Staves 
should  be  connected  about  one-third  the  distance  from  the  top  by  a  %-m 
dowel  to  hold  them  in  position  during  erection.  The  bottom  yjlanks  should  be 
dressed  on  four  sides,  and  the  edges  of  each  plank  should  be  bored  with  holes 
not  over  3  ft  apart  for  ^i-in  dowels.       • 

Taper.  The  batter  to  each  side  should  not  be  less  than  H  in  nor  more  than 
^  in  per  ft. 

Hoops  should  be  of  round  wrought  iron  or  mild  steel  of  good  quality.  Wrought 
iron  is  preferable  because  it  does  not  rust  as  easily  as  steel.  There  should  be  no 
welds  in  any  of  the  hoops.  Where  more  than  one  length  of  iron  is  necessary, 
lugs  should  be  used  to  make  the  joints;  and  when  more  than  one  piece  is  necessary 
the  several  pieces  constituting  one  hoop  should  be  tied  together  in  preparing  for 
shipment.  Hoops  for  fire-tanks  should  be  of  such  size  and  spacing  that  the  stress 
in  no  hoop  will  exceed  1 2  500  lb  per  sq  in  when  computed  from  the  area  at  root 
of  thread.  For  general  purposes,  a  stress  of  15  000  lb  per  sq  in  is  permissible. 
On  acccount  of  the  swelling  of  the  bottom  planks,  the  hoops  near  the  bottom 
may  be  subjected  to  a  stress  greater  than  that  due  to  the  water-pressure  alone; 
additional  hoops,  therefore,  should  be  provided.  For  tanks  up  to  20  ft  in  diam.- 
eter,  one  hoop  of  the  size  used  next  above  it  should  be  placed  around  the  bottom 
opposite  the  croze  and  not  counted  upon  as  withstanding  any  water-pressure. 
For  tanks  20  ft  or  more  in  diameter,  two  hoops,  as  above,  should  be  used. 
Hoops  with  UPSET  ends  must  not  be  used.  The  top  hoop  should  be  placed 
within  2  in  of  the  top  of  staves,  so  that  the  overflow-pipe  may  be  inserted  as  high 
as  possible.  Hoops  should  be  so  placed  that  the  lugs  will  not  be  in  a  vertical 
line.  No  hoop  should  be  less  than  %  in  in  diameter.  All  should  be  cleaned 
of  mill-scale  and  rust  and  painted  one  coat  of  red  lead,  lampblack  and  boiled  oil 
before  erecting. 

Note.  The  strength  of  a  tank  depends  chiefly  on  its  hoops.  Round  hoops 
are  specified  because  they  do  not  rust  rapidly;    a  slight  amount  of  rust  does 

*  These  notes  have  been  condensed  from  specifications  published  by  the  Inspection 
Department  of  the  Factory  Mutual  Fire  Insurance  Company,  31  Milk  Street,  Boston;  ft 
most  excellent  pamphlet.  '    J 


Wooden  Tanks 


1399 


not  have  the  same  weakening  effect  as  on  a  flat  hoop,  and  round  hoops  are  not 
likely  to  burst  when  the  tank  swells,  as  they  will  sink  into  the  wood. 

Spacing  of  Hoops.  The  hoops  should  be  spaced  so  that  each  one  will 
have  the  same  stress  per  square  inch,  and  no  space  should  be  greater  than  21  in. 
To  meet  this  requirement  the  hoops  must  be  spaced  quite  close  together  at 
the  bottom,  the  space   between  them  gradually  increasing  towards  the  top. 


^^1 


Tt- 


^^ 


Fig.  5.     Support  for  Bottom  of  Tank  - — 

Fig.  3  shows  the  proper  spacing  of  hoops  for  a  tank  18  ft  in 
diameter,  with  18-ft  staves.  The  spacing  for  seven  other 
sizes  of  tanks  is  given  in  the  pamphlet  referred  to.  It 
may  be  computed  by  the  following  formula: 

Spacing  of  hoops  in  inches  = 

2.6  X  diameter  in  feet  x  // 

For  strength  of  a  H-in  rod  use  3  750;  of  a  %-in  rod,  5  250; 
of  a  i-in  rod,  6  875;  and  of  a  ij^i-in  rod,  8  625. 

H  is  the  distance  from  surface  of  the  water  to  center  of 
hoop  in  feet. 

Example.  How  far  apart  should  i-in  hoops  be  placed,  at 
15  ft  2  in  from  top  of  tank,  on  a  tank  20  ft  diameter? 

6875 


Fig. 


T 

3.  Diagram 
of  Hoop-spacing 
for  Tanks 


Solution. 


Spacing  =  - 


=  8%  in 


2.6  X  20  X  15 

Lugs  should  be  as  strong  as  the  hoops.  A  lug  similar  to 
Fig.  4  is  simple  and  fulfils  the  requirement  for  strength. 
Malleable  lugs  are  required. 
Support.  The  weight  of  the  tank  should  be  supported  entirely  from  its 
bottom;  and  in  no  event  should  any  weight  come  on  the  bottom  of  the  staves. 
The  planks  upon  which  the  tank-bottom  rests  should  cover  at  least  one-fifth 
the  area  of  the  bottom,  should  be  not  over  18  in  apart,  and  of  such  thickness 
that  the  bottom  of  the  staves  will  be  at  least  i  in  from  the  floor  (see  Fig.  5). 

The  Discharge-Pipe  should  preferably  leave  the  bottom  of  the  tank  at  its 
center  and  extend  up  inside  of  the  tank  4  in,  to  allow  the  sediment  to  collect 
in  the  bottom  of  the  tank. 


1400      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 


The  Overflow-Pipe  should  be  placed  as  near  the  top  of  the  tank  as  possible, 
discharging  either  through  side  or  bottom,  as  may  be  desired.  An  overflow 
is  much  to  be  preferred  to  a  telltale,  as  the  latter  is  liable  to  get  out  of 
order. 

Heating.     Tanks  of  moderate  size  need  to  be  provided  with  some  means  to 
prevent  freezmg.     When  a  tank  is  in  an  enclosed  room,  as  in  a  mill-tower,  the 
best  method  is  to  keep  the  room  warm  by  a  coil  of  steam-pipe  with  a  return  to 
the  boiler-room.     A  covered  tank  out  of  doors  may  often  be  similarly  heated  by 
placing  the  steam-pipe  in  the  bottom  of  the  tank.     With  a  tank  located  on 
a  high  trestle,  or  at  a  distance  from  the  steam-supply,  it  is  often  impracti- 
cable to  arrange  a  return-pipe.     In  this  case  steam  may  be  blown  directly  into 
the  water  in  the  tank.     A  i-in  pipe  is  generally  sufficient  for  this  purpose.     It 
should  be  carried  to  the  top  of  the  tank  and  there  bend  over  and  dip  down- 
wards, so  that  its  outlet  is  about  i  ft  below  the  high-water  line.     A  check- 
valve  should  be  placed  in  this 
2  in.  horizontal  nailing  strips 
spaced  about  3  ft.  apart.;. 


:i  in.  ail  '^p.lce 


2  in.  ait  ^])<toe  \ 


Ifr 


2  in.  an  ^pace 


HZ 


2  Thicknesses  of  tai  i  ed  paper,     K  i".  Tongued  and 
around  each  box  except  outside,   grooved  sheathing. 
Fig.  6.     Method  of  Frostproofing  Pipes 


steam-pipe,  near  its  point  of 
discharge,  to  prevent  water 
being  drawn  back  by  siphon- 
action  when  the  steam  is  shut 
off.  The  water  in  fire-tanks 
must  be  kept  from  freezing  by 
means  of  a  water-heater  which 
either  heats  a  coil  in  the  tank, 
or  circulates  a  current  of  water 
through  the  tank. 

Frostproofing  for  Pipes. 
The  discharge-pipe  from  a 
tank  on  a  trestle,  or  from  one 
elevated  above  a  roof,  must 
be  protected  from  freezing. 
The  common  practice  is  to 
enclose  the  pipe  in  a  double, 
triple,  or  quadruple  box  made 
of  boards  and  tarred  paper,  as 


shown  in  Fig.  6.  If  steam  is  supplied  to  the  tank,  the  steam-pipe  is  carried 
inside  the  box.  In  New  England,  New  York  State  and  Canada  the  quadruple 
boxing  is  generally  used,  whereas  in  the  milder  regions  to  the  south  triple  or 
double  boxing  is  used.  The  boxing  should  always  be  carried  down  into  the 
ground  below  the  frost-line,  and  a  good  tight  joint  made  at  the  underside  of 
the  tank. 

Covers.  For  economy  in  heating  and  to  prevent  birds,  leaves,  etc.,  from 
getting  into  the  water,  all  out-of-door  tanks  should  be  covered.  A  double, 
cover  is  recommended  consisting  of  a  tight  flat  cover  made  of  matched  boards 
supported  by  joists  which  span  the  top  of  the  tank,  and  above  this  a  shingled, 
conical  roof.  To  prevent  the  covering  from  being  blown  off,  it  should  be  firmly 
fastened  to  the  top  of  the  tank  by  straps  of  iron.  In  order  to  keep  out  the 
wind  particular  attention  should  be  given  to  making  a  tight  joint  where  the 
roof  rests  on  the  top  of  the  staves. 

Scuttles  should  be  arranged  in  both  the  conical  and  flat  covers  to  give  access 
to  the  inside  of  the  tank  and  a  substantial,  permanent  ladder  erected  to  give 
easy  access  to  the  top  of  the  tank. 


Pumps  for  Fire-Streams 
Dimensions  of  Tanks  of  Standard  Sizes 


1401 


Size. 

Thickness  of 

0    M 

Approx- 
imate 

net 
capac- 
ity, 
gal 

Outside 
dimensions 

lumber  after 
being  machined 

51 

D 

m 

-c 

Hoops 

Aver- 
age 

diam- 
eter, 

ft     in 

Length 

of 
stave, 

ft 

Staves, 
in 

Bot- 
tom, 
in 

A— >!  ^ 

g 

Num- 
ber of 

Size, 
in 

A, 

in 

B, 

in 

c, 

in 

10  coo 

13      4 

12 

2H 

2\i 

3K2 

% 

2H 

II 

H 

15  000 

14      6 

14 

2% 

2M 

3'/2 

H 

2% 

14 

H 

20  000 

IS      6 

16 

2M 

2H 

3V2 

% 

2H 

h? 

H 

% 

25000 

17      6 

16 

2% 

2% 

3H 

H 

2% 

!   4 
12 

30000 

18      0 

18 

2% 

23/4 

3K2 

% 

2')  8 

4 
16 

SO  000 

22      0 

20 

2% 

2X1 

3H 

H 

2-)8 

4 

75  000 

24      6 

24 

2% 

2% 

3H 

H 

2% 

(  21 

I 

100  000 

28      6 

24 

2?.i 

2Y^ 

3K2 

H 

2% 

5 

29 

I 

Pumps  for  Fire 

taction  in  buildings, 
the  following  table. 


•Streams.     The  dimensions  of  steam-pumps  for  fire-pro- 
approved  by  the  Board  of  Underwriters,  can  be  found  in 


Underwriter  Steam  Fire-Pumps 

Size  in  inches 

1^ 

Size  in  inche? 

Over-all  dimen- 

.ti CI 

sions  of  largest 
pump  of  given 

.§1 

•*-  c 

U-,      ^ 

0) 

la 

0  0 
SB 

If 

Q  g 

0 

■ft 

,0 

bO 

Q 

m  ft 

ft 

n 

> 
1 

c2 

1 

1 

> 

1 

capacity 

ft  M 

1 

in 

in 

in 

h.p. 

in 

in 

in 

in 

in 

in 

in 

ft     in 

ft   in 

ft   in 

gal 

(14 

7 

12  1 
12^ 

Soo 

14 

7H 

80 

8 

6 

3 

4 

3 

2 

I 

9    ^^ 

5    2 

7    5 

250 

(16 

8 

10) 

750 

ji6 
1  16 

9 

12  j 
12  \ 

"5 

10 

7 

3K2 

4 

33'^2 

2M 

ii/i 

9    5 

5    2 

8    0 

375 

1000 

(18 

1  18H 

10 

101/2 

12 

10 

150 

12 

8 

4 

5 

4 

2-)^ 

iV^ 

10    8 

5  7^2 

8  10 

500 

1500 

20 

12 

16 

200 

14 

10 

5 

6 

5 

2I/2 

iH 

12    5 

5    7  . 

8  11 

750 

The  capacities  given  in  last  column  are  desirable;  but  in  case  the  suction-pipe  is  short 
and  the  lift  low,  a  tank  of  not  less  than  one-half  the  capacity  stated  may  sometimes  bo 
used. 


1402      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 

Notes  on  Steel  Tanks* 

Steel  Tanks  of  sizes  commonly  used  for  fire-protection  cost  from  40  to  100% 
more  than  wooden  tanks.  The  additional  cost  for  large  tanks  is  relatively 
less  than  for  small  tanks.  A  steel  tank  of  about  40  000-gal  capacity  or  over 
can  be  erected  on  a  steel  trestle  at  about  the  same  cost  as  a  wooden  tank,  since 
a  saving  can  be  made  in  the  cost  of  supports  by  making  a  hemispherical  or 
conical  bottom  to  the  steel  tank  and  supporting  the  tank  directly  on  the  legs 
of  the  trestle,  thus  saving  the  expense  of  horizontal  supporting  beams.  A  steel 
tank  is  superior  to  a  wooden  tank  for  the  following  reasons:  (i)  It  will  last 
for  an  indefinite  time  if  kept  thoroughly  painted  inside  and  out,  whereas  a 
wooden  tank  will  have  to  be  replaced  in  from  twelve  to  thirty  years,  usually 
in  about  fifteen  years;  (2)  it  will  be  absolutely  tight  when  once  well  erected 
and  properly  cared  for,  whereas  a  wooden  tank  will  shrink  and  leak  if  the  water 
gets  low;  (3)  it  will  not  be  at  all  Hkely  to  burst  suddenly,  if  originally  correctly 
designed,  even  if  painting  is  neglected,  for  experience  shows  that  a  few  spots 
will  first  rust  through  and  thus  show  the  weak  condition  by  small  leaks,  whereas 
a  wooden  tank,  if  neglected,  may  burst  its  hoops  suddenly  and  cause  serious 
damage.  The  objections  to  steel  tanks  are  that:  (i)  They  require  skilled  boiler- 
makers  to  erect  them,  thus  adding  considerable  to  the  cost  when  erected  at  a 
distance  from  a  boiler-shop;  (2)  they  are  more  difficult  to  protect  against  freez- 
ing; (3)  they  give  more  trouble  by  sweating  when  placed  in  a  mill-tower;  (4) 
they  deteriorate  rapidly  if  painting  is  neglected. 

Stresses  in  Cylindrical  Tanks. f  The  intensities  of  stresses  in  lb  per 
sq  in  found  in  cylindrical  tanks  are  as  follows:  A  tensile  stress  due  to  hj'dro- 
static  pressure  at  any  vertical  joint  or  section  of  the  shell  of  a  tank  filled  with 
water, 

S  =  62.5  IJD/{2  X  12  /)  =  2.6  HD/t 

A  compressive  stress  at  any  horizontal  joint  or  section,  due  to  the  weight  of 
the  stack, 

S  =  IV/iwD  X  12  0  =  0.026  W/Dt 

A  stress  at  any  horizontal  joint  rr  section,  tensile  on  the  windward  side  and 
compressive  on  the  leeward  side,  due  to  the  wind,  ^'2  =  0.106  M/DH.  (See 
Self-Sustaining  Steel  Chimneys,  page  1376.)  In  the  above  equation,  //  =  height 
of  tank  in  ft  above  section  considered,  D  =  diameter  in  ft,  t  =  thickness  of 
shell  in  in,  W  =  weight  of  tank  in  lb,  and  M  =  bending  moment  in  ft-lb.  The 
conditions  for  overturning  from  wind  are  most  severe  when  the  tank  is  empty. 
Stand-Pipes  wore  much  used  for  storage-reservoirs  at  one  time.  They 
usually  varied  from  12  to  30  ft  in  diameter  and  from  35  to  120  ft  in  height. 
A  tank  built  in  1889  at  Greenwich,  Conn.,  was  80  ft  in  diameter  and  30  ft  in 
height.  Its  capacity  was  i  300  000  gal.  A  stand-pipe  built  in  1876  at  Winona, 
Minn,  was  4  ft  in  diameter  by  210  ft  in  height.  The  steel  cylinder  was  sur- 
rounded by  a  masonry  tower.  A  long  list  of  failures,  mostly  due  to  faulty 
design,  are  recorded  against  the  stand-pipe.  Because  of  this  and  the  superior 
advantage  of  the  elevated  water-tower,  few  are  now  built.  General  Specifica- 
tions for  Elevated  Steel  Tanks  on  Towers,  and  for  Stand-pipes  (Trans.  Am.  Soc. 
C.  E.,  Vol.  64,  1909,  pages  548  to  566), and  General  Specifications  for  Steel,  Water, 
and  Oil-Tanks  (Proc.  Am.  Ry.  Eng.  Asso.,  vol.  13,  191 2),  are  both  reprinted  in 
Ketchum's  Structural  Engineers'  Handbook. 

*  Inspection  Department  of  the  Factory  Mutual  Insurance  Company,  Boston. 
t  From  Notes  by  Robins  Fleming. 


Capacities  of  Pipes  and  Cylinders 


1403 


Contents  in  Cubic  Feet  and  U.  S.  Gallons  of  Pipes  and  Cylinders  of 
Various  Diameters  and  One  Foot  in  Length 

I  gallon  =  231  cu  in.     i  cu  ft  =  7.4805  gal 


For 

[ft  in 

Fori 

ft  in 

Fori 

ft  in 

Diam- 

length 

Diam- 

length 

length 

Diam- 

eter in 

Cuft, 

U.S. 

eter  in 

Cuft, 

U.S. 

eter  in 

Cu  ft, 

U.  S. 

inches  * 

also 

gal 

inches 

also 

gal. 

inches 

also 

gal. 

area  in 

231 

area  in 

231 

area  in 

231 

sq  ft 

cu  in 

sqft 

cu  in 

sqft 

cu  in 

H 

0 . 0003 

0.0025 

6H 

0.248s 

1.859 

19 

1.969 

14-73 

Ma 

0 . 000s 

0 . 0040 

7 

0.2673 

1.999 

19K2 

2.074 

IS. SI 

H 

0.0008 

0.0057 

7H 

0.2867 

2.145 

20 

2.182 

16.32 

Via 

O.OOIO 

0.0078 

7H 

0.3068 

2.295 

20l/^ 

2.292 

17  15 

Vz 

0.0014 

0.0102 

7-Xi 

0.3276 

2.450 

21 

2.40s 

17.99 

He 

0.0017 

0.0129 

8 

0.3491 

2. 611 

21 1/^ 

2.521 

18.86 

% 

0.0021 

0.0159 

8K 

0.3712 

2.777 

22 

2.640 

19-75 

iMe 

0 . 0026 

0 . 0193 

m 

0.3941 

2.948 

22H 

2.761 

20.66 

% 

0.0031 

0 . 0230 

m 

0.4176 

3.125 

23 

2.885 

21.58 

i-Mo 

0.0036 

0 . 0269 

9 

0.4418 

3.30s 

23K2 

3  012 

22.53. 

y^ 

0.0042 

0.0312 

9H 

0.4667 

3.491 

24 

3.142 

23.50 

^•}U 

0.0048 

0.0359 

9K2 

0.4022 

3-682 

25 

3.409 

25  50 

1 

0.005s 

0.0408 

9% 

0.S185 

3.879 

26 

3.687 

27.58 

iH 

0.0085 

0.0638 

10 

0.54S4 

4.080 

27 

3.976 

29.74^  ~ 

lYi 

0.0123 

0.0918 

ioi/4 

O.S730 

4.286 

28 

4.276 

31-99 

m 

0.0167 

0.1249 

10 '/i 

0.6013 

4.498 

29 

4.587 

34-31       : 

2 

0.0218 

0.1632 

loYi 

0.6303 

4.71s 

30 

4.909 

36.72 

2H 

0.0276 

0.2066 

II 

0.6600 

4.937 

31 

5. 241 

39-21 

2K2 

0.0341 

0.25.50 

iiKi 

0.6903 

5.164 

32 

5.585 

41.78 

2H 

0.0412 

0.3085 

II 1/2 

0.7213 

5.396 

33 

5-940 

44-43 

3 

0.0491 

0.3672 

ii-M 

0.7530 

5.633 

34 

6.305 

47-16 

3H 

0.0576 

0.4309 

12 

0.78.54 

5.875 

35 

6.681 

49  98 

3'/2 

0.0668 

0.4998 

12K2 

0.8522 

6.375 

36 

7.069 

52.88 

M 

0.0767 

0.5738 

13 

0.9218 

6.895 

37 

7.467 

55.86 

4 

0.0873 

0.6528 

13K2 

0.9940 

7.436 

38 

7.876 

58.92 

4H 

0.0985 

0.7369 

14 

1.0690 

7.997 

39 

8.296 

62.06 

4H 

0.1134 

0.8263 

14K' 

I . 1470 

8.578 

40 

8.727 

65.28 

4% 

0.1 231 

0 . 9206 

IS 

1.2270 

9.180 

41 

9  168 

68.58 

S 

0.1364 

1.0200 

15K2 

I. 3100 

9.801 

42 

9.621 

71.97 

SH 

0.1503 

I. 1250 

16 

1.3960 

10.440 

43 

10.085 

75.44 

S'/2 

0.1650' 

I . 2340 

i6J^^ 

1.4850 

II. no 

44 

10. 559 

78.99 

sH 

0.1803 

1.3490 

17 

1.5760 

11.790 

45 

11.045 

82.62 

6 

0.1963 

I . 4690 

I7'/2 

I . 6700 

12.490 

46 

II. 541 

86.33 

6H 

0.2131 

I . S940 

18 

1.7680 

13.220 

47 

12.048 

90.13 

GVz 

0.2304 

1.7240 

iSVz 

1.8670 

13.960 

48 

12.566 

94.00 

*  Actual. 

To  find  the  capacity  of  pipes  greater  than  those  given,  look  In  the  table  for  a 
pipe  of  one-half  the  given  size  and  multiply  its  capacity  by  4,  or  one  of  one- 
third  its  size  and  multiply  its  capacity  by  9,  etc.  To  find  the  weight  of  water 
in  any  of  the  given  sizes,  multiply  the  capacity  in  cubic  feet  by  the  weight  of  a 
cubic  foot  of  water  at  the  temperature  of  the  water  in  the  pipe. 

To  find  the  capacity  of  a  cylinder  in  U.  S.  gallons,  multiply  the  length  by  the 
square  of  the  diameter  and  by  0.0034, 


1404      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 


Cylindrical  Vessels,  Tanks,  Cisterns,  Etc. 

Diameter  in  feet  and  inches,  area  in  square  feet,  and  U.  S.  gallons  capacity  for  i  ft 

in  dep:h 

I  gallon  =  231  cu  in  =  0.1337  cu  ft 


Diam, 

Area, 

Gal, 

i-ft 
depth 

Diam 

Area, 

Gal, 

i-ft 

depth 

Diam, 

Area, 

Gal. 

I-ft 
depth 

ft    in 

sqft* 

ft 

in 

sqft* 

ft    in 

sqft* 

0.785 

5.87 

5 

8 

25.22 

188.66 

19 

283.53 

2120.9 

I      I 

0.922 

6. 8  J 

5 

9 

^^5. 97 

194.25 

19    3 

291.04 

2177. I 

I      2 

1.069 

8.00 

5 

10 

26.73 

199.92 

19    6 

298.65 

2234.0 

I      3 

1.227 

9.18 

5 

II 

27  49 

205 . 67 

19    9 

306.35 

2291.7 

I      4 

1.396 

10.44 

6 

28.27 

211. 51 

20 

314  16 

2350.1 

I      5 

1.576 

11.79 

6 

3 

30.68 

229.50 

20    3 

322.06 

2409.2 

I      6 

1.767 

13.22 

6 

6 

33.18 

24S.23 

20    6 

330.06 

2469.1 

I      7 

1.969 

14.73 

6 

9 

35.78 

267.69 

20    9 

3.38.16 

2529.6 

I      8 

2.182 

16.32 

7 

3S.43 

287.83 

21 

346.36 

2591  0 

I      9 

2.405 

17-99 

7 

3 

41.28 

308.81 

21    3 

354  66 

2653.0 

I     10 

2.640 

19-75 

7 

6 

44-18 

330.48 

21    6 

363.05 

2715.8 

I     II 

2.88s 

21.58 

7 

9 

47.17 

352.88 

21    9 

371.54 

2779  3 

2 

3  142 

23.50 

8 

50.27 

376.01 

22 

380.13 

2843.6 

2      I 

3.409 

25.50 

8 

3 

53.46 

399.88 

22    3 

388.82 

2908.6 

2      2 

3.687 

27.58 

8 

6 

56.75 

424.48 

22    6 

397.61 

2974.3 

2      3 

3.976 

29.74 

8 

9 

60.13 

449.82 

22    9 

406.49 

3040 . 8 

2      4 

4.276 

31.99 

9 

63-62 

475.89 

23 

415-48 

3108.0 

2      5 

4.587 

34  31 

9 

3 

67.20 

502.70 

23    3 

424-56 

3175.9 

2      6 

4-909 

36.72 

9 

6 

70.88 

530.24 

23    6 

433.74 

3244.6 

2      7 

5  241 

39  21 

9 

9 

74  66 

558.51 

23    9 

443.01 

3314.0 

2      8 

5.585 

41.78 

10 

78.54 

587.52 

24 

452.39 

3384.1 

2      9 

5  940 

44.43 

10 

3 

82.52 

617.26 

24    3 

461.86 

3455.0 

2    10 

6.305 

47.16 

10 

6 

86.59 

647.74 

24    6 

471.44 

3526.6 

2    II 

6.681 

49.98 

10 

9 

90.76 

678.95 

24    9 

481. II 

3598.9 

3 

7.069 

52.88 

II 

9.5.03 

710.90 

25 

490.87 

3672.0 

3      I 

7.467 

55.86 

II 

3 

99-40 

743.58 

25    3 

500.74 

3745.8 

3      2 

7.876 

58.92 

II 

6 

103.87 

776.99 

25    6 

510.71 

38203 

3      3 

8.296 

62.06 

II 

9 

108.43 

811  14 

25    9 

520.77 

3895.6 

3      4 

8.727 

65.28 

12 

113.10 

846.03 

26 

530.93 

3971  6 

3      5 

9.168 

.68.58 

12 

3 

117.86 

881.65 

26    3 

541.19 

4048.4 

3      6 

9  621 

71.97 

12 

6 

122.72 

918.00 

26    6 

551.55 

4125.9 

3      7 

10.085 

75.44 

12 

9 

127.68 

955.09 

26    9 

562.00 

4204.1 

3      8 

10.5.59 

78.99 

13 

132.73 

992.01 

27 

572.56 

4283  0 

3      9 

11.045 

82.62 

13 

3 

137.89 

1031.5 

27    3 

588.21 

4362.7 

3      TO 

II. 541 

86.33 

13 

6 

143.14 

1070.8 

27    6 

593.96 

4443.1 

3     II 

12.048 

90.13 

13 

9 

148.49 

mo. 8 

27    9 

604.81 

4.S24.3 

12.566 

94.00 

14 

153.94 

1151.5 

28 

615.75 

4606.2 

4      I 

13.095 

97.96 

14 

3 

159.48 

"93  0 

28    3 

626.80 

4688.8 

4      2 

13.635 

102.00 

14 

6 

165.13 

1235.3 

28    6 

637.94 

4772.1 

4      3 

14.186 

106.12 

14 

9 

170.87 

1278.2 

28    9 

649.18 

4856.2 

4      4 

14.748 

110.32 

15 

176.71 

132 I. 9 

29 

660.52 

4941.0 

4      5 

15.321 

114  61 

15 

3 

182.65 

1366.4 

29    3 

671.96 

5026 . 6 

4      6 

15.90 

118.97 

15 

6 

1S8.69 

1411.5 

29    6 

683.49 

5112.9 

4      7 

16.50 

123.42 

15 

9 

194.83 

1457.4 

29    9 

695.13 

5199.9 

4      8 

17.10 

127.95 

16 

201.06 

1504. I 

30 

706.86 

5287.7 

4      9 

17.72 

132.56 

16 

3 

207.39 

155 I. 4 

30    3 

718.69 

5376.2 

4     10 

18.35 

137-25 

16 

6 

213  82 

1599.5 

30    6 

730.62 

5465.4 

4     II 

18.99 

142.02 

16 

9 

220.35 

1648.4 

30    9 

742.64 

5555.4 

19  63 

146.88 

17 

226.98 

1697.9 

31 

754.77 

5646.1 

5       I 

20  29 

151.82 

17 

3 

233.71 

1748.2 

31    3 

766.99 

5737.5 

5      2 

20.97 

156.83 

17 

6 

240.53 

1799.3 

31    6 

779  31 

5829.7 

5      3 

21.65 

161.93 

17 

9 

247.45 

1851.1 

31     9 

791-73 

5922.6 

S      4 

22.34 

167.12 

18 

254.47 

1903.6 

32 

804 . 25 

6016.2 

5      S 

23.04 

172.38 

18 

3 

261.59 

19.56.8 

32    3 

816.86 

6110.6 

5      6 

23.76 

177.72 

18 

6 

268.80 

2010.8 

32    6 

829.58 

6205.7 

5      7 

24.48 

183.15 

18 

9 

276 . 12 

2065.5 

842.39 

6301.5 

*  AI30  cubic  feet  for  i  ft  in  depth. 


Capacities  of  Cisterns  and  Tanks 


1405 


Capacity  of  Cisterns  and  Tanks 
Number  of  barrels  ^iH  gal)  in  cisterns  and  tanks 


Diameter,  ft 

Depth, 
ft 

5 

6 

7 

8 

9 

10 

II 

12 

13 

5 

23. 3 

33.6 

45.7 

59-7 

75.5 

93.2 

112. 8 

134.3 

157.6 

6 

28.0 

40.3 

54.8 

71.7 

90.6 

111.9 

135.4 

161. 1 

189. 1 

7 

32.7 

47-0 

64.0 

83.6 

105.7 

130.6 

158.0 

188.0 

220.6 

8 

37. 3 

53.7 

73.1 

95.5 

120.9 

149.2 

180.5 

214.8 

252.1 

9 

42. o 

60.4 

82.2 

107.4 

136.0 

167.9 

203 . 1 

241.7 

283.7 

10 

46.7 

67.1 

91.4 

119-4 

151.1 

186.5 

225.7 

268.6 

315.2 

II 

51.3 

73.9 

100.5 

131-3 

166.2 

205 . 1 

248.2 

295.4 

346.7 

12 

56.0 

80.6 

109.7 

143-2 

181.3 

223.8 

270.8 

322.3 

378.2 

13 

60.7 

87.3 

118. 8 

155.2 

196.4 

242.4 

293 -4 

349.1 

409.7 

14 

65.3 

94.0 

127.9 

167. 1 

211. 5 

261. 1 

315.9 

376.0 

441.3 

15 

70.0 

100.7 

137. 1 

1790 

226.6 

289.8 

338.5 

402.8 

472.8 

i6 

74-7 

107.4 

146.2 

191-0 

241.7 

298.4 

361 . 1 

429.7 

504.3 

17 

79.3 

114. 1 

155.4 

202.9 

256.8 

317.0 

383.6 

456.6 

535.8 

i8 

84.0 

120.9 

164.5 

214.8 

272.0 

335.7 

406.2 

483.4 

567.3 

19 

88.7 

127.6 

173.6 

226.8 

287.0 

354.3 

428.8 

510.3 

598.0 

20 

93.3 

134.3 

182.8 

238.7 

302.1 

373.0 

451.3 

537.1 

630.4 

Diameter,  ft 

Depth, 

• 

14 

15 

16 

17 

18 

19 

20 

21 

22 

5 

182.8 

209.8 

238.7 

269.5 

302.1 

336.6 

373.0 

411. 2 

451.3 

6 

219.3 

251.8 

286.5 

323-4 

362.6 

404.0 

447.6 

493.5 

541.6 

7 

255.9 

293.7 

334.2 

377.3 

423.0 

471.3 

522.2 

575.7 

631.9 

8 

292.4 

335.7 

382.0 

431.2 

483.4 

538.6 

596.8 

658.0 

722.1 

9 

329.0 

377.7 

429.7 

485.1 

543.8 

605.9 

671.4 

740.2 

812.4 

10 

365  5 

419.6 

477-4 

539.0 

604.3 

673.3 

746.0 

822.5 

902.7 

II 

402.1 

461.6 

525.2 

592.9 

667.7 

740.6 

820.6 

904.7 

992.9 

12 

438.6 

503.5 

572.9 

646.8 

725.1 

807.9 

895.2 

987.0 

1083.2 

13 

475.2 

545.5 

620.7 

700.7 

785.5 

875.2 

969.8 

IC69.2 

1173.5 

14 

511. 8 

587.5 

668.2 

754.6 

846.0 

942.6 

1044.4 

II51.5 

1263.7 

15 

548.3 

629.4 

716.2 

808.5 

906.4 

1009.9 

IIIQ.O 

1233.7 

1354.0 

i6 

584.9 

671.4 

773.9 

862.4/ 

966.8 

1077.2 

1193.6 

1315.9 

1444.3 

17 

621.4 

713.4 

811. 6 

916.3 

1027.2 

1044 . 6 

1268.2 

1398.2 

1534.5 

i8 

658.0 

755.3 

859.4 

970.2 

1087.7 

1211.9 

1342.8 

1480.4 

1624.8 

19 

694 -5 

797.3 

907.1 

1024. I 

1148.1 

1279.2 

1417.4 

1562.7 

1715.1 

20 

731. 1 

839.3 

954.9 

1078.0 

1208.5    1346.5 

1492.0 

1644.9 

1805.3 

Diameter,  ft 

Depth, 

23 

24 

25 

26 

27 

28 

29 

30 

5 

493.3 

537.1 

582 

8 

630.4 

679.8 

731.1 

784.2 

839.3 

6 

592.0 

644. 5 

699 

4 

756.5 

815.8 

877.3 

941. 1 

1007. I 

7 

690.6 

752.0 

815 

9 

882.5 

951.7 

1023.5 

1097.9 

1175.0 

8 

789 -3 

859.4 

932 

5 

1008.6 

1087.7 

1169.7 

1254.8 

1342.8 

9 

887.9 

966.8 

1049 

I 

1134.7 

1223.6 

1316.0 

I4II.6 

1510.7 

10 

986.6 

1074.2 

1165 

6 

1260.8 

1359.6 

1462.2 

1568.2 

1678.5 

II 

1085.2 

1181.7 

1282 

2 

1386.8 

1495.6 

1608.7 

1723.0 

1846.4 

12 

1183.9 

1289. I 

1398 

7 

1512.9 

1631.5 

1754.6 

1882.2 

2014.2 

13 

1282.6 

1396.5 

151S 

3 

1639.0 

1767.5 

1900.8 

2039.0 

2182.0 

14 

1381.2 

1503.9 

1 63 1 

9 

1765.1 

1903.4 

2047.1 

2195.9 

2343.9 

IS 

1479-9 

1611.4 

1748 

4 

1891 . I 

2039.4 

2193  3 

2352.7 

2517.8 

i6 

1578. 5 

1718.8 

1865 

0 

2017.2 

2175.4 

2339.5 

2509.6 

2685.6 

17 

1677.2 

1826.2 

1981 

6 

2143.3 

2311.3 

2485.7 

2666.4 

2853.5 

i8 

1775-9 

1933.6 

2098 

I 

2269.4 

2447.3 

2631.9 

2823.3 

3021.3 

19 

1874-5 

2041 . I 

2214 

7 

2395.4 

2583.2 

2778.1 

2980.1 

3189.2 

20 

1973.2 

2148.5 

2321 

2 

2521.5 

2719.2 

2924.4 

3137.0 

3357.0 

For  tanks  that  are  tapering,  measure  the  diameter  four-tenths  from  large  end. 


1406     Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 


Number  of  U.  S.  Gallons  in  Rectangular  Tanks 

For  One  Foot  in  Depth 

I  cu  ft  =  7-4805  gal 


Width, 
ft 


2.5 

3 

35 

4 

4.5 

S 

55 

6 

6.5 

7 


Length  of  tank,  ft 


29.92 


37-40 
46.75 


44-88 
56.10 
67.32 


52.36 
65.45 
78.54 
91.64 


67.32 
84.16 
100.99 
117.82 
134-65 
151.48 


74.81 
93-51 
112.21 
130.91 
149.61 
168.31 
187.01 


82.29 
102 . 80 
123-43 
144.00 
164-57 
185 . 14 
205.71 
226.28 


89.77 
112. 21 
134.65 
157.09 
179-53 
201 . 97 
224.41 
246.86 
269.30 


6.5 


97-25 
121.56 

145-87 
170.18 
194-49 
218.80 
243  II 
267.43 
291-74 
316.05 


104-73 
130.91 
157  09 
183-27 
209.45 
235-63 
261.82 
288.00 
314.18 
340.36 
366.54 


Width, 
ft 


2.5 

3 

3  5 

4 

4-5 

5 

5^5 

6 

6.5 

7 

7.5 

8 

8.5 

9 

9-5 
10 
10.5 
II 
II. 5 


Length  of  tank,  ft 


112. 21 
140.26 
168.31 
196.36 
224.41 
252.47 
280.52 
308.57 
336.62 
364.67 
392.72 
420.78 


134-65 
168.31 

202 . 97 
235-63 
269.30 
302.96 
336.62 
370.28 
403-94 
437-60 
471.27 
504-93 
538.59 
572.25 
605.92 


142.13 

177.66 
213.19 
248.73 
284.26 
319-79 
355-32 
390.85 
426.39 
461 . 92 
497-45 
532.98 
568.51 
604 . 05 
639.58 
675 


149.61 
187.01 
224.41 
261.82 
299 . 22 
336.62 
374-03 
411  43 
448.83 
486.23 
523  64 
561.04 
598.44 
635.84 
673 .25 
710.65 
748.05 


157.09 
196.36 
235  63 
274.90 
314  18 
353  45 
392.72 
432.00 
471 • 27 
510.54 
549-81 
589-08 
628.36 
667.63 
706 . 90 
746.17 
785-45 
824.73 


164-57 
205 . 71 
246.86 
288.00 
329- 14 
370.28 
41143 
452.57 
493-71 
534-85 
575-00 
617.14 
658.28 
690.42 
740.56 
781.71 
822.86 
864.00 
905.14 


172.05 
215.06 
258 . 07 
301 . 09 
344  10 
387.11 
430.13 
473.14 
516.15 
5.50.16 
602.18 
645 . 19 
688.20 
731.21 
774-23 
817.24 
860.26 
903.26 
946.27 
989.29 


179  53 

224.41 
269.30 
314- 18 
359  06 
403-94 
448.83 
493-71 
538.59 
583.47 
628.36 
673.24 
718.12 
703.00 
807.89 
852.77 
897-66 
942.56 
987 .43 
1032  3 
1077 . 2 


To  find  weight  of  water  in  pounds  at  62°  F.,  multiply  the  number  of  gallons 
by  8H. 

Example.  To  find  number  of  gallons  in  a  rectangular  tank  that  is  7.5  ft  by 
10  ft.,  the  water  being  4  ft  deep.  Look  in  the  extreme  left-hand  column  for 
7.5  and  opposite  to  this  in  the  column  headed  10  read  561.04,  which  being 
multiplied  by  4,  the  depth  of  water  in  the  tank,  gives  2244.2,  the  number  of 
gallons  required. 


Plumbing  and  Drainage  1407 

(2)    PLUMBING  AND  DRAINAGE 

Reliable  Rules  for  Plumbing  and  Drainage.  The  water-supply  of 
buildings,  including  the  apparatus  for  heating  water,  the  system  of  drainage 
and  sewage,  and  the  various  fixtures  connected  therewith,  are  installed  by  the 
plumber,  usually  in  accordance  with  specifications  prepared  by  the  architect 
and  subject  to  municipal  regulations.  An  efficient  and  safe  system  of  plumbing 
is  a  matter  of  vital  importance.  The  following  may  be  used  as  a  rehable  guide 
in  any  locality. 

Extracts  *  from  the  Rules  and  Regulations  of  the  Department  of 
Buildings  of  the  City  of  New  York,  Adopted  April  23,  19 12 

Definitions  of  Terms 

(i2)t  The  term  private  sewer  is  applied  to  main  sewers  that  are  not  con- 
structed by  and  under  the  supervision  of  the  Department  of  Sewers. 

(13)  The  term  house-sewer  is  applied  to  that  part  of  the  main  drain  or  sewer 
extending  from  a  jxiint  2  ft  outside  of  the  outer  wall  of  building-vault  or  area  to 
its  connection  with  public  sewer,  private  sewer  or  cesspool. 

(14)  The  term  house-drain  is  applied  to  that  part  of  the  main  horizontal 
drain  and  its  branches  inside  the  walls  of  the  building-vault  or  area  and  extend- 
ing to  and  connecting  with  the  house-sewer. 

(15)  The  term  soil-pipe  is  applied  to  any  vertical  line  of  pipe  extending 
through  roof,  receiving  the  discharge  of  one  or  more  water-closets  with  or  with- 
out other  fixtures. 

(16)  The  term  waste-pipe  is  applied  to  any  pipe,  extending  through  roof, 
receiving  the  discharge  from  any  fixtures  except  water-closets, 

(17)  The  term  vent-pipe  is  applied  to  any  special  pipe  provided  to  ventilate 
the  system  of  piping  and  to  prevent  trap-siphonage  and  back-pressure. 

Materials  and  Workmanship 
Soil-Pipe  and  Vent-Pipe.     (19)  All  cast-iron  pipes  and  fittings  must  be 
uncoated,  sound,  cylindrical,  and   smooth,  free    from  cracks,  sand-holes  and 
other  defects,  and  of  uniform  thickness  and  of  the  grade  known  in  commerce  as 

EXTRA  heavy. 

(20)  Pipe,  including  the  hub,  shall  weigh  not  less  than  the  following  average 
weights  per  linear  foot:  » 


Diameters 

Weights  per 

linear  foot, 

lb 

2  in                                                                                               

13 

17 

20 

27 

33H 

45 

54 

3  in              ,   .           

5  in          .   .   

7  in                 .              

8  in                                                                          

12  in                                                                          

*  These  numbered  paragraphs,  from  (12)  to  (174).  extracts  from  Building  Regulations, 
are  unedited,  except  in  those  details  which  affect  typographical  uniformity  throughout 
the  book.     Editor-in-chief. 

t  Paragraph-numbers  are  the  same  as  those  in  the  Official  Regulations.  Missing  num- 
bers indicate  Daraeraohs  Durooselv  omitt«d. 


1408      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 

(22)  All  joints  must  be  made  with  picked  oakum  and  molten  lead  and  be  made 
gas-tight.  Twelve  (12)  oz  of  line,  soft  pig  lead  must  be  used  at  each  joint  for 
each  inch  in  the  diameter  of  the  pipe. 

(24)  Wrought-iron  and  steel  water-pipes,  vent-pipes,  waste-pipes  and  soil- 
pipes  must  be  galvanized. 

(29)  All  brass  pipe  for  soil-pipes,  waste-pipes,  and  vent-pipes  and  solder-nip- 
ples must  be  thoroughly  annealed,  seamless-drawn,  brass  tubing  of  standard 
iron-pipe  gauge. 

Lead  Waste-Pipes.  (37)  The  use  of  lead  pipes  is  restricted  to  the  short 
branches  of  the  soil-pipes  and  waste-pipes,  iiends,  traps,  and  roof-connections 
of  inside  leaders.  Short  branches  of  lead  pipe  shall  be  construed  to  mean  not 
more  than 

8  ft  of  1 3. 2 -in  pipe 
5  ft  of  2-in  pipe 
2  ft  of  3 -in  pipe 
2  ft  of  4-in  pipe 

(sS)  All  connections  between  lead  pipes  and  between  lead  and  brass  or  copper 
pipes  must  be  made  by  means  of  wiped  solder  joints. 

(39)  All  lead  waste,  soil,  vent,  and  flush-pipes  must  be  of  the  best  quality, 
known  in  commerce  as  D,  and  of  not  less  than.the  following  weights  per  linear  foot: 


Diameters 


Weights  per 

linear  foot, 

lb 


iH  in  (for  flush-pipes  only) . 
i^^  in 

2  in 

3  in 

4  and  4^  in 


2H 
3 
4 
6 


(40)  All  lead  traps  and  bends  must  be  of  the  same  weights  and  thicknesses 
as  their  corresponding  pipe-branches.  Sheet  lead  for  roof-flashings  mu.st  be 
6-lb  lead  and  must  extend  not  less  than  6  in  from  the  pipe,  and  the  joint  made 
water-tight. 

(41)  Copper  tubing  when  used  for  inside  leader  roof-connections  must  be' 
seamless-drawn  tubing  not  less  than  22  gauge,  and  when  used  for  roof -flashings 
must  be  not  less  than  18  gauge. 

Yard,  Area  and  Other  Drains 

(54)  All  yards,  areas,  and  courts  exceeding  15  sq  ft  in  area  must  be  drained 
into  the  sewer.  A  shaft  open  at  the  top  and  not  exceeding  25  sq  ft  in  area,  and 
which  cannot  be  connected  in  back  of  a  leader,  yard,  court,  or  area  drain-trap, 
may  be  drained  into  a  publicly  placed,  water-supplied,  properly  tapped  and 
vented  slop-sink. 

(59)  These  drains,  when  sewer-connected,  must  have  connections  not  less 
than  3  in  in  diameter.  They  should  be  controlled  by  one  trap,  the  leader-trap 
if  possible. 

Leaders 

(60)  Every  building  shall  be  kept  provided  with  proper  metallic  gutters  and 
rain-leaders  for  conducting  water  from  all  roofs  in  such  manner  as  shall  protect 
the  walls  and  foundations  of  said  buildings  from  injury.  In  no  case  shall  the 
water  from  any  rain-leader  be  allowed  to  flow  upon  the  sidewalk  or  adjoining 
property,  but  the  same  shall  be  conducted  by  proper  pipes  to  the  sewer.  If 
there  be  no  sewer  in  the  street  upon  which  the  buildings  front,  then  the  water 


House-Sewer  and  Fresh-Air  Inlet 


1409 


from  said  leaders  shall  be  conducted  by  proper  pipes  below  the  surface  of  the 
sidewalk  to  the  street-gutter,  or  may  be  conducted  by  extra-heavy  cast-iron 
pipe  to  a  leeching  cesspool  located  at  least  20  ft  from  any  building.  No  plumb- 
ing fixtures  shall  discharge  into  a  leeching  cesspool. 

(61)  Inside  leaders  must  be  made  of  cast  iron,  wrought  iron,  or  steel,  with 
roof-connections  made  gas-tight  and  water-tight  by  means  of  a  heavy  lead  or 
copper-drawn  tubing  wiped  to  a  brass  ferrule  or  nipple  calked  or  screwed  into 
the  pipe. 

(62)  Outside  leaders  may  be  of  sheet  metal,  but  they  must  connect  with  the 
house-drain  by  means  of  a  cast-iron  pipe  extending  vertically  5  ft  above  the 
grade-level. 

(63)  Leaders  must  be  trapped  with  cast-iron  running  traps  so  placed  as  to 
prevent  freezing. 

(64)  Rain-water  leaders  must  not  be  used  as  soil-pipes,  waste-pipes  or  vent- 
pipes,  nor  shall  any  such  pipe  be  used  as  a  leader. 

The  House-Sewer,  House-Drain,  House-Trap  and  Fresh-Air 
Inlet 

(70)  The  house-drain  must  properly  connect  with  the  house-sewer  at  a  point 
2  ft  outside  of  the  outer  front  vault  or  area-wall  of  the  building.  An  arched  or 
other  proper  opening  in  the  wall  must  be  provided  for  the  drain  to  prevent 
damage  by  settlement. 

(71)  The  house-drain  if  above  the  cellar-floor,  must  be  supported  at  inter- 
vals of  10  ft  by  8-in  brick  piers  or  suspended  from  the  floor-beams,  or  be  other- 
wise properly  supported  by  heavy  iron-pipe  hangers  at  intervals  of  not  more 
than  10  ft. 

(72)  No  steam-exhaust,  boiler  blow-ofT,  or  drip-pipe  shall  be  connected  with 
the  house-drain.  Such  pipes  must  first  discharge  into  a  proper  condensing  tank, 
and  from  this  a  proper  outlet  to  the  house-sewer  outside  of  the  building  must  be 
provided.  In  low-pressure  steam-systems  the  condensing  tank  may  be  omitted, 
but  the  waste-connection  must  be  otherwise  as  above  required. 

(73)  The  house-drain  and  house-sewer  must  be  run  as  direct  as  possible, 
with  a  fall  of  at  least  H  in  per  ft,  all  changes  in  direction  made  with  proper 
fittings,  and  all  connections  made  with  Y  branches  and  one-eighth  and  one-six- 
teenth bends. 

Size  of  House-Sewer.  (74)  The  house-sewer  and  house-drain  must  be  at 
least  4  in  in  diameter  where  water-closets  discharge  into  them..  Where  rain- 
water discharges  into  them,  the  house-sewer  and  house-drain  up  to  the  leader- 
connections  must  be  in  accordance  with  the  following  table: 


Diameter  of 

For  a  fall  of 

For  a  fall  of 

Yi  in  per  foot. 

\i  in  per  foot. 

pipe, 

sq  ft  of  drainage- 

sq  ft  of  drainage- 

area 

area 

3 

I  200 

I  500 

4 

2  500 

3  200 

5 

4500 

6000 

6 

8000 

10  000 

7 

12  400 

15  600 

8 

18  000 

22  500 

9 

25  000 

31  500 

10 

41  000 

59000 

12 

69000 

98  000 

1410       Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 

(75)  Full-size  Y  and  T-branch  fittings  for  hand-hole  clean-outs  must  be  pro- 
vided where  required  on  house-drain  and  its  branches.  No  clean-out  need  be 
larger  than  6  in  in  diameter. 

(76)  An  iron  running-trap  must  be  placed  on  the  house-drain  near  the  wall 
of  the  house,  and  oji  the  sewer-side  of  all  connections,  except  a  Y  fitting  used  to 
receive  the  discharge  from  an  automatic  sewage-lift,  oil-separator  or  a  drip- 
pipe  where  one  is  used.  If  placed  outside  the  house  or  below  the  cellar-floor 
it  must  be  made  accessible  in  a  brick  manhole,  the  walls  of  which  must  be  S  in 
thick,  with  an  iron  or  flagstone  cover.  When  outside  the  house  it  must  never 
be  less  than  3  ft  below  the  surface  of  the  ground. 

(79)  A  FRESH-AIR  INLET  must  be  Connected  with  the  house-drain  just  inside 
of  the  house-trap  and  extended  to  the  outer  air,  terminating  with  a  return-bend, 
with  open  end  i  ft  above  the  grade  at  most  available  point,  to  be  determined  by 
the  superintendent  of  buildings  and  shown  on  plans.  The  fresh-air  inlet-pipe 
must  be  of  the  same  diameter  as  the  house-drain.  An  automatic  device  approved 
by  the  superintendent  of  buildings  may  be  used  when  set  in  a  manner  satis- 
factory to  him. 

Note.  The  fresh-air  inlet  and  running  trap  prescribed  by  Sections  76  and  79 
are  not  required  in  many  cities,  and  it  is  better  to  omit  them  where  not  re- 
quired. 

Soil-Pipes,  Waste-Pipes  and  Vent-Pipes 

(8t)  All  main,  soil,  waste  or  vent-pipes  must  be  of  iron,  steel,  or  brass. 
(90)  The  diameters  of  soil-pipes  and  waste-pipes  must  not  be  less  than  those 
given  in  the  following  table: 


Main  soil-pipes 4  in 

Main  soil-pipes  for  water-closets  on  five  or  more  floors 5  in 

Branch  soil-pipes 4  in 

Main  waste-pipes 2  in 

Main  waste-pipes  for  kitchen-sinks  on  five  or  more  floors 3  in 

Branch  waste-pipes  for  laundry-tubs iH  in 

When  set  in  ranges  of  three  or  more 2  in 

Branch  waste  for  kitchen-sinks 2  in 

Branch  waste  for  urinals 2  in 

Branch  waste  for  other  fixtures 1 1 2  in 


(97)  The  SIZES  OF  VENT-PIPES  throughout  must  not  be  less  than  the  follow- 
ing: 

For  main  vents,  2  in  in  diameter;  for  water-closets  on  three  or  more  floors, 
3  in  in  diameter;  for  other  fixtures  on  less  than  seven  floors,  2  in  in  diameter; 
3-in  vent-pipe  will  be  permitted  for  less  than  nine  stories;  for  more  than  eight 
and  less  than  sixteen  stories,  4  in  in  diameter;  for  more  than  fifteen  and  less 
than  twenty-two  stories,  5  in  in  diameter;  for  more  than  twenty-one  stories  the 
size  of  vent-pipe  shall  be  determined  by  the  superintendent  of  buildings. 

For  fixtures  other  than  water-closets  and  slop-sinks  and  for  more  than  eight 
stories,  vent-pipes  may  be  i  in  smaller  than  above  stated. 

Traps 

(loi)  Every  fixture  must  be  separately  trapped  by  a  water-sealing  trap  placed 
as  close  to  the  fixture-outlet  as  possible  and  no  trap  shall  be  placed  more  than 
2  ft  from  any  fixture. 


Water-closets  1411 

(102)  A  set  of  not  more  than  three  wash-trays  may  connect  with  a  single  trap, 
or  into  the  trap  of  an  adjoining  sink,  provided  both  sink  and  tub  waste-outlets 
are  on  the  same  side  of  the  waste-line  and  the  sink  is  nearest  the  line.  When  so 
connected  the  waste-pipe  from  tlie  wash-trays  must  be  branched  in  below  the 
water-seal. 

(103)  The  discharge  from  any  fixture  must  not  pass  through  more  than  one 
trap  before  reaching  the  house-drain. 

(109)  All  earthenware  traps  must  have  approved  heavy  brass  floor-plates 
properly  secured  to  the  branch  soil-pipe  and  bolted  to  the  trap-flange  and  the 
joint  made  gas-tight.  The  use  of  rubber  washers -for  floor-connections  is  pro- 
hibited. All  floor-flanges  must  be  set  in  place  and  inspected  before  any  water- 
closet  is  set  thereon. 

(no)  No  trap  shall  be  placed  at  the  foot  of  main  soil-  and  waste-pipe  lines. 

(112)  The  sizes  for  traps  must  not  be  less  than  those  given  in  the  following 
table: 


Traps  for  water-closets 4  in  in  diam. 

Traps  for  slop-sinks 2  in  in  diam. 

Traps  for  kitchen-sinks 2  in  in  diam. 

Traps  for  wash-trays 2  in  in  diam. 

Traps  for  urinals 2  in  in  diam. 

Traps  for  shower-baths 2  in  in  diam. 

Traps  for  other  fixtures i V^  in  in  diam. 


Traps  for  leaders,  areas,  floor  and  other  drains  must  be  at  least  3  in  in  diam- 
eter. 

Water-Closets 

(124)  In  tenement-houses,  lodging-houses,  factories,  workshops,  and  all 
public  buildings  the  entire  water-closet  apartment  and  side  walls  to  a  height 
of  6  in  from  the  floor,  except  at  the  door,  must  be  made  water-proof  with  asphalt, 
cement,  tile,  metal,  or  other  water-proof  material  as  approved  by  the  superin- 
tendent of  buildings. 

(127)  The  general  water-closet  accommodation  of  any  building  cannot  be 
placed  in  the  cellar  nor  can  any  water-closet  be  placed  outside  of  a  building, 
except  to  replace  an  existing  water-closet. 

(130)  In  all  sewer-connected  occupied  buildings  there  must  be  at  least  one 
water-closet,  and  there  must  be  additional  closets  so  that  there  wiU  never  be 
more  than  fifteen  persons  per  closet. 

(123)  In  lodging-houses  there  must  be  one  water-closet  on  each  floor,  and 
when  there  are  more  than  fifteen  persons  on  a  floor,  there  must  be  one  additional 
water-closet  for  every  fifteen  additional  persons  or  fraction  thereof. 

(135)  Water-closets  and  urinals  must  never  be  connected  directly  with  or 
flushed  from  the  water-supply  pipes,  except  when  flushometer-valves  are  used, 

(139)  Iron  water-closet  and  urinal-cisterns  and  automatic  water-closets 
and  urinal-cisterns  are  prohibited  unless  approved  by  the  superintendent  of 
buildings. 

(140)  The  copper  lining  of  water-closets  and  urinal-cisterns  must  not  be  lighter 
than  To-oz  copper. 

(141)  Water-closet  flush-pipes  must  not  be  less  than  iH  in  and  urinal  flush- 
pipes  I  in  in  diameter,  and  if  of  lead  must  not  weigh  less  than  2H  lb  and  2  lb 
per  lin  ft.    Flush-couplings  must  be  of  full  size  of  the  pipe. 


1112      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 

Sinks  and  Wash-Tubs 

(147)  In  all  houses  sinks  must  be  entirely  open,  on  iron  legs  or  brackets, 
without  any  enclosing  woodwork. 

(148)  Wooden  wash-tubs  are  prohibited,  except  when  used  in  hotels,  restau- 
rants or  bottling  establishments  for  washing  dishes  or  bottles.  Cement  or 
artificial  stone  tubs  will  not  be  permitted  unless  approved  by  the  superintendent 
of  buildings. 

Testing  the  Plumbing-System 

(171)  The  entire  plumbing  and  draining-system  within  the  building  must  be 
tested  by  the  plumber,  in  the  presence  of  a  plumbing  inspector,  under  a  water- 
test.  All  pipes  must  remain  uncovered  in  every  part  until  they  have  success- 
fully passed  the  test.  The  plumber  must  securely  close  all  openings  as  directed 
by  the  inspector  of  plumbing.  The  use  of  wooden  plugs  for  this  purpose  la 
prohibited. 

(172)  The  water- test  will  be  applied  by  closing  the  lower  end  of  the  main 
house-drain  and  filling  the  pipes  to  the  highest  opening  above  the  roof  with 
water.  The  water-test  shall  include  at  one  time  the  house-drain  and  branches, 
all  vertical  and  horizontal  soil,  waste  and  vent  and  leader-lines  and  all  branches 
therefrom  to  point  above  the  surface  of  the  finished  floor  and  beyond  the  fin- 
ished face  of  walls  and  partitions.  If  the  drain  or  any  part  of  the  system  is  to 
be  tested  separately,  there  must  be  a  head  of  water  at  least  6  ft  above  all  parts 
of  the  work  so  tested,  and  special  provision  must  be  made  for  including  all 
joints  and  connections  in  at  least  one  test. 

(17,3)  After  the  completion  of  the  plumbing-work,  in  any  new  or  altered 
building  and  before  the  building  is  occupied,  a  final  smoke-test  must  be  applied 
in  the  presence  of  the  plumbing-inspector.  Except  that  for  a  building  not  over 
six  stories  in  height,  a  peppermint-test  may  be  apphed. 

(174)  The  material  and  labor  for  the  tests  must  be  furnished  by  the  plumber. 
Where  the  peppermint-test  is  used,  2  oz  of  oil  of  peppermint  must  be  provided 
for  each  line  up  to  five  stories  and  cellar  in  height,  and  an  additional  ounce  of 
oil  of  peppermint  must  be  provided  for  each  line  when  lines  are  more  than  five 
stories  in  height. 

Traps 

A  trap  is  a  device  which  permits  the  free  passage  of  liquids  through  it,  and 
also  of  any  solid  matters  that  may  be  carried  by  the  liquid,  while  at  the  same 
time  preventing  the  passage  of  air  or  gas  in  either  direction.  Traps  used  for 
plumbing  purposes  are  shaped  so  that  an  amount  of  water  sufficient  to  close  the 
passage  and  prevent  the  passage  of  air  will  stand  in  them  at  all  times.  The 
principle  of  the  common  trap  is  shown  in  Fig.  7.  The  pipe  T  receives  the  waste 
from  a  sink  or  wash-basin,  while  the  lower  end  B  connects  with  the  sewer. 
Sewer-gas  rises  in  pipe  B,  but  is  prevented  from  passing  to  the  fixture  by  the 
water  which  stands  in  the  trap.  The  depth  of  water  through  which  gas  must 
pass  to  efi'ect  a  passage  is  termed  the  watek-seal.  The  water-seal  in  the  trap, 
Fig.  7,  is  the  distance  S.  All  plumbing-pipes  which  connect  with  a  sewerage- 
system  require  to  be  trapped  to  prevent  sewer-gas  from  passing  through  them 
to  the  fixture  and  into  the  room  in  which  the  fixture  is  located. 

Ventilation  of  Traps.  When  a  considerable  body  of  water  rushes  down 
through  a  pipe  it  forms  a  suction,  and  if  the  pipe  is  made  air-tight,  this  suction 
is  often  sufficient  to  prevent  enough  water  remaining  in  the  trap  to  form  a  seal, 
thus  leaving  an  opening  for  the  passage  f  1  sewer-gas,  as  in  Fig.  8.  By  connecting 
the  upper  bend  of  a  trap  with  the  outs' de  air  by  means  of  a  pipe,  as  at  F,  Fig.  8^   ,| 


Traps 


1413 


the  suction  will  be  stopped,  and  the  water  in  the  pipe  T  will  not  fall  below  the 
level  of  the  outlet  at  h.  Several  non-siphoning  traps  have  been  patented  for 
the  purpose  of  obviating  the  necessity  of  back-venting,  but  they  are  used  to  a 
comparatively  limited  extent.    There  are  also  several  varieties  of  back-pressure 


Fig.  7.    Water-seal  of  Trap 


Fig.  8.     Water-trap  Unsealed 


traps,  designed  to  prevent  the  sewage  from  flowing  back  into  the  house-drain. 
These  are  in  the  nature  of  check-valves,  and  are  used  principally  in  seaport- 
towns  where  tide- water  might  possibl}'  force  the  sewage  back.  The  more  com- 
mon shapes  of  lead  traps  used  in  plumbing,  with  their  trade  names,  are  showii 


Half  S  y 

or  P  /A  V 


^ 


Fig.  9.    Types  of  Traps 


in  Fig.  9.  The  same  shapes  are  also  made  of  cast  iron.  The  pipes  marked  V 
are  the  vent-connections.  The  drum-trap  shown  in  Fig.  10  has  a  deeper  seal 
than  those  shown  in  Fig.  9,  and  is  commonly  used  under  kitchen-sinks,  bath-tubs 
and  wash-trays.  Drum-traps  are  not  easily  siphoned,  even  when  not  vented. 
The  traps  for  water-closets  are  commonly  formed  in  the  fixture. 


1414     Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 

Grease-Traps.  The  waste-water  from  kitchen-sinks  always  contains  con- 
siderable grease,  which  if  permitted  to  enter  the  soil-pipe  system  is  liable  to  clog 
the  pipes  by  adhering  to  the  walls.  In  certain  localities  grease  gives  much  more 
trouble  than  in  others,  due  to  the  chemical  composition  of  the  water.  In  Col- 
orado and  many  other  places  it  is  necessary  to  connect  the  waste  from  kitchen- 


^Top  of  Ground 


Fig.  10.    Drum-trap 


Fig.  11.     Outdoor  Grease-trap 


sinks  with  a  large  grease-trap,  which  collects  and  holds  the  grease,  but  permits 
the  water  to  pass  into  the  sewer  system.  After  a  time  the  accumulated  grease 
fills  the  trap  and  must  be  removed.  On  account  of  this  it  is  desirable  to  use  a 
large  trap,  and  whenever  possible  it  should  be  placed  underground,  just  outside 
the  house,  and  as  near  to  the  sink  as  practicable.     Grease-traps  to  be  placed 

underground  are  commonly  made  of 
24-in  vitrified  drain-tile  or  cement  pipe, 
and  should  be  about  4  ft  deep.  They 
may  also  be  built  of  brick  in  cement 
mortar.  Fig.  11  shows  a  section 
■J TT — ^^        Q      <  I   /  through   such    a   grease-trap   and   the 

^J     ^    [j---"^^y'---*-T4-'-'-ir--  "^^^^  ^"^  outlet-pipes.     When  the  sink 

<'.^  Or  ^  v.^zc^^-.r-r-  <^,  <:  is  in  a  basement  or  an  upper  story,  or 

when  the  building  occupies  the  entire 
lot,  the  grease-trap  must  be  placed 
under  the  sink.  When  so  placed,  a 
round  lead  trap  12  or  14  in  in  diameter 
may  be  used,  with  a  large  trap-screw 
in  the  top  for  removing  the  grease. 
Fig.  12  shows  a  section  through  such  a 
trap  and  the  way  in  which  the  connec- 
tions should  be  made.  A  better  form 
Some  city  ordinances  require  that  inside 


Fig.  12.    Lead  Grease-trap 


of  grease-trap  is  made  of  ca.st  iron. 

grease-traps  shall  have  a  chiUing-jacket  for  the  purpose  of  more  perfectly 
separating  the  grease  and  thus  preventing  any  of  it  from  entering  the  waste- 
pipes.  To  be  effective,  a  grease-trap  must  have  a  capacity  of  at  least  twice 
the  amount  of  greasy  water  that  will  be  discharged  into  it  at  any  one  time. 


Supply-Pipes  and  House-Tanks  1415 

Supply-Pipes.  These  may  be  of  lead,  brass,  galvanized  iron,  tin-lined  lead, 
or  block  tin.  Lead  pipe  offers  the  least  resistance  to  the  flow  of  water,  is  easily 
bent  to  suit  any  situation,  and  easy  curves  are  readily  made.  It  is  generally 
considered  more  durable  underground  than  galvanized-iron  pipe.  The  grade 
known  a.s  A,  or  strong,  is  the  lightest  that  should  ever  be  used,  and  when  the 
supply  is  taken  from  city  mains,  in  which  there  is  a  considerable  pressure,  A  A, 
or  extra-strong  pipe,  should  be  used.  Galvanized-iron  pipe  is  probably  more 
extensively  used  than  any  other  material  for  water-supply  pipes  in  buildings, 
except  where  nickel-plated  pipe  is  required,  in  which  case  brass  piping  is  com- 
monly used.  Brass  pipe  used  for  water-supply  should  be  what  is  known  as  iron- 
pipe  SIZE.  Brass  piping  is  preferable  to  galvanized  iron  or  lead  for  conveying 
hot  water,  and  is  largely  used  in  the  better  class  of  buildings.  Tin-hned  iron 
and  lead  pipes  and  pipes  of  block  tin  are  usually  considered  as  offering  the 
greatest  resistance  to  corrosion  or  chemical  action,  and  should  always  be  used 
for  conveying  ale,  beer  and  other  liquors.  Tin-lined  iron  pipe  is  made  by  pouring 
melted  tin  into  a  wrought-iron  pipe.  While  in  a  fluid  state  the  tin  is  inseparably 
united  to  the  iron,  and  the  result  is  one  solid  pipe  composed  of  two  metals  which 
CANNOT  BE  TORN  APART.  It  IS  essentially  different  from  iron  pipe  merely 
dipped  in  tin,  and  immeasurably  superior  to  iron  pipe  lined  with  a  separate 
tin  pipe  that  will  become  detached.  Its  fittings  are  lined  with  tin  to  match. 
Hot  water  will  not  injure  it,  rats  will  not  gnaw  it,  and  thieves  will  not  cut  it 
out.  Either  hot  or  cold  water  may  stand  in  block-tin  pipes  and  yet  be  drawn 
from  them  pure  and  free  from  poison  or  rust.  Lead-lined  pipe  is  made  in  the 
same  way  and  insures  delivering  the  water  to  the  house  just  as  it  comes  from  the 
mains  unchanged  by  the  chemical  action  which  often  results  from  contact  with' 
wrought-iron  pipe. 

Seamless-Drawn  Benedict  Nickel  Tubing  is  used  to  some  extent  for  the 
exposed  plumbing-pipes  in  high-class  residences,  ofTice  and  public  buildings. 
Being  pure  white  metal  throughout  it  cannot  rub  or  wear  brassy  or  become 
discolored.  It  is  made  in  all  the  regular  iron-pipe  sizes,  and  necessary  fittings 
are  supplied  of  the  same  metal.* 

House-Tanks.  Where  the  pressure  in  the  street-mains  is  not  great  enough 
to  furnish  a  sufficient  volume  of  water  for  supplying  the  fixtures  at  all  times,  or 
in  cases  of  a  private  water-supply,  a  tank  should  be  placed  in  the  attic,  or  ele- 
vated at  least  6  ft  above  the  highest  fixture  to  be  supplied.  In  some  cases  the 
fixtures  in  the  lower  story  are  supplied  direct  from  the  street  mains,  while  those 
in  the  upper  story  are  supplied  from  a  tank.  The  advantage  of  a  tank  is  that  it 
will  fill  gradually  from  a  very  small  stream,  and  thus  form  a  reservoir  from 
which  a  larger  volume  can  be  drawn  in  a  shorter  space  of  time  than  could  be 
obtained  direct  from  the  service-pipes.  Storage-tanks  should  always  be  pro- 
vided with  an  overflow-pipe  of  ample  size  and  when  supplied  from  the  street- 
mains  the  supply  should  be  controlled  by  a  ball-cock  and  float.  Storage-tanks 
of  moderate  size  are  preferably  made  of  wood  lined  with  planished  or  tinned 
copper.  Sheet  lead,  zinc  or  galvanized  iron  should  not  be  used  for  lining  tankij 
containing  water  for  drinking  or  cooking  purposes,  and  are  not  as  durable  as 
copper,  even  when  the  effect  on  the  water  need  not  be  considered. 

The  Size  of  Tank  Required  will  depend  largely  upon  the  character  of  the 
supply.  Tanks  supplied  from  the  street-main  in  which  the  pressure  is  fairly 
constant  need  not  have  a  capacity  exceeding  i6o  gal.  W^here  the  water  is 
pumped  into  the  tank  by  a  windmill  or  hot-air  engine,  the  tank  should  have  a 
capacity  sufiicient  for  a  three  or  four  days'  supply  at  least. 

*  For  further  information  consult  the  Benedict  &  Burnham  Manufacturing  Company, 
.Waterbury,  Conn. 


1416     Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 


Amount  of  Water  Required  for  Various  Purposes.  The  amount  of 
water  required  for  household  purposes  has  been  found  to  be  about  25  gal  for  each 
person,  large  or  small,  but  waste  will  triple  that  amount  sometimes.  A  horse 
will  drink  about  7  gal  per  day  and  a  cow  from  5  to  6  gal  per  day.  A  carriage  re- 
quires from  9  to  16  gal  for  washing. 

Size  of  Supply-Pipes.  The  proper  diameter  of  supply-pipes  depends  upon 
several  considerations,  such  as  the  number  and  size  of  faucets  that  are  hkely  to 
be  discharging  water  at  the  same  time,  the  urgency  of  the  demand,  the  length  of 
the  pipes  and  number  of  angles,  and  upon  the  pressure.  There  is  no  objection 
to  having  a  pipe  larger  than  is  really  necessary,  except  from  the  standpoint  of 
cost.  Service-pipes  should  always  be  one  size  larger  than  the  tap  in  the  street- 
main.  The  following  table  affords  a  fair  guide  for  proportioning  the  supply- 
branches  to  plumbing-fixtures.  If  the  pressure  is  less  than  20  lb  per  sq  in  the 
system  may  be  rated  as  low  pressure,  and  if  above  20  lb  as  high  pressure. 


Supply-branches 


Low 
pressure. 


High 
pressure, 


To  Bath-cocks 

Basin-cocks 

Water-closet  flush-tank . 
Water-closet  flush-valve 

Sitz  or  foot-bath 

Kitchen  sinks 

Pantry  sinks 

Slop-sinks 

Urinals 


H  to  I 

iH  to  iH 

\*i  to  Yk 

H  to  y^ 

%  to  ^4 

H  to  y^ 


Hto  H 
iH  to  \\h 

1/^tO     % 

Hto  H 


With  high-pressure  systems,  dwellings  of  five  or  six  rooms  are  sometimes, 
for  economy,  supplied  entirely  through  H-'m  pipe. 

Minimum  Diameter  of  Waste-Pipes.  The  following  are  considered  as 
the  smallest  diameters  allowable  for  waste-pipes.  The  diameters  required  in 
New  York  City  are  given  on  page  1410. 

Bath  and  sink-wastes,  iM  in. 

Basin  and  urinal-wastes,  iH  in. 

Wash-trays,  i^  in  from  each  compartment,  entered  into  4-in  drum-trap  and 
3-in  outlet  from  trap. 

Water-closet  trap,  2}^^  in. 


Approximate  Spacing  for  Tacks 

on  Lead  Pipes 

Size  of  pipe, 

Vertical  pipe 

Horizontal  pipe 

Distance  apart 

Distance  apart 

Hot, 

Cold. 

Hot. 

Cold. 

m 

m 

in 

in 

H 

19 

25 

14 

17 

H 

20 

26 

IS 

18 

% 

21 

27 

16 

19 

I 

22 

28 

17 

20 

iH 

23 

29 

18 

21 

iH 

24 

30 

18 

22 

Lead  Pipe 


1417 


Designation  of  Lead  Pipe.  The  different  thicknesses  of  lead  pipe  were 
formerly  designated  by  letters  as  in  Table  H,  page  1418,  but  are  now  more 
commonly  designated  as  in  Table  G,  following,  which  may  be  considered  as 
generally  accepted  by  dealers. 

Table  G.     Weights  and  Sizes  of  Lead  Pipe 


Caliber 


H-in  Tubing 

Fish  seine 

^i-in  Aqueduct 

Extra  light 

Light 

Medium 

Strong 

Extra  strong 

H-in  Aqueduct 

Extra  light 

Light 

Medium 

Strong 

AA 

Extra  strong 

Extra  extra  strong. . 

^^-in  Aqueduct 

Extra  hght 

Light 

Medium 

Strong 

Extra  strong 

Extra  extra  strong.. 
^4-in  Aqueduct 

Extra  light 

Light 

Medium 

Strong 

Extra  strong 

Extra  extra  strong, 
^^-in  Aqueduct 

Extra  light 

Light 

i-in   Aqueduct 

Extra  light 

Light 

Medium 

Strong 

Extra  strong 

Extra  extra  strong. 
iH-in  Aqueduct 

Extra  light 

Light 

Medium 

Strong 

Extra  strong 

Extra  extra  strong. 


Weight  per 
foot 


lb 


Caliber 


i3'^-in  Aqueduct 

Extra  light 

Light 

Medium 

Strong 

Extra  strong 

Extra  extra  strong. . 
iJ4-in  Extra  light 

Light 

Medium 

Strong 

Extra  strong 

2-in    Waste 

Extra  light 

Light 

Medium 

Strong 

Extra  strong 

Extra  extra  strong . . 
2j'^-in  Waste 

Light 

Medium,  Me  thick. 

Strong,  V4  thick... . 

Extra  strong,  YiQ 
thick 

Extra  extra  strong, 

^^  thick 

3-in    Waste 

Light 

Medium,  Me  thick. 

Strong,  H  thick 

Extra  strong,  Me 
thick 

Extra  extra  strong, 

^i  thick 

3^i-in  Waste 

Strong,  Vi  thick  — 

Extra    strong,    Me 

thick 

4-in    Waste 

Medium 

Strong,  H  thick 

Extra  strong,  Me 
thick 

Extra  extra  strong, 

^i  thick 

S-in    Waste 


Weight  per 
foot 


1418      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  i 

Coils  of  supply-pipe  weigh  about  200  lb;  aqueduct  about  90  lb;  suction- 
pipe,  loo  to  180  lb  each. 

Block-tin  pipe  is  stronger  for  a  given  weight  per  foot  than  lead  pipe  or  tin 
\ined  lead  pipe.     As  compared  with  lead  pipe  its  strength  is  as  shz  to  i. 

Tin-lined  and  lead-lined  iron  pipe  is  made  with  inside  diameters  of  H,  H,  ij 
iH,  iy-2  and  2  in,  and  in  lo-ft  lengths,  threaded  without  couphngs.  Tin-lined 
and  lead-lined  fittings  are  also  made  (see  page  1415). 


Weights  and  Sizes  of  Sheet  Lead 


1 

^ 

Thickness,  in, . . 

K21 

Ho 

He 

He 
full 

H4 

%2 

H 

M 

H 

full 

% 

H 

% 

Lb  per  sq  ft 

2H 

3 

3H 

4 

5 

6 

8 

10 

12 

14 

16 

20 

24 

Table  H.    Thickness  and  Strength  of  Lead  Pipes 


Mean 

Safe 

Mean 

Safe 

Cali- 

Weight 

Thick- 

burst- 

work- 

Cali- 

Weight 

Thick- 

burst- 

work- 

ber. 

Mark 

per 
foot, 
lb   oz 

ness, 

ing- 

ing 

ber- 

Mark 

per 

foot, 

lb    oz 

ness, 

ing- 

ing 

in 

in 

pres- 
sure, 

pres- 
sure, 

in 

in 

pres- 
sure, 

pres- 
sure, 

lb 

lb 

lb 

lb 

H 

AAA 

I  12 

0.18 

1968 

492 

I 

A 

4    0 

0.21 

857 

214 

H 

AA 

I    S 

o.is 

I  627 

406 

I 

B 

3    4 

0.17 

745 

186 

H 

A 

I     2 

0.13 

I  381 

347 

I 

C 

2    8 

0.14 

562 

140 

H 

B 

I    0 

0.125 

1342 

335 

I 

D 

2    4 

0.125 

518 

129 

C 

0  14 
0  10 

O.II 

I  187 

296 
271 

I 
I 

E 

2    0 
I    8 

O.IO 

0.09 

475 
325 

118 
81 

0.087 

1085 

Vie 

0    gYz 

0.08 

775 

193 

iH 

AAA 

6  12 

0.275 

962 

240 

H 

AAA 

3    0 

0.25 

1787 

446 

iH 

AA 

5  12 

0.25 

823 

205 

H 

2     8 

0.225 

1655 

413 

iH 

A 

4  II 

0.21 

685 

171 

H 

AA 

2    0 

0.18 

1393 

343 

iH 

B 

3  II 

0.17 

546 

136 

H 

A 

I  10 

0.16 

1285 

321 

iH 

C 

3    0 

0.135 

420 

105 

H 

B 

I     3 

0.125 

980 

245 

iH 

D 

2    8 

0.125 

350 

87 

H 

C 

I     0 

O.IO 

782 

195 

iH 

2    0 

0.095 

322 

80 

H 

D 

0    9 

0.065 

468 

117 

iH 

AAA 

8    0 

0.29 

742 

185 

V2 

0  10 

0.07 

556 

139 

iH 

AA 

7    0 

0.25 

700 

175 

H 

0  12 

0.09 

625 

156 

iH 

A 

6    4 

0.22 

628 

157 

H 

AAA 

3    8 

0.23 

1548 

387 

iH 

B 

5    0 

0.18 

S06 

126 

% 

AA 

2  12 

0.21 

1380 

345 

H 

C 

4    4 

0.15 

430 

107 

5/i 

A 

2    8 

0.18 

I  152 

288 

H 

D 

3    8 

0.14 

31S 

78 

% 

B 

2    0 

0.16 

987 

246 

m 

3    0 

0.12 

245 

61 

H 

C 

I    7 

O.II7 

795 

198 

iM 

B 

5    0 

116 

H 

D 

I    4 

O.IO 

708 

177 

iK 

C 

4    0 

93 

H 

AAA 

4  14 

0.29 

1462 

365 

1% 

D 

3  10 

0.125 

318 

79 

H 

AA 

3    8 

0.225 

I  225 

306 

2 

AAA 

10  II 

0.30 

611. 

152 

H 

A 

3    0 

0.19 

I  072 

268 

2 

AA 

8  14 

0.25 

5" 

127 

H 

B 

2    3 

O.IS 

865 

216 

2 

A 

7    0 

0.21 

40s 

lOI 

H 

0 

I    12 

0.125 

782 

19s 

2 

B 

6    0 

0.19 

360 

90 

H 

D 

I     3 

0.09 

S05 

126 

2 

C 

5    0 

0.16 

260 

65 

I 

AAA 

6    0 

0.30 

I  230 

307 

2 

D 

4    0 

0.09 

200 

50 

I 

AA 

4    8 

0.23 

910 

227 

Sewer-Pipe 
Weight  and  Sizes  of  Pure  Block-Tin  Pipe 


1419 


Size  inside 
diameter 


Weight  per  foot, 


4 

4.5,6 
4.  S.*6.  8 
4.  5.  6,  8 
5,6,8,  lo 
9,  12,  i6 


Size  inside 
diameter 


Weight  per  foot, 
lb 


9,  12,  i6 
12,  i6 
20,  28 

24  and  upwards 
32  and  upwards 


Sewer-Pipe 

There  are  three  kinds  of  sewer-pipe  or  drain-pipe  offered  in  the  market,  (i) 

SALT-GLAZED  VITRIFIED  CLAY  PIPE,    (2)    SLIP-GLAZED  CLAY  PIPE  and  (3)    CEMENT 

PIPE.  The  name  of  the  latter  sufficiently  indicates  what  it  is  without  any  de- 
scription. The  SLIP-GLAZED  CLAY  PIPE  is  made  of  what  is  known  as  fire-clay, 
such  as  fire-brick  clay,  which  retains  its  porosity  when  subjected  to  the  most 
intense  heat.  It  is  glazed  with  another  kind  of  clay,  known  as  slip,  which,  when 
subjected  to  heat,  melts,  creating  a  very  thin  glazing,  and  which,  being  a  foreign 
SUBSTANCE  TO  THE  BODY  OF  THE  PIPE,  is  liable  to  wear  or  scale  off .  Salt-glazed 
CLAY  PIPE  is  made  of  a  clay,  which,  when  subjected  to  an  intense  heat,  becomes 
vitreous  or  glass-like.  It  is  glazed  by  the  vapors  of  salt,  the  salt  being  thrown 
in  the  fire,  thereby  creating  a  vapor  which  unites  chemically  with  the  clay,  and 
forms  a  glazing,  which  will  not  scale  or  wear  off,  and  is  impervious  to  the  action 
of  acids,  gases,  steam,  or  any  other  known  substance.  It  unites  with  the  clay 
in  such  a  manner  as  to  form  part  of  the  body  of  the  pipe,  and  is  therefore 
indestructible.  Salt-glazed  pipe  can  only  be  made  from  clay  that  will  vitrify, 
that  is,  when  subjected  to  an  intense  heat  will  become  a  hard,  compact,  non- 
porous  body.  It  should  be  borne  in  mind  that  slip-glazing  is  only  resorted  to 
when  the  clays  are  of  such  a  nature  that  they  will  not  vitrify. 

The  Material  of  Drain-Pipes  should  be  a  hard,  vitreous  substance;  not 
porous,  since  this  would  lead  to  the  absorption  of  the  impure  contents  of  the  drain, 
would  have  less  actual  strength  to  resist  pressure,  would  be  more  affected  by 
the  frost  or  by  the  formation  of  crystals  in  connection  with  certain  chemical 
combinations,  or  would  be  more  susceptible  to  the  chemical  action  of  the  con- 
stituents of  the  sewerage. 

Sewer-Pipes  Should  be  Salt-Glazed,  as  this  requires  them  to  be  subjected 
to  a  much  more  intense  heat  than  is  needed  for  slip-glazing,  and  thus  secures  a 
harder  material.  Cement  pipes  made  without  metal  reinforcement  have  not 
proved  sufficiently  strong  and  durable  to  be  used  with  confidence  in  any  im- 
portant work.  When  reinforced  with  metal,  however,  they  have  ample  strength, 
and  reinforced-cement  sewer-pipes  of  large  diameter  are  used  to  a  considerable 
extent  in  Europe. 

For  determining  the  diameter  of  house-sewers,  the  table  on  page  1409  will 
serve  as  a  good  guide.     Storm-sewers  should  be  proportioned  to  the  area  drained. 

The  maximum  rainfall,  as  shown  by  statistics,  is  about  i  in  per  hour,  except 
during  very  heavy  storms,  equal  to  27  225  gal  per  hour  for  each  acre,  or  453  gal 
per  minute  per  acre.  Owing  to  various  obstructions,  not  more  than  from  50  to 
75%  of  the  rainfall  will  reach  the  drain  within  the  same  hour,  and  allowance 
should  be  made  for  this  fact  in  determining  size  of  storm-sewer  required. 


1120      Hydraulics,  riumbing  and  Drainage,  and  Gas-l^iping     Part  3 


Carrying  Capacity  of  Sewer-Pipfe 

Gallons  per  minute 

Size  of 
pipe. 

Fall  per  loo  ft 

in 

I  in 

2  in 

3  in 

6  in 

9  in 

I  ft 

2  ft 

3  ft 

3 
4 
6 

13 

27 

75 

19 
38 
105 

23 
47 
129 

32 
66 
183 

40 
8i 
224 

46 
93 
258 

64 
131 
364 

79 
163 

450 

8 
9 

10 

153 

205 

267 

216 
290 
378 

265 
355 
463 

375 
503 
755 

460 
617 
803 

527 
712 
926 

750 
I  006 
I  310 

923 
I  240 
I  613 

12 

15 
i8 

422 

740 
I  168 

596 
I  021 
I  651 

730  . 

1  282 

2  022 

I  033 
I  818 
2860 

I  273 
2224 
3508 

I  468 
2464 
4045 

2  076 
3617 

5  704 

2554 
4467 
7047 

24 
.27 

30 
36 

2396 

4407 
5906 
9707 

3  387 
6  211 
8352 
13769 

4  155 
7674 
10223 
16  816 

5874 
10883 
14298 
23763 

7202 
13257 
17  714 
29  284 

8303 
15344 
20  204 
33722 

II  744 
21  771 
28  129 
47523 

14466 
26  622 
35513 
58406 

Quantities  of  Cement,  Sand  and  of  Cement  Mortar  for  Sewer-Pipe  Joints 

Prepared  by  J.  N.  Hazlehurst 
For  each  100  ft  of  sewer  (with  Portland  cement,  375  lb  net  per  bbl) 


Size  of 

Proportions: 

I  Cement  to 

I  Sand 

2  Sand 

pipe, 
in 

Length, 
•    ft 

Mortar, 
cu  yd 

Pipe  per 

Pipe  per 

Cement, 

Sand, 

bbl 

Cement, 

Sand, 

bbl 

bbl 

cu  yd 

cement, 
linft 

bbl 

cu  yd 

cement, 
linft 

.6 

2V2 

0.003 

0.01248 

0.00201 

803 

0.00855 

0.00252 

1168 

8 

2l/i 

0.038 

0.15808 

0 . 02546 

633 

0.10830 

0.03192 

923 

10 

2\^ 

0.058 

0.24128 

0.03886 

410 

0.16530 

0.04872 

605 

12 

^Vi 

0.089 

0.37024 

0.05963 

270 

0.25365 

0.07476 

394 

15 

2\i 

0.123 

0.51268 

0.08241 

195 

0.35055 

0.10332 

285 

18 

2\i 

0.167 

0.69472 

0.11189 

144 

0.47595 

0.14018 

210 

20 

2\^ 

0.237 

0.98592 

0.15879 

lOI 

0.67545 

0.19908 

148 

24 

2\<, 

0.299 

1.24384 

0.20033 

80 

0.85215 

0.25116 

117 

27 

3 

0.492 

2.04672 

0.32964 

49 

I . 40220 

0.41328 

71 

30 

3 

0.548 

2.27968 

0.36716 

44 

I. 56180 

0.46032 

64 

36 

3 

0.849 

3.53184 

0.56883 

29 

2.41965 

0.71316 

41 

Plumbing  Specialties 

The  Kenney  Flushometer.  This  is  a  gravity  valve  designed  for  flushing 
all  water-closets,  urinals  and  slop-sinks  in  a  building  direct  from  one  tank 
situated  in  the  attic  or  where  most  desirable,  thus  dispensing  with  the  individual 
overhead  tank.  The  pipe  from  the  main  tank  is  run  down  to  the  different  floors 
either  exposed  or  concealed  and  branches  taken  off  from  there  to  the  flushom- 


Plumbing  Specialties  1421 

eter.  The  operation  of  the  flushomcter  is  to  pull  the  handle  forward,  which 
raises  the  main  valve  off  its  seat,  making  a  direct  connection  from  the  flushom- 
cter to  the  tank.  After  the  handle  is  released  the  valve  closes  slowly  of  its 
own  accord  against  a  high  or  low  pressure.  It  is  constructed  without  springs 
or  cup-leathers  and  closes  by  gravity,  is  built  to  stand  the  hardest  service, 
and  yet  is  so  simple  in  construction  and  operation  that  the  same  valve  is  used 
for  all  requirements,  the  only  differences  in  adjustment  being  those  necessary 
for  work  on  high  or  low  pressure.  The  flushometer  is  extensively  used  for 
flushing  closets  in  buildings  in  the  Eastern  States,  including  many  large  office- 
buildings,  factories,  schools,  hospitals,  and  the  better  class  of  residences;  also 
on  steamships  and  yachts. 

Filters.  There  are  few  cities  in  which  the  public  water-supply  is  not  greatly 
improved  in  wholesomeness  by  being  filtered,  and  in  many  places  filtering  is 
absolutely  necessary.  The  filter  should  be  large  enough  so  that  the  velocity  of 
the  water  passing  through  it  will  be  low  and  it  should  be  so  arranged  that  the 
flow  of  water  can  be  reversed  and  the  accumulated  impurities  washed  into  a 
waste-pipe.  In  the  country  a  filter  suitable  for  rain-water  may  be  built  un- 
derground, the  filtering  process  being  accomplished  by  beds  of  sand  and  gravel. 
For  city  buildings,  however,  a  portable  filter  located  in  the  basement  should  be 
used.  An  ordinary  sand  filter,  either  pressure  or  gravity,  will  clarify  water  of 
all  mechanical  impurities,  suitable  for  plunge-baths,  and  other  general  uses  in 
a  building.  To  provide  a  perfectly  sterile  water,  however,  the  filter  must  be 
fitted  with  a  coagulating  apparatus  to  automatically  feed  a  proportionate  dose 
of  coagulant  to  the  raw  water.  Those  so-called  filters  which  are  made  to  screw 
onto  the  nozzle  of  an  ordinary  faucet  should  be  considered  merely  as  strainers, 
and  even  for  that  purpose  they  soon  become  foul. 

Instantaneous  Water-Heaters  are  a  great  convenience  for  heating  water 
for  baths  and  wash-basins  in  buildings  in  which  a  constant  supply  of  hot  water 
is  not  provided,  and  especially  in  residences  where  the  cooking  is  done  by  gas. 
They  are  cylindrical  in  shape,  made  of  nickel-plated  copper,  and  are  usually 
set  on  a  nickel-plated  shelf  attached  to  the  wall  close  to  the  fixture  to  be  supplied. 
A  heater  io|.^  in  in  diameter  and  30  in  high  will  heat  20  gal  of  water  in  eight 
minutes  at  a  cost  of  i^  to  2  cts  with  gas  at  $1  per  i  000  cu  ft.  A  large  line  of 
these  heaters  is  made  by  the  Humphry  Manufacturing  and  Plating  Company, 
Kalamazoo,  Mich.,  for  both  gas  and  gasolene,  although  gas  is  preferable  when 
it  can  be  had.     The  cost  of  heaters  varies  from  $15  to  $45,  according  to  size. 

An  Automatic  Water-Heater  which  maintains  water  at  any  desired  tem- 
perature without  attention,  provided  the  building  has  a  supply  of  live  steam,  is 
made  by  James  B.  Clow  &  Sons,  the  supply  of  steam  being  automatically  regu- 
lated by  a  thermostat.  It  will  be  found  especially  desirable  in  hospitals,  hotels, 
apartment-houses  and  public  institutions.  The  heater  is  made  in  four  sizes, 
with  capacities  of  i  500,  2  500,  4  000  and  6  500  gal  per  hour. 

The  Climax  Cellar-Drainer  *  is  a  simple  device  for  raising  water  from  6  to 
10  ft  without  attention  or  power,  except  a  supply  of  steam  or  water.  It  is  used 
principally  for  draining  cellars,  wheel-pits,  furnace-pits,  etc.,  when  they  are 
too  low  to  drain  into  the  sewer.  For  such  places  a  box  or  barrel  is  sunk  so  that 
all  of  the  water  will  run  into  it,  and  the  drainer  is  set  in  this  receiver  and  the  dis- 
charge-pipe run  to  a  sink  or  open  drain.  The  drainer  performs  its  functions  by 
passing  water  or  steam  under  pressure  through  the  drainer-point  or  jet,  thus 
creating  a  suction  which  draws  the  water  from  the  receiver  in  which  it  is  placed 
into  the  discharge-pipe,  and  both  the  jet-water  and  cellar-water  are  discharged 

•  Manufactured  by  Jas.  B,  Clow  &  Sons. 


1422      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 

together.  As  long  as  the  city  water  or  steam  passes  through  the  drainer-pipe, 
this  suction  and  discharge  continues.  The  supply  of  water  or  steam  is  turned 
on  or  off  automatically,  so  that  there  is  no  consumption  of  city  water  or  steam 
except  when  the  drainer  is  removing  water.  This  drainer  will  operate  with  a 
pressure  of  15  lb  or  more,  the  heavier  the  pressure  the  greater  the  amount  of 
dead  water  discharged.  When  the  drainage- water  does  not  have  to  be  raised 
more  than  10  ft,  this  is  the  most  economical  apparatus  that  can  be  used,  as  the 
amount  of  city  water  consumed  is  very  small.  The  Climax  Drainer  is  made  in 
six  sizes,  costing  from  $25  to  $160. 

Sewage-Ejectment.  Mechanical  ejectment  of  sewage  is  resorted  to  in  cases 
where  the  street-sewer  is  abov^e  the  level  of  the  area  to  be  drained.  This  con- 
dition is  found  principally  in  the  subbasement-lloors  of  tall  buildings,  under- 
ground public-comfort  stations  and  underground  passenger-stations.  A  system 
of  mechanical  ejectment  consists  of  a  gravity  drainage-system  to  a  receiving 
tank  or  sump  located  in  a  water-tight  pit  at  the  lowest  part  of  the  drainage- 
system,  and  a  pump  or  conpressed-air  ejector  to  raise  the  sewage  and  discharge 
it  into  the  street-sewer.  There  are  three  types  of  apparatus  used  to  raise  sew- 
age to  the  street  sewers,  centrifugal  pumps,  piston-pumps,  and  compressed-air 
ejectors.  The  compressed-air  ejectors,  however,  are  commonly  used  owing  to 
their  numerous  advantages.  They  are  automatic  and  almost  noiseless  in  opera- 
tion, are  perfectly  odorless,  and  have  but  few  working  parts  that  can  get  out 
of  order.  Sewage-ejectment  apparatus  is  generally  installed  in  duplicate  so 
that  one  set  may  be  cut  out  of  service  for  cleaning  or  repairs,  without  inter- 
rupting the  drainage-service. 

Plunge-Baths 

An  Example  of  the  Construction  and  Details  of  a  Small  Plt^nge- 
Bath  or  Swimming-Bath.  The  following  is  a  description,  with  illustrations, 
of  the  bath  in  the  house  of  the  Racquet  and  Tennis  Club  on  Forty-third  Street, 
New  York  City.* 

"The  swimming-bath  has  inside  dimensions  of  15  by  22  ft  and  is  about  9  ft 
in  total  depth.  It  was  built  in  a  pit  about  19  by  26  ft  and  about  8  ft  deep  below 
the  main  excavation,  which  was  blasted  out  of  solid  rock.  A  concrete  invert 
I  ft  or  more  in  thickness  was  laid  over  the  bottom,  serving  as  a  footing  on 
which  the  12-in  walls  of  common  red  brick  were  laid  in  cement.  They  were 
built  close  to  the  rough  vertical  faces  of  the  excavation,  and  the  spaces  behind 
them  were  filled  with  concrete  or  cement  mortar  or  were  flushed  with  grout. 
Then  on  the  inner  surface  of  the  walls  and  on  top  of  the  concrete  Iwttom  lining 
a  waterproofing  of  six  layers  of  felt  with  lapped  joints  was  mopped  on  with  hot 
tar  and  flashed  around  the  iron  outlet-pipe,  which  also  had  a  wide  calked  lead 
flange  extending  between  the  layers  of  felt.  On  the  bottom  of  this  water-proof 
coat  an  8-in  inverted  segmental  flat  floor-arch  of  common  brick  was  laid,  and  on 
its  skewbacks  4-in  vertical  brick  walls  were  built  against  the  water-proofed  sides. 
The  bottom  was  then  lined  with  vitrified  white  tile  and  the  sides  were  faced  with 
English  white  enameled  brick.  The  tops  of  the  walls  were  coped  with  beveled 
and  molded  white-marble  slabs  which  are  about  2  ft  above  the  floor-level  and 
are  surmounted  at  one  side  and  one  end  by  a  low  heavy  rail  with  twisted  orna- 
mental posts,  all  of  brass.  A  similar  horizontal  hand-rail  is  carried  along  the 
inside  wall  of  the  bath  just  above  water-level  and  a  curved  brass  hand-rail  is 
fastened  to  the  wall  above  the  narrow  brick-and-marble  stairs  at  one  end.     The 

*  The  illustrations  and  accompanying  descriptions  are  taken  by  permission  from  the 
Engineering  Record  of  Nov.  3,  1900. 


Plunge-Baths 


1423 


swimming-bath  occupies  one  corner  of  the  room  and  its  elevated  marble  plat- 
form extends  entirely  across  it,  forming  a  diving-platform  which  is  reached  by 
two  marble  steps.  All  the  water-supply  is  filtered  and  it  can  be  warmed  by  in- 
jecting steam  into  the  delivery-pipe  at  the  filter.  The  water  enters  through  the 
open  upturned  end  of  a  2-in  brass  pipe  projecting  a  foot  or  more  through  the 
wall  above  the  top  of  the  bath  and  delivering  a  solid  jet  unless  it  is  reduced  by 
the  regulating  valve  or  is  formed  into  a  fan-shaped  cascade  by  means  of  a 


I 


Brass  _ 
Railing 


Floor  Strainer 

Inlet  ^       WA 


.=2=t 


CROSS-SECTION 
Brass- Railing 


i 


I 
id  I 


ELEVATION 
Fig.  13.    Plunge-bath 


special  nozzle  which  can  be  screwed  in  the  open  end  of  the  pipe.  When  the 
bath  is  much  used  a  small  stream  of  water  is  constantly  admitted  and  causes 
a  continual  gentle  circulation  and  corresponding  overflow,  and  the  entire  con- 
tents are  pumped  out  and  the  bath  cleaned  every  two  or  three  days.  There 
are  two  overflows,  an  open  one  about  8  ft  above  the  bottom  and  a  valved  one 
a  foot  lower.  C.  L.  W.  Eidlitz  was  the  architect  of  the  house  and  the  water- 
proofing was  done  by  the  T.  New  Construction  Company." 

Symbols  for  Plumbing.     Figs.  14,  15  and  16  show  the  symbols  suggested 
in  "  Plumbing-Plans  and  Specifications  "  for  designating  plumbing-work  on  plans 


1424      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 

and  details,  and  generally  accepted  for  the  purpose.  It  is  just  as  necessary 
to  have  conventional  symbols  to  indicate  plumbing-work  and  fixtures,  as  it  is 
to  have  symbols  to  show-windows,  doors,  steps,  partitions  and  other  struc- 


^  Ferrule  Ct^ 


Symbol  for  lead  pipe 


.  Cold  water  ) 

•  Hot -water  >  Fresh- water  pipes 

•  Circulation  ) 

-  Cold  water ) 

-  Hot-water  V   Salt-water  pipes 
Circulation} 


Symbols  for  water-pipes 


Symbol  for 
cast-iron  pipe 


Symbol  for 
wrought  pipe 


Globe  valve       Gate-valve       Plain  view 

of  valve      Angle- valve 
One-line  symbols  for  valycs 


T 


Check- valve 


Plan  of  T-handlo 
stop-cock 


Fig.  14.    Symbols  for  Plumbing-pipes  and  Valves 

tural  details  on  architectural  drawings.  Before  these  symbols  became  generally 
used  there  was  no  unifonnity  in  the  drawing  of  plumbing-plans,  and  this  lack 
of  standards  often  led  to  serious  confusion.    For  instance,  if  plans  from  teo 


Symbols  for  Plumbing- Work 


1425 


different  offices  were  examined,  the  chances  were  that  on  no  two  of  them  would 
the  symbols  have  been  alike.     Further,  plans  prepared  in  the  same  office  at 


Side  view  T-handle  Plan-view  of  Side  view  of 

Btop-cocic         .lever-handle  stoi)-cock      lever-handle 
*     stop- cock. 


Symbol  for 
faucet 


Top  view' 
of  faucet 


•         #  • 

1'      vx"      %" 

hot      cold  circulation. 

Plan-symbols  for 
water-supply  risers 


Inlet 


^"%^  I  Beams 

f    1        [I 


% 


4x6x3  deep 
Symbol  for  a  suction-tank 


3"  soil   2  Vent? 

Symbols  for  soil  and 
Vent-stacks  Qnj)lans 


Symbol  foi 
non-6iphon.trap 


I  BeamN 
Symbdljor  house -tank 


Sy^mbol  for  meter 


Plan-symbol  for 
a  water-heater 


X 


{™} 


4^fTTTTTn^ 


Elevation-symbol  for 
a  water-heater 
Fig.  15.    Miscellaneous  Plumbing-symbols 


Symbol  for 
hot- water  tank 


different  times,  or  one  set  of  plans  on  which  several  different  draughtsmen  had 
worked,  would  often  show  as  many  different  symbols  for  a  water-closet  or  lava- 
tory as  there  were  workmen  engaged  on  the  drawings.    That  was  rather  con- 


1426      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 


fusing  to  plumbers  who  had  to  take  off  quantities  from  the  plans;  for,  often 
the  symbols  were  so  strange  and  bore  so  little  resemblance  to  the  fixtures  or 
apparatus  that  some  of  them  were  liable  to  be  overlooked.     It  is  owing  to  this 


Symbol  for  plan  of  pump         Symbol  for  elevation  of  pump       '       Plan-symbol  for  bath-tub 

/Si 


mz 


^ 


"tf- 


o. 


Elevation-symbol 
for  bath-tub 


plan-symbol  for  £levatioii-symbol        Plan-sym"bol  for 

lavatory  for  lavatory  water-closet 


Ort^ 


End-symbol  for       Side-symbol  for 
water-closet  water-closet 


Plan  symbol  for  sink 


_il_ 

V                   1 

k 

9 

Elevation-symbol  for  sinTc 

Fig.  16.     Symbols  for  Plumbing-fixtures 


Elevation-symbol  for 

■  ^eedle,  shower  and 

spray -bath 


Plan-symbol  for  needle, 
shower  and^spray-bath 


uncertainty  wherever  it  exists  from  this  cause,  that  there  is  a  wide  range  of 
prices  in  the  bids  submitted,  and  all  of  them  are  unreasonably  high  for  the 
amount  of  work  to  be  done.  To  avoid  confusion  and  secure  good  piices,  these 
standard  symbol  shoul'^  he  used. 


Expansion  of  Plumbing-Pipes 


1427 


Expansion  of  Soil  and  Waste-Stacks.  In  tall  buildings,  provision  should 
be  made  in  the  soil-stacks  and  connections  to  take  care  of  the  expansion,  con- 
traction, settlements,  swaying  and  other  movements  of  the  building.  This 
movement  is  no  inconsideral)le  amount,  in  some  localities  the  settlement  alone 
amounting  to  as  much  as  5  in  when  the  foundations  are  not  carried  to  l)ed-rock. 
In  Chicago,  for  instance,  most  of  the  sky-scrapers  which  were  built  on  com- 
pressible foundation-beds  are  out  of  plumb  and  lean  far  out  over  the  plumb- 
line.  One  building  in  particular  leaned  so  that  the  top  was  30  in  outside  of 
the  line  of  the  foundation.  Most  of  the  earlier  heavy  buildings  there  erected 
on  "  floating  foundations  "  are  carried  on  jacks,  and  periodically  jacked  up  as 
settlement  occurs.  When  the  building  finally  comes  to  rest,  the  jacks  are 
removed  and  the  walls  filled  in  with  masonry.  The  settlement  which  takes 
place  will  range  in  such  buildings  from  3  to  5  in.  These  various  move- 
ments, expansion,  contraction,  settlement,  racking  out  of  plumb,  also  sway- 
ing of  high  buildings  as  they  follow  the  sun  in  its  course  from  East  to 
West,  will  prove  destructive  to  steam-pipes  and  plumbing-pipes  if  provision 
is  not  made  to  take  care  of  them.  Steam-pipes  always  have  expansion-loops, 
but  it  is  only  recently  that  the  proper  attention  has  been  given  to  soil  and 
vent-stacks  and  pipes;  and 
then  only  after  as  many  as 
150  water-closets  in  one  build- 
ing were  broken  through  faulty 
installation,  or  rigid  connec- 
tions. The  remedy  is  to  put 
expansion- joints  (Fig.  17)  in 
the   soil    and    vent-stacks    of 


Normal 


Collapsed 
Expansion- joints 


Stretched, 


Bent 
Fig.  17. 

tall  buildings,  and  to  connect  all  water-closets  to  the  soil-pipes  by  means 
of  flexible  or  collapsible  connections  which  will  stretch,  collapse,  or  stretch  on 
one  side,  and  collapse  on  the  other,  according  to  the  stress  to  which  they  arft 
subjected.  These  flexible  fittings  should  be  placed  as  close  to  the  closets  as 
possible,  and  should  be  used  also  in  connection  with  slop-sinks  and  inside  rain- 
leaders.  For  inside  rain-leaders  the  number  of  corrugations  can  be  increased 
in  proportion  to  the  height  of  the  building.  Ordinary  stock  fittings  have  a 
range  of  about  2  in.  That  is,  they  will  stretch  about  i  in  and  collapse  i  in. 
For  rain-leaders  in  tall  buildings,  however,  greater  range  than  that  is  desirable. 
Two  corrugations  would  be  sufficient  for  a  rain-leader  in  an  ordinary  building 
not  over  100  ft  in  height;  then,  for  taller  buildings,  it  is  well  to  allow  an  extra 
corrugation  for  each  additional  100  ft  or  fraction  thereof.  The  flexibility  of 
these  fittings  can  be  seen  in  the  accompanying  illustrations  of  Fig.  17. 

Shrinkage  in  Buildings.     Ninety-seven  per  cent  of  buildings  erected  have 

wooden  floor-construction,  and  the  floor-joists,  when  they  dry  out,  shrink. 
This  is  the  cause  of  many  thousands  of  closets  being  broken  annually,  and  the 
destroying  of  the  seal  at  the  closet-connection  of  those  which  are  not  broken, 
unless  they  are  provided  with  a  flexible  floor-flange  or  fitting.  The  amount 
of  shrinkage  of  floor-beams  of  difl'erent  depths,  can  be  found  in  the  following 
table,  compiled  from  information  furnished  by  the  United  States  Government, 
Department  of  Agriculture,  Division  of  Forestry,  in  Bulletin  No.  10.  Besides 
the  shrinkage  of  the  individual  tiers  of  joists,  there  is  the  multiple  shrink- 
age of  all  the  tiers  when  bearing-partitions,  supporting  the  joists  at  the 
middle  in  a  building,  rest  on  sills  at  each  floor  which  are  laid  on  top  of 
the  joists,  instead  of  extending  down  through  to  the  plate  which  supports  the 
tier  of  joists.  When  the  framing  is  properly  done,  there  is  only  the  shrinkage 
of  the  one  tier  of  beams  to  take  into  consideration.    When  improperly  framed. 


1428      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 

there  might  be  three  or  four  shrinkages  affecting  the  top  floor  of  the  building. 
Even  though  the  timbers  are  dry  and  seasoned  when  put  in,  by  the  time  the 
plasterers  are  through  the  joists  are  wet  and  swollen  from  the  moisture  in  the 
plaster  and  from  the  rain  which  saturates  the  timbers  before  the  building  is  en- 
closed. It  is  safe  to  assume,  therefore,  that  a  12-in  joist  will  shrink  almost  H 
\n,  and  an  i8-in  joist  about  %  in. 


Table  of  Shrinkage  of  Timbers 


Depth  of  green 

or  wet  timber, 

in 

Amount  lost  by 

shrinkage,  4%, 

in 

Depth  of  timber 
when  dry,  in 

6 

0.24 

5.76 

•    8 

0.32 

7.68 

10 

0.40 

9.60 

12 

0.48 

11.52 

14 

0.56 

13-44 

16 

0.64 

15.36 

18 

0.72 

17.28 

20 

0.80 

19.20 

Floor-Connections  for  Water-Closets.  No  water-closet  can  be  considered 
sanitary  which  depends  upon  a  putty-joint,  slip-joint,  rigid-gasket  joint  or 
rigid  connection  of  any  kind  for  a  seal.  Improved  metal-to-metal  floor-flanges 
now  cost  no  more  than  rigid-gasket  joints  formerly  did,  and  they  are  flexible, 
water-tight,  will  remain  permanently  tight,  and  protect  the  closets  from  being 
broken  by  shrinkage  or  other  movement  of  the  building  or  piping.  The  only 
way  to  get  a  perfectly  sanitary  water-closet  is  to  specify  a  flexible,  metal-to- 
metal,  closet  floor-flange  with  it. 

Expansion  of  Hot-Water  Pipes.  In  all  tall  buildings  expansion-loops 
ought  to  be  placed  in  both  the  hot-water  and  the  circulation-pipes,  to  permit 
the  expansion  and  contraction  of  the  lines  without  injury  to  the  system.  These 
loops  are  usually  from  6  to  8  ft  long,  made  up  with  elbows,  and  extend  into  the 
floor  of  the  building.  Generally  the  hot-water  and  circulation-pipes  are  sup- 
ported midway  between  loops  so  that  they  can  expand  both  up  and  down.  The 
length  that  water-pipes  will  expand  depends  upon  the  degree  to  which  they  are 
heated,  and  the  materials  of  which  the  pipes  are  made.  The  first  of  the  follow- 
ing three  tables  gives  the  expansion  of  cast-iron  pipes,  the  second  the  expansion 
of  wrought-iron  pipes,  and  the  third  the  expansion  of  brass  pipes. 


Expansion  of  Cast-iron  Pipes 


Temper- 
ature of  air 
when  pipe 

is  fitted, 
degrees  F. 

Length  of 

pipe  when 

fitted, 

ft 

Length  of  pipe  when  heated  to 

215°  F. 
ft          in 

265°  F. 
ft          in 

■ 

297°  F. 
ft          in 

338°  F. 
ft         in 

0 
32 

64 

100 
100 
100 

100      1.59 
100      I . 36 
100      I. 12 

100      1.96 
100      1.6s 
100      1.43 

100      2.20 
100      1.96 
100      1.73 

100      2 . 50 
100      2 . 27 
100      2.00 

Softening  Hard  Water 
Expansion  of  Wrought-Iron  Pipe 


1429 


Temper- 
ature of  air 
when  pipe 
is  fitted, 
degrees  F. 

Length  of 

pipe  when 

fitted, 

ft 

Length  of  pipe  when  heated  to 

215°  F. 
ft          in 

265°  F. 
ft          in 

297°  F. 
ft         in 

338°  F. 
ft          in 

0 

32 
64 

100 
100 
100 

100      1.72 
100      1.47 
100      I. 21 

100      2.21 
100      1.78 
100      I. 61 

100      2.31 
100      2.12 
100      1.87 

100      2.70 
100      2.45 
100      2.iy 

Expansion  of  Brass  Pipe 


Temper- 
ature of  air 
when  pipe 

is  fitted, 
degrees  F. 

Length  of 

pipe  when 

fitted, 

ft 



Length  of  pipe  when  heated  to 

215 

ft 

^F. 
in 

265°  F. 
ft          in 

297°  F. 
ft          in 

338°  F. 
ft          in 

0 
32 
64 

100 
100 
100 

100 
100 
100 

2  58 
2  19 
I  81 

100      3  18 
100      2.79 
100      2 . 41 

100      3.56 
100      3.18 
100      2.79 

100      4.05 
100      3  67 
100      3  28 

Softening  Hard  Water  for  Domestic  Use.  In  many  parts  of  the  country 
the  water  is  temporarily  hard,  permanently  hard  or  both  temporarily 
AND  PERMANENTLY  HARD.  This  is  due  to  the  fact  that  in  those  regions  the 
underlying  rock  is  limestone,  and  in  percolating  through  the  limestone  the 
water,  which  originally  was  soft,  dissolves  carbonates  and  sulphates  of  lime  or 
magnesia  from  the  rock.  The  solvent  capacity  of  water  for  lime  and  magnesia 
is  greater  when  the  water  is  cold  than  when  it  is  hot.  Therefore,  deep- well 
water  in  limestone-regions  is  usually  saturated  with  lime  or  magnesia,  and  when 
heated  in  water-tanks  or  boilers  the  point  of  saturation  is  lowered  and  lime  13 
precipitated  or  liberated  in  the  form  of  hard  scale  or  incrustation.  The  effect 
of  boiler-incrustation  is  to  shorten  the  life  of  the  boiler  and  decrease  the  efificiency 
of  the  boiler  while  in  use.     It  is  estimated  that: 

He-in  lime-scale  means  a  loss  of  13%  of  fuel. 
H-in  lime-scale  means  a  loss  of  22%  of  fuel. 
H-in  lime-scale  means  a  loss  of  38%  of  fuel. 
%-in  lime-scale  means  a  loss  of  50%  of  fuel. 
y2-'m  lime-scale  means  a  loss  of  60%  of  fuel. 
%-in  lime-scale  means  a  loss  of  91%  of  fuel. 

These  values  are  probably  a  little  high,  but  making  due  allowance,  the  table 
will  serve  to  show  the  loss  due  to  the  use  of  hard  water.  In  the  laundry  the 
increased  consumption  of  soap  to  soften  hard  water  is  a  further  item  of  expense. 
It  requires  about  i  lb  of  soap  to  soften  100  gal  of  moderately-hard  water, 
besides  the  soap  required  for  washing  after  the  water  has  been  softened. 
Besides  the  expense,  hard  water  forms  an  insoluble  curd  when  washing  which 
makes  it  particularly  annoying  to  hotel-guests;  therefore,  it  is  advisable  to 
treat  all  hard  water  for  large  hotel-buildings,  laundries  and  for  many  indus- 
trial purposes.  Permanently  hard  waters  contain  sulphates  of  lime  or  mag- 
nesia.     Temporarily  hard  waters   contain    carbonates  of   lime  or   magnesia. 


1430     Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 

Temporaiily  and  permanently  hard  waters  contain  both  carbonates  and 
sulphates  of  hme  or  magnesia.  Temporarily  hard  waters  are  softened  by 
adding  lime-water  to  the  raw  water  to  remove  the  carbonates  of  lime.  This 
is  known  as  the  Clark  Process.  Permanently  hard  waters  are  softened 
by  the  Porter  Process,  which  consists  of  adding  soda-ash  to  the  raw  water. 
Stock  types  of  apparatus  are  manufactured  for  this  purpose,  and  may  be  hud 
with  capacities  of  any  required  amount. 

Heating  Water  with  Steam-Coils.  The  following  constants  will  be  found 
convenient  for  proportioning  steam-coils  for  heating  water: 

W  =  gallons  of  water  to  be  heated. 

W  -r-  lo  =  sq  ft  of  iron  pipe-coil  required  for  exhaust-steam. 

W  -r-  15=  sq  ft  of  copper  pipe-coil  required  for  exhaust-steam. 

W  X  0.07  =  sq  ft  of  iron  pipe-coil  for  5  lb  pressure-steam. 

W  X  0.045  =  sq  ft  of  copper  pipe-coil  for  5  lb  pressure-steam. 

W  X  0.05  =  sq.ft  of  iron  pipe-coil  for  25  lb  steam-pressure. 

W  X  0.035  =  sq  ft  of  copper  pipe-coil  for  25  lb  steam-pressure. 

W  X  0.04  =  sq  ft  of  iron  pipe-coil  for  50  lb  steam-pressure. 

W  X  0.25  =  sq  ft  of  copper  pipe-coil  required  for  50  lb  steam-pressure. 

W  X  0.03  =  sq  ft  of  iron  pipe-coil  required  for  75  lb  steam-pressure. 

W  X  0.02  =  sq  ft  of  copper  pipe-coil  required  for  75  lb  steam-pressure. 

Capacity  of  Water-Backs.  The  average  size  of  water-back  having  about 
110  sq  in,  or  about  ^i  sq  ft  of  exposed  surface,  will  heat  to  the  ordinary  temper- 
ature of  domestic  hot  water,  180°  F.,  about  21  gal  of  water  an  hour.  It  will 
heat  about  17  gal  of  water  to  the  boiling-point  with  an  ordinary  fire.  With  a 
fire  such  as  is  used  for  roasting,  washing,  or  baking,  a  water-back  of  this  same  size 
will  heat  about  23  gal  of  water  to  the  boiling-point,  or  27  gal  to  a  temperature 
of  180°  F.  Wrought-iron  pipe  heating-coils  will  heat  from  30  to  40  gal  of  water 
under  the  same  conditions,  and  copper  pipes  will  heat  from  45  to  60  gal  per  hour 
for  each  square  foot  of  surface  exposed  to  the  fire.  In  calculating  the  heating 
capacity  of  water-backs  or  coils,  the  average  temperature  of  the  water  is  taken. 
Thus,  if  water  at  60°  is  heated  to  200°  F.,  the  average  temperature  of  the  water 
would  be  (60 -|-  200)  -^  2  =  130°  F.,  and  the  range  of  temperature  through  which 
it  is  heated  would  be  200  —  60  =  140°  F. 

Value  of  Pipe-Covering.  Hot-water  pipes  and  hot-water  tanks  when 
uncovered  lose  by  radiation  from  their  surface  about  13  heat-units  per  minute 
per  square  foot  of  surface.  To  prevent  this  loss  of  heat  and  consequent  extra 
consumption  of  coal,  hot-water  pipes,  circulation-pipes  and  hot-water  tanks  in 
large  institutions  are  generally  covered  with  some  non-heat-conducting  material. 
The  value  of  pipe-covering  is  not  proportional  to  its  thickness.  Sectional  pipe- 
coverings  average  about  1%  in  in  thickness  and  reduce  the  loss  by  radiation 
about  90%.  Doubling  the  thickness  of  pipe-covering  saves  only  about  another 
5%  of  heat-loss.  In  specifying  covering  for  pipes  and  boilers,  therefore,  a  thick- 
ness of  I H  in  will  be  sufTicient.  Carbonate  of  magnesia  is  a  very  poor  conductor 
of  heat.  Therefore,  it  is  a  good  material  for  covering  hot-water  pipes.  Carbon- 
ate of  lime,  on  the  other  hand,  is  not  a  good  covering  material,  although  it 
often  masquerades  as  carbonate  of  magnesia.  When  magnesia  pipe-covering  is 
specified,  therefore,  it  is  well  to  require  a  composition  containing  from  80  to  90% 
of  magnesia,  and  require  a  test  to  be  made  at  the  expense  of  the  contractor,  but 
by  a  chemist  named  by  the  architect.  The  following  coverings  are  the  best 
materials  for  hot-water  pipes,  in  the  order  in  which  they  are  named.  Nonpareil 
Cork,  Magnesia,  Asbestos  Air-Cell  and  Imperial  Asbestos. 


Illuminating-Gas  1431 

(3)   ILLUMINATING-GAS   AND    GAS-PlPlNG* 

Varieties  of  Gas.  Five  varieties  of  gas  are  now  commonly  used  for  light- 
ing and  cooking,  namely: 

(i)  Coal-Gas,  which  is  made  by  heating  bituminous  coal  in  air-tight  retorts. 
This  is  the  most  common  variety  of  gas  furnished  for  the  lighting  of  cities  and 
towns. 

(2)  Water-Gas,  which  is  made  usually  from  anthracite  coal  and  steam,  and 
is  quite  extensively  used  in  Eastern  cities.  Gas  made  by  this  process  contains 
less  carbon  than  good  coal-gas,  and  conseciuently  does  not  give  as  bright  a  light, 
although  it  burns  perfectly  in  heating-burners.  When  used  for  lighting  purposes 
it  is  enriched  in  carbon  by  vaporizing  a  quantity  of  petroleum  by  heat  and  in- 
jecting it  into  the  hot  gas  before  it  leaves  the  generator.  Pure  water-gas  is 
lighter  and  has  less  odor  than  coal-gas. 

(3)  Natural  Gas  is  obtained  from  holes  or  wells  which  are  drilled  in  the  ground. 
In  localities  where  it  can  be  obtained  it  furnishes  cheap  light  and  fuel.  The 
natural  gas  obtained  in  the  hard-coal  regions  develops  more  heat  per  cubic  foot  in 
burning  than  any  other  kind  of  gas  except  acetylene.  Natural  gas  is  usually  under 
greater  pressure  in  the  street-mains  and  house-pipes  than  manufactured  gas. 

(4)  Acetylene-Gas.  Used  almost  exclusively  for  the  lighting  of  isolated 
buildings,  or  for  public  buildings  in  towns  or  cities  where  there  is  no  public  gas- 
supply,  and  commonly  generated  on  the  premises.  It  is  formed  by  bringing 
water  and  calcium  carbide  in  contact.  Calcium  carbide  is  produced  by  the 
electrical  fusion  of  coke  and  lime.  It  is  now  a  commercial  article  produced  in 
large  quantities  and  sold  at  a  moderate  price.  It  is  a  very  hard  substance  like 
dark  granite,  has  a  very  slight  odor,  will  not  burn  or  explode,  and  can  be  handled 
in  any  quantity  with  perfect  safety.  The  fact  that  carbide  begins  to  disintegrate 
and  give  off  acetylene  at  the  slightest  touch  of  moisture  makes  it  practicable  to 
generate  the  gas  in  small  quantities  for  single  buildings. 

Process  of  Generating  Acetylene-Gas.  The  satisfactory  production  of  acety- 
lene-gas requires  a  generator  which  shall  feed  carbide  of  sufficient  size  and  weight 
to  be  plunged  a  sufficient  depth  under  the  water  in  the  generator-chamber  to 
insure  coolness  and  proper  washing.  The  carbide-chamber  must  be  so  arranged 
and  protected  that  no  gas  can  return  to  it  to  be  wasted  when  the  chamber  is 
refilled  and  permeate  the  house  with  its  smell.  It  must  feed  carbide  loosely 
and  in  very  small  quantities,  in  order  to  provide  for  perfect  coolness  by  free 
access  of  water  to  all  of  the  carbide.  It  must  work  automatically  and  with 
absolute  certainty.  Acetylene-gas  to  be  pure  must  be  thoroughly  washed. 
Impure  acetylene,  as  with  any  other  illuminating-gas,  means  a  discoloration  of 
the  flame,  diminished  illuminating  power,  clogging  of  pipes  and  burners  with 
carbon  and  other  foreign  matter,  and  smoky  burners,  causing  blackening  of 
ceilings  and  tarnished  and  soiled  woodwork  and  upholstery.  It  is  now  gener- 
ally agreed  that  the  requirements  above  outlined  can  be  attained  only  by  a 
generator  of  the  plunger-type.  Portable  generators  which  may  be  set  in  the 
cellar  or  basement  of  any  building  are  manufactured  in  great  variety;  it  is  esti- 
mated that  100  000  acetylene-gas  generators  are  now  in  use  in  the  United  States. 
They  are  made  in  sizes  of  5,  10,  15,  20  and  up  to  500-Hghts  capacity.  In  all 
machines  dropping  carbide  into  water  there  should  be  a  connection  open  from 
the  carbide-holding  receptacle  to  the  safety-vent  run  out  of  doors  from  the 
gasometer.  It  is  claimed  that  for  a  given  degree  of  illumination,  acetylene  is 
cheaper  than  dollar  gas.     A  large  residence  may  be  lighted  for  about  $2.50  a 

•  See,  also,  Lighting  and  Illumination  of  Buildings,  page  i437- 


1432     Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping     Part  3 

month.  To  develop  the  full  illuminating  power  of  the  gas  it  is  necessary  to 
use  a  burner-tip  having  the  thinnest  slit  obtainable,  the  illuminating  power  of 
the  gas  being  about  fifteen  times  that  of  coal-gas,  for  the  same  consumption. 
The  light  is  a  clear  white,  very  nearly  resembling  sunlight  in  color  and  dif- 
fusiveness, with  none  of  the  red  of  the  incandescent  lamp,  the  orange  of  the 
ordinary  gas-flame,  or  the  green  tone  of  the  incandescent  mantle;  and  it  possesses 
the  quaHty,  unique  among  artificial  ilUiminants,  of  reproducing  even  the  most 
delicate  shades  of  color  as  faithfully  as  sunlight.  Even  when  used  with  mantle- 
burners,  as  it  may  be  with  great  economy,  acetylene-light  presents  a  strong  dis- 
similarity from  ordinary  gas  under  the  same  conditions.  Acetylene  corrodes 
silver  and  copper,  but  does  not  affect  brass,  iron,  lead,  tin,  or  zinc.  A  govern- 
ment specification  for  a  complete  apparatus  for  acetylene-gas  was  published  in 
Engineering  News  of  Feb.  4,  1904. 

(5)  Gasoline-Gas  is  a  mixture  of  gasoline  vapor  with  air.  It  is  never  piped 
but  is  generated  close  to  the  burner,  and  is  seldom  used  for  lighting  except  for 
street  stands,  and  the  like.     It  is  much  used  for  fuel,  however. 

Gasoline  changes  from  the  liquid  to  the  gaseous  form  under  ordinary  atmos- 
pheric pressure,  at  temperatures  above  40°  ¥.,  the  evaporation  being  -  cry  slow 
at  40°,  quite  rapid  at  70°,  and  furious  at  212°.  If  a  tank  containing  liquid  gaso- 
line is  left  open  to  the  air,  the  liquid  will  all  pass  away  in  the  form  of  gas. 

Although  generally  considered  dangerous,  it  is  only  so  when  carelessly  or 
ignorantly  handled.  To  produce  i  000  cu  ft  of  gas  of  good  quaHty  requires 
about  4^^  gal  of  the  best  grade  of  gasoHne.  An  ordinary  burner  consumes 
about  5  cu  ft  per  hour. 


Piping  a  House  for  Gas*t 

General  Principles  and  Requirements.  Ordinary  wrought-iron  pipe,  such 
as  is  used  for  steam  or  water,  is  suitable  and  proper  for  all  kinds  of  gas. 
Galvanized  malleable-iron  fittings,  in  distinction  from  plain  iron,  are  very 
superior.  The  coating  of  zinc  inside  and  out  effectually  and  permanently 
covers  all  blow-hofes,  makes  the  work  solid  and  durable,  and  avoids  the  use 
of  perishable  cement.  Before  the  pipe  is  placed  in  position  it  should  be 
looked  and  blown  through.  It  is  not  infrequently  obstructed,  and  this  pre- 
caution will  save  much  damage  and  annoyance.  What  is  known  as  gas-fitters' 
cement  never  should  be  used.  It  cracks  off  easily,  in  warm  places  it  will  melt, 
and  it  can  be  dissolved  by  several  different  kinds  of  gas.  Nothing  but  solid 
metals  is  admissible  for  confming  gas  of  any  kind.  When  pipes  under  floors 
run  across  floor-timbers,  the  latter  should  be  cut  into  near  their  ends,  or  where 
supported  on  partitions,  and  not  near  the  middle  of  spans.  It  is  evident  that 
a  lo-in  timber  notched  2  in  in  the  middle  is  no  stronger  than  an  8-in  timber. 
All  branch  outlet-pipes  should  be  taken  from  the  sides  or  tops  of  running  lines. 
Bracket-pipes  should  run  up  from  below,  and  not  drop  from  above.  Never  drop  a 
center  pipe  from  the  bottom  of  a  running  line.  Always  take  such  outlet  from  the 
side  of  the  pipe.  The  whole  system  of  piping  must  be  free  from  low  places  or 
traps,  and  decline  toward  the  main  rising  pipe,  which  should  run  up  in  a  partition 
as  near  the  center  of  the  building  as  is  practicable.  It  is  obvious  that  where  gas 
is  distributed  from  the  center  of  a  building,  smaller  running  lines  of  pipe  will  be 
needed  than  when  the  main  pipe  runs  up  on  one  end.     Hence,  timbers  will  not 

•  Circular  issued  by  tlie  Gilbert  &  Barker  Manufacturing  Company, 
t  See,  also,  Lighting  and  Illumination  of  Buildings,  pages  1437  to  1456. 


Gas-Piping  1433 

require  as  deep  cutting,  and  the  flow  of  gas  will  be  more  regular  and  even.  For 
the  same  reason  in  large  buildings,  more  than  one  riser  may  be  advisable.  When 
a  building  has  different  heights  of  post,  it  is  always  better  to  have  an  in- 
dependent rising  pipe  for  each  height  of  post,  than  to  drop  a  system  of  piping 
from  a  higher  to  a  lower  post,  or  to  grade  to  a  low  point  and  establish 
drip-pipes.  Drip-pipes  in  a  building  should  always  be  avoided.  The  whole 
system  of  piping  should  be  so  arranged  tliat  any  condensed  gas  will  flow  back 
through  the  system  and  into  the  service-pipe  in  the  ground.  All  outlet-pipes 
should  be  so  securely  and  rigidly  fastened  in  position  that  there  will  be  no  possi- 
bility of  their  moving  when  the  gas-fixtures  are  attached.  Center  pipes  should 
rest  on  a  solid  support  fastened  to  the  floor-timbers  near  their  tops.  The  pipe 
should  be  securely  fastened  to  the  support  to  prevent  lateral  movement.  The 
drop-pipe  must  be  perfectly  plumb,  and  imss  through  a  guide  fastened  near  the 
bottom  of  the  timbers,  which  will  keep  them  in  position  despite  the  assault 
of  lathers,  masons  and  others.  In  the  absence  of  express  directions  to  the 
contrary,  outlets  for  brackets  should  generally  be  5  ft  6  in  high  from  the  floor* 
except  that  it  is  usual  to  put  them  6  ft  high  in  halls  and  bath-rooms.  The  upright 
pipes  should  be  plumb,  so  that  the  nipples  that  project  through  the  walls  will  be 
level.  The  nipples  should  project  noj:  more  than  %  in  from  the  face  of  the 
plastering.  Laths  and  plaster  together  are  usually  %  in  thick;  hence  the 
nipples  should  project  1I/2  in  from  the  face  of  the  studding.  Drop  center  pipes 
should  project  iVz  in  below  the  furring,  or  timbers  if  there  is  no  furring,  where 
it  is  known  that  there  will  be  no  stucco  or  centerpieces  used.  Where  center- 
pieces are  to  be  used,  or  where  there  is  a  doubt  whether  they  will  be  or  not, 
then  the  drop-pipes  should  be  left  about  a  foot  below  the  furring.  All  pipes 
being  properly  fastened,  the  drop-pipe  can  be  safely  taken  out  and  cut  to  the 
right  length  when  gas-fixtures  are  put  on.  Gas-pipes  should  never  be  placed  on 
the  bottoms  of  floor-timbers  that  are  to  be  lathed  and  plastered,  because  they 
are  inaccessible  in  the  contingency  of  leakage,  or  when  alterations  are  desired, 
and  gas-fixtures  are  insecure.  The  whole  S3'stem  of  piping  should  be  proved  to 
be  air  and  gas-tight  under  a  pressure  of  air  that  will  raise  a  column  of  mercury 
6  in  high  in  a  glass  tube.  The  pipes  are  either  tight  or  they  leak.  There  is  no 
middle  ground.  If  they  are  tight  the  mercury  will  not  fall  a  particle.  A  piece 
of  paper  should  be  pasted  on  the  glass  tube,  even  with  the  mercury,  to  mark  its 
height  while  the  pressure  is  on.  The  system  of  piping  should  remain  under 
test  for  at  least  a  half-hour.  It  should  be  the  duty  of  the  person  in  charge  of 
the  construction  of  the  building  to  thoroughly  inspect  the  system  of  gas-fitting; 
surely  as  much  so  as  to  inspect  any  other  part  of  the  building.  He  should  know 
from  personal  observation  that  the  specifications  are  complied  with.  After 
being  satisfied  that  the  mercury  does  not  fall  he  should  cause  caps  on  the  out- 
lets to  be  loosened  in  different  parts  of  the  building,  first  loosening  one  to  let 
some  air  escape,  at  th,e  same  time  observing  if  the  mercury  falls,  then  tightening 
it  and  repeating  the  operation  at  other  points.  This  plan  will  prove  whether  the 
pipes  are  free  from  obstruction  or  not.  When  he  is  satisfied  that  the  whole 
work  is  properly  and  perfectly  executed,  he  should  give  the  gas-fitter  a  certificate 
to  that  effect. 

The  following  requirements  from  specifications  published  by  the  Denver  Gas 
and  Electric  Company  are  worthy  of  attention.  Always  use  fittings  in  making 
turns;  do  not  bend  pipe.  Do  not  use  unions  in  concealed  work;  use  long  screws 
or  right-and-left  couplings.  Long  runs  of  approximately  horizontal  pipe  must 
be  firmly  supported  at  short  intervals  to  prevent  sagging. 


1434      Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 

Rules  and  Table  for  Proportioning  Sizes  of  House-Pipes  for  Gas*t 

Rules  Governing  Sizes  of  Gas-Pipes.  The  table  on  page  143S  is  based 
on  the  well-known  formula  for  the  flow  of  gas  through  pipes.  The  friction, 
and  therefore  the  pressure  necessary  to  overcome  the  friction,  increases  with 
the  quantity  of  gas  that  goes  through,  and  as  the  aim  of  the  table  is  to  have 
the  loss  in  pressure  not  exceed  Ho  in  water-pressure  in  30  ft,  the  size  of  the  pipe 
increases  in  going  from  an  extremity  toward  the  meter,  as  each  section  has  an 
increasing  number  of  outlets  to  supply.  The  quantity  of  gas  the  piping  may 
be  called  on  to  pass  through  is  stated  in  terms  of  f^-in  outlets,  instead  of 
cubic  feet,  outlets  being  used  as  a  unit  instead  of  burners,  because  at  the 
time  of  first  inspection  the  number  of  burners  may  not  be  definitely  determined. 
In  making  the  table,  each  H-in  outlet  was  assumed  to  require  a  supply  of  10 
cu  ft  per  hour.     In  using  the  table  observe  the  following  rules:  J 

(i]  No  house-riser  shall  be  less  than  %  in.  The  house-riser  is  considered  to 
extend  from  the  cellar  to  the  ceiling  of  the  first  story.  Above  the  ceiling  the 
pipe  must  be  extended  of  the  same  size  as  the  riser,  until  the  first  branch  line  is 
taken  off. 

(2)  No  house-pipe  shall  be  less  than  %  in.  An  extension  to  existing  piping 
may  be  made  of  H-in  pipe  to  supply  not  more  than  one  outlet,  provided  said 
pipe  is  not  over  6  ft  long. 

(3)  No  gas-range  shall  be  connected  with  a  smaller  pipe  than  %  in. 

(4)  In  figuring  out  the  size  of  pipe,  always  start  at  the  extremities  of  the 
system,  and  work  toward  the  meter. 

(5)  In  using  the  table,  the  lengths  of  pipe  to  be  used  in  each  case  are  the 
lengths  measured  from  one  branch  or  point  of  juncture  to  another,  disregarding 
elbows  or  turns.  Such  lengths  will  be  hereafter  spoken  of  as  sections.  No 
change  in  size  of  pipe  may  be  made  except  at  branches  or  outlets,  each  section 
therefore  being  made  of  but  one  size  of  pipe. 

(6)  If  any  outlet  is  larger  tlian  %  in  it  must  be  counted  as  more  than  one,  in 
accordance  with  the  schedule  below: 

Size  of  outlet,  inches H     %     i     iH    iH     2     2H     3        4 

Value  in  table .... 2      4      7     11     16     28    44    64     112 

(7)  If  the  exact  number  of  outlets  given  cannot  be  found  in  the  table,  take 
the  next  larger  number. 

(8)  If,  for  the  number  of  outlets  given,  the  exact  length  of  the  section  which 
feeds  these  outlets  cannot  be  found  in  the  table,  the  next  larger  length,  corre- 
sponding to  the  outlets  given,  must  be  taken  to  determine  the  size  of  pipe  re- 
quired. Thus,  if  there  are  eight  outlets  to  be  fed  through  55  ft  of  pipe,  the  length 
next  larger  than  55  in  the  eight-outlet  line  in  the  table  is  100,  and  as  this  is  in 
the  i34-in  column,  that  size  pipe  would  be  required. 

(9)  For  any  given  number  of  outlets,  do  not  use  a  smaller  size  pipe  than  the 
smallest  size  that  contains  a  figure  in  the  table  for  that  number  of  outlets. 
Thus,  to  feed  15  outlets,  no  smaller  size  pipe  than  i  in  may  be  used,  no  matter 
how  short  the  .section  may  be. 

(10)  In  any  piping- plan,  in  any  continuous  run  from  an  extremity  to  the 
meter,  there  may  not  be  used  a  longer  length  of  any  size  pipe  than  found  in  the 
table  for  that  size,  as  50  ft  for  %  in,  70  ft  for  i  in,  etc.  If  any  one  section  would 
exceed  the  limit  length,  it  must  be  made  of  larger  pipe.    Thus,  6  outlets  could 

*  The  Denver  Gas  and  Electric  Company. 
i     t  Sec,  also,  Lighting  and  Illumination  of  Buildings,  pages  1437  to  1456. 

t  With  the  exception  of  tyix)graphical  changes  made  to  conform  to  the  rest  of  the 
base,  these  rules  are  quoted  literally.     Editor-in-chief. 


Gas-Piping 


1435 


Table  Showing  the  Correct  Sizes  of  House-Pipes  for  Different  Lengths  of 
Pipes  and  Number  of  Outlets 


Number 
of  %-m 

Lengths  of  pipes  in 

feet 

outlets 

^i-in 

i/^i-in 

%-in  I 

-in 

iH-in 

iH-in 

2-in 

2yz-m 

3-in 

4-in 

pipe 

pipe 

pipe   J 

ipe 

pipe 

pipe  ' 

pipe 

pipe 

pipe 

pipe 

I 

20 

30 

50 

70 

100 

150 

200 

300 

400 

600 

2 

27 

50 

70 

100 

150 

200 

300 

400 

600 

3 

12 

50 

70 

100 

150 

200 

300 

400 

600 

4 

50 

70 

100 

150 

200 

300 

400 

600 

5 

33 

70 

100 

150 

200 

300 

400 

600 

6 

24 

70 

100 

ISO 

200 

300 

400 

600 

7 

18 

70 

100 

150 

200 

300 

400 

600 

8 

13 

50 

100 

150 

200 

300 

400 

eoo 

9 

44 

100 

150 

200 

300 

400 

600 

10 

35 

100 

ISO 

200 

300 

400 

600 

II 

30 

50 

150 

200 

300 

400 

600 

12 

25 

.  75 

ISO 

200 

300 

400 

600 

13 

21 

60 

ISO 

200 

300 

400 

600 

14 

18 

53 

130 

200 

300 

400 

600 

15 

16 

45 

IIS 

200 

300 

400 

600 

i6 

14 

41 

100 

200 

300 

400 

600 

17 

12 

36 

90 

200 

300 

400 

600 

i8 

32 

80 

200 

300 

400 

60Q^^ 

19 

29 

73 

200 

300 

400 

600 

20 

27 

65 

200 

300 

400 

600 

21 

24 

58 

200 

300 

400 

600 

22 

22 

53 

200 

300 

400 

600 

23 

20 

49 

200 

300 

400 

600 

24 

18 

45 

196 

300 

400 

600 

25 

17 

42 

175 

300 

400 

600 

30 

12 

30 

120 

300 

400 

600 

35 

22 

90 

270 

400 

600 

40 

17 

70 

210 

400 

600 

45 

13 

55 

165 

400 

600 

50 

45 

135 

330 

600 

65 



27 

80 

2CO 

600 

75 

20 

60 

ISO 

600 

TOO 

33 

80 

360 

125 

22 

so 

230 

150 

15 

35 

160 

175 

28 

120 

200 

' 

21 

90 

250 

' 

14 

59 

not  be  fed  through  75  ft  of  i-in  pipe,  but  i\i  in  would  have  to  be  used.  When 
two  or  more  successive  sections  work  out  to  the  same  size  of  pipe  and  their  total 
leagth  or  sum  exceeds  the  longest  length  in  the  table  for  that  size  pipe,  make  the 
section  nearest  the  meter  of  the  next  larger  size.  For  example,  if  we  have  5  out- 
lets to  be  supplied  through  45  ft  of  pipe,  and  these  5  and  5  more,  making  10 
in  all,  through  30  ft  of  pipe,  we  should  find  by  the  table  that  10  outlets  through 
30  ft  would  require  i-in  pipe,  and  that  5  outlets  through  45  ft  would  also  require 
I -in  pipe,  but  as  the  sum  of  the  two  sections,  30  plus  45  equals  75  ft,  is  longer 
than  the  amount  of  i  in  that  may  be  used  in  any  continuous  run,  the  30-ft  sec- 
tion, being  the  one  nearer  the  nieter,  m"'=it  be  made  of  iH-in  pipe.    The  applica* 


1436     Hydraulics,  Plumbing  and  Drainage,  and  Gas-Piping    Part  3 

tion  of  the  limit  in  length  of  any  one  size  in  a  continuous  run  may  also  be  shown 
as  follows:  Eight  outlets  will  allow  of  13  ft  of  %An  pipe  in  the  section  between 
the  eighth  and  ninth  outlet  (counting  from  the  extremity  of  the  system  toward 
the  meter),  provided  that  this  13  ft  added  to  the  total  length  of  %-in  pipe  that 
may  have  been  used  between  the  extremity  of  the  run  and  the  eighth  outlet 
does  not  exceed  50  ft,  which,  according  to  the  table,  is  the  greatest  length  of 
%  in  allowable  in  any  one  branch  of  the  system.  Therefore,  up  to  the  eighth 
outlet,  37  ft  of  H-in  pipe  could  have  been  used,  and  yet  allow  13  ft  of  %  in  to  be 
used  in  the  section  between  the  eighth  and  ninth  outlet.  If  more  than  37  ft 
had  been  used,  then  the  entire  13  ft  between  the  eighth  and  ninth  outlets  would 
have  to  be  of  i-in  pipe. 


Fig.  18.    Diagram  of  Gas-piping 

(11)  Never  supply  gas  from  a  smaller  size  of  pipe  to  a  larger  one.  If  we  have 
25  outlets  to  be  supplied  through  200  ft  of  pipe,  and  these  25  and  5  more,  making 
30  in  all,  through  100  ft  of  pipe  we  should  find  by  the  table  that  25  outlets 
through  200  ft  would  require  2j^-in  pipe,  and  30  outlets  through  100  ft  would 
require  2-in  piping,  but  as  under  this  condition  a  2-in  pipe  would  be  supplying 
a  2j'^-in  pipe,  the  loo-ft  section  must  be  made  2\i  in.  The  sizes  of  pipes  In  Fig. 
18  are  in  accordance  with  the  foregoing  rules  and  the  table. 


Lighting  and  Illumination  of  Buildings  1437 


LIGHTING  AND  ILLUMINATION  OF  BUILDINGS* 

By 
W.  H.  TIMBIE 

ASSOCIATE     PROFESSOR     OF     ELECTRICAL     ENGINEERING,     MASSACSUSETtS     INSfiTUTE     OF 
TECHNOLOGY 

General  Principles.  Objects  are  illuminated  for  the  sole  purpose  of  making 
them  visible  to  the  eye.  The  eye,  then,  is  the  natural  starting-point.  When 
passing  upon  the  merits  of  any  scheme  of  ordinary  illumination,  that  which 
should  mark  it  as  a  success  or  failure  should  be  the  general  effect  of  the  scheme 
upon  the  eye.  Success  should  be  measured  largely  by  the  degree  of  clearness 
with  which  the  objects  are  perceived  by  the  eye,  as  to  shape  and  color.  If  cer- 
tain parts  of  a  room  or  street  are  too  brilUantly  lighted,  objects  in  the  dimmer 
portions  are  not  perceived  by  the  eye.  If  a  certain  side  of  one  object  is  too 
highly  illuminated,  the  general  shape  of  the  object  is  lost,  as  the  eye  does  not 
readily  perceive  its  more  dimly  lighted  parts.  This  is  because  the  eye  auto- 
matically adjusts  itself  to  the  most  brilliantly  lighted  area  within  its  view,  and, 
accordingly,  is  out  of  adjustment  for  perceiving  the  rest.  We  should  get  rid  of 
the  idea,  therefore,  that  a  light  of  intense  brilliancy  is  the  thing  to  be  sought. 
It  is,  in  general,  highly  undesirable.  A  room  may  appear  brilliantly  lighted 
and  yet  objects  looked  at  may  not  be  sufficiently  well  illuminated  for  reading 
or  for  working  purposes.  The  lights  appear  brilliant  to  the  eye,  but  because 
they  throw  their  strongest  rays  in  other  directions  than  those  in  which  they  are 
needed  for  use,  they  do  not  give  efficient  illumination. 

Distinction  between  Light  and  Illumination.  There  is  not  only  a  great 
difference  between  light  and  illumination,  but  there  is  a  great  difference  be- 
tween a  brilliantly  lighted  room  and  a  well-illuminated  one.  When  anybody  is 
asked  whether  a  room  is  well  illuminated  or  not,  the  chances  are  ten  to  one  that 
he  at  once  looks  at  the  light  itself.  If  the  fight  appears  to  him  to  be  brilliant  and 
dazzling,  he  will  invariably  say,  "Why,  of  course,  the  room  is  well  lighted."  He 
should  first  look  away  from  the  light  at  the  objects  around  the  room  or  under- 
neath the  light.  If  these  can  be  seen  clearly  and  easily,  then  the  room  is  well 
ILLUMINATED.  Afterwards  he  should  look  at  the  lights  themselves,  and  if  they  ap- 
pear soft  and  pleasing  to  his  eyesight  the  room  is  well  lighted.  A  room  in  which 
the  lights  appear  soft  to  the  eye  and  yet  in  which  the  eye  can  distinguish  objects 
clearly  is  both  well  Hghted  and  well  illuminated.  A  room  in  which  the  objects 
appear  clear  to  the  eye  while  the  lights  remain  dazzling  is  well  illuminated  but 
badly  lighted.  A  room  in  which  the  fights  appear  soft  to  the  eye  and  the  objects 
not  clearly  iUuminated,  is  well  lighted,  but  badly  illuminated.  A  room  in  which 
the  lights  appear  dazzling  to  the  eye  and  the  surrounding  objects  or  those  under- 
neath appear  not  clear  to  the  eyesight  is  both  badly  lighted  and  badly  illuminated. 
An  axiom  in  good  artificial  illumination  is  to  keep  the  illumination  of  objects  as 
strong  as  is  necessary,  but  the  intensity  or  brilliancy  of  the  lights  as  low  as  pos- 
sible. By  doing  the  first  we  enable  the  eye  to  see  better;  by  doing  the  second  we 
enable  the  eye  to  feel  better  and  suffer  less  from  temporary  discomfort  or  per- 
manent' injury.  It  is  not  generally  understood  that  a  light  which  is  dazzling  and 
brilliant  to  the  eyesight  may  not  be  giving  as  much  illumination  as  another 
source  of  light  which  appears  soft,  or  even  dim,  by  comparison.  Thus  an  open 
gas-fight  is  more  dazzling  than  an  enclosed  fight,  but  is  less  efficient  in  illumi- 

•  See.  also.  Illuminatine-Gas  and  Gas-Piping,  pages  1431  to  1436. 


1438  Lighting  and  Illuminaition  of  Buildings  Part  3 

nating  a  room.  The  problem,  then,  resolves  itself  into  two  parts.  The  first  step 
should  be  to  secure  a  kind  of  lamp  which  will  cause  objects  to  appear  in  their 
accustomed  colors;  that  is,  the  colors  in  which  they  appear  by  sunlight.  The 
second  is  to  so  distribute  the  lamps  that  the  several  illuminated  surfaces  receive 
their  share  of  the  light,  and  yet  no  bright  light  is  thrown  directly  into  the  eyes. 
Nature  of  Light.  All  space  is  supposed  to  be  filled  with  a  medium  infinitely 
lighter  than  air,  called  ether.  The  sensation  of  light  is  experienced  when  certain 
wave-motions  in  this  ether  are  transmitted  to  the  eye.  These  wave-motions  are 
called  LIGHT- WAVES.  Light-waves  differ  from  one  another  in  length  and  violence. 
The  DIFFERENCE  IN  LENGTH  causes  a  difference  in  color.  Thus  short  waves  may 
be  blue  or  violet,  while  longer  waves  may  be  red  or  orange.  If  we  have  a  source 
of  light  which  sends  out  long  ether-waves,  we  may  expect  a  predominance  of  red 
and  orange  light  in  it.  The  sunlight  contains  waves  of  practically  all  lengths  and 
thus  is  composed  of  all  colors.  The  difference  in  violence  of  the  waves  gives 
rise  to  a  difference  in  intensity  of  the  light.  When  these  light-waves  strike  any 
object,  they  are  partly  reflected  and  partly  absorbed.  Substances  differ  widely 
as  to  the  percentage  of  light  they  absorb  and  the  percentage  they  reflect.  If 
two  objects  are  illuminated  by  the  same  amount  of  light,  the  one  which  absorbs 
the  less  light  and  reflects  the  more  will  appear  the  brighter.  Some  objects  reflect 
light-waves  of  a  certain  length  only,  and  absorb  all  the  rest.  It  is  this  prop- 
erty that  gives  color  to  objects.  Suppose,  for  instance,  that  a  piece  of  cloth 
were  receiving  light  from  the  sun,  all  of  which  it  absorbed  except  the  waves  of 
proper  length  to  cause  a  sensation  of  green  to  the  eye.  The  green  waves  only 
would  then  come  from  the  cloth  to  the  eye,  all  the  rest  being  absorbed,  and  the 
cloth  would  appear  green.  If  it  absorbed  waves  of  all  lengths,  it  would  appear 
black,  because  no  light  would  be  reflected  from  it  to  the  eye.  If  now  the  piece 
of  cloth,  which  absorbs  all  wave-lengths  except  that  of  green,  were  exposed  to  a 
source  of  light  which  was  emitting  all  colors  except  green,  there  being  no  green 
waves  to  be  reflected  from  it,  the  cloth  in  this  light  would  appear  black.  Sup- 
pose a  piece  of  cloth  absorbed  all  colors  but  two,  say  violet  and  red.  When  light 
having  all  wave-lengths  fell  upon  it,  it  would  absorb  all  the  waves  except  violet 
and  red.  These  two,  the  cloth  would  reflect  as  a  mixture  and  would  appear 
purple.  If,  however,  the  source  of  light  contained  no  violet  waves,  it  could  only 
reflect  the  red  waves  and  appear  red.  This  light,  then,  would  not  cause  the 
cloth  to  show  its  normal  color.  So  in  choosing  an  artificial  source  of  light,  it  is 
necessary  to  select  one  which  will  send  out  all  wave-lengths,  if  we  wish  to  have 
the  different  objects  appear  in  their  normal  colors. 

Table  I.     Colors  of  Light-Sources* 


Sun  (at  zenith) White  (all  colors) 

Electric  arc Violet-white 

Candle Orange-yellow 

Kerosene Pale  orange-yellow 

Gas-flame Pale  orange-yellow 

Wekbich  r^aO  S  Nearly  white  to  amber,  depending  upon 

WelsDacn  ^gas) j      romposition  of  mantle 

Acetylene-flame Almost  white 

Carbon,  incandescent Reddish  white 

Tungsten  or  Mazda Yellowish  white 

Mercury-arc.   Blue-green 

Moore  tube  (carbon  dioxide) White 


•  Compiled  by  R.  F.  Pierce,  Welsbach  Company. 


Intensity  of  Illumination 


14S9 


Experiment  has  shown  that  no  artificial  Hght  except  the  CO2  Moore  tube  is 
even  a  remote  approximation  to  dayhght.  The  Welsbach  white  mantle  gives  a 
much  whiter  light  than  the  tungsten-lamp,  although  neither  can  be  said  to 
approximate  daylight. 

Light-Intensity  or  Brilliancy.  Candle-Power.  The  brilliancy  of  a  source 
of  Hght  is  stated  as  its  candle-power;  that  is,  the  number  of  standard  candles 
to  which  it  is  equivalent.  Thus  an  ordinary  open  gas-flame,  consuming  5  cu  ft 
of  gas  per  hour,  is  equivalent  in  brilliancy  to  about  18  candles,  and  is  said  to  have 
an  intensity  of  18  candle-power.  Welsbach  lamps,  consuming  3  cu  ft  per  hour, 
average  about  75  candle-power;  that  is,  they  are  equivalent  to  75  candles. 
Since  no  two  sources  of  light  have  the  same  amount  of  luminous  surface,  it  is 
customary  to  rate  a  lamp  by  the  number  of  candle-power  per  square  inch  of  its 
apparent  (or  projected)  surface.  Thus  an  ordinary  candle-flame  has  about  H 
sq  in  of  area,  and  its  intensity  would  be  rated  as  3  candle-power  per  square  inch; 
that  is,  the  candle-power  it  would  have  if  its  area  consisted  of  exactly  i  sq  in. 
This  is  often  called  the  intrinsic  brilliancy  of  a  light-source.* 


Table  II. 


Accepted  Values  of  Intrinsic  Brilliancy  for  Various  Light- 
Sovirces  now  in  Use  * 


Light-Source 


Candle-power 
per  sq  in 


Moore  tube 

Frosted  electric  incandescent-lamp 

Candle 

Gas-flame 

Oil-lamp 

Cooper-Hewitt  lamp 

Welsbach  gas-mantle 

Acetylene-burner 

Enclosed  alternating-current  arc-lamp .... 

Enclosed  direct-current  arc-lamp 

Incandescent  lamps: 

Carbon,  3.5  watts  per  candle 

Carbon,  3.1  watts  per  candle 

Gem,  2.5  watts  per  candle 

Tantalum,  2.0  watts  per  candle 

Mazda  or  tungsten  1.25  watts  per  candle 

Mazda  or  tungsten,  i.o  watt  per  candle  . 

Nernst,  1.5  watts  per  candle 

Sun,  on  horizon 

Flaming  arc-lamp 

Mazda,  nitrogen-filled 

Open  arc-lamp 

Open  arc-crater 

Sun,  30°  above  horizon 

Sun,  at  zenith 


0.3-1. 75 

^5 

3-4 

3-8 

3-8 

17 

20-50 

75-100 

75-200 

ioa-500 

375 
480 
625 
750 
875 

1  000 

2  200 
2  000 
5000 
7  700 

3  OOa-50  000 
200  000 
500  000 
600  000 


*  E.  B.  Rowe,  Holophane  Works. 

Intensity  of  Illumination.     Foot-Candle.     The  extent  to  which  a  surface  is 
illuminated  is  measured  in  foot-candles.     A  surface  has  i  foot-candle  illumi- 


*  The  total  amount  of  light  given  out  by  a  light-source  is  measured  in  lumens. 
the  definition  and  use  of  this  term  see  any  standard  book  on  illumination. 


For 


1440  Lighting  and  Illumination  of  Buildings  Part  3 

nation  when  it  is  placed,  at  right-angles  to  the  light-rays,  i  ft  away  from  a  light  of 
I  candle-power  intensity.  Thus  a  paper  placed  i  ft  away  from  a  i6-candle- 
power  incandescent  lamp  would  be  illuminated  to  16  foot-candles. 

Law  of  Inverse  Squares.  The  farther  away  from  the  light  the  above  paper 
is  held  the  less  the  illumination.  But  if  it  were  held  2  ft  away,  that  is,  twice  as 
far  as  stated  above,  it  would  not  have  one-half  the  illumination.  The  illumi- 
nation which  an  object  receives  varies  inversely  as  the  square  of  the  distance 
from  the  source.  Thus,  in  this  example  the  paper  would  receive  one-fourth  as 
much  illumination,  or  4  foot-candles.  If  it  were  held  3  ft  away,  it  would  be  il- 
luminated by  one-ninth  of  16,  or  1.6  foot-candles. 

Rule.  To  find  the  intensity  of  illumination  on  any  surface,  at  right-angles  to 
light-rays,  divide  the  candle-power  of  the  lamp  by  the  square  of  the  distance 
in  FEET.  The  result  will  be  foot-candle  illumination.  This  is  called  the  law 
OF  INVERSE  squares.  Accordingly,  an  unshaded  32-candle-power  lamp  will 
illuminate  a  surface  facing  it  squarely  and  i  ft  away  from  it  with  an  intensity  of 
32  foot-candles,  but  a  surface  4  ft  away,  with  only  32/4^,  or  2  foot-candles. 

Candle-Power  and  Foot-Candle.  Careful  distinction  should  be  made 
between  candle-power  and  foot-candle.  Candle-power  is  the  measure  of 
the  intensity  of  a  source  of  light.  The  foot-candle  is  the  measure  of  the 
intensity  of  illumination  of  some  surface  upon  which  the  light  falls. 

Example  i.  What  is  the  illumination  on  a  surface  5  ft  from  a  32-candle- 
power  lamp? 

32 

Solution. =  1.28  ft-candles. 

5x5 

Example  2.  The  illumination  required  on  a  printed  page  for  easy  reading  is 
about  2  foot-candles,  (i)  How  high  above  a  reading-table  should  a  i6-candlc- 
power  lamp  be  hung?     (2)  A  32-candle-power  lamp? 

Solution.     —  =  2         x^=S        x=Vs=  2.83(1  (i) 


—„  =  2x^=i6x  =  4h  (2) 

x^ 

The  Primary  Function  of  a  Lighting-Installation  is  to  supply  sufficient 
illumination  as  required  by  the  character  of  the  work  to  which  the  lighted  space 
is  devoted.  The  following  table  can  be  used  in  computing  the  amount  of  elec- 
tric power  or  of  gas  necessary  to  satisfactorily  illuminate  the  various  rooms  in- 
cluded. 

Since  the  lower  efficiencies  of  the  indirect  and  semiindirect  systems  are  largely 
compensated  by  the  lower  intensities  required  as  compared  to  direct  lighting, 
the  same  watts  per  square  foot  may  be  allowed  in  either  case,  provided  the  con- 
ditions are  fairly  favorable  to  the  use  of  the  indirect  and  semiindirect  systems, 
namely,  light-cream  or  yellow  ceilings.  The  following  table  is  based  upon  rooms 
of  average  proportions  with  light-cream,  or  yellow  ceilings  and  medium  walls. 
High,  narrow  rooms  may  require  about  10%  more,  and  low,  wide  rooms  about 
10%  less,  energy.  Similar  allowances  may  be  made  for  dark  or  light  walls, 
respectively. 

Three  Systems  of  General  Illumination.  To  secure  the  proper  illumina- 
tion, as  indicated  in  Table  III,  there  are  three  general  systems. 


Power  Required  for  Illumination 


Table  III. 


Amount  of  Gas  or  of  Electric  Power  Required  to  Illumi- 
nate Rooms  Used  for  Various  Purposes 


Class  of  service 


Armory  or  drill-hall 

Auditorium 

Barber-shop 

Church  (see  Auditorium) 

Draft  in  g-rooin 

Factory  (general  illumination) 

Hospital  (corridor) 

Hospital  (operating-room) 

Hotel  (lobby) 

Hotel  (ball-room) 

Hotel  (dining-room) 

Hotel  (restaurant) 

Hotel  (kitchen) 

Hotel  (writing-room,  general  illumination  only) 

Hotel  (billiard-room,  general  illumination  only) 

Hotel  (buffet) 

Library  (reading-room) 

Library  (stacks) 

Oflfice  (banking  and  accounting) 

Office  (general) 

Oflfice  (private) 

Ofifice  (stenographic) 

Residence  (bedroom) 

Residence  (dining-room) 

Residence  (hall) 

Residence  (living-room) 

Residence  (music-room) 

Residence  (kitchen) 

School  (assembly  or  class-room) 

School  (class-room,  business  colleges) 

Stores    (piano,    furniture,   haberdashery,   dry-goods, 

automobile,  clothing,  cigar) 

Stores  (book,  shoe,  hardware) 

Warehouses 


*  Cu  ft  of 

gas  per  sq  ft 

per  hour 


0.02   -0.02S 

0.04  -o.os 

0.06   -0.07 


O.IO  -0.II2 
O.OI   -0.02 
0.016-0.02 
0.14   -0.15 
0.06   -0.065 

0.05  -0.052 
0.04  -0.045 
0.06  -0.07 
o.os  -0.052 
0.052-0.06 
0.06  -0.065 
0.065-0.072 
0.055-0.06 
0.012-0.024 
o  06  -0.065 
o .  052-0 .  06 
0.05  -0.52 
0.06  -0.07 

0.012 
0.036-0.04 

0.008 
0.036-0.04 
0.02  -0.025 
0.05  -0.052 
0.04  -0.045 
o . 055-0 . 06 

0.06  -0.07 
0.055-0.06 
0.012-0.036 


*Watrts 
per  sq  ft 


0.5-0.6 
10-1.3 
I -5-1  7 

2.5-2.8 
2.5-0.5 
0.4-0.5 
3.5-3.9 
1. 5-1-6 
I  2-1.3 

l.O-I.I 

I. 5-1. 7 
I. 2-1. 3 
I  3-1. 5 
I. 5-1. 6 
I. 6-1. 8 
1.4-1.5 
0.3-0.6 
1. 5-1. 6 
I  3-1  5^ 
I  2-1.3 
I-S-I.7 

0.3 
0.9-1.0 

0.2 
0.9-1.0 
0.5-0.6 
I. 2-1. 3 

I.O-I.I 

1-4-1.5 

I  5-1-7 
I  4-1  -  5 
0.3-0.9 


*  These  figures  are  based  upon  the  use  of  Welsbach  reflex  lamps  and  Mazda  electric 
lamps.  For  Welsbach  klmrtic  lamps  and  nitrogen-filled  tungsten-lamps  (type  C  Mazda) 
use  about  0.6  the  values  in  the  first  and  second  columns,  respectively.  Data  on  gas 
supplied  by  R.  F.  Pierce,  Welsbach  Company. 

(i)  Direct  Lighting.  A  system  is  designated  as  dirfxt  when  more  than  one- 
half  the  light  reaches  the  area  to  be  illuminated  by  coming  directly  from  the 
light-source,  without  being  reflected  from  the  ceiling  or  walls.  This  includes  all 
systems  using  lamps  with  clear,  frosted,  translucent,  or  opalescent  globes,  or 
reflectors,  in  which  the  light  is  reflected  downward.  It  is  the  most  efficient  sys- 
tem, was  the  first  to  be  used,  and  is  still  the  most  common.  The  color  of  the 
walls  or  ceiling  has  less  efl"ect  in  this  system  than  in  the  others. 

(2)  Indirect  Lighting.  A  system  is  designated  indirect  when  all  the  light  is 
thrown  first  on  the  ceiling  and  walls,  and  reflected  from  these  to  the  surface  to  be 
illuminated.  Any  system  which  conceals  the  source  of  light  by  opaque  reflec- 
tors is  thus  INDIRECT.    Light  finish  must  always  be  used  on  the  walls  and  ceiling 


1442  Lighting  and  Illumination  of  Buildings  Part  3 

with  this  system.  Even  then,  the  efficiency  is  usually  lower  than  that  of  a  direct 
system,  but  the  total  absence  of  glare  and  shadows  and  the  even  distribution  of 
light  make  this  a  popular  scheme  in  restaurants,  show-rooms,  etc.,  where  deco- 
rative lighting  is  desired. 

(3)  Semiindirect  Lighting.  This  system  throws  most  of  the  light  to  the  walls 
and  ceiling,  but  allows  a  small  percentage  to  be  diffused  through  the  reflector 
straight  to  the  area  to  be  illuminated.'  This  system  is  rapidly  coming  into 
favor  because  apparently  we  have  become  accustomed  to  looking  for  the  source 
of  light  and  miss  it  when  it  is  concealed  as  in  the  indirect  system.  The 
totally  indirect  fixtures  often  show  up  rather  unpleasantly  as  a  dark  spot 
against  a  light  background.*  This  is  avoided  in  the  semiindirect  system.  The 
slightly  higher  efficiency  of  this  system  is  another  advantage  over  the  indirect. 
Any  given  room  may  usually  be  lighted  by  any  one  of  the  three  systems  al- 
though it  is  generally  true  that  conditions  are  such  as  to  make  one  of  the  three 
more  desirable  than  either  of  the  other  two.  The  following  paragraphs  show  in 
detail  how  each  system  may  be  worked  out  for  a  given  room. 

General  Considerations  f  in  Direct  Lighting 

Outlets  and  Lamps.  Outlets  should  hd  located  in  the  centers  of  as  nearly  as 
possible  square  and  equal  areas  into  which  the  ceiling,  for  the  purpose  of  calcu- 
lation, may  be  subdivided.  The  greater  the  number  of  outlets  the  more  uniform 
the  illumination  and  the  greater  the  freedom  from  annoying  shadows.  Unless 
great  care  is  used  in  planning  the  directions  in  which  the  light  is  received  by  illu- 
minated surfaces,  a  disagreeable  glare  from  glazed  paper  is  likely  to  be  present. 
The  greater  the  height  of  lamps  above  the  illuminated  area,  the  more  uniform 
the  illumination.  Figures  suggestive  of  good  practice  in  selection  of  mount- 
ing-heights are  given  in  Table  IV,  page  i444- 

General  Considerations  in  Indirect  and  Semiindirect  Lighting 

Outlets  and  Lamps.  The  location  of  outlets  should  in  general  conform  to 
the  requirements  for  direct  lighting,  that  is,  at  the  centers  of  approximately 
square  and  equal  areas.  Since  glare  from  glazed  papers  is  minimized  when  most 
of  the  light  is  received  from  ceiling-reflection,  larger  and  fewer  units  are  permis- 
sible than  in  the  case  of  direct  lighting.  The  nearer  to  the  ceiling  the  lamps  are 
placed,  the  less  uniform  the  illumination  and,  within  reasonable  limits,  the  higher 
the  illuminating  efficiency  of  the  installation.  Generally  speaking,  lamps  should 
not  be  placed  less  than  2  ft  from  the  ceiling.  Aside  from  this,  the  position  of  a 
fixture  should  be  determined  by  artistic  considerations  and  reflectors  selected 
which  will  direct  most  of  the  light  upon  the  ceiling  without  concentrating  it 
enough  to  illuminate  the  ceiling  unevenly. 

A.  The  Interior  Colorings  and  Finishes. t  (i)  Ceilings  especially  should  be 
of  nearly  white,  cream,  or  light-buff  colors  to  efficiently  diffuse  the  light  down- 
ward. Dark  greens,  reds,  or  blues  are  not  advisable  since  the  reduction  in  illumi- 
nation caused  by  a  green  color,  over  a  cream  tint,  may  easily  be  from  30%  to 
60%.  On  the  other  hand,  this  system  shows  very  plainly  all  dirt  and  discolor- 
ations  on  the  ceiling,  and  no  colors  should  be  used  that  are  so  light  as  to  easily 
show  dirt,  where  there  may  not  be  careful  cleaning. 

*  This  unpleasant  effect  can  sometimes  be  avoided  by  illuminating  the  underside  of  the 
fixture. 

t  By  R.  F.  Pierce,  Welsbach  Company  and  G.  S.  Fobes,  Macbeth-Evans  Compaoy. 
i  By  G.  S.  Fobes,  Macbeth-Evans  Company. 


General  Considerations  in  Indirect  and  Semiindireet  Lighting     1443 

(2)  Finishes  preferably  should  be  matt,  or  satin,  rather  than  glazed  or  var- 
nished. From  the  matt  ceiling-surface  the  maximum  light  will  always  be  down- 
ward, but  the  varnished  ceiling  will  reflect  specularly,  directing  light  sidewise  or 
showing  lamp-images  and  glare. 

(3)  Tints  and  details  of  decoration  should  be  considered  together  with  the 
lighting-system,  so  that  daylight-colors  and  reliefs  will  not  be  reversed  or  dis- 
torted by  colored  light  from  artificial  illuminants  and  shadows. 

B.  The  Positions  of  Outlets  and  of  Fixtures,  (i)  Semiindireet  units 
should,  if  possible,  be  placed  above  the  places  where  maximum  light  is 
wanted. 

(2)  Fixtures  should  not  be  so  close  to  side  walls  as  to  cause  light-spots  running 
down  across  picture-moldings,  etc. 

(3)  Outlets  should  be  placed  logically  with  reference  to  the  ceiling-panels,  so 
that  the  more  brightly  illuminated  ceiling-areas  will  be  the  ones  that  on  account 
of  their  tints,  shapes,  or  decorations,  will  naturally  bear  emphasis.  If  the  panels 
are  deep  (deep  beams),  and  one  outlet  is  in  each  panel,  it  will  ordinarily  be 
located  at  the  center.  If  several  panels  intervene  between  units,  the  fixtures 
should  be  on  the  beams  rather  than  in  the  panels,  to  prevent  dark  ceiling-areas 
in  the  shadows  of  the  beams. 

(4)  Spacing  should  be  such  as  to  have  the  illuminated  ceiling-areas  overlap  if 
tiie  ceiling-surfape  is  uniform. 

C.  The  Proper  Lamp  and  Bowl-Sizes,  (i)  Ordinarily  the  symmetrical 
appearance  of  fixtures  with  respect  to  the  other  interior  furnishings  will  largely 
determine  their  sizes,  although  the  bowls  should  never  be  so  small  as  not  to  com- 
pletely conceal  and  nearly  surround  the  lamp-bulb. 

(2)  The  smaller  the  bowl  and  the  brighter  the  lamp,  the  less  effective  the  semi- 
indirect  system  becomes,  and  the  more  the  effect  approaches  direct  lighting. 

D.  Shapes  and  Styles  of  Bowls,  (i)  Bowls  used  close  together  or  hung  far 
from  the  ceiling  should  be  of  the  focusing  (upward)  distribution,  while  broadly 
distributing  bowls  are  better  when  used  singly,  or  when  fairly  wide  apart  and 
close  to  the  ceiling. 

(2)  Bowls  too  flat  in  shape  may  waste  considerable  light  sidewise  to  the  upper 
walls  and  therefore  be  inefficient. 

(3)  Wide  open-top  bowls  should  not  be  used  in  halls,  etc.,  where  the  bare 
lamps  are  visible  to  the  observer  from  above,  nor  on  or  below  the  level  of  a  bal- 
cony or  mezzanine. 

E.  Care  of  Fixtures,  (i)  The  average  saving  in  light  (expressed  in  terms  of 
cost  of  current)  that  results  from  washing  once  and  dusting  once  monthly,  will 
be  from  four  to  ten  times  the  cost  of  such  cleaning.  Bowls  often  collect  films 
of  dust  which  are  not  visible  and  which  materially  reduce  the  efficiency  both  of 
reflection  and  transmission. 

(2)  A  bowl  with  a  dust-cap,  button-ornament,  or  small  area  of  thick  glass  at 
the  bottom,  will  allow  dead  insects  or  dirt  to  collect  at  that  point  without 
marring  the  appearance  of  the  unit. 

(3)  Dilute  ammonia  is  an  excellent  glass-cleanser. 

•  (4)  Fixtures  should  be  arranged  to  be  lowered,  for  cleaning,  from  above  if  on  a 
very  high  ceiling  in  a  church  or  similar  structure. 

(5)  It  should  be  possible  to  easily  raise  the  lamp  or  lamps  from  within  the 
bowl,  to  allow  of  dusting  or  wiping  out. 

Figures  suggestive  of  good  practice  in  the  selection  of  mounting-heights  and 
types  of  light-distribution  are  given  in  Table  VI. 


1444  Lighting  and  Illumination  of  Buildings 

Table  IV.     Direct  System 

LAMP-SIZE,   MOUNTING-HEIGHT  AND   SPACING* 


I>art  3 


Commercial 

Watts  per 
square 

foot  =  IV 

Ideal 

spacing 

Mount- 

size of  lamps 

=  di 

stance 

Minimum 

Maximum 

ing- 

in  watts  =  W 

and  cubic 

/i 

spacing- 

spacing- 

height 

and  cubic  feet 

feet  per 

V 

distance 

distance 

per  hour 

square  foot 

V 

w 

ft 

Watts    cu  ft 

Watts    cu  ft 

ft 

in 

ft       in 

ft       in 

7  to  10 

40          1.6 

0.5      0.02 

9 

0 

8        0 

10        0 

1.5      0.06 

5 

2 

4        6 

6        0 

2.5     "o.io 

4 

0 

3        9 

4        3 

8  to  13 

6o         3.0 

0.5      0.02 

II 

0 

9        6 

12        9 

1.5      0.06 

6 

4 

5        6 

7        3 

2.5      o.io 

4 

II 

4        6 

5        6 

12  to  l6 

loo         4.0 

0.5      0.02 

14 

5 

12        6 

16        0 

1.5      0.06 

8 

2 

7        0 

9        6 

2.5        O.IO 

6 

4 

5        8 

7        0 

14  to  20 

150         6.0 

0.5        0.02 

17 

4 

15        0 

20        0 

1.5        0.06 

10 

0 

9        0 

II        0 

2.5        O.IO 

7 

9 

7        0 

8        6 

17  to  27 

250        10. 0 

0.5        0.02 

22 

5 

20        0 

25        0 

1.5        0.06 

12 

II 

II        9 

14        3 

2.5        O.IO 

10 

0 

9        0 

II        0 

25  to  35 

400        16 . 0 

0.5        0.02 

28 

2 

25        0 

31        6 

I. 5      0.06 

16 

4 

15        0 

17        9 

2.5        O.IO 

12 

7 

II        6 

13        6 

30  to  40 

500        20.0 

0.5      0.02 

31 

7 

28        0 

35        6 

1.5     0.06 

18 

6 

16        6 

20        9 

2.5        O.IO 

14 

2 

12        6 

15        0 

*  To  determine  the  size  of  equivalent  Welsbach  lamps  allow  i  cu  ft  per  hour  for  each 
25  watts.     Adapted  from  the  Electric  Journal,  by  A.  J.  Airston. 

The  Designing  of  General  Illumination  by  Each  System  Using 
Tungsten  or  Welsbach  Lamps 

(i)  From  Table  III  should  be  determined  the  watts  per  square  foot  desirable 
for  the  given  class  of  work,  and  the  total  number  of  watts  necessary  should 
then  be  computed. 

(2)  From  Table  IV  should  be  obtained  the  size  of  unit  desirable  for  a  given 
height  of  room  and  the  number  and  spacing  of  fixtures  then  computed. 

(3)  The  ceiling  should  be  laid  off  in  squares  the  sides  of  which  are  as  nearly  as 
possible  equal  to  the  value  of  the  ideal  spacing.  One  fixture  should  be  located 
at  the  center  of  each  square. 

(4)  Each  lamp  should  be  checked  up  on  the  plan  to  see  that  it  is  useful  and 
clear  of  obstacles,  and  the  layout  incorporated  into  the  building  plans  using  the 
standard  methods  and  symbols  for  electricity  or  gas  as  the  case  may  be. 


Standard  Symbols  for  Gas-Piping  Plans  1445 

Table  V.     Standard  Symbols  for  Gas-Piping  Plans* 

W  4  Ceiling-outlet;   gas  only.     Numeral  indicates  the  number  of 

single-mantle  gas-lamps. 

®  Single-lamp  outlet  (ceiling-units,  pendants,  etc.);  gas  only. 


Ceiling-outlet;    combination.        f   indicates  4  electric    lamps 
and  2  single-mantle  gas-lamps. 

Bracket-outlet;  gas  only.     Numeral  indicates  the  number  of 
gas-lamps. 

|DJ<  J_  Bracket-outlet;   combination.        f  indicates   4   electric   lamps 

^  and  2  gas-lamps. 


m^ 


2 


Baseboard-outlet;    gas  only.      Numeral   indicates  number  of 

gas-lamps. 


)il(  Floor-outlet;  gas  only. 

Q  Special  outlet  (for  portable  lamp,  heater,  etc.) ;  gas  only. 

2  Outlet  for  outdoor-standard  or   pedestal;    gas  only.      |  indi- 

jSS  "s"  cates  2  gas-lamps,  with  5  mantles  per  lamp. 

Outlet  for  outdoor  standard  or   pedestal;    combination.      Ys 
^  ^  indicates  6  electric  lamps,  and  2  gas-lamps,  with  5  mantles 

^  per  lamp. 

Arc-lamp  outlet;    gas  only.     Numeral   indicates   the  number 
W  ^  of  mantles. 

p-j-.  2  Pump  or  pneumatic  lighting-system.     Numeral  indicates  the 

number  of  lamps  to  be  operated  from  one  pump. 

Push-button  for  magnet-valve.      The  numeral  indicates  the 
number  of  lamps  to  be  operated  from  one  push-button  switch. 

Meter-outlet. 

Main  or  supply-pipe  concealed  under  floor. 
Main  or  supply-pipe  concealed  under  floor  above. 
Main  or  supply-pipe  exposed. 
Branch  pipe  concealed  under  floor. 
Branch  pipe  concealed  under  floor  above. 
Branch  pipe  exposed. 


—0^-0 '  Street  gas-main. 

l|l|l|  Battery-outlet. 

0  Riser. 


'  Illuminating  Engineering  Laboratories,  Welsbach  Company. 


1446 


Lighting  and  Illumination  of  Buildings 


Part  3 


Distance  from  Floor  to  Center  of  Wall-Outlets  * 


Living-room . 

Chambers 

Offices 

Corridors .  .  . . 


Push-button     switches     or 
pneumatic  pumps 


•  Illuminating  Engineering  Laboratories,  Welsbach  Company. 

Examples  of  Design  of  Lighting-System  for  accounting-office,  63  by  25  ft 
with  13-ft  ceiling  (Fig.  1).    Walls  and  ceiling-light  in  color. 


^ 

^ 

<>■ 

A 

A 

A 

<^ 

A 

A 

A 

_  J 

~ 

-<>- 

A 

A 

A 

A 

A 

A 

A 

A 

A 

{ 

<>• 

^ 

^>- 

A 

A 

•<;^ 

<;^ 

A 

A 

A 

i 

^ 

^ 

A 

A 

A 

A 

A 

A 

A 

A 

^ 

Watts  per  sq  ft 
Total  watts 
Unit,  size  of 


Number  of  .units 


Spacing  (average)  desired  =  6  ft  4  in  (Table  IV) 
Number  of  rows  =  25/6H  =  four 

Number  of  outlets  per  row  ==  40/4  =  ten 
Spacing  between  rows         =  25/4  =  6H  ft 
Spacing  in  rows  =  63/10  =  6H  ft 

Spacing-average  =  6  ft  4  in.    . 


Fig.  1.    Plan  of  Ceiling-lights 
Direct  System 
=  1. 5  (Table  III)    1^ 
=  1.5  X  63  X  25  =  2  400  (nearly) 
=  60  watt  electric  (Table  IV) 

=  3  cu  ft  per  hour,  ordinary  inclosed  gas,  or )    u^  1.1 
=  2  cu  ft  per  hour,  Welsbach  kinetic  )        ^  ^ 

2  400/60  ==  forty 


-63  ft— 


K 


Fig.  lA.    Modification  of  Plan  Shown  in  Fig.  1 

Fig.  1a  is  a  modification  of  the  plan  shown  in  Fig.  1,  and  is  a  great  improve 
nent.    It  will  not  produce  such  even  illumination  but  will  result  in  a  much  more 


Distrioution  of  Light  by  Reflectors 


1447 


artistic  effect,  especially  if  fixtures  are  chosen  which  harmonize  with  the  fur- 
nishings of  the  room.  The  lamps  are  placed  in  groups  of  four  on  ten  fixtures 
and  these  are  equally  spaced 
throughout  the  room.  Here 
again  it  is  always  possible  to 
use  lamps  of  higher  wattage 
at  any  point  where  the  illu- 
mination is  not  sufficient. 
The  importance  of  a  proper 
choice  of  reflector  is  shown 
from  a  study  of  Figs.  2  to 
5.*  It  will  be  noted  in  Fig. 
2  how  a  bare  tungsten-lamp 
throws  the  greater  part  of 
its  light  to  the  walls.  The 
distribution  of  any  light  can  be  controlled  to  a  remarkable  extent  by  the  use 


Distribution  of  Candle-power  about  a  Bare 
Tungsten  Lamp 


Fig.   3.     Holophane   Reflector.     Extensive       Fig.  4.     Holophane  Reflector.     Intensive 
Distribution  of  Light  Distribution  of  Light 


of  the  proper  reflector.     Figs.  3  to  5  shdw  hoW  the'  several  types  61  Hoiophand 
teflectors  distribute  the  light. 


*  Furnished  by  E.  B.  Rdwe',  df  t^e  Hotophairie  Works; 


1448 


Lighting  and  Illumination  of  Buildings 


Parts 


Fig.  5. 


Holophane  Reflector.    Focusing 
Effect  on  Light 


Fig.  6.  Example  of  Type  of  Fixtui 
Used  in  Semiindirect  System.  Mac 
beth-Evans  Company 


Indirect  or  Semiindirect  Systems,  for  Electricity 


Watts  per  sq  ft 

Total  watts 

Average  spacing 

Select  25/2 

Number  of  units  in  row 

Spacing  in  row 

Type  of  reflector 

Distance  from  reflector  to  ceiling 

Number  of  units 

Watts  per  unit 

Lamps  per  unit 


=  i.S  (Table  III) 

=  2  400,  nearly 

-  14  to  24  ft  (Table  VI)* 

=  14  ft  for  lamps  in  two  rows 

=  63/12.5  =  five 

==  63/5  =  12  ft  7  in,  about 

=  Concentrating  (Table  VI) 

=  30  in  (Table  VI) 

=  two  rows  of  five  each  =  ten 

=  2  400/10  =«  240 

=  one,  250  watts 

four,  60  watts 

six,  40  watts 


Calculations  for  this  Example  for  Gas-Lighting 

Welsbach  kinetic  burner  used. 

Cu  ft  per  hour  per  sq  ft  =  0.06  X  0.6  =  0.036  (Table  III) 

Total  hourly  consumption         =  63  X  25  X  0.036  =  57  cu  ft  per  hour. 

Average  spacing  (see  above)      =  12^6  ft 

Number  of  units  =  ten 

Consumption  per  unit  =  57/10  =  6 

Reflector  and  mounting-height  as  in  preceding  problem 

Lamps  per  unit  =  one,  6  cu  ft 

Lamps  per  unit  =  two,  3  cu  ft,  etc. 

*  See  How  to  Use  Table  VI,  immediately  following  the  Table. 


Ceiling-Outlets  and  Reflectors 


1449 


Table  VI.    For  Determining  Number  of  Ceiling-Outlets,  Type  of  Reflector 
and  the  Distance  from  Top  of  Reflector  to  Ceiling  for 
Indirect  and  Semiindirect  Lighting  * 


a 

1 
1 

20 

19 
i8 
17 
i6 
15 
14 
13 

12 

II 

10 
9'/2 

9 
SH 
8 

Distributing 

48 

48 

48 

5'-o 

6'-6 

u 

0 

^O 

K 

Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

48 

5'-o 

6'-6 

f-o 

48 

48 

5'-o 

6'-o 

48 

6'-o 

6'-6 

6'-6 
42 

48 

48 

6'-o 

42 

5'-o 

6'-o 

6'-o 
42 

4'-6 

C'-o 

36 

4'-6 

6'-o 

6'-o 

42 

42 

4'-6 

5'-6 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

Distributing 
Concentrating 

36 

42 

5'-6 

5'-^ 
'30 

4'-6 

30 

36 

4'-6 

S'-o 
30 

5'-o 

30 

48 

5'-o 
30 

30 

30 

36 

48 
24 

30 

42 

30 

48 
24 

24 

36 

48 

24 

36 

24 

30 

42 

48 

24 

42 

24 

36 

42 

i8 
i8 

30 

30 
18 

42 
18 

24 

36 

18 

30 

36 

18 

24 

30 

18 

24 

12 

18 

1 

••■]■■■ 

••"T"" 

1 

lO 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34     36 

38 

40 

One  side  of  the  limiting  square  in  feet  that  can  be  uniformly  illumi- 
nated from  one  center  outlet 

Table  VI  gives  the  distance  in  inches  (except  as  noted)  from  the  top  of  the  rellector  to 
the  ceiling  to  obtain  the  desired  distribution  of  light  from  one  ceiling-outlet. 

Where  values  are  not  given  to  the  left,  it  is  advisable  to  submit  data  to  illuminating 
engineers  and  for  greater  ceiling-heights  than  20  ft. 

*  H.  B.  Wheeler,  X-Ray  Eye-Comfort  Company. 


1450 


Lighting  and  Illumination  of  Buildings 


Part  3 


An  idea  of  the  appearance  of  some  of  the  typical  modern  fixtures  using  gas 
or  electricity  in  these  systems  of  lighting  may  be  obtained  from  Figs.  6,  7 
and  8. 

m 


Fig.  7.  Type  of  Fixture  in  Indirect 
Illumination.  National  X-Ray 
Reflector  Company 


Fig.  8.  Fixture  Used  for  Gas  by 
Either  Indirect  or  Semiindirect 
System 


How  to  Use  Table  VI.  In  the  first  column  of  Table  VI  is  located  the  height 
of  ceiling,  in  this  case,  13  ft.  The  last  square  to  the  right  of  this  figure,  which 
has  a  number  in  it,  is  noted.  In  this  case  the  last  square  to  the  right  of  13  ft^ 
which  has  a  number  in  it,  contains  the  number  48.  By  following  this  column 
containing  the  number  48  down  to  the  figures  printed  in  heavy  type  at  the  bottom 
of  the  table,  the  heavy-faced  number  in  this  case  is  found  to  be  24.  This  24  is 
the  length  of  the  side  of  the  largest  square  which  a  single  fixture  can  properly  illu- 
minate when  the  ceiling  is  13  ft  high.  The  48  which  is  opposite  the  13  is  merely 
the  number  of  inches  the  fixture  must  be  hung  from  the  ceiling.  Thus  the 
largest  squares  into  which  we  can  possibly  divide  the  ceiling  have  24-ft  sides. 
But  a  room  25  ft  wide  cannot  be  divided  into  24-ft  squares.  We  are  compelled, 
therefore,  to  divide  it  into  squares  of  a  smaller  size,  since  the  fixtures  will  not 
illuminate  any  larger  square.  The  greatest  length  into  which  we  can  divide 
25  ft  is  121.^  ft.  We  may,  then,  decide  to  use  fixtures  which  will  illuminate  14-ft 
squares.  Locate  the  number  14  in  heavy  type  at  bottom  of  table,  and  trace  up 
the  column  in  which  it  is  found  until  the  square  is  reached  which  is  opposite  the 
ceiling-height  of  13  ft.  Plere  the  number  30  is  found.  This  means  we  must 
hang  the  fixture  so  that  the  top  of  it  is  30  in  from  the  ceiling  in  order  to  get  the 
desired  results.  Looking  along  the  squares  to  the  right  of  the  one  in  which  we 
find  the  30,  we  find  the  word  concentrating,  which  signifies  the.  tvne  of  reflector 
advised  for  this  installation. 


Illumination  by  Gas 


14Si 


School-Room  Lighting.*  The  following  illumination-constants  have  been 
worked  out  by  experiments  and  experience  covering  a  wide  range  of  conditions. 
In  each  of  the  following  cases  light  tinted  walls  and  ceilings  are  taken  as  a 
standard. 

Auditoriums  and  Lecture-Halls.  Since  no  continuous  reading  is  required  here, 
0.75  watt  per  sq  ft,  direct  system,  is  all  that  is  needed,  if  it  is  properly 
diffused  to  a  pleasant  softness. 

Class-Rooms  and  Laboratories.  These  must  be  lighted  for  the  purpose  of  writ- 
ing notes  and  taking  accurate  readings  of  instruments.  Thus  iH  watts  per  sq  ft,, 
direct  system,  are  required. 

Wood- Working  Shops.  The  surfaces  here  are  generally  high  and  offer  good 
reflecting  properties,  so  that  iH  watts  per  sq  ft,  direct  system,  are  sufficient. 

Machine-Shops.  Because  the  belts,  machines  and  dingy  floors  offer  great 
absorbing  surfaces  at  least  2  watts  per  sq  ft,  direct  system,  are  necessary. 

Foundries.  The  dark  molding-sand  and  the  dust  and  smoke  in  the  air  make 
3  watts  per  sq  ft,  direct  system,  necessary. 

Drafting-Rooms.  The  semiindirect  system  with  2H  watts  per  sq  ft  (about 
the  equivalent  of  1^4  watts  per  sq  ft,  direct  system)  has  proved  highly  satis- 
factory. 

Illumination  by  Gas.f  Recent  progress  in  incandescent  gas-lighting  has 
resulted  in  the  development  of  appliances  in  which  practically  all  of  the  short- 
comings of  previous  types  are  overcome,  and  except  for  inaccessible  locations, 
or  where  lamps  are  very  infrequently  lighted,  there  is  little  to  choose  between  the- 
two  illuminants,  gas  and  electricity,  upon  the  score  of  convenience  or  of  artistic 
possibiHties,  while  the  greater  economy  of  gas-lighting  (often  in  the  ratio  of  about 
2y2  to  i)  coupled  with  the  freedom  from  interruption  which  characterizes  gas- 
service  makes  it  desirable  to  pipe  all  buildings,  particularly  residences,  for  gas 
throughout,  preferably  installing  combination-fixtures  and  providing  wall-out- 
lets and  baseboard-outlets  for  the  connection  of  the  various  gas-operated  con- 
veniences which  are  being  developed  in  rapidly  increasing  numbers. 


Welsbach  Kinetic-Burner    Lamps    With  Nearest   Equivalent    Sizes    in    Electric 
Incandescent  Lamps 


Lamps 


Mazda 
watts 


Nitrogen-filled 

Mazda  (Type  C> 

watts 


T  mantle 

2  mantles 

3  mantles 

4  mantles 

5  mantles 

6  mantles 
8  mantles 

10  mantles 


2.5  cu  ft  per  hour. 

5.0  cu  ft  per  hour. 

7.5  cu  ft  per  hour, 
lo.o  cu  ft  per  hour. , 
12.5  cu  ft  per  hour., 
15.0  cu  ft  per  hour.. 
20.0  cu  ft  per  hour. , 
25,0  cu  ft  per  hour. , 


two,  40 
ISO 
•250 
six,  40 
400 
Soo 


Soo 
750 


Gas-Lamps  are  available  in  a  variety  of  types  and  sizes.  The  most  recent 
development  is  the  kinetic  burner  of  the  Welsbach  Company  in  which  the 
efficiency  is  increased  by  from  50%  to  100%  over  the  previous  types.  With 
this  burner  no  enclosing  glassware  or  housings  are  required,  and  the  lamp  is  said 


A.  L.  Williston. 


f  R.  F.  Pierce,  Welsbach  Company. 


1452  Lighting  and  Illumination  of  Buildings  Part  3 

to  require  no  attention  beyond  the  renewal  of  mantles  every  2  cxx5  burnirtg- 
hours.  There  is  practically  no  depreciation  in  candle-power  during  this  interval. 
Ignition  is  accomplished  either  by  a  pilot-flame  burning  about  Ho  cu  ft  per  hour, 
or  by  electrical  means,  and  several  types  of  distant  control  are  available.  The 
following  table  gives  the  sizes  in  which  these  lamps  may  be  obtained  and  the 
nearest  equivalent  sizes  in  electric  incandescent  lamps. 

Selection  of  Illuminants 

(i)  Factors  favorable  to  the  use  of  electricity: 
Units  less  than  60  candle-power  required. 
Lamps  in  inaccessible  positions. 
Lamps  lighted  at  infrequent  intervals. 
Lamps  placed  very  close  to  ceiling  (12  in  or  less). 
Poor  gas  service  as  regards: 

Pressure-regulation  (more  than  50%  variation  from  minimum). 

Non-uniformity  of  gas-quality. 

Imperfect  purification. 
Good  electric  service  as  regards: 

Voltage-regulation. 

Freedom  from  liability  to  derangement  by  accident. 
Non-rigid  fixtures. 
(2)  Factors  favorable  to  the  use  of  gas: 
Units  of  60  candle-power  or  more. 
Accessible  locations. 
Frequent  use  of  lamps. 
Lamps  placed  15  in  or  more  from  ceiling. 
Good  gas  service  as  regards: 

Pressure-regulation  (not  more  than  50%  variation  from  minimum). 

Uniformity  of  gas-quality  (chemical  composition). 

Proper  purification. 
Poor  electric  service  as  regards: 

Voltage-regulation   (more  than  5%  variation  from  maximum)  most 
likely  on  alternating-current  circuits. 

Liability  to  derangement  by  accident  (overhead  circuits). 

Rigid  fixtures. 

Hygiene.*  From  the  hygienic  point  of  view  there  is  little  to  choose  between 
the  two  illuminants.  The  investigations  of  Dr.  Rideal  have  shown  that:  (i)  Gas- 
light positively  improves  the  air  for  breathing  purposes  under  the  actual  condi- 
tions of  use.  The  causes  of  this  improvement  are  the  acceleration  of  ventila- 
tion, the  destruction  of  disease-germs  and  the  addition  of  necessary'  moisture. 
Gas-burners  give  rise  to  stronger  air-currents  and  invariably  produce  a  more 
active  ventilation  and  diffusion  of  air  than  electric  lights;  hence,  along  with 
the  products  of  the  gas-burner,  the  exhalations  of  persons  present  are  more 
rapidly  removed;  (2)  The  ascending  currents  of  air  from  the  gas-lights  on 
reaching  the  ceilings  rapidly  part  with  their  heat,  which  is  conducted  away  by 
the  rafters  and  joists;  (3)  The  electric  lamps  produce  more  heat  than  is  com- 
monly accredited  to  them,  and  this  is  the  explanation  of  the  unexpected  result 
that  the  average  temperature  of  the  room  is  practically  the  same  under  either  il- 
luminant,  and  that  the  electric  light  does  not  show  the  superiority  in  coolness 
usually  claimed.     When  excessive  temperatures  are  encountered  in  gas-lighted 

*  See  Relative  Hygienic  Values  of  Gas  and  Electric  Lighting,  by  Samuel  Rideal,  Trans- 
actions Royal  Sanitary  Institute,  March,  1908. 


Diffusion  of  Light  through  Windows  14^ 

rooms,  it  will  be  found  due  to  the  radiant  heat  from  low-hung  lamps  of  ex- 
cessive size.  On  "account  of  the  economy  of  gas-lighting,  it  is  a  common  prac" 
tice  to  provide  from  four  to  six  times  as  much  illumination  as  is  required- 
Dr.  Rideal's  tests  also  emphasized,  what  is  a  matter  of  common  experience, 
that  under  direct  lighting,  the  lower  brilliancy  of  the  gas-mantle  reduced  the 
glare  from  glazed  papers  to  such  an  extent  as  to  be  noticeable  in  the  results: 
"The  sensitiveness  of  the  eye  to  light  as  measured  in  the  perception-test  dimin- 
ished very  markedly  after  exposure  to  the  electric  light,  while  no  corresponding 
effect  is  noticeable  after  the  eye  has  been  subjected  to  gaslight.  All  the  results 
point  strongly  in  the  same  direction,  namely,  that  gaslight,  as  used  in  these 
experiments,  is  less  fatiguing  to  the  eye  than  electric  light."  Under  senii- 
indirect  or  indirect  lighting,  of  coursej  no  such  disparity  in  effect  is  found. 
The  Foregoing  Rules  Indicate  the  General  Practice  in  planning  the  illu- 
mination of  a  room.  It  must  be  said,  however,  that  this  set  of  rules  must  not  be 
followed  too  slavishly.  In  illumination  no  rules  can  take  the  place  of  judgment 
and  intelligence.  Each  project  must  be  considered  more  or  less  as  a  problem  by  . 
itself,  for  which  previous  experience  and  former  installations  should  be  made  to 
furnish  data  and  to  suggest  methods.  It  is  well,  therefore,  when  planning  the 
illumination  of  a  room,  to  visit  as  many  similar  rooms  as  possible,  note  the  effect 
of  the  systems  in  use  and  obtain  data  as  to  their  efficiency,  cost,  etc.  The  most 
successful  scheme  may  then  be  used  as  the  basis  for  planning  the  desired  instal- 
lation. 

The  Diffusion  of  Light  through  Windows  * 

Tests  on  the  Diffusion  of  Light  by  Glass.  Abstracts  from  report  of 
Charles  L.  Norton,  on  an  elaborate  series  of  tests  made  at  the  Massachusetts  In- 
stitute of  Technology  :t  The  results  of  the  tests  on  a  score  or  more  of  different 
glasses  may  be  stated  briefly.  We  may  increase  the  light  in  a  room  30  ft  or 
more  deep  to  from  three  to  fifteen  times  its  present  effect  by  using  factory- 
ribbed  GLASS  instead  of  plane  glass  in  the  upper  sashes.  By  using  prisms 
we  may,  under  certain  conditions,  increase  the  effective  light  to  fifty  times  its 
present  strength.  The  gain  in  effective  light  on  substituting  ribbed  glass  or 
prisms  for  plane  glass  is  much  greater  when  the  sky-angle  is  small,  as  in  the  case 
of  windows  opening  upon  light-shafts  or  narrow  alleys.  The  increase  in  the 
strength  of  the  light  directly  opposite  a  window  in  which  ribbed  glass  or 
prisms  have  been  substituted  for  plane  glass  is  at  times  such  as  to  light  a  desk  or 
table  50  ft  from  the  window  better  than  one  20  ft  from  the  window  had  pre- 
viously been  lighted. 

The  Kinds  of  Glass  Tested  were  as  follows: 

(i)  Ground  glass  of  different  degrees  of  fineness. 

(2)  Rough  plate  or  hammered  glass. 

(3)  Ribbed  or  corrugated  glass,  with  five,  and  eleven  and  twenty-one  ribs  to 
the  inch,  the  corrugations  being  sinusoidal  in  outline,  as  in  A,  Fig.  9,  and  the 
back  of  the  plate  smooth. 

(4)  Glass  known  as  maze,  Florentine  or  figured,  in  which  a  raised  pattern 
is  worked  upon  one  side,  practically  roughening  the  whole  surface. 

(5)  Wash-board  glass,  corrugated,  with  twenty-one  ribs  to  the  inch  on  one 
side  and  five  ribs  to  the  inch  on  the  other  side,  the  ribs  being  parallel. 

(6)  Skylight-glass,  which  has  five  ribs  to  the  inch  on  each  side,  the  groove  on 
one  side  being  opposite  the  rib  on  the  other,  giving  a  sinuous  section  B,  Fig.  9. 

♦  See,  also,  the  subjects  Pressed  Prism-Plate  Glass  and  Prism  Glass,  Part  III,  pages 
IS77  to  1579. 
t  From  Report  No.  Ill,  Insurance  Engineering  Experiment  Station,  September,  1903, 


1454 


Lighting  and  Illumination  of  Buildings 


Part  3 


Fig.  9.    Types  of  Ribbed  or  Prism-glass 


(7)  Ripple-glass,  with  rippled  surfaces  on  both  sides;  of  very  beautiful  appear- 
ance and  a  clear  white  color. 

(8)  Glass  ribbed  on  one  side  and  figured  on  the  other. 

(9)  Ribl)ed  glass  with  a  wire  net  pressed  into  it,  to  increase  its  resistance  to  fire. 
Of  these  several  specimens,  one  or  two  may  be  dismissed  with  brief  mention. 

Groiuid  glass  is  of  little  value,  except  as  a  softening  medium  for  bright  sunlight. 

Its  rapidly  increasing  opaqueness 
with  moisture  and  dust  makes  it 
undesirable  as  a  window-glass. 
The  common  rough  plate  has  very 
little  action  as  a  difl^using-medium, 
giving  no  perceptible  change  in 
the  effective  light.  Ripple-glass 
has  great  value  as  a  diffusing- 
medium  in  small  rooms  with 
nearly  open  horizon.  Of  the  ribbed 
glasses,  the  fine  Factory-Ribbed, 
with  twenty-one  ribs  to  the  inch, 
is  distinctly  the  best,  not  in  all 
probability  because  of  the  fine- 
ness, but  because  of  the  greater 
sharpness  of  the  corrugations. 
The  Ribbed  wire-glass  is  about  20%  less  effective  than  the  ordinary  Factory- 
Ribbed  glass.  The  addition  of  a  second  corrugation  upon  the  back  of  the  plate 
giving  the  Skylight  and  Wash-Board  glass  is  of  no  apparent  value.  The  raised 
pattern  imprinted  upon  one  surface  of  the  glass,  as  in  the  case  of  the  Maze 
glass,  gives  the  widest  diffusion,  especially  in  bright  sunlight.  A  raised  figure, 
when  worked  upon  the  back  of  the  Ribbed  glass,  renders  it  less  offensive  to  the 
eye  in  bright  sunlight,  but  less  effective  in  deep  rooms.  The  only  glasses  of 
this  group  which  it  is  worth  while,  then,  to  discuss  further  are  the  F'actory- 
Ribbed  and  the  Maze  glass. 

The  second  group  comprises  the  following  glasses: 
(i)  The  Luxfer  prisms. 

(2)  The  Solar  prisms. 

(3)  The  Daylight-prisms. 

(4)  The  glass  of  prismatic  section  made  by  the  Mississippi  Glass  Company. 

(5)  Three-way  prisms. 

(6)  Maltby  prisms. 

The  Luxfer  prism  consists  of  a  plate  smooth  on  one  side  and  deeply  notched 
on  the  other  as  in  C,  Fig.  9,  the  teeth  or  prisms  being  of  very  flat,  smooth 
faces  of  brilliant  appearance.  The  glass  is  clear  white,  and  the  prisms  used  in 
canopies  and  in  the  major  part  of  the  vertical  glazing  are  made  in  tiles  or  plates 
about  4  in  square.  Tiles  are  built  up  in  large  sheets  in  frames  of  copper  or  brass, 
so  made  as  to  give  to  the  sheets  of  tiles  a  strength  and  durability  far  in  excess 
of  a  single  sheet  of  the  same  size.  The  Luxfer  prisms  are  made  for  factory- 
use  in  large  sheets,  as  well  as  in  the  small  tiles.  The  Solar  prisms  are  made  in 
small  tiles,  which  are  held  together  in  a  metal  frame  to  make  large  sheets.  The 
main  difference  between  the  Solar  and  Luxfer  prisms  is  that  the  under  face  of  the 
former  prism  is  curved  instead  of  plane,  as  in  D,  Fig.  9.  The  Daylight-prisms 
tested  were  made  in  large  sheets  and  of  approximately  the  same  cross-section  and 
general  app>earance  as  the  Luxfer  prisms  for  factory-use.  No  tiles  of  Daylight- 
prisms  were  tested,  as  none  came  to  hand  in  time  for  the  test.  The  Mississippi 
prism  glass  is  much  like  the  other  prisms  is  cross-section,  but  the  ridges  or 


Diffusion  of  Light  through  Windows 


1455 


Refraction   of    Light   in 
Prism-glass 


Ribbed    and 


prisms  do  not  run  across  the  plate  in  a  straight  line,  but  in  a  wavy  or  sinuous  line. 
No  advantage  arising  from  this  over  the  straight-edge  prism  was  detected. 

Conclusions,     (i)  The  conditions  in  a  room  less  than  15  ft  deep  are  such 
that,  except  with  a  skyhght  of  less  than  45°,  it  is  not  advisable  to  alter  the  general 
course  of  the  light  by  using  a  prismatic  or  ribbed  glass.     A  nearly  hemispherical 
diffusion,  such  as  is  given  by  the 
Maze   or   Ripple-glass,   is   ordi- 
narily preferable. 

(2)  When  a  room  is  from  20 
to  60  ft  deep,  or  even  more,  and 
has  a  skylight  of  60°  or  less,  the 
ribbed  and  prismatic  glass  results 
in  a  very  great  gain  in  effective 
light.  The  gain  in  brilHancy  is 
such  as  to  make  a  basement  with 
prism-canopies  as  light  as  a 
second  story  with  plane  glass. 

Rooms  with  windows  opening 
upon  light-shafts  and  narrow 
alleys  with  very  limited  openings 
to  the  sky,  where  the  available 
hght  is  now  small,  may  have  the  light  20  ft  back  from  the  window  increased  ten 
or  twenty  times  by  using  prisms;  and,  by  using  canopies  of  prisms,  it  is  some- 
times possible  to  strengthen  the  light  fifty  to  one  hundred  times.  With  sky- 
angles  of  30°,  or  less,  and  in  deep  rooms,  the  relative  efficiency  of  the  prism 
tile  increases  greatly.  The  refraction  of  the  incident  ray  in  a  case  of  the  ribbed 
glass  and  prism  is  shown  in  Fig.  10.  Ribbed 
and  maze  glass  are  of  very  great  value  in 
softening  the  light,  especially  in  the  case  of 
such  windows  as  are  exposed  to  the  direct 
sun,  aside  from  their  effectiveness  in  strength- 
ening the  light  at  distant  points.  With 
the  Maze  glass,  the  artist  may  have,  in  all 
weather  and  in  all  directions,  what  is  in  effect 
a  much-desired  north  light.  The  photog- 
rapher may  have  in  this  way  as  well  diffused 
a  light  as  he  now  has  with  cloth  screens  or 
shades,  and  with  a  much  greater  intensity. 
To  be  efficient  in  rooms  20  ft  deep  or  more, 
ribbed  glass  should  be  set  with  its  ribs  hori- 
zontal, and  where  the  sunlight  falls  upon  it,  it 
should  be  provided  with  thin  white  shades. 
All  inferences  drawn  from  the  test  are  made 
upon  the  assumption  that  the  windows 
are  to  be  glazed  with  diffusing  glass  only 
in  the  upper  half,  which  is  the  common 
practice.  If  the  lower  sash  is  to  be  glazed 
a    further   increase   of   about    25%    may    be 


Fig.  11.     Basement  and  First  Story 
Lighted  from  Court 


with    diffusing   glass    as    well, 
expected. 

Considering  both  expense  and  efficiency,  the  following  general  suggestions  are 
given:  Use  Maze  or  Ripple-glass  in  small  rooms  or  offices  not  more  than  15  or  20  ft 
deep;  use  Factory-Ribbed  glass  in  rooms  from  30  to  50  ft  deep,  with  sky-angles  of 
60°  or  more;  use  prisms  or  Factory-Ribbed  glass,  in  sheets,  in  all  vertical  win- 


1456  Lighting  and  Illumination  of  Buildings  Part  c 

dows  in  rooms  more  than  from  50  to  60  ft  deep,  with  sky-angle  of  less  than  45** 
With  a  sky-angle  of  less  than  30°  use  prisms  in  canopies.  Fig.  11  shows  ar 
effective  method  of  lighting  the  basement  and  first  story  where  the  light  mus1 
come  from  a  court. 

Reference  Books  on  Illumination 

Practical  Illumination,  1907.     Cravath  and  Lansingh. 

Art  of  Illumination,  1902.     Louis  Bell. 

Electrical  Illuminating  Engineering,  1908.     Barrows. 

Light,  Visible  and  Invisible.     Sylvanus  Thompson. 

American  Practice  of  Gas-Lighting.     \V.  P.  Gerhard. 

Color  Values.     C.  R.  Clifford. 

Radiation,  Light  and  Illumination,  1909.     C.  P.  Steinmetz. 

Illumination  and  Photometry,  19 10.     Wickenden. 

Electric-Lamps,  1908.     Maurice  Solomon. 

Illumination,  its  Distribution  and  Measurement,  19 10.     Alex.  Pelhan  Trotter 

Photometric  Measurements,  1904.     W.  M.  Stine. 

Proceedings  and  Transactions  of  Illuminating  Engineering  Society. 

Proceedings  and  Transactions  of  American  Institute  of  Electrical  Engineers. 

Proceedings  and  Transactions  of  National  Electric  Light  Association. 

Proceedings  and  Transactions  of  American  Gas  Institute. 

The  Illuminating  Engineer  (New  York). 

The  Illuminating  Engineer  (London)  with  which  is  combined  the  Transactioni 

of  the  London  Illuminating  Engineering  Society. 
Foster's  Engineers'  Pocket-Book,  1908. 
Standard  Handbook  for  Electrical  Engineers,  1908. 
.Engineering  Section,  Holophane  No.  2  Data  Book. 

Bulletins  of  the  Engineering  Department,  National  Electric  Lamp  Association 
Bulletins  of  the  General  Electric  Company. 
Tungsten  Illumination,  19 10.     Westinghouse  Company. 
The  Electrical  SoHcitor's  Handbook,  19 10.    National  Electric  Light  Associa 

tion. 
Gas  Solicitor's  Handbook,  1910.     Welsbach  Company, 
Factory  Lighting,  C.  E.  Clewell. 
American  Electricians'  Handbook,  Terrell  Crofto 


Electric  Work  for  Buildings 


1457 


ELECTRIC  WORK  FOR  BUILDINGS 


By 

W.  H.  TIMBIE 

Associate   professor    of   electrical   engineering,   Massachusetts   institute   of 

technology 

General  Considerations  and  Definitions.  Electrical  energy  is  now  in  com- 
mon use,  furnishing  power,  heat  and  light,  operating  bells  and  buzzers,  and 
transmitting  messages  by  telephone  and  telegraph.  In  order  to  accomplish 
these  results,  a  current  of  electricity  must  flow  around  an  electric  circuit.  The 
nature  of  electricity  is  not  known,  but  the  flow  of  it  through  an  electric  circuit 
is  analogous  to  the  flow  of  water  through  a  system  of  pipes. 

Current.  Amperes.  The  flow  of  water  is  measured  in  gallons  per  second. 
The  flow  of  electricity  is  measured  in  amperes.  An  ampere-flow  of  electricity 
is  analogous  to  a  gallon-per-second  flow  of  water..  The  amperes  thus  indicate 
the  quantity  of  electricity  flowing  through  an  electrical  appliance  in  one  second. 
About  y2  ampere  is  flowing  through  an  ordinary  carbon-filament  incandescent 
lamp  when  it  is  glowing  at 
1 6  candle-power.  The  same  -I 
current  of  y2  ampere  causes  a  ^ 
modern  tungsten  lamp  to  pro- 
duce over  40  candle-power. 
An  arc-lamp  usually  requires 
a  flow  of  from  5  to  10  amperes. 

Pressure.  Volts.  When  a 
current  of  water  flows  from 
one  point  to  another  in  a  pipe- 
system,  it  is  always  because 
there  is  a  hydraulic  pressure 
present  causing  it  to  flow. 
This  pressure  is  usually  meas- 
ured in  pounds  per  square 
inch.  Similarly,  when  a  cur- 
rent of  electricity  flows  from 
one  point  to  another  in  -an 
electric  circuit,  it  is  because  there  is  an  electric  pressure  present  which 
causes  it  to  flow.  This  electric  pressure  is  measured  in  volts.  An  electric 
pressure  of  i  volt  is  analogous  to  a  hydraulic  pressure  of  i  lb  per  sq  in.  The 
pressure  which  causes  the  J^i-ampere  current  to  flow  through  an  incandescent 
lamp  is  usually  no  volts.  The  electric  company  instals  at  least  two  wires  in  a 
residence  and  then  maintains  an  electric  pressure  of  no  volts  between  them 
just  as  the  water  company  maintains  a  pressure  in  the  water-pipes.  This 
electric  pressure  is  at  all  times  tending  to  force  electricity  from  one  wire  to  the 
other  wire  across  the  space  between  the  two  wires,  just  as  the  water-pressure 
tends  to  force  the  water  out  from  the  pipe.  The  rubber  insulation  is  put  on  to 
prevent  this  flow,  very  much  as  the  strength  and  compactness  of  the  iron  pre- 
vents the  flow  of  water  through  the  walls  of  the  pipe.  But  when  one  terminal 
of  a  lamp  is  connected  to  one  wire  and  the  other  terminal  to  the  other  wire,  the 
electric  pressure  tending  to  send  a  current  from  one  wire  to  the  other,  sends  a 
current  through  the  lamp  and  causes  it  to  glow.    We  mark  the  wire  bringing  the 


^110^ 

volts 

+ 

X 

• 

s 

y 

J 

-A 

. 

J 

■3 

+ 

^ 

. 

+ 

^ 

- 

Fig.  1. 


Current  Always  Flows  from  (+)  to  (— ) 


1458  Electric  Work  for  Buildings  Part  3 

current  to  the  lamp  (+).  The  wire  taking  the  current  away,  we  mark  (— ). 
Thus  in  Fig.  1,  if  the  current  comes  in  on  the  wire  marked  (.r),  this  wire  is  (+) 
and  the  wire  {y)  is  ( — ).  A  pressure  of  no  volts  is  maintained  which  tends  to 
cause  a  current  to  flow  across  from  the  wire  (x)  to  the  wire  {y).  No  current  can 
flow,  however,  unless  some  path  is  afforded  between  the  two  wires.  For  in- 
stance, no  current  is  flowing  through  lamp  Li,  because  the  open  switch  A  makes 
a  gap  across  which  the  current  cannot  pass.  Switch  B,  however,  is  closed,  thus 
allowing  the  pressure  to  force  a  current  from  the  wire  (x)  through  the  lamp 
Li  to  the  wire  (y)  and  back  into  the  street-mains.  Of  course  the  electric  com- 
pany maintains  the  no-volt  pressure  between  the  wires  (x)  and  (y)  whether  any 
current  is  drawn  from  the  wires  or  not,  just  as  a  water  company  maintains  the 
pressure  in  the  water-mains  whether  any  water  is  drawn  from  the  pipes  or  not. 
Resistance.  Ohms.  The  fact  that  a  current  of  only  ^  ampere  flows  through 
an  incandescent  lamp  when  a  pressure  of  no  volts  is  applied  to  it,  is  due  to  the 
RESISTANCE  of  the  fine  filament.  This  resistance  of  the  filament  is  analogous 
to  the  resistance  which  a  pipe  of  small  bore  ofl"ers  to  the  flow  .of  water.  The 
resistance  of  an  electrical  appliance  is  merely  the  ratio  of  the  pressure  to  the 
current  which  that  pressure  can  force  through  it.     As  an  equation,  it  is  expressed 

,  pressure 

Resistance  = 

current 

When  the  pressure  is  measured  in  volts  and  the  current  in  amperes,  the  re- 
sistance is  then  in  ohms.     Thus 

Ohms  = ■ 

amperes 

Thus,  since  a  pressure  of  no  volts  forces  H  ampere  through  an  ordinary  in- 
candescent lamp,  the  resistance  of  the  lamp  is  wojy^  =  220  ohms. 

Ohm*s  Law.  This  relation  between  pressure,  current  and  resistance  is  called 
Ohm's  law.     It  is  written  in  symbols  in  the  three  forms 

R  =  E/I 

E  =  IR 

I  =  E/R 
where  * 

R  =  resistance  in  ohms; 
E  =  pressure  in  volts; 
I  =»  current  in  amperes. 

Example.    An  electric  flat-iron  has  a  resistance  of  35  ohms.     What  current 
will  flow  through  it  when  it  is  put  across  a  no- volt  circuit? 
/  =  E/R  =  110/35  =  3.14  amperes 

Example.  An  electric  toaster  takes  il^  amperes  when  on  a  115-volt  circuit. 
What  resistance  does  it  have? 

R  =  E/I  =  115/1.5  =  76.6  ohms 

Insulators  and  Conductors.  In  order  that  practically  no  current  may 
leak  from  one  wire  to  the  other,  the  wires  are  covered  with  rubber.  This  rubber 
covering  offers  such  high  resistance  to  the  flow  of  an  electric  current  that,  al- 
though two  wires  may  lie  very  close  to  one  another  with  only  this  rubber  be- 
tween them,  practically  no  current  leaks  through  the  rubber  from  one  wire  to 
the  other.  Materials  such  as  rubber,  glas^,  porcelain,  dry  wood,  etc.,  have  this 
resisting  property  and  are  said  to  be  insulators.  Metals,  on  the  other  hand, 
offer  very  little  resistance  to  the  flow  of  an  electric  current  and  are  called  con- 


Power  in  Electric  Work  14^ 

DUCTORS.  A  copper  wire  Ho  in  in  diameter  has  a  resistance  of  only  Hooo 
of  an  ohm  per  foot.  Accordingly,  because  of  their  low  resistance,  copper  wires 
are  generally  used  to  carry  electric  currents,  and  because  of  its  high  resistance, 
rubber  is  generally  used  as  a  covering  of  the  copper  wires  to  prevent  leakage 
from  one  wire  to  another.  Wire,  approved  by  the  National  Board  of  Fire  Under- 
writers and  installed  according  to  their  rules,  will  have  the  proper  insulating 
covering  for  each  installation.  ^ 

Power.  Watts.  The  flow  of  an  electric  current  has  been  likened  to  the  flow 
of  water  through  a  pipe.  A  current  of  water  is  measured  by  the  number  of 
gallons,  or  pounds,  flowing  per  minute;  a  current  of  electricity  is  measured  by 
the  number  of  amperes.  The  power  required  to  keep  a  current  of  water  flowing 
is  the  product  of  the  current  in  pounds  per  minute  by  the  head,  or  pressure, 
in  FEET.  This  gives  the  power  in  foot-pounds  per  minute.  To  reduce  to 
horse-power,  it  is  necessary  merely  to  divide  by  s^  coo.     Thus 

(pounds  per  minute)  x  (feet) 

■ •  =  horse-power 

33  ooo 

In  exactly  the  same  way,  the  power  required  to  keep  a  current  of  electricity 
flowing  is  the  product  of  the  current  in  amperes  by  the  pressure  in  volts. 
This  gives  the  power  in  watts. 

Watts  =  amperes  x  volts 

The  term  watt  is  merely  a  unit  of  power,  and  denotes  the  power  used  when 
one  volt  causes  one  ampere  of  current  to  flow.     The  watts  consumed  when  any 
given  current  flows  under  any  pressure  can  always  be  found  by  multiplying  the- 
current  in  amperes  by  the  pressure  in  volts.     Thus,  if  an  incandescent  lamp 
takes  0.5  iampere  when  burning  on  a  iio-volt  line,  the  power  consumed  equals     . 

0.5  X  110=^  55  watts 
That  is, 

Power  =  current  x  pressure 
or 

Watts  =  amperes  x  volts 

Example.  What  power  is  consumed  by  a  motor  which  runs  on  a  2 20- volt 
circuit,  if  it  takes  4  amperes? 

Watts  =  amperes  x  volts  =  4  X  220 
Power  =  880  watts 

Incandescent  lamps  are  rated  as  to  the  voltage  of  the  line  on  which  they  can 
run,  and  also  as  to  the  amount  of  electric  power  it  takes  to  keep  them  glowing. 
Thus,  a  carbon-filament  lamp  may  be  rated  as  a  no-volt,  50- watt  lamp.     A 
tungsten-lamp  may  be  rated  as  a  no-volt,  25-watt  lamp.     This  means  that  both 
lamps  are  intended  to  run  on  a  no- volt  circuit,  but  that  it  takes  twice  as  much 
power  to  keep  the  carbon-filament  lamp  glowing  as  it  does  to  keep  the  tungsten- 
lamp  glowing.  H 
The  Power-Equation.     The  above  relation  between  volts,   amperes  and 
watts  is  usually  expressed  in  the  form  of  an  equation: 
P  =  7E 
I  =  P/E 
E  =  P/I 
where 

p  =  power  in  .watts; 
I  =  current  in  amperes; 
E  =  pressure  in  volts. 


1460  Electric  Work  for  Buildings  Part  3 

Example.  What  current  does  a  40-watt  tungsten-lamp  take  when  running  on 
a  1 1 5- volt  circuit? 

I  «=  P/E  =  40/115  =  0.348  arripere 

Power.  Kilowatt  and  Horse-Power.  Because  the  watt  is  so  small  a  unit 
of  power,  being  only  0.74  ft-lb  per  second,  a  larger  unit,  the  kilowatt,  is  gener- 
ally used  in  connection  with  machines,  etc. 

I  kilowatt  =  I  000  watts  =  i  H  horse-power 

Thus  a  motor  drawing  10  amperes  from  a  220-volt  line  would  take  10  X  220  = 
2  200  watts  =  2  200/1  000  =2.2  kilowatts. 

At  80%  efficiency  this  motor  would  give  out  80%  of  2.2  =  1.76  kilowatts  = 
1.76  X  i]'i=  2yi  horse-power. 

Horse-Power-Hour.  Kilowatt-Hour.  When  a  -man  buys  mechanical 
power  to  run  machinery,  he  has  to  pay  not  only  according  to  the  horse-power 
he  uses  but  also  according  to  the  number  of  hours  he  uses  the  power.  For  in- 
stance, he  may  use  40  horse-power  for  i  hour  and  pay  $1.20  for  it,  that  is,  at 
the  rate  of  3  cts  for  each  horse-power-hour.  If  he  uses  40  horse-power  for 
2  hours  he  would  have  to  pay  twice  as  much,  because  he  has  used  the  same 
power  twice  as  long.  Another  way  of  stating  the  same  fact  is  to  say  that 
he  used  twice  as  many  horse-power-hours.  For  in  the  first  instance  he  used 
40  X  I,  or  40  horse-power-hours,  and  in  the  second  40  X  2,  or  80  horse-power- 
hours.  In  other  words,  he  did  twice  as  much  work  in  the  second  case  as  he 
did  in  the  first,  or  received  twice  as  much  energy.  The  unit  of  work  or  energy, 
then,  is  the  horse-power-hour,  and  is  the  work  done  in  i  hour  by  a  i -horse- 
power machine. 

Example.  How  much  work  is  done  by  a  machine  dehvering  15  h.p.  when  it 
is  run  for  8  hours? 

I  h.p.  in  I  hr  does    i  h,p.-hr 
15  h.p.  in  I  hr  does  15  h.p.-hr 
15  h.p.  in  8  hr  does  8  x  15,  or  120  h.p.-hr 
That  is 

Work  =  horse-power  x  hours 
or 

15  X  8=  120 h.p.-hr 

Similarly,  electric  power  is  sold  by  the  kilowatt-hour.  This  unit  is  the  work 
or  energy  delivered  in  one  hour  by  a  i -kilowatt  machine. 

For  lighting  purposes  electrical  energy  is  usually  sold  for  from  10  to  15  cts  per 
kilo  watt- hour.     Thus  at  1 2  cts  per  kw-hr  the  monthly  bill  for  burning  a  40-watt 
lamp  on  an  average  of  5  hours  per  day  would  be  computed  as  follows: 
For  I  month  of  30  days  the  lamp  is  burning 

30  X  5  =  150  hours 
To  use  a  40-watt  lamp  150  hours  consumes 

40  X  150  =  6  000  watt-hours  =  6  000/ 1  000  =  6  kilowatt-hours 
At  12  cts  per  kw-hr,  6  kw-hr  cost 

6  X  12  =  $0.72 

An  instrument  called  a  kilowatt-hour  meter  is  placed  in  each  house  to  meas- 
ure the  number  of  kilowatt-hours  which  each  customer  consumes.  See  M  in 
Fig.  13  for  location  of  Kilowatt-hour  meter,  and  Fig.  18  for  method  of  con- 
nection in  typical  installation. 

Heating-Effect  of  Current.     An  electric  current  always  heats  the  material 


Fuses  and  Circuit-Breakers  1461 

the  current  heats  the  fine  tungsten  wire  until  it  glows;  the  electric  heaters  for 
chafing-dishes,  toasters,  etc.  Even  the  wires  carrying  the  current  to  and  from 
the  lamps  are  heated  by  the  passage  of  the  current  through  them.  But  since  the 
heating  elTect  for  a  given  current  is  directly  proportional  to  the  resistance  of 
the  conductor,  and  the  conductors  always  have  very  little  resistance,  the  heat- 
ing here  is  very  slight  indeed.  If  conductors  of  smaller  size,  and  therefore  of 
a  higher  resistance,  were  used,  the  heating  would  be  very  pronoimced;  in  fact, 
it  would  soften  the  rubber  insulation  and  might  even  produce  a  temperature  high 
enough  to  set  fire  to  the  building.  For  this  reason  The  National  Board  of 
Fire  Underwriters  issues  a  table  specifying  the  size  of  wire  which  must  be  used 
f  jr  each  amount  of  current.  If  smaller  wire  is  used,  the  resistance  of  it  might 
be  great  enough  to  raise  the  temperature  to  a  dangerous  degree.  On  the  other 
hand,  if  a  greater  current  than  allowed  by  this  table  is  sent  over  the  wire,  the 
temperature  will  also  rise,  because  the  heating  of  a  current  is  also  directly  pro- 
portional to  the  SQUARE  OF  THE  CURRENT.  Thus,  doubling  the  current  which  a 
certain  wire  is  carrying  will  quadruple  the  amount  of  heat  which  the  wire  must 
radiate.     For  this  Tables  III  and  IV,  see  pages  1473  and  1474. 

Fuses  and  Circuit-Breakers.  Use  is  made  of  the  heating  effect  of  a  current 
to  protect  a  circuit  against  too  much  current,  very  much  as  a  boiler  is  pro- 
tected by  a  safety-valve  against  too  much  pressure.  A  small  piece  of  fusible 
metal,  generally  a  mixture  of  lead  and  bismuth,  is  inserted  in  the  circuit  in  such 
a  way  that  all  the  current  which  passes  through  the  circuit  must  also  pass  through 


Fig.  2.     Enclosed  Fuse 

this  piece  of  metal.  This  device  is  called  a  fuse:  Any  current  which  would  be 
dangerous  to  the  circuit  melts  this  fuse,  opens  the  circuit  at  this  point,  and  thus 
protects  the  rest  of  the  circuit  from  the  effects  of  the  current.  The  cause  of 
the  large  current  may  be  then  removed  and  a  new  fuse  inserted  in  place  of  the 
old  one.  Circuit-breakers  are  also  used  to  protect  a  circuit  against  too  much 
current.  They  are  automatic  switches  controlled  by  an  electro-magnet  and 
are  made  in  a  variety  of  styles.  They  operate  upon  the  principle  that  when 
an  electric  current  passes  through  a  coil  of  wire  it  makes  a  magnet  of  the  coil. 
The  coil  is  so  adjusted  that  when  a  current  of  a  certain  number  of  amperes 
passes  through  it,  it  attracts  to  itself  a  small  piece  of  iron.  The  motion  of  this 
piece  of  iron  opens  the  circuit.  Fuses  and  circuit-breakers  are  thus  automatic 
safety-devices  required  for  the  protection  of  all  constant-potential  systems 
whatever  the  voltage.  Both  are  for  the  purpose  of  protecting  the  wires  from 
damage  due  to  the  presence  of  too  much  current  from  any  cause  whatever. 
The  ordinary  fuse  consists  of  a  porcelain  base  that  has  suitable  terminals  for 
inserting  a  fuse  between  the  ends  of  a  wire.  It  must  be  constructed  so  that  the 
blowing  out  of  a  fuse  can  do  no  damage,  that  is,  set  anything  on  fire,  and  placed 
where  it  can  easily  be  reached  to  replace  the  fuse.  Formerly  a  piece  of  fuse-wire, 
called  a  link-fuse,  was  used  in  cut-outs,  but  the  underwriters  now  require  en- 
closed fuses   (Fig.  2)  or  fusible  plugs  which  screw  into  a  receptacle.     Fuse- 


1462  Electric  Work  for  Buildings  Part  3 

plugs  may  be  used  for  currents  up  to  30  amperes;  above  that  enclosed  fuses 
must  be  used.  Fuse-plugs  and  enclosed  fuses  are  somewhat  more  expensive 
than  the  link-fuse,  but  are  considered  safer.  A  fuse  cut-out  or  circuit- 
Breaker  is  required  at  or  near  the  place  where  the  wires  enter  a  building,  and 
every  circuit  of  twelve  i6-c.p.  carbon-lights  or  of  sixteen  40-watt  tungsten-lights 
must  be  protected  by  a  cut-out.  Circuit-breakers  are  more  expensive  than 
fusible  cut-outs,  and  are  generally  used  only  on  switchboards  for  large  in- 
stallations and  where  it  is  desirable  to  open  the  circuit  instantly  on  certain 
loads,  which  a  fuse  cannot  be  depended  on  to  do  with  any  degree  of  accuracy, 
owing  to  both  time  and  surrounding  temperature-factors.  Circuit-breakers  are 
also  used  largely  on  installations  where  the  variation  in  load  is  large  and  fre- 
quent and  the  repeated  burning  out  of  fuse  would  become  expensive  not  only 
for  renewals  but  also  on  account  of  the  time  required  to  replace  them. 

Lamps.  Two  kinds  of  lamps  are  used  for  electric  lighting,  incandescent 
LAMPS  and  ARC-LAMPS.  The  former  are  used  principally  for  interior  illumination, 
although  sometimes  used  for  street-lighting,  especially  where  the  streets  are 
thickly  shaded  by  trees.  Arc-lamps  are  especially  adapted  for  street-lighting 
and  for  large  interiors  where  they  can  be  kept  concealed  or  above  the  range  of 
the  eye,  as  in  railway-stations,  stores,  etc.  An  incandescent  lamp  as  com- 
monly made  consists  of  a  glass  bulb  containing  a  simple  carbon  or  a  tungsten 
conductor  the  ends  of  which  are  connected  to  the  source  of  the  electric  current. 
When  the  current  flows  through  the  filament  it  heats  it  to  such  a  degree  that  it 
becomes  incandescent;  hence  the  name  of  the  lamp.  The  lamps  with  the  fila- 
ment of  finely-drawn  tungsten  represent  the  latest  type  and  are  superior  in 
every  way  to  those  having  a  carbon  filament.  Tungsten-lamps  require  about 
one-third  as  much  power  to  produce  the  same  candle-power  as  carbon-lamps, 
and  have  a  much  longer  life. 

Voltages.  In  order  that  the  current  shall  cause  the  lamp  to  give  its  rated 
CANDLE-POWER,  it  must  be  designed  for  the  voltage  at  which  the  system  is  run. 
If  the  voltage  of  the  current  is  much  greater  than  that  for  which  the  lamp  is 
designed  it  will  quickly  burn  out  the  filament,  while  if  the  voltage  of  the  current 
is  below  that  of  the  lamp,  it  will  not  give  its  rated  candle-power,  a  voltage  10% 
lower  reducing  the  candle-power  about  one-half.  The  voltage  commonly  used 
for  tungsten-lamps  is  from  100  to  130.  Tungsten-lamps  are  also  made  for  volt- 
ages of  from  20  to  260.  Two  to  four  candle-power  lamps,  for  illuminating 
signs  or  decorative  purposes,  are  made  for  from  10  to  13  volts  by  3.^-volt 
steps,  these  lamps  being  commonly  used  in  series,  ten  lamps  on  a  100  to  130- 
volt  circuit.  Two  5-watt  lamps,  50  volts,  are  also  often  used  in  series  on  a 
loo-volt  circuit. 

Candle-Power.  Incandescent  lamps  of  from  100  to  130  volts  are  commonly 
made  15,  20,  25,  40,  60,  100,  150,  250,  400  and  500  watts.  These  lamps  average 
I  candle-power  for  every  i.i  watts.  For  the  method  of  computing  the  number, 
size  and  distribution  of  tungsten-lamps  for  illuminating  a  given  room  see  pages 
1476  to  1478. 

Arc-Lamps.  These  are  of  two  kinds,  open  arc-lamps  and  enclosed  arc- 
lamps,  the  latter  being  generally  used  for  interior  illumination.  The  light  from 
the  enclosed  arc  is  much  softer  and  steadier  than  that  from  the  old-style  open 
arc;  there  are  no  sparks,  and  the  life  of  the  carbon  is  from  twelve  to  fifteen 
times  as  great  as  in  the  open  arc. 

"  Direct-Current  Open  Arcs  usually  require  about  10  amperes  at  45 
volts,  or  450  watts.  The  range  of  voltage  is  from  42  to  52  for  ordinary  con- 
stant-current arcs.    The  most  satisfactory  light  is  given  by  from  45  to  47  volts. 


Electric  Machines  and  Currents  1403 

Arc-lights  used  for  stereopticon-lan terns  may  use  as  high  as  25  amperes  and 
provision  should  always  be  made  in  the  wiring-plans  for  such  a  light  for  suffi- 
ciently large  wires  to  be  installed  to  carry  one  and  one-half  times  this  current. 

**  Direct-Current  Enclosed  Arcs  consume  about  5  amperes  at  80  volts,  or 
400  watts."  Arc-lamps  generally  require  a  resistance  in  series  with  the  arc 
in  order  to  regulate  properly.  This  resistance  is  usually  placed  within  the  struc- 
ture of  the  lamp,  and  may  be  so  adjusted  that  a  single  lamp  can  be  made  to 
burn  well  on  any  circuit  from  100  to  130  volts. 

Dynamo-Electric  Machines.  There  are  three  classes  of  dynamo-electric 
machines: 

(i)  Generators  for  generating  an  electric  current. 

(2)  Motors  for  converting  electrical  into  mechanical  energy. 

(3)  Transformers  and  rotary  converters. 

(a)  Transformers  for  converting  one  voltage  into  a  higher  or  lower 

voltage.     Converters  and  transformers  belong  to  the  same  class. 

(b)  Rotary   converters   for   changing   alternating   currents    to   direct 

currents  or  vice  versa. 

A  dynamo  is  either  a  motor  or  a  generator.  A  motor  is  the  same  machine  as 
a  generator,  but  with  the  nature  of  its  operation  reversed.  Generators  are 
of  two  general  classes,  namely,  continuous-current  and  alternating-current 
machines;  the  latter  are  commonly  called  alternators.  Generators  and 
motors  of  all  kinds  vary  in  voltage,  current  and  speed,  according  to  the  pur- 
pose for  which  they  are  designed.  A  transformer  consists  essentially  of  tw6~ 
coils  of  wire,  one  coarse  and  one  fine,  wound  upon  an  iron  core.  Its  function 
is  to  convert  electrical  energy  from  one  voltage  to  another.  If  it  reduces  the 
voltage  it  is  known  as  a  step-down  transformer,  and  if  it  raises  it,  it  is  known 
as  a  step-up  transformer.  A  transformer  has  no  moving  parts  and  requires  no 
attendant. 

Kinds  of  Currents  Produced.  There  are  two  kinds  of  electrical  currents 
commonly  used  for  light  and  power  in  buildings,  (i)  direct  currents,  and  (2) 
alternating  currents. 

"A  direct  current  is  uniform  in  strength  and  direction,  while  an  alternating 
current  rapidly  rises  from  zero  to  a  maximum,  falls  to  zero,  reverses  its  direction, 
attains  a  maximum  in  the  new  direction  and  again  returns  to  zero.  A  complete 
set  of  these  changes  is  called  a  cycle.  The  number  of  times  the  current  goes 
through  these  changes  during  each  second  is  called  the  frequency  of  the  current. 
The  frequency  commonly  used  for  incandescent  lighting  is  60  cycles  per 
second;  that  is,  the  current  goes  through  the  above  changes  in  value  60  times 
per  second.  A  frequency  of  25  cycles  is  also  in  common  use,  especially  for  run- 
ning motors,  although  it  is  not  so  satisfactory  for  use  with  incandescent  lights. 
If  a  direct  current  is  likened  to  the  steady  flow  of  water  through  a  pipe-system, 
an  alternating  current  may  be  likened  to  the  rapid  surging  back  and  forth  of 
water  in  a  pii)e-system.  More  difficulty  was  experienced  in  utilizing  these  rapid 
surges  of  electricity  than  in  developing  direct-current  apparatus.  Consequently 
the  use  of  the  alternating  current  was  retarded  but  is  now  becoming  general. 
The  advantages  of  alternating  over  direct  currents  are:  (i)  Greater  simplicity 
of  dynamos  and  motors,  no  commutators  being  required  in  some  types;  (2)  the 
feasibility  of  obtaining  high  voltages  by  means  of  transformers  for  cheapening 
the  cost  of  transmission;  (3)  the  facility  of  transforming  from  one  voltage  to 
another,  either  higher  or  lower,  for  different  purposes. "  * 

•  Adapted  from  Kent's  Pocket  Book. 


1464  Electric  Work  for  Buildings  Part  3 

Table  I.    Average  Current  Taken  by  Direct-Current  Motors 


Horse- 
power 

Amperes  on 
I  ID- volt  line 

Amperes  on 
220-volt  line 

Horse- 
power 

Amperes  on 
1 10- volt  line 

Amperes  on 
220-volt  line 

% 

I 

2 

3 
5 

lO 

15 

20 

3 

5-4 
9 
17 

25 

40 
58 
76 
114 

150 

1.5 
2.7 
4.5 
8.5 

12.5 

20 

29 

38 

57 

75 

25 
30 
35 
40 
50 
60 
75 
85 
100 

186 

222      - 
260 
296 

93 
III 
130 
148 
18S 
220 
275 
312 
366 

The  current  taken  by  single-phase  alternating-current  motors  can  be  found 
by  noting  the  current  taken  by  a  direct-current  motor  of  the  same  size  and  volt- 
age, and  dividing  this  current  by  the  power-factor  of  the  alternating-current 
motor.  To  find  the  current  taken  by  each  terminal  of  a  three-wire,  three-phase 
alternating-current  motor,  divide  the  current  taken  by  a  single-phase  alternat- 
ing-current motor  of  the  same  size  and  voltage  by  1.73. 

Example.  What  current  is  taken  by  a  5 -horse-power,  alternating-current, 
220-volt,  induction-motor  of  80%  power-factor? 

Soiution.  A  5 -horse-power,  direct-current,  220-volt  motor  takes  20  amperes. 
A  single-phase,  5-horse-power,  220-volt  motor  of  ^0%  power-factor  takes  20/. 80 
=  25  amperes. 

Electric-Lighting  Systems  Commonly  Used  for  Supplying  the 
Electrical  Energy  to  Lamps 

Direct-Current,  Constant-Potential  Systems.  The  systems  most  used 
in  America  are: 

(i)  Two-wire  system  largely  used  for  incandescent  lighting  from  small 
plants,  as  for  a  large  office-building  or  factory.  It  is  usually  operated  at  no 
volts. 

(2)  Three- WIRE  system  used  in  small  towns  for  the  lighting  of  buildings  from 
the  public  mains,  usually  operated  at  220  voltsr  Also  in  large  cities  with  under- 
ground conduit-system.     See  pages  1466  to  1468. 

Five-wire  and  seven-wire  systems  with  high  voltage  have  been  used  in 
Europe,  but  very  little  in  America. 

Alternating-Current,  Constant-Potential  Systems.  There  are  two  sys- 
tems: 

(i)  Single -PHASE  system.  Current  transmitted  to  building  at  from  i  000  to 
2  000  volts  and  reduced  to  from  50  to  no  volts  by  a  transformer.  The  term 
phase  is  used  in  connection  with  alternatiiig-current  systems  only  in  the  sense 
of  circuit.  Thus  a  single-phase  system  means  an  alternating-current  system 
sending  out  power  from  one  circuit  only  of  the  generator.  A  three-phase  system 
has  three  circuits. 

(2)  Three-phase  system.  Three  or  four  wires  are  used.  This  system  is 
most  used  for  lighting  from  public  plants,  principally  because  it  enables  both 
lights  and  motors  to  be  operated  from  the  public  dynamo  and  is  the  most  econom- 
ical in  wire.  (See  Table  II.)  Both  of  these  systems  are  used  for  incandescent 
lighting  and  for  power  from  central  stations.  For  a  comparison  of  a  three- 
wire  direct  current  with  a  three-phase,  three-wire  alternating  current,  see  pages 


no     no 

f«volt,s|«volts>- 

— Lfm  ■ '  ■  ■nr — i 

no 

T 

no 

<volts> 

1 

no 

^volts^ 

<— 550-v 
volts 

Tl 

1 

Fig.  3.     Five  Lamps  in  Series  on  a  5 50- Volt  Line. 
Each  Lamp  has  a  Voltage  of  no  Volts  Across  It 


Electric-Lighting  Systems  1465 

1468-9.  An  alternating  current  may  be  changed  to  a  direct  current  at  a  sub- 
station by  a  rotary  converter  or  by  a  mercury-arc  rectifier.  The  latter  is  very 
generally  used  in  garages  in  order  to  convert  an  alternating  current  into  a  direct 
current  for  charging  storage- 
batteries. 

Methods  of  Connecting 
Lamps.  There  are  three  ways 
of  connecting  lamps  to  the  dis- 
tribution-wires: (i)  in  series; 
(2)  in  parallel;  and  (3)  in 
parallel  series. 

(i)  Lamps  in  Series. 
Lamps  are  said  to  be  connected 
in  series  when  they  are  arranged 
one  after  the  other,  so  that 
the  same  current  flows  through 
all  the  lamps.  The  most  com- 
mon example  of  this  system  is  the  lighting  of  electric  cars  and  the  stations  on 
an  electric-railway  line.  The  voltage  of  such  lines  is  usually  550  volts.  Since 
the  ordinary  incandescent  lamp  requires  but  no  volts,  five  .of  these  are  placed 
in  series  as  in  Fig.  3.  Each  lamp  now  has  a  pressure  of  no  volts  across  it,  and 
the  set  of  five  lamps  requires  550  volts  across  it,  and  so 
can  be  placed  across  the  railway  supply-wires.  When 
lamps  are  arranged  in  series  the  total  resistance  of  the 
circuit  is  the  sum  of  the  resistances  of  the  several  parts, 
and  the  voltage  required  to  force  the  current  through  a 
number  of  lamps  in  series  is  the  sum  of  the  voltages 
required  for  the  separate  lamps.  Thus  the  voltage 
required  to  supply  the  proper  current  for  four  52-volt 
lamps  is 4  X  52  =  208  volts.  Arc-lamps  for  street-lighting 
are  often  connected  in  series,  but  incandescent  lamps  are 
very  seldom  connected  in  series  except  as  described  above 
or  for  decorative  purposes  or  electric  signs.  Where  lamps 
of  low  voltage,  as  in  signs,  etc.,  are  used  on  no-volt 
systems  it  is  necessary  to  connect  them  in  series.  The 
underwriters,  do  not  approve  connecting  incandescent 
lamps  in  series.  The  series  system  requires  that  the  same 
current  flow  through  each  lamp,  and  if  one  lamp  burns 
out  the  circuit  is  broken  and  all  of  the  lamps  will  go  out, 
unless  some  provision  is  made  for  maintaining  the  circuit 
around  the  dead  lamps. 

(2)  Lamps  in  Parallel.  This  is  the  common  method 
of  connecting  incandescent  lamps.  It  is  illustrated  in 
Fig.  4.  With  this  system  the  pressure  in  each  lamp  is  the 
same  as  in  the  distributing  fines,  and  any  lamp  may  be 
turned  on  or  off  without  affecting  the  other  lamps.  For 
this  system  the  pressure  or  voltage  must  be  kept  con- 
stant, while  the  current  or  quan^ty  of  electricity  flow- 
ing in  the  lines  will  depend  upon  the  number  of  lamps  that  are  burning. 
Thus  with  twelve  i6-candle-power  lamps  of  no  voltage  on  a  parallel  circuit, 
each  lamp  requiring  0.51  ampere  when  all  the  lamps  are  burning,  a  current  of 
6.12  amperes,  or  673.2*  watts,  will  be  required.  With  but  one  lamp  burning, 
•  Watts  being  equal  to  amperes  times  voltage. 


4.  Four  Lamps 
in  Parallel.  Each 
Lamp  Has  the  Full- 
line  Pressure  of  no 
Volts  Across  It 


1466 


Electric  Work  for  Buildings 


Part  3 


a  current  of  only  0.51  ampere  will  flow.  The  voltage,  however,  must  be  the 
same  for  one  lamp  as  for  the  twelve.  For  lamps  in  parallel,  therefore,  a  con- 
stant-potential system  is  required.  The  current  for  lamps  m  parallel  may 
be  turned  on  or  off  at  the  lamp,  or  a  switch-loop  may  be  run  any  distance 
and  the  contact  made  by  a  switch  (5)  as  for  the  lower  lamp  (Fig.  4). 

(3)  Lamps  in  Parallel  Series.    This  method  is  a  xrombination  of  the  other 
two.    Parallel  lines  are  run  as  in  the  parallel  system,  but  two  or  more  lamps 


^IIO-Vt^ 


Fig.  5.    Lamps  in  Parallel  Series 


Fig.  6.    Lamps  in  Parallel  Series 


are  connected  in  series  between  them  as  in  Figs.  5  and  6.  This  method  of  con- 
necting lamps  is  used  principally  in  places  where  it  is  desired  to  operate  lamps 
on  a  power  system.  Fig.  5  shows  a  series  of  five  lamps  operated  on  a  500-volt 
system  and  Fig.  6  a  series  of  two  lamps  on  a  220-volt  system  using  no-volt 
lamps.    Any  number  of  series  may  be  connected  across  the  mains,  each  series 

__      being  independent  of  the 


Fig.  7.  The  Three-wire  Edison  System.  220  Volts 
Between  Outside  Wires;  Only  no  Volts  Between  Either 
Outside  Wire  and  Neutral  Wire 


others.  But  in  each 
series  if  one  light  burns 
out,  the  others  in  the 
same  series  will  be  use- 
less, and  one  lamp  alone 
cannot  be  used.  The 
sum  of  the  voltages  of 
the  lamps  in  series  must 
be  approximately  equal 
to  the  voltage    between 


the  mains.     There  are  a  number  of  special  cases  in  which  this  method  of 
connection  may  be  used. 

The  Edison  Three-Wire  System.  Figs.  4,  5  and  6  are  examples  of  the 
two-wire  system  of  distribution,  which  is  the  system  recommended  for  average- 
sized  office-buildings,  apartment-houses,  theaters  and  stores.  Where  power 
for  motors  is  to  be  taken  from  the  same  plant  as  the  lighting  current,  and  where 
the  power  is  not  too  great  a  portion  of  the  capacity  of  the  installation,  this  two- 
wire  system  may  also  be  used.  Separate  mains,  however,  should  under  all  cir- 
cumstances be  run  for  the  motors,  as  the  variation  in  load  and,  consequently, 
the  current-demand  on  the  mains  would  cause  a  very  appreciivble  fluctuation  in 


Electric-Lighting  Systems 


1407 


candle-power  of  the  lamps,  if  on  the  same  mains  with  the  motors.     Where  com- 
paratively long  Unes  are  required  and  the  amount  of  current  to  be  supplied  is 


D.  denotes  Dynamo 


CO. 
L. 
M. 


Cut-out 

Lamp 

Motor 


JioV, 


220  V. 


ic.ol 


Fig.  8.     Example  of  Three-wire  System  of  Wiring 

large  the  titree-wire  system  is  ur>cd.  By  this  system  two  voltages  or  pressures 
can  he  supplied,  no  and  220  volts  being  those  generally  adopted,  the  no-volt 
circuit  supplying  the  arc  and 

To  Cut-out  Cabinet 


Second  Story 


incandescent  lights  and  the 
220-volt  circuit  the  motors. 
Fig.  7  shows  how  the  wires 
are  run  and  connections 
made.  The  pressure  between 
the  two  outside  wires  is  the 
full  voltage  transmitted  from 
the  generator,  usually  220 
volts  for  interior  wiring. 
The  current  in  these  two 
wires  flows  in  opposite  direc- 
tions. The  middle  wire, 
called  the  neutral  wire, 
forms  one  side  of  two  cir- 
cuits, the  current  from  one 
circuit  tending  to  flow  in 
one  direction  and  that  from 
the  other  circuit  in  the  oppo- 
site direction;  consequently 
when  currents  of  the  same 
strength,  in  amperes,  are 
flowing  in  both  circuits  they 
neutralize  each  other  in  the 
middle  wire  and  there  will 
be  no  current  flowing  in  this 

wire.     With  a  current  of  10  amperes  flowing  in  one   circuit  and   one  of   6 
amperes  in  the  other  circuit,  the  current  flowing  in  the  neutral  wire  will  be  4 


Fig.  9.  The  Wiring  of  a  Cabinet.  Showing  How  to 
Divide  a  Three- wire  System  into  Six  Two-wire  Cir- 
cuits, Three  Circuits  to  Each  Leg 


1468 


Electric  Work  for  Buildings 


Part  3 


Phase 


^110-> 
volts 


Phase 
~No.3 


Phase 
No.2 


amperes.    To  obtain  the  greatest  benefit  from  this  system,  it  should  always  be 
installed  so  that  there  will  be  nearly  the  same  load  or  number  of  lamps  on  each 

side  of  the  neutral  wire.  Even 
then  there  will  be  times  when 
more  lamps  will  be  burning  on  one 
side  than  on  the  other,  so  that  it 
is  necessary  to  give  some  size  to 
the  neutral  wire.  The  neutral 
wire  is  seldom  made  less  than 
one-half  the  cross-section  of  the 
outer  wires.  For  distributing 
mains  in  buildings  carrying  lamps 
only,  the  neutral  wire  should  be 
of  the  SAME  SIZE  as  the  outer 
wires.  From  Table  II  it  will  be 
seen  that  the  three-wire  system 
effects  a  considerable  saving  in 
copper,  amounting  to  fully  60% 
of  the  ordinary  two-wire  no- volt 
system.  As  a  rule,  in  supplying 
current  for  light  and  power  from 
one  plant,  the  main^wires  only  are 
arranged  on  the  three-wire  system 
and  the  distributing  wires  are  run 


Fig.     10 

Alternating  Current. 


To  Street  Mains 
Three-phase,     Three-wire     System, 


Compare  with  Fig.  11 


on  the  two-wire  system  as  in  Fig.  8.  When  using  the  three-wire  system  for 
lighting  only,  the  three  wires  are  usually  run  no  farther  within  the  building 
than  to  the  centers  of  disfribu- 


tion,  and  from  these  centers 
two  wires  are  run  for  each  cir- 
cuit, the  circuits  being  divided 
as  equally  as  possible  on  the 
two  sides  of  the  three-wire 
system  as  shown  by  Fig.  9. 
Three-wire  mains  are  now  very 
commonly  used  where  the  cur- 
rent exceeds  100  amperes. 
When  motors  are  operated 
from  the  three- wire  system  they 
are  usually  connected  only  to 
the  outside  wires.  Motors 
used  on  three-wire  incandes- 
cent-lighting systems  should 
be  wound  for  220  volts. 

Comparison  of  the  Three- 
Phase  and  Three-Wire  Edi- 
son Systems.  The  wiring  for 
the  Edison  three-wire  direct- 
current  system  is  the  same  as 
that  for  the  three- wire,  three- 
phase  alternating-current  sys- 


Leg  N0.1 


-220^ 
volts 


Leg  N0.2 


To  Street  Mains 

Fig.    11.     Three-wire   System,   Direct  Current. 

Compare  with  Fig.  10 


tem,  the  only  difference  being  that  the  voltage  between  any  two  wires  of 
a  three-phase  system  is  the  same.  Thus  in  Fig.  10  which  represents  a  three- 
wire,  tbree-ph^sc  system  the  voltage  between  the  wires  A  and  B  (phase  No.  i) 


Wire-Calculations  1469 

IS  no  volts;  between  B  and  C  (phase  No.  2)  is  no  volts;  and  between  A 
and  C  (phase  No.  3)  is  no  volts.  But  in  Fig.  11,  which  represents  a  three- 
wire  direct-current  system,  in  which  the  voltage  across  A  and  B,  and  B  and 
C,  is  no  volts,  the  voltage  across  A  and  C  is  220  volts  or  twice  that  across 
either  leg. 

Table  II.      Relative  Weight  of  Copper  Required  in  Different  Systems  for 
Equal  Effective  Voltage 


Direct-current,  ordinary  two- wire  system 

Direct-current,  three-wire  system,  all  wires  of  same  size . 
Direct-current,  three-wire  system,  neutral,  one-half  size.. 

Alternating-current,  single-phase  two-wire  system 

Three-phase  three-wire 

Three-phase  four-wire 


i  .000 
0.375 
0.313 
1 .000 
0.750 
0.333 


Wire-Calculations 

Wire-Gauges.*  As  the  diameter  of  wires  is  ordinarily  designated  by  the 
number  of  a  wire-gauge,  and  as  there  are  a  number  of  wire-gauges  in  common  use, 
some  knowledge  of  those  used  for  copper  wire  is  necessary.  The  Brown  &  Sharpe, 
or  B.  &  S.,  gauge  (see  page  1474)  is  almost  exclusively  used  in  America  in  connec- 
tion with  electrical  work,  except  where  the  size  of  the  wire  is  designated  in  cir- 
cular mils.  The  sizes  of  wire  given  by  this  gauge  range  from  No.  0000  (0,46  in) 
to  No.  40  (0.0031  in),  but  No.  14  is  the  smallest  size  permitted  for  interior  wiring. 
The  No.  10  wire  has  a  diameter  of  about  Ho  in  and  its  resistance  per  i  000  ft 
is  very  nearly  i  ohm.  For  any  given  number  of  this  gauge  a  wire  three  numbers 
higher  has  verj'-  nearly  half  the  cross-section,  and  one  three  numbers  lower  has 
twice  the  cross-section;  thus  a  No.  13  wire  has  very  nearly  one-half  the  cross- 
section  of  a  No.  10  wire,  and  a  No.  7  has  twice  the  cross-section  of  a  No.  10, 
or  four  times  that  of  a  No.  13. 

The  Circular-Mil  Wire-Gauge.  This  gauge  was  designed  by  the  engineer- 
ing department  of  the  Edison  Company  especially  for  the  designation  of  copper 
wire  for  electrical  work,  and  is  now  in  general  use  in  this  country.  In  practice 
the  B.  &  S.  gauge  is  commonly  used  for  designating  wires  up  to  No.  o  or  No.  00, 
and  all  wires  above  that  size  are  designated  by  circular  mils  (cm.).  The  size 
of  wire  required  is  often  determined  in  circular  mils  and  designated  by  the  corre- 
sponding B.  &  S.  gauge-number,  which  is  readily  done  by  means  of  Table  III, 
page  1473.  Copper  wire  is  sold  by  the  pound  if  bare  or  of  the  numerous 
weather-proof  varieties,  but  rubber-covered  wire  is  sold  by  the  i  000  ft. 

The  basis  of  the  circular-mil  gauge  is  the  area  of  a  wire  Mooo  in  in  diameter 
(i  mil  =  o.ooi  in);  consequently,  i  cm.  =  0.0000007854  sq  in.  As  the  areas  of 
circles  vary  as  the  squares  of  their  diameters,  it  follows  that  the  sectional  area 
of  a  wire  2  mils  in  diameter  =  4  cm.,  of  a  wire  10  mils  in  diameter  100  cm.,  and 
so  on. 

When  wires  are  designated  by  circular  mils,  the  sectional  area  and  not  the 
diameter  is  generally  given,  cm.  always  referring  to  sectional  area.  The  diam- 
eter of  a  wire  in  mils  or  in  thousandths  of  an  inch  =  square  root  of  its  area 
in  circular  mils. 

Thus  the  diameter  of  a  wire  of  3  600  cm.  =  60  mils,  or  0.060  in. 

The  diameter  of  a  wire  14  400  cm.  =  120  mils  =0.12  in. 

The  area  of  a  wire  0.162  in  in  diameter,  or  162  mils,  =  1622=  26244  cm. 
*  For  other  causes,  see  pages  401,  402,  403,  i473,  1509,  1510.  IS12  and  1600. 


1470  Electric  Work  for  Buildings  Part  3 

To  reduce  circular  mils  to  square  inches.     Multiply  by  7  854  and  point  off 
ten  places  of  decimals.     Thus,  5  000  cm.  =  7  854  x  5  000  =  o.oo39270cxx3  sq  in. 
To  obtain  the  sectional  area  of  a  square  or  rectangular  bar  in  circular  mils. 

Multiply  together  its  dimensions  in  mils  and  the  product  by  1.273. 

Example.     What  is  the  sectional  area  in  circular  mils  of  a  bar  H  in  X  H  in? 

Solution.  H  in  =0.125  in  =  125  mils,  H  in  =  0.250  in  =  250  mils;  125  x 
250  X  1.273  =  39781.25  cm. 

The  weight  of  bare  copper  wire  per  i  000  ft  =  cm.  x  0.003027  lb.  Thus  the 
weight  of  I  000  ft  of  copper  wire  having  a  sectional  area  of  2  000  cm.  =  0.003027 
x  2  000  =  6.054  lb.  Table  IV,  page  i474»  gives  the  dimensions  and  weights  of 
bare  copper  wire  from  No.  18  to  No.  0000  B.  &  S. 

Carrying  Capacity  of  Copper  Wire.  The  safe  carrying  capacity  of  copper 
wire  for  interior  wiring  is  practically  fixed  by  the  underwriters,  and  if  the  ca- 
pacity-limits given  in  the  table  published  by  them  are  exceeded  it  would  tend 
to  destroy  the  right  to  recover  insurance  in  case  of  fire.  The  safe  carrying 
capacity  of  rubber-covered  and  weather-proof  wires  given  by  the  National 
Board  of  Fire  Underwriters  is  shown  by  Table  III,  page  1473.',  The  lower  am- 
pere-capacity assigned  to  rubber-covered  wires  is  due  to  the  fact  that  the 
rubber  insulation  would  deteriorate  in  quality  under  a  temperature  as  high 
as  that  allowed  for  weather-proof  wire;  that  is,  the  rubber  covering  makes 
necessary  a  lower  rate  ot  heat-development  than  is  required  for  safety  from  fire. 
No  wire  smaller  than  No.  14  may  be  used  under  insurance-rules,  except  that 
No.  16  may  be  used  for  flexible  cord  and  No.  18  for  fixture-wiring.  Nos.  13, 
II,  9  and  7  are  not  usually  carried  in  stock  and  can  only  be  purchased  on 
special  order.  Rubber-covered  wire  must  be  used  for  service-wires,  for  mold- 
ing-work and  in  damp  places;  it  is  more  expensive  than  weather-proof  wire. 
The  latter  wire  may  be  used  in  open  or  exposed  places  and  for  outside 
line-wires. 

Drop  of  Potential.  When  an  electric  current  flows  through  a  wire  of  any 
appreciable  length  the  pressure  becomes  reduced  by  the  resistance  of  the  wire, 
so  that  if  the  current  enters  the  wire  at,  say,  no  volts,  at  the  extreme  end  of  the 
circuit  it  will  be  somewhat  less,  depending  upon  the  length  and  sectional  area  of 
the  wire.  This  loss  in  voltage  is  called  drop  of  potential.  Drop  of  potential 
corresponds  to  loss  of  head  in  hydraulics.  As  a  drop  of  voltage  materially 
below  that  for  which  the  lamps  are  designed  means  diminished  candle-power, 
it  is  very  important  that  the  wires  be  proportioned  so  that  the  drop  shall  not  be 
sufficient  to  affect  the  illumination.  The  table  for  safe  carrying  capacity  for 
wires  has  nothing  to  do  with  the  drop  of  potential  which  these  currents  will 
cause  in  the  wires.  Accordingly,  mains  and  distributing  wires  may  be  capable 
of  carrying  the  number  of  amperes  in  accordance  with  Table  III,  page  1473, 
and  yet  cause  a  drop  of  potential  of  such  magnitude  that  the  most  distant  lamps 
will  burn  only  at  a  dull  red.  It  is  therefore  necessary,  in  computing  the  size  of 
these  mains  and  distributing  wires,  to  consider  two  things: 

(i)  That  the  wire  is  large  enough,  according  to  the  underwriters'  table, 
to  carry  the  current  safely. 

(2)  That  the  potential  drop  from  the  generator  to  the  farthest  lainp  shall 
not  be  excessive.  An  excessive  drop  in  voltage  also  means  increased  cost  for 
light  and  not  enough  copper  in  the  wires. 

Where  the  current  is  supplied  from  the  public  mains  it  is  usual  to  specify  a 
2%  drop,  but  where  the  current  is  produced  cheaply,  as  by  a  dynamo  on  the 
premises,  a  3%  or  5%  drop  may  be  allowed.  Not  more  than  a  5%  drop  on  short 
r!i<itnnr*»e   cVirtiilrl    hp   nprmittpd.  even  wherp  verv  rhpan  work    is  dr^sired.      The 


Wire- Calculations 


1471 


drop  in  volts  (not  in  percentage)  =  current  in  line  X  resistance  of  line,  or  drop 
in  volts  =  amperes  X  ohms. 

Example.  What  will  be  the  drop  in  a  circuit  of  No.  14  copper  wire  280  ft 
long,  supplying  nine  lamps,  requiring  4.5  amperes? 

Solution.  From  Table  IV,  page  i474,  it  is  found  that  the  resistance  of  No. 
14  wire  is  2.527  ohms  per  i  000  ft;  hence  for  280  ft  it  will  be  2.527  X  0.280  = 
0.7075  ohm,  and  drop  in  volts  =  4.5  X  0.7075  =  3.1837  volts.  The  voltage  for 
this  current  (0.5  ampere  per  lamp)  will  be  about  no;  consequently  the  per- 
centage of  drop  =  3.1837/110  =  2  91o%,  nearly.  A  2%  drop  on  a  pressure  of 
no  volts  is  2.2  volts. 

Load- Center.  The  meaning  of  this  term  may  best  be  illustrated  by  an  exam- 
ple.    Let  Fig.  12  represent  a  circuit  carrying  six  lamps,  the  first  lamp  being 


-10- 


Vm  i 


j^yvu 


L 


H^- 


Fig.  12.     The  Point  D  is  the  Load-center 


40  ft  from  the  cut-out,  or  source  of  supply.  The  whole  of  the  current  must  be 
transmitted  through  this  40  ft,  but  from  that  point  it  will  gradually  fall  off,  and 
the  average  current  will  only  extend  to  the  point  CD,  halfway  between  the 
extreme  lamps.  Or,  in  other  words,  the  load-center  is  analogous  to  the  center 
of  gravity  of  the  lamps  on  the  circuit.  The  load-center  determines  the  length  of 
the  line  in  the  rules  for  finding  the  necessary  size  of  wire. 

Distributing  Centers  are  the  points  in  a  building  where  the  cut-out  cabinets 
are  located  and  the  branch  circuits  taken  off. 

Calculations  for  Size  of  Wire  for  Incandescent  Lighting.  The  sizes  of 
wires  for  interior  lighting  are  or  should  be  always  determined  on  a  basis  of  a  fixed 
drop  of  potential,  usually  2  volts  on  the  distributing  circuit  and  from  2  to  3 
volts  on  the  feeders  or  mains.*  The  size  of  wire  may  be  determined  either  in 
terms  of  its  sectional  area  in  circular  mils  or  in  terms  of  its  resistance  in  ohms 
per  I  000  ft.  Knowing  the  sectional  area  in  circular  mils,  one  may  find  the 
corresponding  gauge-number  from  Table  III,  page  i473.  or  if  the  resistance  in 
ohms  per  i  000  ft  is  known,  the  corresponding  gauge-number  may  be  found 
from  Table  IV,  page  1474.  i* 

*  Many  municipal  lighting  companies  require  that  there  shall  be  no  more  than  3% 
V)tal  drop  in  the  wiring  for  interior  lighting. 


1472  Electric  Work  for  Buildings  Part  3 

The  formula  for  circular  mils  is  as  follows: 

^.      ,         .,       10.4  X  2  d  xNxc 

Circular  mils  =  Ki) 

V 

The  formula  for  resistance  per  i  000  ft  of  wire  is 

^    .  I  ooot>  ,  . 

Resistance  =  — -.  (2) 

N  Xc  X2d 

In  both  these  form.ulas  d  =  distance  in  feet,  one  way,  from  cut-out  to  load- 
center  (see  page  1471)  for  distributing  wires,  or  from  entrance  cut-out  or  source 
of  current  to  distributing  center  for  main  lines  or  feeders,  c  =  current  in  am- 
peres PER  LAMP.  N  =  number  of  lamps  supplied,  v  =  drop  in  volts.  Both 
formulas  apply  to  any  voltage  and  to  any  two-wire  system.  To  use  these 
formulas  for  the  ordinary  three-wire  system,  let  N  =  maximum  number  cf 
lamps  on  one  side  of  the  neutral  wire  and  double  the  drop  in  volts.  The 
neutral  or  middle  wire  should  be  of  the  same  size  as  the  outside  wires. 

Example.  The  distance  from  the  cut-out  to  load-center  of  a  circuit  carrying 
sixteen  40-watt,  iio-volt  lamps  is  50  ft.  What  size  of  wire  should  be  used  for  a 
drop  of  2  volts? 

Solution.    d=  50;   N  =  16;   c=  40/110=  0.364;  and  v=  2. 
By  Formula  (i), 

„.      ,        .,       10.4  X  100  X  16  X  0.364 

Circular  mils  =  =  3  030 

2 

Table  III,  page  1473,  shows  that  the  next  larger  size  of  wire  is  4  107  cm., 

equivalent  to  a  No.  14  wire. 

By  Formula  (2), 

I  000  X  2 

Resistance  per  i  000  ft  = =  4.59 

12  X  0.364  X  100 

which  we  see  from  Table  IV,  page  1474,  is  about  the  resistance  of  a  No.  16  wire; 
but  as  No.  14  is  the  smallest  wire  permitted  that  size  must  be  used. 

Example.  The  distance  from  the  entrance  cut-out,  where  the  wires  enter  the 
building,  to  the  main  distributing  center  of  a  building  is  100  ft.  The  total  num- 
ber of  i6-candle-power,  iio-volt  carbon-lamps  supplied  is  ninety.  What  is 
the  size  of  the  mains  that  should  be  used  on  the  two-wire  system  with  a  drop 
of  2  volts?  (A  i6-candle-power  no- volt  carbon  lamp  takes  approximately 
0.51  ampere.) 

Solution.     d=  100;  A^  =  90-;  c=  0.51;  v=  2 
By  Formula  (i), 

.        10.4  X  200  X  90x0.51 

Circular  mils  =  =  47  800 

2 

In  Table  III  it  is  seen  that  No.  3  wire  must  be  used.  If  a  drop  of  3  volts  is 
allowed  the  sectional  area  required  will  be  33  048  cm.,  which  requires  a  No.  5 
wire.  The  weight  per  i  000  ft  of  No.  3  weather-proof  wire  (Table  IV)  is  200  lb 
and  of  No.  5  wire  125  lb;  consequently,  the  saving  in  weight  of  wire  by  using 
a  drop  of  3  volts  instead  of  2  is  75  lb,  or  37^%  of  200,  and  as  wire  is  sold  by  the 
pound,  the  saving  in  cost  with  a  3%  drop  ranges  from  30  to  40%  of  a  2%  drop. 

Example.  With  the  same  conditions  as  given  in  the  preceding  example 
what  is  the  size  of  the  wire  that  will  be  required  for  the  ordinary  three-wire 


Wire-  Calculations 


Table  IH.     Carrying  Capacity  of  Wires  and  Cables 

FOR  INTERIOR  CONDUCTORS,  ALL  VOLTAGES 
From  the  National  Electrical  Code 


No.  of 

Capacity  in  amperes 

wire, 

Circular 

B.&S. 

mils 

Rubber- 

Weather- 

gauge * 

covered 

proof 

i8 

I  624 

3 

5 

i6 

2583 

6 

10 

14 

4  107 

15 

.20 

12 

6530 

20 

25 

10 

10380 

25 

30 

8 

16  510 

35 
50 

50 

70 

6 

26  250 

5 

33100 

55 

80 

4 

41  740 

70 

90 

3 

52630 

80 

100 

2 

66  370 

90 

125 

I 

83690 

100 

150 

0 

105500 

125 

200 

00 

133  100 

150 

225 

000 

167  800 

175 

275 

0000 

211  600 

225 

325 

Cables 

200  000 

200 

300 

300  000 

275 

400 

400  000 

32s 

Soo 

500  000 

400 

600 

600000 

4SO 

680 

700  000 

500 

760 

800  000 

550 

840 

900  000 

600 

920 

I  000  000 

650 

I  000 

I  100  000 

690 

1080 

I  200  000 

730 

I  150 

I  300  000 

770 

I  220 

I  400  000 

810 

I  290 

I  500000 

850 

1360 

I  600  000 

890 

I  430 

I  700  000 

930 

I  490 

I  800  000 

970 

1550 

I  900  000 

I  010 

I  610 

2  000  000 

I  050 

1670 

A  current  of  one  ampere  will  supply  two  i6-candle-power  carbon  lamps. 
Solution.     In  this  case  we  use  one-half  of  iV",  or  45,  and  2  v  instead  of  v;  then 


Circular  mils  = 


10.4  X  200  X  45  X  o.5i 


■■  II  920 


or  just  ONE-FOURTH  the  section  required  for  the  two-wire  system.  The  size 
of  wire  required  is  No.  8;  a  No.  9  would  answer  if  it  could  be  had.  Comparing 
the  weight  of  wire  required  with  the  two-wire  system  gives  two  No.  3  wires 
weighing  400  lb  per  i  000  ft,  and  with  the  three-wire  system  three  No.  8  wires 
weighing  207  lb;  hence,  the  saving  in  cost  is  nearly  50%  and  if  No.  9  wire  were 
obtainable  the  saving  would  be  55%.     With  a  drop  of  3%  (s-S  volts)  the  cir- 

1  -1  '    A  e      ^u    4.1.    '      '  4.  ^°-4  X  200  X  45  X  0.51 

Cular  mils  required  for  the  three-wire  system  =  ■ — =  7  230, 

6.6 


im 


Electric  Work  for  Buildings 


Part  3 


requiring  No.  lo  \^ires.  The  current  in  amperes  in  the  two-wire  system  =  N  x 
c  =  45.9,  and  in  the  three-wire  system  Yi  N  x  c=  22.95.  Referring  to  Table  III 
it  is  seen  that  the  smallest  size  of  weather-proof  wire  permitted  for  45.9  amperes 
is  No.  8;  consequently,  No.  8  wire  could  be  used  with  the  two-wire  system  and 
comply  with  the  underwriters'  rules,  but  the  drop  in  potential  would  be  45.9  X 
0.2  X  0.6285  (amperes  x  resistance  of  line)  =  5.77  volts;   or  over  5%. 

For  the  three-wire  system,  the  current  being  23  amperes,  the  smallest  weather- 
proof wire  permitted  by  Table  III  is  No.  12,  which  would  give  a  drop  of  7.4 
volts,  or  3.8  volts  on  each  side,  or  about  3^%  of  the  lamp-voltage.  Except 
on  very  short  lines  a  2%  drop  will  always  demand  larger  wires  than  required 
by  the  underwriters,  and  this  is  also  usually  true  of  a  3%  drop. 


Tab^e  IV.     Dimensions,  Weights  and  Resistances  of  Copper  Wire 


Weight  in  lb  per 

Gauge- 
number, 
B.&S. 

Diameter 
in  mils 

Area  in 
cir.  mils 

Area  in 
sq  in 

I  000  ft 

Bare 

Weather- 
proof* 
wire 

Ohms  per 
I  000  ft 

wire 

at  20°  C. 
or  68°  F. 

OCXXJ 

460 

211  600 

0.166190 

640.73 

800 

0.04893 

000 

410 

167800 

0.131790 

508. 12 

666 

0.06170 

00 

36s 

133  100 

0.104520 

402.97 

500 

0.07780 

0 

325 

105  500 

0.082887 

319-74 

363 

0.09811 

I 

289 

83690 

0.065732 

253  43 

313 

0.1237 

2 

258 

66370 

0.052128 

200.98 

250 

0.1560 

3 

229 

52630 

0.041339 

159.38 

200 

0.1967 

4 

204 

41  740 

0.032784 

126.40 

144 

0.2480 

5 

182 

33  100 

0.02S999 

100.23 

125 

0.3128 

6 

162 

26250 

0.020618 

79-49 

105 

0.3944 

7 

144 

20  820 

0.016351 

63 -03 

87 

0.4973 

8 

128 

16.510 

0  012967 

49-99 

69 

0.6271 

9 
10 

114 

102 

13090 
10380 

0.010283 
0.008155 

39-65 
31-44 

0.7908 
0.9972 

50 

II 

91 
81 

8234 

6  530 

0.006466 
0.005129 

24-93 
19.77 

1-257 
1.586 

12 

31 

13 
14 

72 
64 

5  178 
4  107 

0.004067 
0.003225 

15.68 

1-999 

2.527 

12.44 

22 

15 
16 

57 
51 

3  257 
2  583 

0 . 002558 

9.86 

3  179 
4.009* 

0.002'528 

7.82 

14 

17 
18 

45 
40 

204S 
1  624 

0  00160" 

6.20 

5.055 

0.001275 

4.92 

" 

6  374 

*  Approximate  weigRt  oi  w«atlref-proof  line-wire  for  outdoor  work  is  10%  Ife^  than 
here  given. 

To  find  the  smallest  size  of  wire  that  will  comply  with  the  underwriters'  rules 
it  is  only  nfeccssary  to  compute  the  total  current  in  amperes,  and  from  Table  III 
select  the  wire  having  a  capacity  equal  to  or  next  above  the  required  number  of 
amperes.  Table  VI  shows  at  a  glance  the  maximum  number  of  i6-candle-powci.' 
iid-volt  carbon  lamps  permitted  by  the  National  Code. 

Formulas  (i)  and  (2),  page  1472,  may  also  be  used  for  motor- wiring,  if  the 
required  current  in  amperes  is  known,  by  substituting  the  given  rmmber  of  am- 
peres for  N  X  c. 


Wire-Calculations 


1475 


Table  V.     Maximum  Length  of  Line  for  Given  Number  of  Lamps  tiiat  can 
be  Used  with  a  Two-Per-Cent  Drop.     Two-Wire  System 

Based  on  Vz  ampere  per  carbon-lamp.     One  3  2 -candle-power  carbon-lamp  = 
two  i6-candle-power  carbon-lamps.     Four  40-watt  tungsten- 
lamps  =  three  i6-candle-Rower  carbon-lamps 


No.  of 
wire, 
B.&S. 
gauge 


Number  of  i6-candle-power,  no- volt  carbon-lamps 


Maximum  length  of  line,  one  side,  in  feet 


139 

104 

83 

76 

70 

52 

42 

221 

166 

133 

120 

no 

83 

66 

264 

211 

192 

176 

132 

105 

326 

297 

272 

440 

204 
334 

163 
267 

Number  of  i6-candle- power,  no- volt  lamps 


36 


60 


70 


Maximum  length  of  line,  one  side,  in  feet 


35 
55 
88 
136 
220 


44 
70 
109 
178 

225 


37 
58 
91 
148 
187 
236 


52 

81 
133 
168 

212 

268 


42 
65 
107 

135 

170 
214 

270 


54 
89 
112 
141 
180 
225 
285 


37 
76 
96 
121 
153 
193 
243 


40 
66 
84 
106 
134 
169 
213 


59 
75 
94 
119 
150 
190 


53 
67 
85 
107 
135 
170 


For  three-wire  mains  with  220  volts  between  outer  wires  and  same  number  of  lamps  on 
each  side,  length  of  wire  may  be  increased  four  times. 


Table  VI.     Maximum  Carrying  Capacity  of  Wires  in  Terms  of  i6-CandIe- 
Power  iio-Volt  Lamps,  However  Short  the  Wires  May  Be 

Based  on  H  ampere  per  lamp 
Four  40-watt  tungsten-lamps  =  three  i6-candle-power  carbon-lamps 


No.  of 

Number  of  lamps 

No.  of 

Numbpr  of  lamps 

wire. 

B.&S. 

Rubber- 

Weather- 

B.&S. 

Rubber- 

Weather- 

gauge 

covered 

,   proof 

gauge 

covered 

proof 

14 

24 

32 

4 

130 

184 

12 

34 

46 

3 

152 

220 

10 

48 

64 

2 

180 

262 

8 

66 

92 

I 

214 

312 

6 

92 

130 

0 

254 

370 

5 

108 

154 

00 

300 

440 

1476 


Electric  Work  for  Buildings 


Part  3 


Example.  What  should  be  the  size  of  the  wires  to  be  run  to  a  motor  that 
i-equires  30  amperes  at  220  volts  and  is  situated  200  ft  from  the  distributing 
pole,  the  drop  in  volts  not  to  exceed  2%? 

Solution.     Using  Formula  (i),  and  substituting  30  ior  N  X  c,  we  have 


Circular  mils  ■■ 


10.4  X  400  X  30 
4.4 


=  26400 


which  requires  a  No.  5  wire. 


Either  the  watts  or  the  current  in  amperes  is 
stamped  on  every  motor. 
If  watts  are  given,  the 
current  in  amperes  may 
be  found  by  dividing  the 
watts  by  the  voltage.  If 
kilowatts  are  given,  multi- 
ply by  I  000  and  then 
divide  by  the  voltage. 

Wiring-Tables.  Sev- 
eral forms  of  wiring-tables 
which  are  very  useful  to 
electricians  are  published  in 
various  books  on  electric- 
ity. For  ordinary  interior 
wiring  for  iio-volt,  16- 
candle-power  carbon- 
lamps,  Table  V,  computed 
by  Mr.  Kidder,  will  show 
at  a  glance  the  number 
of  wire,  B.  &  S.  gauge, 
required  to  supply  the 
given  number  of  lamps  by 
first  ascertaining  the  length 
of  line  (one  way)  through 
which  the  average  current 
flows,  as  explained  under 
Load-Center.  (See  page 
1471  and  Fig.  12.) 

Simple  Example  of 
Wiring.  To  show  the 
method  of  wiring  an  or- 
dinary building  for  incan- 
descent lighting  we  will 
take  a  two-story  building 
having  a  floor-plan  as 
shown  in  Fig.  13.  Most 
of  the  light-outlets  are  on 
.  the  ceiling  and  are  indi- 
cated by  a  small  circle. 
The  outlet  marked  £  is  a 
special  outlet  for  heating, 
etc.,  and  must  be  described 
in  the  specifications.  Let  us  assume  it  is  to  take  320  watts.  This  is  equiva- 
lent to  adding  eight  40-watt  lamps  to  this  circuit.  F  and  G  are  wall-outlets. 
The  meanings  of  the  symbols  used  are  explained  on  pages  1484-5-    The  numbers 


Fig.  13. 


Wiring-diagram  for  Second  Story.    For  Mean- 
ing of  Symbols,  see  pages  1484-5- 


Wire-Calculations 


1477 


I  and  2  inside  the  circles  denote  the  number  of  i6-candle-power  carbon-lamps 
to  the  outlet.  The  same  number  of  25-watt  or  40- watt  tungsten-lamps  may 
always  be  used  without  overloading  the  circuits.  See  pages  1398  and  1399 
for  Standard- Wiring  Symbols.  The  current  to  be  obtained  from  the  wires  of 
the  public  lighting  company,  which  carry  a  current  at  220  volts  between  the 
outside  wires,  and  at  no  volts  between  either  outside  wire  and  the  neutral 
wire.  The  feed-wires  for  the  building  should  enter  through  the  alley-wall  at 
about  the  level  of  the  second 
floor  and  should  drop  in  the 
partition  just  inside  the  wall 
for  the  main  fuse-block  and 
switch,  which  should  be  in 
a  small  cabinet  and  the 
meter  (M).  The  distribu- 
tion-cabinet should  be  lo- 
cated near  the  center  of  the 
building,  say  at  DC,  and 
there  should  be  a  cabinet 
in  each  story.  From  this 
cabinet  we  will  run  four  cir- 
cuits for  each  story,  which 
are  indicated  by  the  letters 
A,  B,  C  and  D.  Circuit  A 
shows  the  wires  run  for  a 
switch  on  the  wall  near  the 
door  of  each  of  four  rooms 
to  control  the  lights  in  those 
rooms.  All  of  the  lights  on 
circuit  C  should  be  controlled 
by  keys  in  the  lamp-sockets. 


F.F,  FUSE-PLUGS 


S.8,  KNIFE-SWITCHES 


Fig.  14.    Cabinet-wiring  for  Knife-switch  Control 


The  lights  on  circuits  B  and  D  are  not  switched, 
except  the  outlet  at  head  of  stairs,  which  is  controlled  by  a  snap  or  push-button 
switch  at  S.  For  a  first-class  job  all  of  the  four  circuits  would  be  controlled 
by  knife-switches  in  the  cabinet,  as  shown  in  Fig.  14;  but  this  is  not  absolutely 
necessary. 

Size  of  Wires.  The  load-center  of  circuits  A,  C,  and  D  would  be  at  about 
the  points  marked  X  (Fig.  13).  For  circuit  B  take  one-half  the  distance  ab 
and  add  to  it  the  distance  from  c  to  the  cabinet.  In  figuring  the  length 
of  line,  6  ft  should  be  added  for  the  drop  from  ceiling  to  the  cabinet.  Let  us  as- 
sume that  tungsten-lamps  are  to  be  used.  In  computing  the  current  taken  by 
each  lamp  it  is  always  assumed  that  no  smaller  than  a  40-watt  tungsten  is  used. 

The  drop-lights,  marked -Q-  would  probably  be  25-watt  lamps,  but  must  be 
counted  as  40-watt,  according  to  the  underwriters*  rules.  The  number  of  40- 
watt  lamps  and  length  of  wire  for  each  circuit  are  as  follows: 

Circuit  A,  8  lights,  41  ft  one  way  to  load-center. 
Circuit  B,  II  lights,  52  ft  one  way  to  load-center. 
Circuit  C,  16  lights,  37  ft  one  way  to  load-center. 
Circuit  D,  12  lights,  59  ft  one  way  to  load-center. 
Total  number  of  lamps,  47. 

From  Table  V  we  see  that  the  maximum  length  of  line  one  way  for  No.  14 
wire  carrying  twelve  carbon  or  sixteen  40-watt  lamps  is  70  ft.  Consequently, 
all  of  the  lamp-circuits  can  be  No.  14  wire,  which  is  the  smallest  size  permittM. 


147S 


Electric  Work  for  Buildings 


Part  3 


Feed-Wires.  These  should  be  run  on  the  three-wire  system.  Allowing  for 
?  X  47  or  94  lamps  in  first  and  second  stories  and  eight  in  basement,  the  feed- 
wires  must  be  capable  of  supplying  102  lamps.  Each  40-watt  lamp  would  take 
40/110  =  0.364  ampere.  The  distance  from  outside  the  building  to  distribution- 
cabinet  is  about  72  ft,  allowing  for  three  drops.  Using  Formula  (1),  and 
assuming  that  there  will  be  fifty-one  lamps  on  each  side  of  the  three-wire  system, 
and  doubling  the  drop  in  volts,  gives 

^.      ,         .,       10.4  X  144  X  0.364  X  51       r,    . 
Circular  mils  =  =  6  960  cm. 


which  calls  for  No.  11  wire;  but  as  this  size  is  not  carried  in  stock  we  must  use 
No.  10.  From  the  second  story  to  the  third  No.  12  wires  could  be  used.  For 
almost  all  buildings  lighted  from  a  central  station  the  lamp-circuits  will  not 
usually  require  a  wire  larger  than  No.  14,  so  that  about  the  only  wires  which 
the  architect  needs  to  look  after  are  the  wires  which  run  to  the  distribution- 
cabinets. 

Switches.  A  switch  is  a  device  for  opening  or  closing  a  circuit  at  will  either 
at  the  fixture  or  at  any  other  point.  In  the  better  class  of  buildings  the  majority, 
if  not  all,  of  the  ceiling-lights  are  controlled  by 
switches  placed  at  a  convenient  place  on  a  side 
wall.  Lights  may  be  controlled  at  any  distance 
from  the  fixture  by  running  a  switch-loop. 
For  controlling  either  a  single  lamp  or  fixture, 
or  any  number  of  lamps,  a  switch-loop  is  run 
as  shown  on  circuits  A  and  C,  as  in  Fig.  13. 
As  shown  also  in  Fig.  4,  one  side  of  the  loop 
must  be  connected  with  one  of  the  distributing 


X 


<^Lamp 

InBulating 
Material 
A B  Cy  D  E 


^~az^r^ 


Fig.  15.  The  Lamp  May  Be  Turned  Ofif  or  On 
From  Any  of  the  Five  Points,  A,  B,  C,  Z>, 
or£ 


Fig.  16.  The  Lamps  May  Be 
Turned  Off  or  On  From  Either 
the  First  or  Second  Story 


wires  and  the  other  side  to  the  lamp.  When  a  number  of  lamps  are 
to  be  controlled  by  one  switch,  as  in  the  case  of  hall-lights,  and  the  lamps 
in  large  rooms,  such  as  churches,  theaters,  concert-halls,  etc.,  a  separate 
circuit  is  usually  run  for  those  lamps,  and  a  switch  anywhere  in  one  of  the 
distributing  lines  will  turn  on  or  ofif  all  of  the  lights  on  that  line.  As  the 
underwriters  do  not  permit  more  than  twelve  i6-candle-power  carbon  or  sixteen 
40-watt  tungsten-lamps  on  one  circuit,  not  more  than  these  numbers  of  lamps 
can  be  controlled  by  one  switch,  except  where  the  switch  is  placed  on  the 
mains.  It  is  also  practicable  to  control  one  lamp  from  two  or  three  places. 
Thus  by  a  duplex  or  three-point  switch  and  proper  wiring,  a  lamp  may  be  lighted 
or  turned  ofif  from  either  the  first  or  second  story  at  will.  By  means  of  two 
three-point  switches  and  one  four-point  switch  a  first-story  hall-lamp  may  be 


Conduit-Systems  1479 

controlled  at  will  from  either  the  first,  second  or  third  stories.  Fig.  15  shows 
the  method  of  control  from  any  number  of  points,  since  any  number  of  4-point 
snap-switches,  such  as  B,  C  and  D,  can  be  inserted  between  the  3-point  switches 
A  and  E  if  more  points  of  control  are  needed.  Fig.  16  shows  one  method  of 
wiring  for  controlling  a  hall-light  from  first  and  second  stories  by  means  of  two 
3-point  switches.  With  the  switches  in  the  position  shown  the  circuit  is  broketi, 
as  there  is  no  connection  between  the  lamps  and  line  B.  By  turning  either 
switch  a  connection  is  made  with  line  B  and  the  current  will  flow. 

Kinds  of  Switches.  For  controlling  lamps  from  one  point  three  kinds  of 
switches  are  used,  namely,  snap-switches,  flush  or  push-button  switches 
and  knife-switches.  When  less  than  eight  lamps  are  controlled  by  the  switch, 
a  flush  or  push-button  switch  is  commonly  used  where  a  neat  appearance  is  desir- 
able, and  in  places  where  this  is  of  no 
importance,  a  snap-switch  is  used,  as  it  is 
the  cheaper.  Where  a  circuit  of  twelve  or 
more  lamps  is  controlled  by  a  switch,  a 
double-pole  (d.p.)  knife-switch  (Fig.  17) 
is  commonly  used,  being  generally  placed 
in  a  cabinet.  Knife-switches  should  always 
be  used  on  main  wires.  Snap  and  push- 
button switches  are  made  both  single  and 
double  pole.  A  single-pole  switch  opens 
only  one  side  of  the  circuit  and  a  double- 
pole  switch  both  sides.  A  double-pole 
knife-switch   necessarily   opens  both   sides.  Fig.  17.    Common  Knife-switch 

A    switch    used    on    a    three-wire    system 

must  have  three  poles.  Double-pole  snap  and  push-button  switches  are  seldom 
used  for  less  than  twelve  lamps.  Duplex  switches,  sometimes  called  three- 
point  switches,  are  usually  of  the  snap  or  of  the  push-button  type. 

Conduit-Systems.  As  weather-proof  or  rubber-covered  wire  cannot  be  run 
in  brick  walls  or  floors  of  brick,  terra-cotta,  or  concrete  without  some  protection 
other  than  the  covering  of  the  wires,  it  is  necessary  in  such  places  to  run  the 
wires  in  tubes  or  conduits,  and  in  fire-proof  buildings  all  of  the  lighting-wires 
are  generally  run  in  a  system  of  conduits. 

Kinds  of  Conduits.  There  are  two  kinds  of  interior  conduits  now  in  com- 
mon use: 

(i)  Lined  Mild-Steel  Pipe.  The  lining  consists  of  a  thin  coat  of  enamel 
which  must  be  impervious  to  water,  sulphuric  acid,  acetic  acid,  hydrochloric 
acid  and  carbonate-of-soda  solutions.  For  regular  conduit  systems  only  mild- 
steel  piping  of  the  same  thickness  as  ordinary  gas-piping  is  approved  by  the 
underwriters.  The  conduit  must  be  continuous  from  outlet  to  outlet  or  junction- 
boxes  or  cabinets  and  must  properly  enter  and  be  secured  to  all  fittings,  and  the 
entire  system  must  be  mechanically  secured  in  position.  Mild-steel  pipe  may 
be  galvanized,  coated,  or  enameled  on  the  outside,  but  it  must  be  enameled  on 
the  inside  as  stated  above.  Rigid  conduit,  whether  lined  or  unlined,  are 
installed  in  the  same  manner  as  a  good  job  of  gas-fitting,  except  that  for  conduits 
the  pipe  may  be  bent  to  a  curve  and  no  elbow  can  be  used  having  less  than 
sM-\n  radius  for  the  inner  edge.  Wherever  branches  are  taken  off,  junction- 
boxes  must  be  provided  and  every  outlet  must  have  an  approved  outlet-box  or 
plate.  The  wire  drawn  into  conduits  must  be  of  at  least  No.  14  size,  rubber- 
covered  and  with  double  braid.  All  conduit-systems  must  be  grounded  by 
connecting  the  steel  pipe  by  a  conductor  to  the  gas  or  water  system. 


1480  Electric  Work  for  Buildings  Part  3 

(2)  Flexible  Armored  Conduit.  This  is  made  of  metal  ribbon  wound  spirally, 
is  generally  used  in  wiring  old  houses  because  it  is  easier  to  install.  Circular 
LOOM  is  flexible  woven  tubing  treated  with  insulating  material  that  makes  it  hold 
its  shape.  This  may  be  used  in  dry  places  and  for  outlets  through  plastering 
if  it  extends  back  to  the  nearest  porcelain  knob  holding  the  wire  which  the 
conduit  covers. 

National  Electrical  Code.  The  National  Board  of  Fire  Underwriters,  in 
conjunction  with  committees  from  the  American  Institute  of  Architects,  and 
from  the  national  associations  of  electrical,  mechanical  and  railway  engineers, 
have  prepared  a  code  of  rules  and  requirements  for  the  installation  of  electrical 
lighting  which  is  the  generally  recognized  standard  and  with  which  all  interior 
wiring  must  comply  if  it  is  desired  to  obtain  insurance  on  the  building.  This 
code  has  also  been  made  a  part  of  the  ordinances  of  most  of  the  larger  cities. 
It  is  revised  every  two  years,  in  the  odd-numbered  years.  The  National  Board 
of  Underwriters  also  publishes,  semi-annually,  a  supplement  to  the  National 
Electrical  Code  which  contains  a  list  of  all  articles  that  have  been  examined 
and  approved  for  use  in  connection  with  the  code,  together  with  the  names  of 
the  manufacturers.  Articles  not  included  in  this  list  will  not  be  passed  by  the 
inspectors.  Copies  of  the  code  and  supplement  can  be  obtained  from  the  nearest 
Underwriters'  Inspection  Bureau,  or  by  writing  to  the  Underwriters'  Labora- 
tories, 382  Ohio  Street,  Chicago,  111.  The  following  requirements  apply  to 
almost  every  installation,  and  every  architect  should  be  conversant  with  them. 

Extracts  from  the  National  Electrical  Code* 

(i)  All  wire  for  concealed  work  must  be  of  the  best  approved  rubber-covered 
brands,  as  shown  in  List  of  Fittings.  No  wire  smaller  than  No.  14  B.  &  S.  gauge 
to  be  used.     All  wire  run  in  conduits  must  have  double-braid  covering. 

(2)  Where  wires  are  concealed  and  run  parallel  to  joists  they  must  be  sup- 
ported on  porceMn  knobs  which  hold  the  wires  at  least  i  in  from  woodwork 
or  surface  wired  over.  Knobs  must  be  securely  fastened  and  must  be  placed 
EVERY  4H  FT.  Where  wires  are  run  through  joists  they  must  be  bushed 
with  porcelain  tubes  the  entire  width  of  joists.  All  wires  must  be  drawn  tight, 
so  as  to  have  all  slack  removed. 

(3)  In  concealed  work  all  wires  must  be  separated  from  each  other  by 
AT  least  5  IN.  Where  wires  run  down  partitions,  especially  partitions  formed 
by  2  by  4-in  studs,  the  wires  must  be  so  supported  as  to  run  in  the  middle  of 
partition.  If  more  than  two  wires  are  run  down  partition  between  studs,  they 
must  be  separated  by  at  least  5  in. 

(4)  Where  wires  pass  through  floors  they  must  be  protected  from  the  floor 
up  to  a  point  5  ft  above  the  floor  with  conduit  or  with  boxing.  There  must 
always  be  a  space  of  i  in  between  the  wires  and  the  boxing. 

(5)  All  joints  must  be  securely  soldered  and  taped.  A  splice  to  be  approved 
must  be  both  mechanically  and  electrically  secure  without  solder,  but  must  be 
soldered  unless  made  with  some  form  of  approved  splicing-device.  Joints  to 
be  properly  taped  require,  where  rubber-covered  wire  is  used,  first  to  be  taped 
with  rubber  tape  and  then  with  friction-tape.  The  insulation  of  a  joint  must 
equal  that  on  the  conductors. 

(6)  Where  wires  enter  the  building  they  must  be  provided  with  drip-loops. 

(7)  There  must  be  a  main  cut-out  and  switch  installed  in  an  easily  acces- 
sible place,  as  near  as  possible  to  the  point  where  the  wires  enter  the  building. 

*  The  numbers  here  given  do  not  correspond  with  those  in  the  code,  and  several  of 
the  rules  are  much  abridged.  They  are  intended  to  give  the  substance,  rather  than  the 
exact  language. 


General  Suggestions  for  Electric  Work 


1481 


This  will  require  that  cut-out  and  switch  be  placed  where  there  is  no  need  of  a 
1 2 -ft  ladder  to  reach  them. 

(8)  Every  lighting-circuit  of  66o  watts  must  be  protected  by  a  cut-out. 
This  will  limit  the  number  to  twelve  i6-candle-power  or  sixteen  40-watt  lights 
on  a  two-wire,  iio-volt  circuit,  and  to  thirty-two  40-watt  or  twenty  i6-candle- 
power  lights  on  a  three- wire,  2 20- volt  circuit.  By  special  permission,  where  No.  14 
wire  is  carried  directly  to  keyless  sockets,  and  where  the  location  of  the  sockets 
is  such  as  to  render  unlikely  the  attachment  of  flexible  cords  thereto,  the  circuits 
may  be  so  arranged  that  not  more  than  i  320  watts  (or  32  sockets)  may  be  de- 
pendent upon  the  final  cut-out.  Sockets  are  to  be  considered  as  requiring  not 
less  than  40  watts  each. 

(9)  All  cut-outs  must  be  placed  in  an  asbestos-lined  cabinet.  The  as- 
bestos must  be  at  least  H  in  in  thickness  and  securely  held  in  place  by  shellac 
and  tacks.  Lumber  of  which  cabinet  is  made  must  be  at  least  %  in  in  thickness. 
Cabinet  must  be  furnished  with  snug-fitting  door;  door  to  be  hung  by  strong 
hinges  and  to  be  furnished  with  a  suitable  catch. 

(10)  Cut-outs  to  be  approved  must  be  of  the  plug  or  of  the  cartridge-type. 

(11)  Enclosed  arc-lamps  and  incandescent  lamps  must  not  be  placed  on  same 
circuit.  Arcs  must  be  on  separate  circuits  by  themselves.  Each  arc-light  must 
be  protected  by  an  approved  cut-out.  The  cut-outs  are  to  be  placed  in  an  as- 
bestos-lined cabinet. 

(12)  The  practice  of  using  fused  rosettes  will  not  be  approved,  except  in  mills. 

(13)  Where  wires  run  down  the  side  wall  they  must  be  protected  from  me- 
chanical injury. 

(14)  All  outlets  must  be  made  to  conform  to  Rule  24,  National  Electrical  Code. 

(15)  Fans  in  series  will  not  be  approved. 

(16)  Runs  of  lamp-cord  will  not  be  approved.  Lamp-cord  is  designed  to  be 
used  for  drops  only.     Ordinary  insulated  wire  must  be  run  to  place  desired. 

(17)  Electric  heaters  must  be  installed  in  accordance  with  Rule  25  a-f,  National 
Electrical  Code. 

General  Suggestions  for  Electric  Work* 

General  Principles  and  Recommendations.  In  all  electric-work  con- 
ductors, however  well  insulated,  should  always  be  treated  as  bare,  to  the  end 
that  under  no  conditions, 
existing  or  likely  to  exist, 
can  a  grounding  or  short 
circuit  occur,  and  so  that 
all  leakage  from  con- 
ductor to  conductor,  or 
between  conductor  and 
ground,  may  be  reduced 
to  the  minimum.  In 
all  wiring  special  atten- 
tion must  be  paid  to  the  mechanical  execution  of  the  work.  Careful  and 
neat  running,  connecting,  soldering,  taping  of  conductors,  and  securing  and 
attaching  of  fittings,  are  specially  conducive  to  security  and  efficiency,  and  will 
be  strongly  insisted  on.  In  laying  out  an  installation,  except  for  constant-cur- 
rent systems,  the  work  should,  if  possible,  be  started  frora  a  center  of  distri- 
bution, and  the  switches  and  cut-outs,  controlling  and  connected  with  the  several 
branches,  be  grouped  together  in  a  safe  and  easily  accessible  place,  where  they 
can  be  readily  got  at  for  attention  or  repairs.     The  load  should  be  divided  as 

*  Preface  to  the  National  Electrical  Code 


Fig.  18. 


Potential  Wire 


Main  Fuse  Block 
Outside  Wall 

Main  Switch,  Fuse-block  and  Meter  Located  Near 
the  Point  of  Entrance  of  the  Service-wires 


1482  Electric  Work  for  Buildings  Part  3 

erenly  as  possible  among  the  branches,  and  all  complicated  and  unnecessary 
wiring  avoided.  The  use  of  wireways  for  rendering  concealed  wiring  per- 
manently accessible  is  most  heartily  indorsed  and  recommended;  and  this 
method  of  accessible  concealed  construction  is  advised  for  general  use.  Arch- 
itects are  urged,  when  drawing  plans  and  specifications,  to  make  provision  for 
the  channeling  and  pocketing  of  buildings  for  electric-light  or  power-wires,  and 
in  specifications  for  electric  gas-lighting  to  require  a  two-wire  circuit,  whether 
the  building  is  to  be  wired  for  electric  lighting  or  not,  so  that  no  part  of  the 
gas-fixtures  or  gas-piping  be  allowed  to  be  used  for  the  gas-lighting  circuit. 
Fig.  18  shows  a  common  arrangement  of  main  cut-out,  switch  and  meter,  to 
comply  with  Rule  7,  page  1480.  The  main  cut-out  and  switch  should  be  as 
near  as  possible  to  the  outside  wall,  but  the  meter  may  be  at  some  distance  from 
the  switch  if  desirable  for  any  reason. 

Specifications  for  Interior  Wiring* 

Specifications  for  Interior  Wiring  should  provide: 

(i)  That  the  wiring  shall  be  installed  in  accordance  with  the  latest  rules  and 
requirements  of  the  National  Board  of  Fire  Underwriters,  the  local  ordinances, 
and  the  rules  of  the  local  electric  light  company,  where  current  is  to  be  taken 
from  the  public  mains. 

(2)  No  electrical  device  or  material  of  any  kind  to  be  used  that  is  not  approved 
by  the  Underwriters'  National  Electric  Association,  and  all  articles  must  have 
the  name  or  trade-mark  of  the  manufacturer  and  the  rating  in  volts  and  amperes 
or  other  proper  units  marked  where  they  may  readily  be  observed  after  the 
device  is  installed. 

Requirements  (i)  and  (2)  are  sufficient  to  insure  a  safe  installation. 

(3)  Contractor  must  obtain  a  satisfactory  certificate  of  inspection  from  the 
city  inspector  or  from  the  inspector  of  the  local  board  of  fire-underwriters. 

(4)  If  the  wires  are  to  run  in  a  conduit  system  it  should  be  so  specified.  When 
a  conduit  system  is  used,  the  wires  should  not  be  drawn  in  until  all  mechan- 
ical work  as  far  as  possible  is  completed.  It  is  best  to  wait  until  after  the 
plastering  is  dry.     All  conduit  systems  must  be  grounded, 

(5)  Size  of  Wires.  The  best  method  is  to  specify  the  size  of  all  wires,  no  wire 
to  be  less  than  No.  14  B.  &  S.  gauge;  but  if  the  architect  does  not  care  to  do  this, 
the  following  clause  is  sufficient,  provided  he  can  have  confidence  that  the 
contractor  will  comply  with  it:  "All  wires  must  be  of  such  size  that  the  drop 
in  potential  at  farthest  light-outlet  shall  not  exceed  2%  under  maximum  load." 

(6)  Cut-out  cabinets  and  where  they  are  to  be  placed;  also  location  of  main- 
line cut-out  and  fuse.  For  buildings  containing  not  more  than  forty  lights,  one 
distributing  point  is  generally  sufficient,  although  in  large  houses  it  is  often 
convenient  to  have  a  cut-out  cabinet  in  each  story. 

(7)  Number  and  kind  of  switches.  All  outlets  should  be  marked  on  the 
plans,  and  the  number  of  lights  indicated  by  figures  1,  2,  3,  4,  etc.,  as  in  Fig.  13. 
See  pages  1484  and  1485  for  standard  symbols.  The  location  of  all  switches 
for  controlling  lights  should  also  be  indicated  on  the  plans. 

Approximate  Cost  of  Wiring  for  Incandescent  Lighting.  Approximate 
estimates  of  the  cost  of  wiring  buildings  for  electric  lighting  are  usually  based  on 
the  number  of  outlets  (not  lamps).  The  actual  cost  will  depend  upon  the  num- 
ber of  pounds  of  wire  required,  the  kind  and  number  of  switches,  character  of 
cut-oiit  cabinets,  etc.,  and  the  time  required  to  do  the  work,  so  that  a  close 

*  Wiring  specifications  for  buildings  having  their  own  generating  plant  shoxild  be  pre- 
pared by  an  expert. 


Specifications  for  Interior  Wiring  1483 

estimate  cannot  be  made  without  plans  and  specifications.  Again,  wages  and 
prices  of  material  vary  to  a  considerable  extent  in  different  parts  of  the  country, 
so  that  an  estimate  that  would  be  about  right  for  one  locality  would  not  sufl5ce 
for  another.  The  following  figures,*  however,  will  enable  anyone  to  form  an 
approximate  idea  of  what  any  proposed  wiring-job  will  cost. 

Count  cost  of  labor  as  not  more  than  one-third  the  cost  of  the  installation. 

For  knob-and-tube  work  in  new  houses  of  less  than  •  seventeen  outlets  or 
twenty-five  lamps,  with  no  switches  except  main  switch  and  a  rough  cut-out 
box  lined  with  asbestos,  allow  $1.50  per  outlet. 

For  same  class  of  work,  from  25  to  100  lamps,  allow  $1.75  to  $2.00  per  outlet. 

The  extra  labor  involved  in  wiring  old  buildings  will  add  from  30  to  50%  to 
the  above  figures. 

For  each  switch-loop  with  a  single-pole  snap-switch,  add  from  $1.50  to  $1.75. 

For  each  switch-loop  with  single-pole  push-button  switch,  add  from  ^2.25  to 
$2.50. 

For  each  lamp  controlled  by  duplex  or  three-point  switches,  add  from  $5  to 
$6. 

For  each  hardwood  cut-out  cabinet  with  door  and  lock,  add  from  $7  up  ac- 
cording to  number  of  circuits  and  finish. 

Iron  cut-out  cabinets  cost  from  $8.50  up. 

Ordinary  exposed  wiring,  as  in  factories,  can  usually  be  run  for  from  $1.00 
to  $1.75  per  drop,  including  rosettes,  cord  and  sockets,  the  cost  depending  very 
largely  upon  how  closely  the  drops  are  spaced. 

Small  installations  with  iron-armored  conduit  will  probably  cost  from  $5  to 
$6  per  outlet.     Large  installations  will  cost  somewhat  less. 

A  private  lighting-plant  of  200  lamps,  wired  on  the  concealed  knob-and-tube 
system,  will  cost  from  $1  250  to  $1  500,  and  a  similar  plant  with  600  lamps  will 
cost  from  $2  500  to  $3  000.  These  prices  include  engine,  dynamo-switchboard, 
etc.,  complete,  and  wiring,  but  no  switches  for  controlling  lamps. 

The  iron-armored  conduit-system  will  add  about  $2.75  per  outlet. 

None  of  the  above  estimates  include  the  cost  of  fixtures  except  in  the  case  of 
exposed  wiring. 

Drop-cord  and  sockets  cost  about  90  cts  per  lamp.  Single-lamp  fixtures  may 
be  purchased  from  $1.25  upwards;  double-lamp  fixtures  from  $2  upwards. 
Combination-fixtures  cost  about  25%  more  than  straight  electric  fixtures. 

The  price  of  rubber-covered  wire  varies  from  $8  to  $60  per  i  000  ft  according 
to  size,  and  of  weather-proof  wire  from  16  cts  to  25  cts  per  pound. 

*  These  are  pre-war  prices  and  the  data  are  retained  for  purposes  of  comparison  of 
relative  values. 


1484 


Electric  Work  for  Buildings 


Part  3 


I* 


.21 . 


Standard  Wiring-Symbols  Adopted  by  the  National  Contractors'  Association 
and  the  American  Institute  of  Architects 

Copyrighted 

VtV         Ceiling-outlet;  electric  only.     Numeral  in  center   indicates   number   of 
y~^  standard  i6-c.p.  incandescent  lamps.* 

y%(.\_       Ceiling-outlet;   combination.     %  indicates  4-i6c.p.  standard  ^^ 

\m\%  incandescent  lamps  and  2  gas-burners.     If  gas  only.  59^ 

^    Yl^  Bracket-outlet;  electric  only.     Numeral   in  center  indicates 

W)^^^  number  of  standard  i6-c.p.  incandescent  lamps. 

^)^^4.        Bracket-outlet;    combination.     \  indicates  4-16  c.p.  stand- 
^T/ms^  ard  incandescent  lamps  and  2  gas  burners.     If  gas  only. 

Wall  or  baseboard  receptacle-outlet.    Numeral  in  center  indi- 
cates number  of  standard  i6-c.p.  incandescent  lamps. 
Floor-outlet.     Numeral  in  center  indicates  number  of  Standard  i6-c.p. 

incandescent  lamps. 
Outlet  for  outdoor  standard  or  pedestal,  electric  only.     Numeral  indicates 

number  of  standard  i6-c.p.  incandescent  lamps. 
Outlet   for    outdoor    standard    or    pedestal;     combination.     %    indicates 
6-16  c.p.  standard  incandescent  lamps;   6  gas-burners. 

Drop-cord  outlet. 

One-lamp  outlet,  for  lamp- receptacle. 

Arc -lamp  outlet. 

Special  outlet  for  lighting,  heating 

specifications. 
Ceiling-fan  outlet. 

S.  P.  switch-outlet. 

D.P.  switch-outlets. 

3-way  switch-outlet. 

4-way  switch-outlet. 

Automatic  door  switch -outlet. 

Electrolier  switch-outlet. 

Meter-outlet. 


and  power-current,  as  described  in 


Show  as  many  symbols  as  there 
are  switches.  Or  in  case  of  a 
very  large  group  of  switches, 
indicate  number  of  switches  by 
a  Roman  numeral,  thus; 
S'XII,  meaning  12  single-pole 
switches. 

Describe  type  of  switch  in  speci- 
fications, that  is,  Hush  or  sur- 
face, push-button  or  snap. 


^^^^H        Distribution-panel. 

^^^^P        Junction  or  pull-boK. 

J(^h)/        Motor-outlet.     Numeral  in  center  indicates  horse-power. 

L^><C]         Motor-control  outlet. 
^^\—'f^        Transformer. 

*  If  tungsten-lamps  are  used  instead  of  carbon-lamps,  the  figure  in  the  circle  may 
stand  for  the  number  of  2S-watt  tungsten-lamps,  a  25-watt  tungsten-lamp  being  the 
nearest  in  candle-power  to  a  i6-candle-power  carbon-lamp  though  consuming  less  than 
one-half  the  power.  Since  tungsten-lamps  average  about  i.i  watts  to  the  candle-power, 
many  architects  place  in  the  circle  the  number  of  watts  to  be  used.     Dividing  this  number 


Standard  Wiring-Symbols  1485 

Standard  Wiring-Symbols  Adopted  by  the  National  Contractors'  Association 
and  the  American  Institute  of  Architects  (Continued) 

Main  or  feeder-run  concealed  under  -floor. 

Main  or  feeder-run  concealed  under  floor  above. 

Main  or  feeder-run  exposed. 

Branch  circuit-run  concealed  under  floor. 

Branch  circuit-run  concealed  under  floor  above. 

Branch  circuit-run  exposed. 


-I 


•  Riser. 

Uj  Telephone-outlet;   private  service. 

f^  Telephone-outlet;  public  service. 

M  Bell-outlet. 

lJI  Buzzer-outlet. 

[FJ2  Push-button  outlet.    Numeral  indicates  number  of  pushes. 

~~~\0  Annunciator.    Numeral  indicates  number  of  points* 

-— •  Speaking-tube. 

""^^C)  Watchman-clock  outlet. 

Watchman-station  outlet. 

Master  time-clock  outlet. 

I 

--— JT)  Secondary  time-clock  outlet. 

I  T  I  Door-opener. 

jTpl  Special  outlet  for  signal-systems,  as  described  in  specifications. 

I  I  I  I  I  I  Battery-outlet. 

I  '  I  '  I  Circuit  for  clock,  telephorie,  bell  or  other  service,  run  under  floor, 

_____^__     _______  concealed.    Kind  of  service  watited  ascertained  by  symbol  to 

*"  which  line  connects. 

.  .  Circuit  for  clock,  telephone,  bell  of  oihtt  service,  run  Uhder 

""      "  floor  above,  concealed.    Kind  of  service  wanted  ascertained 

by  symbol  to  which  line  connects. 
Heights  of  center  of  wall-outlets  (unless  otherwise  specified) : 

Living-rooms • ' S  ft  6  in 

Chambers 5  ft  b  ifl 

Offices 6  ft  o  m 

Corridors •  -  • 6  f t  3  m 

Heights  of  switches  (unless  otherwise  specified) 4  f t  o  m 

by  i.T  gives  the  candle-power  per  outlet.  Thus  V^  means  enough  tungsten-IampS 
can  be  placed  in  this  outlet  to  total  120  watts,  three  y3<  40-watt  lamps,  or  two  60- watt 
lamps,  etc.     The  candle-power  in  any  case  would  be  lao/i.i  =  no  candle-power. 


1486  Architectural  Acoustics  Part  3 


AECHITECTURAL    ACOUSTICS* 

By 
WALLACE   C.   SABINE 

LATE  PROFESSOR  OF  PHYSICS,  HARVARD  UNIVERSITY 

Architectural  Acoustics  a  Rational  Engineering  Problem.  Because 
familiarity  with  the  phenomena  of  sound  has  so  far  outstripped  the  adequate 
study  of  the  problems  involved,  many  of  them  have  been  popularly  shrouded  in 
a  wholly  unnecessary  mystery.  Of  none,  perhaps,  is  this  more  true  than  of 
ARCHITECTURAL  ACOUSTICS.  The  Conditions  surrounding  the  transmission  of 
speech  in  an  enclosed  auditorium  are  complicated,  it  is  true,  but  are  only  such 
as  will  yield  an  exact  solution  in  the  light  of  adequate  data.  It  is  not  un- 
reasonable, therefore,  to  include  problems  of  architectural  acoustics  among  the 

RATIONAL  ENGINEERING  PROBLEMS. 

Character  and  Application  of  the  Problem.  The  problem  of  architec- 
tural acoustics  is  necessarily  complex,  and  each  room  presents  many  conditions 
which  contribute  to  the  result  in  a  greater  or  less  degree,  according  to  circum- 
stances. To  take  justly  into  account  these  varied  conditions,  the  solution  of 
the  problem  should  be  quantitative,  not  merely  qualitative;  and  to  reach 
its  highest  usefulness  and  the  dignity  of  an  engineering  science  it  should  be  such 
that  its  application  can  precede,  not  merely  follow,  the  construction  of  the 
building. 

Conditions  and  Factors  of  the  Problem.  In  order  that  hearing  may  be 
good  in  any  auditorium  it  is  necessary  that  the  sound  should  be  sufficiently  loud, 
that  the  simultaneous  components  of  a  complex  sound  should  maintain  their 
proper  relative  intensities,  and  that  the  successive  sounds  in  rapidly  moving 
articulation,  either  of  speech  or  of  music,  should  be  clear  and  distinct,  free  from 
each  other  and  from  ejJtraneous  noises.  These  three  are  the  necessary,  as  they 
are  the  entirely  sufficient,  conditions  for  good  hearing.  Scientifically  the  prob- 
lem involves  three  factors: 

* 

(i)    Reverberation. 

(2)  Interference. 

(3)  Resonance. 

As  an  engineering  problem  it  involves  the  shape  of  the  auditorium,  its  dimen- 
sions, and  the  materials  of  which  it  is  composed. 

Rate  of  Absorption  of  Sound.  Sound,  being  energy,  once  produced  in  a 
confined  space,  will  continue  until  it  is  either  transmitted  by  the  boundary  walls 
or  is  transformed  into  some  other  kind  of  energy,  generally  heat.  This  process 
of  decay  is  called  absorption.  Thus,  in  the  lecture-room  of  Harvard  Univer- 
sity, in  which,  and  in  behalf  of  which,  this  investngation  was  begun,  the  rate 

*  Adapted  and  reproduced  by  permission  from  a  paper  read  by  Dr.  W.  C.  Sabine 
before  the  Franklin  Institute,  Philadelphia,  October  30,  1914  and  published  in  the 
January  1915  issue  of  the  Journal  of  the  FrankUn  Institute.  For' information  regard- 
ing further  data,  see  other  papers  and  treatises  on  the  subject  by  the  author  of  this 
article. 


Architectural  Acoustics  1487 

OF  ABSORPTION  was  so  small  that  a  word  spoken  in  an  ordinary  tone  of  voice  was 
audible  for  five  and  a  half  seconds  afterwards.  During  this  time  even  a  very 
dehberate  speaker  would  have  uttered  the  twelve  or  fifteen  succeeding  syllables. 
Thus  the  successive  enunciations  blended  into  a  loud  sound,  through  which  and 
above  which  it  was  necessary  to  hear  and  distinguish  the  orderly  progression  of 
the  speech.  Across  the  room  this  could  not  be  done;  even  near  the  speaker 
it  could  be  done  only  with  an  feffort  wearisome  in  the  extreme  if  long  main- 
tained. 

Multiple  Reflection,  Reverberation  and  Echoes.  With  an  audience  filling 
the  room  the  conditions  were  not  so  bad,  but  still  not  tolerable.  This  may  be 
regarded,  if  one  so  chooses,  as  a  process  of  multiple  reflection  from  walls, 
from  ceiling,  and  from  floor,  first  from  one  and  then  another,  losing  a  little  at 
each  reflection  until  ultimately  inaudible.  This  phenomenon  will  be  called 
REVERBERATION,  including,  as  a  special  case,  the  echo.  It  must  be  observed, 
however,  that,  in  general,  reverberation  results  in  a  mass  of  sound  filling  the 
whole  room  and  incapable  of  analysis  into  its  distinct  reflections.  It  is  thus  more 
difficult  to  recognize  and  impossible  to  locate.  The  term  echo  will  be  reserved 
for  that  particular  case  in  which  a  short,  sharp  sound  is  distinctly  repeated  by 
reflection,  either  once  from  a  single  surface,  or  several  times  from  two  or  more 
surfaces. 

Rate  of  Decay  of  Sound.  In  the  general  case  of  reverberation  we  are 
concerned  only  with  the  rate  of  decay  of  the  sound.  In  the  special  case  of 
the  echo  we  are  concerned  not  merely  with  its  intensity,  but  with  the  interval 
of  time  elapsing  between  the  initial  sound  and  the  moment  it  reaches  the  ob- 
server. In  the  room  mentioned  as  the  occasion  of  this  investigation  no  discrete 
echo  was  distinctly  perceptible,  and  the  case  will  serve  excellently  as  an  illustra- 
tion of  the  more  general  type  of  reverberation. 

Duration  of  Audibility  of  Residual  Sound.  After  preliminary  gropings, 
first  in  the  literature  and  then  with  several  optical  devices  for  measuring  the 
intensity  of  sound,  all  established  methods  were  abandoned.  Instead,  the  rate 
OF  DECAY  was  measured  by  measuring  what  was  inversely  proportional  to  it, 
the  duration  of  audibility  of  the  reverberation,  or,  as  it  will  be  called  here,  the 
DURATION  OF  AUDIBILITY  OF  THE  RESIDUAL  SOUND.  These  experiments  may  be 
explained  to  advantage  here,  for  they  will  give  more  clearly  than  would  abstract 
discussion  an  idea  of  the  nature  of  reverberation. 

Shape  of  Room  and  Nature  of  Furnishings.  Broadly  considered  there 
are  two,  and  only  two,  variables  in  a  room,  shape  (including  size),  and  materials 
(including  furnishings).  In  designing  an  auditorium  an  architect  can  give  con- 
sideration to  both;  in  repair- work  for  bad  acoustic  conditions  it  is  generally 
impracticable  to  change  the  shape,  and  only  variations  in  materials  and 
furnishings  are  allowable.  This  was,  therefore,  the  line  of  work  in  this 
case. 

The  Relative  Absorbing  Power  of  Different  Substances.  It  was  evident 
that,  other  things  being  equal,  the  rate  at  which  the  reverberation  would  dis- 
appear was  proportional  to  the  rate  at  which  the  sound  was  absorbed.  The 
first  work,  therefore,  was  to  determine  the  relative  absorbing  power  of  various 
substances.  With  an  organ-pipe  as  a  constant  source  of  sound,  and  a  suitable 
chronograph  for  recording,  the  duration  of  audibility  of  a  sound  after  the  source 
had  ceased  in  this  room  when  empty  was  found  to  be  5.62  seconds.  All  the 
cushions  from  the  seats  in  Sanders  Theater,  Boston,  Mass.,  were  then  brought 
over  and  stored  in  the  lobby.     On  bringing  into  the  lecture-room  a  number 


1488  Architectural  Acoustics  Part  3 

of  cushions,  having  a  total  length  of  8.2  meters,  the  duration  of  audibility  fell 
to  5.33  seconds.  On  bringing  in  cushions  of  a  total  length  of  17  meters  the 
sound  in  the  room  after  the  organ-pipe  ceased  was  audible  for  but  4.94  seconds. 
Evidently  the  cushions  were  strong  absorbents  and  rapidly  improving  the  room, 
at  least  to  the  extent  of  diminishing  the  reverberation.  The  result  was  inter- 
esting and  the  process  was  continued.  Little  by  little  more  cushions  were 
brought  into  the  room,  and  each  time  the  duration  of  audibility  was  meas- 
ured. When  all  the  seats,  436  in  number,  were  covered,  the  sound  was  audi- 
ble for  2.03  seconds.  Then  the  aisles  were  covered,  and  then  the  platform. 
Still  there  were  more  cushions,  almost  half  as  many  more.  These  were  brought 
into  the  room,  a  few  at  a  time,  as  before,  and  draped  on  a  scafifolding  that  had 
been  erected  around  the  room,  the  duration  of  the  sound  being  recorded  each 
time.  Finally,  when  all  the  cushions  from  a  theater  seating  nearly  1 500 
persons  were  placed  in  the  room,  covering  the  seats,  the  aisles,  the  platform, 
and  the  rear  wall  to  the  ceiling,  the  duration  of  audibility  of  the  residual 
sound  was  1.14  seconds.  This  experiment,  requiring,  of  course,  several  nights* 
work,  having  been  completed,  all  the  cushions  were  removed  and  the  room 
was  in  readiness  for  the  test  of  other  absorbents.  It  was  evident  that  a 
STANDARD  OF  COMPARISON  had  been  established.  Curtains  of  chenille,  i.i 
meters  wide  and  17  meters  in  total  length,  were  draped  in  the  room.  The 
duration  of  audibility  was  then  4.51  seconds.  Turning  to  the  data  that  had  just 
been  collected,  it  appeared  that  this  amount  of  chenille  was  equivalent  to  30 
meters  of  cushions  from  Sanders  Theater.  Oriental  rugs  (Herez,  Demirjik,  and 
Hindoostanee)  were  tested  in  a  similar  manner,  as  were  also  cretonne  cloth, 
canvas,  and  hair-felt.  Similar  experiments,  but  in  a  smaller  room,  determined 
the  absorbing  power  of  a  man  and  of  a  woman,  always  by  determining  the  num- 
ber of  running  meters  of  Sanders  Theater  cushions  that  would  produce  the  same 
effect.  This  process  of  comparing  two  absorbents  by  actually  substituting  one 
for  the  other  is  laborious,  and  it  is  given  here  only  to  show  the  first  steps  in  the 
development  of  a  method.  Without  going  into  details,  it  is  sufficient  here  to 
say  that  this  method  was  so  perfected  as  to  give  not  merely  relative,  but  abso- 
lute, COEFFICIENTS  OF  ABSORPTION. 

CoeflScients  of  Absorption.  In  this  manner  a  number  of  coefficients 
OF  ABSORPTION  Were  determined  for  objects  and  materials  which  could  be 
brought  into  and  removed  from  the  room,  for  sounds  having  a  pitch  an  octave 
above  middle  C.  In  the  following  table  the  numerical  values  are  the  abso- 
lute COEFFICIENTS  OF  ABSORPTION: 


Oil-paintings,  inclusive  of  frames o. 28 

Carpet-rugs o.  20 

Oriental  rugs,  extra  heavy o .  29 

Cheese-cloth 0.019 

Cretonne  cloth o.  15 

Shelia  curtains •. o. 23 

Hair-felt,  2.5  cm.  thick,  8  cm.  from  wall o. 78 

Cork,  2.5  cm.  thick,  loose  on  floor o.  16 

Linoleum,  loose  on  floor 0.12 


When  the  objects  arc  not  extended  surfaces,  such  as  carpets  or  rugs,  but 
essentially  spacial  units,  it  is  not  easy  to  express  the  absorption  as  an  absolute 
coefl5cient.  In  the  following  table  the  absorption  of  each  object  is  expressed  in 
terms  of  a  square  meter  of  complete  absorption: 


Architectural  Acoustics 


1489 


Audience,  per  person o. 44 

Isolated  woman 0. 54 

Isolated  man o. 48 

Plain,  ash  settees 0.039 

Plain,  ash  settees,  per  single  seat 0.0077 

Plain,  ash  chairs,  bent  wood 0.0082 

Upholstered  settees,  hair  and  leather i .  10 

Upholstered  settees,  per  single  seat . .  / o. 28 

Upholstered  chairs,  similar  in  style 0.30 

Hair-cushions,  per  seat 0.21 

Elastic-felt  cushions,  per  seat o. 20 


Coefladent  of  Absorption  of  Floors,  Ceilings  and  Wall-Surfaces.    Of 

even  greater  importance  was  the  determination  of  the  coefficient  of  absorp- 
tion of  floors,  ceilings,  and 
wall-surfaces.  The  accom-  ^^ 
plishment  of  this  called  for  a 
very  considerable  extension 
of  the  method  adopted.  If 
the  reverberation  in  a  room 
as  changed  by  the  addition 
of  absorbing  material  are 
plotted,  the  resulting  curve 
will  be  found  to  be  a  portion 
of  a  hyperbola  with  dis- 
placed axes.  An  example  of 
such  a  curve,  as  obtained  in 
the  lecture-room  of  the  Fogg 
Art  Museum,  •  Cambridge, 
Mass.,  is  plotted  in  the 
diagram  in  Fig.  1.  If  now 
the  origin  of  this  curve  is 

displaced  so  that  the  axes  of  coordinates  are  the  asymptotes  of  the  rectangular 
hj^perbola  (Fig.  2),  the  displacement  of  the  origin  measures  the  initial  absorbing 
power  of  the  room,  its  floors,  walls  and  ceilings.  Such  experiments  were  carried 
out  in  a  large  number  of  rooms  in  which  the  different  component  materials 
entered  in  very  different  degrees,  and  an  elimination  between  these  different 
experiments  gave  the  following  coefficient  of  absorption  for  different 
materials: 


K. 

X 

Q.. 

<^ 

?-. 

<^ 

"" 

■"^ 

-0- 

-0. 

0      20    40   60    80  100  120140160  180  200  220  240260280300 
Length  of  cushions  in  meters 

Fig.  1.     Curve  Showing  the  Relation  of  Duration  of 
Residual  Sound  to  Added  Absorbing  Material 


Open  window i .  000 

Wooden  sheathing,  hard  pine 0.061 

Plaster  on  wooden  lath o. 034 

Plaster  on  wire  lath 0.033 

Glass,  single  thickness 0.027 

Plaster  on  tile 0.025 

Brick  set  in  Portland  cement o. 025 


Calculating  the  Reverberation  for  Any  Room.  If  the  experiments  in 
these  rooms  are  plotted  in  a  single  diagram,  the  result  is  a  family  of  hyperbo^a^ 
(Fig.  3)  showing  a  very  interesting  relationship  to  the  volumes  of  the  rooms, 
indeed,  if  from  these  hyperbolas  the  parameter,  which  equals  the  product  of  the 


1400 


Architectural  Acoustics 


I»art  8 


coordinates,  is  determined,  it  will  be  found  to  be  linearly  proportional  to  the 
volume  of  the  room.  These  results  are  plotted  in  Fig.  4,  showing  how  strict 
the  proportionaUty  is  even  over  a  very  great  range  in  volume.    We  have  thus 

at    hand    a    ready    method 

10 1 1 1 1 1 \ \ 1 \ \ \ \ \ 1 1 1  of  calculating  the  REVERBER- 
ATION for  any  room,  its 
volume  and  the  materials  of 
which  it  is  composed  being 
known.  The  first  five  years 
of  the  investigation  were 
devoted  to  viohn  C,  the  C  an 
octave  above  middle  C,  hav- 
ing a  VIBRATION-FREQUENCY 

of  512  vibrations  per  second. 
This  pitch  was  chosen  be- 
cause, in  the  art  of  telephony, 
it  was  regarded  at  that  time 
as  the  characteristic  pitch 
Fig.  2.     Curve  5  Plotted  as  Part  of  its  Corresponding    determining    the    conditions 


§  5 
I  * 
^   3 


p 

■ 

'. 

\ 

* 

; 

s 

\ 

\ 

V, 

^ 

^'" 

._. 

320        400 
Cushions 


of   articulate    speech.      The 


Rectangular  Hyperbola.     The  Solid  Part  was  Deter- 
mined Experimentally.     The  Displacement  of  This  . 
to   the  Right   Measures  the   Absorbing   Power  of    planning  of  Symphony  Hall, 
the  Walls  of  the   Room                                              Boston,    Mass.,     forced    an 

extension  of  this  investiga- 
tion to  notes  over  the  whole  range  of  the  musical  scale,  three  octaves  below 
and  three  octaves  above  violin-C. 

Absorption-Coefficient  of  an  Audience.  In  the  very  nature  of  the  prob- 
lem, the  most  important  datum  is  the  absorption-coefficient  of  an  audience, 
and  the  determination  of 
this  was  the  first  task  un- 
dertaken. By  means  of  a 
lecture  on  one  of  the  recent 
developments  of  physics, 
wireless  telegraphy,  an 
audience  was  thus  drawn 
together  and  at  the  end  of 
the  lecture  requested  to 
remain  for  the  experiment. 
In  this  attempt  the  effort 
was  made  to  determine  the 
coefficients  for  the  five 
octaves  from  C2128  to 
C 62048,  including  notes  E 
and  G  in  each  octave. 
For  several  reasons  the 
experiment  was  not  a  suc- 
cess. A  threatening  thun- 
derstorm made  the  audi- 
ence a  small  one,  and  the  sultriness  of  the  atmosphere  made  open  windows 
necessary;  while  the  attempt  to  cover  so  many  notes,  thirteen  in  all,  prolonged 
the  experiment  beyond  the  endurance  of  the  audience.  While  this  experiment 
failed,  another,  the  following  summer,  was  more  successful.  In  the  year  that 
had  elapsed  the  necessity  of  carrying  the  investigation  further  than  the  limits 
intended  became  evident,  and  now  the  experiment  was  carried  from  C164  to 


f 

\  \ 

\  \ 

v 

«^ 

fil 

'    \ 

\ 

,  \ 

\ 

^  - 

'f''4 

\ 

\  \ 

\ 

\^ 

i 

\ 

\ 

\ 

S, 

X 

1 

\  '' 

'\ 

'\ 

\ 

s 

'^- 

.^ 

n    1 

\ 

\ 

\ 

''\ 

^s. 

"^ 

^^- 

■^^ 

?    n 

\\ 

\ 

s 

\ 

"^v 

^ 

-^ 

■-^ 

^ 

^-- 

-12- 

5  3 

0  . 

^ 

\^\^ 

%\ 

^s 

.^^ 

^8. 

^9- 

-10- 

^ 

"^ — 

41-. 

■ — 

__ 

^ 

->-- 

3? 

-- 

~__ 

— ■ 

-~ 

.i~' 

--?; 

--": 

---^ 

-w- 

^2. 
se= 

r^-£- 

^^ 

i^ 

Wi 

m 

:m 

&^ 

0       10    20   30   40    50    CO    70    80    90  100  110  120  130  110150 
120         180         240         300         360         420 
640        720         900       1080       1200 
Total  absorbing  material 
Fig.  3.     Curves  Entered  as  Parts  of  their  Corresponding 
Rectangular  Hyperbolas.     Three  Scales  are  Employed 
for  the  Volumes,  by  Groups,  1-7,  8-1 1,  and  12 


Architectural  Acoustics 


1491 


12 

150 

450 
300 

'11 

/ 

i^ 

/ 

9000 

10800  12C00 

aflOO 

r/ 

^ 

X 

1 

/ 

» 

~~ 

^60 

/ 

1200  1800 

2400   3000 

3000   4200 

^ 

n^/1 

: 

/J 

'3 

600         800        1000 
Volumes  of  rooms 


C 74096,  but  included  only  the  C  notes,  seven  notes  in  all.  Moreover,  bearing 
in  mind  the  experiences  of  the  previous  summer,  it  was  recognized  that  even 
seven  notes  would  come  dangerously  near  overtaxing  the  patience  of  the 
audience.       Inasmuch    as 

the  COEFFICIENT  OF  AB- 
SORPTION for  C4512  hac^ 
already  been  determined 
six  years  before,  in  the  in- 
vestigations mentioned,  the 
coefficient  for  this  note  was 
not  redetermined.  The 
experiment  was  therefore 
carried  out  for  the  lower 
three  and  the  upper  three 
notes  of  the  seven.  The 
audience,  on  the  night  of 
this  experiment,  was  much 
larger  than  that  which  came 
the  previous  summer,  the  pj^  4  The  Parameters  ;&,  Plotted  Against  the  Volumes 
night    was    a    more    com-  ^^f  the  Rooms,  Showing  the  Two  Proportional 

fortable  one,   and   it   was 

possible  to  close  the  windows  during  the  experiment.  The  conditions  were 
thus  fairly  satisfactory.  In  order  to  get  as  much  data  as  possible,  and  in  as 
short  a  time,  there  were  nine  observers  stationed  at  different  points  in  the  room. 

These  observers,  whose  kindness  and  skill 
it  is  a  pleasure  to  acknowledge,  had  pre 
pared  themselves,  by  previous  practice,  for 
this  one  experiment.  The  results  of  the 
experiment  are  shown  on  the  lower  curve 
in  Fig.  5.     This  curve  gives  the  coefficient 

OF     ABSORPTION    PER    PERSON.      It    is    tO    be 

observed  that  one  of  the  points  falls  clearly 
ofif  the  smooth  curve  drawn  through  the 
other  points.  The  observations  on  which 
this  point  is  based  were,  however,  much 
disturbed  by  a  street-car  passing  not  far 
from  the  building,  and  the  departure  of  this 
observation  from  the  curve  does  not  indi- 
cate a  real  departure  in  the  coefficient,  nor 
should  it  cast  much  doubt  on  the  rest  of  the 
work,  in  view  of  the  circumstances  under 
which  it  was  secured.  Counteracting  the, 
perhaps,  bad  impression  which  this  point 
may  give,  it  is  considerable  satisfaction  to 
note  how  accurately  the  point  for  C4512, 
determined  six  years  before  by  a  different 
set  of  observers,  falls  on  the  smooth  curve 
Fig.  5.  Absorbing  Power  of  an  Audi-  through  the  remaining  points.  The  upper 
ence  for  Different  Notes  curve  represents  the  absorbing  power  of  an 

audience  per  square  meter,  as  ordinarily 
seated.  The  vertical  ordinates  are  expressed  in  terms  of  total  absorption 
by  a  square  meter  of  surface.  For  the  upper  curve  the  ordinates  are  thus  the 
ordinary  coefficients  of  absorption.    The  several  notes  are  at  octave-intervals 


9 -^ 

,8 -/ 

V  bp 

3  —^ 

2  J- 

1 


C« 


1492 


Architectural  Acoustics 


Part  3 


as  follows:  C164,  C2128,  C3  (middle  C)  256,  C4512,  €51024,  C6^04$,  C74096. 
In  the  audience  on  which  these  observations  were  taken  there  were  77  women 
and  105  men.  The  courtesy  of  the  audience  in  remaining  for  the  experiment 
and  the  really  remarkable  silence  which  they  maintained  are  gratefully 
acknowledged. 

Absorption  of  Sound  by  Wooden  Sheathing.  •  The  next  experiment  waS 
on  the  determination  of  the  absorption  of  sound  by  wooden  sheathing.  It  is 
not  an  easy  matter  to  find  conditions  suitable  for  this  experiment.  The  room  in 
which  the  absorption  by  wooden  sheathing  was  determined  in  the  earlier  exper- 
iments was  not  available  for  these.  It  was  available  then  only  because  the 
building  was  new  and  empty.  When  these  more  elaborate  experiments  were 
under  way  the  room  became  occupied,  and  in  a  manner  that  did  not  admit  of  its 

being  cleared.  Quite  a  little  searching  In 
the  neighborhood  of  Boston  failed  to  dis- 
cover an  entirely  suitable  room.  The 
best  one  available  adjoined  a  night-lunch 
room.  The  night-lunch  was  bought  out 
for  a  couple  of  nights,  and  the  experiment 
was  tried.  The  work  of  both  nights  was 
much  disturbed.  The  trafBc  past  the 
building  did  not  stop  until  nearly  two 
o'clock,  and  began  again  at  four.  The 
interest  of  those  passing  on  foot  through- 
out the  night,  and  the  necessity  of  repeated 
explanations  to  the  police,  greatly  inter- 
fered with  the  work.  This  detailed  state- 
ment of  the  conditions  under  which  the 
experiment  was  tried  is  made  by  way  of 
explanation  of  the  irregularity  of  the 
observations  recorded  on  the  curve,  and 
of  the  failure  to  carry  this  particular  line 
of  work  further.  On  the  first  night  seven 
points  were  obtained  for  the  seven  notes 
C164  to  C74096.  The  reduction  of  these 
results  on  the  following  day  showed 
variations  indicative  of  maxima  and 
minima,  which,  to  be  accurately  located, 
would  require  the  determination  of  inter- 
mediate points.  In  the  experiment  on 
the  following  ni:;ht,  points  were  deter- 
mined for  the  E  and  G  notes  in  each 
Other  points  would  have  been  determitied, 


.12 
.11 

•^ 

"^, 

J 

/ 

•\ 

V 

/ 

.10 
.09 
.08 
.07 
.06 
,05 
.04 
.03 
.02 
.01 

/ 

\ 

/ 

/ 

\ 

I         J 

/ 

/ 

v.^ 

/ 

-2      C3     C,      C,"     c,     c, 

Absorbing  Power  of   Wooden 
Sheathing 


octave  between  C212S  and  CC2048. 

but  time  did  not  permit.  It  is  obvious  that  the  intermediate  points  in  the  loWer 
and  in  the  higher  octave  were  desirable,  but  no  pipes  were  to  be  had  on  such 
short  notice  for  this  part  of  the  range,  and  in  their  absence  the  data  could  ftot 
be  obtained.  In  the  diagram,  Fig.  ^6,  the  points  lying  on  the  vertical  lines  were 
determined  the  first  night.  The  pv)ints  lying  between  the  vertical  lines  were 
determined  the  second  night.  The  shea  thin-?  of  the  room  is  of  North  Carolina 
pine,  2  centimeters  thick.  The  absorption  is  here  due  almost  wholly  to  yielding 
of  the  sheathing  as  a  whole.  It  is  not  possible  now  to  learn  as  much  in  regard 
to  the  framing  and  arrangement  of  the  studding  in  the  particular  room  tested 
as  is  desirable.  The  accuracy  with  which  these  points  fall  on  a  smooth  curve  Is, 
perhaps,  all  that  could  be  expected  in  view  of  the  difficulty  under  which  the  ob- 


Architectural  Acoustics 


1493 


servations  were  conducted  and  the  limited  time  available.  One  point  in  par- 
ticular falls  far  off  from  this  curve,  the  point  for  C3256,  by  an  amount  which 
is,  to  say  the  least,  serious,  and  which  can  be  justified  only  by  the  conditions 
under  which  the  work  was  done.  The  general  trend  of  the  curve  seems,  how- 
ever, established  beyond  reasonable  doubt.  It  is  interesting  to  note  that  there 
is  one  point  of  maximum  absorption,  which  is  due  to  resonance  between  the 
walls  and  the  sound,  and  that  this  point  of  maximum  absorption  lies  in  the 
lower  part,  though  not  in  the  lowest  part,  of  the  range  of  pitch  tested.  It 
would  have  been  interesting  to  determine,  had  the  time  and  facilities  permitted, 
the  shape  of  the  curve  beyond  C74096,  and  to  see  if  it  rises  indefinitely,  or  shows, 
as  is  far  more  likely,  a  succession  of  maxima. 

Absorption  of  Sound  by  Cushions.  The  experiment  was  then  directed  to 
the  determination  of  the  absorption  of  sound  by  cushions,  and  for  this  purpose 
return  was  made  to  the  constant-temper- 
ature room.  Working  in  the  manner 
indicated  in  the  earlier  papers  for  sub- 
stances which  could  be  carried  in  and  out 
of  a  room,  the  curves  represented  in  Fig. 
7  were  obtained.  Curve  i  shows  the 
ABSORPTION-COEFFICIENT  for  the  Sanders 
Theater  cushions,  with  which  the  whole 
investigation  was  begun  ten  years  ago 
(1904).  These  cushions  were  of  a  partic- 
ularly open  grade  of  packing,  a  sort  of 
wiry  grass  or  vegetable  fiber.  They  were 
covered  with  canvas  ticking,  and  that,  in 
turn,  with  a  very  thin,  cloth  covering. 
Curve  2  is  for  cushions  borrowed  from 
the  Phillips  Brooks  House.  They  were  of 
a  high  grade,  filled  with  long,  curly  hair, 
and  covered  with  canvas  ticking,  which 
was,  in  turn,  covered  by  a  long-nap  plush. 
Curve  3  is  for  the  cushion  of  Appleton 
Chapel,  hair-covered  with  a  leatherette, 
and  showing  a  sharper  maximum  and  a 
more  rapid  diminution  in  absorption  for 
the  higher  frequencies,  as  would  be  ex- 
pected under  such  conditions.  Curve  4 
is  probably  the  most  interesting,  because  for  more  standard  commercial  con- 
ditions ordinarily  used  in  churches.  This  curve  is  for  the  elastic-felt  cushions 
of  commerce,  of  elastic  cotton  covered  with  ticking  and  short-nap  plush.  The 
absorbing  power  is  per  square  meter  of  surface.  It  is  to  be  observed  that  all 
four  curves  fall  off  for  the  higher  frequencies,  all  show  a  maximum  located 
within  an  octave,  and  three  of  the  curves  show  a  curious  hump -in  the  second 
octave.  This  break  in  the  curve  is  a  genuine  phenomenon,  as  it  was  tested 
time  after  time.  It  is  perhaps  due  to  a  secondary  resonance,  and  it  is  to 
be  observed  that  it  is  the  more  pronounced  in  those  curves  that  have  the 
sharper  resonance  in  their  principal  maxima. 

Effects  of  Interference  of  Sound- Waves.  In  both  articulate  speech  and 
in  music  the  source  of  sound  is  rapidly  and,  in  general,  abruptly  changing  in 
pitch,  quality  and  loudness.  In  music  one  pitch  is  held  during  the  length  of 
a  note.  In  articulate  speech  the  unit  or  element  of  constancy  is  the  syllable. 
Indeed,  in  speech  it  is  even  less  than  the  length  of  a  syllable,  for  the  open- vowel. 


.9 

/ 

\ 

.8 

I 

\ 

^ 

V 

\ 

.6 

T 

/ 

7 

\ 

N 

^\ 

.5 
.4 
.3 

/ 

'1/ 

^ 

\ 

\ 

V 

7 

\ 

\ 

/^ 

r 

>, 

\ 

\ 

^6 

Fig.  7.    Absorbing  Power  of  Cushions 


1494  Architectural  Acoustics  Part  3 

sound  which  forms  the  body  of  a  syllable  usually  has  a  consonantal  opening  and 
closing.  During  the  constancy  of  an  element,  either  of  music  or  of  speech,  a 
train  of  sound-waves  spreads  spherically  from  the  source,  just  as  a  train  of  cir- 
cular waves  spreads  outward  from  a  rocking  boat  on  the  surface  of  still  water 
Different  portions  of  this  train  of  spherical  waves  strike  different  surfaces  of  the 
auditorium  and  are  reflected.  After  such  reflection  they  begin  to  cross  each 
other's  paths.  If  their  paths  are  so  different  in  length  that  one  train  of  waves 
has  entirely  passed  before  the  other  arrives  at  a  particular  point,  the  only 
phenomenon  at  that  point  is  prolongation  of  the  sound.  If  the  space  between 
the  two  trains  of  waves  is  sufficiently  great,  the  efifect  will  be  that  of  an  echo. 
If  there  are  a  number  of  such  trains  of  waves  thus  widely  spaced,  the  effect  will 
be  that  of  multiple  echoes.  On  the  other  hand,  if  two  trains  of  waves  have 
traveled  so  nearly  equal  paths  that  they  overlap,  they  will,  dependent  on  the 
difference  in  length  of  the  paths  which  they  have  traveled,  either  reinforce  or 
mutually  destroy  each  other.  Just  as  two  equal  trains  of  water-waves  crossing 
each  other  may  entirely  neutralize  each  other  if  the  crest  of  one  and  the  trough 
of  the  other  arrive  together,  so  two  sounds,  coming  from  the  same  source,  in 
crossing  each  other  may  produce  silence.  This  phenomenon  is  called  interfer- 
ence, and  is  a  common  phenomenon  in  all  types  of  wave-motion.  Of  course, 
this  phenomenon  has  its  complement.  If  the  two  trains  of  water-waves  so  cross 
that  the  crest  of  one  coincides  with  the  crest  of  the  other  and  trough  with  trough, 
the  effects  will  be  added  together.  If  the  two  sound-waves  are  similarly  retarded, 
the  one  on  the  other,  their  effects  will  also  be  added.  If  the  two  trains  of  waves 
are  equal  in  intensity,  the  combined  intensity  will  be  quadruple  that  of  either  of 
the  trains  separately,  as  above  explained,  or  zero,  depending  on  their  relative 
retardation.  The  effect  of  this  phenomenon  is  to  produce  regions  in  an  audito- 
rium of  LOUDNESS  and  regions  of  comparative  or  even  complete  silence.  It  is 
a  partial  explanation  of  the  so-called  deaf  regions  in  an  auditorium. 

Distribution  of  Intensity  of  Sound.  It  is  not  difficult  to  observe  this 
phenomenon  directly.  It  is  difficult,  however,  to  measure  and  record  the  phe- 
nomenon in  such  a  manner  as  to  permit  of  an  accurate  chart  of  the  result.  With- 
out going  into  the  details  of  the  method  employed,  the  result  of  these  measure- 
ments for  a  room  very  similar  to  the  Congregational  Church  in  Naugatuck, 
Conn.,  is  shown  in  the  accompanying  chart.  The  room  experimented  in  was 
a  simple,  rectangular  room  with  plain  side  walls  and  ends  and  with  a  barrel 
or  cylindrical  ceiling  with  the  center  of  curvature  at  the  floor-level.  The  result 
is  clearly  represented  in  Fig.  8,  in  which. the  intensity  of  the  sound  has  been 
indicated  by  contour-lines  in  the  manner  employed  in  the  drawing  of  the  geo- 
detic survey-maps.  The  phenomenon  indicated  in  these  diagrams  was  not 
ephemeral,  but  was  constant  so  long  as  the  source  of  sound  continued,  and  re- 
peated itself  with  almost  perfect  accuracy  day  after  day.  Nor  was  the  phenom- 
enon one  which  could  be  observed  merely  instrumentally.  To  an  observer 
moving  about  in  the  room  it  was  quite  as  striking  a  phenomenon  as  the  dia- 
gram suggests.  At  the  points  in  the  room  indicated  as  high  maxima  of  inten- 
sity in  the  diagram  the  sound  was  so  loud  as  to  be  disagreeable,  at  other  points 
so  low  as  to  be  scarcely  audible.  It  should  be  added  that  this  distribution  of 
intensity  is  with  the  source  of  sound  at  the  center  of  the  room  at  tha  head-level. 
Had  the  source  of  sound  been  at  one  end  and  on  the  axis  of  the  cylindrical  ceiling, 
the  distribution  of  intensity  would  still  have  been  bilaterally  symmetrical,  but 
not  symmetrical  about  the  transverse  axis. 

Interference-Systems  and  Reverberation.  When  a  source  of  sound  is  main- 
tained constant  for  a  sufficiently  long  time,  a  few  seconds  will  ordinarily  sufficej 
the  sound  becomes  steady  at  every  point  in  the  room.    The  distribution  of  the- 


Architectural  Acoustics 


1495 


intensity  of  sound  under  these  conditions  is  called  the  interference-system, 
for  that  particular  note,  of  the  room  or  space  in  question.  If  the  source  of  sound 
is  suddenly  stopped,  it  requires  some  time  for  the  sound  in  the  room  to  be  ab- 
sorbed. This  prolongation  of  sound  after  the  source  has  ceased  is  called  rever- 
beration. If  the  source  of  sound,  instead  of  being  maintained,  is  short  and 
sharp,  it  travels  as  a  discrete  wave  or  group  of  waves  about  the  room,  reflected 


Distribution  of  Intensity  of  Sound 


from  wall  to  wall,  producing  echoes.  In  the  Greek  theater  there  was  ordinarily 
but  one  echo,  "doubling  the  case-ending, "  while  in  the  modern  auditorium  there 
are  many,  generally  arriving  at  a  less  interval  of  time  after  the  direct  sound,  and 
therefore  less  distinguishable,  but  stronger  and  therefore  more  disturbing. 

Photographing  Air-Disturbances.    The  formation  and  the  propagation  of 
ECHOES  may  be  admirably  stuiiied  by  an  ailaptation  of  the  so-called  schlieren- 


1493  Architectural  Acoustics  Part  3 


Fig.  9.    Photograph  of  Sound-wave.    Vertical  Section 


Fig.  10.    Photograph  of  Sound-wave,    Vertical  Section 


Architectural  Acoustics  1497 


Fig.  11.    Photograph  of  Sound-wave  and  Echoes.    Vertical  Section 


Fig.  12.    Photograph  of  Sound-wave  and  Echoes.    Vertical  Section 


1498 


Architectural  Acoustics 


Part  3 


METHODE  device  for  photographing  air-disturbances.  It  is  suflScient  here  to  say 
that  the  adaptation  of  this  method  to  the  problem  in  hand  consists  in  the  con- 
struction of  a  MODEL  in  proper  scale,  of  the  auditorium  to  be  studied  and  an  inves- 


Fig.  13.    Photograph  of  Sound-wave  and  Echoes.    Horizontal  Section 

'ligation  of  the  propagation  through  it  of  a  proportionally  scaled  sound-wave.  To 
examine  the  formation  of  echoes  in  a  vertical  section,  the  sides  of  a  model  are 
taken  oflf  and,  as  the  sound  is  passing  through  it,  it  is  illuminated  instantaneously 


Fig.  14.    Photograph  of  Sound-wave  and  Echoes.    Horizontal  Section 

by  the  light  from  a  very  fine  and  somewhat  distant  electric  spark.  In  the  accom- 
panying illustrations,  reduced  from  the  photographs,  the  silhouettes  show  parts  of 
the  shadows  cast  by  the  model,  and  all  within  are  direct  nhotographs  of  the  actual 


Architectural  Acoustics  ,  1499 

sound-wave  and  its  echoes.  Figs.  9  to  12  show  the  sound  and  its  echoes  at 
different  stages  in  their  propagation  through  the  room,  the  particular  part  of 
the  auditorium  under  investigation  being  the  New  Theater  in  New  York  City.    It 


Fig.  15.    Photograph  of  Sound-wave  and  Echoes.    Horizontal  Section 

is  not  difificult  to  identify  the  master-wave  and  the  various  echoes  which  it 
generates,  nor,  knowing  the  velocity  of  sound,  to  compute  the  interval  at  which 
the  echo  is  heard.    To  show  the  generation  of  echoes  and  their  propagation  in 


Fig.  18.    Photograph  of  Sound-wave  and  Echoes.    Horizontal  Section 

a  horizontal  plane,  the  ceiling  and  floor  of  the  model  are  removed  and  the  photo- 
graph taken  in  a  vertical  direction.  The  photographs  shown  in  Figs.  13  to  16 
show  the  echoes  produced  in  the  horizontal  plane  passing  through  the  marble 
parapet  in  front  of  the  box. 


1500  Specific  Gravity  Part  3 

Solution  of  Problems  Possible  in  Advance  of  Construction.  While 
these  several  factors,  reverberation,  interference  and  echo,  in  an  audi- 
torium at  all  comphcated  are  themselves  complicated,  nevertheless  they  are 
capable  of  an  exact  solution,  or,  at  least,  of  a  solution  as  accurate  as  are  the 
architect's  plans  in  actual  construction;  and  it  is  entirely  possible  to  calculate 
in  advance  of  construction  whether  or  not  an  auditorium  will  be  good,  and,  if 
not,  to  determine  the  factors  contributing  to  its  poor  acoustics  and  a  method  for 
its  correction. 

SPECIFIC    GRAVITY 

The  Specific  Gravity  of  a  substance  is  the  number  which  expresses  the  ratio 
that  the  weight  of  a  given  volume  of  the  substance  bears  to  the  weight  of  the 
same  volume  of  distilled  water  at  a  temperature  of  62°  F.;  or,  the  specific  gravity 
of  a  body  is  equal  to  its  weight  divided  by  the  weight  of  an  equal  volume  of  water. 
The  specific  gravity  of  a  substance,  multiplied  by  the  weight  of  a  cubic  foot  of 
water,  will  give  the  weight  of  a  cubic  foot  of  the  given  substance.  The  weight 
of  a  cubic  foot  of  water,  at  62°  F.  and  at  the  sea-level,  is  about  62.355  lb.*  The 
specific  gravity  of  a  solid  substance  may  be  determined  by  first  weighing  a  por- 
tion of  it  in  air  and  then  in  water  and  dividing  the  weight  in  air  by  the  loss  of  the 
weight  in  water;   the  quotient  is  the  specific  gravity  required. 

Example.  A  piece  of  granite  weighs  5.32  lb  in  air;  when  immersed  in  water 
it  weighs  3.32  lb. 

Solution.  Weight  in  air  (5.32  lb)  divided  by  loss  of  weight  in  water  (2  lb)  =* 
2.66,  the  specific  gravity. 

2.66  X  62.355  lb  =  165.84  lb  =  weight  per  cubic  foot 

Note,    i  cu  ft  =  7.48  gal. 

*  The  textbooks  differ  slightly  in  regard  to  this  value. 


Specific  Gravity 


1501 


Specific  Gravities  and  Weights  per  Cubic  Foot  of  Various  Substances* 


The  basis  for  specific  gravities  is  pure  water  at  62°  F., 

barometer  30  in.     Weight  of  i  cu  ft  of  water, 

62.355  lb 


Agate, 2. 5  to  2 . 8 

Air,  atmospheric  at  60°  F.,  under  pressure  of  one  atmos- 
phere, or  14.7  lb  per  sq  in,  weight  His  the  weight  of  water 

Alabaster,  carbonate 2 .61  to  2 .  76 

Alcohol,  absolute,  at  32°  F 

Alcohol,  50  per  cent 

Alcohol,  95  per  cent 

Alcohol,  commercial 

Alder,  dry  j 0.42  to  i.oi 

Alum 


Aluminum,  hammered 

Aluminum,  drawn 

Aluminum,  sheet 

Aluminum,  pure 

Aluminum,  cast 

Amalgam 13.7  to  14.  i 

Amber 

Ambergris 

Ammonia,  60°  F 

Antimony,  cast 

Antimony,  native 

Apple-wood,  dry  f 0.66  to  i . 25 

Arsenic 5-7   to  5  •  8 

Asbestos 2.1    to  3  •  o 

Asbestos  sheathing-paper 

Ash,  American  white,  dry  t 

Ashes  of  soft  coal,  solidly  packed 

Asphalt,  for  street-paving 

Asphaltum i.ii  to  1.23 

Ballast,  brick,  gravel 

Bamboo,  dry  f 

Barium 

Bary  tes 

Basalt  or  trap-rock,  average 

Jersey  City,  N.  J 

Duluth,  Minn 

Staten  Island,  N.  Y 

Beech,  dryf 06. 5  to  1. 12 

Beeswax 

Benzine 

Beer. 


Birch,  dry  t 0-52  to  1.08 

Bismuth,  cast 9-76  to  9.90 

Blood,  at  32°  F 

Bone 1.8    to  2 .  o 

Borax 17    to  1.8 

Boxwood,  French,  dry  t 


Average 

specific 

gravity. 

Water  =  i 


2.6 


0.794 
0-934 
0.815 
0.833 
0.55 
1.72 
2.75 
2.68 
2.67 
2.67 
2.56 
13.92 
1.08 
0.87 
0.894 
6.70 
6.67 
0.75 
5.73 
2.81 
1.20 
0.61 
0.70 
1.60 
1.15 
1.79 
0.36 
3.88 
4.45 
2.96 
3-00 
2.9s 
2.86 
0.74 
0.95 
0.69 
1.04 
0.65 
9.82 
1.06 
1.90 
1.75 
1-33 


*  The  values  given  in  this  table  for  specific  gravities  and  for  weights  per  cubic  foot  are 
AVERAGE  values.  In  the  computations  and  compilations  of  these  tables  the  Editor 
is  greatly  indebted  to  Mr.  T,  Z.  Talley  for  valuable  assistance. 

t  The  word  "dry"  in  this  connection  indicates  that  the  wood  contains  not  more  tkan 
15%  of  moisture,  Green  timbers  usually  weigh  from  one-fifth  to  nearly  one-half  more 
than  dry;  ordinary  building-timbers,  tolerably  seasoned,  one-sixth  more. 


1502 


Specific  Gravity 


Part 


Specific  Gravities  and  Weights  per  Cubic  Foot  of  Various  Substance^  * 
(Continued) 


The  basis  for  specific  gravities  is  pure  ift^ater  at  62°  F., 

barometer  30  in.     Weight  of  i  cu  ft  of  water, 

62.355  ib 


Boxwood,  Dutch,  dry  f 

Boxwood,  Brazilian,  dry  f 

Brass  (copper  and  zinc),  cast 7.8  to  9. 

Brass,  rolled 

Brass,  sheet 

Brass,  wire 

Bricks,  building 

Bricks,  common . 

Bricks,  light,  inferior . 

Bricks,  lime-sand 

Bricks,  Magnesia • 

Bricks,  pressed 

Bricks,  pressed,  hard 

Bricks,  soft 

Bricks,  fire 

Bricks,  paving * 

Brickwork,  pressed  brick,  fine  joints 

Brickwork,  medium  quality 

Brickwork,  coarse,  inferior,  soft 

Brickwork,  at  125  lb  per  cu  ft,  i  cu  yd  equals  1.507  tons 

and  17.92  cu  ft  equal  i  ton 

Bromine 

Bronze,  coin 

Bronze,  gun-metal 

Bronze,  ordinary , 

Bronze,  aluminum 

Butter 

Butternut-tree,  dry  t 

Cadmium 8 . 6  to  8 . 7 

Calcite 2 . 6  to  2 . 8 

Calcium 

Camphor,  dry 

Caoutchouc  (India  Rubber) 

Carbon  disulphide 

Castor-oil 

Cedar,  red  and  white,  dry  t 

Cement,  Natural  (Rosendale) ,  loose 

Cement,  Portland ,  loose 

Cement,  Natural,  solid 

Cement,  Portland,  solid 

Chalk 

Champagne 

Charcoal  of  pines  and  oaks , 

Cherry,  dry  t 

Chestnut,  dry  f 

Chromium 

Cider 


Average 

specific 

gravity. 

Water  =  i 


I  035 

8.45 
8.56 
8.24 
8.69 

1.922 
1.442 
2.163 
2.643 
2.163 
2.403 
1.602 

2.403 

2.24 
2.00 
1.60 


319 
8.66 
8.60 
8.40 
7.70 
0.86 
0.38 
8.65 
2.70 
1.58 
0.99 
0.93 
1.29 
0.96 
0.45 
1.04 
1-35 
2.9s 
315 
2.35 
0.99 


0.66 
0.63 
500 
1.02 


*  The  values  given  in  this  table  for  specific  gravities  and  for  weights  per  cubic  foot  are 
AVERAGE  values. 

t  The  word  "  dry  "  in  this  connection  indicates  that  the  wood  contains  not  more  than 
15%  of  moisture.  Green  timbers  usually  weigh  from  one-fifth  to  nearly  one-half  more 
than  dry;  ordinary  building-timbers,  tolerably  seasoned,  one-sbcth  more. 


Specific  Gravity 


1503 


Specific  Gravities  and  Weights  per  Cubic  Foot  of  Various  Substances  ♦ 
(Continued) 


The  basis  for  specific  gravities  is  pure  water  at  62°  P., 

barometer  30  in.     Weight  of  i  cu  ft  of  water, 

62.355  lb 


Cinnabar 

Clay,  potters',  dry 1.8  to  2.1 

Clay,  dry,  in  lump,  loose 

Coal,  anthracite,  1.3  to  1.84;  of  Penn.,  1.3  to  1.7 

Coal,  anthracite,  broken,  of  any  size,  loose,  average 

Coal,  anthracite,  broken,  moderately  shaken 

Coal,  anthracite,  broken,  heaped  bushel,  loose,  77  to  83  lb 

Coal,  anthracite,  broken,  a  ton  loose  occupies  40  to  43 

cu  ft 


Average 

specific 

gravity. 

Water  =  i 


Coal,  bituminous,  solid,  i .  2  to  i .  5 

Coal,  bituminous,  solid,  Cambria  Co.,  Pa.,  1.27  to  1.34. 

Coal,  bituminous,  broken,  of  any  size,  loose 

Coal,  bituminous,  moderately  shaken 

Coal,  bitumirious,  a  heaped  bushel,  loose,  70  to  78 

Coal,  bituminous,  i  ton  occupies  43  to  48  cu  ft 

Coke,  loose,  good  quality 

Coke,  loose,  a  heaped  bushel,  35  to  42  lb 

Coke,  loose,  i  ton  occupies  80  to  97  cu  ft 

Concrete,  stone 130  to  150 

Concrete,  cinder 100  to  no 

Copper,  hammered 8.8  to  9.0 

Copper,  rolled 8 . 9  to  9 .  o 

Copper,  drawn  wire 8.8  to  9.0 

Copper,  sheet 

Copper,  cast , 8. 6  to  8.9 

Copper,  melted 

Cork,  dry 

Corundum,  pure 3.92  to  4.01 

Creosote  oil i .  04  to  i .  10 

Cypress,  American,  dry  f 

Dogwood,  dry  f 

Douglas  fir,  dry  f 

Earth,  common  loam,  perfectly  dry,  loose 

Earth,  common  loam,  perfectly  dry,  shaken 

Earth,  common  loam,  perfectly  dry,  rammed 

Earth,  common  loam,  slightly  moist,  loose 

Earth,  common  loam,  more  moist,  loose 

Earth,  common  loam,  more  moist,  shaken 

Earth,  common  loam,  more  moist,  packed 

Earth,  common  loam,  as  soft,  flowing  mud 

Earth,  common  loam,  as  soft,  flowing  mud,  well-pressed 
Ebony 


Elder-pith . . 
Elm,  dryf. 
Elm,  rock. . 
Emerald . . . 


8.12 
1.90 
1. 01 
I. SO 


2.33 
1.68 
8.9s 
8.9s 
8.89 
8.72 
8.82 
8.23 
0.24 
3.96 
1.07 
0.55 
-0.7s 
o.Si 


1.22 

1.09 

0.076 

0.56 

0.80 

2.70 


*  The  values  given  in  this  table  for  specific  gravities  and  for  weights  per  cubic  foot  are 
AVERAGE  values. 

t  The  word  "dry"  in  this  connection  indicates  that  the  wood  contains  not  more  than 
15%  of  moisture.  Green  timbers  usually  weigh  from  one-fifth  to  nearly  one-half  more 
than  dry;  ordinary  building-timbers,  tolerably  seasoned,  one-sixth  more. 


1504 


Specific  Gravity 


Specific  Gravities  and  Weights  per  Cubic  Foot  of  Various  Substances  *1 
(Continued) 


The  basis  for  specific  gravities  is  pure  water  at  62°  F., 

barometer  30  in.     Weight  of  i  cu  ft  of  water, 

62.355  lb 

Emery 

Fats 

Feldspar 

Filbert-tree,  dry  f 

Fir,  Douglas  (see  Douglas  Fir) . 

Flint... 

Gamboge 

Garnet 3-4  to  4-3 

Glass,  optical 

Glass,  flint 

Glass,  white '. '. 

Glass,  plate 

Glass,  green 

Glass,  floor,  heavy 

Glass,  window 

Gneiss  (see  Granites). 

Gold,  pure 

Gold,  hammered,  nati>:e 

Gold,  cast 

Granites  and  gneiss,  Connecticut,  Greenwich 

California,  Penryn  (hornblende) 

Nev/  York 

Maryland,  Port  Deposit 

Massachusetts,  Quincy  (hornblende) 

Wisconsin,  Athelstane 

Georgia,  Lithornia  and  Stone  Mountain 

Minnesota 

California,  Rocklin  (muscovite) 

Rhode  Island,  Westerley 

Connecticut,  New  London 

New  Hampshire,  Keene 

Maine,  Hallowell 

New  Hampshire,  Concord 

Vermont,  Barre 

Wisconsin,  Montello 

Colorado,  Georgetown  (biotite) 

Maine,  Fox  Island 

Massachusetts,  Rockport 

Graphite 

Gravel,  dry -. 

Gravel,  wet 

Greenstone,  trap 2.8  to  3.2 

Grindstone 

Gum  arabic 

Gun-metal  (see  Bronze). 

Gunpowder  (granular) , 

Gutta-percha 


Average 

Average 

specific 

weight  of 

gravity. 

icuft 

Water  =  i 

lb 

4.00 

249. 5 

0.93 

58.0 

2.57 

160.2 

0.60 

37-5 

2.63 

164.0 

1.20 

74.8 

3.85 

240.1 

3.45 

215.0 

3.00 

187.0 

2.89 

180.2 

2.80 

174-6 

2.67 

166.5 

2.53 

158.0 

2.50 

156.0 

19.50 

I  215.9 

19.40 

I  209.7 

19.258 

I  200.8 

2.84 

177.3 

2.77 

172.9 

2.74 

171. 0 

2.72 

169.6 

2.70 

168.5 

2.70 

168.5^ 

2.69 

167. 9fl 

2.68 

167.3'" 

2.68 

167.3 

2.67 

166.7 

2.66 

166.0 

2.66 

166.0 

2.6s 

165.2,^ 

2.65 

165.^ 

2.65 

165. 2:S 

2.64 

164.6 

2.63 

164.0 

2.63 

164.0 

2.61 

162.7 

2.26 

140.0 

1.79 

112. 0 

2.00 

125.0 

3.00 

187.0 

2.14 

133.  s 

1.32 

82.5 

I. GO 

62.4 

0.98 

61.0 

*  The  values  given  in  this  table  for  specific  gravities  and  for  weights  per  cubic  foot  are 
AVERAGE  values. 

t  The  word  "  dry  "  in  this  connection  indicates  that  the  wood  contains  not  more  than 
15%  of  moisture.     Green  timbers  usually  weigh  from  one-fifth  to  nearly  one-half  morf  , 
than  4ry;  ordinary  building-timbers,  tolerably  seasoned,  one-sixth  more,  jfll 


specific  Gravity 


1505 


Specific  Gravities  and  Weights  per  Cubic  Foot  of  Various  Substances  * 
(Continued) 


The  basis  for  specific  gravities  is  pure  water  at  62°  F., 
barometer  30  in.     Weight  of  i  cu  ft  of  water 
62.355  lb 


Average 

specific 

gravity. 

Water  =  i 


Average 

weight  of 

I  cu  ft 

lb 


Gypsum,  natural  rock,  free  from  surface-water 

Gypsum,  crushed  rock,  not  calcined,  all  passing  i-in 

ring 

Gypsum,  ground  rock,  90%  passing  100  mesh,  dried, 

not  calcined 

Gypsum,  Plaster-of-Paris,  stucco,  stiff  mortar,  set  and 

dried  out 

Gypsum,  Plaster-of -Paris,   stucco,    ground  rock,  90% 

passing  100  mesh,  calcined,  loose 

well  shaken  down  or  in  bins ♦.  . .  . 

Hackmatack  (see  Larch). 

Hay,  loose,  in  stacks,  about  512  cu  ft  per  ton 

Hemlock,  dry  t 

Hickory,  pignut,  dry  f .  .  .  . '. 

Hickory,  mocker-nut,  dry  f •  •  •• 

Hickory,  shagbark,  dry  t 

Hickory,  nutmeg,  dry  f 

Hickory,  pecan,  dry  f 

Hickory,  bitternut,  dry  f 

Hickory   water,  dry  f 

Holly 

Honey 

Horn 

Hornblende 3.0  to  3.5 

Ice 88  to  .914- 

Iodine 

Iridium,  pure 

Iron,  cast 6.9  to  74 

Iron,  gray,  foundry,  cold 

Iron,  gray,  foundry,  molten 

Iron,  wrought 

Ivory 

Juniper-wood 

Kaolin 

Lava ■ 

Larch,  or  hackmatack,  dry  +  • 

Lard 

Lead,  commercial,  cast 

Lead,  commercial,  sheet 

Lead,  pure 

Lead,  molten 

Lignum-vitjr,  dry  f .  .  . o. 65  to  i . 33 

Limestone,  Illinois 

Indiana 

Kentucky 

Michigan 

Minnesota 

Missouri 

New  York 

Average  of  limestones 

Linseed-oil 


2.30 

1-52 
1-25 

1.22 

0.96 
1 .11 


0.42 
0.89 
0.85 
0.81 
0.78 
0.78 
0.77 
0.73 
0.76 

1  •45 
1.69 
3-25 
0.89 
4-94 

22 .  12 
7.2 
7.  21 
6.94 
7.70 
1.88 
0.57 
2.  20 

2  .65 
0.5s 
o .  9 1 

II  .36 

II  .40 

II  .42 

10.40 

0.99 

2.57 

2.50 

2.68s 

2.44 

2.655 

2.32 

2.71 

2.60 

0.935 


143 -o 

950 
78.0 

77.0* 

60.0 
70.0 


26.2 
SS.6 
53.1 
50.6 


45 -o 

47-4 

90.5 

105.5 

202.7 

56.0 

308.0 

I  3790 

448.9 

450.0 

433 -o 

480.0 

117. 0 

35.6 

137-2 

165.2 

34-3 
58.7 
708.0 
710.8 
713.0 
648.8 
41  to  84 
160.4 
155-8 
167.4 
152  .1 
165-6 
144-8 
169.0 

162 . 1 
58.3 


*  The  values  given  in  this  table  for  specific  gravities  and  for  weights  per  cubic  foot  are 
VERAGE  values. 

fThe  word  "dry"  in  this  connection  indicates  that  the  wood  contains  not  more  than 
.5%  of  moisture.  Green  timbers  usually  weigh  from  one-fifth  to  nearly  one-half  mo'"' 
han  dry;   ordinary  builditig-timbers,  tolerably  seasoned,  one-sixth  more. 


1506 


Specific  Gravity 


Specific  Gravities  and  Weights  per  Cubic  Foot  o|  Various  Substances  * 
(Continued) 


The  basis  for  specific  gravities  is  pure  water  at  62°  F., 

barometer  30  in.    Weight  of  i  cu  ft  of  water, 

62.355  lb 


Locust,  dry  f .  • , 

Magnesite , 

Magnesium,  pure 

Mahogany 0.56  to  1.06 

Manganese,  pure 

Manganese,  ore,  red 

Manganese,  ore,  black 

Marble,  average 2.6  to  164.4 

domestic. 

New  York 

California 

Georgia 

Vermont,  Dorset 

foreign, 

Parian 

African 

Carrara 

Biscayan 

British 

French 

Marl 


Masonry,  brickwork  (see  Brickwork) 

Masonry,  concrete,  stone 

Masonry,  concrete,  cinder 

Masonry,  granite,  dressed 

Masonry,  granite,  rubble  in  cement 

Masonry,  Hmestone,  dressed 

Masonry,  marble,  dressed  for  buildings. 

Masonry,  sandstone 

Mastic,  gum  resin 

Mercury,  at  32°  F 

Mica , 

Milk,  at  32°  F 

Molybdenum,  pure 

Mortar,  lime 

Mortar,  cement 

Mud,  dry,  close 

Mud,  wet,  moderately  pressed 

Mud,  wet,  fluid 

Mulberry-tree,  dry  f 

Naptha-oil,  wood,  at  32°  F 

Nickel 


.2.75  to  3.1 


Oak,  live,  dry  f 0.88  to  1.02 

Oak,  white,  dryf 0.66  to  0.88 

Oak,  red  and  black,  dry  f 

Ochre 

Olive-oil,  32°  F 


Average 

specific 

gravity. 

Water  =  i 


0.71 

3.0 

1.72 

o.8i 

8.00 

4.01 

3.45 

2.6 

2.83 
2.75 
2.73 
2.66 

2.84 
2.80 
2.72 
2.71 
2.71 
2.6s 
2.10 

2.33 
1.68 
2.64 
2.48 
2.60 
2.72" 
2.41 
0.8s 
13.62 
2.93 
1.032 
8.63 
1.65 
1.68 


0.75 
0.85 
8.56 
0.95 
0.77 

350 
0.916 


*  The  values  given  in  this  table  for  specific  gravities  and  for  weights  per  cubic  foot  are 
AVERAGE  values. 

t  The  word  "  dry  "  in  this  connection  indicates  that  the  wood  contains  not  more  than 
15%  of  moisture.  Green  timbers  usually  weigh  from  one-fifth  to  nearly  one-half  more 
than  dry;  ordinary  building-timbers,  tolerably  seasoned,  one-sixth  more. 


Specific  Gravity 


1507 


Specific  Gravities  and  Weights  per  Cubic  Foot  of  Various  Substances  "*= 
(Continued) 


The  basis  for  specific  gravities  is  pure  water  at  62°  F., 

barometer  30  in.     Weight  of  i  cu  ft  of  water, 

62.355  lb 


Oolitic  stofies . , 
Opal. 


Opium 

Orange-tree . 
Palladium . . . 
Paper . 


ParafHn 

Pear-tree  wood,  dry  f 

Peat,  pressed 

Petroleum,  oil 

Pine,  Cuban,  dry  t 

Pine,  yellow,  long-leaf,  dry. . . 

Pine,  loblolly,  dry 

Pine,  yellow,  short-leaf,  dry. 

Pine,  red,  Norway,  dry 

Pine,  spruce,  dry 

Pine,  white,  dry 

Pitch 


Plaster  of  Paris  (see  Gypsum)  . 

Platinum 

Plumbago 

Poplar,  dry  f 

Porcelain,  china 

Porphyry 

Potash 

Potassium 

Pumice-stone 

Quartz 

Quince-tree  wood,  dry  f 

Red  lead 

Resin 


Rock-crystal . 

Rosewood 

Rosin 


Rubber,  India , 

Ruby 

Salt,  coarse,  per  struck  bushel,  Syracuse,  N.  Y.,  56  lb. . 

Saltpetre 

Sand,  of  pure  quartz,  perfectly  dry  and  loose 

Sand,  of  pure  quartz,  voids  full  of  water 

Sand,  of  pure  quartz,  very  large  and  small  grains,  dry. . , 
Sandstone,  average 

Massachusetts,  Longmeadow 

Connecticut,  Portland 

New  York 2.40  to  2.70 

New  Jersey,  Belleville 

Pennsylvania 

Virginia,  BrivStow 


Average 

specific 

gravity. 

Water  =  i 


a. 25 

2. IS 
1-34 

0.71 
11,80 
0.9s 
0.88 
0.67 
0.72 
0.878 
0.63 
0.61 
0.53 
o.Sl 
0.50 
0.44 
0.38 
1.08 
2.25 

21.50 

2.10 
0.47 
2.30 
2.76 
2.26 

0.86s 

0.92 

2.65 

0.71 

8.94 

1.09 

2.60 

0.73 

1. 10 

0.93 

390 

2.02 


2.44 
2.49 
2.50 
2.60 
2.40 
2.63 
2.60 


'  The  values  given  in  this  table  for  specific  gravities  and  for  weights  per  cubic  foot  are 
AVERAGE  values. 

t  The  word  "  dry  "  in  this  connection  indicates  that  the  wood  contains  not  more  than 
15%  of  moisture.  Green  timbers  usually  weigh  from  one-fifth  to  nearly  one-half  more 
than  dry;  ordinary  building-timbers,  tolerably  seasoned,  one-sixth  more. 


1508 


Specific  Gravity 


Part 


Specific  Gravities  and  Weights  per  Cubic  Foot  of  Various  Substances* 
(Continued) 


The  basis  for  specific  gravities  is  pure  water  at  62"  F., 

barometer  30  in.     Weight  of  i  cu  ft  of  water, 

62.355  lb 


Sandstone,  (continued) 

Ohio 

Michigan 

Wisconsin 

Minnesota 

.Colorado 

California,  Angel  Island. 

Shales,  red  or  black 

Silica 


Silver 

Slate 

Snow,  freshly  fallen 

Snow,  moistened,  compacted  by  rain. 

Soapstone 

Sodium 

Spelter 

Spirit,  rectified • 

Spruce 

Steel,  cast 

Steel,  wrought 

Sugar. 


Sycamore,  dry. 

Talc 

Tallow 

Tamarack 

Tar 


Teak 

Tellurium 

Tiles,  solid 

Tin,  rolled 

Tin,  cast 

Tin,  molten 

Trap  (see  Basalt). 

Tungsten 

Turpentine 

Type-metal,  cast. . 

Uranium 

Urine 


Vinegar 

Walnut,  black,  dry 

Water,  pure  rain,  distilled,  at  32°  F.,  barometer  30  in 

Water,  pure  rain,  distilled,  at  62°  F.,  barometer  30  in 

Water,  pure  rain,  distilled,  at  212°  F.,  barometer  30  in 

Water,  sea.  .• i  .026  to  i  .030 

Wax  (see  Beeswax). 

Willow 

Wine 

Zinc  or  spelter 6.8  to  7.2 


Average 

specific 

gravity. 

Water  =  i 


2.22 
2.35 
2.22 

2.25 
2.33 
2.73 
2.60 

2.66 
10.50 
2.81 


2.73 

0.978 

7.10 

0.824 

0.40 

7.9 

7.85 

1.60 

0.58 

2.81 

0.94 

0.38 

1. 00 

0.70 

6.27 

2.20 

7.40 

7.30 

7.02 

19.129 
0.87 
10.45 
18.49 
1.02 
1.08 
0.60 

1. 00 
1.028 

0.49 

1. 01 

7.00 


*  The  values  given  in  this  table  for  specific  gravities  and  for  weights  per.  cubic  foot  are 

AVERAGE  values. 

t  The  word  "  dry  '*  in  this  connection  indicates  that  the  wood  contains  not  more  than 
15%  ^f  moisture.  Green  timbers  usually  weigh  from  one-fifth  to  nearly  one-half  more 
than  dry;  ordinary  building-timbers,  tolerably  seasoned,  one-sixth  more. 


Wire-Gauges  and  Metal-Data  1509 


WIRE-GAUGES*  AND  METAL-DATA 

A  Wire-Gauge  is  a  method^of  designating  the  diameter  of  wires  or  the  thick- 
ness of  sheets  of  metal  by  the  numbers  of  a  table  arranged  on  a  certain  fixed  basis. 
There  are  at  the  present  time  several  gauges,  resulting  in  great  confusion, 
Table  XIII,  page  402,  gives  the  diameters  of  the  gauges  in  common  use.  The 
only  legal  gauge  in  this  country  is  the  United  States  standard  gauge,  described 
on  page  1600.  It  is  used  by  most  of  the  manufacturers  of  sheet  iron  and  steel 
and  tin  plate.  The  Brown  &  Sharpe  gauge  is  commonly  used  for  designating 
size  of  copper  wires  (see  page  15 10);  also  for  sheet  copper  and  brass.  Nearly 
all  copper  wire,  bare  and  insulated,  is  ordered,  manufactured,  and  carried  in 
stock  in  accordance  with  this  gauge.  This  might  be  called  the  Copper  Wire 
Gauge.  The  American  Steel  &  Wire  Company  uses  the  old  Washburn  & 
Moen  and  Roebhng  gauges  for  ail  their  steel  and  iron  wire  and  also  for  wire  nails. 
The  sectional  areas  for  these  gauges  are  given  on  pages  403  and  15 12,  taken  from 
the  Roebhng  and  American  Steel  &  Wire  Company's  lists.  When  placing  orders 
for  sheets  and  wire,  it  is  always  best  to  specify  the  weight  per  square  or  linear 
foot  or  the  thickness  or  diameter  in  thousandths  of  an  inch  or  in  circular  mils. 
The  gauge  for  steel  wire,  used  by  the  J.  A.  Roebhng's  Sons  Company,  is  given 
on  page  403,  and  the  circular-m.il  gauge  on  page  i473-  The  gauge  used  bj^  this 
company  is  the  same  as  the  Washburn  &  Moen  gauge,  or  the  American  Steel 
&  Wire  gauge,  except  that  the  diameters  in. most  cases  are  given  to  the  nearest 
mil.  This  gauge  is  so  generally  used  for  steel  wire  that  it  is  sometimes  called 
the  Steel  Wire  Gauge  or  the  Market  Wire  Gauge.  The  Birmingham  Wire  gauge 
is  the  same  as  Stubs'  Iron-Wire  gauge,  but  entirely  different  from  Stubs'  Steel- 
Wire  gauge.  Galvanized  telegraph  and  telephone-v/ire,  both  bare  and  insu- 
lated, and  galvanized  armor-wire  are  usually  designated  by  this  gauge.  Its 
use  is  not  very  extensive  and  is  becoming  less.  The  new  British  Standard  gauge 
is  the  legal  standard  for  Great  Britain  and  is  used  there  for  all  kinds  of  wire. 
Its  use  in  this  country  is  very  limited.  It  is  known,  also,  as  the  English  Legal 
standard  gauge  and  the  Imperial  Wire  gauge. 

*  See,  also,  pages  401,  402,  403,  1469,  1473,  1510,  1512,  and  i6o«. 


1510 


Wire-Gauges  and  Metal-Data 


Weights  in  Pounds  per  Square  Foot  of  Sheets  of  Wrought  Iron,  Steel,  Copper, 
*         and  Brass 

Thickness  by  American  (Brown  &  Sharpe)  gai^ge  • 


No.  of 
gauge 

Thickness 
in  inches 

Iron 

Steel 

Copper 

Brass 

oooo 

0.46 

18.40 

18.77 

20.84 

19.69 

ooo 

0.4096 

16.39 

16.71 

18.56 

17-53 

oo 

0.3648 

14-59 

14.88 

16.53 

15.61 

o 

0.3249 

12.99 

13.25 

14.72 

13.90 

I 

0.2893 

11.57 

11.80 

13  II 

12.38 

2 

0.2576 

10.31 

10.51 

11.67 

11.03 

3 

0.2294 

918 

9.36 

10.39 

9.82 

4 

0.2043 

8.17 

8.34 

9.26 

8.74 

5 

0.1819 

7.28 

7.42 

8.24 

7.79 

6 

0,1620 

6.48 

6.61 

7.34 

6.93 

7 

0.1443 

5. 77 

5. 89 

6.54 

6.18 

8 

0.128S 

5. 14 

5.24 

5.82 

5.50 

9 

0.1144 

4.58 

4.67 

5.18 

4.90 

10 

0.1019 

4.08 

4.16 

4.62 

4.36 

II 

0.0907  . 

3.63 

3.70 

4  II 

3.88 

12 

0.0808 

3-23 

3-30 

3.66 

3.46 

13 

0.0720 

2.88 

2.94 

3.26 

3-08 

14 

0.0641 

2.56 

2.61 

2.90 

2.74 

15 

0.0571 

2.28 

2.33 

2.59 

2.44 

i6 

0.0508 

2.03 

2.07 

2.30 

2.18 

17 

0.0453 

1. 81 

1. 85 

2.05 

1-94 

18 

0.0403 

1. 61 

1.64 

1.83 

1.73 

19 

0.03S9 

1.44 

1.46 

1.63 

1.54 

20 

0.0320 

1.28 

1.30 

1. 45 

1.37 

21 

0.0285 

1. 14 

1.16 

1.29 

1.22 

22 

0.0253 

1. 01 

1.03 

I. IS 

1.08 

23 

0.0226 

0.903 

0.921 

1.02 

0.966 

24 

0.0201 

0.804 

0.820 

0.911 

0.860 

25 

0.0179 

0.716 

0.730 

0.811 

0.766 

26 

0.0159 

0.638 

0.650 

0.722 

0.682 

27 

0.0142 

0.568 

0.579 

0.643 

0.608 

28 

0.0126 

0.506 

0.516 

0.573 

0.541 

29 

0.0113 

0.450 

0.450 

0.510 

0.482 

30 

O.OIOO 

0.401 

0.403 

0.454 

0.429 

31 

0.0089 

0.3S7 

0.364 

0.404 

0.382 

32 

0.0080 

0.318 

0.324 

0.360 

0.340 

33 

0.0071 

0.283 

0.289 

0.321 

0.303 

34 

0.0063 

0.252 

0.257 

0.286 

0.270 

35 

0.0056 

0.224 

0.229 

0.254 

0.240 

Specific  gravity 

7.704 
480.00 

7.85 
489.60 

8.72 
543.6 

8.24 
513.6 

Weight  per  cubic  foot 

Weight  per  cubic  inch 

0.2778 

0.2833 

0.3146 

0.2972 

♦  For  other  gauges  see  pages  401,  402,  403,  1469,  1473,  1509,  1512,  and  1600, 


Weights  of  Metal  Sheets  and  Bars 


1511 


n  xr-i  sfO  NfO  sfO  Nr-i  ^  V*"  N!-<  ^90  SfH  sf<l  v^  ^00  rt\  xjl>  eS^.spO  io~s        NpO  v-*  nJO  \f  1  N?0  v*  Np6 


rOMiOTra»Q<Ot^t^a>rOQvQOOQOOOOOOOQOOC>v? 
OOOOOMMMC^roiOt^OiM  rovO  00  m  -rj-oo  '£>  ^r  ro  fO  -^VO  <?>  ro 


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I  M  fO  "*  10<0  t^CSO  Oi  iH 


■rt  Tf  rvj  (o  CO  t->  fOvO  ro« 

O   M   fO  1000   N  t—  M  10  C 
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1512  Wire-Gauges  and  Metal-Data 

Sizes  and  Weights  of  Smooth  Steel  Wire* 
As  made  by  the  Amefican  Steel  &  Wire  Company 


No. 

of 

gauge 


oooooo 

ooooo 

coco 

ooo 

CO 


5 
l6 


13 
14 
IS 
i6 
17 
i8 
19 


23 
24 


Diameters 


Fractions 
of  inch 


^%2 


%2 

"h" 


%2 


Me 


1/^2 


Decimals 
of  inch 


0.461S 

0. 4375 

0-4305 

0.40625 

03938 

0.3750 

0.3625 

0.34375 

0.3310 

0.3125 

0.306s 

0.2830 

0.2812s 

0..  2625 

0.2500 

0.2437 

0.2253 

0.21875 

0 . 2070 

0.1920 

0.1875 

0.1770 

0.1620 

0.15625 

0.1483 

0.1350 

0.125 

0.1205 

0.1055 

0.09375 

0.0915 

0.0800 

0 . 0720 

0.0625 

0.0540 

0.0475 

0.0410 

0.0348 

0.0317 

0.03125 

0.0286 

0.0258 

0.0230 


Milli- 
meters 


11.72 

II. II 

10.93 

10.32 

10.00 
9.525 
9  2075 
8.731 
8.407 
7.938 
7.785 
7.188 
7.144 
6.668 
6.350 
6.190 
5.723 
5. 556 
5.258 
4.877 
4.763 
4.496 
4. 115 
3.969 
3.767 
3.429 
3.17s 
3061 
2.680 
2.381 
2.324 
2.032 
1.829 
1.58S 
1-372 
1.207 
1. 041 
0.8839 
0.8052 
0.7938 
0.7264 
0.6553 
0.5842 


Sectional 
area, 
sq  in 


0.16728 

0.15033 

0.14556 

0.12962 

0.12180 

0.11045 

0.10321 

0.092806 

0.086049 

0.076699 

0.073782 

0.062902 

0.062126 

0.0541 19 

o . 049087 

0.046645 

0.039867 

0.037583 

0.033654 

0.028953 

0.027612 

0.024606 

0.020612 

0.019175 

0.017273 

O.OI4ST4 

0.012272 

o. 01 I 404 

0.0087417 

0.0069029 

0.0065755 

0.0050266 

0.004071S 

0.0030680 

0.0022902 

0.0017721 

0.0013203 

0.00095115 

o . 00078924 

0.00076699 

0.00064242 

0.00052279 

0.00041548 


Weight  t 


Pounds 

per 
100  feet 


56.81 

51.05 

49-43 

44.02 

41.36 

37.51 

35.05 

31-52 

29.22 

26.05 

25.06 

21.36 

21.10 

18.38 

16.67 

15-84 

13-54 

12.76 

11-43 
9-832 
9 -.377 
8.356 
7.000 
6.512 
5.866 
4.861 
4.168 
3.873 
2.969 
2.344 
2.233 
1.707 
1.383 
1.042 
0.7778 
0.6018 
0.4484 
0.3230 
0.2680 
0.2605 
0.2182 
0.1775 
0.1411 


Pounds 
per  mile 


2999-0 
2696.0 
2610.0 
2324 -0 
2184.0 
1980.0 
1851 -o 
1664.0 
1543  o 

1375-0 

1323 -0 

1128.0 
1114.0 

970.4 
880.2 
836.4 
714-8 
673-9 
603.4 
519-2 
495.1 

441 -2 
369.6 
343.8 
309.7 
256.7 
220.0 
204.5 
156.7 
123.8 
117.9 
90.13 
73.01 

55-01 
41.07 
31-77 
23.67 
17  05 
14  15 
13  75 

11-52 

9-37 

7-45 


*  For  other  gauges,  see  pages  401,  402,  403,  1469,  1473,  1509,  1510  and  1600. 
t  For  iron  wire,  the  values  in  columns  6  and  7  should  be  multiplied  by  0.98  and  for 
copper  wire,  by  1.12. 


Kinds  of  Wire 


1513 


Kinds  of  Wire  Manufactured  by  the  American  Steel  and  Wire 
Company 

Market-wire,  Nos.  oooo  to  i8. 

Annealed  stone-wire  or  weaving-wire,  Nos.  i6  to  47. 

Tinned  market- wire,  Nos.  o  to  18. 

Tinned  stone-wire,  Nos.  16  to  40. 

Gun-screw  wire,  finished  with  great  care  as  regards  roundness  and  exactness 
to  gauge,  Nos.  18  to  50. 

Machinery-wire,  Nos.  00000  to  18. 

Cast-steel  wire,  y2-m  diameter,  down  to  No.  26. 

Drill  and  needle-steel  wire,  Nos.  12  to  25. 

The  term  market-wire  applies  to  the  ordinary  and  most  used  forms  of  Bes- 
semer ANNEALED,  BRIGHT,  GALVANIZED,  TINNED  and  COPPERED  wireS. 

Galvanizied-Iron-Wire  Strand.  The  diameter,  list-price  per  100  ft,  weight 
per  100  feet  and  approximate  breaking-load  in  poimds  for  this  wire  is  given  in 
Tabic  XVI,  Chapter  XI. 


1514 


Metal-Data 


Part 


Weights  and  Areas  of  Square  and  Round  Bars  and  Circumferences  of 
Round  Steel  Bars* 

Weights  are  for  steel,  at  489.6  lb  per  cu  ft 


Thickness 

or 
diameter. 

Weight  of 

D  bar 
I  ft  long. 

Weight  of 

0  bar 
I  ft  long, 

Area  of 
n  bar, 

Area  of 
0  bar. 

Circumfer- 
ence oi 
0  bar, 

in 

lb 

lb 

sq  in 

sq  in 

in 

M« 

0.013 

O.OIO 

0 . 0039 

0 . 0031 

0.1963 

5/64 

0.021 

0.016 

0.0061 

0.0048 

0.2454 

H2 

0.030 

0.023 

0.0088 

0.0069 

0.2945 

lU. 

0.041 

0.032 

0.0120 

0.0094 

0.3436 

H 

0.053 

0.042 

0.0156 

0.0123 

■     0.3927 

9/64 

0.067 

0.053 

0.0198 

0.0155 

0.4418 

^A2 

0.083 

0.065 

0.0244 

0.0192 

0.4909 

lj'64 

O.IOO 

0.079 

0.0295 

0.0232 

0.5400 

3/6 

0.120 

0.094 

0.0352 

0.0276 

0.5890 

1^4 

0.140 

O.IIO 

0.0413 

0.0324 

0.6381 

^^2 

0.163 

0.128 

0.0479 

0.0376 

0.6872 

1%4 

0.187 

0.147 

0.0549 

0.0431 

0.7363 

h' 

0.213 

0.167 

0.0625 

0.0491 

0.7854 

1%4 

0.240 

0.188 

0.0706 

0.0554 

0.834s 

%2 

0.269 

0.2II 

0.0791 

0.0621 

0.8836 

1^4 

0.300 

0.235 

0.0881 

0.0692 

0.9327 

Me 

0.332 

0.261 

0.0977 

0.0767 

0.9817 

IH2 

0.402 

0.316 

0.1182 

0.0928 

1.0799 

H 

0.478 

0.376 

0.1406 

0.1104 

1.1781 

1^2 

0.561 

0.441 

0.1650 

0.1296 

1.2763 

TU 

0.651 

O.5II 

0.1914 

O.I5C3 

1.3744 

1^2 

0.747 

0.587 

0.2197 

0.1726 

1.4726 

1/^ 

0.850 

0.668 

0.2500 

0.1963 

1.5708 

15:^2 

0.960 

0.754 

0.2822 

0.2217 

1.6690 

He 

1.076 

0.845 

0.3164 

0.2485 

I. 7671 

1%2 

II99 

0.941 

0.3525 

0.2769 

1.8653 

^4 

1.328 

1.043 

0.3906 

0.3068 

1.9635 

ii/a 

1.607 

1.262 

0.4727 

0.3712 

2.1598 

M 

1-913 

1.502 

0.5625 

0.4418 

2.3562 

13/6 

2.245 

1.763 

0 . 6602 

0.5185 

2.5525 

Ti 

2.603 

2.044 

0.7656 

0.6013 

2.7489 

15/6 

2.989 

2.347 

0.8789 

0.6903 

2.9452 

•  Adapted  from  the  191 2  Edition  of  the  Handbook  of  the  Cambria  Steel  Company, 
Johnstown,  Pa. 


Weights  and  Areas  of  Steel  Bars 


1515 


Weights  and  Areas  of  Square  and  Round  Steel  Bars  * 

Weights  are  for  steel,  at  489.6  lb  per  cu  ft 


Thick- 

D 

0 

Thick- 

D 

0 

ness, 

Weight 

Weight 

ness, 

Weight 

•    \ 

Vcight 

in 

Area, 

per 

Area, 

per 

in 

Area, 

per 

Area, 

per 

sq  in 

foot, 
lb 

sq  in 

foot, 
lb 

sq  in 

foot, 
lb 

sq  in 

foot, 
lb 

I 

1. 000 

3.400 

0.785 

2.670 

3 

9.000 

30.60 

7.069 

24.03 

Me 

1. 129 

3.838 

0.887 

3.014 

He 

9.379 

31-89 

7.366 

25.04    ' 

H 

1.266 

4-303 

0.994 

3-379 

H 

9.766 

33.20 

7.670 

26.08 

3/i6 

1. 410 

4.795 

1. 108 

3-766 

Vie 

10.16 

34.55 

7.980 

27.13 

H 

1.563 

5.312 

1.227 

4-173 

H 

10.56 

35.92 

8.296 

28.20 

Vl6 

1-723 

5  857 

l.35i 

4.600 

Mo 

10.97 

37.31 

8.618 

29  30 

% 

1.891 

6.428 

1.485 

5- 049 

H 

11.39 

38.73 

8.946 

30.42 

Mo 

2.066 

7.026 

1.623 

5.518 

Mo 

11. 82 

40.18 

9.281 

31.56 

H 

2. 250 

7.650 

1.767. 

6.008 

H 

12.25 

41.65 

9.621 

32.71 

»/l6 

2.441 

8.301 

1. 918 

6.520 

He. 

12.69 

43  14 

9.968 

33  90 

H 

2.641 

8.978 

2.074 

7.051. 

H 

13.14 

44.68 

10.32 

35.09 

1H6 

2.848 

9.682 

2.237 

7.604 

Hie 

13-60 

46.24 

10.68 

36.31 

H 

3  063 

10.41 

2.405 

8.178 

H 

14.06 

47.82 

11.05 

37.56 

1^6 

3.285 

II. 17 

2.580 

8.773 

'3/i6 

14.54 

49.42 

11.42 

38.81 

^i 

3 -516 

11.95 

2.761 

9  388 

li 

15.02 

51.  OS 

11.79 

40.10 

1^6 

3-754 

12.76 

2.948 

10.02 

15/16 

15.50 

52.71 

12.18 

41.40 

2 

4.000 

13.60 

3.142 

10.68 

4 

16.00 

54.40 

12.57 

42.73 

Mo 

4-254 

14.46 

3  341 

11.36 

i/ie 

16.50 

56.11 

12.96 

44.07 

}4 

4  516 

15.35 

3.547 

12.06 

H 

17.02 

57.85 

13.36 

45.44 

3/16 

4.785 

16.27 

3.758 

12.78 

•Me 

17.54 

59.62 

13  77 

46.83 

H 

5.063 

17.22 

3.976 

13.52 

H 

18.06 

61.41 

14.19 

48.24 

Me 

5.348 

18.19 

4.200 

14.28 

Me 

18.60 

63.23 

14.61 

49.66 

% 

5.641 

19.18 

4.430 

15.07 

H 

19.14 

65.  oS 

15.03 

51. II 

Me 

5.941 

20.20 

4.666 

15.86 

Mo 

19.69 

66.95 

15-47 

52.58 

U 

6.250 

21.25 

4.909 

16.69 

H 

20.25 

68.85 

15.90 

54.07 

»/l8 

6.566 

22.33 

5.157 

17.53 

Me 

20.82 

70.78 

16.35 

55.59 

H 

6.891 

23.43 

5.412 

18  40 

H 

21.39 

72.73 

16.80 

57.12 

iHe 

7.223 

24.56 

5.673 

19.29 

iHe 

21.97 

74.70 

17.26 

58.67 

3/4 

7.563 

25  71 

5.940 

20.20 

H 

22.56 

76.71 

17.72 

60.25 

1^6 

7.910 

26.90 

6.213 

21.12 

me 

23.16 

78.74 

18.19 

61.84 

'A 

8.266 

28.10 

6.492 

22.07 

%      • 

23.77 

80.81 

18.67 

63.46 

15/16 

8.629 

29.34 

6.777 

23.04 

iMe 

24.38 

82.89 

19  15 

65.10 

*  Adapted  from  the  19 12  Editioa  of  the  Handbook  of  the  Cambria.  Steel  Comoany, 
Johnstown,  P^v 


1516 


Metal-Data 


Part  3 


Weights  and  Areas  of  Square  and  Round  Steel  Bars  ' 
Weights  are  for  steel,  at  489.6  lb  per  cu  ft 


(Continued) 


Thick- 

a 

0 

Thick- 

D 

0 

ness, 

• 

Weight 

Weight 

ness, 

Weight 

\ 

Veight 

in 

Area, 

per 

Area, 

per 

m 

Area, 

per 

Area, 

per 

sq  in 

foot, 
lb 

sq  in 

foot, 
lb 

sq  in 

foot, 
lb 

sq  m 

foot, 
lb 

5 

25.00 

85.00 

19-64 

66.76 

7 

49.00 

166.6 

38.49 

130.9 

Me 

25.63 

87.14 

20.13 

68.44 

M 

52.. S6 

178.7 

41.28 

140.4 

H 

26.27 

89.30 

20.63 

70.14 

\'i 

56.25 

191  3 

44.18 

150.2 

Me 

26.91 

91.49 

21.14 

71.86 

% 

60.06 

204.2 

47.17 

160.3 

M 

27.56 

93.72 

21.65 

73.60 

8 

64.00 

217.6 

50.27 

171. 0 

Me 

28.22 

95.96 

22.17 

75.37 

\i 

6^.06 

231.4 

53.46 

181. 8 

% 

28.89 

98.23 

22.69 

77.15 

'A 

72.25 

245.6 

56.75 

193.0 

Me 

29.57 

100.5 

23.22 

78.95 

M 

76.56 

260.3 

60.13 

204.4 

\^ 

30.25 

102.8 

23.76 

80.77 

9 

81.00 

275.4 

63.62 

216.3 

Me 

30.94 

105.2 

24.30 

82.62 

M 

85.56 

290.9 

67.20 

228. 5 

% 

31.64 

107.6 

24.85 

84.49 

\h. 

90.25 

306.8 

70.88 

241.0 

iHe 

32.35 

IIO.O 

25.41 

86.38 

Ml 

95.06 

323.2 

74.66 

253.9 

'M 

3306 

112. 4 

25.97 

88.29 

10 

100. 0 

340.0 

78.54 

267.0 

iMe 

33  79 

114. 9 

26.54 

90.22 

H 

105. 1 

357-2 

82.52 

280.6 

% 

34.52 

117. 4 

27.11 

92.17 

Vi 

no. 3 

374.9 

86.59 

294.4 

iMe 

35.25 

"99 

27.69 

94.14 

M 

115. 6 

392.9 

90.76 

308.6 

6 

36.00 

122.4 

28.27 

96.14 

II 

121. 0 

411. 4 

95.03 

323.1 

% 

37.52 

127.6 

20.47 

100.2 

\\ 

126.6 

430.3 

99.40 

337-9 

M 

39  06 

132.8 

30.68 

104.3 

¥2 

132.3 

449-6 

103.9 

353-1 

34 

40.64 

138.2 

31.92 

108.5 

M* 

138. 1 

469.4 

108.4 

368.6 

^^ 

42.25 

143.6 

33.18 

112. 8 

12 

144.0 

489.6 

113. 1 

384.5. 

H 

43.89 

149.2 

34-47 

117. 2 

M 

45.56 

154.9 

35.79 

121. 7 

^4 

47.27 

160.8 

37.12 

126.2 

*  Adapted  from  the  19 12  Edition  of  the  Handbook  of  the  Cambria  Steel  Company, 
Johnstown,  Pa. 


Weights  of  Flat  Steel  Bars 


Weights  in  Pounds  of  Flat  Rolled  Steel  Bars 

PER   LINEAR   FOOT 

One  cubic  foot  of  steel  weighs  489.6  lb 
For  thicknesses  from  He  in  to  %&  in  and  widths  from  H  in  to  %  in 


Width  of  bar. 

inches 

Thickness, 
inches 

\i 

Me 

% 

Me 

\2 

Yi^ 

Y^ 

iHe 

3/4 

M6 

0.053 

0.066 

0.080 

0.093 

0.106 

0.120 

0.133 

0.146 

O.IS9 

%4 

0.066 

0.083 

O.IOO 

0.116 

0.133 

0.149 

0.166 

0.183 

0.199 

%2 

0.080 

O.IOO 

0.120 

0.139 

O.IS9 

0.179 

0.199 

0.219 

0.239 

yU 

0.093 

0.II6 

0.139 

0.163 

0.186 

0.209 

0.232 

0.256 

0.279' 

H 

0.106 

0.133 

0.159 

0.186 

0.212 

0.239 

0.266 

0.292 

0.319 

%4. 

0.120 

0.149 

0.179 

0.209 

0.239 

0.269 

0.299 

0.329 

0.3.59 

^M 

0.133 

0.166 

0.199 

0.232 

0.266 

0.299 

0.332 

0.365 

0.398 

1Kg4 

0.146 

0.183 

0.219 

0.256 

0.292 

0.329 

0.365 

0.402 

0.438 

M6 

0.159 

0.199 

0.239 

0.279 

0.319 

0.359 

0.398 

0.438 

0.478 

1%4 

0.173 

0.216 

0.259 

0.302 

0.345 

0.388 

0.432 

0.475 

0.518 

7/32 

0.186 

0 .  232 

0.279 

0.325 

0.372 

0.418 

0.465 

0.511 

0.558 

1%4 

0.199 

0.249 

0.299 

0.349 

0.398 

0.448 

0.498 

0.548 

0.598 

M 

0.213 

0.266 

0.319 

0.372 

0.425 

0.478 

0.531 

0.584 

0.638 

1%4 

0.226 

0.282 

0.339 

0.395 

0.452 

0.508 

0.564 

0.621 

0.677 

%2 

0.239 

0.299 

0.359 

0.418 

0.478 

0.538 

0.598 

0.657 

0.717 

1%4 

0.252 

0.31S 

0.379 

0.442 

0.505 

0.568 

0.631 

0.694 

0.757 

Mfl 

0.266 

0.332 

0.398 

0.465 

0.531 

0.598 

0.664 

0.730 

0.797 

2144 

0.279 

0.349 

0.418 

0.488 

0.558 

0.628 

0.697 

0.767 

0.827 

11/^-2 

0.292 

0.365 

0.438 

0.511 

0.584 

0.657 

0.730 

0.804 

0.877 

2)64 

0.305' 

0.382 

0.458 

0-535 

0.611 

0.687 

0.764 

0.840 

0.916 

3/^ 

0.319 

0.398 

0.478 

0.5.58 

0.638 

0.717 

0.797 

0.877 

0.956 

2  5/64 

0.332 

0.41S 

0.498 

0.581 

0.664 

0.747 

0.830 

0.913 

0.996 

l-%2 

0.34s 

0.432 

0.518 

0.604 

0.691 

0.777 

0.863 

0.950 

1.04 

2/64 

0.359 

0.448 

0.538 

0.628 

0.717 

0.807 

0.896 

0.986 

1.08 

lu 

0.372 

0.465 

0.558 

0.651 

0.744 

0.837 

0.930 

1.02 

1. 12 

2%4 

0.38s 

0.481 

0.578 

0.674 

0.770 

0.867 

0.963 

1.06 

1. 16 

1-/32 

0.398 

0.498 

0.598 

0.697 

0.797 

0.896 

0.996 

1. 10 

1.20 

3^.4 

0.412 

0.515 

0.618 

0.721 

0.823 

0.926 

1.03 

1.13 

1.24 

/2 

0.42s 

0.531 

0.638 

0.744 

0.850 

0.956 

1.06 

1. 17 

1.28 

3%4 

0.438 

0.548 

0.657 

0.767 

0.877 

0.986 

1. 10 

1. 21 

1. 31 

17/^2 

0.452 

0.564 

0.677 

0.790 

0.903 

1.02 

1.13 

1.24 

1.35 

35/^4 

0.465 

0.581 

0.697 

0.813 

0.930 

1.05 

1. 16 

1.28 

1.39 

9-16 

0.478 

0.598 

0.717 

0.837 

0.956 

1.08 

1.20 

1.31 

1.43 

1518 


Metal-Data 


Weights  in  Pounds  of  Flat  Rolled  Steel  Bars  (Continued) 

PER   LINEAR   FOOT 

For  thicknesses  from  Me  to  2  in  and  widths  from  i  to  3  in 


Width  of  bar. 

inches 

Thickness, 
inches 

I 

\\k 

1M2 

iM 

2 

2M 

2M 

2-3-1 

3 

Ms 

0.21 

0.26 

0.32 

0.37 

0.43 

0.48 

0.53 

0..58 

0.63 

H 

o.*42 

0.53 

0.64 

0.7s 

0.85 

0.96 

1.06 

1.17 

1.28 

3/16 

0.63 

0.79 

0  96 

I. II 

1.28 

1.44 

1.59 

1-75 

1.91 

M 

0.85 

1.06 

1.28 

• 

1.49 

1.70 

I-9I 

2.12 

2.34 

2.55 

•Me 

I  06 

1.33 

1.59 

1.86 

2.12 

2.39 

2.65 

2.92 

3.19 

% 

1.28 

I  59 

1.92 

2.23 

2..SS 

2.87 

3-19 

3  51 

3  83 

lU 

1.49 

1.86 

2.23 

2.60 

2.98 

3  35 

3.72 

4.09 

4.46 

Vi 

1.70 

2.12' 

2.55 

2.98 

3.40 

3.83 

4-25 

4.67 

5.10 

Mo 

1.92 

2.39 

2.87 

3.35 

3.83 

4  30 

4.78 

5.26 

5.74 

% 

2.12 

2.65 

3.19 

3  72 

4.2s 

4.78 

5  31 

5.84 

6.38 

iMo 

2.34 

2.92 

3.51 

4.09 

4.67 

5.26 

5.84 

6.43 

7.02 

M 

2.55 

3- 19 

3.83 

4-47 

5.10 

5.7s 

6.38 

7.02 

7.65 

i-Me 

2.76 

3.45 

4.14 

4.84 

5.53 

6.21 

6.90 

7.60 

8.29 

Ms 

2.98 

3.72 

4-47 

5.20 

5.95 

6.69 

7-44 

8.18 

8.93 

iMe 

3  19 

3-99 

4.78 

5.58 

6.38 

7.18 

7-97 

8.77 

9-57 

I 

3-40 

4-25 

510 

5.95 

6.80 

7.65 

8.50 

9.35 

10.20 

iMe 

3.61 

4.52 

5. 42 

6.32 

7.22 

8.13 

9  03 

9  93 

10.84 

1 1/8 

3.83 

4.78 

5-74 

6.70 

7. 65 

8.61 

9  57 

10.52 

11.48 

iMe 

4.04 

5.05 

6.06 

7.07 

8.08 

909 

10.10 

11. II 

12.12 

i'/4 

4-25 

5. 31 

6.38 

7-44 

8.50 

9-57 

10.63 

11.69 

12.75 

iMe 

4.46 

5.58 

6.69 

7.81 

8.93 

10.04 

II.  16 

12.27 

13.39 

i5i 

4.67 

5.84 

7.02 

8.18 

9  35 

10.52 

11.69 

12.85 

14.03 

iMo 

4.89 

6. II 

7-34 

8.56 

978 

11.00 

12.22 

13.44 

14.66 

1M2 

S-io 

6.38 

7.*65 

8.93 

10.20 

11.48 

12.75 

14.03 

15.30 

iMe 

5-32 

6.64 

7  97 

9  30 

10.63 

11.95 

13  28 

14.61 

15  94 

154 

5.52 

6.90 

8.29 

9  67 

II.  OS 

12.43 

13.81 

15-19 

16.58 

i^Me 

5-74 

7.17 

8.61 

10.04 

11.47 

12.91 

14  34 

15.78 

17-22 

iM 

5. 95 

7-44 

8.93 

10.42 

11.90 

13.40 

14.88 

16.37 

17.85 

iiMe 

6.16 

7.70 

9.24 

10.79 

12.33 

13-86 

15.40 

16.95 

18.49 

1^4 

6.38 

7.97 

957 

II.  15 

12.75 

14  34 

15.94 

17.53 

19.13 

i^Me 

6.59 

8.24 

9.88 

11.53 

13  18 

1483 

16.47 

18.12 

19  77 

2 

1 

6.80 

8.50 

10.20 

11.90 

13.60 

15.30 

17.00 

18.70 

20.40 

Weights  of  Fiat  Steel  Bars 


Weights  in  Pounds  of  Flat  Rolled  Steel  Bars  (Continued) 

PER   LINEAR   FOOT 

For  thicknesses  from  He  to  2  in  and  widths  from  33^  to  7 H  in 


Width  of  bar, 

nches 

Thickness, 
inches 

3H 

4 

4V2 

5 

5H 

6 

6H 

7 

lYi 

M6 

0.75 

0.85 

0.96 

1.06 

1. 17 

1.28 

1-39 

1-49 

1.60 

'A 

1-49 

1.70 

1.92 

2.13 

2.34 

2.55 

2.77 

2.98 

3-19 

3/l6 

2.23 

2.55 

2.87 

3-19 

3  51 

3-83 

4.14 

4.46 

4-78 

H 

2.98 

3.40 

3.83 

4-25 

4-67 

S-io 

5  53 

5-95 

6.36 

Me 

3-72 

4-25 

4.78 

5  31 

5.84 

6.38 

6.90 

7-44 

7-97 

% 

4-47 

5-10 

5.74 

6.38 

7.02 

7.65 

8.29 

8.93 

9-57 

Vi6 

5. 20 

5.95 

6.70 

7-44 

8.18 

8.93 

9.67 

10.41. 

11.16 

V2 

5.95 

6.80 

7-65 

8.50 

9-35 

10.20 

11.05 

11.90 

12.75 

9/16 

6.70 

7.65 

8.61 

9-57 

10.52 

11.48 

12.43 

13.39 

14-34 

% 

7-44 

8.50 

9-57 

10.63 

11.69 

12.75 

13  81 

14.87 

15.94 

me 

8.18 

9-35 

10.52 

11.69 

12.85 

14.03 

15-20 

16.36 

17-53 

% 

8.93 

10.20 

11.48 

12.75 

14.03 

15.30 

16.58 

17.85 

19-13 

13/16 

967 

11.05 

12.43 

13-81 

15.19 

16.58 

17-95 

19-34 

20.72 

Ti 

10.41 

11.90 

13.39 

14.87 

16.36 

17-85 

19-34 

20.83 

22.32 

15/16 

II.  16 

12.75 

14  34 

15.94 

17.53 

19.13 

20.72 

22.32 

23.91 

I 

11.90 

1360 

15-30 

17.00 

18.70 

20.40 

22.10 

23.80 

25-50 

iMs 

12.65 

14-45 

16.26 

18.06 

19-87 

21.68 

23.48 

25 -29 

27.10 

iH 

13.39 

15.30 

17.22 

19.13 

21.04 

22.95 

24  87 

26.78 

28.68 

iMe       • 

14  13 

16.15 

18.17 

20.19 

22.21 

24.23 

26.24 

28.26 

30.28 

iH 

14.87 

17.00 

1913 

21.25 

23-38 

25.50 

27.62 

29.75 

31.88 

I  Ms 

15.62 

17.85 

20.08 

22.32 

24-54 

26.78 

29.01 

31.23 

3348 

m 

16.36 

18.70 

21.04 

23.38 

25-71 

28.05 

30.39 

32.72 

35  06 

iV\& 

17.10 

19 -85 

21.99 

24.44 

26.88 

29-33 

31.77 

34-21 

36.66 

l\i 

17.85 

20.40 

22.95 

25  50 

28.05 

30.60 

33-15 

35-70 

38-26 

i^ie 

18.60 

21.25 

23.91 

26.57 

2^.22 

31.88 

34-53 

37-19 

39-84 

iH 

19 -34 

22.10 

24.87 

27.63 

30.39 

33.15 

35-91 

38.67 

41.44 

ii/ie 

20.08 

22.95 

25.82 

28.69 

31-55 

34.43 

37-30 

40.16 

43-03 

1% 

20.83 

23.80 

26.78 

29.75 

32.73 

35.70 

38.68 

41.65 

44-63 

i^Me 

21.57 

24.65 

27.73 

30.81 

33-89 

36.98 

40.05 

43-14 

46.22 

l7/i 

22.31 

25   50 

28.69 

31.87 

35-06 

38.25 

41.44 

44-63 

47-82 

115/6 

23.06 

26.35 

29.64 

32.94 

36.23 

39  53 

42.82 

46.12 

49.41 

2 

23.80 

27.20 

30.60 

34.00 

37.40 

40.80 

44.20 

47.60 

51.00 

1520 


Metal-Data 


Weights  in  Pounds  of  Flat  Rolled  Steel  Bars  (Continued) 

PER   LINEAR   FOOT 

For  thicknesses  from  He  to  2  in  and  widths  from  8  to  12  in 


Width  of  bar. 

inches 

Thickness, 
inches 

8 

SH 

9 

9M2 

10 

io3^ 

11 

iiH 

12 

Me 

1.70 

i.8i 

1. 91 

2.02 

2.13 

2.23 

2.34 

2.45 

2-55 

% 

340 

3.61 

3.82 

4.04 

4.25 

4.46 

4.68 

4-89 

5-10 

3/lG 

5  10 

5.42 

5.74 

6.06 

6.38 

6.70 

7.02 

7.32 

7.6s 

H 

6.80 

7.22 

7.65 

8.03 

8.50 

8.92 

9.34 

9-78 

10.20 

Mo 

8.50 

903 

9.56 

10.10 

10.62 

11.16 

11.68 

12.22 

12.75 

% 

10.20 

10.84 

11.48 

12.12 

12.75 

T3.39 

14.03 

14.68 

15.30 

I'ia 

11.90 

12.64 

13.40 

14.14 

14-88 

15.62 

16.36 

17.12 

17.85 

u  ■ 

13.60 

14.44 

15.30 

16.16 

17.00 

17.85 

18.70 

19.55 

20.40 

Vie 

15.30 

16.26 

17.22 

.18.18 

19.14 

20.08 

21.02 

22.00 

22.95 

% 

17.00 

18.06 

19-13 

20.19 

21.25 

22.32 

23.38 

24.44 

25 -50 

iHe 

18.70 

19.86 

21.04 

22.21 

23.38 

24-54 

25.70 

26.88 

28.05 

% 

20.40 

21.68 

22.96 

24.23 

25.50 

26.78 

28.05 

29 .33 

30.60 

i-Me 

22.10 

23.48 

24.86 

26.24 

27.62 

29.00 

30.40 

31.76 

33.15 

% 

23.80 

25.30 

26.78 

28.26 

29.75 

31.24 

32.72 

34.21 

35.70 

15/16 

25.50 

27.10 

28.69 

30.28 

31.88 

33.48 

35.06 

36.66 

38.25 

I 

27.20 

28.90 

30.60 

32.30 

34.00 

35.70 

37.40 

39.10 

40.80 

iMe 

28.90 

30.70 

32.52 

34.32 

36.12 

37.92 

39.74 

41.54 

43.3s 

iH 

30.60 

32.52 

34-43 

36.34 

38.25 

40.17 

42.08 

44-00 

45.90 

I-/16 

32.30 

34.32 

36.34 

38.36 

40.38 

42.40 

44.42 

46:44 

48.4s 

I'/i 

3400 

36.12 

38.26 

40.37 

42.50 

44.63 

46.76 

48.88 

51.00 

iMe 

35.70 

37.93 

40.16 

42.40 

44.64 

46.86 

49.08 

51-32 

53-55 

l3.^ 

37.40 

39-74 

42.08 

44-41 

46.75 

49.08 

51.42 

53-76 

56.10 

iMe 

39.10 

41.54 

44  00 

46.44 

48.88 

51.32 

53  76 

56.21 

58.6s 

1V2 

40.80 

43.35 

45.90 

48.45 

51.00 

53.55 

56.10 

58.65 

61.20 

iy\& 

42.50 

45.16 

47-82 

50.48 

53.14 

55.78 

58.42 

61.10 

63  75 

iH 

44.20 

46.96 

49-73 

52.49 

55.25 

58.02 

60.78 

63.54 

66.30 

iiMe 

45.90 

48.76 

51-64 

54.51 

57-38 

60.24 

63  10 

65.98 

68.85 

1% 

47.60 

50.58 

53-56 

56.53 

59.50 

62.48 

65.45 

68.43 

71-40 

ii^e 

49.30 

52.38 

55.46 

58.54 

61.62 

64.70 

67.80 

70.86 

73-95 

iVs 

51.00 

54.20 

57.38 

60.56 

63.7s 

66.94 

70.12 

73.31 

76.50 

i»Mfl 

52.70 

56.00 

59.29 

62.58 

65.88 

69.18 

72.46 

75-76 

79-05 

2 

54.40 

57.80 

61,20 

64.60 

68.00 

71.40 

74.80 

78.20 

81.60 

Estimating  Weights  of  Metals 


1521 


Rtiles  for  Estimating  the  Weight  of  any  Piece  of  Wrought 
Iron,  Steel  or  Cast  Iron 

Wrought  Iron. 

One  cubic  foot  of  wrought  iron  weighs 480  lb 

One  square  foot,  one  inch  thick,  weighs 40  lb 

One  square  inch,  one  foot  long,  weighs 3^^  lb 

To  find  the  weight  per  square  foot  of  sheet  iron,  multiply  the  thickness  in 
inches  by  40. 

To  find  the  weight  per  linear  foot  of  bars  of  any  section,  multiply  the  cross- 
sectional  area  in  square  inches  by  3H. 

Steel. 

One  cubic  foot  of  steel  weighs 489.6  lb 

(Or  just  2%  more  than  wrought  iron.) 

One  square  foot,  one  inch  thick,  weighs 40.8  lb 

One  square  inch,  one  foot  long,  weighs 3.4  lb 

To  find  the  weight  per  linear  foot,  of  bars  of  any  section,  multiply  the  cross- 
sectional  area  in  square  inches  by  3.4;  or,  if  the  weight  is  known,  the  exact  sec- 
tional area  may  be  obtained  by  dividing  by  3.4. 

Cast  Iron. 

One  cubic  foot  of  cast  iron  weighs 450  lb 

One  square  foot,  one  inch  thick,  weighs sjHlh 

One  square  inch,  one  foot  long,  weighs . , 3H  lb 

One  cubic  inch  weighs 0.26  lb 

The  weight  of  irregular  castings  must  be  estimated  by  the  cubic  inch. 


Rules  for  Weights  of  Castings 

Multiply  the  weight  of  the  pattern  by  18  for  cast  iron,  13  for  brass,  19  for  lead, 
12.2  for  tin,  1 1.4  for  zinc;   the  product  is  the  weight  of  the  casting. 

Reduction  for  Round  Cores  and  Core-Prints 

Rule.  Multiply  the  square  of  the  diameter  by  the  length  of  the  core  in  inches, 
and  the  product  multiplied  by  0.017  is  the  weight  of  the  pine  core  to  be  deducted 
from  the  weight  of  the  pattern. 

Shrinkage  in  Castings 


Pattern-makers'  Rule 


Cast  iron . .  H 

Brass He 

Lead % 

Tin M2 

Zinc Mq 


of  an  inch  longer  per  linear  foot 


1522 


Metal-Data 


Part  3 


Weights  of  Square  Ca&t-Iron  Columns  in  Pounds  per  Linear  Foot* 

an 

b 

20  +  2b 

t 

Thicknes 

s  of  metal,  inches 

•H  in, 

Vi  in, 

%  in. 

I  in, 

iH  in. 

iH  in, 

iy2  in. 

1%  in. 

2  in, 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

It) 

lb 

If        -Ml. .<>!!;; 

18.6 

21. 1 

23.3 

25.0 

26.4 

27-3 

28.1 

.....   Mt    vi.. 

22.5 

25.8 

•    28.7 

3^3 

33.4 

35.1 

37.5 

i6 

26.4 

30.5 

34.2 

37.5 

40.4 

45- 0 

46.9 

49.2 

50.0 

i8 

30.3 

35.2 

39.7 

43.8 

47.4 

50.8 

56.3 

60.2 

62.5 

20 

34  2 

39-8 

45.1 

50.0 

54-5 

58.6 

65.6 

71.1 

75.0 

22 

38.1 

44.5 

50.6 

56.3 

61.5 

66.4 

75.0 

82.0 

87.5 

24 

42.0 

49.2 

56.1 

62.5 

68.5 

74.2 

84.4 

!    930 

100.0 

26 

45.9 

53.9 

61.5 

68.8 

75.6 

82.0 

93.8 

103-9 

112.5 

28 

49-8 

58.6 

67.0 

75.0 

82  6 

89.8 

103.1 

114.8 

125.0 

■',^1  ,k 

:,53.7 

63.3 

72.5- 

81.3 

89.6 

97.7 

112.5 

125.8 

137.5 

^  ^ 

57.6 

68.0 

77.9 

87.5 

96.7 

105. 5 

121. 9 

136.7 

150.0 

34 

61.5 

72.7 

83.4 

93.8 

103.7 

113.3 

131. 3 

147-7 

162.5 

36 

65.4 

77.3 

88.9 

100. 0 

110.7 

121. 1 

140.6 

158.6 

175.0 

38 

693 

82.0 

94.3 

106.3 

117. 8 

128.9 

150.0 

169.5 

187.5 

40 

73.2 

86.7 

99-8 

112.5 

124.8 

.  136.7 

159.4 

•180.5 

200.0 

42 

771 

91-4 

105. 3 

118. 8 

131. 8 

144.5 

168.8 

191.4 

212.5 

44 

81.0 

.    96.1 

no. 8 

125.0 

138.8 

152.3 

178.1 

202.3 

225.0 

46 

849 

100  8 

116. 2 

131. 3 

145  9 

160.2 

187.5 

213-3 

237.5 

48 

88.8 

105.  S 

121. 7 

137.5 

152  9 

168.0 

196.9 

224.2 

250.0 

50 

92.8 

no. 2 

127.2 

143.8 

159.9 

175-8 

206.3 

235.2 

262.5 

52 

96.7 

114.^ 

13I2.6 

iSO.o 

167.0 

183.6 

215.6 

246.1 

275.0 

54 

100.6 

119-5 

138.1 

156.3 

174.0 

191.4 

225.0 

257.0 

,  287.5 

56 

104.5 

124.2 

143-6 

162,5 

181. 0 

199-2 

234.4 

268.0 

300.0 

58 

108.4 

128.9 

149.0 

168.8 

188.1 

207.0 

243.8 

278.9 

312.5 

60 

112. 3 

133.6 

154.5 

175.0 

195.1 

214.9 

253.2 

289.8 

325.0 

62 

116. 2 

1383 

160.0 

181.3 

202.1 

222.7 

262.5 

300.8 

337.5 

64 

120  I 

1-43-0 

16S.4 

187.5 

205.2 

230.5 

271.9 

311. 7 

350.0 

66 

124.0 

147.7 

170.9 

193-8 

216.2 

238.3 

281.3 

322.7 

362.5 

68 

127.9 

152.3 

176.4 

200.0 

223.2 

246.1 

290.6 

333.6 

375-0 

70 

131. 8 

157.0 

181. 8 

206.3 

230.3 

253-9 

300.0 

344. 5 

387.5 

72 

135.7 

161. 7 

187-3 

212.^ 

237.3 

261.7 

309.4 

355.5 

400.0 

74 

139.6 

166.4 

192.8 

218.8 

244 -3 

269.5 

318.8 

366.4 

412.5 

76 

143  5 

171. 1 

198.3 

225.0 

251-3 

277.3 

328.1 

377.3 

425-0 

78 

1-47.4 

175.8 

203.7 

231.3 

2.58.4 

285.2 

337.5 

388.3 

437-5 

fea 

151. 3 

180.5 

207.2 

237-5 

265.4 

293.0 

346.9 

399.2 

450.0 

*  Birkmire. 

t  a  and  b  =  either  side,  outside  measurement, 
been  made  in  this  table  for  corners  counted  twice. 


2  a  -\-  2  b  =  number.     Allowance  has 


Example.  What  is  the  weight  per  linear  foot  of  a  12  by  16  by  i  in  thick 
column? 

Solution.  2  a-\-  2b=  24+  32  =  56.  Opposite  this  number,  under  i-in-thick 
metal,  we  find  162,5,  or  weight  per  linear  foot  of  a  column  12  by  16  by  i-in-thick. 

Note.  For  flanges,  brackets,  etc.,  calculate  the  cubical  contents  of  same  and 
multiply  by  0.26;  cast  iron  averages  450  lb  per  cu  ft. 


Weights  of  Cast-iron  Columns 


1523 


Weights  per  Linear  Foot  of  Circular  Cast-iron  Columns  *  f 

Outside 

Thickness  of  metal,  inches 

diameter, 

/z  in. 

H'm, 

Hin, 

>Hn, 

I  in, 

iH  in. 

iH  in. 

1%  in. 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

3 

12.3 

14.6 

16.60 

18.30 

19.6 

4 

17.2 

21.0 

24.00 

27.00 

29-S 

32.1 

33*8 

35. 4 

5 

22.1 

27.0 

31.30 

35.50 

39.3 

43.0 

46.0 

49.0 

6 

27.0 

33.0 

39.00 

44.00 

49-1 

54.1 

58.3 

62.4 

7 

32.0 

39-1 

46.00 

53.00 

59-0 

65-1 

70.6 

76.1 

8 

36.8 

45.3 

53.40 

61.20 

69.1 

76.1 

83.1 

89.5 

9 

41.7 

51.4 

61.10 

70.00 

78.6 

87.1 

95-1 

103.1 

10 

46.6 

57-5 

68.13 

78.41 

88.4 

98.0 

107.4 

116. 4 

II 

51.6 

64.0 

75.50 

87.10 

98.2 

109.1 

120.1 

130.1 

12 

56.5 

70.0 

82.87 

96.10 

108.0 

120.0 

132.1 

143.5 

13 

61.4 

76.0 

90.23 

104.20 

118. 1 

131 -2 

144-2 

157. 1 

14 

66.3 

82.1 

97-60 

113.20 

128.1 

142.0 

156.5 

170.4 

15 

71.2 

88.2 

104.96 

121.40 

137 -5 

153-3 

169.4 

184. 1 

i6 

76.1 

94.4 

112.33 

130.10 

147-3 

164-3 

181. 0 

197.4 

17 

81.0 

100.5 

120.10 

139 -10 

157 -I 

175-4 

193.3 

211.0 

i8 

86.0 

107.0 

127.00 

147  00 

167.0 

186.4 

206.0 

224.4 

19 

gi.o 

1130 

134-40 

156.00 

177. 1 

197 -5 

218. 1 

238.0 

20 

96.0 

119. 0 

142.10 

164.30 

186.6 

208.8 

230.1 

i    251.5 

21                   I 

00.6 

125.0 

149- 10 

173.10 

196.6 

219.6 

242.4 

1    265 . 0 

22                   I 

05.6 

131.2 

156.50 

181. so 

206.2 

230.6 

255.0 

278.0 

23                 I 

10.5 

137-3 

-164.10 

190.10 

216. 1 

242.0 

267.0 

292.0 

24                 I 

15.4 

143.5 

171.20 

199.00 

^26.6 

253-0 

279-2 

30s. 4 

Thick] 

less  of  m 

etal,  ind 

les 

Outside       _ 

diameter,        ^ 
inches 

K2  in, 

IH  in, 

2  in. 

2\i  in. 

2K  in, 

2%  in. 

1^4  in, 

1%  in. 

-lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

3 
4 
5 

51.54 

54.1 

55.84 

57.5 

6 

66.30 

69.9 

73.02 

76.0 

"78'6 

80.84 

82.83 

7 

81.00 

85.6 

90.20 

94.3 

98.2 

ioi.70 

105.00 

107.84 

8 

95.80 

101.8 

107.40 

■   112. 8 

117. 8 

122.60 

127.00 

131.20 

9             I 

10.50 

117.7 

124.60 

131 -2 

137  5 

143-40 

149  10 

154.50 

10                   I 

25.20 

133.7 

142. CO 

149-6 

157.1 

164.30 

171.20 

177.80 

II             I 

40.00 

149.6 

159.00 

168.0 

176.8 

185.20 

193-30 

201 . 10 

12                   I 

54.70 

165.6 

176.00 

186.4 

196.4 

206.00 

215.40 

224.40 

13               I 

69.40 

181. 5 

193.30 

204.8 

216.0 

226.90 

237.50 

247.70 

14              I 

84.10 

197.4 

210.50 

223.2 

235.7 

247.70 

259  60 

271.10 

15              I 

98.90 

213.4 

527-70 

241.6 

255.3 

268.20 

281 . 70 

294.40 

l6                 2 

13.50 

229.4 

244 -90 

260:0 

274.9 

'289.50 

303 -70 

317.70 

17                   2 

28.30 

245.3 

262.00 

278.4 

294. 5 

310.30 

325.80 

341  00 

I8                 2 

43.00 

261.3 

279-20 

296.8 

314.2 

331.20 

348.00 

364-30 

19             2 

57.70 

277.2 

296.40 

315.2 

338.8 

352.10 

370.00 

387-70 

20             2 

72.50 

293.2 

313.60 

333-6 

353.4 

372.90 

392 . 10 

411.00 

21              2 

87.20 

309.0 

330.80 

352. 1 

373.1 

393.80 

414.20 

434.30 

22             3 

02.00 

325  I 

348.00 

370.5 

393.0 

414.60 

436.30 

457.60 

23              3 

16.70 

341  0 

365.10 

388.9 

412.3 

435.50 

458.40 

481.00 

24              3 

31.40 

357.0 

382.30 

407.3 

432.0 

456.40 

480.50 

504.20 

*  Birkmii'^. 

t  The  table  is  arranged  for  the  weight  of  plain  shaft.    For  brackets,  flanges,  etc.,  cal- 
culate the  cubical  contents  and  multiply  by  0.26, 


1524 


Metal-Data 


Part  3 


Weight  of  Cast-iron  Plates 
Weights,  in  Pounds,  of  Cast-iron  Plates  One  Inch  Thick 

Calculated  at  450  lb  per  cu  ft 


Width, 

inches 

Length, 
inches 

6  in. 

8  in. 

10  in, 

12  m, 

14  m. 

16  in, 

18  in, 

20  m, 

24  m, 

30  m, 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

lb 

4 

6.25 

8.3 

10.4 

12.5 

14.6 

16.6 

18.7 

20.8 

25 

31 

6 

9.37 

12. 5 

15.6 

18.7 

21.8 

25.0 

28.1 

31.2 

38 

47 

8 

12.50 

16.6 

20.8 

25.0 

29.1 

33.3 

37.4 

41.6 

50 

62 

10 

15.60 

20.8 

26.0 

31.2 

36.4 

41.6 

46.8 

52.0 

63 

78 

12 

18.70 

25.0 

31.2 

37.5 

43.7 

49-9 

56.2 

62.4 

75 

94 

14 

21.80 

29.2 

36.4 

43.7 

51.0 

58.2 

65.5 

72.8 

88 

109 

16 

24.90 

33.3 

41.6 

50.0 

58.2 

66.6 

74.9 

83.2 

100 

125 

18 

28.10 

37.5 

46.8 

56.2 

65. 5 

74.9 

84.2 

93.6 

113 

140 

20 

31.20 

41.6 

52.0 

62.3 

72.8 

83.2 

93.6 

104.0 

125 

156 

22 

34.30 

45.8 

57.2 

68.6 

80.1 

91-5 

103.0 

114. 4 

138 

172 

24 

37.50 

50.0 

62.4 

75.0 

87.4 

99.8 

112. 3 

124.8 

150 

187 

26 

40.60 

54.0 

67.6 

81.2 

94.6 

108.2 

121. 7 

135.2 

163 

203 

28 

43.60 

58.2 

72.8 

87. S 

101.9 

116. 5 

131. 0 

145.6 

175 

218 

30 

46.80 

62.4 

78.0 

93.7 

109.2 

124.8 

140.4 

156.0 

188 

234 

32 

49.80 

66.6 

83.2 

100. 0 

116. 5 

133. 1 

150.3 

166.4 

200 

250 

36 

56.10 

75.0 

93.6 

112. 5 

131  0 

150.0 

168.4 

187.2 

225 

281 

For  larger  plates  take  size  of  plate  one-half  smaller  and  multiply  by  2.  Thus 
a  plate  28  by  32  in  will  weigh  twice  as  much  as  one  14  by  32  in.  For  plates  more 
or  less  than  one  inch  in  thickness  multiply  weight  of  plate  by  thickness  in  inches. 


Approximate  Weights  of  Square-Ribbed  Cast-Iron  Column-Bases 

The  following  table,  giving  the  weight  of  cast-iron  column-bases,  will  be  useful 
when  estimating  the  steel  and  iron  in  tall  buildings.* 


Size  of 

Size  of 

square 

Weight, 

square 

Weight, 

base. 

lb 

base, 

lb 

in     . 

in 

22X22 

600 

32X32 

1340 

24X24 

750 

34X34 

1450 

26X26 

880 

36X36 

I  600 

28X28 

I  020 

38X38 

I  720 

30X30 

I  180 

40X40 

I  850 

'  H.  G.  Tyrrell,  in  Architects  and  Builders  Magazine,  January,  1903, 


Screw-Threads,  Nuts  and  Bolt-Heads 


1525 


Screw-Threads,  Nuts,  and  Bolt-Heads 

Standard  Screw-Threads 

Recommended  by  Franklin  Institute,  December  15,  1864,  and  adopted  by  Navy  De- 
partment of  the  United  States;  by  the  R.  R.  Master  Mechanics'  and  Master  Car-Builders* 
Associations;  by  Jones  &  Laughlin  Steel  Company;  and  by  many  other  of  the  promi- 
nent engineering  and  mechanical  establishments  of  the  country. 


Angle  of  thread  60**.    Flat  at  top  and  bottom  H  of  pitch. 


Diam 

Diam  at 

Area  at 

Diam 

Threads 

Diam  at 

Area  at 

of 

Threads 

root  of 

root  of 

of 

root  of 

root  of 

screw, 

per  inch 

thread, 

thread. 

screw, 

per 
inch 

thread, 

thread, 

in 

in 

sq  in 

in 

in 

sq  in 

M 

20 

0.185 

-    0.027 

2 

4H 

1. 712 

2.302 

Vxi, 

18 

0.240 

0.045 

2\i 

4H 

1.962 

3.023 

v% 

16 

0.294 

0.068 

2I/2 

4 

2.176 

3.719 

Me 

14 

0.344 

0.093 

2Y^ 

4 

2.426 

4.620 

V2 

13 

0.400 

0.126 

3 

3V2 

2.629 

5.428 

%6 

12 

0.454 

0.162 

3H 

3H 

2.879 

6.510 

% 

II 

0.507 

0.202 

Z\'i 

3H 

3  100 

7  548 

% 

10 

0.620 

0.302 

3% 

3 

3.317 

8.641 

% 

9 

0.731 

0.420 

4 

3 

3  567 

9  963 

I 

8 

0.837 

0.550 

aH 

2li 

3  798 

11.329 

\M 

7 

0.940 

0.694 

aYi 

23/4 

4.028 

12.753 

iH 

7 

1.065 

0.893 

4^4 

2% 

4.256 

14.226 

^% 

6 

1. 160 

1.057 

5 

2H 

4.480 

15.763 

iH 

6 

1.284 

1.295 

sH 

2H 

4  730 

17.572 

iH 

5K2 

1.389 

1.51S 

5^2 

2% 

4.953 

19.267 

1% 

5 

1. 491 

1.746 

5H 

2% 

5.203 

21 . 262 

l7/i 

5 

1. 616 

2.051 

6 

2U 

5. 423 

23.098 

Nuts  and  Bolt-Heads  are  determined  by  the  following  rules,  which  apply  to  both 
square  and  hexagon  nuts: 

Short  diameter  of  rough  nut  =  iVz  X  diam  of  bolt  +  \^  int. 

Short  diameter  of  finished  nut  =  i^^i  X  diam  of  bolt  +  He  in. 

Thickness  of  rough  nut  =  diam  of  bolt. 

Thickness  of  finished  nut  =  diam  of  bolt  —  Me  in. 

Short  diameter  of  rough  head  =  iVz  X  diam  of  bolt  -{-  H  in. 

Short  diameter  of  finished  head  =  iVz  X  diam  of  bolt  +  Me  in. 

Thickness  of  rough  head  =  Vz  short  diam  of  head. 

Thickness  of  finished  head  =  diam  of  bolt  —  Me  in. 

The  long  diameter  of  a  hexagon  nut  may  be  determined  by  multiplying  the  short  di- 
ameter by  1.15  s,  and  the  long  diameter  of  a  square  nut  by  multiplying  the  short  diameter 
by  1. 414. 


1526 


Metal-Data 
Standard  Dimensions  of  Nuts  and  Bolt-Heads 


Thick- 

Thick- 

Thick- 

Short 

Short 

Long 

Long 

ness, 

ness, 

ness, 

Diam 

of 

bolt 

diam, 
rough       f 

diam, 
inished 

diam, 
rough 

diam, 
rough 

rough. 
Nut 

finished. 
Both 

r,  11,1 

rough. 
Head 

^ 

ri!!^' 

u 

H 

H 

7/16 

3^64 

Mo 

H 

Me 

H 

Me 

1?§2 

m2 

iHe 

1M2 

Me 

H 

1%4 

H 

^He 

H 

S^4 

6%4 

H 

Me 

11/^2 

Me 

2%2 

2  3/^2 

9/10 

IM64 

Me 

3/^ 

25/^4 

H 

^^ 

1^6 

I 

1I564 

H 

Me 

Me 

916 

31/^2 

2^k 

1% 

12  3/64 

M6 

H 

31/^4 

H 

iHe 

I 

I>^2 

iMe 

1I/2 
l4%4 

5i 
M 

Me 
iMe 

1M32 

H 

iH 

1^6 

H 

1^6 

l3/i 

12H2 

2H2 

H 

iMe 

2^2 

I 

IH 

iMe 

iH 

2l%4 

I 

iMe 

IMe 

iH 

iiM« 

l3/4 

2H2 

2M6 

iJ^ 

iMc 

2%2 

iH 

2 

11^6 

25/6 

25  36.1 

iKi 

iMe  . 

I 

i3/i 

2-M6 

2H 

2l%2 

33/^2 

I3/^ 

iMe 

l3/2 

iH 

23/^ 

2^6 

234 

32M64 

m 

iMe 

iMe 

iH 

2M6 

21/^ 

231/^2 

3% 

iH 

iMe 

l%2 

1% 

23/4 

211/6 

3'M6 

3"/64 

iM 

iiHo 

iH 

l74 

2IM6 

2j-i 

3»H2 

4^32 

i>i 

iiMe 

llMl2 

2 

3^ 

3M6 

3H 

42}^64 

2 

iiMe 

iMe 

2M 

3H 

3M6 

4M6 

4«>'64 

21/ 

2M6 

iM 

2H 

3T^ 

3IM6 

4H 

531/64 

2H 

2M6 

iiMe 

23/1 

4H 

4M6 

42^62 

6 

23/4 

21 1/6 

2H 

3 

4H 

4^6 

53/^ 

6i7;i2 

3 

2iMe 

2M6 

3'/4 

5 

A'YlB 

51  Me 

7M6 

3V4 

3Me 

21/2 

3V2 

5H 

SMe 

6%4 

73  9/64 

3H 

3Me 

21H6 

3% 

5% 

51  He 

621,^2 

8ii 

3M 

31  He 

2li 

4 

6\i 

61/6 

7H2 

841/64 

4 

3iMe 

3H6 

4M 

m 

7^6 

7M6 

9M6 

4}4 

4M6 

3H 

4V^ 

m 

613/6 

731,^2 

9M 

4I/2 

4M6 

3M6 

4% 

7H 

7Me 

81^2 

loH 

4M 

4HI6 

3-H 

5 

7H 

7«/l6 

82  ^^2 

I049/^4 

5 

4IM6 

3»Me 

5H 

8 

7iMe 

9?'32 

Il2%4 

5^/4 

She 

4 

5H 

mi 

85/ e 

92  3/^2 

1174 

5H 

5146 

4M6 

5M 

SH 

811/6 

I0-)^2 

1234 

SKi 

5^  Me 

4% 

6 

9H 

9M6 

1019^2 

i2iMe 

6 

5»M6 

4M6 

Weights  of  Bolts  and  Nuts 
Weights  of  One  Hundred  Bolts  With  Square  Heads  and  Nuts 

INCLUDES   WEIGHT   OF   NUT 

Hoopes  &  Townsend's  List 


1527 


Length 
under 
head 

to  point 
in 


r>4 

2 

2H 
2H 
2'H 

3 

4 

5 

6 

7 

iM 
8 
9 


13 
14 
15 
i6 
17 
i8 
19 


Diameter  of  bolts 


lb 

7.00 

7. SO 

8. CO 

8.50 

9.00 

9  50 

10.00 

11.00 

12.00 

13  00 

14.00 

15.00 

16.00 


lb 
10.50 

11.25 
12.00 
12.75 
13.50 
14.25 

15.00 

16.50 
18.00 

19.50 

21.00 
22.50 
24.00 

25.50 

27.00 

28.50 
30.00 


lb 
15 .  20 
16.30 
17.40 
18.50 
19.60 
20.70 
21.80 
24.00 
26.20 
28.40 
30.60 
32.80 
35.00 
37.20 
39.40 
41.60 
43.80 
46.00 
48:20 
50.40 
52.60 


Y'z  in, 
lb 


4.18 


22.50 
23.82 
25.15 
25.47 
27.80 
29.12 
30.45 
33.10 
35.75 
33. 40 
41.05 
43.70 
46.35 
49.00 
51.65 
54  30 
59 -60 
64.90 
70.20 
75.50 
80.80 
86.10 
91.40 
96.70 
102.00 
107.30 
112.60 
117.90 
123.20 

5.45 


39.50 

41.62 

43-75 

45.88 

48.00 

50.12 

52.25 

56.50 

60.75 

65.00 

69.25 

73.50 

77.75 

82.00 

86.25 

90.50 

94.75 

103.25 

III. 75 

120.25 

128.75 

137.25 

145.75 

154.25 

162.75 

171.00 

179.50 

188.00 

206.50 

8.52 


Vi  m, 
lb 


63.00 

66.00 

6^.00 

72.00 

75.00 

78.00 

81.00 

87.00 

93.10 

99  05 

IQS.20 

III. 25 

17.30 

123-35 

29.40 

135.00 

141.50 

153.60 

165.70 

177.80 

189.90 

202.00 

214.10 

226.20 

238.30 

250.40 

262 . 60 

274  70 

286.80 


/'S  in, 
lb 


109.00 
113  25 
117.50 
121.75 
126.00 
134.2s 
142.50 
151.00 
159. 55 
168.00 
176.60 
185.00 
193.65 
202.00 
210.70 
227.7s 
224.80 
261.85 
278 . 9c 
295.9s 
313.00 
330.05 
347.10 
364  IS 
381.20 
398.25 
415.30 

16.70 


Weights  of  Nuts  and  Bolt-Heads,  in  Pounds 

For  calculating  the  weight  of  longer  bolts 


Diameter  of  bolt,  in  inches 

M 

% 

Yz 

5^ 

H 

% 

Weight  of  hexagon  nut  and  head. . . 
Weight  of  square  nut  and  head 

0.017 
0.021 

0.057 
0.069 

0.128 
0.164 

0.267 
0.320 

0.43 
0.55 

0.73 
0.88 

Diameter  of  bolt,  in  inches . 

I 

m 

1K2 

1% 

2 

2\i 

3 

Weight  of  hexagon  nut  and  head . . . 
Weight  of  square  nut  and  head 

1. 10 
1. 31 

2.14 
2.56 

3.78 

4.42 

5.6 

7.0 

8.75 
10.50 

17 
21 

28.8 
36.4 

1528  Metal-Data  Part  3 

Weights  of  Rivets  and  Round-Headed  Bolts  Without  Nuts.     Steel 


POUNDS   PER  HUNDRED 


Length, 

H  in 

■}4  in 

^6  in 

I  in 

1%  in 

iH  in 

I'^iin 

H'm 

in 

diam 

diam 

diam 

diam 

diam 

diam 

diam 

diam 

iH 

5.5 

12.8 

22.0 

293 

43.9 

66.6 

93-3 

127 

iVz 

6.3 

14.2 

24.1 

32.4 

48.2 

72.1 

100 

136 

iH 

7.0 

15.5 

26.3 

35. 5 

52.5 

77-7 

107 

145 

2 

7.9 

16.9 

28.5 

38.7 

56.7 

83.3 

114 

153 

2H 

8.7 

18.3 

30.7 

41.8 

61.0 

88.8 

121 

162 

2yz 

9-4 

19.7 

32.8 

44.9 

65.2 

94-4 

128 

171 

2->4 

10.2 

21. 1 

3S.0 

48.0 

69. 5 

100. 

136 

179 

3 

II. 0 

22.5 

37.2 

51. 1 

73.7 

105. 

143 

188 

3H 

II. 7 

23.9 

39-3 

54.3 

78.0 

Ill 

150 

197 

s'A 

12.6 

25.3 

41.5 

57.4 

82.3 

116 

157 

205 

3% 

13.4 

26.7 

43.7 

60.5 

86.5 

122 

164 

214 

4 

14. 1 

28.1 

45.9 

G3.6 

90.8 

128 

170 

223 

4U 

14-9 

29.4 

48.0 

66.7 

95.0 

134 

177 

231 

4H 

15.7 

30.8 

50.2 

69.9 

99-3 

139 

185 

240 

4% 

16.5 

32.2 

52.4 

730 

104 

145 

192 

349 

5 

17.2 

33.6 

54. 5 

76.1 

108 

150 

199 

258 

SH 

18. 1 

35.0 

56.7 

79-2 

112 

156 

206 

266 

sVz 

18.8 

36.4 

58.9 

82.3 

116 

161 

213 

275 

sH 

19.6 

37.8 

61. 1 

•85.5 

120 

166 

220 

284 

6 

20.4 

39.2 

63.2 

88.6 

124 

172 

227 

292 

6H 

21.9 

42.0 

67.6 

95.1 

133 

184 

241 

310 

7 

235 

44.7 

71.9 

lOI 

142 

195 

255 

327 

7K2 

25.1 

47.5 

76.1 

108 

150 

206 

269 

345 

8 

26.6 

SO. 3 

80.6 

114 

159 

217 

284 

362 

8H 

28.2 

53.1 

85.0 

120 

167 

227 

•298 

379 

9 

29.8 

55.9 

89.3 

126 

176 

239 

312 

397 

9H 

31-3 

58.7 

93-7 

133 

18S 

250 

325 

414 

10 

32.8 

61.4 

98.0 

139 

193 

261 

340 

431 

loV^ 

34-5 

64.2 

103 

145 

202 

272 

354 

449 

II 

36.0 

67.0 

107 

151 

210 

284 

368 

466 

iii/i 

37.6 

69.8 

III 

158 

218 

295 

382 

484 

12 

39-2 

72. 5 

115 

164 

227 

306 

396 

501 

Heads 

1.8 

5.8 

II. I 

13.6 

22.6 

39- 0 

58.0 

83.5 

For  length  of 

shaft  re 

quired  to 

form  riv€ 

t-head,  s 

i^  Table 

IV,  page 

420. 

Nails  1529 

NAn.S  AND  SCREWS* 

Nails.  Based  upon  the  process  of  manufacture  there  are  three  kinds  of  nails 
in  common  use,  namely,  plate  or  cut  nails,  wire  nails,  and  clinch-nails.  These 
are  briefly  described  in  the  following  subdivisions  of  this  article  and  other  data 
bearing  on  the  subject  is  included. 

(i)  Cut  Nails.  Cut  nails  are  made  from  a  strip  of  rolled  iron  or  steel  of  the 
same  thickness  as  the  finished  nail  and  a  little  wider  than  its  length,  the  fiber 
of  the  iron  being  parallel  with  the  length  of  the  nail.  Special  machinery  cuts 
the  nails  out  in  alternate  wedge-shaped  slices,  the  heads  are  then  stamped 
on  them  and  the  finished  n'ails  droj^ped  into  the  casks.  Cut  nails  made  from  iron 
are  generally  preferred  for  use  in  exposed  positions.  Cut  nails  are  made  in  a 
variety  of  shapes  to  suit  special  uses.  For  ordinary  use  in  building,  nails  of  three 
different  shapes  are  made,  and  the  nails  are  called  common  nails,  finish-nails 
and  CASING-NAILS.  The  common  nails  are  used  for  rough  work,  finish-nails  for 
finished  work,  and  casing-nails  for  flooring,  matched  ceiling  and  sometimes  for 
pine  casings,  although  the  heads  are  rather  too  large  for  finish-work.  Cut  nails 
are  beginning  to  return  to  favor  as  they  have  holding  power  and  lasting  qualities 
superior  to  wire  nails. 

(2)  Brads.  Brads  are  thin  nails  with  a  small  head,  used  for  smaU  finish,  panel- 
moldings,  etc.     They  vary  from  H  to  2  in  in  length. 

(3)  Clout-Nails.  Clout-nails  are  made  with  broad,  flat  heads,  and  are  sold 
in  sizes  varying  from  %  to  2y>  in  in  length.  They  are  used  chiefly  for  fastening 
gutters  and  metal- work.  Special  nails  are  also  made  for  lathing,  slating,  shing- 
ling, etc. 

(4)  Wire  Nails.  These  have  of  late  years  become  as  common  as  the  cut  nails, 
and  are  sold  at  about  the  same  price.  They  are  said  to  be  stronger  for  driving 
than  the  cut  nails,  not  so  liable  to  bend  or  break,  especially  when  driven  into  hard 
woods,  and  less  liable  to  split  the  wood;  for  these  reasons  they  are  generally 
preferred  by  carpenters.  Wire  nails  are  made  from  wire,  of  the  same  section- 
diameter  as  the  shank  of  the  nail,  by  a  machine  which  cuts  the  wire  in  even 
lengths,  heads  and  points  them,  and;  when  desired,  also  barbs  them.  In  general 
the  same  classification  is  used  for  cut  nails.  It  should  be  noticed  that  the  gauge 
of  the  wire  and  the  shape  of  the  head  vary  in  the  different  kinds,  and  that  some 
are  barbed,  others  plain.  The  various  types  of  wire  nails  are  drawn  round, 
SMOOTH  or  BARBED,  for  the  domestic  trade;  for  export  they  are  drawn  oval, 
SQUARE,  or  DIAMOND-SHAPED,  according  to  the  country  to  which  they  are  to  be 
shipped  and  its  requirements.  It  is  customary  to  charge  15  cents  more  per  100 
lb  for  standard  nails,  barbed,  than  for  the  same  nails,  smooth. 

(5)  Clinch-Nails.  These  are  made  from  open-hearth  or  Bessemer-steel  wire. 
Any  ordinary  wire  nail  will  chnch,  especially  when  made  with  duck-bill  or 
flattened  points  for  clinching  purposes,  or  even  otherwise,  if  annealed.  These 
nails  are  used  only  in  places  where  it  is  desired  to  turn  over  the  ends  of  the  nails 
to  form  a  clinch,  as  in  the  case  of  battens  or  cleats. 

(6)  Length  and  Weight  of  Nails.  The  length  of  nails  is  designated  by  pen- 
nies id's).  This  classification  originally  represented  the  price  in  English  pence 
per  100  nails,  as  2d  per  100,  etc.  In  that  sense  it  is  of  course  now  obsolete,  but 
it  is  stiU  retained  and  is  practically  uniform  with  the  various  manufacturers, 
both  for  cut  and  wire  nails.  The  weights  expressed  in  pennies  run  from  two 
pennies  to  sixty  pennies,  the  larger  sizes  being  designated  by  fractions  of  an  inch. 

*  Condensed  from  article  by  Thomas  Nolan  in  chapter  on  Builders'  Hardware  in  re- 
vised edition  of  Building  Construction  and  Superintendence,  Part  II,  Carpenters'  Work' 
by  F.  E.  Kidder, 


1530  Nails  and  Screws  Part  3 

The  sizes  and  lengths  of  various  kinds  of  nails  and  tacks  are  given  in  tables  on 
pages  153 1    to   1534. 

(7)  Sizes  of  Nails  for  Different  Classes  of  Work.  It  is  imperative  for  first- 
class  work  that  nails  of  proper  size  should  be  used  and  to  insure  the  best  results 
it  is  well  in  certain  classes  of  work  to  specify  the  sizes  which  are  to  be  used.  For 
framing,  twentypenny,  fortypenny  and  sixtypenny  nails,  or  spikes,  are  used, 
according  to  the  size  of  the  timber.  For  sheathing  and  roof-boarding,  under- 
floors  and  cross-bridging,  tenpenny  common  nails  should  be  used.  For  over- 
floors  tenpenny  floor-nails  or  casing-nails  should  be  used  for  jointed  boards,  and 
ninepenny  or  tenpenny  for  matched  flooring,  although  eightpenny  nails  are 
sometimes  used.  Ceiling  when  H  in  thick  is  generally  put  up  with  eightpenny 
casing-nails,  and  when  thinner  stuff  is  used,  with  sixpenny  nails.  For  inside 
finish  any  size  of  finish-nails  or  brads  from  eightpenny  down  to  twopenny  is  used, 
according  to  the  thickness  and  size  of  the  moldings.  For  pieces  exceeding  i  in 
in  thickness,  tenpenny  nails  should  be  used.  Clapboarding  is  generally  put  on 
with  sixpenny  finish-nails  or  casing-nails.  Fourpenny  nails  should  be  used  for 
shingling  and  slating,  and  threepenny  for  lathing.  For  slating,  galvanized  nails 
should  be  used,  and  they  are  also  better  for  shingling.  Whether  wire  or  cut  nails 
should  be  used  may  generally  be  left  to  the  builder;  but  in  places  where  there  is 
any  danger  of  the  nails  being  drawn  out  either  by  the  warping  of  the  boards  or 
from  the  pull  of  the  nail,  cut  nails  should  be  used,  as  they  have  greater  holding 
power  than  the  wire  nails  under  certain  conditions.  It  is  generally  understood 
that  a  wire  nail  will  hold  more  firmly  when  barbed  than  when  smooth.  (See 
page  1 531  for  tests.) 

(8)  Copper  and  Brass  Nails.  Nails  are  also  made  of  copper  and  cast  brass, 
and  these  are  sometimes  used  in  connection  with  boat-building,  refrigerator- 
work,  etc.  One  wing  of  the  Physical  Laboratory  Building  of  Harvard  College 
is  put  together  entirely  with  brass  and  copper.  As  the  rooms  were  intended  for 
use  in  delicate  electrical  work,  no  iron  was  used  in  their  construction. 

(9)  Cement-coated  Wire  Nails.  The  coating  consists  of  various  resinous 
gums  mixed  by  a  secret  formula,  and  put  on  the  nails  by  a  baking-process  which 
involves  the  use  of  quite  complicated  machinery.  Although  the  chief  market 
for  coated  nails  is  among  the  users  of  packages  to  be  shipped,  there  is  a  limited 
market  for  them  among  builders,  for  construction-purposes.  The  chief  merit  of 
the  coating  is  that  it  gives  the  nail  an  adhesive  resistance  approximately  twice 
that  of  ordinary  wire  nails.  This  quality  appeals  especially  to  the  manufacturers 
and  users  of  packages  to  be  shipped,  for  which  strength  is  particularly  wanted.  It 
is  desirable  for  construction-purposes  also,  but  the  lack  of  holding  power  in  plain 
wire  nails  is  not  so  apparent  in  building.  About  90%  of  the  output  goes  to  box- 
factories  and  large  shippers.*  Cement-coated  nails  are  quite  widely  used,  also, 
in  laying  both  ordinary  and  parquetry-flooring.  The  use  of  these  nails,  with  a 
special  head  which  leaves  a  small  hole,  gives  a  firm  floor  and  prevents  springing. 
Though  the  makers  do  not  claim  that  the  nails  are  absolutely  rust-proof,  they  do 
claim  that  nails  thus  treated  will  resist  the  effects  of  moisture  from  20  to  50% 
better  than  the  uncoated  wire  nails.  But  it  is  when  in  use  that  the  non-rusting 
quality  is  most  evident.  There  is  more  coating  on  the  nails  than  is  actually 
necessary  for  holding  power.  The  heat  caused  by  the  friction  of  driving  the 
nail  softens  the  coating  and  the  surplus  is  forced  toward  the  head,  completely 
closing  the  opening;  this  prevents  the  admission  of  moisture  between  the  wood 
and  the  nail.  Under  similar  conditions,  the  life  of  a  cement-coated  nail  will  be 
about  twice  as  long  as  that  of  an  uncoated  one.  Less  force  is  needed  to  drive  a 
coated  nail  as  the  softened  coating  forms  a  lubricant.    These  nails  are  made  in 

*  Of  this  amount  about  60%  is  made  by  the  J.  C.  Pearson  Company. 


Holding  Power  of  Nails 


1531 


two  types,  differing  only  in  the  heads,  and  are  either  coolers  or  sinkers. 
The  former  have  large  flat  heads;  the  latter,  heads  slightly  reinforced  by  counter- 
sinking. They  are  made  to  replace  common  nails,  in  sizes  from  H  in  to  i  in, 
and  are  used  for  framing,  boarding,  shingling  and  staging,  and  for  boxes  and 
crates.  Results  of  tests  made  with  cement-coated  nails  to  determine  their 
adhesive  resistance  in  comparison  with  the  common  smooth-wire  nails  are  given 
below. 

The  following  table  shows  the  result  of  tests  made  at  the  United  States  Arsenal, 
Watertown,  Mass.,  in  1902,  the  wood  being  pine: 

Comparative  Adhesive  Resistance  of  Common  Smooth- Wire  Nails  and 

Cement-Coated  Nails 
All  nails  were  driven  into  the  same  piece  and  were  perpendicular  to  the  grain 


Size  and  name 


Tenpenny,  common,  smooth.  .  , 

Tenpenny,  coated 

Ninepenny,  common,  smooth.  . 

Ninepenny,  coated • 

Eightpenny,  common,  smooth. 

Eightpenny,  coated 

Sixpenny,  common,  smooth.  . . , 
Sixpenny,  coated 


Diameter, 


0.145 
0.117 
0.132 
0.114 
0.132 
0.112 
0.097 
0.092 


Length 
driven,* 


2;  2 

2H 


iH 


Adhesive 

resistance,  t 

lb 


167 
418 
182 
327 
189 
316 
106 
226 


*  All  of  the  nails  were  left  with  their  heads  projecting  from  ] 
t  Average  of  three  trials. 


:  to  H 


Holding  Power  of  Nails.  A  committee  appointed  by  the  Wheeling  nail- 
manufacturers,  a  number  of  years  ago,  to  test  the  comparative  holding  power  of 
cut  and  wire  nails,  published  the  following  data,  although  the  kind  of  wood  is  not 
named. 

Pounds  Required  to  Pull  Nails  Out 


Cut 

Wire 

Cut 

Wire 

Twentypenny 

Tenpenny 

Eightpenny 

I  593 
908 
597 

703 
31S 

227 

Sixpenny 

383 

286 

200 
123 

Fourpenny  . 

The  holding  power  of  nails  varies  with  the  kind  of  wood  into  which  they  are 
driven.  Austin  T.  Byrne  gives  the  relative  holding  power  of  woods  as  about  ad 
follows:  White  pine,  i;  yellow  pine,  1.5;  white  oak,  3;  chestnut,  1.6;  beech,  3.2; 
[feycamore,  2;   elm,  2;   basswood,  1.2. 

Comparative  Holding  Power  of  Cut  and  Wire  Nails 
Very  thorough  tests  of  the  comparative  holding  power  of  wire  nails  and  cut 
tiails  of  equal  lengths  and  weights  were  made  at  the  U.  S,  Arsenal  in  1892  and 
1893.  From  forty  series,  comprising  forty  sizes  of  nails  driven  in  spruce  wood,  it 
was  found  that  the  cut  nails  showed  an  average  superiority  of  60.50%,  the  com- 
mon nails  showing  an  average  superiority  of  47 -51%  and  the  finishing-nalls  an 
iivera^e  of  72.22%.  In  eighteen  series,  comprising  six  sizes  of  box-nails  driverb 
into  pine,  wood,  in  three  ways  the  cut  nails  showed  an  average  superiority  o^ 
99-93%'    I"  "<^  series  of  tests  did  the  wire  nails  hold  as  much  as  the  cut  nails* 


1532 


Nails  and  Screws 


Quantity  of  Nails  Required  for  Different  Kinds  of  Work 


For  I  coo  shingles  allow  5  lb  fourpenny  nails  or  3\i  lb  threepenny 

I  000  laths,  7  lb  threepenny  fine,  or  for  100  sq  yd  of  lathing,  10  lb  threepenny  fine 

I  000  sq  ft  of  beveled  siding,  18  lb  sixpenny 

I  000  sq  ft  of  sheathing,  20  lb  eightpenny  or  25  lb  tenpenny 

I  000  sq  ft  of  flooring,  30  lb  eightpenny  or  4O  lb  tenpenny 

I  000  sq  ft  of  studding,  15  lb  tenpenny  and  s  lb  twentypenny 

I  000  sq  ft  of  I  by  2H-in  furring,  12-in  centers,  9  lb  eightpenny  or  14  lb  tenpenny 

I  000  sq  ft  of  I  by  2^^-in  furring,  i6-in  centers,  7  lb  eightpenny  or  10  lb  tenpenny 


Cut  Steel  Nails  and  Spikes 

Sizes,  lengths,  and  approximate  number  per  pound 

Taken  from  the  Handbook  of  the  Cambria  Steel  Company 


Sizes 

Ivength, 
inches 

Common 

Clinch 

Finishing 

Casing 
and  box 

Fencing 

Spikes 

2d 

3d 
Ad 
Sd 
6d 
Id 
8d 
gd 

lOd 

I2d 
i6d 

20d 
25d 
30d 

40d 
sod 
6od 

I 

iy2 

2 

2% 

2\^. 
2% 

3 

3K2 

4 

A\i 

A\i 

5 

5K2 

6 

7 

740 
460 
280 
210 
160 
120 
88 
73 
60 
46 
33 
23 
20 

12 
10 

8 

4CO 
260 
180 

I  100 
880 
530 

17 
14 

II 
9 

6 

sVi 

5 

420 
300 
210 
180 
130 

107 

88 
70 
52 
38 

125 

100 
80 
68 
52 
48 
40 
34 
24 

350 
300 
210 
168 
130 
104 
96 
86 
76 

100 
80 
60 
52 
38 
26 
20 
18 
16 

30 
26 
20 
16 

Sizes 

Length, 
inches 

Barrel 

Light 
barrel 

Slating 

Sizes 

Lent 
incl 

Jth, 
les 

Flat 
grip, 
fine 

I  462 

I  300 

I  100 

800 

650 

Edge- 
grip, 
fine 

"96o' 
750 
600 

'"2d" 

""3d" 

""^d" 
5d 
M 
Id 
M 
9d 
lod 

I2d 

i6d 

% 

I 

iH 

i|4 

iVs 

iH 

i?4 

2 

2H 

2H 

2% 

3 

3H 

3H 

750 
600 
Soo 
450 
310 
280 
210 
190 

400 
304 

224 

I 

2d 

3d 
Ad 

340 

280 

Tobacco 

Brads 

Shingle 

220 
180 

130 
97 
85 
68 
58 
48 

120 
94 
74 
62 
50 
40 
27 

90 
72 
60 

Nails,  Spikes  and  Tacks 


1533 


Steel-Wire  Nails,  Spikes,  and  Tacks 

SIZE,    LENGTH,    GAUGE   AND   APPROXIMATE   NUMBER   TO   THE   POUND 

Compiled  from  Catalogue  of  American  Steel  and  Wire  Company,  1910 

American  Steel  and  Wire  Company's  gauge.     (See  page  151 2.) 


Common  nails  and  brads  * 

Casing-nails  \ 

Finishing-nailst 

Number 

Number 

Number 

Size 

Length, 

Gauge 

to 

Gauge 

to 

Gauge 

to 

in 

pound 

pound 

pound 

2d 

I 

15 

876 

15I/2    . 

I  010 

16I/2 

I3SI 

3d 

iM 

14 

568 

I4V^ 

63s 

15K2 

807 

4</ 

\Vi 

12^2 

316 

14 

473 

15 

S84 

5^ 

1% 

121/^ 

271 

14 

406 

IS 

500 

6^ 

2 

IIK2 

181 

12^^ 

236 

13 

309 

7d 

2J/1 

IIV2 

161 

12^.2 

210 

13 

238 

Sd 

2yi. 

io'/4 

106 

11^2 

145 

1 2 1/2 

189 

9d 

2% 

loH 

96 

I1I/2 

132 

12  K2 

172 

lod 

3 

9 

69 

loH 

94 

IIK2 

121 

I2d 

3'/i 

9 

63 

IOK2 

87 

iiH 

113 

i6d 

3V2 

8 

49 

10 

71 

II 

90 

20d 

4 

6 

31 

9 

52 

10 

62 

3od 

4V2 

5 

24 

9 

46 

Aod 

5 

4 

18 

8 

35 

sod 
6od 

sVi 

6 

3 

2 

14 
II 

Shingle-nails 

Number 

Size 

Length, 

Gauge 

to 

Spikes  t 

in 

pound 

3d 

iVi 

13 

429 

Size 

Length, 
in 

Gauge 

Number 
to 

3\U 
Ad 

1% 
iy2 

I2l/^ 
12 

34S 
274 

pound 

Sd 

iM 

12 

.23s 

6d 

12 

204 

Id 

2H 

II 

139 

lOd 

3 

6 

41 

Sd 

2H 

II 

I2S 

12d 

3^4 

6 

38 

gd 

2% 

II 

114 

i6d 

3K2 

5 

30 

lOd 

3 

10 

83 

20d 

4 

4K> 

4 

23 

30d 

3 

17 

Fine  nails 

4od 
sod 

5 

5H 

2 
I 

13 
10 

2d 

I 

16K2 

I3SI 

God 

6 

I 

5/    tt 

9 

3d 

1% 

IS 

778 

1" 
8" 
9" 

7 
8 
9 

716 

7 
4 
3H 

4d 

2d 

extra  fine 

1I/2 

}  ^ 

14 
17 

473 
iS6o 

10" 

10 

w 

3 

3d 
extra  fine 

1     iH 

12" 

12 

w 

2\^ 

16 

I  CIS 

*  Common  brads  differ  from  common  nails  only  in  the  head  and  point, 
t  Lengths  are  the  same  as  common  nails  for  corresponding  size. 

X  Spikes  are  made  with  chisel-points  and  diamond  points;  also  with  convex  heads  and 
fiat  heads. 


1534 

Nails  and  Screws 

Part  3 

Steel-Wire 

Nails  (Continued) 

Clinch-nails 

Fence-nails  * 

Slating-nails  * 

Number 

Number 

Number 

Size 

Length, 

Gauge 

to 

Gauge 

to 

Gauge 

to 

in 

pound 

pound 

pound 

2d 

I 

14 

710 

12 

411 

3d 

iH 

13 

429 

No  5  smallest 

10K2 

225 

4d 
5d 

i\^ 

274 

235 

I0l/'2 

187 

1)4 

12 

10 

142 

10 

142 

6d 
Id 
U 

2 

2H 
2H 

II 
II 
10 

157 
139 
99 

10 
9 
9 

124 

92 
82 

9 

103 

Barbed  roofing-nails  t 

9d 

2-Xl 

10 

90 

8 

62 

^4"XNo  13 

714. 

lOd 

3 

9 

69 

7 

50 

^8"XNoi2 

469 

12d 

3H 

9 

62 

6 

40 

i"XNo  12 

411 

i6d 

3li 

8 

49 

5 

30 

iH"XNoi2 

365 

20i 

4 

7 

37 

4 

23 

iH"XNoii 

251 

*  Length  same  as  clinch-nails  of  corresponding  size. 

t  Roofing-nails  are  designated  by  the  length,  not  by  penny.     These  nails  are  made  in 
lengths  up  to  2  in. 

Wire  Tacks 


Title, 
ounce 

Number 

Title, 
ounce 

Length, 
in 

Number 

per 
pound 

Title, 
ounce 

Length, 
in 

Number 

per 
pound 

in 

per 
pound 

I 

2 

2H 

3 

H 
Me 

16  000 
10666 
8000 
6  400 
5  333 

4 
6 
8 
10 
12 

Me 
•Me 

iHe 
% 

4  000 
2666 
2  000 
I  600 
1333 

14 
16 
18 
20 
22 
24 

i-Me 

iMe 
I 

iHe 

iH 

I  143 
I  000 
888 
800 
727 
666 

Wire  carpet -tacks  are  made  polished,  blued,  tinned,  or  coppered;  there  are  also  uphol- 
sterers' and  bill-posters'  or  railroad  tacks. 

Expansion-Bolts.  These  are  commonly  used  for  bolting 
wood  or  iron  to  masonry  that  is  already  built.  A  hole  is 
drilled  in  the  masonry  of  such  size  that  the  expansion-nut  will 
fit  closely,  and  when  the  bolt  is  screwed  up  the  nut  expands 
and  binds  firmly  in  the  masonry.  The  illustration  shows  the 
Evans  expansion-bolt,  which  is  also  furnished  with  screw-head 
bolts.  There  are  other  forms  of  expansion-bolts  on  the  market. 
From  experiments  on  expansion-bolts  it  was  found  that  the 
holding  capacity  was  264  lb  per  sq  in  when  embedded  in  i :  2 
Portland  cement  mortar,  843  per  sq  in  when  embedded  in 
sulphur  and  485  lb  per  sq  in  when  embedded  in  lead.  For 
average  working  unit-stresses  it  is  safe  to  use  about  one-fifth  of 
.    When  the  work  is  exposed  to  rain  or  moisture  sulphur  should 


Expansion-bolt 
the  values  given 


Screws  1535 

not  be  used  as  the  acid  which  results  will  rust  the  metal  and  will  also  tend  to 
disintegrate  the  masonwork  at  the  point  of  entrance  of  the  bolt. 

Screws.  The  substitution  of  screws  for  nails  in  building  operations  is  a 
marked  feature  of  modern  work.  Trimming  hardware  of  all  descriptions  is  put 
on  with  screws,  and  a  great  deal  of  panel-work,  inside  finish,  etc.,  is  put  together 
with  them.  Stop-beads,  the  casings  of  plumbing-fixtures,  etc.,  should  be  fas- 
tened with  screws,  as  well  as  all  kinds  of  store  and  office-fixtures,  and  cabinet- 
work in  general,  except  where  the  joints  are  glued.  Screws  are  also  largely  used 
in  making  furniture.  They  present  a  neater  appearance  than  nails,  have  greater 
holding  power  and  are  less  apt  to  injure  the  material  if  it  should  be  removed  and 
replaced.  By  making  holes  for  the  screws  with  a  bit,  all  danger  of  splitting  the 
finish  is  averted.  The  ordinary  type  of  screw  has  a  gimlet-point  by  which  it  can 
be  turned  into  the  wood  without  the  aid  of  a  bit.  The  heads  are  made  in  various 
forms  to  suit  different  uses.  Screws  are  made  ordinarily  of  steel,  but  sometimes; 
of  brass  and  bronze.  The  latter  sort  are  used  for  screwing  in  place  finished  hard- 
ware of  the  same  material,  and  have  heads  finished  to  correspond  with  the  trim- 
mings. Steel  screws,  also,  are  finished  with  blue,  bronze,  lacquered,  galvailized, 
or  tinned  surface,  to  match  the  cheaper  class  of  trimmings.  The  galvanized 
finish  is  used  in  building  operations  at  the  seasliore.  Screws  with  blue  surface, 
called  RLUED  screws,  are  generally  used  with  japanned  hardware  and  for  stop- 
beads,  and  wherever  a  cheap  round-headed  screw  is  desired.  Silver,  nickel,  and 
gold-plated  screws  are  also  manufactured  for  use  in  connection  with  similar 
hardware.  Steel  screws  for  wood  are  made  in  twenty  different  lengths,  varying 
from  li  to  6  in,  and  each  length  of  screw  has  from  six  to  eighteen  varieties  in 
thickness,  there  being  in  all  thirty-one  dif- 
ferent gauges;  so  that  altogether  there  are 
in  the  market  about  two  hundred  and  fifty 
different  sizes  of  ordinary  screws  used  for 
woodwork.  The  most  common  shapes  are 
the  ordinary  flat  head,  round  head  and  oval 
head.  The  oval-head  screw  is  tapered  for 
countersinking  but  is  slightly  rounded  on  top.  Lag  and  Coach-screws 

Patent  diamond-point  steel  screws  are  made 

especially  for  driving  with  a  hammer.  These  can  be  driven  with  a  hammer 
their  entire  length  into  any  hard  wood,  and  then  held  by  one  or  two  turns  as 
securely  as  the  ordinary  screw.  In  ordering  screws  both  the  length  and 
number  of  the  gauge  or  diameter  of  the  shank,  the  material  and  finish,  and 
the  use  to  which  they  are  to  be  put,  should  be  given. 

Screws  for  Metal  have  the  same  diameter  throughout  and  the  threads  are  V- 
shaped. 

Sizes  of  Screws.  The  sizes  of  screws  are  given  in  length  in  inches  and  the 
number  of  the  gauge,  the  gauge  denoting  the  diameter.  Thus,  a  i-in  No.  12  screw 
is  I  in  long  and  0.2158  in  in  diameter.  The  gauge-numbers  range  from  o  to  30 
and  the  lengths  from  H  to  6  in.  The  lengths  vary  by  eighths  of  an  inch  up  to 
I  in,  by  quarters  of  an  inch  up  to  3  in  and  by  halves  of  an  inch  up  to  5  in.  Screws 
from  %  to  4\-2  in  long  are  made  in  about  sixteen  different  gauge-numbers.  Table 
XIII,  page  402,  gives  the  diameter  to  four  places  in  decimals  of  an  inch  of  the 
American  screw-gauge.  It  should  be  noticed  that,  unlike  the  ordinary  wire- 
gauges,  the  o  of  the  screw-gauge  indicates  the  diameter  of  the  smallest  screw 
while  the  diameter  of  the  screw  increases  with  the  number  of  the  gauge. 

Lag-Screws  and  Coach-Screws  are  large,  heavy  screws  used  where  great 
strength  is  required,  as  in  heavy  framing,  and  for  fixing  ironwork  to  timber. 


D 


1536 


Data  on  Excavating 


Part  3 


Lag-screws  with  conical  point  are  made  with  diameters  of  Me,  H,  Me,  Vz,  ^le,  H, 
%,  and  I  in,  and  in  lengths  from  1^2  to  12  in;  coach-screws  in  diameters  from  Me 
to  %  in  and  in  lengths  from  1^2  to  12  in.  For  putting  in  lag-screws  a  hole 
should  be  bored  which  has  a  diameter  a  little  greater  than  the  unthreaded  shank 
of  the  screw  and  it  should  be  bored  to  a  depth  corresponding  to  the  length  of  the 
unthreaded  shank.  A  second  hole  should  then  be  bored  at  the  bottom  of  the 
first  hole  of  a  diameter  somewhat  less  than  that  of  the  threaded  shank  and  to  a 
depth  of  about  half  its  length. 

Holdmg  Power  of  Lag-Screws 
Tests  made  by  A.  J.  Cox,  University  of  Iowa,  1891,  quoted  by  Kent,  page  324 


Kind  of  wood 

Size  of 
screw, 

in 

Size  of 

hole 
bored, 

in 

Length 

in 
wood, 

in 

Maximum 
resist- 
ance, 

lb 

Number 

of 

tests 

Seasoned  white  oak 

'A 

9/16 

I2 

4H 

3 

4K2 

4 

4 

8037 
6480 
8780 
3800 
3  40.'5 

3 

I 
2 

2 
2 

Seasoned  white  oak 

Seasoned  white  oak 

Yellow-pine  st'ck .... 

White  cedar,  unseasoned 

Hoopes  &  Townsend  give  the  force  required  to  draw  screws  out  of  yellow  pine 
as  follows: 


Screw 

Wood,  depth 

Force,  pounds 


\^  in 


3M  in 

4960 


'H  in 


4  m 
6  000 


4  m 
7  685 


T^in 


5  in 
II  500 


6  in 
12620 


Wooden-screws  are  sold  by  the  gross,  lag-screws  and  coach-screws  by  the 
pound. 

DATA  ON  EXCAVATING  * 

Excavating  is  almost  invariably  measured  by  the  cubic  yard  of  27  cu  ft.  For 
measuring  excavations  of  irregular  depth  see  page  65.  For  computing  the  con- 
tents of  wells  and  cesspools,  the  circular  area  in  square  feet  may  be  obtained  from 
the  table  on  page  51,  and  this  circular  area  multiplied  by  the  depth  in  feet  will 
give  the  contents  in  cubic  feet.  The  cost  of  excavating  and  removing  earth  is 
ordinarily  made  up  of  the  following  items: 

(i)  Loosening  the  earth  for  the  shovelers; 

(2)  Loading  by  shovels  into  carts  or  barrows; 

I3)  Hauling  or  wheeling  it  away,  including  emptying  and  returning; 

(4)  Spreading  it  out  on  the  dump; 

For  every  large  job,  such  as  railroad-work,  it  is  also  necessary  to  make  an  al- 
lowance for  keeping  the  hauling-road  in  repair,  for  sharpening  and  repair  of  tools, 
and  for  carts,  harness,  superintendence  and  water-carriers.  Where  the  dirt 
excavated  can  be  spread  over  the  ground  immediately  surrounding  the  excava- 
tion the  loosened  dirt  may  be  removed  by  scrapers  without  shoveling. 

Data  for  Estimating  Cost  of  Loosening  Earth.  Two  men  with  a  plough  and 
team  of  horses  will  loosen  from  20  to  30  cu  yd  of  strong,  heavy  soil  per  hour  or 

*  All  prices  given  are  pre-war  prices  and  are  retained  for  purposes  of  comparison  of 


Data  on  Excavating  1537 

from  40  to  60  cu  yd  of  ordinary  loam.  One  man  with  a  pick  will  loosen  iH  yd 
per  hour  of  stifiE  clay  or  cemented  gravel,  4  yd  of  common  loam,  or  6  yd  of  light 
sand. 

The  average  quantity  of  loosened  earth  that  a  man  can  shovel  into  a  cart 
per  hour  is: 

Loam  or  sand .• 2 .0  cu  yd 

Clay  and  heavy  soils i .  7  cu  yd 

Rock ' 1.0  cu  yd 

Average  earth  when  loosened  swells  to  from  iH  to  iH  times  its  original  bulk 

in  place. 

The  capacity  of  vehicles  used  for  moving  excavated  materials  is  about  as 

follows: 

Wheelbarrows "  3  to    4  cu  f t 

One-horse  dump-carts 18  to  22  cu  ft 

Two-horse  dump-wagons 27  to  45  cu  ft  * 

Drag-scrapers 3  to    7  cu  ft 

Wheel-scrapers 10  to  17  cu  ft 

Dump-cars  on  rails 27  to  80  cu  ft 

The  Economical  Length  of  Haul  with  drag-scrapers  is  about  150  f t ;  with 
wheeled  scrapers,  500  ft;  with  wheelbarrows,  250  ft;  with  one-horse  dump-carts, 
600  ft.f     The  average  speed  of  horses  is  given  as  about  200  ft  per  minute. 

Much  valuable  data  for  estimating  %  the  cost  of  excavating  may  be  found  in 
the  Civil  Engineer's  Handbooks. 

Weight  of  Earth,  Sand  and  Gravel.  For  general  calculations  the  following 
average  values  may  be  taken: 


14  cu  ft  of  chalk  weigh  i  ton 
18  cu  ft  of  clay  weigh  i  ton 
21  cu  ft  of  earth  weigh  i  ton 


19  cu  ft  of  gravel  weigh  i  ton 
22  cu  ft  of  sand  weigh  i  ton 


Rock-Excavation.  A  cubic  yard  of  rock,  in  place,  when  broken  up  by  blasting 
for  removal  by  wheelbarrows  or  carts,  will  occupy  a  space  of  about  iH  cu  yd; 
consequently  the  cost  of  hauling  or  removal  is  abo«ut  50%  more  than  for  dirt. 

*'  With  labor  at  $1  per  day,  the  actual  cost  for  loosening  haid  rock,  including 
tools,  drilHng,  powder,  etc.,  will  average  about  45  cents  per  cubic  yard,  in  place, 
under  all  ordinary  circumstances.  In  practice  it  will  generally  range  between  30 
and  60  cents,  depending  on  the  position  of  the  strata,  hardness,  toughness,  water 
and  other  considerations.  Soft  shales  and  other  allied  rocks  may  frequently  be 
loosened  by  pick  and  plough  as  low  as  15  to  20  cents,  while  on  the  other  hand  shal- 
low cuttings  of  very  tough  rock  with  an  unfavorable  position  of  strata,  especially 
in  the  bottoms  of  excavations,  may  cost  $1  per  cu  yd,  or  even  considerably  more. 
The  quarrying  of  average  hard  rock  requires  about  H  to  H  lb  of  powder  per  cu  yd, 
in  place,  but  the  nature  of  the  rock,  the  position  of  the  strata,  etc.,  may  increase 
it  to  1^2  lb  or  more.  Soft  rock  frequently  requires  more  powder  than  hard.  A 
good  churn-driller  will  drill  8  to  10  ft  in  depth  of  holes  about  2^/^  ft  deep  and  2  in 
diameter  per  day  in  average  hard  rock,  at  from  12  to  18  cents  per  ft."  § 

*  The  ordinary  load  for  two-horse  wagons  such  as  are  commonly  used  for  hauling  dirt, 
sand  and  gravel  is  from  i  M  to  i  y2  cu  yd. 
t  Inspectors'  Pocket-Book,  by  A.  T.  Byrne, 
i  See,  also,  Handbook  of  Cost  Data,  by  H.  P.  Gillette. 
I  The  Civil  Engineer's  Pocket-Book,  J.  C.  Trautwine. 


1538  Data  on  Stonework  Part  3 


DATA  ON  STONEWORK* 

Kinds  of  Stonework.  The  commonest  kind  of  stonework,  that  is,  for  walls, 
is  called  rubblework.  No  work  whatever  is  done  on  the  stones  except  to 
break  them  up  with  a  hammer.  If  the  wall  is  built  in  courses  it  is  designated 
COURSED  RUBBLE.  When  the  stones  showing  on  the  outside  face  of  the  wall 
are  squared,  the  work  is  designated  ashlar.  Ashlar  is  of  two  kinds:  coursed 
ASHLAR,  in  which  the  stones  are  laid  to  form  courses  around  the  building,  all  of 
the  stones  in  any  course  being  of  the  same  height,  and  broken  ashlar,  in  which 
stones  of  different  heights  are  used.  Hammer-dressed  ashlar  designates  work 
where  the  stones  are  roughly  squared  with  a  hammer.  This  is  a  very  cheap  class 
of  work.  Good  ashlar  work  should  be  squared  on  the  bench  with  chisels,  and 
with  beds  and  end-joints  cut  sc^uare  to  the  face.  Stonework  which  requires  a 
chisel  or  any  other  tool  except  a  hammer  for  dressing  is  called  cut  work.  Cut 
work  costs  considerably  more  than  hammer-dressed  work. 

Measurement  of  Stonework.  Rough  stone  from  the  quarry  is  usually  sold 
under  two  classifications:  rubble-stone  and  dimension-stone.  Rubble  includes 
the  pieces  of  irregular  size  most  easily  obtained  from  the  quarry,  and  suitable  for 
cutting  into  ashlar  12  in  or  less  in  height  and  about  2  ft  long.  Stone  ordered  to 
be  of  a  certain  size,  to  square  over  24  in  each  way  and  to  be  of  a  particular  thick- 
ness, is  called  dlmension-stone.  The  price  of  the  latter  varies  from  two  to 
four  times  the  price  of  rubble.  Rubble  is  generally  sold  by  the  ton  or  car- 
load. Footings  and  flagging  are  usually  sold  by  the  square  foot;  dimension- 
stone  by  the  cubic  foot.  In  Boston,  granite  blocks  for  foundations  are  usually 
sold  by  the  ton. 

In  Estimating  on  the  Cost  of  Stonework  put  into  a  building,  the  custom  varies 
with  different  localities,  and  even  among  contractors  in  the  same  city.  Dimen- 
sion-stone footings,  that  is,  squared  stones  2  ft  or  more  in  width,  are  usually 
measured  by  the  square  foot.  If  built  of  large  rubble  or  irregular  stones  the 
footings  are  measured  in  with  the  wall,  allowance  being  made  for  the  projections 
of  the  footings.  Rubblework  is  almost  universally  measured  by  the  perch  of 
i6)>^  cu  ft.  The  author  has  been  unable  to  find  any  locality  where  the  legal 
perch  of  24%  cu  ft  is  used  by  stone-masons.  In  Philadelphia,  St.  Louis  and  some 
sections  of  Illinois,  22  cu  ft  are  called  a  perch.  Railroad- work  is  usually  meas- 
ured by  the  cubic  yard.  When  stonework  is  let  by  the  perch,  the  number  of 
cubic  feet  to  the  perch  should  be  stated  in  the  contract,  and  it  should  be  stated, 
also,  whether  or  not  openings  are  to  be  deducted.  As  a  rule  no  deductions  are 
made  for  openings  of  less  than  70  superficial  feet. 

Data  for  Estimating  Cost.f  The  price  of  common  rubble  as  it  comes  from 
the  quarry  will  vary  from  55  cts  to  $1.65  per  ton,  free  on  board  cars  at  point  of 
delivery,  according  to  the  cost  of  quarrying,  transportation,  etc.  $1.35  a  perch 
is  probably  a  fair  average. 

A  ton  of  most  of  the  different  kinds  of  stones  will  make  from  i  perch  to  iH 
perches. 

The  cost  of  laying  one  perch  of  stone  may  be  estimated  by  the  following  items: 

Labor:  mason  2%  hrs,  helper  1%  hrr>,  based  on  two  helpers  to  three  masons; 
sand  Vs  load;  lime  M  bu,  or  if  laid  in  all-cement  mortar,  one  perch  will  require 
from  H  to  Yi  bbl  of  cement. 

At  average  wages,  rubble  cellar- walls,  from  18  in  to  2  ft  thick,  laid  in  lime  mor- 

*  The  prices  given  are  pre-war  prices. 

t  For  wages  dififerent  from  those  named,  the  average  costs  may  be  calculated  by  pro- 
portion. 


Flagstones  and  Curbing  15S9 

tar,  vary  in  cost  from  $2.75  to  $4.50  per  perch,  $3.50  a  perch  being  a  fair  a\^ragei 
in  all-cement  mortar,  from  $3.50  to  $4.50  per  perch. 

The  cost  of  ashlar  depends  very  largely  upon  the  kind  of  stone  used  and  the 
distance  it  has  to  be  brought.  The  price  of  the  rough  stock  on  the  cars  at  the 
point  of  deUvery  may  vary  from  75  cts  to  $1.35  per  cu  ft  for  granite  and  from 
60  cts  to  $1.10  for  sandstones  and  limestones,  depending  largely  upon  cost  of 
transportation,  i  cu  ft  of  stone  should  make  2  sq  ft  of  ashlar,  at  least.  Some 
quarries  get  out  stone  especially  suitable  for  ashlar  and  sell  it  at  about  30  cts  per 
lin  ft  for  courses  12  in  high. 

The  cost  of  cutting  ashlar,  with  stone-cutters'  wages  at  $4  per  day,  will  average 
about  15  cts  per  sq  ft  for  soft  stones,  from  15  to  20  cts  per  sq  ft  for  hard  sand- 
stones and  limestones,  and  from  25  to  30  cts  for  granite.  The  cost  of  setting  ash- 
lar will  vary  from  10  cts  per  sq  ft  to  25  cts  for  soft  stones  or  30  cts  for  granite, 
15  cts  being  an  average  price  for  sandstones  and  limestones. 

The  cost  of  cut-stone  trimmings  depends  so  largely  upon  the  kind  of  stone 
that  it  is  quite  impossil^le  to  give  prices  that  would  be  of  very  much  service. 
The  following  figures,  however,  may  serve  as  a  general  guide  in  forming  a  rough 
estimate,  the  prices  if  anything  being  probably  a  little  above  the  cost  of  th^ 
local  stone  in  most  localities. 

Flagstones  for  Sidewalks,  ordinary  stock,  natural  surface,  3  in  thick,  with 
joints  pitched  to  Hue,  m  lengths,  along  walk,  from  3  to  5  ft,  will  cost,  for  a  3-ft 
walk,  about  10  cts  per  sq  ft,  or  if  2  in  thick,  7  cts;  for  a  4-ft  walk,  10  cts;  and  for 
a  s-ft  walk,  12  cts  per  sq  ft.  The  cost  of  laying  all  sizes  will  average  about  4  cts 
per  sq  ft.    The  above  figures  do  not  include  the  cost  of  hauUng. 

Curbing.  4  by  24-in  granite  will  cost  at  the  quarry  from  3oto  35  cts  per  lin  ft; 
digging  and  setting  will  cost  from  12  to  14  cts  additional;  and  the  cost  of  freight 
and  hauling  must  also  be  added.  -. 

Cut  Bluestone.  The  following  figures  show  the  approximate  cost  of  cut 
bluestone  for  various  uses: 


Flagstone,  5  in,  size  8  by  10  ft,  edges  and  top  bush-hammered,  per  square 
foot  face-measure 

Flagstone,  4  in,  size  5  by  5  ft,  select  stock,  edges  clean-cut,  natural  top, 
per  square  foot 

Door-sills,  8  by  12  in,  clean-cut,  per  Hnear  foot 

Window-sills,  5  by  12  in,  clean-cut,  per  linear  foot 

Window-sills,  4  by  8  in,  clean-cut,  per  linear  foot 

W^indow-sills,  5  by  8  in,  clean-cut,  per  linear  foot 

Lintels,  4  by  10  in,  clean-cut,  per  linear  foot 

Lintels,  8  by  12  in,  clean-cut,  per  linear  foot 

Water-table,  8  by  12  in,  clean-cut,  per  linear  foot 

Coping,  4  by  21  in,  clean-cut,  fier  linear  foot 

Coping,  4  by  21  in,  rock-face  edges  and  top,  per  linear  foot 

Coping,  3  by  15  in,  rock-face  edges  and  top,  per  linear  foot 

Coping,  3  by  18  in,  rock-face  edges  and  top,  per  linear  foot 

Steps,  sawed  stock,  7  by  14  in,  per  linear  foot 

Platform,  6  in  thick,  per  square  foot 


To  the  prices  of  cut  stone  above  given  must  be  added  the  cost  of  setting,  which, 
for  water-tables,  steps,  etc.,  will  be  about  10  cts  per  linear  foot,  and  for  window- 
sills,  etc.,  about  5  cts  per  Hnear  foot.  For  fitting,  about  10  cts  per  cu  ft,  and  for 
trimming  the  joints  after  the  pieces  are  set  in  place,  about  5  cts  per  cu  ft  should 
also  be  added. 


1540  Data  on  Bricks  and  Brickwork  Part  3 

DATA  ON  BRICKS  AND  BRICKWORK  * 

Clay  Bricks.  The  word  brick  as  commonly  used  refers  to  a  block  made  from 
clay,  molded  into  the  required  shape  and  burned  in  a  kiln;  and,  until  quite  re- 
cently, practically  all  bricks  were  made  from  clay.  At  the  present  time,  how- 
ever, bricks  are  also  made  from  sand  and  lime.  Clay  bricks  may  be  broadly 
classified  as  common  bricks,  face-bricks,  fire-bricks  and  paving-bricks.  As  to 
the  process  of  manufacture,  bricks  are  classified  as  soft-mud  bricks,  stiff-mud 
bricks,  dry-pressed  bricks  and  repressed  bricks. 

Soft-Mud  Bricks  are  made  by  tempering  clay  with  water  until  it  becomes  soft 
and  plastic  and  then  pressing  it  into  molds  either  by  hand  or  by  a  machine. 
Practically  all  handmade  bricks  are  soft-mud  bricks.  Soft-mud  bricks  are  often 
REPRESSED  to  make  face-bricks. 

Stifif-Mud  Bricks  are  machine-made.  The  clay  is  first  ground,  and  only 
enough  water  is  added  to  make  a  stiff  mud.  The  stiff  clay  is  forced  through  a  die 
or  dies  in  the  machine  in  a  continuous  stream,  which  is  cut  up  automatically  into 
pieces  the  size  either  of  the  end  or  side  of  the  brick.  If  the  opening  is  the  size  of 
the  end  of  the  brick,  the  bricks  are  end-cut  bricks;  if  of  the  size  of  the  side  of  the 
brick,  they  are  side-cut  bricks.  Stiff-mud  bricks  can  readily  be  distinguished 
from  soft-mud  bricks  by  their  appearance.  As  good  if  not  better  bricks  can  be 
made  by  the  soft-mud  process  as  by  the  stiff-mud  process,  and  in  the  Eastern 
States  the  soft-mud  bricks  are  probably  the  stronger.  As  far  as  the  author's 
observation  has  extended  in  the  Western  States,  the  stiff-mud  bricks  are  as  a  rule 
preferable  to  those  made  by  the  soft-mud  process.  Stiff-mud  bricks  are  usually 
heavier  than  soft-mud  bricks  or  hand-made  bricks. 

Dry-pressed  Bricks  are  made  almost  entirely  for  face-work,  although  in  some 
localities  dry-pressed  bricks  are  also  used  as  common  bricks.  Hydraulic-pressed 
bricks  are  dry-pressed. 

Molded  Bricks  are  always  dry-pressed.  Very  fine  bricks  are  made  by  this 
process. 

Burning  of  Bricks.  Bricks  made  by  any  of  the  above  processes  require  to  be 
burned  in  a  kiln.  According  to  their  position  in  the  kiln,  common  bricks  are 
designated  arch-bricks  or  hard-burned  bricks,  red  bricks  or  well-burned 
bricks,  and  salmon  bricks  or  soft  bricks.  As  a  rule,  salmon  bricks  are  not  fit  to 
use  in  an  exterior  or  bearing- wall. 

Color  of  Bricks.  The  color  of  bricks  depends  principally  upon  the  presence 
of  iron,  lime,  or  magnesia  in  the  clay.  A  large  proportion  of  oxide  of  iron  gives 
a  clear  bright  red.  Magnesia  produces  a  brown  color,  and  when  in  the  presence 
of  iron,  a  light-drab  color.  Dry-pressed  bricks  are  often  colored  artificially 
either  by  mixing  clays  of  different  composition,  or  by  mixing  mineral  colors  with 
the  finely  ground  clay. 

Fire-Bricks  are  ordinarily  made  from  a  mixture  of  flint  clay  and  plastic  clay. 
They  are  usually  white,  or  white  mixed  with  brown,  in  color  and  are  used  for  the 
lining  of  furnaces,  fireplaces  and  tall  chimneys. 

Paving-Bricks  are  very  hard  bricks,  usually  vitrified  or  annealed.  They  are 
much  more  expensive  than  common  bricks  and  are  seldom  used  in  buildings. 

Size  and  Weight  of  Clay  Bricks.  In  this  country  there  is  no  legal  standard  for 
the  size  of  bricks,  and  the  dimensions  vary  with  the  maker  and  also  with  the 

*  For  a  complete  description  of  clay  bricks,  their  process  of  manufacture,  etc.,  and  also 
of  all  kinds  of  brickwork,  see  Chapter  VII,  Part  I,  of  Building  Construction  and  Super- 
intendence, by  F.  E.  Kidder. 


Sand-Lime  Bricks  1541 

locality.  Common  standard  sizes  are  8  by  3,'^Ahy  2)4  in.  and  8  by  3J^  by  2}i  in. 
In  the  New  England  States  the  common  brick  averages  about  7^4  by  3%  by  2V4  in. 
In  most  of  the  Western  States  common  bricks  measure  about  8K'  by  /^%  by  iVz  in, 
and  the  thicknesses  of  the  walls  measure  about  9,  13,  18  and  22  in  for  thicknesses 
of  I,  i\-2,  2  and  2M>  bricks.  The  sizes  of  all  common  bricks  vary  considerably  in 
each  lot,  according  to  the  degree  to  which  they  are  burned;  the  hard  bricks  being 
from  H  to  -Me  in  smaller  than  the  salmon  bricks.  In  England  the  common 
standard  is  8-)4  by  4}^  by  2>.i  in.  Pressed  bricks  or  face-bricks  are  more  uniform 
in  size,  as  most  of  the  manufacturers  use  the  same  size  of  mold.  The  prevailing 
sizes  for  pressed  bricks  are  8^8  l)y  ^M  by  2%  and  8^i  by  4  by  2>4  in.  Pressed 
bricks  are  also  made  iK>  in  thick  and  12  by  4  by  iK"  in,  those  of  the  latter  size  be- 
ing generally  termed^ roman  bricks  or  tiles. 

The  WEIGHT  OF  I5RICKS  varies  considerably  with  the  quality  of  the  clay  from 
which  they  are  made,  and  also,  of  course,  with  their  size.  Common  bricks 
average  about  ^Yi  lb  each,  and  pressed  bricks  vary  from  5  to  5^/2  lb  each.  For 
the  STRENGTH  OF  BRICKS  and  brickwork,  see  Chapter  V.  The  fire-bricks  are 
made  in  various  forms  to  suit  the  required  work.  A  straight  brick  measures 
9  by  /[Yi  by  2K'  in  and  weighs  about  7  lb.  To  secure  the  best  results  fire-bricks 
should  be  laid  in  the  same  clay  from  which  they  are  manufactured,  this  being 
mixed  with  water  into  a  thin  paste.  The  thinner  the  joint,  the  better  the  wall 
will  stand  heat.  For  paving-bricks  the  size  and  weight  vary  according  to  the 
locality  and  to  the  requirements  of  the  specifications.  Former  standards  were, 
2y2  by  4  by  8  in,  required  61  bricks  to  the  square  yard,  on  edge,  and  weighed  7  lb 
each.  Repressed  bricks,  21^2  by  4  by  8^^  in,  require  58  to  the  square  yard 
and  weigh  6^^  lb  each.  Metropolitan  bricks  were  3  by  4  by  9  in,  required  45 
to  the  square  yard,  and  weighed  <^\i  lb  each.* 

Lime-Mortar  Bricks. f  General  Description.  The  so-called  sand-lime 
bricks  were  originally  made  of  lime  mortar,  molded  in  brick  form  and  hardened 
by  exposure  to  the  air.  Such  bricks  are  said  to  have  been  largely  used  in  ancient 
times,  and  it  is  claimed  that  remains  of  such  materials  are  now  in  evidence  and  in 
a  good  state  of  preservation.  It  is  known  that  they  were  formerly  used  in  Europe 
in  localities  where  other  materials  were  not  readily  available,  and  that  they  have 
been  used  in  some  localities  in  this  country  during  the  past  thirty-five  years. 
The  writer  knows  of  several  houses  in  Haddonficld,  N.  J.,  built  of  such  bricks, 
generally  with  the  exterior  surfaces  plastered.  One  of  them,  however,  said  to  be 
about  twenty-five  years  old,  has  not  been  plastered,  and  an  inspection  (19 15) 
shows  the  bricks  to  be  in  an  excellent  state  of  preservation.  Lime-mortar  bricks 
harden  by  the  absorption  of  carbonic-acid  gas  from  the  air.  This  gas  enters 
into  combination  with  the  lime,  forming  carbonate  of  lime.  I  he  hardening  proc- 
ess requires  several  weeks'  exposure  under  cover  and  the  product  has  not  virtues 
sufTicient  to  commend  it  where  other  materials  are  available. 

Sand-Lime  Bricks.  It  was  discovered  in  Germany  about  1875  that  lime- 
mortar  bricks  could  be  hardened  in  a  few  hours  under  heat  and  pressure,  and  it 
was  found  later  that  the  chemical  reaction  under  the  new  process  differs  essen- 
tially from  that  just  described,  and  that  the  percentage  of  lime  can  be  greatly 
reduced.  The  fundamental  principles  of  sand-lime-brick  n;i^nufacture  are  now 
common  property  and  only  the  details  of  the  manufacture  are  patentable. 
Sand-hme  bricks  were  first  made  in  Germany  about  1880,  and  the  more  extended 
commercial  development  of  the  industry  dates  back  in  Europe  to  about  1888, 

*  Building  Inspectors'  Pocket-book,  A.  T.  Byrne. 

t  Condensed  from  article  on  Sand-Lime  Bricks  by  Professor  Thomas  Nolan  in  the  re- 
vised edition  of  Building  Construction  and  Superintendence,  Part  I,  Masons'  Work,  by 
F.  E.  Kidder. 


1542  Data  on  Bricks  and  Brickwork  Part  3 

and  in  this  country,  to  about  1900.  There  are  now  (1915)  several  factories  in 
operation  in  this  country. 

Manufacture  of  Sand-Lime  Bricks.  Pure  sih'ca  sand,  mixed  with  from  5  to 
10%  of  high-calcium  Hme  and  a  certain  proportion  of  water,  is  molded  under 
very  high  pressure  into  the  form  of  bricks.  These  are  piled  loosely  on  cars  hold- 
ing about  1000  bricks  each  and  placed  in  a  steel  cylinder  large  enough  to  hold 
from  TO  to  20  cars.  The  cylinder  is  then  closed  and  steam  is  turned  in  and  main- 
tained at  a  pressure  of  from  1 20  to  135  lb  to  the  square  inch  for  from  8  to  10  hours, 
when  the  cylinder  is  opened  and  the  bricks  removed,  ready  for  use.  The  tre- 
mendous pressure,  which  is  said  to  be  100  tons  on  each  brick,  under  which  the 
bricks  are  formed,  causes  great  density  and  a  bringing  of  the  component  elements 
into  close  contact.  The  heat  in  the  cylinder  dries  the  bricks  and  causes  a  chemi- 
cal reaction  between  the  lime  and  a  portion  of  the  silica,  forming  a  hydrosilicate 
of  lime,  an  insoluble  and  durable  element,  which  bonds  the  remaining  particles 
of  the  sand  together  and  forms  a  comparatively  strong  cementing  material. 
The  small  residue  of  uncombined  lime  combines,  in  the  course  of  time,  either 
with  silica  or  with  carbonic-acid  gas  from  the  air,  until  no  free  lime  remains.  The 
bricks  thus  become  harder  and  stronger  with  age.  In  regard  to  the  constitution 
of  sand-lime  bricks,  Edwin  C.  Eckel  says:*  "It  may  be  safely  assumed  that  a 
sand-lime  brick  as  marketed  consists  of  (i)  sand-grains  held  together  by  a  net- 
work of  (2)  hydrous  lime  silicate,  with  probably  (if  a  magnesian  lime  is  used) 
some  allied  magnesium  silicate,  and  (3)  Hme  hydrate  or  a  mixture  of  lime  and 
magnesia  hydrates.  These  three  elements  will  always  be  present,  and  the  struc- 
tural value  of  the  l)rick  will  deixind  in  large  part  on  the  relative  percentage  in 
which  the  sand  and  the  hydrates  occur." 

Quality  of  Sand-Lime  Bricks.  The  quality  of  the  product  depends  mainly 
upon  the  selection  and  treatment  of  the  sand  and  the  lime.  Pure  silica  sands, 
containing  a  large  percentage  of  fme  grains  passing  through  screens  of  from  80  to 
150  mesh,  are  preferal)le.  Clay  or  kaolin  are  dangerous  elements  and  should  not 
be  present  in  quantities  of  more  than  5%.  The  lime  should  be,  preferably,  high- 
calcium  lime,  the  magnesium  silicates  formed  by  impure  limes  not  being  as  strong 
as  calcium  silicates.  Some  manufacturers  use  ready-hydrated  lime,  others 
hydrate  the  lime  themselves,  before  mixing  it  with  the  sand,  and  others  grind  the 
quicklime,  mix  it  with  the  sand  and  slake  it  in  the  sand.  The  other  most  im- 
portant element  affecting  quality  is  the  press.  After  pressing  and  before  steam- 
ing, the  bricks  are  very  fragile  and  the  press  should  be  such  that  they  are 
subjected  to  no  shaking  or  friction  after  the  pressure  is  removed  from  the  mold. 
Vertical  clay-brick  presses  have  been  commonly  used,  but  do  not  appear  to  be 
well  adapted  to  the  purpose.    The  rotary  table-presses  seem  to  be  most  successful. 

Tests  of  Sand-Lime  Bricks.  If  the  sand  is  reasonably  clean  and  pure,  and  the 
lime  finely  divided,  and  if  the  bricks  are  sound  and  have  a  good  metallic  ring, 
they  will  stand  weather-exposure  well.  If  a  brick  stands  in  still  water  for  an 
hour  and  the  moisture  rises  more  than  Vi  in,  it  is  not  a  first-class  brick;  if  the 
moisture  rises  2  in,  its  use  for  facings  is  questionable;  and  if  the  moisture  rises 
3  in,  it  should  not  be  used  on  outside  work  of  any  importance.  Authentic  tests  f 
have  been  made  forrrushing,  fire-resistance,  frost-resistance,  acid-resistance  and 
absorption,  from  which  it  may  be  concluded  that  under  proper  conditions  of 

*  "  The  Production  of  Lime  and  Sand-lime  Brick  in  1906,"  in  the  Government  Report, 
dated  1907  and  published  in  1908,  on  The  Mineral  Resources  of  the  United  States  for  the 
Calendar  Year,  1906. 

t  See,  also,  Tests  Upon  Sand-Lime  Bricks,  made  by  Ira  H.  Woolson,  November,  1905, 
at  the  Testing  Laboratory,  Columbia  University,  New  York,  for  The  National  Association 
of  Manufacturers  of  Sand-Lime  Products. 


Glazed  and  Enameled  Bricks  1543 

manufacture  sand-Hmc  l)ricks  arc  produced  having  the  following  physical  char- 
acteristics: Crushing  strength,  average,  between  2  500  and  3  000  lb  per  sq  in,  al- 
tliough  some  specimens  have  shown  over  5  000  lb  per  sq  in;  modulus  of  rupture, 
average,  about  450  lb  per  sq  in;  fire-resistance,  but  little  inferior  to  that  of  fire- 
brick; frost-resistance,  generally  good;  acid-resistance,  superior;  absorption, 
from  7  to  10%  in  48  hours;  rate  of  absorption,  slower  than  for  clay  bricks; 
average  absorption  for  complete  saturation,  14%;  reduction  of  compressive 
strength  by  saturation  for  absorption-test,  average  33%. 

Special  Properties  of  Sand-Lime  Bricks.  The  bricks  are  square,  straight, 
uniform  in  size  and  homogeneous  in  composition  and  density.  They  cleave 
accurately  under  the  stroke  of  the  trowel  and  present  a  weather-surface  with  the 
good  qualities  of  stone.  They  can  be  cut,  carved  or  sand-blasted,  are  easily 
washed  clean  and  show  no  efflorescence.  These  claims  are  well  established  for 
properly  manufactured  sand-hmc  bricks.  It  should  be  further  stated  that  com- 
mon bricks  and  facings  are  made  in  the  same  press,  the  only  aifference  being  in 
the  selection  of  the  materials  and  in  the  handUng  of  the  raw  bricks.  It  is  there- 
fore claimed  that  a  rational  and  homogeneous  exterior  wall-structure  is  possible, 
since  backings  and  facings  may  be  built  and  bonded  in  even  courses,  with 
Flemish  or  other  ornamental  bonds.  Some  factories,  however,  manufactured, 
at  first,  inferior  bricks  and  care  should  still  be  taken  in  selections  from  their  out- 
puts. Freciuently  the  ordinary  runs  of  sand-lime  bricks  are  not  as  strong  as  the 
average  clay  building  bricks  and  some  of  them  are  too  low  in  their  resistance  to 
frost. 

Colors  of  Sand-Lime  Bricks.  The  natural  color  is  pearl-gray,  varying  in 
warmth  with  the  composition  of  the  sand.  Permanent  colors  are  produced  by 
introducing  mineral  oxides  with  the  raw  materials  in  quantities  varying  accord- 
ing to  the  intensity  of  color  desired;  but  as  the  oxides  are  foreign  materials  in 
the  bricks,  they  affect  the  ciuality  of  the  latter  in  proportion  to  the  quantity 
used. 

Glazed  and  Enameled  Bricks.  The  terms  glazed  brick  and  enam- 
eled BRICK,  as  commonly  used,  refer  practically  to  the  same  product,  and 
neither  includes  what  is  known  as  salt-glazed  brick.  The  enameled  or 
glazed  bricks  are  generally  dipped  or  sprayed  and  then  burned,  whereas  the . 
salt-glaze  is  obtained  by  the  Introduction  of  salt  into  the  fire-boxes  of  kilns 
while  the  bricks  are  being  burned.  Glazed  or  enameled  bricks  are  generally 
divided  into  two  classes:  (1)  true  enameled  bricks,  which  have  a  glaze  contain- 
ing the  coloring  matter  applied  to  it  without  any  intermediate  slip;  (2)  bricks 
which  have  a  transparent  glaze  placed  over  a  white  or  colored  slip,  the  slip 
coming  between  the  glaze  and  the  material  to  be  glazed.  The  latter  is  the 
process  most  used  in  this  country.  Manufacturers  differ  as  to  which  process 
produces  the  best  bricks  although  it  would  seem  as  though  the  true  enamel 
would  not  chip  or  peel  as  readily.  These  bricks  can  be  made  in  a  variety  of 
colors,  from  white  to  dark  green  or  chocolate,  and  either  in  a  highly  glazed 
FINISH  or  in  a  dull,  satin-finish,  the  latter  finish  being  quite  desirable  in 
many  instances  on  account  of  its  doing  away  with  the  glare  of  the  more  highly 
glazed  bricks  or  tiles.  An  enameled  surface  may  be  distinguished  from  a 
glazed  surface  by  chipping  off  a  piece  of  the  brick.  The  glazed  brick  will  show 
the  layer  of  slip  between  the  glaze  and  the  body  of  the  brick;  while  the  enam- 
eled brick  will  show  no  line  of  demarcation  between  the  body  of  the  brick  and 
the  enamel.  American  enameled  and  glazed  bricks  are  now  extens'vely  used 
for  the  exterior  surfaces  of  buildings,  particulariy  for  street-fronts  and  light- 
courts,  and  for  interior  side  walls  and  partitions  of  rooms  or  buildings  used  for  a 
great  variety  of  purposes. 


1544  Data  on  Bricks  and  Brickwork  Part  3 

Sizes  of  Enameled  Bricks.  Enameled  bricks  are  made  in  two  regular  sizes:  (i) 
English  oize,  9  by  3-in  enameled  surface,  41'j-in  bed,  and  (2)  American  size,  8^8  by 
2K-in  enameled  surface,  4H-in  bed.  The  English-size  bricks  cost  about  $10  per 
I  000  more  than  the  American,  but  on  account  of  the  saving  in  the  number  of 
bricks,  labor  of  laying  and  mortar  in  joints,  the  former  really  effect  a  saving  of 
about  7  cts  per  sq  ft.  Enameled  bricks  are  made,  also,  with  a  12  by  4H-in 
enameled  surface,  2H-in  bed. 

Cost  of  Enameled  Bricks.*  The  selling  price  of  enameled  bricks  varies  from 
$75  per  I  000  for  the  American  size  to  $85  for  the  English  size  and  Gioo  for  the 
12  by  4\i  by  2i/4-in  size;  and  at  these  prices  the  cost  of  the  bricks  per  square 
foot  is: 

cts 

American  size,  7  bricks  to  the  foot ." . . . .' 52H 

EngHsh  size,  5  H  bricks  to  the  foot 4SH 

English  flat,  3%  bricks  to  the  foot 36 

12  by  4H  by  2H-)n,  3  bricks  to  the  foot 30 

Colors  of  Enameled  Bricks.  The  standard  colors  carried  in  stock  are  white, 
cream  and  buff;   other  colors  are  made  to  order. 

Estimating  Quantities  and  Cost  of  Brickwork  * 

Methods  of  Calculation.  The  almost  universal  method  of  calculating  the 
cost  of  brickwork  is  by  estimating  the  number  of  thousands  of  bricks,  wall- 
measure,  and  then  multiplying  by  a  certain  price  per  thousand,  which  is  usually 
determined  by  experience  and  which  is  intended  to  include  every  item  affecting 
the  cost,  and  very  often  the  profit.  All  of  the  common  brickwork  in  any  given 
building  is  usually  figured  at  the  same  price  per  thousand  bricks,  the  adjustment 
for  the  more  expensive  portions  of  the  work  being  made  in  the  manner  of  measur- 
ing.    The  principle  underlying  this  system  is  explained  as  follows: 

"  The  plain  dead  wall  of  brickwork  is  taken  as  the  standard,  and  the  more 
difficult,  complicated,  ornamental,  or  hazardous  kinds  of  work  are  measured  up 
to  it  so  as  to  make  the  compensation  eciual.  To  illustrate,  if,  in  one  day,  a  man 
can  lay  2  000  bricks  in  a  plain  dead  wall,  and  can  lay  only  500  in  a  pier,  arch,  or 
chimney-top  in  the  same  time,  the  cost  of  labor  per  thousand  in  such  work  is 
four  times  as  much  as  in  the  dead  wall,  and  he  is  entitled  to  extra  compensation; 
but  instead  of  varying  the  price,  the  custom  is  to  vary  the  measurement  to  com- 
pensate for  the  difference  in  the  time,  and  thus  endeavor  to  secure  a  uniform 
price  per  thousand  for  all  descriptions  of  ordinary  brickwork,  instead  of  a  differ- 
ent price  for  the  execution  of  the  various  kinds  of  work."t 

Measurements  of  Brick- Quantities.  Plain  walls  are  quite  universally  figured 
at  IS  bricks  to  the  square  foot  of  an  8  or  9-in  wall,  22V2  bricks  per  square  foot 
of  a  12  or  13-in  wall,  30  bricks  per  square  foot  of  a  16  or  17-in  wall,  and  7H 
bricks  for  each  additional  4  or  4}  2  in  in  the  thickness  of  the  wall.  These  figures 
are  used  without  regard  to  the  size  of  the  bricks,  the  effect  of  the  latter  being 
taken  into  account  in  fixing  the  price  per  thousand.  No  deduction  is  made  for 
OPENINGS  of  less  than  80  sup  ft,  and  when  deductions  are  made  for  larger  openings 
the  width  is  measured  2  ft  less  than  the  actual  width.  Hollow  walls  are  also 
measured  as  if  solid.     To  the  number  of  bricks  thus  obtained  is  added  the 

*  The  prices  given  are  pre-war  prices. 

t  From  Rules  of  Measurement  adopted  by  the  Brick  Contractors'  Exchange  of  Denver, 
Col. 


Measurements  of  Brick-Quantities  154?5 

measurement  for  piers,  chimneys,  arches,  etc.  Footings  are  generally  measured 
in  with  the  wall  by  adding  the  width  of  the  projection  to  the  height  of  the  wall. 
Thus  if  the  footings  project  6  in  on  each  side  of  the  wall,  i  ft  is  added  to  the  actual 
height  of  the  wall.  Chimney-breasts  and  pilasters  are  measured  by  multi- 
plying the  girth  of  each  breast  or  pilaster  from  the  intersections  with  the  wall  by 
the  height,  and  then  by  the  number  of  bricks  corresponding  with  the  thickness  of 
the  projection.  Flues  in  chimneys  are  always  measured  solid.  Detached 
chimneys  and  chimney-tops  are  measured  as  a  wall  having  a  length  equal  to  the 
sum  of  the  side  and  two  ends  of  the  chimney,  and  a  thickness  equal  to  the  width 
of  the  chimney.  Thus  a  chimney  measuring  3  ft  by  i  ft  4  in  would  be  measured 
as  a  16  or  17-in  wall,  5  ft  8  in  long.  The  rule  for  independent  piers  is  to 
multiply  the  height  of  each  pier  by  the  distance  around  it  in  feet,  and  consider 
the  product  as  the  superficial  area  of  a  wall  whose  thickness  is  equal  to  the  width 
of  the  pier.  In  practice,  many  masons  measure  only  one  side  and  one  end  of  a 
pier  or  chimney.  Arches  of  common  bricks  over  openings  of  less  than  80  sup  ft 
are  usually  disregarded  in  estimating.  If  the  arch  is  over  an  opening  larger  than 
80  sq  ft,  the  height  of  the  wall  is  measured  from  the  springing-line  of  the  arch. 
No  deduction  is  made  in  the  wall-measurement  for  stone  sills,  caps,  or  belt- 
courses,  nor  for  stone  ashlar,  if  the  same  is  set  by  the  brick-mason.  If  the  ashlar 
is  set  by  the  stone-mason,  the  thickness  of  the  ashlar  is  deducted  from  the  thick- 
ness of  the  wall.  The  sum  of  all  of  these  measurements  represents  a  certain 
number  of  thousands  of  bricks,  and  the  whole  is  then  multiplied  by  a  common 
price  per  thousand,  as  $6,  $8,  $12,  or  $16,  according  to  whatever  the  cost  of  plain 
brickwork  may  be.  If  the  building  is  to  be  faced  with  pressed  bricks,  the  actual 
cost  cf  the  pressed  bricks,  as  nearly  as  it  can  be  computed,  is  added  to  the  esti- 
mated price  of  the  common  brickwork,  nothing  being  added  for  laying  the  pressed 
bricks,  nor  anything  deducted  from  the  common-brick  measurement,  the  meas- 
urement of  the  common  work  displaced  by  the  pressed  bricks  being  assumed  to 
offset  the  difference  in  the  cost  of  laying  the  pressed  and  common  brickwork. 
In  arriving  at  the  cost  of  the  pressed  bricks,  the  external  superficial  area  of 
the  walls  faced  with  such  bricks  is  computed,  and  all  openings,  belt-courses,  stone 
caps,  etc.,  are  deducted.  Five-in  stone  sills  are  not  usually  deducted.  If  a  por- 
tion of  the  wall  is  covered  by  a  porch,  so  that  common  bricks  may  be  used  back 
of  it,  this  space,  also,  is  deducted.  The  net  pressed-brick  surface  is  then  multi- 
plied by  6,  6K',  or  7  to  obtain  the  number  of  bricks  required,  6y2  giving  about 
the  number  of  pressed  bricks  of  the  standard  size  required  to  the  square  foot. 
The  topping  out  of  chimneys,  if  of  face-brick,  is  measured  by  girting  the  chim- 
neys, multiplying  by  the  heights,  and  adding  the  sums  to  the  wall-area. 

Example.  As  a  simple  example  of  this  system  of  estimating  consider  a  small 
brick  house,  28  by  32  ft  in  plan,  without  cross- walls,  the  basement-walls  being 
13  in  thick,  with  footings  2  ft  6  in  wide;  the  first-story  walls,  13  in  thick;  the 
second-story  walls,  9  in  thick;  the  height  of  the  basement- walls  from  the  trench  to 
the  top  of  the  first-story  joists,  8  ft  6  in;  the  height  of  the  walls  from  the  first- 
story  joists  to  the  top  of  the  second-story  joists,  10  ft  6  in;  and  from  the  second- 
story  joists  to  the  plate,  9  ft. 

Wall-Measurements.  Basement- walls:  120  ft  (girth  of  building)  by  9  ft 
10  in  (height  and  projection  of  footing)  by  2  2j'i  bricks  per  square  foot;  equal  to 
26  550  bricks. 

First-story  walls:  120  ft  by  10  ft  6  in  by  22 J.^  bricks  per  square  foot;  equal 
to  28  360  bricks. 

Second-story  walls:  120  ft  by  9  ft  by  15  bricks  per  square  loot;  equal  to 
16  200  bricks. 

Topping  out  two  chimneys,  each  i  ft  9  in  by  i  ft  5  in  by  14  ft  high  above  roof; 


1546  Data  on  Bricks  and  Brickwork  Part  3 

2  by  14  ft  by  (1  ft  5  in  plus  1  ft  9  in  plus  i  ft  5  in)  by  30  bricks  per  square  foot; 
equal  to  3  850  bricks. 

Total  brickwork:    74  960  bricks.     At  $9  per  i  000,  the  cost  is  $674.64. 

Pressed  Bricks.  From  the  grade  to  the  under  side  of  the  plates,  the  wall 
measures  22  ft  6  in  and  it  is  to  be  faced  with  pressed  bricks  of  the  standard  size, 
costing  $15  per  i  000.  The  door-openings  and  window-openings  measure  384 
sup  ft. 

The  surface  of  pressed  bricks  equals  120  by  2  2  3' 2  ft,  equal  to 2  700  sq  ft 

The  deduction  for  openings  is 384  sq  ft 

Area,  after  deduction 2  316  sq  ft 

Addition  for  two  chimneys,  2  by  14  by  6  ft  4  in,  equal  to 177  sq  ft 

Total  2  493  sq  ft 

2  493  by  6y2  equals  16  204  pressed  bricks,  which,  at  $15  per  i  000  cost,  equals 
$243. 

The  total  amount  of  the  bid  is  $674.64  plus  $243,  or  $917.64. 

The  above  figures  are  supposed  to  include  the  necessary  lime,  sand,  water, 
scaffolding,  etc.,  required  to  make  the  mortar  and  put  up  the  walls,  and  also  a, 
profit  for  the  contractor;  but  anything  in  the  way  o£  ironwork,  such  as  ties, 
thimbles,  ash-doors,  etc.,  are  figured  as  additions  to  this  amount. 

Detailed  Estimates  of  Brickwork.  In  estimating  by  the  above  method,  the 
price  per  thousand  is  to  some  extent  a  matter  of  guesswork,  and  while  an  expe- 
rienced contractor  may  perhaps  make  as  accurate  an  estimate  by  this  method  as 
is  possible  by  any,  yet  it  is  often  necessary  to  estimate  the  work  in  detail;  and 
even  when  the  work  has  been  estimated  as  above,  it  is  necessary  for  the  con- 
tractor to  know  how  many  bricks  and  how  much  sand  and  lime  will  be  required 
to  do  the  work.     The  following  data  will  assist  in  making  such  detailed  estimates. 

With  the  size  of  bricks  used  in  the  Western  States,  from  16^2  to  17^^  common 
bricks  are  required  to  the  cubic  foot  after  deducting  openings,  and  figuring  the 
thickness  of  walls  at  8,  12,  16,  20  in,  etc.,  the  actual  number  of  bricks  required 
will  run  about  two-thirds  of  the  wall-measure  when  the  openings  are  of  about 
the  average  number  and  size. 

The  number  of  pressed  bricks  will  be  about  6  or  Syi  bricks  to  the  foot,  after 
deducting  openings. 

To  lay  I  000  common  bricks,  kiln-count,  requires  2V2  bushels  or  200  lb  of  white 
lime  and  H  cu  yd  of  sand.  For  a  good  lime-and-cement  mortar,  allow  2  bushels 
of  lime,  I  bbl  of  cement  and  H  cu  yd  of  sand.  For  i  :  3  cement-and-sand 
mortar,  allow  iVi  bbl  of  cement  and  %  cu  yd  of  sand,  or  one-half  a  load. 

To  lay  I  000  pressed  bricks  with  buttered  joints  will  require  2  bushels  of  lime 
(160  lb)  and  H  cu  yd  of  sand;  with  spread  joints,  from  2  to  2^2  bushels  of  lime 
and  from  %  to  yz  cu  yd  of  sand. 

If  colored  mortar  is  used,  about  $1  per  i  000  bricks  should  be  added  for  the 
mortar-color. 

A  brick-mason,  working  on  a  city  job  under  a  good  foreman,  will  lay,  on  an 
average,  60  pressed  (face)  bricks  per  hour,  and  from  150  to  175  common  bricks 
per  hour,  160  being  a  fair  average.  In  country  towns  the  average  is  nearer  120 
per  hour. 

With  wages  at  62 ^/^  cts  per  hour  for  masons,  31 M  cts  for  hod-carriers,  and  34% 
cts  for  mortar-mixers  and  carriers,  sand  at  60  cts  per  cu  yd,  and  lime  at  40  cts 
per  bushel  of  80  lb,  brick-masons  in  Denver  state  that  the  average  cost  of  laying 
common  bricks  in  12-in  walls  is  about  $6  per  i  000,  kiln-count,  and  of  laying 
pressed  bricks  about  $10  per  i  000. 


Mortar-Colors.    Efflorescence  154"/ 

For  common  brickwork,  one  helper  will  be  required  for  every  mason,  and  on 
9-in  walls,  faced  with  pressed  bricks,  one  helper  to  every  two  masons.  In  build- 
ing common-brick  fireplaces  and  chimneys  one  mason  and  heli)er  will  lay  about 
600  bricks  in  a  day  of  nine  hours. 

As  a  rule,  chimneys  built  of  common  bricks  and  with  4-in  walls  cost  about  50 
cts  per  running  foot,  in  height,  for  single  flues,  and  90  cts  for  double  flues. 

Space  Required  for  Piling  Bricks.  One  thousand  bricks  closely  stacked 
occupy  about  56  cu  ft  of  space.  One  thousand  old  bricks,  cleaned  and  loosely 
stacked,  occupy  about  72  cu  ft. 

A  brick-layer's  hod  measures  21  by  7  by  7  in,  and  will  hold  18  bricks. 

A  mortar-hod  measures  24  by  12  by  12,  and  12  in  across  the  top. 

Mortar-Colors  are  usually  in  the  form  of  dry  powders,  or  of  pulp  or  paste. 
The  powders  are  put  up  in  barrels,  the  number  of  pounds  to  the  barrel  and  price 
per  pound  being  about  as  follows: 

Red,  in  500-lb  barrels,  dry from  1^4  to  2      cts  per  lb 

Brown,  in  450-lb  barrels,  dry from  iH  to  2^  cts  per  lb 

Buff,  in  400-lb  barrels,  dry from  1%  to  lYz  cts  per  lb 

Black,  in  i  000-lb  barrels,  dry from  3      to  3)2  cts  per  lb 

For  lots  of  less  than  full  barrels  an  extra  charge  is  sometimes  made  for  packing 
and  drayage. 

In  pulp  or  paste-form: 

Red,  brown  and  buff 1^4  cts  per  lb 

Black 3      cts  per  lb 

All  other  colors 2      cts  per  lb 

Colors  in  paste-form  can  be  obtained  in  casks,  barrels,  half-barrels  and  kegs, 
all  (except  black  and  buff)  weighing,  in  casks,  900  lb;  in  barrels,  550  lb;  and  in 
half-barrels,  375  lb.  The  buff  weighs,  in  casks,  700  lb;  in  barrels,  450  lb;  and  in 
half-barrels,  300  lb.  Black  weighs,  in  barrels,  450  lb;  and  in  half-barrels,  275  lb. 
To  color  the  mortar  for  laying  i  000  bricks  with  H-'m  joints  requires  about  50 
lb  of  red,  terra-cotta  color,  amber,  fern-green  and  salmon;  40  lb  for  buff,  brown, 
colonial  drab  or  French  gray;  and  25  lb  for  black.  For  wider  joints,  a  larger 
quantity  of  stain  must  be  used.  For  paste-colors  an  average  mixture  is,  i 
bucket  of  paste-color  to  7  buckets  of  mortar  for  brickwork  with  14-in  joints. 
When  the  colors  are  in  the  form  of  dry  powder  they  are  first  mixed  with  dry 
sand,  the  cold  slaked  lime  is  then  added  and  again  mixed  thoroughly.  It  is  very 
important  that  the  color  be  uniformly  mixed.  If  it  is  not  added  at  first,  but  left 
until  the  mortar  is  made,  the  labor  of  mixing  is  doubled.  The  more  thorough 
the  mixing  the  less  color  is  required.  Mortar  colors  should  never  be  mixed  with 
hot  lime.  When  the  color  is  in  the  form  of  a  pulp  or  paste,  it  should  be  thor- 
oughly hoed  in,  in  order  to  secure  a  uniform  and  smooth  shade.  For  very  fine 
pressed  bricks,  the  stained  mortar  should  be  strained  through  a  coarse  sieve. 

Efflorescence  on  Brickwork.  A  white  efflorescence  often  appears  on 
brickwork,  especially  in  moist  climates  and  damp  places.  It  may  spread  over 
large  areas  of  the  wall-surface  although  originating  in  the  mortar  joints.  Solu- 
ble salts,  principally  of  soda,  potash  and  magnesia,  in  the  cement  or  lime  mortar, 
are  dissolved  by  the  water  absorbed  by  the  mortar  and  later  precipitated  on  the 
surface  of  the  brickwork  as  a  white  deposit,  when  the  water  evaporates.  This 
deposit  seems  to  be  greater  with  the  natural  than  with  the  Portland-cement  mor- 
tars and  still  heavier  with  lime  mortar.  The  origin  of  the  eflioresence  may  be  m 
the  bricks  themselves  as  well  as  in  the  mortar  used.  This  is  the  case  when  the 
bricks  are  made  from  clays  containing  iron  pyrites  or  burned  with  sulphurous 


1548  Lime  Part  3 

coal.  Moisture  in  such  bricks  tends  to  dissolve  the  sulphate  of  magnesia  arid 
sulphate  of  lime,  which,  in  the  evaporation  of  the  water,  are  deposited  on  the 
surface  as  crystals  of  these  salts.  Efflorescence  may  result,  also,  from  water 
impregnated  from  the  mortar,  absorbed  by  the  bricks  and  then  evaporated, 
leaving  the  whitish  deposits;  and  it  is  sometimes  caused  by  adulterations  in 
certain  mortar-colors.  As  a  preventive.  General  Gilmore  recommended  the 
addition  to  every  300  lb  of  the  cement  powder,  100  lb  of  quicklime,  and  from  8 
to  12  lb  of  any  cheap  animal  fat,  whix^h  is  to  be  thoroughly  incorporated  with 
the  quicklime  before  the  latter  is  slaked,  preparatory  to  adding  it  to  the  cement. 
The  alkaline  salts  tend  to  be  saponieied  by  the  fat.  This  is  not  an  entirely 
satisfactory  treatment,  and  as  a  rule  it  only  partly  prevents  or  removes  the 
objectionable  deposits;  and  this  addition  to  the  cement  retards  its  setting  and 
somewhat  diminishes  its  strength.  It  is  claimed  by  some  that  boiled  linseed- 
oil,  applied  to  brickwork  in  two  coats,  will  lessen  the  absorption  of  moisture  for 
from  one  to  three  years  and  thus  lessen  the  tendency  to  efflorescence.  It  is 
usually  mixed  in  the  proportion  of  2  gal  of  oil  to  300  lb  of  dry  cement,  either  with- 
er without  lime;  but  it  is  injured  by  the  mortar  and,  like  the  fat,  retards  the 
setting  of  the  cement  mortar  and  weakens  it.  In  order  to  diminish  the  chances 
of  efflorescence  on  brickwork,  the  walls  should  be  made  as  impervious  as  possible 
by  laying  the  bricks  in  a  rich  well-mixed  Portland-cement  mortar  and  filling  all 
joints  full  and  solid.  If  the  building  is  on  damp  ground,  carefully  constructed 
DAMP-PROOF  courses  of  the  proper  materials  should  be  built  into  the  walls  or  a 
course  of  horizontal  joints  near  the  bottom  of  the  walls  should  be  waterproofed. 
Reasonably  hard  bricks  should  be  used  for  facing,  projections  and  exposed  top 
surfaces  waterproofed  and  provided  with  drips,  and  the  roof,  cornice  and  gutters 
made  water-tight.  When  efflorescence  is  due  to  the  penetration  of  rain-water  or 
moisture  into  the  brickwork  and  it  is  required  to  preserve  the  texture  and  color 
of  the  work,  the  surface  may  be  coated  with  preparations  of  paraffine  or  with 
various  patented  waterproofing  mixtures.  The  preparations  containing 
paraffine  are  usually  applied  hot,  and  the  walls,  also,  are  heated  by  portable 
heaters  previous  to  the  application.  They  give  fairly  good  results,  but  are 
quite  expensive,  owing  to  the  time  and  labor  required  for  their  application. 
Brick  walls  may  be  rendered  impervious  to  moisture  by  washes  applied  by  the 
Sylvester  process.  These  washes  consist  of  an  alum-solution  made  by  dis- 
solving I  lb  of  alum  per  gallon  of  water,  and  a  soap-solution  made  by  dissolving 
2H  lb  of  pure  hard  soap  per  gallon  of  water.  The  brick  walls  should  be  dry  and 
clean  and  it  is  recommended  that  they  should  not  be  colder  than  50°  F.  The 
soap- wash  is  made  boiling  hot  and  then  applied  to  the  brickwork.  The  tem- 
perature of  the  alum-solution  is  usually  from  60°  to  70°  F.  when  put  on.  One 
wash  is  applied  and  allowed  to  dry  for  about  24  hours,  after  which  the  other  wash 
is  put  over  it.  When  aluminium  sulphate,  improperly  called  alum,  is  substi- 
tuted for  the  alum,  the  cost  of  the  wash  is  less,  only  two-thirds  as  much  sulphate 
as  alum  is  required  and  the  results  are  better. 

LIME* 

Nature  and  Properties  of  Lime.  Chemically,  lime  is  calcium  oxide.  Used 
in  a  broader  sense,  it  is  the  class-name  of  a  great  variety  of  products  manu- 
factured by  the  calcination  of  limestone.  Limestone  consists  of  the  carbonates 
of  calcium  and  magnesium  which  vary  widely  in  their  ratio  to  each  other.  The 
limestones  used  in  the  manufacture  of  lime  products  may  be  divided  into  two 

•  Valuable  practical  data  relating  to  lime  and  plaster  has  been  furnished  by  the  Charles 
Warner  Company,  of  Wilmington,  Del. 


Specifications  for  Quicklime  1549 

classes,  calcium  limestones  and  dolomitic  limestones.  High-calcium  lime- 
stones contain  only  a  relatively  low  percentage  of  magnesium  carbonate,  while 
dolomitic  limestones  contain  a  considerable  amount  of  it.  Dolomitic  hmestone 
usually  corresponds  roughly  to  the  theoretical  formula  of  dolomite  (CaCOa) 
(MgCOs).  The  CALCINATION  of  limestone  consists  of  heating  to  expel  the  carbon 
dioxide.  The  product  resulting  from  calcination  of  limestone  is  known  as 
quicklime  and  possesses  great  affinity  for  water.  Slaking  is  the  process  of 
adding  water  to  quicklime.  During  the  process  of  slaking,  heat  is  energetically 
evolved  and  much  of  the  water  driven  off  in  the  form  of  steam.  During  this 
slaking  process,  also,  high-calcium  quicklimes  must  be  agitated  and  stirred  con- 
tinually or  a  portion  will  fail  to  receive  the  proper  quantity  of  water  and  will 
contain  unslaked  particles  which  are  likely  to  slake  after  being  used  in  the  work, 
causing  popping,  pitting  and  disintegration.  Dolomitic  hmes  do  not  slake  so 
energetically,  and  while  they  should  be  stirred  while  slaking,  this  is  not  so  neces- 
sary as  with  high-calcium  lii.ies.  Either  class  of  quicklime,  through  faulty  manu- 
facture, is  likely  to  contain  over-burned  portions  which  slake  with  difficulty  and 
may  cause  popping,  etc.,  if  the  lime-paste  is  not  carefully  screened  before  use. 
The  setting  and  hardening  of  common  lime  mortar  is  due,  first,  to  the  drying 
out  and,  secondly,  to  the  absorption  of  carbon  dioxide  from  the  atmosphere  and 
the  formation  of  crystals  of  calcium  carbonate  to  which  the  strength  of  the  mor- 
tar is  ascribed.  In  the  manufacture  and  use  of  common  lime  mortar,  therefore, 
the  raw  material,  limestone,  is  first  calcined,  and  the  carbon  dioxide  expelled;  it 
is  then  slaked  with  water  and  forms  calcium  hj^droxide,  in  which  the  water  is 
gradually  replaced  by  carbon  dioxide.  The  lime  thus  eventually  returns  to  its 
original  carbonate  form.  As  far  as  the  ultimate  result  is  concerned,  there  is 
generally  little  ditference  between  high-calcium  and  dolomitic  quicklimes. 
Owing  to  greater  familiarity  with  one  or  the  other  of  the  classes  of  lime,  archi- 
tects and  builders  in  certain  sections  of  the  country  prefer  one  to  the  other. 

Specifications  for  Quicklime.  The  lime  industry  has  in  recent  years  been 
made  the  subject  of  careful  study  and  the  following  clauses  give  the  various 
requirements  of  Standard  Specifications  for  QuickUme  adopted  by  the  American 
Society  for  Testing  Materials  in  1915. 

1.  Definition.  Quicklime  is  a  material  the  major  part  of  which  is  calcium 
oxide  or  calcium  and  magnesium  oxides,  which  will  slake  on  the  addition  of  water. 

2.  Grades.     Quicklime  is  divided  into  two  grades: 

(a)  Selected.  Shall  be  well -byrned,  picked  free  from  ashes,  Core,  clinker  or 
other  foreign  material. 

(b)  Run-of-Kiln.     Shall  be  well-liurned,  without  selection. 

3.  Forms.     Quicklime  is  shipped  in  two  forms: 
(a)  Lump.     Shall  be  kiln-size. 

{b)  Pulverized  Lime.     Lump  lime  reduced  in  size  to  pa«s  a  K-in  screen. 

4.  Classes.  Quicklime  is  divided  into  four  classes:  (a)  High-Calcium;  (b) 
Calcium;    (<:).Magnesian;    (d)  High-Magnesian. 

5.  Basis  of  Purchase.  The  particular  grade,  form  and  class  of  quicklime 
desired  shall  be  specified  in  advance  by  the  purchaser. 

I.    Chemical  Properties  and  Tests 
(A)  Sampling 

6.  Lime  in  Bulk.  When  quicklime  is  shipped  in  bulk,  the  sample  shall  be  so 
taken  that  it  will  represent  an  average  of  all  parts  of  the  shipment  from  top  to 
bottom,  and  shall  not  contain  a  disproportionate  share  of  the  top  and  bottom 
layers,  which  are  most  subject  to  changes.  The  samples  shall  comprise  at  least 
10  shovelfuls  taken  from  different  parts  of  the  shipment.     The  total  sample 


1550 


Lime 


Parts 


taken  sh;ill  weigh  at  least  loo  lb  and  shall  he  crushed  to  pass  a  i-in  ring  and 
quartered  to  provide  a  15-lb  sample  for  the  laboratory. 

7.  Lime  in  Barrels.  When  quicklime  is  shipped  in  barrels,  at  least  3%  of 
the  number  of  barrels  shall  be  sampled.  They  shall  be  taken  from  various  parts 
of  the  shipment,  dumped,  mixed  and  sampled  as  specified  in  Section  6. 

8.  Laboratory  Samples.  All  samples  to  be  sent  to  the  laboratory  shall  be 
immediately  transferred  to  an  air-tight  container  in  which  the  unused  portion 
shall  be  stored  till  the  quicklime  is  finally  accepted  or  rejected  by  purchaser. 

(B)  Chemical  Tests 

9.  Chemical  Properties,  (a)  The  classes  and  chemical  properties  of  quick- 
lime shall  be  determined  by  standard  methods  of  chemical  analysis,  (b) 
Samples  shall  be  taken  as  specified  in  Sections  6,  7  and  8.  (c)  Quicklime  shall 
conform  to  the  following  requirements  as  to  chemical  composition: 


Chemical 

Composition 

Properties  considered 

High-Calcium 

Calcium 

Magnesian 

High- 
Magnesian 

Select- 
ed 

Run 

of 
kiln 

Select- 
ed 

Run 
of 
kiln 

Select- 
ed 

Run 
of 
kiln 

Select- 
ed 

Run 
of 
kiln 

Calcium  oxide,  per  cent. . 

Magnesium  oxide,  per  ct . 

Calcium  oxide  plus  mag- 
nesium oxide,  min,  per 
cent .          

90 
(min) 

90 

3 

5 

90 
(min) 

5 

7-  =) 

85-90 

90 
3 

85-90 

85 
5 

7  •  "5 

10-25 

90 
3 

5 

10-25 

85 
5 

7.5 

25 
(min) 

90 
3 

5 

25 
(min) 

5 
7.5 

Carbon  dioxide,  max,  per 
cent                  

Silica  plus  alumina  plus 
oxide  of  iron,  max,  per 

n.  Physical  Properties  and  Tests 

10.  Percentage  of  Waste.  An  average  5-lb  sample  shall  be  put  into  a  box 
and  slaked  by,  an  experienced  operator  with  suflicient  water  to  produce  the 
maximum  quantity  of  lime  putty,  care  being  taken  to  avoid  burning  or  drown- 
ing the  lime.  It  shall  be  allowed  to  stand  for  24  hours  and  then  washed  through 
a  20-mesh  sieve  by  a  stream  of  water  having  a  moderate  pressure.  No  material 
shall  be  rubbed  through  the  screens.  Not  over  3%  of  the  weight  of  the  selected 
quickhme  nor  over  5%  of  the  weight  of  the  run-of-kiln  quicklime  shall  be 
retained  on  the  sieve.  The  sample  of  lump  lime  taken  for  this  test  shall  be 
broken  so  that  all  of  it  will  pass  a  i-in  screen  and  be  retained  on  a  }4-m  screen. 
Pulverized  lime  shall  be  tested  as  received. 

III.  Inspection  and  Rejection 

11.  Inspection,     (a)  All  quicklime  shall  be  subject  to  inspection. 

(b)  The  quicklime  may  be  inspected  either  at  the  place  of  manufacture  or  the 
point  of  delivery,  as  arranged  at  time  of  purchase. 

(c)  The  inspector  representing  the  purchaser  shall  have  free  entry,  at  all  times 
while  work  on  the  contract  of  the  purchaser  is  being  performed,  to  all  parts  of 
the  manufacturer's  works  which  concern  the  manufacture  of  the  quicklime 
ordered.  The  manufacturer  shall  afford  the  inspector  all  reasonable  facilities 
for  inspection  and  sampling,  which  shall  be  so  conducted  as  not  to  interfere  un- 
necessarilv  with  the  operation  of  the  works. 


Specifications  for  Hydrated  Lime  1551 

(d)  The  purchaser  may  make  the  tests  to  govern  the  acceptance  or  rejection 
of  the  ciuicklime  in  his  own  laboratory  or  elsewhere.  Such  tests,  however,  shall 
be  made  at  the  expense  of  the  purchaser, 

12.  Rejection.  Unless  otherwise  specified,  any  rejection  based  on  failure 
to  pass  tests  prescribed  in  accordance  with  these  specifications  shall  be  reported 
within  five  days  from  the  taking  of  samples. 

13.  Rehearing.  Samples  which  represent  rejected  quicklime,  shall  be  pre- 
served in  air-tight  containers  for  live  days  from  the  date  of  the  test-report.  In 
case  of  dissatisfaction  with  the  results  of  the  tests,  the  manufacturer  may  make 
claim  for  a  rehearing  within  that  time. 

Hydrated  Lime.  The  slaking  of  quicklime  is  an  operation  which  is  almoslj 
invarial:)ly  carried  on  by  laborers  who  have  little  or  no  conception  of  the  impor-' 
tance  of  their  task.  As  a  result,  many  failures  have  been  charged  to  lime  in  the 
past  which  actually  w-ere  due  to  improper  preparation  during  the  slaking  opera- 
tion. The  new  product  knov/n  as  hydrated  lime  has  been  offered  widely  to  the 
trade  in  recent  years  and  has  met  with  much  success.  Hydrated  lime  is  a  dry 
flocculent  powder  resulting  from  the  slaking  of  quicklime  by  mechanical  means,, 
with  an  amount  of  water  which  is  sufBcient  to  satisfy  the  calcium  oxide,  but 
insufRcient  to  make  a  paste  or  putty.  Hydrated  lime  is  manufactured  in  me- 
chanical hydrators  in  which  the  batches  of  .quicklime  and  water  used  are  carefully 
proportioned  by  weight.  After  passing  from  the  hydrator,  hydrated  Hme  is 
subjected  to  a  mechanical  system  of  separation  which  eliminates  the  coarse  or 
impure  particles  which  may  cause  popping,  etc.  Hydrated  lime  is  sold  in  bags  of 
definite  weight  and  requires  only  to  be  mixed  with  sand  and  water  to  make  the 
mortar.  The  bags  have  usually  been  made  of  heavy  burlap  or  duck  cloth,  con- 
taining 100  lb,  or  of  paper,  containing  40  lb.  Several  of  the  more  prominent 
manufacturers  of  hydrated  lime  in  the  United  States  employ  chemists  who 
regularly  superintend  the  manufacture  of  hydrated  lime,  just  as  the  chemists  in 
Portland-cement  factories  superintend  the  proportioning  of  the  raw  mix  going 
to  the  kilns  to  be  burned  for  Portland  cement.  The  hydrated  lime  manufac- 
tured under  such  chemical  supervision  is  a  reliable  product  free  from  tendencies 
which  might  give  rise  to  popping,  pitting  or  disintegration.  Hydrated  lime  of 
good  quality  may  l)e  used  for  almost  any  purpose  for  which  lime  mortar  is  used, 
and  is  by  some  considered  a  more  reliable  product  than  quicklime.  Among  the 
newer  uses  for  hydrated  lime  may  be  mentioned  its  employment  in  cement  mor- 
tars and  concrete.  An  addition  of  about  15%  of  hydrated  lime  to  cement 
mortar  or  concrete  decreases  its  permeability  to  water,  reduces  the  cracking 
due  to  shrinkage,  etc.,  and  increases  the  plasticity  of  the  mortar  or  concrete, 
thus  preventing  separation  of  the  sand,  stone  and  cement  and  causing  the  mix- 
ture to  flow  and  fill  the  forms  more  readily.     (See  Macgregor  tests,  page  276.) 

Specifications  for  Hydrated  Lime.  The  following  clauses  give  the  various 
requirements  of  Standard  Specifications  for  Hydrated  Lime  adopted  by  the 
American  Society  for  Testing  Materials  in  1915. 

1.  Definition.  Hydrated  lime  is  a  dry  flocculent  powder  resulting  from  the 
hydration  of  quicklime. 

2.  Classes.  Hydrated  Hme  is  commercially  divided  into  four  classes:  (a) 
High-Calcium;    (b)  Calcium;    (c)  Magnesian;    (d)  High-Magnesian. 

3.  Basis  of  Purchase.  The  particular  type  of  hydrated  lime  desired  shall 
be  specified  in  advance  of  purchase, 

I.   Chemical  Properties  and  Tests 

4.  Sampling.  The  sample  shall  be  a  fair  average  of  the  shipment.  Three  j)er 
cent  of  the  packages  shall  be  sampled.  The  sample  shall  be  taken  from  the 
surface  to  the  center  of  the  package.     A  2-lb  sample  to  be  sent  to  the  laboratory 


1552 


Lime 


Pari  3 


shall  immediately  be  transferred  to  an  air-tight  container,  in  which  the  unused 
portion  shall  be  stored  until  the  hydrated  lime  has  been  finally  accepted  or  re- 
jected by  the  purchaser. 

5.  Chemical  Properties,  (a)  The  classes  and  chemical  properties  of  hy- 
drated Ume  shall  be  determined  by  standard  methods  of  chemical  analysis,  (b) 
The  non-volatile  portion  of  hydrated  Hme  shall  conform  to  the  following  require- 
ments as  to  chemical  composition: 

Chemical  Composition 


Properties  considered 

High- 
Calcium 

Calcium 

Magnesian 

High- 
Magnesian 

Calcium  oxide,  per  cent 

Magnesium  oxide,  per  cent.  . 
Silica  plus  alumina  plus  oxide 

of  iron,  max,  per  cent 

Carbon  dioxide,  max,  percent 
Water 

£9o(min) 

5 

Sufficient  to 
hydrate  the 
calcium-ox- 
ide content 

85-90 

5 

Sufficient  to 
hydrate  the 
calcium-ox- 
ide content 

10-25 
5 

Sufficient  to 
hydrate  the 
calcium-ox- 
ide content 

25  (min) 
5 

Sufficient  to 
hydrate  the 
calcium-ox- 
ide content 

II.    Physical  Properties  and  Tests 

6.  Fineness.  A  loo-g.  sample  shall  leave  by  weight  a  residue  of  not  over 
5%  on  a  standard  loo-mesh  sieve  and  not  over  0.5%  on  a  standard  30-mesh 
sieve. 

7.  Constancy  of  Volume.  Hydrated  lime  shall  be  tested  to  determine  its 
constancy  of  volume  in  the  following  manner:  Equal  parts  of  hydrated  lime 
under  test  and  volume-constant  Portland  cement  shall  be  thoroughly  mixed 
together  and  gauged  with  water  to  a  paste.  Only  sufficient  water  shall  be 
used  to  make  the  mixture  workable.  From  this  paste  a  pat  about  3  in  in  diam- 
eter and  1 2  in  thick  at  the  center,  tapering  to  a  thin  edge,  shall  be  made  on  a 
dean  glass  plate  about  4  in  square.  This  pat  shall  be  allowed  to  harden  24 
hours  in  moist  air  and  shall  be  without  popping,  checking,  cracking,  warping 
or  disintegration  after  5  hours'  exposure  to  steam  above  boihng  water  in  a 
loosely  closed  vessel. 

in.    Packing  and  Marking 

8.  Packing.  Hydrated  lime  shall  be  packed  either  in  cloth  or  paper  bags 
and  the  weight  shall  be  plainly  marked  on  each  package. 

9.  Marking.  The  name  of  the  manufacturer  shall  be  legibly  marked  or 
tagged  on  each  package. 

IV.    Inspection  and  Rejection 

10.  Inspection,     (a)  All  hydrated  lime  shall  be  subject  to  inspection. 

(b)  The  hydrated  Hme  may  be  inspected  either  at  the  place  of  manufacture 
or  the  point  of  delivery,  as  arranged  at  the  time  of  purchase. 

(c)  The  inspector  representing  the  purchaser  shall  have  free  entry,  at  all  times 
while  work  on  the  contract  of  the  purchaser  is  being  performed,  to  all  parts  of  the 
manufacturer's  works  which  concern  the  manufacture  of  the  hydrated  Hme 
ordered.  The  manufacturer  shall  all'ord  the  inspector  all  reasonable  facilities 
for  inspection  and  sampling,  which  shall  })e  so  conducted  as  not  to  interfere  un- 
necessarily with  the  operation  of  the  works. 

(d)  The  purchaser  may  make  the  tests  to  govern  the  acceptance  or  rejection 
of  the  hydrated  lime  in  his  own  laboratory  or  elsewhere.  Such  tests,  however, 
shall  be  made  at  the  expense  of  the  purchaser. 


Sand  and  Gravel  1553 

11.  Rejection.  Unless  otherwise  specified,  any  rejection  based  on  failure  to 
pass  tests  prescribed  in  these  specifications  shall  be  reported  within  five  working 
days  from  the  taking  of  samples. 

12.  Rehearing.  Samples  which  represent  rejected  hydrated  lime  shall  be 
preserved  in  air-tight  containers  for  five  days  from  the  date  of  the  test-report. 
In  case  of  dissatisfaction  with  the  results  of  the  tests,  the  manufacturer  may 
make  claim  for  a  rehearing  within  that  time. 

Alca  Lime.  A  recent  development  in  the  lime  industry  is  Alca  Lime.*  This 
is  a  matendl  said  to  combine  the  plasticity  and  sand-carrying  qualities  of  lime 
mortar  with  the  strength,  hardness  and  quicker  set  of  the  gypsum  plasters. 
It  is  composed  of  approximately  85%  of  hydrated  lime  and  15%  of  a  specially 
prepared  material  containing  alumina  and  silica  in  such  proportions  as  to  com- 
bine, forming  bodies  which  greatly  contribute  to  the  strength,  hardness  and 
plasticity  of  the  product.  It  is  sold  in  loo-lb  packages  and  requires  only  to  be 
mixed  with  sand  and  water  before  use.  When  used  for  plastering,  it  has  the 
characteristics  of  lime  mortar,  and  while  it  becomes  hard  and  strong,  it  is  claimed 
that  it  is  free  from  the  so-called  sounding-board  effects  noticed  in  some  hard-wall 
plasters.  It  is  not  injured  by  water  and  is  often  used  for  outside  stucco-work 
and  also  as  a  brick-laying  mortar  in  place  of  lime  mortar  gauged  with  Portland 
cement.  The  manufacturers'  directions  for  the  use  of  Alca  Lime  should  be  care- 
fully observed,  and  this  may  be  said  of  all  prepared  plastering  or  cementing 
materials. 

Useful  Data  on  Quicklime.  Quicklime  is  shipped  either  in  barrels  or  in  bulk. 
In  dry  climates  it  will  keep  for  a  long  time  in  bulk,  but  in  damp  climates  and 
along  the  coast  it  soon  slakes  unless  enclosed  in  barrels.  By  Act  of  Congress, 
August  23,  19 1 6,  it  is  required  that  Hme  in  barrels  shall  be  packed  only  in  barrels 
containing  280  lb  or  iSo  lb,  net  weight.  When  shipped  in  bulk  it  is  generally 
sold  by  the  bushel  of  80  lb,  3H  bushels  or  280  lb,  net,  of  Hme  being  considered 
as  equivalent  to  a  large  barrel.  Other  weights  are  180  lb,  net,  per  small  barrel, 
and  64  lb  per  cu  ft.  The  average  yield  of  lime-paste  from  the  best  Easfern 
limes  has  been  found  to  be  2.62  times  the  bulk  of  unslaked  lime.  A  barrel  of 
good  quality  well-burned  lime  should  make  8  cu  ft,  or  20  pails,  of  lime-paste  or 
putty.  Careful  experiments  conducted  by  United  States  engineers  have 
demonstrated  that  the  best  mortar  is  obtained  by  mixing  one  part  of  lime  paste 
to  two  parts  of  sand. 

Cements.     For  data  on  cements,  see  Chapter  III. 

SAND  AND  GRAVEL 

Sand  is  obtained  from  banks  or  pits,  from  river-beds  and  from  the  seashore. 
Pit-sand  or  bank-sand,  free  from  clay  or  earthy  materials,  is  generally  considered 
the  best  for  mortar,  although  excellent  sand  is  often  obtained  from  river-beds. 
Sea-sand  contains  alkaline  salts  which  attract  and  retain  moisture  and  which, 
unless  thoroughly  washed,  cause  efiiorescence  when  used  in  brickwork.  Both 
sea-sand  and  river-sand  have  more  or  less  rounded  grains,  to  which  lime  or  cement 
will  not  adhere  as  well  as  to  sharp,  angular  grains.  Both  are  extensively  used, 
however,  for  lack  of  better  materials.  The  use  of  sand  in  mortar  is  to  prevent 
excessive  shrinkage  and  to  save  the  cost  of  lime  or  cement.  Sand,  when  used  in 
the  proportion  of  i  :  2,  strengthens  lime  mortar,  but  any  addition  of  sand  to 
cement  weakens  it. 

Screening  Sand.  Sand  for  mortar  must  ordinarily  be  screened.  Sand  for 
brown  mortar  for  plastering  or  common  brickwork  is  ordinarily  run  through  a 

*  This  is  a  patented  article  and  is  offered  for  sale  by  many  licenses  in  the  United  States 
under  the  Spackraan  patents. 


1554  Lathing  and  Plastering  Part  3 

No.  4  screen  having  4  by  4  meshes  to  the  inch.  For  sand  finish  and  mortar  for 
pressed  brickwork,  either  a  No.  10  or  a  No.  12  screen  with  10  by  10  or  12  by  12 
meshes  to  the  inch  is  commonly  used.  For  rubble  stonework  the  sand  is  not 
ordinarily  screened,  unless  it  contains  much  gravx'l,  in  which  case  it  should  be 
screened  through  a  ^-in  mesh. 

.  Weight  of  Sand.  Dry  sand  weighs  from  80  to  115  lb  per  cu  ft.  The  aver- 
age weight  of  damp  (not  wet)  sand  is  about  96  lb  per  cu  ft,  or  about  2  600  lb 
per  cu  yd.  The  voids  for  ordinary  sand  range  from  0.3  to  0.5  of  the  volume,  the 
average  for  screened  sand  suitable  for  mortar  being  0.35  of  the  volume. '  The 
more  uneven  the  grains  in  size  the  smaller  the  percentage  of  the  voids.  A 
one-horse  load  of  sand  contains  about  22  cu  ft.  Two-horse  loads  vary  from 
iM  to  2  yd.  The  amount  hauled  per  load  in  the  larger  cities  is  generally  fixed 
by  the  Team  Owners'  Association.  i}4  yd  is  a  fair  load,  i>^  yd  a  good  load 
and  2  yd  a  large  load. 


LATHING  AND  PLASTERING 

Wooden  Laths  should  be  well  seasoned,  free  from  sap,  bark  and  dead  knots. 
Bark  on  laths  is  quite  sure  to  stain  the  plaster.  White  pine  is  generally  con- 
sidered the  best  wood  for  laths,  although  spruce  and  hemlock  laths  are  much 
used.  Hard  pine  is  not  a  good  material,  as  it  contains  too  much  pitch.  The 
regular  size  of  laths  is  K  in  by  i  y-z  in  by  4  ft.  The  width  and  thickness  vary  some- 
what in  different  rpills.  There  is  a  new  lath  on  the  market,  which  is  only  32  in 
long  and  which  costs  from  $1.75  to  $2  less  than  the  48-in  lengths.  Laths  are 
sold  by  the  thousand,  in  bunches  containing  100  laths,  from  $4.50  to  $5.50  be- 
ing about  the  average  prices.     (Pre-war  prices.) 

Metal  Lathing.     (See  Chapter  XXIII,  pages  883  to  887.) 

Plastering  on  laths  is  generally  done  in  three  coats.*  The  first  coat  is  called 
the  scratch-coat;  the  second,  the  brown  coat,  and  the  third,  the  white  coat, 
SKiM-co.\T,  or  FINISH.  On  brickwork  or  stonework  the  scratch-coat  is  generally 
omitted.  For  first-class  work  each  coat  should  be  permitted  to  dry  thoroughly 
before  the  next  coat  is  appHed,  and  under  no  circumstances  should  the  finish- 
coat  be  applied  before  the  brown  coat  is  thoroughly  drJ^ 

Drawn  Workjs  a  brown  coat  appUed  to  a  scratch-coat  from  the  same  staging, 
immediately  after  the  scratch-coat  is  applied.  It  is  a  little  cheaper  than  dry 
SCRATCH,  and  much  of  it  is  done  in  the  Western  States. 

The  Scratch-Coat  should  always  be  made  rich  iii  lime,  and  should  contain  1 H 
bu  of  hair,  or  an  equivalent  quantity  of  fiber  to  each  cask  of  lime,  or  i  bu  of  hair 
to  2  of  lime.  A  proportion  of  one  part  hme-paste  to  two  parts  of  sand  will  re- 
'quire  I  cask  (23.^  bu)  of  Hme  to  5H  bbl  of  screened  sand. 

,;  The  Brown  Coat  should  contain  i  cask  (2^2  bu)  of  lime  to  7  bbl  of  screened 
sand,  and  i  bu  of  hair  to  5  of  lime.  Very  Httle  plaster  is  mixed  by  measure,  how- 
ever, the  usual  custom  being  to  mix  as  much  sand  with  the  slaked  hme  as  the 
mortar-mixer  thinks  it  will  stand  and  give  satisfaction,  the  tendency  being  always 
to  make  the  lime  go  as  far  as  possible. 

The  Third  or  Finishing  Coat  is  designated  by  various  terms,  such  as  skim- 
coat,  WHITE  COAT,  putty-coat,  sand-finish,  ctc.     The  skim-coat  as  used  in  the 

♦  In  the  Eastern  States,  dwellings  of  moderate  cost  are  generally  plastered  with  two- 
coat  work,  the  first  or  scratch-coat  being  brought  nearly  to  the  grounds,  and  carefully 
straightened  to  receive  the  skim-coat. 


Plastering  1555 

Eastern  States  is  generally  composed  of  lime-putty  and  washed  beach-sand  in 
equal  proportions. 

Sand  Finish,  which  has  a  rough  surface  resembling  coarse  sandpaper,  is  mixed 
in  the  same  way,  only  that  coarser  sand  and  more  of  it  is  used,  and  it  is  finished 
with  a  wooden  or  cork-faced  float. 

White  Coating  or  Hard  Finish  generally  means  a  composition  of  lime-putty 
and  plaster  of  Paris,  to  which  marble-dust  is  sometimes  added.  Plaster  of  Paris 
and  marble-dust  when  used  should  not  be  mixed  with  the  lime-putty  until  a  few 
moments  before  using,  and  no  more  should  be  prepared  at  one  time  than  can  be 
used  up  at  once,  as  it  soon  SETS,  after  which  it  should  not  be  used.  The  skim- 
coat  or  hard  finish  should  be  finished  with  a  steel  trowel  and  wet  brush.  The 
more  the  work  is  troweled  the  harder  it  becomes.  A  superior  hard  finish  is  ob- 
tained by  mixing  4  parts  of  Best's  Kecne's  cement  to  i  part  hme-putty. 

Mortar  for  Plastering.  .  To  make  sure  that  the  lime  is  well  slaked,  it  Is  cus- 
tomary to  require  that  the  mortar  for  plastering  shall  be  mixed  at  least  seven 
days  before  it  is  used. 

Hair  such  as  is  used  by  plasterers  is  obtained  from  the  hides  of  cattle,  and  after 
being  washed  and  dried  is  put  up  in  paper  bags,  each  bag  being  supposed  to  con- 
tain I  bushel  of  hair  when  beaten  up.  Each  package  is  supposed  to  weigh  from 
7  to  8  lb  but  the  weight  often  falls  short.  Asbestos  and  Manilla  fiber  are  both 
used  in  place  of  hair;  they  are  cleaner  than  hair  and  are  said  to  be  less  injured  by 
the  lime.  It  is  much  better  to  add  the  hair  to  the  lime-paste  after  it  is  cold 
and  before  mixing  in  the  sand,  as  hot  lime,  and  the  steam  caused  by  the  slaking, 
burn  or  rot  the  hair  so  as  to  greatly  weaken  it.  The  common  practice  is  to  put 
the  hair  in  the  mortar-box,  run  off  the  hot  lime  as  soon  as  it  is  slaked,  throw  in 
the  sand  and  mix  the  whole  together.  It  is  then  thrown  out  of  the  box  into  a 
pile  and  a  new  batch  mixed  up. 

Machine-Made  Mortar.  In  several  of  the  larger  cities  plants  have  been 
equipped  for  the  mixing  of  mortar  by  machinery.  Machine-mixed  mortar  should 
be  much  better  than  the  ordinary  hand-mixed  mortar,  for  the  reason  that  time 
can  be  given  for  the  lime  to  slake,  the  lime  and  sand  can  be  accurately  measured, 
and  the  hair  and  lime  are  not  mixed  with  the  lime  until  just  before  delivery.  The 
mixing  may  also  be  more  thoroughly  and  evenly  done  by  machinery  than  is 
possible  by  hand. 

Improved  Wall-Plasters.  Owing  to  the  difficulty  of  obtaining  sufficient  space 
in  building  operations  in  central  sections  of  large  cities  to  properly  slake  sufficient 
lime  mortar  to  carry  on  the  plastering  with  the  necessary  speed,  other  kinds  of 
plastering  materials  have  come  into  existence  in  recent  years.  These  are  known 
as  gypsum  plasters  or  hard-wall  plasters.  The  base  of  these  products  is 
calcium  sulphate  or  gypsum  which  has  been  calcined  to  partially  expel  the 
water.  The  setting  and  hardening  of  these  products  is  dependent  upon  their 
combining  chemically  with  the  gauging  water  and  crystallizing  in  the  same 
chemical  form  as  the  material  possessed  before  calcination.  All  hard-wall 
plasters  contain  material  added  for  the  purpose  of  controlling  the  set.  The 
straight  calcined  gypsum  sets  in  a  very  few  minutes,  which  time  would  be  en- 
tirely too  short  to  permit  the  workmen  to  apply  the  plaster  to  the  wall  and 
straighten  it  up  before  it  had  set.  These  plasters  are  characterized,  also,  by 
their  inability  to  carry  as  much  sand  as  lime  mortar.  Many  of  them  contain 
other  substances,  such  as  clay  or  hydrated  lime,  added  to  improve  their  plastic- 
ity. Hard-wall  plasters  manufactured  in  the  eastern  part  of  the  United  States 
from  rock-gypsum  invariably  contain  15%,  more  or  less,  of  clay  or  hydrate, 
'^,dHed  for  this  purpose.     Plasters  made  in  Kansas,  Oklahoma,  Texas  and  other 


1556  Lathing  and  Plastering  Part  3 

Western  and  Southwestern  States  are  made  from  earth-gypsum.  In  the  case 
of  these  materials,  clay  and  hydrated  lime  are  not  added,  for  the  reason  that  the 
earth-gypsum  contains  considerable  clay  matter,  which  renders  further  additions 
unnecessary. 

Use  of  Hard-Wall  Plasters.  Hard-wall  plasters  are  found  to  be  very  con- 
venient in  cases  where  space  and  time  are  the  most  important  elements  in  the 
building  operation.  They  set  more  rapidly  than  lime  plasters,  thus  permitting 
the  white  coating  and  finishing  of  the  job  to  be  completed  earlier.  While  hard- 
wall  plasters  become  extremely  hard,  this  property  is  sometimes  considered 
objectionable,  as  it  may  give  rise  to  what  is  called  the  sounding-board  effect. 

Keene's  Cement  Plasters.  Asdistinguished  from  theordinary  hard-wall  plasters, 
there  exists  another  class  of  gypsum-products  which,  however,  are  somewhat 
different  in  the  method  of  preparation  and  behavior.  In  the  manufacture  of 
these  materials,  the  gypsum  is  calcined,  immersed  in  a  bath  of  alum  or  similar 
chemical  and  recalcined.  The  name  Keene's  cement  is  usually  applied  to  these 
materials,  which  are  made  by  several  manufacturers  in  this  country.  These  are 
slow-setting  and  ultimately  attain  great  strength  and  hardness.  Keene's  cement 
is  generally  used  with  considerable  Hme-putty  or  hydrated  lime.  The  use  of 
equal  parts  of  hydrated  lime  and  Keene's  cement  in  making  a  plastering  material 
is  often  recommended  and  found  in  specifications.  (For  Alca  lime  used  as  a 
wall-plaster,  see  page  1553.) 

Advantages  of  Improved  Wall-Plasters.  Among  the  advantages  gained  by 
the  use  of  these  plasters  are  uniformity  in  strength  and  quality,  extra  hardness 
and  toughness,  freedom  from  pitting,  saving  in  time  required  in  making  and  dry- 
ing, minimum  danger  from  frost  while  being  applied  and  before  set,  less  weight 
and  moisture  in  the  building,  and,  in  some  cases,  greater  resistance  to  the  action 
of  fire. 

Measuring  Plasterers'  Work.  Lathing  is  always  figured  by  the  square  yard 
and  is  generally  included  with  the  plastering,  although  in  small  country  towns  the 
carpenter  often  puts  on  the  laths.  Plastering  on  plane  surfaces,  such  as  walls 
and  ceilings,  is  always  measured  by  the  square  yard,  whether  it  is  one-coat,  two- 
coat,  or  three-coat  work,  or  lime  or  hard  plaster.  In  regard  to  deductions  for 
openings,  custom  varies  somewhat  in  different  parts  of  the  country  and  also  with 
different  contractors.  Some  plasterers  allow  one-half  the  area  of  openings  for 
ordinary  doors  and  windows,  while  others  make  no  allowance  for  openings  of  less 
than  7  sq  yd. 

Miscellaneous  Details.  Returns  of  chimney-breasts,  pilasters  and  all  strips 
less  than  12  in  in  width  should  be  measured  as  12  in  wide.  Closets,  soffits  of 
stairs,  etc.,  are  generally  figured  at  a  higher  rate  than  plain  walls  or  ceilings,  as  it 
is  not  as  easy  to  get  at  them.  For  circular  or  elliptical  work,  domes  or  groined 
ceilings,  an  additional  price  is  made.  If  the  plastering  cannot  be  done  from 
trestles  an  additional  charge  must  be  made  for  staging.  Whenever  plastering  is 
done  by  measurement  the  contract  should  definitely  state  whether  or  not  open- 
ings are  to  be  deducted,  and  a  special  price  should  be  made  for  the  stucco-work, 
based  on  the  full-size  details. 

Cornices  and  Moldings.  Stucco  cornices  and  molded  work  are  generally 
measured  by  the  superficial  foot,  measuring  on  the  profile  of  the  molding.  When 
less  than  1 2  in  in  girth  they  are  usually  rated  as  i  ft.  For  each  internal  angle  i 
lin  ft  should  be  added,  and  for  external  angles,  2  lin  ft.  For  cornices  on  circular 
or  elliptical  work  an  additional  price  should  be  charged.  Enriched  moldings  are 
generally  figured  by  the  linear  foot,  the  price  depending  upon  the  design  and  size 
of  the  mold. 


Cost  of  Lathing  and  Plastering  1557 

Quantities  of  Materials  for  Lathing  and  Plastering 

Miscellaneous  Data.  To  cover  loo  sq  yd  requires  from  i  400  to  1  soolaihs, 
or  say  i  450  for  an  average  jol),  and  10  lb  of  threepenny  fine  nails. 

Three-coat  plastering  on  wooden  laths,  plaster-of-Paris  finish,  will  require 
from  10  to  12  bu  of  lime,  13^2  cu  yd  of  sand,  2  bu  of  hair  and  100  lb  of  plaster  of 
Paris  per  100  sq  yd. 

If  the  finish-coat  is  omitted,  deduct  2  bu  of  hme  and  all  of  the  plaster  of  Paris. 

If  sand-finished,  omit  the  plaster  of  Paris  and  add  J-^  cu  yd  of  sand. 

To  cover  100  sci  yd  with  two  coats  on  brick  or  stone  walls,  tlie  brown  coat  and 
finishing  coats,  will  require  from  8  to  10  bu  of  lime,  i^{!  cu  yd  of  sand,  and  100  lb 
of  plaster  of  Paris,  to  100  sq  yd. 

Using  Best's  Keenc's  cement  for  brown  mortar  and  Keene's  finish  on  expanded- 
metal  lath  will  require,  for  brown  mortar,  550  lb  of  cement,  5V2  bu  of  lime,  2  cu 
yd  of  sand  and  2  bu  of  hair;  for  the  finish,  joo  lb  of  cement  and  i  bu  of  lime  per 
100  yd. 

Hard  plasters  on  expanded-mctal  lath,  plaster-of-Paris  finish,  require,  for 
brown  mortar,  2  000  lb  of  plaster  and  2  cu  yd  of  sand;  for  the  finish,  i  bu  of  lime 
and  100  lb  of  plaster  of  Paris  per  100  yd. 

Cost  of  Lathing  and  Plastering.  The  average  price  for  putting  on  wooden 
laths,  labor  only,  is  4^4  cts  per  yard.  For  expanded  or  sheet-metal  laths  on 
wooden  studding,  s^i  cts;   on  steel  studding,  wired,  from  10  to  12  cts. 

The  cost  of  putting  three  coats  on  laths,  plaster-of-Paris  finish,  labor  only, 
runs  about  22  cts  per  yard. 

With  sand  finish  the  cost  is  about  23  cts. 

These  figures  are  based  on  plasterers'  wages  at  75  cts  per  hoiir,  and  50  cts- 
per  hour  for  hod-carriers  and  mortar  mixers. 

The  following  schedule  *  gives  the  average  cost  of  different  kinds  of  plastering, 
based  on  lime  at  40  cts  per  bushel,  sand  at  75  cts  per  load  of  lU'  cu  yd,  hair  at  40 
cts  per  bushel,  plaster  of  Paris  at  50  cts  per  100  lb. 

Scratch  and  brown  coat  (lime)  on  wooden  laths 25  cts  per  sq  yd. 

Three  coats  (lime)  on  wooden  laths,  plaster-of-Paris  finish  . .     30  cts  per  sq  yd. 

Three  coats  (lime)  on  wooden  laths,  sand  finish 30  cts  per  sq  yd. 

Brown  coat  and  finish  on  brick  walls 23  cts  per  sq  yd. 

For  hard-wall  plaster  instead  of  Hme,  add 3  cts  per  sq  yd. 

Three   coats    (lime),   plaster-of-Paris   finish,   metal  lath  on 

wooden  studding 65  cts  per  sq  yd. 

Three  coats  (lime)  plaster-of-Paris  finish,  metal  lath  on  steel 

studding 68  cts  per  sq  yd. 

For  Keene's  cement  finish,  add 10  cts  per  sq  yd. 

For  blocking  in  imitation  of  tile,  add 50  cts  per  sq  yd. 

Two  coats   hard-wall  plaster,   pLister-of-Paris  finish,  metal 

lath,  wooden  studding '. 70  cts  per  sq  yd. 

Two  coats   hard-wall  plaster,   plaster-of-Paris  finish,  metal 

lath  on  steel  studs 73  cts  per  sq  yd. 

For  Keene's  cement  finish,  add 10  cts  per  sq  yd. 

Portland  cement,  brown  coat,  finished  with  Keene's  cement 

blocked  in  imitation  of  tile,  3  by  6  in $2.80  per  sq  yd. 

For  running  base,"  9  in  high,  in  Best's  Keene's  cement 10  cts  per  ft. 

For  running  plain  moldings  in  plaster  of  Paris,  from  3  to  5  cts  per  inch  of  girth. 
For  finishing  shafts  of  columns,  from  16  to  24  in  in  diam.,  from  12  to  14  ft  high, 
$3  per  column  (labor  only). 

*  These  are  pre-war  prices  and  the  unit  values  per  sq  yd  must  be  largely  increased  on 
account  of  the  increase  in  wacres  and  materials. 


155S 


Lumber  and  Carpenters'  Work 


Parts 


These  prices,  of  course,  vary  somewhat  in  different  sections  of  the  country. 
In  some  locaHties  prices  for  materials  or  labor  are  less,  in  others  higher. 

Staff  is  a  composition  of  plaster  of  Paris  and  hemp-fiber,  cast  in  molds,  and 
nailed  or  wired  in  place.  All  of  the  buildings  of  the  Columbian  Exix>sition  at 
Chicago  (1893)  were  covered  with  this  material  and  all  of  the  temporary  build- 
ings of  the  St.  Louis  Exposition  (1904).  It  is  not  sufficiently  durable  for  per- 
manent work  unless  it  is  frequently  painted.  The  cost  of  staff,  as  used  on  the 
buildings  at  Chicago  in  1893,  varied  from  $2  to  $2.25  per  sq  yd. 


DATA  ON  LUMBER  AND  CARPENTERS'  WORK* 

Relative  Hardness  of  Woods.  Taking  shell-bark  hickory  as  the  highest 
standard  of  our  forest-trees,  and  calling  that  100,  other  trees  will  compare  with  it 
for  hardness  as  follows: 


Shell-bark  hickory 100 

Pignut  hickory 96 

White  oak 84 

White  ash 77 

Dogwood 75 

Scrub-oak 73 

White  hazel 72 

Apple-tree 70 

Red  oak 69 

White  beech 65 

Black  walnut 65 

Black  birch 62 


Yellow  oak 60 

Hard  maple 56 

White  elm 58 

Red  cedar 56 

Wild  cherry 55 

Yellow  pine 54 

Chestnut 52 

Yellow  poplar 51 

Butternut 43 

White  birch 43 

White  pine 30 


Weight  of  Rough  Lumber  per  i  000  Feet 

BOARD-MEASURE,    APPROXIMATE 
For  weight  of  various  woods  see  tables  on  pages  1501  to  1508 


Kind  of  wood 


Ash 

Chestnut 

Hemlock 

Maple,  hard. . . 
Maple,  soft .  . . . 

Oak,  red 

Oak,  white 

Pine,  long-leaf 

Pine,  white 

Poplar 

Spruce 

Sycamore 

W^alnut,  black. 


Green  from 

saw, 

lb 


4  600 

4  200 
5400 

5  000 
5  500 
5  700" 
4500 
3500 
4  000 

3  ISO 

4  750 
4900 


Shipping- 
dry, 
lb 


3000 
4150 
3650 
4250 
4500 
3500 
2  500 
3000 

2  700 

3  200 

4  000 


Well- 
seasoned, 
lb 


3  500 

3900 
3300 

4  000 
4  100 

2  400 
2  900 
2300 
3000 
3800 


Kiln-dried, 
lb 


3  200 

3400 
3000 
3400 
3600 


2  200 

2400 

2  200 

*  A  comprehensive  booklet  giving  the  rules  for  the  grading  and  classification  of  yellow- 
pine  lumber  and  dressed  stock  may  be  obtained  from  The  Southern  Pine  Association, 
New  Orleans,  La. 


Measurement  of  Rough  Lumber 


1559 


Framing-Lumber  may  commonly  be  purchased  in  any  of  the  following  nomi- 
nal sizes,  except  that  common  pine,  spruce,  and  hemlock  cannot  usually  be  ob- 
tained in  larger  sizes  than  12  by  12  in. 


Nominal  Sizes  of  Framing-Lumber 

ill 

in 

in 

in 

2X4 

3X  6 

4X12 

8X12 

2     X  6 

3X  8 

4X14 

8X14 

2X8 

3X10 

6X  6 

^      10X10 

2    Xio 

3X12 

6X  8 

10X12 

2    X12 

3X14 

6X10 

10X14 

2     X14 

3X16 

6X12 

10X16 

2     X16 

4X  4 

6X14 

12X12 

2I/2X12 

4X  6 

6X16 

12X14 

2V2X14 

4X  8 

8X  8 

12X16 

2HX16 

4X10 

8X10 

14X14 
14X16 

In  some  of  the  New  England  mills,  the  following  sizes,  also,  are  sawed:  2  by  3, 
2  by  5,  2  by  7,  2  by  9,  3  by  4  and  3  by  5  in.  These  sizes  are  not  commonly  carried 
in  stock,  and  in  .most  localities  would  have  to  be  obtained  by  ripping  larger 
gizes.  Most  of  the  long-leaf  yellow  pine  and  Douglas  fir  is  shipped  surfaced 
ONE  SIDE  AND  EDGE,  the  actual  dimensions  being  from  Yi  in  to  %  in,  and  some- 
times y2  in,  scant  of  the  nominal  dimensions.  When  framing-lumber  is  required^ 
to  be  full  to  dimensions  it  should  be  ordered  in  the  rough,  and  a  Special  contract 
made  on  that  understanding. 

Lengths  oi  Framing-Timbers.  All  timber  is  cut  and  sold  in  even  lengths,  as 
10,  12,  14  and  16  ft.  Odd  and  fractional  lengths  are  counted  as  the  next  higher 
even  length;  consequently  it  is,  in  certain  cases,  possible  and  economical  to  plan 
buildings  so  that  timbers  of  even  lengths  may  be  used  without  waste. 

Measurement  of  Rough  Lumber.  All  rough  lumber  is  sold  by  the  foot, 
board-measure,  one  foot  being  the  equivalent  of  a  board  i  ft  wide,  i  ft  long,  and 
I  in  thick.  To  compute  the  board-measure  in  any  board,  plank,  or  timber,  di- 
vide the  nominal  sectional  area,  in  inches,  by  12,  and  multiply  by  the  length  in 
feet.  Thus  the  number  of  feet  in  a  2  by  4-in  scantling,  8  ft  long  =  (2  x  4/12)  X 
8=  51,^  ft,  board-measure.  A  lo-in  board,  12  ft  long,  contains  (i  X  10/12)  x 
12  =  10  ft,  board-measure.  Extensive  tables  are  published  showing  the  feet,  in 
board  measure,  for  almost  any  commercial  size  of  timber.  The  following  table, 
however,  although  compact,  will  enable  one  to  readily  estimate  the  number  of 
FEET  in  any  of  the  standard  sizes  of  boards,  planks,  or  timbers.  To  use  the  table, 
find  the  product  of  the  lateral  dimensions  of  the  cross-section;  then  in  the 
column  having  a  heading  equal  to  this  product,  and  in  the  horizontal  line  oppo- 
site the  given  length  will  be  found  the  number  of  feet  in  board-measure.  Thus, 
for  a  3  by  4,  2  by  6,  or  i  by  12-in  timber  look  in  the  column  headed  12;  for  a  2 
by  12,  4  by  6,  or  3  by  8-in  piece,  look  in  the  column  headed  24.  For  lengths  not 
given  in  the  table,  take  either  twice  the  length  and  divide  by  2,  or  one-half  the 
length  and  multiply  by  2.  Where  timbers  of  the  same  size  abut  end  to  end,  it 
economizes  labor  in  reducing  to  board-measure  to  take  the  full  length;  for  this 
reason  the  lengths  in  the  table  are  carried  beyond  those  for  single  sticks. 


Lumber  and  Carpenters'  Work 


Part  3 


Table  of  Board-Measure 

For  explanation,  see  page  1559 


Sectional  area  in  square  inches 

Length 

1- 

in  feet 

4 

6 

8 

IC 

12 

14 

16 

18 

20 

ft  in 

ft* 

ft  in 

ft 

in 

ft* 

ft  in 

ft  in 

ft* 

ft  in 

6 

2 

3 

3 

4   0 

5 

0 

6 

7   0 

8   0 

9 

10   0 

8 

2 

8 

4 

5   4 

6 

8 

•8 

9   4 

10   8 

12 

13   4 

10 

3 

4 

5 

6   8 

8 

4 

10 

II   8 

13   4 

15 

16   8 

12 

4 

0 

6 

8   0 

10 

0 

12 

14   0 

16   0 

18 

20   0 

14 

4 

8 

7 

9   4 

11 

8 

14 

16   4 

18   8 

21 

23   4 

i6 

5 

4 

8 

10   8 

13 

4 

16 

18   8 

21   4 

24 

26   8 

18 

6 

0 

•  9 

12   0 

15 

0 

18 

21   0 

24   0 

27 

30   0 

20 

G 

8 

10 

1^      4 

16 

8 

20 

23   4 

26   8 

30 

33   4 

22 

7 

4 

II 

14   8 

18 

4 

22 

25   8 

29   4 

33 

36   8 

24 

8 

0 

12 

16   0 

20 

0 

24 

28   0 

32   0 

36 

40   0 

26 

8 

8 

13 

17   4 

21 

8 

26 

30   4 

34   8 

39 

43   4 

28 

9 

4 

14 

18   8 

23 

4 

28 

32   8 

37   4 

42 

46   8 

30 

10 

0 

15 

20   0 

25 

0 

30 

35   0 

40   0 

45 

50   0 

32 

ID 

8 

16 

21   4 

26 

8 

32 

37   4 

42   8 

48 

53   4 

34 

II 

4 

17 

22   8 

28 

4 

34 

39   8 

45   4 

51 

56   8 

36 

12 

0 

18 

24   0 

30 

0 

36 

42   0 

48   0 

54 

60   0 

38 

12 

8 

19 

25   4 

31 

8 

38 

44   4 

50   8 

57 

63   4 

40 

13 

4 

20 

26   8 

33 

4 

40 

46   8 

53   4 

60 

66   8 

42 

14 

0 

21 

28   0 

35 

0 

42 

49   0 

56   0 

63 

70   0 

Sectional  ar 

ea  in  sc 

luare  inc 

hes 

24 

28 

30 

32 

35 

36 

40 

42 

48 

6 

ft* 

ft   in 

ft* 

ft 

in 

ft 

in 

ft* 

ft   in 

It  * 

ft* 

12 

14   0 

15 

16 

0 

17 

6 

18 

20   0 

21 

24 

8 

16 

18   8 

20 

21 

4 

23 

4 

24 

26   8 

28 

32 

10 

20 

23   4 

25 

26 

8 

29 

2 

30 

33   4 

35 

40 

12 

24 

28    0 

30 

32 

0 

35 

0 

36 

40   0 

42 

48 

14 

28 

32    8 

35 

37 

4 

40 

16 

42 

46   8 

49 

56 

i6 

32 

37    4 

40 

42 

8 

46 

8 

48 

53   4 

56 

64 

18 

36 

42    0 

45 

48 

0 

52 

6 

54 

60   0 

63 

72 

20 

40 

46    8 

50 

53 

4 

58 

4 

60 

66   8 

70 

80 

22 

44 

51    4 

55 

58 

8 

64 

2 

66 

73   4 

77 

88 

24 

48 

56        0 

60 

64 

0 

70 

0 

72 

80   0 

84 

96 

26 

52 

60    8 

65 

69 

4. 

75 

ro 

78 

86   8 

91 

104 

28 

56 

6S    4 

70 

74 

8 

81 

8 

84 

93   4 

98 

112 

30 

60 

70    0 

75 

80 

0 

87 

6 

90 

100   0 

105 

120 

32 

r>4 

74    8 

80 

85 

4 

93 

4 

96 

106   8 

112 

128 

34 

68 

79    4 

85 

90 

8 

99 

2 

102 

113   4 

119 

136 

36 

72 

84    0 

90 

96 

0 

105 

0 

108 

120   0 

126 

144 

38 

76 

88    8 

95 

lOI 

4 

no 

0 

114 

126   8 

133 

152 

40 

80 

93    4 

100 

106 

8 

116 

8 

120 

133   4 

140 

160 

42 

84 

98    0 

105 

112 

0 

122 

6 

126 

140   0 

147 

168 

*  The  mca»ur<;ments  in  these  columns  come  out  in  even  feet. 


Board-Measure 


1561 


Table  of  Board-Measure  (Continued) 

For  explanation,  see  page  1559 


Length 

Sectional  area  in 

square  inches 

• 

_ 

in  feet 

56 

60 

64 

72 

8a 

84 

96 

100 

112 

1 

ft 

in 

ft* 

ft  in 

ft* 

ft 

in 

ft* 

ft* 

ft 

in 

ft  in 

4 

18 

8 

20 

21  4 

24 

26 

8 

28 

32 

33 

4 

37  4 

6 

28 

0 

30 

32  0 

36 

40 

0 

42 

48 

50 

0 

56  0 

.  8 

37 

4 

40 

42  8 

48 

53 

4 

56 

64 

66 

8 

74  8 

10 

46 

8 

50 

53  4 

60 

66 

8 

70 

80 

83 

4 

93  4 

12 

56 

0 

60 

64  0 

72 

80 

0 

84 

96 

100 

0 

112  0 

14 

65 

4 

70 

74  8 

84 

93 

4- 

98 

112 

116 

8 

130  8 

16 

74 

8 

80 

85  4 

96 

106 

8 

112 

128 

133 

4 

149  4 

18 

84 

0 

90 

96  0 

108 

120 

0 

126 

144 

150 

0 

168  0 

20 

93 

4 

100 

106  8 

120 

133 

4 

140 

160 

166 

8 

186  8 

22 

102 

8 

110 

117  4 

132 

146 

8 

154 

176 

183 

4 

205  4 

24 

112 

0 

120 

128  0 

144 

160 

0 

168 

192 

200 

0 

224  0 

26   • 

121 

4 

130 

138  8 

156 

173 

4 

182 

208 

216 

8 

242  8 

28 

130 

8 

140 

149  4 

168 

186 

8 

196 

224 

233 

4 

261  4 

30 

140 

0 

150 

160  0 

180 

200 

0 

210 

240 

250 

0 

280  0 

32 

149 

4 

160 

170  8 

192 

213 

4 

224 

256 

266 

8 

298  8 

34 

158 

8 

170 

181  4 

204 

226 

8 

238 

272 

283 

4 

317  4 

36 

168 

0 

180 

192  0 

216 

240 

0 

252 

288 

300 

0 

336  0 

38 

177 

4 

190 

202  8 

228 

253 

4 

266 

304 

316 

8 

354  8 

40 

186 

8 

200 

213  4 

240 

266 

8 

280 

320 

333 

4 

373  4 

42 

196 

0 

210 

224  0 

252 

280 

0 

294 

336 

350 

0 

392  0 

44 

205 

4 

220 

234  8 

264 

293 

4 

308 

352 

366 

8 

410  8 

46 

214 

8 

230 

245  4 

276 

306 

8 

322 

36S 

383 

4 

429  4 

48 

224 

0 

240 

256  0 

288 

320 

0 

336 

384 

400 

0 

448  0 

50 

233 

4 

250 

266  8 

300 

333 

4 

350 

400 

416 

8 

466  8 

52 

242 

8 

260 

277  4 

312 

346 

8 

364 

416 

433 

4 

485  4 

54 

252 

0 

270 

288  0 

324 

360 

0 

378 

432 

450 

0 

S04  0 

56 

261 

4 

280 

298  8 

336 

373 

4 

392 

448 

466 

8 

522  8 

58 

270 

8 

290 

309  4 

348 

386 

8 

406 

464 

483 

4 

541  4 

60 

280 

0 

300 

320  0 

360 

400 

0 

420 

480 

500 

0 

560  0 

62 

289 

4 

310 

330  8 

372 

413 

4 

434 

496 

516 

8 

578  8 

64 

298 

8 

320 

341  4 

384 

426 

8 

448 

512 

533 

4 

597  4 

66 

308 

0 

330 

352  0 

396 

440 

0 

462 

528 

550 

0 

616  0 

68 

317 

4 

340 

362  8 

408 

453 

4 

476 

544 

566 

8 

634  8 

70 

326 

8 

350 

373  4 

420 

466 

8 

490 

560 

583 

4 

653  4 

72 

336 

0 

360 

384  0 

432 

480 

0 

504 

576 

600 

0 

672  0 

74 

345 

4 

370 

394  8 

444 

493 

4 

518 

592 

616 

8 

690  8 

76 

354 

8 

380 

405  4 

456 

506 

8 

532 

608 

633 

4 

709  4 

78 

364 

0 

390 

416  0 

468 

520 

0 

546 

624 

650 

c 

728  0 

80 

373 

4 

400 

426  8 

480 

533 

4 

S6o 

640 

666 

8 

746  8 

82 

382 

8 

410 

437  4 

492 

546 

8 

574 

656 

683 

4 

765  4 

84 

392 

0 

420 

448  0 

504 

560 

0 

588 

672 

700 

0 

784  0 

— , —  if 

*  The  measurements  in  these  columns  come  out  in  even  feet. 


1562 


Lumber  and  Carpenters'  Work 


Table  of  Board-Measure  (Continued) 

For  explanation,  see  page  1559 


Length 

Size  and  sectional  area  in  inches 

in  feet 

120 

140 

144 

160 

168 

192 

196 

224 

10X12 

loX 

14 

12X12 

10X16 

12X14 

12X16 

14X14 

14X16 

ft* 

ft 

in 

ft* 

ft  in 

ft* 

ft* 

ft   in 

ft  ■  in 

4 

40 

46 

8 

48 

53  4 

56 

64 

65  4 

74  8 

6 

60 

70 

0 

72 

80  0 

84 

96 

98  0 

112  0 

8 

80 

93 

4 

96 

106  8 

112 

128 

130  8 

149  4 

10 

100 

116 

8 

120 

133  4 

140 

160 

163  4 

186  8 

12 

120 

140 

0 

144 

160  0 

168 

192 

196  0 

224  0 

14 

140 

163 

4 

168 

186  8 

196 

224 

228  8 

261  4 

16 

160 

186 

8 

192 

213  4 

224 

256 

261  4 

298  8 

18 

180 

210 

0 

216 

240  0 

252 

288 

294  0 

336  0 

20 

200 

233 

4 

240 

266  8 

280 

320 

326  8 

373  4 

22 

220 

256 

8 

264 

293  4 

308 

352 

359  4 

410  8 

24 

240 

280 

0 

288 

320  0 

3.36 

384 

392  0 

448  0 

26 

260 

303 

4 

312 

346  8 

364 

416 

424  s 

485  4 

28 

280 

326 

8 

336 

373  4 

392 

448 

457  4 

522  8 

30 

300 

350 

0 

360 

400  0 

420 

480 

490  0 

560  0 

32 

320 

373 

4 

384 

426  8 

448 

512 

522  8 

597  4 

34 

340 

396 

8 

408 

453  4 

476 

544 

555  4 

634  8 

36 

360 

420 

0 

432 

480  0 

504 

576 

588  0 

672  0 

38 

380 

443 

4 

456 

5o5  8 

532 

60S 

620  8 

709  4 

40 

400 

466 

8 

480 

533  4 

560 

640 

653  4 

746  8 

42 

420 

490 

0 

504 

560  0 

588 

672 

686  0 

784  0 

44 

440 

513 

4 

528 

586  8 

616 

704 

718  8 

821  4 

46 

460 

536 

8 

552 

613  4 

644 

736 

■751  4 

858  8 

48 

480 

560 

0 

576 

640  0 

672 

768 

784  0 

896  0 

SO 

500 

583 

4 

600 

666  8 

700 

800 

816  8 

933  4 

52 

520 

606 

8 

624 

693  4 

728^ 

832 

849  4 

970  8 

54 

540 

630 

0 

648 

720  0 

756 

864 

882  0 

I  oc8  0 

56 

560 

653 

4 

672 

746  8 

784 

896 

914  8 

1045  4 

58 

580 

676 

8 

696 

773  4 

812 

928 

947  4 

I  082  8 

60 

600 

700 

0 

720 

800  0 

840 

960 

980  0 

I  120  0 

62 

620 

723 

4 

744 

826  8 

868 

992 

I  012  8 

r  157  4 

64 

640 

746 

8 

768 

853  4 

896 

1024 

I  045  4 

I  194  8 

66 

660 

770 

0 

792 

880  0 

924 

I  056 

I  078  0 

I  232  0 

68 

680 

793 

4 

816 

906  8 

952 

1088 

I  no  8 

I  269  4 

70 

700 

816 

8 

840 

933  4 

980 

I  120 

I  143  4 

I  306  8 

72 

720 

840 

0 

864 

960  0 

I  008 

I  152 

I  176  0 

1344  0 

74 

740 

863 

4 

888 

986  8 

I  036 

I  184 

I  208  8 

I  381  4 

76 

760 

886 

8 

912 

I  013  4 

I  064 

I  216 

I  241  4 

I  418  8 

78 

780 

910 

0 

yi6 

I  040  0 

I  092 

I  248 

I  274  0 

I  456  0 

80 

800 

933 

4 

960 

T  066  8 

I  120 

I  280 

L306  8 

I  493  4 

82 

820 

956 

8 

984 

I  093  4 

I  148 

I  312 

1339  4 

I  S30  8 

84 

840 

980 

0 

I  008 

I  120  0 

I  176 

I  344 

I  372  0 

I  568  0 

'  The  measurements  in  these  columns  conxe  out  in  even  feet. 


Measurement  ot  Lumber  1563 

Measurement  of  Finishing-Lumber,  Flooring,  Ceiling,  Etc.     Most,  if  not 

all,  lumber  for  finishing  is  sawed  for  use  in  thicknesses  of  i  in,  iH  in,  lYz  in,  and 
2  in,  and  some  woods,  such  as  white  pine  and  poplar,  are  sawed  into  thicknesses 
of  2y2  in  and  3  in. 

When  surfaced  both  sides,  the  thickness  is  reduced  to  ^He,  iHe,  iMe,  iH,  2H, 
and  2^yi6  in. 

All  dressed  stock  is  measured  and  sold  strip-count,  that  is,  full  size  of  rough 
material  necessarily  used  in  its  manufacture.  Thus  iHe-in  boards  are  measured 
as  though  iH  in  thick.  The  number  of  feet,  board-measure,  for  i^-in  stock 
(iHe  finished)  is  iH  times  that  in  a  i-in  board,  and  in  the  same  way  for  iH-in 
and  2y2-'m  stock.  1^4 -in  planks  are  always  measured  2  in  thick,  and  2H-in 
stock,  2H  in  thick.  Boards  less  than  i  in  thick  are  measured  the  same  as  i-in 
boards,  but  for  ^^-in  and  %-m  stock  a  reduced  price  is  generally  made. 

Matched  Ordinary  Flooring.*  The  standard  sizes  for  flooring  (other  than 
hardwood,  parqueting  or  parquet-flooring)  are  i  by  3,  i  by  4  and  i  by  6;  or  iH  by 
3,  1 1/4  by  4  and  iH  by  6.  The  thickness  of  i-in  flooring  should  be  ^Vie  in,  and 
of  iH-in  flooring,  i%2  in.  3-in  flooring  should  show  21/4  in  on  the  face,  after  it  is 
laid;  4-in,  33.4  in;   and  6-in,  5H  in. 

Matched  Maple  Flooring  is  usually  made  in  2-in,  2 1 4-in  and  3i/4-in  face,  and 
in  thicknesses  of  i^le,  iMe  and  i^g  in. 

Ceiling,  matched  and  beaded  boards,  is  regularly  stuck  in  the  same  widths  as 
flooring.  The  standard  (nominal)  thicknesses  of  yellow-pine  ceiling  are  H,  \i, 
%  and  H  in,  the  actual  thickness  of  each  being  Me  in  less.  The  %-'m  ceihng  is 
dressed  one  side  only,  the  other  thicknesses  both  sides. 

Yellow  Pine  Drop-Siding.  Dressed  and  matched  yellow  pine  drop-siding  H 
Vi  by  3!/^  and  %  by  53'^  in,  showing  3I/4  and  sH-in  face;  and  worked  shiplap  H 
%  by  3>^  and  %  by  5 J- 2  in,  showing  3  and  5-in  face. 

Beveled  Siding  is  resawed  on  a  bevel  from  stock  i^ie  by  3H  and  i^e  by  5H  in^ 
after  surfacing. 

New  England  Clapboards  are  4  ft  long,  6  in  wide,  y2  in*thick  at  the  butt,  and 
about  %  in  thick  at  the  other  edge.  They  are  put  up  in  bunches  and  sold  by  the 
thousand. 

Rules  for  Estimating  Quantities  of  Sheathing,  Flooring,  Etc.  For  com- 
mon sheathing  laid  horizontally  on  a  wall  or  roof  without  openings,  add  one- 
tenth  to  the  actual  superficial  area  to  allow  for  waste.  On  the  walls  of  dwellings, 
figure  the  walls  as  though  without  openings  and  allow  nothing  for  waste.  If 
sheathing  is  laid  diagonally,  add  one-sixth  to  the  actual  superficial  area. 

For  tight  sheathing  laid  horizontally,  add  one-fifth  for  6-in  boards,  one-seventh 
for  8-in  boards,  and  one-ninth  for  lo-in  boards.  If  laid  diagonally  add  one- 
fourth  for  6-in  boards,  one-sixth  for  8-in  boards,  and  one-eighth  for  lo-in  boards. 

Bor  3-in  matched  flooring  add  one-half  to  the  actual  superficial  area  to  be 
covered. 

For  4-in  flooring  add  one-third  and  for  6-in  flooring  add  one-fifth.  Ceiling  is 
measured  the  same  as  flooring. 

For  drop-siding,  add  one-fifth  to  the  superficial  area. 

For  lap-siding,  laid  4  in  to  the  weather,  add  one-half  to  the  actual  superficial 
area;   if  4y2  in  to  the  weather,  add  one-third. 

*  Everywhere  except  in  New  England  flooring  is  always  understood  to  be  tongued  and 
grooved. 


1564 


Building  Papers,  Felts  and  Quilts 


Parts 


Cost  of  Labor  for  Carpenters'  Work.  There  are  so  many  items  and  con- 
ditions which  enter  into  the  cost  of  carpenters'  work,  and  the  cost  varies  so 
widely  with  the  locality,  that  it  is  quite  impossible  to  give  figures  which  are  of 
general  practical  value,  although  several  books  *  have  been  published  on  esti- 
mating labor  and  materials  for  buildings. 

The  following  figures  of  the  cost,t  for  labor  and  nails,  of  framing  and  putting 
on  sheathing  and  siding  and  laying  flooring  were  computed  on  the  basis  of  car- 
penters' wages  at  $3  a  day  of  eight  hours  (37^2  cts  per  hour).  The  cost. of 
framing  is  almost  always  figured  at  a  certain  price  per  thousand  feet  of  lumber, 
board-measure.  The  cost  of  laying  flooring,  sheathing,  etc.,  is  almost  always 
figured  by  the  square  of  100  sq  ft  (10  by  10  ft). 


Character  of  work 

Cost 

For  setting  up  studding  and  framing  walls  of  wooden 

$10.00  per  1000 
$9.00  to  $10.00  per  1000 

$  8.50  per  1000 

10.00  per  1000 

$1 1 .  00  to  $12 .  00  per  1000 

$1.25 

60  cts  per  square 
75  cts  per  square 

$2 .  00  per  square 
2.25  per  square 
2 .  so  per  square 
3  75  per  square 
6.00  per  square 
8.00  per  square 
$10.00  to  ?i2.oo  per  sq 

For  framing  and  setting  floor- joists,  2  by  8  to  2  by  12.  .  . 
Framing  and  setting  heavy  joists  and  girders,  6  by  12  to 

Framincf  crable  roofs  and  settincf  in  olace            

Framing  hip-roofs  and  setting  in  place     

For  ptrtting  in  bridging,  after  it  is  cut,  per  100  lin  ft  in  the 
row            

For  covering  the  sides  or  roofs  of  wooden  buildings  with 
dressed  sheathing,  laid  horizontally 

The  same,  if  lairl^  diagonally 

The  cost  of  labor  and  nails  for  laying  6-in  flooring,  blind- 
nailed  to  every  joist,  without  dressing  after  laying,  is 
about                     

For  4-in  flooring  not  dressed  allow                        ... 

For  3-in  hard-pine  flooring,  hand-smoothed  or  traversed. 
For  3-in  red-oak  flooring,  hand-smoothed  or  traversed.  . 
For  3-in  white-oak  flooring,  hand-smoothed  or  traversed 
For  3-in  maple  flooring,  hand-smoothed  or  traversed 

BUILDING  PAPERS,  BUILDING  FELTS  AND  QUILTS 

Sheathing-Papers,t  Felts,  Quilts,  Etc.  It  is  well  known  that  frarne  build- 
ings when  merely  sheathed  and  clapboarded  or  shingled  on  the  outside  and  simply 
lathed  and  plastered  on  the  inside,  are  almost  sure  to  be  hot  in  summer  and  cold 
in  winter;  and  as  the  wood  almost  always  shrinks,  cracks  result  through  which 
the  wind  finds  its  way.  For  these  reasons  some  extra  provision  should  be  made 
for  keeping  out  the  wind  and  the  heat  and  cold;  and  it  is  generally  admitted  that 

*  Readers  are  referred  to  The  Building  Estimator's  Reference  Book,  by  F.  R.  Wa|ker, 
The  New  Building  Estimator,  by  William  Arthur,  Handbook  of  Cost  Data,  by  H.  P. 
Gillette  and  the  Estimators'  Price  Book,  by  I.  P.  Hicks.  To  all  of  these,  architects  and 
builders  are  referred  for  detailed  information  and  valuable  data  on  costs  of  laboi  and 
material. 

t  The  wages  of  carpenters  varied  (1916)  in  the  United  States  from  35  to  70  cts  per  hour, 
or  from  $2.80  to  $5.60  per  day  of  8  hours.  For  rates  per  day  higher  than  those  given 
the  figures  showing  the  cost's  in  the  schedule  must  be  raised  proportionately. 

t  The  terms  building  paper  and  sheathing-paper  are  by  the  public  indiscriminately 
applied  to  all  kinds  of  paper  used  in  connection  with  building-construction.  In  the 
trade,  however,  the  term  building  paper  is  confined  to  the  rosin-sized  and  cheaper 
grades  of  paper,  while  the  he? "«'"'■  and  better  grades  are  classed  as  sheathing-papers. 


Building  Papers,  Building  Felts  and  Quills  1565 

there  is  no  material  that  will  do  this  so  well  and  at  so  small  an  expense  as  good 
sheathing-papers  or  sheathing-felts.  The  papers  made  for  this  purpose  are  com- 
monly known  as  sheathing-papers  or  building  papers.  There -is  a  great 
variety  of  sheathing-papers  manufactured,  many  of  them  of  great  excellence, 
and  even  the  best  are  comparatively  inexpensive,  costing  only  about  $i.oo  per 
IOC  sq  ft;  so  that  only  the  better  qualities  of  any  kind  of  felt  or  paper  should  be 
specified.  Where  the  cost  of  the  sheathing-paper  on  an  ordinary  house  is  only 
a  few  dollars,  it  is  poor  economy  to  use  a  cheap  paper,  as  the  labor  of  applying  it 
is  an  important  item  and  the  poorer  the  paper  the  more  difficult  the  work  of  put- 
ting it  on.  The  qualities  which  good  sheathing-paper  should  possess  are  per- 
manence, impenetrability  to  air  and  water  and  sufficient  strength  to  permit  of 
applying  without  tearing.  Protection  or  proof  against  vermin  and  insects  i$ 
another  important  requirement.  It  should  not  be  brittle  nor  have  a  lasting 
strong  odor  and,  for  the  convenience  of  the  builder,  should  be  clean  for  handling. 
There  are  so  many  papers  possessing  all  or  most  of  these  qualities  that  it  is  deemed 
inexpedient  to  mention  particular  brands.  The  architect  should  decide  for  him- 
self, from  the  samples  with  which  he  has  probably  been  furnished,  what  papers 
are  best  adapted  to  the  particular  conditions;  and  he  should  then  specify  those 
brands,  giving,  also,  the  manufacturers'  names,  instead  of  leaving  the  choice  to 
the  builder,  who  will  be  quite  sure  to  be  guided  by  price  rather  than  by  quality. 
Many  object  to  tarred  or  saturated  sheathing-papers  and  felts  because  of  their 
tendency  to  become  brittle  and  because  they  emit  a  strong  odor  and  are  some- 
what disagreeable  to  handle.  On  the  other  hand,  the  advocates  of  tarred  felts 
emphasize  their  cheapness,  warmth  and  even  their  odor,  which  makes  them 
vermin-proof.  The  odor  gradually  disappears  after  the  clapboards,  siding  or 
shingles  are  put  on  and  the  inside  walls  finished.  Sheathing-paper  is  usually 
applied  just  previous  to  putting  on  the  clapboards,  siding,  or  shingles.  It  is 
generally  placed  horizontally  and  should  lap  about  2  in  over  each  sheet  and  over 
the  paper  previously  placed  around  the  window  and  door-frames.  If  sheathing- 
quilt  or  similar  material  is  to  be  placed  under  the  clapboards  or  siding,  laths 
should  be  nailed  vertically  over  it,  opposite  each  stud,  and  the  siding  or  clap- 
boards nailed  to  the  laths;  otherwise  it  will  be  difficult  to  put  them  on  evenly, 
owing  to  the  thickness  and  elastic  quality  of  the  quilt.  Shingles,  however,  may 
be  applied  directly  over  it.  Sheathing-quilt  possesses  marked  fire-resisting 
properties.  The  sheathing-paper  and  the  labor  of  putting  it  on  should  be  in- 
cluded in  the  carpenter's  specifications. 

Rosin-Sized  Building-Papers.  These  are  the  common  grades  of  building 
paper;  they  are  not  water- proof,  and  should  not  be  used  on  roofs  or  on  walls  in 
damp  climates.  In  dry  places  they  protect  from  dust,  draughts,  and  to  some 
extent  from  heat  and  cold.  They  are  generally  either  a  dull  red  or  gray  in  color, 
have  a  hard,  smooth  surface,  and  are  clean  to  handle.  They  are  always  put  up 
in  rolls  36  in  wide  and  usually  contain  500  sq  ft.  The  weight  varies  from  18  to 
40  lb  to  the  roll  of  500  sq  ft. 

Insulating  and  Deadening- Quilts.  Among  the  insulating  and  dcadening- 
quilts  much  in  use  are  those  mentioned  below.  There  are  also  other  good  ma- 
terials in  this  line  which  are  manufactured  and  used  for  insulating  and  deadening 
purposes. 

Sheathing-  Quilt.*  This  consists  of  a  felted  matting  of  eel-grass  held  in  place 
between  two  layers  of  strong  Manila  paper  by  quilting.  "The  long,  flat  fibers 
of  eel-grass  cross  each  other  at  every  angle  and  form  within  each  layer  of  quilt 
innumerable  minute  dead-air  spaces,  that  make  a  soft,  elastic  cushion.    This 

*  Made  by  Samuel  Cabot  (Inc.),  Boston,  Maae. 


1566  Building  Papers,  Felts  and  Quilts  Part  3 

gives  the  most  perfect  conditions  for  non-conduction."  Eel-grass  is  chosen 
for  the  filling  because  of  its  long,  Hat  fibers,  which  especially  adapt  it  for 
felting;  because  of  its  great  durability,*  and  its  resistance  to  fire;  and  because, 
owing  to  the  large  percentage  of  iodine  which  it  contains,  it  is  repellent  to  rats 
and  vermin.  This. quilt  is  made  in  single  and  double-ply  thickness,  and  is  put 
up  in  bales  of  500  sq  ft.  It  is  also  now  made  with  a  covering  of  asbestos,  which 
tend.rs  it  thoroughly  fire-proof.  The  material  is  also  very  efficient  for  heat- 
in  sulatio  .  When  used  for  this  purpose  there  is  no  objection  to  nails  passing 
through  it. 

Keystone  Hair  Insulator.  Another  material  used  for  similar  purposes  is  the 
Keystone  Hair  Insulator.f  This  consists  of  thoroughly  cleansed  catties'  hair, 
between  two  layers  of  strong,  non-porous  building  paper,  securely  stitched  to- 
gether. The  hair  is  chemically  treated,  so  that  it  is  coated  with  lime,  which 
makes  the  finished  material  vermin-proof  and  odorless. 

Mineral -Wool  Deadeners,  which  are  fire-proof  sound-deadening  quilts  of 
rock-fiber  wool  stitched  between  two  sheets  of  building  paper  or  of  asbestos 
paper  according  to  the  grade  desired,  are  made  by  the  Union  Fibre  Company  oT 
Winona,  Minn.,  and  other  firms.  This  company  makes,  also,  what  is  called 
Lith  and  Feltlino,  which  are  sound-deadening  materials  in  board  form.  They 
manufacture,  also,  Linofelt,  a  building-quilt  of  flax-fibers  (unbleached  linen 
threads),  stitched  between  water-proof  paper  or  asbestos  paper  according  to  need. 
It  is  H  in  thick.  Linofelt  for  sheathing  in  place  of  ordinary  building  paper  adds 
from  I  to  i\^2%  to  the  cost  of  a  house. 

Felt-Papers.  There  are  a  great  many  felt-papers  for  lining  floors  and  a  few 
are  made  fire-proof  by  means  of  chemicals.  As  a  rule  these  felts  are  cheaper  than 
Cabot's  QUILT,  although  the  saving  in  an  ordinary  residence  would  be  but  little, 
and  even  among  the  felts  themselves  there  is  quite  a  difference  in  cost.  In 
choosing  a  felt-paper  for  lining,  the  architect  should  select  one  that  is  soft  and 
elastic  enough  to  form  a  cushion,  and  the  thicker  the  felt,  provided  it  has  the 
above  qualities,  the  greater  will  be  its  non-conduction.  Some  felts  are  made 
water-proof  by  an  asphalt  center,  which  is  an  advantage  in  case  of  fire  or  leaks, 
but  some  authorities  think  that  it  is  doubtful  if  such  felts  obstruct  the  passage  of 
sound  as  well  as  felts  without  the  asphalt  center.  The  experience  of  some 
acoustical  experts  seems  to  show  that  one  of  the  best  methods  of  deadening  is  by 
a  combination  of  he'avy  hair-felt  or  felt-paper  with  sheets  of  galvanized  iron. 
Two  layers  of  felt,  each  from  ^2  to  i  in  thick,  are  placed  on  either  side  of  a  single 
layer  of  galvanized  iron,  the  latter  resting  freely  between  the  felt  layers.  This 
form  of  construction  is  to  be  preferred  where  the  deadening-material  is  not  at- 
tached to  the  enclosing  woodwork.  An  additional  layer  of  iron  and  of  felt 
increases  the  effectiveness  of  the  combination. 

Saturated  Felts.J  Common  roofing-felts  are  made  by  saturating  common 
dry  felt  with  coal-tar  pitch.  Roofing-felts  are  commonly  made  in  weights  of  12, 
15,  and  20  lb  to  the  100  sq  ft.  Nothing  lighter  than  12  lb  should  be  used  for 
roofing.  They  are  usually  sold  by  weight.  Asphalt-felts  are  commonly  made 
in  the  same  weights. 

Dry  Saturated  Tarred  Felts  are  specially  run  through  a  tier  of  calenders 
to  give  a  hard,  uniform  surface  and  contain  a  minimum  amount  of  coal-tar. 

•  A  sample  of  eel-grass  250  years  old  and  in  a  perfect  state  of  preservation,  may  be  seen 
at  Mr.  Cabot's  office. 

t  Made  by  H.  W.  Johns-Manville  Company,  New  York. 

X  The  Barrett  Manufacturing  Company  and  others  make  numerous  brands  of  these 
eiicathing  and  roofing-papers. 


Building  Papers,  Building  Felts  and  Quilts  1567 

They  are  especially  adapted  for  slaters'  use,  as  they  will  carry  a  chalk  line  and 
are  easy  to  handle.  The  rolls  are  36  in  wide,  contain  500  sq  ft  and  weigh  about 
30  lb. 

Asbestos  Building  Felts  are  usually  made  about  6,  10,  14  and  16  lb  to  the 
100  sq  ft,  although  different  manufacturers  make  different  weights.  They  come 
in  rolls  36  in  wide  and  are  sold  by  weight. 

Sound-Deadening  Felts.  These  deadening- felts  are  made  by  various  manu- 
facturers. In  one  of  these  felts  *  the  material  itself  is  rather  hard  and  thin,  but 
it  is  pressed  in  such  a  way  as  to  form  small  indentations  or  air-cells.  This  makes 
it  elastic  and  breaks  up  the  sound-waves. 

Asbestos  Sheathing.  Sheathing-papers  or  building  felts,  made  of  asbestos, 
are  used  to  a  considerable  extent  for  floor-linings  and  for  covering  the  outside 
walls  of  wooden  buildings,  principally  on  account  of  their  fire-proof  and  vermin- 
proof  qualities.  These  papers  are  well  known  in  the  trade  and  can  be  procured 
without  difficulty.  They  are  supplied  by  the  manufacturers  in  50  or  loo-lb 
mUs,  36  in  wide,  on  a  basis  of  the  following  scale  of  weights: 

4  lb  to  the  100  sq  ft  18  lb  to  the  100  sq  ft 

6  lb  to  the  100  sq  ft  20  lb  to  the  100  sq  ft 

8  lb  to  the  100  sq  ft  24  lb  to  the  100  sq  ft 

10  lb  to  the  100  sq  ft  32  lb  to  the  100  sq  ft 

12  lb  to  the  100  sq  ft  Me  in  thick 

14  lb  to  the  100  sq  ft  %2  in  thick 

16  lb  to  the  100  sq  ft  H  in  thick 

The  sheathing  in  the  Me,  ^2  and  H-'m  thicknesses  is  used  only  for  special  pur- 
poses where  an  unusually  thick  lining  is  desired  for  possible  fire-protection 
around  exposed  flues,  for  chimney-breasts,  etc.  When  the  weight  of  paper  ex- 
ceeds 32  lb  to  the  square  foot  it  is  known  as  roll-board  and  is  no  longer  classed 
by  weight  per  100  sq  ft,  but  by  thickness.  For  floor-linings,  i6-lb  paper  is  gen- 
erally employed,  this  weight  being  sufficiently  thick  and  strong  to  resist  ordi- 
nary damage  in  application  and  in  handling.  Asbestos  felts  and  building  papers 
appear  to  have  approximately  the  same  effect  in  retarding  the  passage  of  sound- 
waves as  other  felt-papers  of  a  relatively  similar  thickness  and  quality,  while 
their  fire-proof  and  vermin-proof  qualities  are  a  distinct  advantage.  The  cost  of 
asbestos  paper  and  building-felt,  while  somewhat  greater  than  that  of  the  ordi- 
nary papers  used  for  similar  purposes,  is  not  excessive.  The  market  price  varies 
and  depends  upon  the  fluctuations  of  the  market.  For  example,  the  cost  of 
100  sq  ft  of  i6-lb  asbestos  paper  varied  from  32  to  40  cts,  according  to  the 
market,  before  the  war.f 

Water-Proof  Papers.  Neponset  Black  Sheathing  is  water-proof  and 
air-proof,  odorless  and  clean  to  handle,  and  is  an  excellent  paper  under 
siding,  shingles,  slate,  or  tin.  The  rolls  are  36  in  wide,  containing  250  and 
500  sq  ft. 

Neponset  Red  Rope  Sheathing  and  Roofing.  This  is  made  of  rope- 
stock,  has  great  strength  and  flexibility,  and  is  absolutely  water-proof  and  air- 
tight. It  is  one  of  the  best  sheathing-papers  and  makes  a  good  cheap  roofing 
for  sheds,  poultry-houses,  etc.  The  rolls  are  36  in  wide,  containing  100,  250  and 
500  sq  ft. 

*  Neponset  Florian  Sound-Deadening  Felt,  made  by  F.  W.  Bird  &  Son,  East  Walpole, 
Mass. 

t  These  prices  are  now  much  higher. 


1568  Paint  and  Varnish  Part  3 

Parchment  Water-Proof  Sheathing.  There  are  various  parchment-sheath- 
ings  on  the  market  which  are  semitransparent,  have  smooth  surfaces,  and  are 
odorless,  water-proof,  air-proof  and  vermin-proof.  They  are  adapted  for  general 
sheathing  purposes.  In  general  i-ply  weighs  25  lb  to  900  sq  ft;  2-ply,  25  lb  to 
500  sq  ft;  3-ply,  25  lb  to  275  sq  ft.     They  are  36  in  wide. 

Cost  of  Building  and  Sheathing-Papers  in  Place.*  The  following,  al- 
though necessarily  restricted  to  a  few  lines,  will  give  a  general  idea  of  the  cost  of 
different  kinds  and  grades  of  sheathing-papers,  the  prices  given  being  fair  aver- 
ages for  the  materials  applied  to  an  outside  wall  or  roof: 

Price  per  100 
.square  feet 

Common  tarred  felts  (15  lb  per  square) 30  cts 

Red  rosin-sized  sheathing,  best  grades 25  cts 

Monahan's  parchment  sheathing,  single-ply 26  cts 

Monahan's  parchment-sheathing,  double-ply •    40  cts 

Monahan's  ship-rigging  tar-sheathing,  2-ply 75  cts 

"Neponset"  black  (water-proof)  paper 45  cts 

"Neponset"  red-rope  roofmg $1.20 

Sheathing-papers  with  asphalt  center 40  to  50  cts 

Asbestos  building  or  sheathing-felt,  10  lb  per  square 22^^  cts 

Asbestos  building  or  sheathing-felt,  14  lb  per  square :  31]^^  cts 

Cabot's  sheathing-quilt,  single-ply $1.05 

Cabot's  sheathing-quilt,  double-ply $1.25 

Barrett's  specification-felt 35  cts 

Barrett's  defender,  felt -sheathing 80  cts 

Sackett's  water-proof  sheathing 30  cts 

Empire  parchment-sheathing,  i-ply 25  cts 

Empire  parchment-sheathing,  2-ply 36  cts 

Empire  parchment-sheathing,  3-ply 50  cts 

Barrett's  red  rope $1.00 

Barrett's  black,  water-proof  sheathing 40  cts 

PAINT  AND  VARNISH  f 

Pigments  and  Vehicles.  The  solid  ingredient  of  a  paint  is  called  the  pigment, 
and  is  a  line  powder,  nearly  all  of  which  will  pass  through  a  brass-wire  sieve  of 
100  meshes  to  the  linear  inch;  in  fact,  most  pigments  are  much  finer  than  that, 
and  those  formed  as  precipitates  by  chemical  processes  are  so  fine  that  there  is 
no  way  to  measure  them.  The  liquid  part  is  called  the  vehicle.  This  is  usu- 
ally linseed-oil,  sometimes  with  the  addition  of  a  little  turpentine  or  other  volatile 
solvent.  In  the  enamel  paints  it  is  varnish  and  in  kalsomine  and  other  cold- 
water  paints  it  is  a  solution  of  glue,  casein,  albumen,  or  some  similar  cementing 
material.     The  cementing  material  is  sometimes  called  the  binder. 

Ingredients  of  Oil-Paint.  White  lead  and  white  zinc  are  the  common  white 
pigments.  There  are  white  pigments  of  variable  composition  called  leaded  zinc 
and  zinc  lead,  furnace-products,  composed  of  zinc  oxide  and  lead  sulphate. 
There  is  also  a  basic  lead  sulphate,  commercially  called  sublimed  white  lead, 
which  is  a  similar  furnace-product  consisting  chiefly  of  sulphate  of  lead. 
These  composite  white  pigments  are  largely  used  in  mixed  paints,  lithopone 
is  a  mixture  of  sulphide  of  zinc  and  sulphate  of  barium.     It  is  very  white,  fine 

*  All  prices  quoted  are  pre-war  prices  and  the  data  are  retained  for  purposes  of  com- 
parison and  relative  values. 

t  The  editor  is  indebted  to  Professor  Alvah  H.  Sahin  for  valuable  assistance  in  the 


Outside  Painting  1569 

and  opaque  and  largely  used  as  the  basis  of  flat  wall-finishes  for  interior  work, 
but  is  not  durable  for  exterior  work.  It  is  discolored  (grey)  by  strong  light,  but 
this  is  not  a  very  serious  practical  objection.  White  lead  is  used  everywhere, 
but  tends  to  yellow  somewhat  in  the  dark.  White  zinc  is  chiefly  used  on  interior 
work,  being  the  whitest  paint  known.  Both  are  often  mixed  and  both  are  used 
in  mixed  paints.  Yellow  paint  is  commonly  chromate  of  lead,  or  chrome  yellow; 
green  is  chrome  green,  which  is  a  mixture  of  chrome  yellow  and  Prussian  blue; 
blue  is  ultramarine,  or  sometimes  Prussian  blue.  The  brilliant  reds  are  coal-tar 
colors  as  a  rule;  the  dull  reds  and  browns  are  oxides  of  iron.  Ochres  are  dull 
yellow.  Carbon  forms  the  base  of  all  black  paints,  either  as  lampblack,  drop- 
black  (boneblack),  or  graphite.  Linsecd-oil  is  either  raw  or  boiled.  Raw  oil  is 
the  oil  in  its  natural  state  as  it  is  extracted  from  the  seed;  it  should  be  settled 
and  filtered  perfectly  clear;  it  is  yellow  or  greenish  yellow  in  color.  Boiled  oil  is 
raw  oil  which  has  been  heated  to  400°  or  500°  F.  with  compounds  (usually  oxides) 
of  lead  and  manganese;  it  is  darker  in  color  than  raw  oil,  and  dries  quicker. 
Raw  oil  exposed  in  a  thin  film  to  the  air  is  converted  in  about  five  days  into  a 
tough  leathery  substance;  boiled  oil  undergoes  this  change  in  from  10  to  24  hours. 

Driers.  These  are  compounds  of  lead  and  manganese,  dissolved  in  oil,  and 
this  solution  thinned  with  turpentine  or  benzine.  They  act  as  carriers  of  oxygen 
between  the  air  and  the  oil,  and  their  addition  to  a  paint  makes  it  dry  more 
rapidly.  Some  driers  are  also  called  japans.  Not  more  than  10%  by  volume  of 
any  of  these  liquid  driers  should  be  added  to  oil.  Excess  of  drier  causes  the 
paint  to  lack  durability.  Cheap  driers  often  contain  rosin.  It  iS  well  to  specify 
that  driers  and  japans  should  be  free  from  rosin  (not  resin,  as  varnish-resins  are 
present  in  some  of  the  best  driers).  ''^ 

Priming  Coat.  This  is  the  first  coat  applied  to  the  clean  surface.  A  priming 
coat  for  wood  is  chiefly  oil,  and  is  usually  equivalent  to  a  gallon  of  ordinary  paint 
thinned  with  a  gallon  of  raw  linseed-oil.  Paint,  however,  is  not  thinned  to  make 
a  priming  coat  for  structural  metal.  In  all  wood-work,  nail-holes  and  other  de- 
fects are  filled  with  putty  after  the  priming  coat  has  been  applied;  but  if  the 
wood  is  resinous,  knots  and  resinous  places  must  be  covered  with  shellac  varnish 
before  the  priming  coat  is  put  on.  Pitchy  woods,  such  as  southern  yellow  pine 
and  cypress,  do  not  readily  absorb  oil,  and  turpentine  should  be  substituted  for 
part  of  the  oil.  Red  lead  is  successfully  used  as  a  primer  (2  parts  to  i  of  white 
lead)  on  such  woods;  this  is  the  standard  practice  in  England,  and  is  better  than 
the  use  of  all  white  lead. 

Outside  Painting.  The  priming  coat  having  largely  been  absorbed  by  the 
wood,  a  second  and  third  coat  of  paint  are  to  be  applied.  The  most  common 
paint  used  on  houses  is  white  lead.  This  is  commonly  sold  as  paste  white  lead, 
containing  8%  of  oil;  100  lb  of  this  is  equal  to  2.8  gal  in  volume,  and  is  commonly 
mixed  with  sVi  gal  of  raw  Hnseed-oil,  i  qt  of  turpentine  and  i  pt  of  drier  to  make 
6ys  gal  of  paint  for  the  second  coat;  or  with  4  gal  of  oil,  i  pt  of  turpentine  and  i 
pt  of  drier  for  the  finishing  coat.  If  white  zinc  is  used,  gV^  lb  of  dry  zinc  oxide 
and  5.7  lb  of  oil  make  i  gal  of  paint;  to  this,  turpentine  and  drier  should  also 
be  added.  White  lead,  after  about  a  year,  begins  to  chalk,  that  is,  its  surface 
becomes  dry  and  chalky;  this  does  not  indicate  failure,  however,  and  it  makes  a 
good  surface  for  repainting.  Finely  reticulated  checking,  not  extending  through 
the  film,  occurs  later,  and  when  sufficiently  marked  indicates  need  of  repainting. 
In  any  paint,  when  cracks  begin  to  extend  through  to  the  wood,  repainting  is 
called  for;  these  cracks  occur  sooner  on  pitchy  woods.  White  zinc,  if  used  alone 
on  outside  (not  inside)  work,  is  very  hard  and  tends  to  peel  off.  Mixed  paints 
(prepared  proprietary  paints)  generally  contain  zinc  mixed  with  either  white 
lead  or  some  of  the  pigments  based  on  basic  lead  sulphate,  and  some  auxiliary 


1570  Paint  and  Varnish  Part  3 

pigments,  such  as  barytes,  China  clay,  etc.,  ground  in  oil  and  turi)entine  and 
containing  the  necessary  drier.  The  best  of  these  are  excellent,  but  some  are 
very  poor;  the  safest  way  to  use  th^m  is  to  specify  them  bj'  name,  and  use  them 
according  to  the  maker's  directions.  Colored  paints  are  commonly  made  by 
adding  colored  pigments  to  lead  or  zinc;  but  some  dark  paints  contain  only  iron 
oxides,  ochers,  etc.,  as  pigments;  these  weigh  from  12  to  14  lb  per  gal.  Painting 
should  always  be  done  in  dry  weather  and  no  painting  should  be  done  until  the 
inside  plastering  is  dry.  Paint  should  not  be  applied  to  lumber  that  is  not  dry. 
A  week  or  more  should  be  allowed  between  successive  couts.  In  painting  the  out- 
side of  a  house,  the  trim  should  be  painted  first;  then  the  body-color  can  be 
laid  neatly  against  it.  The  final  brushing  should  be  in  the  direction  of  the  grain 
of  the  wood.  It  is  good  practice  to  have  the  successive  coats  (except  for  white 
paint)  vary  a  little  in  color,  to  facilitate  inspection.  White,  light  blue  and  light 
green  are  less  durable  colors  than  yellow,  gray,  or  dark  colors  in  general,  owing 
to  the  fact  that  the  chemical  rays  of  light  penetrate  the  former  more  easily.  A 
gallon  of  paint  will  cover  from  400  to  600  sq  ft  of  surface,  dcpendihg  upon  the 
character  of  the  surface.  Roof-paints  should  contain  a  larger  proportion  of  oil, 
and  a  smaller  amount  of  drier  or  none  at  all.  Three  coats  are  desirable.  Tin 
roofs  and  galvanized-iron  work  should  be  thoroughly  scrubbed  and  then  dried 
before  painting.  The  shingles  on  the  walls  and  roofs  of  a  house  are  sometimes 
stained  with  creosote  stain,  which  consists  of  a  pigment  suspended  in  creosote 
or  some  similar  liquid.     The  creosote  has  some  preservative  effect. 

Inside  Painting.  Door-frames  and  window-frames  should  receive  a  priming 
coat  of  paint  in  the  shop;  if  they  are  to  be  finished  in  varnish  this  paint  will  be 
applied  to  the  back  only.  As  has  already  been  said,  before  any  painting  is  done 
any  resinous  knots  should  be  varnished  with  shellac.  All  interior  surfaces  which 
are  to  be  painted  should  be  puttied  after  the  priming  coat  and  the  putty  should 
be  applied  with  a  wooden  spatula,  not  a  steel  one,  to  avoid  marring  the  surface. 
The  paint  for  the  second  coat  should  contain  as  much  turpentine  as  oil,  that  is, 
its  vehicle  should  be  half  oil  and  half  turpentine.  The  effect  of  this  is  to  make 
the  paint  dry  with  a  dull  instead  of  a  glossy  surface,  flat  surface  being  the 
painter's  term.  To  this  the  next  coat  will  adhere  well.  If  the  next  is  the  final 
coat,  it  may  be  an  ordinary  oil-paint.  When  thoroughly  dry  the  gloss  may  be 
removed  bj'^  lightly  rubbing  it  with  pumice  and  water.  Enamel  paint  consists 
of  pigment  with  varnish  as  a  vehicle.  It  is  harder  and  makes  a  finer  finish  than 
oil-paint.  It  is  also  more  expensive.  It  is  usual  to  apply  it  over  oil-paint,  in 
which  case  the  last  coat  of  oil-paint  should  be  lightly  sandpapered  when  quite 
hard  and  dry.  A  coat  of  enamel  paint  is  then  put  on,  and  when  it  is  dry  it  should 
be  sandpapered  or  rubbed  with  curled  hair.  The  final  coat  of  enamel  is  then  laid 
on  and  it  may  be  rubbed  in  a  Uke  manner  if  a  flat  surface  is  desired,  or  it  may  be 
left  with  the  gloss.  It  is  also  common  practice  for  painters  to  make  a  final 
enamel  finish  by  adding  varnish  to  white  lead  or  white  zinc,  very  little  oil  being 
used  in  this  case.  The  best  varnish  for  this  purpose  is  a  spar-varnish  from 
a  thoroughly  reliable  maker.      The  quicker-drying  varnishes  will  crack  and 

ALLIGATOR. 

Varnish.  There  are  two  principal  kinds  of  varnish,  (i)  spirit  varnishes,  of 
which  shellac  varnish  is  the  most  important,  and  which  consists  essentially  of  a 
resin  dissolved  in  a  volatile  solvent,  and  (2)  oleoresinous  varnishes,  in  which  the 
resinous  ingredient  is  combined  with  linseed-oil,  and  this  compound  is  dissolved 
in  turpentine  or  benzine.  The  oleoresinous  varnishes  are  commercially  the 
more  important,  and  are  largely  used  in  interior  finishing.  A  gallon  of  varnish 
covers  500  sq  ft,  one  coat.  Surfaces  to  be  varnished  are  treated  in  the  following 
manner.    If  the  wood  is  open-grained,  as  oak,  chestnut,  or  ash,  it  first  receives  a 


Repainting  1571 

coat  of  paste-filler.  Liquid  fillers  are  not  desirable,  as  they  form  a  poor  base  for 
subsequent  work.  A  paste- tiller  is  really  a  sort  of  paint,  the  pigment  being  silex, 
or  ground  quartz,  and  the  vehicle  is  a  quick-drying  varnish  made  thin  with  tur- 
pentine or  benzine.  This  is  rubbed  strongly  in  on  the  grain  of  the  wood  with  a 
short  stiff  brush,  and  as  soon  as  it  has  set,  usually  within  half  an  hour,  it  is  rubbed 
off  with  a  harsh  cloth  or  a  handful  of  excelsior,  the  rubbing  being  hard  across  the 
grain  of  the  wood.  If  it  is  desired  to  stain  the  wood,  the  oil-stain  may  be  mixed 
with  the  filler;  but  if  a  close-grained  wood  is  used,  which  needs  no  filler,  the  oil- 
stain  may  be  thinned  to  the  desired  color  with  turpentine  or  benzine  and  applied 
as  a  wash.  In  cleaning  the  filler  out  of  moldings,  corners,  etc.,  a  suitably  shaped 
stick,  but  not  a  steel  implement,  may  be  used.  If  any  puttying  is  necessary  it  is 
done  next.  After  two  days  the  first  coat  of  varnish  is  appHed;  after  five  days  it 
should  be  rubbed  with  curled  hair  or  fine  sandpaper  to  remove  the  gloss,  so  that 
the  next  coat  will  adhere  well;  then  one,  two  or  three  more  coats  of  varnish  are 
added,  five  days  or  more  apart,  each  coat  being  rubbed.  The  last  coat  may 
be  rubbed  or  left  with  the  natural  gloss.  Outside  doors,  window-sills,  jambs, 
inside  blinds,  and  all  surfaces  exposed  to  the  direct  rays  of  the  sun,  should  be 
varnished  with  spar-varnish  and  left  glossy.  If  shellac  varnish  is  used  as  the  in- 
terior finish  it  is  applied  in  the  same  way,  but  at  least  six  coats  should  be  applied. 
Floors  which  are  to  be  varnished  should  be  treated  as  has  been  described;  but 
if  they  are  to  be  waxed  they  should  receive  one  or  two  coats  of  shellac  varnish, 
then  five  or  six  coats  of  wax,  at  intervals  of  a  week,  each  coat  beii>g  well  polishec? 
with  a  weighted  tloor-brush  made  for  the  purpose.  Floor-wax  is  not  beeswax, 
but  is  a  compound  wax  made  for  the  purfx)se.  Shellac  is  a  good  floor-varnish; 
it  discolors  the  wood  less  than  any  other  varnish,  and  dries  rapidly. 

Painting  Plastered  Walls.  Plastered  walls  which  must  be  painted  are  usu- 
ally washed  with  a  solution  of  soap  and  then  with  a  solution  of  alum.  When 
this  is  dry  it  is  sponged  off,  then  allowed  to  dry,  then  oiled,  then  painted.  If  the 
paint  is  apphed  to  the  fresh  piaster  the  lime  in  the  plaster  will  attack  the  paint. 

Repainting.  The  exterior  woodwork  of  a  house  needs  repainting  once  in  five 
to  ten  years,  according  to  climate  and  other  conditions,  although  if  not  done  with 
proper  material  or  sufficient  care  it  will  not  last  as  long  as  this;  the  interior 
should,  with  good  care,  stand  from  fifteen  to  twenty  years,  and  then  may  not 
require  complete  renewal.  Exterior  paint  sometimes  loses  its  luster,  while  the 
body  of  the  paint  is  still  good,  and  in  cases  of  this  kind  it  is  sufficient  to  wash  the 
surface  and  then  give  it  a  coat  of  oil.  This  replaces  the  oil  which  has  superficially 
perished,  imparts  a  gloss  and  brings  out  the  color.  If  the  paint  is  worn  off  so 
as  to  show  the  wood  in  places,  or  is  peeling,  it  must  be  very  carefully  examined. 
In  extreme  cases  it  is  necessary  to  burn  off  the  old  paint;  this  is  done  with  a 
painter's  torch,  a  lamp  which  burns  alcohol,  naphtha,  or  kerosene,  and  which 
furnishes  a  flaring  blast  of  flame,  which  is  directed  against  the  painted  surface 
just  long  enough  to  soften  the  paint  which  is  at  once  removed  with  a  scraper 
while  still  hot.  The  paint  is  not  actually  burned,  but  only  softened  by  the  flame; 
it  may,  however,  be  removed  as  well  as  softened  by  this  method.  Houses  cov- 
ered with  pitchy  wood,  like  southern  pine,  sometimes  require  this  treatment, 
and  the  next  painting  is  found  to  be  more  lasting.  In  many  cases  it  is  sufficient 
to  thoroughly  scrub  the  surface  with  a  stiff  steel- wire  brush.  Interior  surfaces 
may  be  cleaned  (if  the  removal  of  the  old  paint  and  varnish  is  necessary)  with 
varnish-remover;  this  is  a  mixture  of  solvent  liquids,  which  penetrate  the  old 
paint  or  varnish  and  soften  it,  when  it  may  be  removed  with  scrapers  or  brushes. 
There  is  less  danger  of  fire  with  this  method  than  with  the  burning-off  method, 
but  it  is  slower  and  costs  more.  It  must  not  be  forgotten  that  varnish-remover 
is  volatile  and  highly  inflammable  and  must  not  be  used  in  a  room  where  there  is 


1572  Paint  and  Varnish  Part  3 

a  fire.  It  is  especially  suitable  for  cleaning  out  moldings  and  all  irregular  sur- 
faces from  which  the  varnish  may  then  be  removed  with  stiff  brushes,  if  it  is  not 
convenient  to  use  scrapers.  It  is  especially  desirable  to  have  floors  occasionally 
cleaned  in  this  way;  but  if  a  house  has  been  varnished  originally  with  a  first- 
class  varnish  it  may  be  necessary  only  to  wash  it  thoroughly  and  then  apply  an- 
other coat  of  varnish.  Smoke  and  dirt  may  often  be  thoroughly  removed  from 
ceilings  with  the  crumbs  of  fresh  bread,  where  washing  would  not  be  desirable. 
A  io%  solution  of  carbonate  of  soda  (sal  soda)  in  hot  water  may  be  used  to 
remove  old  floor-wax. 

The  Painting  of  Structural  Steel.  Steel  being  usually  more  perishable 
than  wood,  as  well  as  more  expensive,  and  used  for  service  where  its  strength  is 
essential  to  the  stability  of  the  structure,  its  protection  from  corrosion  by  paint- 
ing is  of  much  importance.  It  must  first  of  all  be  recognized  that  the  precaution 
always  taken  in  painting  wood,  to  secure  a  clean  surface  for  the  paint,  must  not 
be  omitted  with  steel.  Mud  and  dirt  must  first  be  removed  from  the  steel;  then 
It  must  be  examined  for  rust,  and  any  rust-spots  must  be  thoroughly  cleaned. 
Loose  scale  may  be  removed  with  wire  brushes,  but  thick  and  closely  adherent 
rust  must  be  removed  with  steel  scrapers,  or  with  hammer  and  chisel  if  necessary. 
No  doubt  the  best  way  to  clean  steel  is  to  use  the  sand-blast,  but  it  is  not  available 
for  much  architectural  work.  In  an^^  case  much  care  must  be  taken  to  obtain  a 
clean  surface.  On  wood  the  priming  coat  sinks  into  the  wood  and  forms  a  perfect 
bond  between  it  and  the  succeeding  coats;  but  on  metal  no  such  thing  is  pos- 
sible and  it  is  a  case  of  simple  adhesion,  which  demands  a  clean  surface  for  effi- 
cient results.  The  paint  for  structural  metal  should  be  tough  and  elastic,  and 
to  as  great  a  degree  as  possible  it  should  be  water-proof.  Less  than  two  coats 
should  never  be  applied,  and  three  are  better.  Paint  is  always  thin  on  edges  and 
angles,  and  also  on  bolt  and  rivet-heads;  it  is  therefore  good  practice,  after  the 
first  full  coat,  to  apply  a  partial  or  striping  coat,  covering  the  angles  and  edges 
and  the  surface  for  at  least  i  in  JDack  from  the  edges,  and  covering  all  bolt- 
heads  and  rivet-heads.  After  this  striping  coat  has  become  dry,  the  second  full 
coat  is  applied,  and  it  may  then  be  assumed  that  the  whole  surface  has  received 
two  full  coats.  At  least  a  week  should  elapse  between  coats.  In  designing  the 
steelwork,  all  cavities  which  may  be  filled  with  rain  during  erection  should  be 
properly  drained;  and  during  erection  all  small  cavities  should  be  filled  with 
cement,  and  all  contact-surfaces  thickly  painted. 

Kinds  of  Paint  for  Structural  Steel.  Red  lead  is  more  generally  used  than 
anything  else  as  a  paint  for  structural  steel.  It  is  a  "  true  red  lead  "  (Pb304),  usu- 
ally made  from  litharge  (PbO),  and  frequently  containing  from  lo  to  20%  of  the 
latter.  If  it  contains  much  litharge,  it  rapidly  thickens  when  mixed  with  oil  and 
finally  hardens;  this  makes  it  a  paint  difficult  to  apply.  If,  however,  the  material 
from  which  it  is  made  is  reduced  to  a  sufficiently  fine  powder  before  it  is  oxidized, 
an  almost  completely  oxidized  red  lead  is  produced,  which  is  as  easily  worked 
as  white  lead,  and  better  in  every  respect.  The  requirements  of  the  govern- 
ment of  the  United  States  have  for  years  called  for  red  lead  of  not  less  than  94% 
of  "  true  red  lead  "  (Pb304),  and  the  Navy  Department,  as  well  as  several  large 
railway  companies,  is  now  using  large  amounts  of  red  lead  which  has  not  less  than 
98%  of  "  true  red  lead."  It  may  now  be  obtained  in  paste-form,  similar  to  white 
lead  and  containing  about  6)2%  of  raw  linseed-oil.  32,  lb  of  red  lead  (dry  pig- 
ment) to  I  gal  of  oil  is  the  maximum  and  this  is  especially  suitable  for  hydraulic 
work;  28  lb  to  i  gal  of  oil  (containing  20  lb  of  pigment  in  a  gallon  of  paint) 
is  more  common;  while  25  lb  to  a  gallon  of  oil  is  a  common  requirement  for  rail- 
road-specifications. Finely  ground  graphite  in  linseed-oil  is  a  favorite  paint 
for  metal;  it  flows  well,  is  easily  applied,  less  expensive  than  red  lead,  and  if  well 


Window-Glass  and  Glazing  1573 

made  gives  excellent  results:  Graphite  is  sometimes  mixed  with  lampblack,  prob- 
ably with  advantage.  Boneblack  is  also  an  important  ingredient  of  carbon 
PAINTS.  Formerly  oxide  of  iron  in  Unseed-oil  was  used  more  than  all  other  paints 
for  this  purpose;  but  while  many  engineers  still  like  it,  its  use  has  very  greatly  di- 
minished. AsPHALTUM  has  been  used  and  is  still  used,,  as  a  varnish  either  alone 
or  in  combination,  and  some  of  these  asphaltic  preparations  are  fairly  satis- 
factory. The  fact  is,  that  a  really  competent  paint-manufacturer  can  make  a 
reasonably  good  paint  out  of  any  of  these,  and  if  the  paint  is  carefully  apphed 
the  results  will  be  satisfactory.  There  are  great  differences  in  painters.  In  re- 
gard to  the  surface  of  structural  steel  covered  by  a  gallon  of  paint,  there  is  a 
great  difference  of  opinion  among  experts.  Some  say  from  300  to  400  sq  ft, 
others  1000  or  120Q  sq  ft.  The  truth  is  that  any  paint  may  be  brushed  out 
into  an  exceedingly  thin  film  by  a  skilled  workman,  while  ordinary  usage  results 
in  a  film  at  least  twice  as  thick.  The  general  opinion  is  that  it  is  not  wise  to  esti- 
mate more  than  400  sq  ft  to  the  gallon  for  one  coat.  Varnish-paints  cover  less 
than  oil-paints,  but  if  well  made  they  are  very  durable. 

Painting  on  Cement  and  Concrete.  Cement  and  concrete-work  are  diffi- 
cult to  paint,  because  they  are  strongly  alkaline  and  even  caustic  when  new. 
Work  in  these  materials  should  be  allowed  to  stand  a  year  or  two  if  possible  be- 
fore it  is  painted;  then  it  may  be  painted  with  any  ordinary  paint.  A  practice 
which  has  been  highly  recommended  is  to  wash  the  surface,  repeatedly  if  possible, 
with  a  strong  solution  of  zinc  sulphate,  the  sulphuric  acid  uniting  with  the  free 
lime  and  the  zinc  being  left  in  the  pores  as  an  oxide  or  hydrate.  Some  prepara- 
tions for  this  purpose  are  on  the  market;  and  while  some  are  probably  good, 
others  are  to  be  distrusted.  The  best  way  is  to  allow  the  surface  to  age,  if  this 
is  at  all  possible. 

WINDOW-GLASS  AND  GLAZING* 

Glazing.  The  glazing  of  windows  originally  belonged  to  the  painter's  trade» 
and  when  glass  is  broken,  it  is  still  customary  to  go  to  a  painter  to  have  it  re- 
placed; but  custom  has  so  changed  in  some  parts  of  the  country,  that  when  new 
windows  are  to  be  glazed,  the  work  is  sometimes  done  at  the  mill  or  factory 
where  the  sashes  are  made,  sometimes  by  the  local  glass-jobber  in  the  town  where 
the  building  is  being  erected,  and  again,  in  other  localities,  the  glazing  of  new 
buildings  is  still  done  by  the  painter.  Common  window-glass  is  usually  set 
with  putty  and  secured  with  triangular  pieces  of  zinc  called  glaziers'  points, 
driven  into  the  wood  over  the  glass  and  covered  with  putty.  In  the  best  work,  a 
thin  layer  of  putty  is  first  put  in  the  rebate  of  the  sash  and  the  glass  is  then  placed 
on  it  and  pushed  down  to  a  solid  bearing.  This  is  called  back-puttying.  The 
points  are  then  driven  about  8  or  10  in  apart  and  the  putty  applied  over  the  glass 
and  points  so  as  to  fill  the  rebate.  Outside  windows  should  always  be  glazed  on 
the  outside  of  the  sash.  Common  window-glass  has  a  slight  bend  in  it,  the  re- 
sult of  its  original  cylindrical  shape;  it  should  be  glazed,  therefore,  with  the 
convex  side  out,  as  this  reduces  to  a  minimum  the  effects  of  the  waviness  when 
looking  through  it  either  from  the  outside  or  inside.  Plate  glass,  in  window- 
sashes  and  door-lights,  should  be  back-puttied  and  secured  by  wooden  beads. 

Leaded  Glass.  It  was  formerly  a  common  practice  for  architects  to  name 
in  the  specifications  a  certain  sum  of  money  to  be  allowed  by  the  carpenter  tor 
the  leaded  glass  and  to  be  expended  under  the  direction  of  the  architect.     Where 

*  Condensed  from  article  on  Window-Glass  and  Glazing  by  Professor  Thomas  Nolan 
in  Building  Construction  and  Superintendence,  Part  II,  Carpenters'  Work,  by  F.  E. 
Kidder. 


1574  Window-Glass  and  Glazing  Part  3 

clear  glass  was  used,  the  pattern  was  sometimes  shown  on  the  drawings  and  the 
glass  was  specified  in  the  same  manner  as  any  other  work.  When  colored  glass 
was  to  be  used,  it  was  customary  to  make  a  definite  allowance  and  then  to  en- 
trust the  work  to  a  good  art-glass  manufacturer.  But  leaded  glass  should  be 
designed,  furnished  and  put  in  place  by  those  who  are  entirely  familiar  with  its 
manufacture  and  its  limitations;  the  purchase  of  the  same  should  be  left  entirely 
in  the  hands  of  the  owner;  ajid  no  specification  as  to  its  price  or  make  should  be 
used  by  the  architect.  The  colored-glass  windows  should  show  as  much  indi- 
vidual artistic  taste  as  any  other  picture  or  decoration  used  in  the  Ijuilding.  The' 
cheap  and  inartistic  leaded  glass  is  fast  becoming  a  thing  of  the  past  and  owners 
are  confining  themselves  to  purely  works  of  art  placed  in  some  appropriate 
location  in  the  building. 

Sheet  Glass.  General  Description.  Common  window-glass  is  technically 
known  as  sheet  glass  or  cylinder  glass.  "It  is  made  by  the  workmen  dip- 
ping a  tube  with  an  enlarged  end  in  the  molten  glass  or  metal  until  from  7  to  10 
lb  are  gathered  up.  Then  it  is  blown  out  sli^^htly  by  the  workman,  taken  on  a 
blowing-tube  and  still  further  blown  and  manipulated,  until  a  cylinder  about 
15  in  in  diameter  and  60  in  long  is  formed.  This  cylinder  has  the  two  ends 
trimmed  off  and  is  then  cut  longitudinally  and  gradually  warmed.  It  is  then 
placed  on  a  large  flat  stone  supported  by  a  carriage,  where  it  is  heated  until  it 
softens  sufficiently  to  open  out  flat;  the  carriage  is  then  pushed  into  the  anneal- 
ing-chamber and  the  sheet  taken  off."  About  the  year  19 10,  sheet  glass  blown 
by  machinery,  utilizing  compressed  air,  was  perfected,  and  the  result  has  been  a 
gradual  decrease  in  its  cost.  The  cylinder  blown  by  compressed  air  is  split  open 
and  flattened  out  in  just  the  same  manner  and  by  the  same  process  as  in  the 
mouth-blown  cylinder. 

Grades  and  Qualities  of  Sheet  Glass.  Sheet  glass  is  graded  as  double-thick, 
or  single-thick,  and  each  thickness  is  further  divided  into  three  qualities,  first, 
second,  or  THIRD,  according  to  its  relative  freedom  from  defects.  The  price  varies 
according  to  the  strength  and  quality.  It  should  be  remembered  that  sheet  glass 
is  always  wavy,  the  result  of  the  flattening  of  the  cylinder.  Many  suppose  that 
by  designating  sheet  glass,  crystal-sheet  glass,  selected-sheet  glass,  or 
SHEET  glass  FREE  FROM  WAVES  AND  IMPERFECTIONS,  a  sheet  glass  free  from  waves 
and  blemishes  can  be  obtained.  The  terms  and  names  do  not  change  the  nature 
of  this  glass,  which  still  remains  sheet  glass,  characterized  by  the  defects  inherent 
in  the  method  by  which  it  is  manufactured.  To  obtain  a  thin  glass,  free  from 
waviness,  plate  glass,  H  in  thick,  sometimes  known  as  crystal  plate,  or  plate 
glass  Me  in  thick,  must  be  specified.  Since  the  improvement  in  the  manufac- 
ture of  window-glass  in  this  country,  scarcely  any  sheet  glass  is  now  imported  for 
glazing  purposes.  A  small  amount  of  Belgian  sheet  glass  is  brought  to  this 
country  and  used  along  the  Atlantic  seaboard  for  picture-framing.  The  low 
prices  of  the  American  sheet  glass,  and  its  excellent  quality,  have  practically 
forced  imported  sheet  glass  out  of  the  market.  All  common  sheet  glass,  without 
regard  to  quality,  is  graded  according  to  thickness,  as  single-thick  or  double- 
thick.  The  thickness  of  the  double-thick  glass  is  a  scant  H  in  while  that  of  the 
single-thick  averages  about  VI2  in.  It  is  customary  to  use  the  double  thickness 
for  sheet  glass  over  24  in  in  width.  The  best  quality  of  sheet  glass  is  specified  as 
A  A,  the  second  as  A  and  the  third  as  B. 

Sizes  of  Sheet  Glass.  The  regular  stock -sizes  vary  by  inches  from  6  to  16  in 
in  width.  Above  that  they  vary  by  even  inches  up  to  60  in  in  width  and  70  in  in 
length  for  double  thickness,  and  up  to  30  by  50  in  for  single  thickness. 

Cost  of  Sheet  Glass.  The  prices  for  sheet  glass,  as  for  all  other  clear  glass, 
vary  with  the  size,  strength  and  quality.     Prices  are  determined  by  a  schedule 


Sheet  Glass 


1575 


or  price-list,*  giving  the  price  for  each  size,  in  both  thicknesses,  and  all  qualities; 
and  from  these  prices  a  very  large  discount  is  allowed.  Fluctuations  in  prices 
are  regulated  by  the  discount,  the  list  usually  remaining  unchanged  for  a  number 
of  years.  The  price-list  prevailing  in  19 13  was  in  use  from  October  i,  1903. 
The  only  way  to  ascertain  the  price  of  a  light  of  glass  of  a  given  size  is  to  find  it 
from  the  price-list,  from  which  the  discount,  quoted  by  the  glass-dealer,  must  be 
deducted.  For  the  benefit  of  the  Pacific  Coast  trade  there  is  a  Western  Glass 
List  t  which  differs  somewhat  from  the  Eastern  list.  The  list  is  for  sheet  glass, 
the  plate  glass  lists  being  the  same  in  the  East  and  West.  The  price  per  square 
foot  increases  rapidly  as  the  size  of  the  pane  increases,  so  that  it  is  much  cheaper 
to  divide  a  large  window  into  eight  or  twelve  lights  than  into  two  lights.  Com- 
pared with  the  cost  of  the  building,  however,  the  glass  is  a  small  item  and  in  the 
better  classes  of  buildings  each  sash  is  usually  glazed  with  a  single  Hght  of  glass. 
In  factories,  workshops,  etc.,  where  there  is  usually  a  large  amount  of  glass- 
surface,  the  size  of  the  lights  is  not  of  so  much  importance,  while  the  saving  by 
using  small  lights  is  quite  an  item;  hence  twelve-light  and  even  sixteen-light 
windows  are  generally  used  in  such  buildings.  The  following  table  shows  quite 
clearly  the  relative  cost  (19 13)  per  square  foot  of  different-sized  panes  of  Ameri- 
can glass,  the  prices  given  being  an  average  at  that  time  for  the  whole  country. 

Comparative  Cost  (1913)  of  American  Sheet  Glass  per  Square  Foot,  Based 

Upon  a  Discount  of  90  and  20  Per  Cent  on  the  List  of 

October  1,  1903  t 


• 

Grades 

Sizes  of  lights  in  inches 

10X12 

15X20 

24X34 

30X36 

36X40 

40X60 

60X70 

1 

Prices  hi  cents  per  square  foot 

Double  strength: 

First  quality 

Second  quality 

Single  strength: 

First  quality 

Second  quality  — 

7.0 
6.0 

5.0 
4.3 

8.3 
7-3 

4.8 
4.5 

9-4 
8.3 

6.4 
5.6 

10. 0 
9.0 

6.8 
6.0 

10.8 
10.0 



14.0 
14.4 

29.2 
27.0     1 

Crystal-Sheet  Glass,  26-Ounce.  This  glass  is  made  by  the  cylinder-process, 
but  is  a  little  thicker  than  the  ordinary  double-strength  glass.  It  is  probably 
the  best  glass  made,  next  to  plate  glass,  but  owing  to  the  method  of  its  manu- 
facture is  necessarily  characterized  by  a  wavy  appearance.  If  good  glass  is 
required  for  first-class  residences,  hotels,  office-buildings,  etc.,  polished  plate 
glass  should  be  used.  The  latter  invariably  gives  satisfaction,  while  sheet  glass, 
no  matter  of  what  thickness,  is  usually  disappointing  in  its  appearance. 

Defects  of  Sheet  Glass.  All  sheet  glass,  when  looked  upon  from  the  outside, 
has  a  wavy,  watery  appearance,  like  the  surface  of  a  lake  slightly  agitated  by 

*  The  price-lists  of  glass  have  been  omitted  as  they  can  readily  be  obtained  from  the 
glass-dealers  in  any  city.  Such  lists  are  not  of  much  service  unless  they  are  complete; 
and  the  full  lists  are  too  long  to  be  inserted  in  a  condensed  handbook. 

t  This  list,  with  discounts  from  the  prices  given,  may  be  obtained  from  the  W.  P.  Fuller 
Company,  San  Francisco,  Cal. 

t  Much  valuable  information  in  regard  to  Window-Glass  and  Glazing  was  furnished  by 
Mr.  S.  C.  Gihnore  of  the  Hires-Turner  Glass  Company,  Philadelphia,  Pa. 


1576  Window-Glass  and  Glazing  Part  3 

the  wind;  and  when  the  sunshine  falls  upon  it  the  irregularity  of  the  surface  is 
greatly  emphasized.  This  characteristic  of  sheet  glass  is  due  to  its  being  made 
in  the  shape  of  a  cylinder  and  then  stretched  or  flattened  out  into  a  sheet,  and  it 
cannot  be  wholly  avoided.  Besides  this  universal  defect,  the  cheaper  grades  are 
often  STRINGY,  BLiSTERY,  SULPHURED,  SMOKED,  or  STAINED;  SO  that,  in  looking 
through  the  glass,  objects  seen  at  a  distance  are  deformed  and  distorted. 

Plate  Glass.  General  Description.  Plate  glass  is  commonly  known  as 
POLISHED  PLATE  GLASS  because  its  surface  is  finely  polished  and  thus  made  clear 
and  transparent.  It  is  more  largely  used  every  year  for  windows  of  fine  resi- 
dences, hotels  and  office-buildings,  where  transparency  is  desired  from  the  inside 
and  an  elegant  appearance  required  on  the  outside.  The  process  of  manufacture 
of  plate  glass  is  entirely  different  from  that  of  sheet  glass.  In  making  plate  glass 
the  metal,  which  is  prepared  with  great  care,  is  melted  in  large  pots  and  then  cast 
on  a  perfectly  flat  cast-iron  table.  "The  width  and  thickness  of  the  plate  is 
determined  by  means  of  metal  strips  called  guns,  which  are  fastened  on,  and  on 
which  a  heavy,  metal  roller  travels.  The  ends  of  the  guns  are  tapered  so  that 
when  the  roller  is  at  one  extremity,  it  and  the  guns  form  three  sides  of  a  shallow, 
rectangular  dish.  The  molten  metal  is  poured  on  and  the  roller  passed  along 
slowly,  forcing  the  metal  in  front  of  it  and  rolling  out  the  sheet."  The  sheet  is 
then  annealed  and  forrris  what  is  known  as  rough  plate,  which  is  used  for  vault- 
lights,  skylights,  floor-lights  and  the  like.  "For  polished  plate  the  rough  plate 
is  carefully  examined  for  flaws,  which  are  cut  out,  leaving  the  largest-sized  sheet 
practicable.  The  plate  is  then  fastened  to  a  revolving  table  by  means  of  plaster 
of  Paris,  and  two  heavy  shoes,  shod  with  cast  iron,  are  mounted  over  it.  The 
table  is  then  revolved  and  sand  and  water  fed  onto  the  surface;  the  shoes  revolve 
also,  going  over  all  parts  of  the  plate  and  grinding  it  down  to  a  true  j^lane. 
Emery-powder  is  then  fed  on,  in  successive  degrees  of  fineness  until  the  plate  is 
made  absolutely  smooth  and  all  grit  removed.  After  this,  new  rubbers,  shod 
with  very  fine  felt,  are  put  on  and  liquid  rouge  is  added  for  the  polishing.  When 
one  side  is  completed  the  other  side  is  similarly  treated,  the  plate  losing  about 
40%  in  weight  by  the  operation." 

Qualities  of  Polished  Plate  Glass.  For  glazing  purposes  there  is  but  one 
quality  of  plate  glass  on  the  market.  The  best  of  this  is  selected  for  manufactur- 
ing mirrors.  At  one  time,  plate  glass  was  extensively  imported,  but  the  gradu- 
ally improving  methods  of  the  American  manufacturers,  as  well  as  the  great 
cheapening  of  the  process,  have  practically  eliminated  imported  plate  glass  from 
the  market.  The  American  plate  glass  is  equal  in  every  respect  to  that  which 
was  imported.  The  usual  thickness  of  polished  plate  glass  is  from  yi  to  Mo  in, 
but  it  can  be  made  thinner  than  this;  and  when  required  for  residence- windows 
or  car-windows,  may  be  obtained  in  ^le  or  H-in  thicknesses.  It  is  manufactured 
from  the  same  thickness  of  rough  plate  used  for  the  ordinary  thicknesses,  but  is 
ground  down  thinner  and,  owing  to  the  additional  cost  of  grinding,  as  well  as  to 
the  risk,  is  more  expensive  than  glass  of  the  ordinary  thickness. 

Cost*  of  Polished  Plate  Glass.  The  cost  of  plate  glass  of  ordinary  thickness 
varies  with  the  size  of  the  lights.  The  net  price  of  polished  plate  glass  (1913) 
glazing  quality,  was  about  45  cts  ($0.45)  per  sq  ft,  for  sizes  of  not  more  than  10 
sq  ft  per  plate,  50  cts  ($0.50)  per  sq  ft  for  sizes  containing  from  10  to  50  sq  ft  per 
plate,  and  65  cts  ($0.65)  per  sq  ft  for  sizes  containing  not  more  than  120  sq  ft  per 
plate.  For  larger  sizes  the  price  increased  rapidly  up  to  $2.00  per  sq  ft.  The 
price,  however,  can  be  accurately  determined  only  by  means  of  a  price-list  and 
discount.  The  price-list  in  use  (19 13)  was  introduced  in  March,  19 10,  and  the 
*  These  are  pre-war  prices  and  the  data  are  retained  for  purposes  of  comparison, 


Window- Glass 


1577 


discount  was  about  90%.  Plate  glass  -yieln  thick  costs  15%  more  than  glass  of 
the  regular  thickness  on  account  of  the  extra  expense  of  grinding  it  down.  Plate 
glass  H  in  thick  costs  from  25  to  40%  more  than  glass  of  the  regular  thickness. 

Sizes  of  Polished  Plate  Glass.  Plate  glass  is  cut  into  stock  sizes,  varying  by 
even  numbers  from  6  by  6  in  up  to  144  by  240  in,  or  138  by  260  in. 

Comparative  Cost  of  Different  Kinds  of  Window-Glass.  The  following 
table  gives  an  idea  of  the  comparative  cost  of  the  different  kinds  and  qualities 
of  glass  used  in  this  country  for  g'azing.  The  prices  for  the  sizes  are  the  19 14, 
net,  average  prices.  The  first  column  of  the  table  gives  the  kinds  of  glass,  and 
includes  both  the  American  plate  and  the  American  sheet  glass.  The  other 
columns  of  the  table  give  the  sizes  of  the  different  lights  in  inches. 


Comparative  Cost  of  DiflFereat  Kinds  of  Window  Glass  • 


Kinds  of  glass 


American  Plate  Glass 

Glazing-quality 

Crystal-sheet  glass,  26-oz 

American  Sheet  Glass 

Double-strength,  first  quality 

Double-strength,  second  quality. . 

Single-strength,  first  quality , 

Single-strength,  second  quality 


Sizes  of  lights  in  inches 


24X32      30X36      36X40     48X60 


$2.35 
1. 00 


0.54 
0.47 
0.37 
0.32 


$3.38 
1. 54 


0.83 
0.73 
0.56 
0.50 


$4.60 
2.34 


.25 
•  13 


$9.80 
6.66 


3-55 
330 


It  will  be  seen  from  this  table  that  the  relative  difference  in  the  cost  of  plate 
and  sheet  glass  decreases  rapidly  as  the  sizes  of  the  lights  increase.  The  prices 
in  this  table  are  based  on  the  list  of  October  i,  1903,  on  a  discount  of  90%  for 
plate  glass,  90  and  20%  for  American  sheet  glass  and  85%  on  A  A  double- 
thick  for  26-OZ  crystal-sheet  glass. 

Wire-Glass.     This  is  described  in  Chapter  XXIII,  page  821. 

Figured  Rolled  Glass.  This  is  a  translucent  or  obscured  glass  with  a  pat- 
tern stamped  on  one  surface.  As  the  molten  metal  is  rolled  out  on  the  table, 
the  design,  cut  into  the  table,  imprints  itself  into  the  soft  glass.  This  kind  of  glass 
has  almost  entirely  supplanted  the  ordinary  ground  glass  because  of  its  greater 
cleanhness.  There  are  several  popular  designs  on  the  market,  made  by  various 
manufacturers.  Some  of  the  designs  in  common  use  are  known  as  moss,  maze, 
COLONIAL,  FLORENTINE,  COBWEB,  etc.  This  glass  is  usually  made  H  in  thick  and 
in  large  sheets  from  24  to  42  in  wide  and  from  8  to  10  ft  long.  Maze,  Floren- 
tine and  COBWEB  designs  can  be  had  either  with  or  without  the  wire  mesh  in 
them.  One  important  property  of  figured  rolled  glass  is  that  of  diffusing  the 
light  which  passes  through  it.  (See,  also,  pages  1453  and  i554-) 
.  Pressed  Prism-Plate  Glass,  f  This  is  manufactured  in  different  patterns  and 
for  different  purposes  and  includes  (i)  Imperial  Prism-Plate  Ornamental  Glass 
in  five  different  patterns,  (2)  Imperial  Prism-Plate  Glass  and  (3)  Imperial  Sky- 
light Prism  Glass.     The  general  description  is  as  follows: 

*  These  are  pre-war  prices  and  the  data  are  retained  for  purposes  of  comparison. 
t  Manufactured  by  the  Pressed  Prism  Plate  Glass  Company,  Chicago,    111.      See, 
also,  pages  1453  to  1456. 


1578  Window-Glass  and  Glazing  Part  3 

(i)  Imperial  Prism-Plate  Ornamental  Glass  is  plate  glass  ground  and  polished 
on  one  side.  It  is  manufactured  in  plates,  54  by  72  or  72  by  54  in,  can  be  cut 
into  smaller  sizes,  and  is  made  in  five  different  stock  patterns.  It  is  used  in 
modern  mercantile,  office  and  public  buildings  for  partitions,  transoms,  door- 
lights,  vestibule  doors,  ornamental  ceiling-lights,  bank-windows  and  other  street- 
windows,  and  in  all  places  where  semiobscurity  and  ornamental  effect  are  desired. 
On  account  of  its  prismatic  qualities  it  gives  a  strong  diffusion  of  light  for  office- 
use  where  privacy  is  desired. 

(2)  Imperial  Prism-Plate  Glass.  This  is  manufactured  in  large  sheets,  54  by; 
72  or  72  by  54  in,  and  can  be  cut  into  smaller  sizes.  It  is  made  in  several  different 
angles  in  order  to  obtain  the  proper  diffusion  of  Ught  for  varying  conditions.  It 
is  a  plate  glass,  ground  and  polished  on  one  side.  There  are  no  wires  or  bars  to 
collect  dirt  and  retard  the  light  and  it  is  very  easily  cleaned.  It  is  used  in  the 
upper  sashes  of  windows  and  in  transoms,  store-fronts,  etc. 

(3)  Imperial  Skylight  Prism  Glass.  This  is  made  in  unit  plates,  18  by  60  in, 
with  a  H-in  back,  and  conforms  to  the  requirements  of  the  Board  of  Fire  Insur- 
ance Underwriters.  It  is  used  for  skylights,  roofs  over  areaways  and  in  light- 
Wells,  etc.  The  possibility  of  leakage  is  lessened  on  account  of  the  large-sized 
plates  in  which  it  may  be  obtained.  These  plates,  however,  can  be  cut  into 
smaller  sizes  if  required.  It  is  particularly  adapted  for  lighting  the  rear  parts 
of  stores  and  for  railway-stations,  sheds,  etc. 

Prism  Glass,  for  glazing  windows,  skylights  and  sidewalk-lights,  is  now  manu- 
factured in  a  large  number  of  forms  in  both  prisms  and  sheets,  and  by  several 
companies.  The  diffusing  properties  of  several  types  are  described  on  pages 
1453  to  1456  under  the  subject  of  Illumination.  This  glass  is  made  with  sharp 
prisms  which  are  glazed  horizontally  in  the  windows  and  by  refracting  the  light 
throw  it  back  horizontally  into  the  rooms,  adding  very  materially  to  the  in- 
terior lighting.  It  is  manufactured  by  several  companies  and  can  be  procured 
from  glass-jobbers  in  practically  all  the  cities  of  the  .Umted  States.  (See,  also, 
page  821.)  Glass  prisms  for  lighting  are  made  of  pieces  of  glass  of  standard  dir 
mensions,  about  4  in  square,  with  a  smooth  outer  surface  and  an  inner  surface  di- 
vided into  a  series  of  prisms.  They  are,  in  many  cases,  formed  into  plates  by 
the  process  of  electroglazing,  the  edges  of  the  prism-lenses  being  welded  together, 
so  to  speak,  by  a  narrow  line  of  copper  which  gives  the  desired  stiffness  and 
strength  for  use  in  large  frames,  and  also  an  attractive  appearance  considered  by 
some  to  be  superior  to  ordinary  leaded  work.  These  prism-plates  can  be  made 
in  any  desired  size,  but  for  very  large  surfaces  two  or  more  plates,  divided  by 
means  of  metal  sash-bars,  are  generally  used.     (See,  also,  page  821.) 

The  commercial  value  of  these  prisms  depends  on  that  property  of  glass  which 
causes  what  is  known  as  retraction.  Prism-plates  recei\  c  the  light  from  the 
sky,  not  necessarily  from  the  sun,  and  refract  or  turn  it  back  into  the  room  which 
is  to  be  lighted.  With  an  ordinary  window  the  light  from  the  sky,  passing 
through  the  glass,  strikes  the  floor  at  a  point  not  very  far  distant  from  the  window. 
As  the  color  of  the  floor  is  usually  dark,  reflecting  perhaps  only  one-tenth  part 
of  the  light  falling  on  it,  the  rear  parts  of  the  room  receive  only  a  small  portion 
of  the  light  which  enters  the  window.  For  this  reason  it  has  been  necessary  to 
make  very  high  stories  for  deep  rooms,  in  order  to  light,  even  moderately,  those 
parts  which  are  at  a  distance  from  the  window.  When  prisms  are  substituted 
for  the  common  window-glass  or  plate  glass,  the  rays  of  light  as  they  enter  the 
glass  are  refracted,  and  by  employing  prisms  of  the  proper  angle,  the  rays  may 
be  given  almost  any  direction.  Moreover,  by  utilizing  different  prisms  in  the 
same  plate,  some  of  the  rays  may  be  directed  to  the  rear  of  the  room  while  others 
are  thrown  so  as  to  strike  near  the  front.    The  prism-plates  do  not  increase  the 


Prism  Glass 


1579 


quantity  of  light  entering  the  window,  but  simply  redistribute  it,  directing  it 
into  those  portions  of  the  room  in  which  it  is  most  needed.  By  thus  changing 
the  direction  of  Hght-rays  a  room  with  a  low  ceiling  can  be  better  lighted  than 
when  sheet  or  plate  glass  is  used.  To  insure  success  in  the  lighting  of  interiors 
by  means  of  prisms  requires,  however,  a  superior  quality  of  glass,  and  careful 
scientific  calculations  and  experiments,  besides  practical  and  attractive  means 
of  glazing  and  methods  of  installation.  These  requirements  have  been  met  by 
the  several  companies  making  these  prisms  and  their  products  may  be  con- 
sidered among  the  relatively  new  building  materials.  They  have  been  very 
successfully  applied  to  the  lighting  of  dark  rooms  by  daylight.  The  application 
of  prisms  to  any  particular  building  depends  upon  the  surrounding  conditions 
and  requirements,  each  case  requiring  some  special  treatment;  but  in  a  general 
way  the  various  appliances  used  in  the  installations  may  be  divided  into  four 
classes  as  follows: 

(i)  Vertical  Plates,  which  are  set  directly  in  the  sashes  in  place  of  the  ordinary 
window-glass.  They  are  commonly  used  for  the  transom-lights  of  store-windows 
and  the  upper  sashes  of  double-hung  windows.  They  may  also  fill  the  entire 
window. 

(2)  Foriluxes,  which  are  vertical  prism-plates  set  in  independent  frames  and 
placed  in  window-openings  substantially  flush  with  the  face  of  the  wall. 

(3)  Canopies,  which  are  external  prism-plates  in  independent  frames,  placed 
over  window-openings  and  set  at  an  angle  with  the  vertical,  a  position  similar  to 
that  of  an  ordinary  awning. 

(4)  Pavement-Prisms,  which  are  set  in  iron  frames  in  the  pavements  or  side- 
walks, in  place  of  the  ordinary  bull's-eye  lights.  In  connection  with  the  pave- 
ment-prisms,    when     a 

well-lighted  basement  is 
desired,  vertical  plates  of 
prisms,  hung  below  and 
opposite  the  pavement- 
lights,  are  often  used. 
These  hanging,  vertical 
plates  receive  the  light 
from  the  pavement- 
prisms,  and  again  chang- 
ing its  direction,  project 
it  horizontally  into  the 
basement.  This  feature 
is     illustrated     in     the 

figure  here  given,  reproduced  through  the  courtesy  of  the  Luxfer  Prism 
Company. 

The  canopies  may  be  made  either  stationary  or  adjustable  and  may  be  em- 
ployed in  a  variety  of  ways,  combining  the  useful  with  the  ornamental.  The 
hanging,  vertical  plates  lend  themselves  to  a  highly  decorative  treatment.  In 
both  the  fixed  and  hanging  vertical  plates  the  prisms  may  be  arranged  to  pro- 
duce ornamental  effects,  and  designs  may  be  inwrought  on  the  face  of  the  prism- 
plates  to  correspond  with  the  designs  worked  into  the  surfaces  of  the  building 
and  with  the  style  of  the  entire  facade.  The  prism-plates  weigh  no  more,  and 
often  less,  than  plate  glass  of  the  same  size,  while  they  are  much  stronger  in 
resisting  wind-pressure,  the  action  of  hail  and  the  impact  of  flying  fragments. 
Although  transmitting  a  very  large  amount  of  light,  these  prism-plates  are  not 
transparent  in  the  ordinary  sense,  and  may  thus  be  used  as  screens  to  hide  un- 
attractive views  or  to  prevent  persons  looking  either  in  or  out  of  a  window.     At 


Refraction  and  Transmission  of  Light  by  Prisms 


1580 


Window-Glass  and  Glazing 


I'art  3 


t;he  same  time  a  maximum  quantity  of  light  is  admitted.  Tiie  prism-plates, 
owing  to  the  still,  durable  manner  in  which  they  are  united  by  the  electro- 
glazing  process,  serve,  also,  as  a  fire-retardant  or  as  a  partial  substitute  for  the 
ordinary  iron  tire-shutters.  The  copper  glazing  forms,  as  it  were,  a  continuous 
rivet,  which  holds  the  individual  prism-lights  together,  even  after  they  have 
become  badly  cracked  by  the  action  of  fire  and  water.  The  details  of  the  vari- 
ous makes  of  piisms  are  too  complicated  to  be  set  forth  in  a  few  pages,  but  they 
are  well  described  in  the  various  handbooks  and  catalogues  published  by  the 
different  manufacturers.  From  a  commercial  point  of  view  the  special  ad- 
vantages of  these  systems  of  interior  lighting  are  manifold.  They  transform 
rooms,  particularly  basements,  otherwise  too  dark  for  occupancy,  into  income- 
producing  spaces;  in  many  buildings  they  do  away  with  the  use  of  light-shafts, 
thus  saving  a  large  amount  of  valuable  floor-space;  and  in  all  large  or  deep 
rooms  they  effect  a  great  saving  in  artificial  lighting.  Once  installed,  there  is 
no  cost  for  maintenance.  The  extent  to  which  these  prisms  have  been  used  by 
architects,  in  both  new  and  old  buildings,  shows  that  they  have  had. a  decided 
influence  upon  commercial  architecture. 

Glass  for  Skylights.  General  Description.  The  glass  ordinarily  used  now 
for  skylights  is  either  rough  or  ribbed  skylight-glass,  and  since  the  great  cheapen- 
ing in  the  process  of  manufacturing  glass  with  wire  mesh  in  it,  wire-glass,  also,  is 
being  largely  used  for  this  purpose.  The  sizes  used  depend  largely  upon  the 
pitch  of  the  skylight,  small  sizes  being  more  desirable  when  the  pitch  is  slight. 
The  weight  of  rough  or  ribbed  glass,  with  or  without  wire  mesh,  is  approximately 
as  follows: 


Weight  of  Rough 

01  Ribbed  Glass 

'  Thickness  in  inches. 
Weight  in  pounds . .  . 

1/8 

2 

Me 

2 1/2 

H 
3I/2 

5 

7 

81.4 

10 

I 

I2K2 

Cost  of  Skylight-Glass.*     The  different  kinds  of  skylight-glass  in  small  quan- 
tities were  quoted  (1914)  about  as  follows: 


Cost  of  Skylight-Glass 

Kinds  of  glass 

Cost 

Rough  or  ribbed  skylight-glass,  ^'^-in                 

6  cts  per  sq  ft 
8  cts  per  sq  ft 
12  cts  per  sq  ft 
16  cts  per  sq  ft 
20  cts  per  sq  ft 
20  cts  per  sq  ft 

Roueh  or  ribbed  skvlicht-class   M-in 

Rough  or  ribbed  wire-glass,  /i-in                         .       

Maze  Cobweb,  or  Florentine  wire-glass 

Sheet  prism  glass 

Glass  for  Mirrors.  Mirrors  are  made  by  silvering  one  side  of  a  sheet  of 
pohshed  plate  glass.  This  is  the  only  kind  of  glass  suitable  for  making  mirrors, 
because,  unless  the  surface  of  glass  is  polished,  the  reflection  is  distorted.  A 
generation  ago,  mirrors  were  made  by  the  old-style  process  of  pressing  the  glass 
by  means  of  heavy  weights  onto  mercury,  backed  by  tinfoil,  the  affinity  of  mer- 
cury for  tin  forming  an  amalgam  which  protected  the  back  of  the  mirrors  and 
gave  the  reflection.  This  was  a  very  slow  and  expensive  process.  During  the 
twenty-five  years  prior  to  1913,  practically  all  of  the  mirrors  made  were 
manufactured  by  what  is  known  as  the  patent-back  process,  in  which  nitrate 

*  The  prices  have  materially  advanced  and  as  they  change  from  year  to  year,  the  man- 
ufacturers' lists  must  be  consulted. 


Memoranda  on  Roofing 


1581 


of  silver  is  precipitated  in  a  film  over  the  surface  of  the  glass,  thus  giving  it  the 
property  of  reflecting.  This  film  is  afterward  covered  and  protected  by  shellac, 
varnish  and  paint.  This  modern  method  of  manufacture  has  made  it  possible 
to  supply  mirrors  in  considerably  less  time,  and  at  a  very  much  lower  cost,  than 
when  manufactured  by  the  old-fashioned  mercury-back  process.  There  are 
many  who  claim  that  in  spite  of  modern  processes  of  manufacture,  the  old 
method  produced  the  best  results  as  far  as  durability  is  concerned.  This  is 
evidenced  by  the  following  statement  inserted  by  Mr.  Kidder  in  the  preceding 
editions  of  the  Pocket-Book:  "There  are  two  kinds  of  mirrors  on  the  market, 
one  the  old  time  reliable  mercury-back  mirror,  the  other  the  nitrate  of  silver,  or 
what  is  better  known  to  the  trade  as  the  patent-back  mirror.  The  latter  is  now 
and  has,  in  recent  years,  been  most  extensively  sold  as  a  substitute  for  the  former. 
In  the  manufacture  of  mercury-back  mirrors  no  chemicals  are  used,  only  two 
metals,  mercury  and  tin-foil.  The  aflinity  of  mercury  for  tin  forms  an  amalgam 
impervious  to  and  not  affected  by  the  atmosphere.  A  mercury-back  mirror  is 
universally  considered  to  be  the  only  durable  and  permanent  mirror.  A  nitrate- 
of-silver  6r  patent-back  mirror  is  produced  by  the  precipitation  of  a  chemical 
solution  of  nitrate  of  silver  and  other  media  on  the  surface  of  the  glass,  to  which 
is  added  one  coat  of  shellac  varnish  overlaid  with  one  or  more  coats  of  paint. 
This  mirror,  irrespective  of  the  quality  of  the  glass  from  which  it  is  made,  will 
steadily  deteriorate  from  the  date  of  its  manufacture  to  that  of  its  final  collapse, 
which  may  occur  at  any  time  from  a  few  months,  but  certainly  within  a  few 
years." 

MEMORANDA  ON  ROOFING 

Shingles.*  The  best  shingles  are  those  made  from  cypress,  cedar,  redwood, 
white  and  yellow  pine  and  spruce,  in  the  order  mentioned.  Redwood,  while 
perhaps  not  quite  as  durable  as  cypress,  is  less  inflammable;  sawed  pine  shingles 
are  inferior  to  cedar,  and  spruce  shingles  are  not  suitable  for  good  work. 


Number  and  Weight  of  Cedar  and  Pine  Shingles  Per  Square  of  One 
Hundred  Square  Feet 


Number 

Weight  per  square 

Number 

Weight 

Length, 

Assumed 

Weather 

of 

of 

of  nails 

width, 

,or  gauge. 

shingles 

nails 

per 

m 

m 

per 

Cedar. 

Pine, 

per 

square, 

square  f 

lb 

lb 

square 

lb 

14 

4 

4 

900 

210 

233 

I  800 

4.50 

15 

4 

A'A 

800 

200 

222 

1600 

4.00 

16 

4 

5 

720 

192 

213 

I  440 

3.60 

18 

4 

SV2 

r)=;5 

197 

218 

I  310 

3.28 

20 

4 

6 

600 

200 

222 

I  200 

3  00 

22 

4 

6j/2 

554 

203 

226 

I  108 

2.77 

24 

4 

7 

S.3 

20(3 

229 

I  030 

2.58 

Sizes  of  Shingles.  Cedar  and  redwood  shingles  as  commonly  sawed  are  20  in 
in  length,  and  cypress  shingles  usually  from  20  to  24  in  long,  the  longer  ones  allow- 

*  For  more  complete  information  see  Kidder's  Building  Construction  and  Superinten- 
dence, Part  II,  Carpenters'  Work,  pages  321  to  325. 

t  To  allow  for  waste,  add  from  6  to  10%.  the  greater  allowance  being  for  the  sbortei 
shingles. 


1582  Memoranda  on  Roofing  Part  3 

ing  a  greater  exposure  to  the  weather.  Redwood  shingles  and  the  cedar  shingles 
from  the  States  of  Washington  and  Oregon,  which  States  furnish  most  of  the 
shingles  used  west  of  the  Mississippi,  are  He  and  ^le  in  thick  at  the  butt; 
cypress  shingles  are  usually  sawed  thicker.  Those  used  in  Boston  are  %&  in 
thick.  Ordinary  roofing-shingles  are  of  random  widths,  varying  from  2y2  to 
14  and  sometimes  16  in.  They  are  put  up  in  bundles,  usually  four  bundles  to 
the  thousand.  A  thousand  common  shingles  means  the  equivalent  of  i  000 
shingles  4  in  wide. 

Dimension-Shingles  are  sawed  to  uniform  width,  either  4,  5,  or  6  in.  Dimen- 
sion-shingles with  the  butt  sawed  to  various  patterns  are  also  carried  in" 
stock. 

On  hip-roofs,  or  for  four  valleys,  add  5%  for  cutting.  On  irregular  roofs  with 
dormer-windows,  add  10%.  It  is  claimed  that  redwood  shingles  will  go  farther 
than  cedar  shingles.  With  a  rise  to  the  roof  of  from  8  to  10  in  to  the  foot,  cedar 
shingles,  or  any  shingles  16  or  18  in  in  length,  should  be  laid  from  4  to  4H  in  to 
the  weather;  with  a  rise  from  10  to  12  in,  from  4H  to  4%  in  to  the  weather; 
and  on  steeper  roofs  they  may  be  laid  from  4y2  to  5  in.  Redwood  shingles  may 
be  laid  H  in  more  to  the  weather.  Some  authorities  allow  slightly  greater  ex- 
posures for  these  lengths.  Where  the  longer  shingles  are  used  the  exposure  to 
the  weather  may  be  increased  up  to  7  in  for  the  24-in  lengths.  On  walls  cedar 
shingles  are  commonly  laid  5  in  to  the  weather,  and  redwood  shingles  6  in. 

Labor.  An  average  shingler  should  lay  i  500  shingles  in  9  hours  on  plain 
work;   on  irregular  roofs  with  dormers,  i  000  per  9  hours. 

Nails.  It  requires  about  5  lb  of  threepenny  or  7>i  lb  of  fourpenny  nails  to 
I  000  shingles. 

Slate  Roofs 

Characteristics  of  Good  Slate.  A  good  slate  should  be  both  hard  and  tough. 
If  the  slate  is  too  soft,  however,  the  nail-holes  will  become  enlarged  and  the  slate 
will  become  loose.  If  it  is  too  brittle  the  slate  will  fly  to  pieces  in  the  process  of 
squaring  and  holing  and  will  be  easily  broken  on  the  roof.  "A  good  slate  should 
give  out  a  sharp  metallic  ring  when  struck  with  the  knuckles;  should  not  splinter 
mder  the  slater's  axe;  should  be  easily  holed  without  danger  of  fracture,  and 
should  not  be  tender  or  friable  at  the  edges."  The  surface  when  freshly  split 
should  have  a  bright  metallic  luster  and  be  free  from  all  loose  flakes  or  dull  sur- 
faces. Very  few  of  the  Vermont  slates,  however,  have  the  metallic  luster  or 
ribbons.  Most  slates  contain  ribbons  or  seams  which  traverse  the  slate  in 
approximately  parallel  directions.  Slates  containing  soft  ribbons  are  inferior 
and  should  not  be  used  in  good  work. 

Color.  The  color  of  slates  varies  from  dark  blue,  bluish  black,  and  purple  to 
gray  and  green.  There  are  also  a  few  quarries  of  red  slate.  The  color  of  the 
slate  does  not  appear  to  indicate  the  quality.  All  slate  quarried  in  Maine  is 
black  as  is  also  that  quarried  in  Virginia,  while  that  quarried  in  Pennsylvania 
and  Maryland  is  also  black  but  borders  on  dark  blue  and  is  advertised  by  some 
firms  as  dark  blue.  Slate  quarried  i-n  New  York  State  is  red,  of  various  tints, 
while  that  quarried  in  Vermont  is  of  various  colors,  such  as  green,  purple,  varie- 
gated, etc.  The  red  and  dark  colors  were  formerly  considered  the  most  effec- 
tive but  at  the  present  time  the  greens  are  going  on  some  of  the  largest  and 
finest  of  the  new  residences.  Some  slates  are  marked  with  bands  or  patches 
of  a  different  color,  and  the  dark-purple  slates  often  have  large  spots  of  light 
green  on  them.  These  sp^ots  do  not  as  a  rule  affect  the  durability  of  the  slate, 
but  they  greatly  detract  from  its  appearance. 


Grading  and  Laying  Slates  1583 

Grading  of  Slates.  The  Monson,  Me.,  slates  and  Brownville,  Me.,  slates 
are  graded  as  follows:  No.  i.  Every  sheet  to  be  full  Mo  in  thick,  both 
sides  smooth  and  all  corners  full  and  square.  No  pieces  to  be  winding  or 
warped. 

No.  2.  Thickness  may  vary  from  M  to  H  in,  all  corners  square,  one  side  gener- 
ally smooth,  one  side  generally  rough,  no  badly  warped  slates. 

The  Bangor,  Pa.,  slates  are  graded: 

No.  I  Clear.     A  pure  slate  without  any  faults  or  blemishes. 

No.  I  Ribbon.  As  well  made  as  No.  i  Clear,  except  that  it  contains  one  or 
more  ribbons  (a  black  band  or  streak  across  the  slate),  which,  however,  are  high 
enough  on  the  slate  to  be  covered  when  laid,  thus  presenting  a  No.  i  roof. 

No.  2  Ribbon.  This  contains  several  ribbons,  some  of  which  cannot  be 
covered  when  laid. 

No.  2  Clear.     A  slate  without  ribbons,  made  from  rough  beds. 

Hard  Beds.  A  clear  Bangor  slate,  not  quite  as  smooth  as  No.  i  Clear,  but 
much  better  than  No.  2  Clear. 

Ordinary  Bent  Slate.  A  smooth  slate  similar  to  No.  i  Clear,  but  bent  at  a 
radius  of  about  1 2  f t. 

Punching.  Formerly  nail-holes  in  slates  were  punched  on  the  Job;  now,  how- 
ever, slates  are  bored  and  countersunk  at  the  quarry,  when  so  ordered.  Archi- 
tects should  always  specify  that  the  slates  are  to  be  bored  and  countersunk,  as 
punching  badly  damages  the  slates. 

Sizes.  The  sizes  of  slates  range  from  9  by  7  in  to  24  by  14  in,  there  being  some 
thirty-seven  different  sizes;  the  more  common  sizes,  however,  are  the  following: 
The  sizes  of  slates  best  adapted  for  plain  roofs  are  the  large  wide  slates,  such  as 
12  by  16  in,  18  by  12  in,  20  by  12  in,  or  24  by  14  in.  Slates  from  8  by  16  to  10 
by  20  in  are  popular  sizes,  9  by  i8-in  slates  being  pr«bably  used  oftener  than 
those  of  any  other  size.  The  11  by  22  and  12  by  24-in  slates  are  used  principally 
on  very  large  high  buildings.  The  lower  grades  of  slate  are  used  largely  on  ware- 
houses and  barns.  The  larger  sizes  make  fewer  joints  in  the  roof,  require  fewer 
nails,  and  diminish  the  number  of  small  pieces  at  hips  and  valleys.  For  roofs 
cut  up  into  small  sections  the  smaller  sizes,  such  as  14  by  7  in  or  16  by  8  in,  look 
the  best. 

Thickness.  Slates  vary  in  thickness  from  H  to  %  in;  Yie  in  is  the  usual  thick- 
ness for  ordinary  sizes  (see  Grading  of  Slates  in  the  preceding  paragraphs).  It 
is  of  utmost  importance  for  architects  to  specify  the  thickness  of  slates,  either 
fully  Me  in  thick,  or  fully  H  in  thick,  to  secure  u  strong  and  durable  roof. 

Laying.  Slates  are  laid  either  on  a  board  sheathing  (rough,  or  tongued  and 
grooved)  covered  with  tarred  or  water-proof  paper  or  felt,  or  on  roofing-laths 
from  2  to  3  in  wide  and  from  i  to  i  H  in  thick,  nailed  to  the  rafters  at  distances 
apart  to  suit  the  gauge  of  the  slates.  Each  slate  should  lap  the  slate  in  the 
second  course  below,  3  in.  The  slates  are  fastened  with  two  threepenny  or  four- 
penny  nails,  one  near  each  upper  corner.  For  slates  20  by  10  in  or  larger,  four- 
penny  nails  should  be  used.  Copper,  composition,  tinned,  or  galvanized  nails 
should  be  used.  Plain-iron  nails  are  speedily  weakened  by  rust,  and  they 
break  and  allow  the  slates  to  be  blown  off.  On  iron  roofs  slates  are  often 
placed  directly  on  small  iron  purlins  spaced  at  suitable  distances  apart  to  receive 
them,  and  fastened  with  wire  or  special  forms  of  fasteners.  The  gauge  of  a 
slate  is  the  portion  exposed  to  the  weather,  which  should  be  one-half  the  re- 
mainder obtained  by  subtracting  3  in  from  the  length  of  the  slate.  Roofs  to  be 
covered  with  slate  should  have  a  rise  of  not  less  than  6  in  to  the  foot  for  20-in  or 
24-in  slates,  or  8  in  for  smaller  sizes. 


1584  Memoranda  on  Roofing  Part  3 

Elastic  Cemfent.  In  first-class  work,  the  top  course  of  slate  on  the  ridge,  and 
slate  for  from  2  to  4  ft  from  all  gutters  and  i  ft  each  way  from  all  valleys  and 
hips,  should  be  bedded  in  elastic  cement. 

Flashings.  By  flashings  are  meant  pieces  of  tin,  zinc,  or  copper  laid  over 
slate  and  up  against  walls,  chimneys,  copings,  etc. 

Coimterflashings  are  of  lead  or  zinc,  and  are  laid  between  the  courses  in  brick, 
and  turned  down  over  the  flashings.  In  flashing  against  stonework,  grooves  or 
reglets  often  have  to  be  cut  to  receive  the  counterflashings. 

Close  and  Open  Valleys.  A  close  valley  is  one  in  which  the  slates  are  mitered 
and  flashed  in  each  course  and  laid  in  cement.  In  such  valleys  no  metal  can  be 
seen.  Close  valleys  should  only  be  used  for  pitches  above  45°.  An  open  valley 
is  one  formed  of  sheets  of  copper  or  zinc  15  or  16  in  wide,  over  which  the 
slates  are  laid* 

Old  English  Method  of  Laying  Slates.*  This  method  of  laying  slate  in- 
volves the  use  of  different  shades  of  colored  slates  in  graduated  courses  and  in 
random  widths  beginning  at  the  eaves,  for  example,  with  slates  28  in  long  and  iH 
in  thick,  and  using  the  different  thicknesses  from  i  H  to  %  in,  in  shorter  lengths, 
in  working  upward  on  the  roof.  The  use  of  this  kind  of  work  for  roofs  has  in- 
creased in  recent  years  and  the  method  possesses  vast  possibilities  for  carry- 
ing out  architects'  ideas  for  varied  artistic  effects.  The  slates  are  made  with ' 
rough-cut  edges  in  all  thicknesses  from  Me  to  lYz  in,  in  a  combination  of  various 
shades  carefully  selected  in  such  prop>ortion  as  to  produce  the  best  possible  har- 
mony, when  laid.  As  all  of  these  colors  and  shades  are  unfading,  the  weathered 
effect  is  obtained  at  once  and  is  permanent.  These  slates  are  made  not  only  in 
usual  sizes,  but  in  the  old  English  style,  to  be  laid  in  graduated  courses  of  dif- 
ferent lengths  and  in  random  widths.  The  Old  English  color-combination  roof- 
ing-slates should  be  specified^to  secure  the  light -and-shadow  effect,  and  it  is  of  the 
utmost  importance  to  specify  the  thickness  desired,  as  the  price  is  the  same  for 
all  sizes,  while  the  cost  varies  according  to  thickness.  When  graduated  courses 
are  desired,  specifications  should  call  for  the  number  of  courses  to  be  laid  in  each 
length  and  thickness  beginning  at  the  eaves  courses,  where  the  thickest  slates 
are  used  in  the  largest  sizes,  sometimes  30  or  even  36  in  in  length,  and  working 
upward  on  the  roof  with  the  shorter  lengths  and  thinner  slates  to  the  ridges  where 
the  smallest  sizes  and  thinnest  slates  are  used.  To  secure  a  rough  effect  at  mini- 
mum cost,  specifications  should  call  for  Old  English  color-combination,  all  slates 
to  be  fully  Vi  in  thick  with  rough  cut  edges  and  graduated  courses  in  sizes  rang- 
ing from  24  by  16  to  12  by  6  in,  with  nail-holes  drilled  and  countersunk.  To 
secure  the  best  rough  effect,  specifications  should  call  for  eaves-courses  not  less 
than  %  in  thick,  stating  the  thickness  desired  for  the  eaves,  and  the  number  of 
courses  desired  in  each  length  and  thickness.  Among  the  good  specimens  of  tho 
Old  English  style  of  roofing  may  be  mentioned  the  buildings  of  Princeton  Uni- 
versity for  the  Graduate  College,  where  different  shades  of  unfading-green 
slates  are  used  in  thicknesses  running  from  1 34  in  at  the  eaves  to  ^i  in  at  the 
ridge. 

Measurement.  Slates  are  sold  by  the  square,  by  which  is  meant  a  sufficient 
number  of  slates  of  any  size  to  cover  100  sq  ft  of  surface  on  a  roof,  with  3  in  of 
lap,  over  the  head  of  those  in  the  second  course  below.  The  square  is  also  the 
basis  on  which  the  cost  of  laying  is  measured.  "Eaves,  hips,  valleys,  and  cut- 
tings against  walls  or  dormers  are  measured  extra;    i  ft  wide  by  their  whole 

*  Full  information  in  regard  to  the  details  of  the  slates  for  this  purpose  and  the  methods 
employed  in  laying  them  can  be  obtained  from  the  various  companies. 


Cost  of  Slates 


1585 


lengtji,  the  extra  charge  being  made  for  waste  material  and  the  increased  labor 
reouired  in  cutting  and  fitting.  Openings  less  than  3  sq  ft  are  not  deducted,  and 
all  cuttings  around  them  are  measured  extra.  Extra  charges  are  also  made  for 
borders,  figures,  and  any  change  of  color  of  the  work  and  for  steeples,  towers,  and 
perpendicular  surfaces."* 

Cost.f  The  cost  of  slates  varies  with  the  size,  color  and  quality.  The  prices 
given  in  the  following  table  were  about  the  average  in  19 15  for  blue-black  slate,  of 
No.  I  grade,  loaded  on  the  cars  at  the  Pennsylvania  quarry.  The  freight  in 
car-load  lots  of  60  scjuares  or  over  to  Philadelphia  from  Bethlehem,  Pa.,  was  60 
cts  per  square,  from  Pennsylvania  to  Omaha,  Neb.,  $2.60  and  from  Vermont, 
about  the  same.  It  will  be  seen  that  slates  of  the  medium  sizes  cost  the  most, 
and  those  of  the  larger  and  smaller  sizes  the  least.  Special  prices' are  quoted  for 
special  sizes.  The  larger  sizes  make  the  cheapest  roofs.  Red  slates  cost  from 
60  to  150%  more  than  black  slates.  The  green  slates  are  more  expensive  than 
the  black  with  the  exception  of  the  Maine  and  Peach  Bottom  varieties. 


Number  and  Cost  t  of  Slates,  and  Pounds  of  Nails  to  100  Square  Feet  of  Roof 
3-inch  Lap 


Sizes  of 

Exposed 

Number  to 

Weights  of 
galvanized 

Cost  per 

slates, 

when  laid, 

a  square 

nails, 

square  at 

in 

in 

lb    oz 

quarry 

14X24 

loV^ 

98 

I      6 

$4-50 

12X24 

io!-2 

115 

I     10 

4.50 

12X22 

9'/^ 

126 

Ad- 

I     12 

4-75 

11X22 

9K2 

138 

I     15 

4-75 

11X20 

8K> 

155 

2      0 

5.2s 

10X20 

SVi 

170 

2      6 

5.2s 

i2Xi8 
10X18 

7M2 

160 

1  13 

2  3 

192 

5.25 

9X18 

iVi 

214 

2      7 

5.25 

12X16 
10X16 
9X16 

6V2 

61/2 

61/2 

18S 

222 

2      2 

2      8* 

247 

3      0 

5.25 

8X16 

61/2 

277 

3d- 

3       2 

5.2s 

10X14 

sYi 

262 

3       0 

8X14 

5!/2 

328 

3     12 

4.75 

7X14 

5/2 

375 

4      4 

4-75 

8X12 

A\i 

400 

4      9 

7X12 

.       aVi 

457 

5      3 

4.25 

6X12 

4/2 

534 

6      I 

4  25 

The  cost' of  blue-black-slate  roofs,  complete,  varies  from  $9  to  $16  per  square, 
depending  on  the  class  of  work  and  remoteness  from  the  quarries.  The  addi- 
tional cost  of  laying  slate  in  elastic  cement  varies  from  $1.75  to  $2.50  per  square. 
An  experienced  roofer  will  lay,  on  an  average,  2I/2  squares  of  slate  in  8  hours. 

Weight.  Slate  roofing  Vie  in  thick  will  weigh  on  the  roof  about  6K2  lb  per  sq  ft, 
and  if  i/4  in  thick,  8%  lb,  the  smaller  sizes  weighing  the  most  on  account  of  the 
lap.     The  actual  weight  of  a  square  foot  of  slate  H  in  thick  is  3.63  lb.     A  cubic 

•  The  Building  Trades  Pocket-book. 

t  These  prices  have  advanced  and  the  manufacturers'  lists  must  be  consulted. 


1586  Memoranda  on  Roofing  Part  3 

foot  of  Vermont  slate  weighs  approximately  175  lb.  The  average  shipping 
weight  for  No.  i,  ^le-in  slates,  is  approximately  725  lb;  for  H-in  slates,  i  000 
lb;  for  H-in  slates,  2  000  lb,  etc. 

Roofing-Tiles 

General  Notes  on  Roofing-Tiles.  The  term  roofing-tile  is  commonly 
understood  to  refer  to  exterior  roof-covering  made  from  clay  in  units  of  various 
shapes  and  laid  with  overlapping  edges.  Clay  or  terra-cotta  roof-tiles  have 
long  been  very  largely  used  in  Europe,  where  their  cost  is  much  less  than  in 
America.  Since  the  year  1893  the  advance  here  in  the  character  and  extent  of  ■ 
roofing-tile  has  been  marked  and  rapid.  This  material  can  now  be  had  at  much 
lower  prices  than  formerly  prevailed,  and  the  result  has  been  that  thousands  of 
squares  of  terra-cotta  tiles  have  been  placed  on  shops  and  factories  which  would 
under  former  conditions  have  been  covered  with  slate  or  metal.  Whether  or  not 
a  tile  roof  is  as  durable  and  satisfactory  as  one  of  No.  i  slate  is  a  much-dis- 
puted question.  Mr.  Kidder  was  of  the  opinion  that,  considering  the  quantities 
used,  slates  have  given  better  satisfaction  than  tiles.  A  tile  roof,  however,  is 
certainly  more  attractive  than  a  slate  roof,  and  it  is  generally  held  that  there 
are  many  roofing-tiles  on  the  market  which  if  properly  laid  prove  as  tight  and 
durable  as  slates.  There  are  so  many  patterns  of  roofing-tiles  that  it  is  impos- 
sible here  to  enter  into  a  description  of  them.  Of  the  various  patterns,  those 
which  interlock  are  considered  from  a  practical  standpoint,  to  make  the  most 
satisfactory  roof. 

Laying  Roofing-Tiles.  Roofing-tiles  have  been  laid  directly  on  a  porous 
book  tile  or  concrete  base  or  on  a  sheathed  surface  over  such  base,  or  they  have 
been  fastened  to  stripping  over  the  sheathing  or  wooden  or  steel  purlins  by  means 
of  copper  wires.  When  thus  fastened  by  wires,  the  joints  were  usually  pointed 
on  the  under  side  after  they  were  laid,  to  prevent  the  entrance  of  dust  or  dry 
snow.  Tiles  of  the  older  patterns  were  nailed  to  the  sheathing,  but  later  on  this 
iuethod  was  superseded  by  the  practice  of  fastening  with  copper  wires  from 
pierced  lugs  near  the  lower  ends  of  the  tiles.  The  best  modern  method,  however, 
seems  to  be  the  one  involving  a  solid  continuous  base  for  the  roofing-tiles,  whether 
or  not  purlins  are  used.  "Such  purlins  should  be  filled  in  between  either  with 
book  tiles  or  a  concrete  base  and  felt  should  be  laid  thereon.  The  book  tiles,  if 
used,  should  be  of  a  porous  quaUty.  Instead  of  regarding  the  nailing  of  tiles  as 
a  defective  method,  we  have  returned  to  it  as  the  only  proper  method  of  fasten- 
ing tiles  and  have  eliminated  tlie  stripping  of  sheathed  roofs  and  the  use  of  copper 
wires.  Such  methods  Would  do  in  some  portions  of  central  Europe  where  the 
winds  and  other  climatic  conditions  are  not  severe,  but  through  a  twenty-five- 
years'  experience  in  the  varied  climatic  conditions  of  the  United  States,  we  have 
found  that  the  nailing  of  tiles  with  copper  nails  is  the  only  satisfactory  method 
of  application.  We  have  also  found  that  a  roof  should  be  sheathed  and  covered 
with  a  good  asphaltum-felt  to  prevent  wind-suction."  *  Roofing-tiles  weigh 
from  750  to  I  200  lb  per  square  of  100  sq  ft. 

•Specifications  for  Tile  Roofing 

The  following  specification  t  contains  valuable  suggestions  for  the  proper  lay- 
ing of  tile  roofs: 

All  pitched  roofs  shall  be  covered  with  ( )  tiles  with  fittings  suitable  for 

*  Quoted  by  permission  from  data  on  roof-tiling,  by  the  Ludowici-Celadon  Company, 
Chicago,  III. 

t  Prepared  from  data  furnished  by  the  Ludowici-Celedon  Companyj  Chicago,  111. 


Roofing-Tiles  1587 

each  pattern  unless  otherwise  selected  by  the  architect.  The  tiles  as  specified 
above  are  to  be  hard-burned,  of  red  color,  and  in  accordance  with  samples  de- 
posited in  the  office  of  the  architect. 

(i)  Preparation  of  Roof.  Before  the  roofer  is  sent  for,  the  owner  or  general 
contractor  is  to  construct  the  roofs  in  strict  accordance  with  the  plans,  sheath  the 
roofs  TIGHT,  have  all  chimneys  and  walls  above  the  roof-line  completed,  have  all 
vent-pipes  put  through  the  roofs,  furnish  all  strips  of  required  width  used  under 
hip-rolls,  furnish  all  i  by  }i-'m  cant-strips  used  under  the  tiles  at  the  eaves  and 
have  all  the  scaffolding  ready  for  the  roofers'  use.  The  metal-contractor  is  to 
have  all  gutters  in  place  on  the  roof  (gutters,  whether  box,  hanging  or  secret' 
gutters,  are  to  extend  over  the  roof -sheathing  and  cant-strips,  and  run  under 
the  felt  and  tiles  at  least  8  in)  and  is  to  have  in  place,  also,  all  valley-metal,  the 
width  of  which  is  to  be  not  less  than  24  in,  with  both  edges  turned  up  H  in 
through  the  entire  length  of  the  valley.  The  valley-metal  is  to  be  fastened  with 
clips  and  never  nailed  or  punctured  in  any  manner.  The  valley-metal  is  to  be 
laid  over  one  layer  of  felt  running  lengthwise  the  entire  distance  of  the  valley. 
The  metal-contractor  is  to  have  in  readiness  all  flaghing-metal  used  alongside 
and  in  front  of  dormers,  gables,  skylights,  towers  and  perpendicular  walls,  and 
around  vent-pipes  and  chimneys,  and  is  to  place  the  same  after  the  arrival  of 
the  tile-roofer  and  under  his  direction. 

(2)  Laying  the  Felt.  After  the  roofs  have  thus  been  prepared  to  receive  the 
felt  and  tiles,  the  tile-roofer  is  to  cover  the  sheathing  of  the  roofs  with  one  thick- 
ness of  asphalt  roofing-felt  weighing  not  less  than  30  lb  to  the  square,  laying  the 
same  with  a  2H-in  lap  and  securing  it  in  place  by  capped  nails.  The  felt  is  to 
be  laid  parallel  with  the  eaves,  lapped  over  all  valley-metal  about  4  in  and  laid 
imder  all  flashing-metal  about  6  in. 

(3)  Laying  the  Tiles.  The  roof  having  thus  been  prepared,  the  tile-layer  is  to 
fasten  the  tiles  with  copper  nails.  The  roofer  is  to  see  that  the  tiles  are  well 
locked  together  and  that  they  lie  smoothly,  and  no  attempt  is  to  be  made  to 
stretch  the  courses.  The  tiles  are  to  be  laid  so  that  the  vertical  lines  are  parallel 
with  each  other  and  at  right-angles  to  the  eaves.  The  tiles  that  verge  along  the 
hips  are  to  be  cut  close  against  the  hip-boards,  and  a  water-tight  joint  made  by 
cementing  cut  hip-tiles  to  the  hip-boards  with  elastic  cement.  Each  piece  of 
hip-roll  is  then  to  be  nailed  to  the  hip-board,  and  the  hip-rolls  are  to  be  cemented 
where  they  lap  each  other.  The  interior  spaces  of  hip-rolls  and  ridge-rolls  are 
not  to  be  filled  with  the  pointing-material. 

Cost  of  Roofing-Tiles.*  The  prices  of  tiles  vary  from  $7  to  $30  per  square, 
according  to  the  character  of  the  surface-finish  and  to  the  pattern.  The  cost 
of  laying,  including  asphalt-felt,  varies  from  $5  to  $10  per  square,  according  to 
the  pattern  of  tiles  used,  the  number  of  layers  of  felt  and  the  character  and 
extent  of  the  roof.  If  roofing-tiles  are  laid  on  book  tiles  or  on  cement,  20% 
must  be  added  to  the  cost  for  laying  on  wooden  sheathing.  Fluctuating  values 
of  copper  make  the  item  of  copper  nails,  when  these  are  used,  one  of  im- 
portance. 

Sheet-Metal  Tiles.  Roofing-tiles  stamped  from  sheet  steel,  plain  or  galvan- 
ized, and  also  from  sheet  copper,  in  imitation  of  clay  tiles,  are  made  by  several 
manufacturers  and  have  been  extensively  used  for  factories  and  buildings  of 
secondary  importance.  The  first  cost  of  these  tiles,  except  those  made  of 
copper,  is  much  less  than  that  of  clay  tiles  and  they  do  riot  require  as  heavy 
roof-framing.  Tin  or  galvanized-iron  tiles,  however,  niust  be  painted  every 
few  years,  so  that  for  a  long  period  of  years  they  probably  cost  as  niuch  as  clay 
tiles  and  more  than  slate. 

•  These  tirices  have  erdvailced  sad  the  ni&nxUUiiiievs'  lists  riiuit  bd  coiisuUed. 


158&  Memoranda  on  Roofing  Part  3 

Tin  Roofs 

The  Sheets.  Roofing-plates  are  made  of  soft  steel  of  various  special  analyses, 
or  wrought  iron  (more  commonly  of  the  former),  covered  with  a  mixture  of  lead 
and  tin,  and  are  designated  terne-plates,  in  distinction  from  plates  coated 
only  with  tin  and  therefore  called  bright  tin.  Roofing-plates  are  coated  by 
two  methods,  (i)  The  original  method  of  coating  the  plates  consisted  in  dip- 
ping the  black  plates  by  hand  Into  the  mixture  of  tin  and  lead,  and  allowing  the 
sheets  to  absorb  all  the  coating  that  was  possible;  and  at  least  one  brand  of 
.roofing-tin  is  still  made  by  this  process.  (2)  The  other  process,  by  which  the  ma- 
jority of  roofing-plates  are  now  made,  is  known  as  the  patent-roller-process, 
by  which  the  plates  are  put  into  a  bath  of  tin  and  lead,  and  are  passed  through 
rolls.  The  pressure  of  these  rolls  leaves  on  the  iron  or  steel  a  thickness  of  coating 
which,  to  a  great  extent,  determines  the  value  of  the  plates.  These  rolls  can  be 
adjusted  to  leave  a  relatively  large  amount  of  coating  on  the  plate,  an  ordinary 
coating,  or  a  very  scant  coating.  The  heavier  the  coating  the  more  valuable  the 
plate.  Some  makers  employ  a  variation  of  this  patent  process,  by  which  the 
plates  are  given  an  extra  dip,  by  hand,  in  an  open  pot,  to  give  a  hand-dipped 
FINISH.  It  is  claimed  that  hand-dipped  plates  will  last  much  longer  than  those 
made  by  the  new  process,  although  the  latter  process  is  much  more  extensively 
used  and  many  good  roofing-sheets  are  made  by  it. 

Brands.  The  best  roofing-plates  always  have  the  brand  stamped  on  them, 
and  as  the  manufacturers  have  a  pecuniary  interest  in  keeping  up  the  reputation 
of  these  brands,  the  only  way  of  being  sure  of  a  good  tin  roof  is  to  specify  a  brand 
of  tin  that  has  a  reputation  for  quality  and  durability.  Some  of  the  best-known 
brands  are  Taylor's  Target-and-Arrow  (formerly  Old  Style);  Merchant's  Old 
Method,  MF;  Follansbee's  Banfield  Process;  and  Margaret.  Machine-made 
plates  are  usually  stamped  with  the  weight  of  coating  per  box  of  112  sheets,  28 
by  20-in  size. 

Sizes  of  Sheets.  The  common  sizes  of  tin  plates  are  10  by  14  in  and  multiples 
of  that  measure.  The  sizes  generally  used  are  14  by  20  in  and  28  by  20  in.  The 
larger  size  is  the  more  economical  to  lay,  and  hence  roofers  prefer  to  use  it;  but 
for  flat  roofs  the  14  by  20-in  size  makes  the  better  roof. 

Thicknesses  of  Sheets.  Terne-plates  are  made  in  two  thicknesses,  IC,  in 
which  the  iron  body  weighs  about  50  lb  per  100  sq  ft,  and  IX,  in  which  it  weighs 
62^^  lb  per  100  sq  ft.  For  roofing,  the  IC,  or  lighter  weight,  is  to  be  preferred, 
because  the  seams  do  not  contract  and  expand  as  much  as  they  do  when  the 
thicker  plates  are  used.  For  spouts,  valleys  and  gutters,  however,  IX  plates 
should  always  be  specified,  and  should  preferably  be  used  for  flashings,  as  they 
are  stiffer  and  less  liable  to  be  dented  or  punched.  The  thickness  of  the  iron 
does  not  add  to  the  durability  of  the  plates,  as  this  depends  entirely  upon  the  tin 
coating. 

Weights  of  Sheets.  The  standard  weight  of  14  by  20-in  IC  terne-plates  is  107 
lb  for  112  sheets,  the  number  usually  packed  in  one  box,  and  of  14  by  20-in  IX 
sheets,  135  lb.  The  28  by  20-in  sheets  should  weigh  just  twice  as  much.  The 
black  sheets,  before  coating,  should  weigh,  per  112  sheets,  from  95  to  100  lb  for 
IC,  14  by  20-in  sheets,  and  from  125  to  130  lb  for  IX,  14  by  20-in  sheets.  The 
difference  between  the  weights  of  the  black  sheets  and  finished  sheets  is  the 
weight  of  the  tin.  A  heavily  coated  tin  should  weigh  from  115  to  120  lb  per  112 
sheets  for  IC,  14  by  20-in  sheets,  and  from  145  to  150  lb  for  IX,  14  by  20-in  sheets. 
The  28  by  20-in  sheets  should,  of  course,  weigh  twice  as  much. 

The  Roof.  Roofs  of  less  than  one-third  pitch  are  made  with  flat  seams  and 
should  preferably  be  covered  with  14  by  20-in  sheets  rather  than  with  28  by  20-in 


Tin  Roofs  1589 

sheets,  because  the  larger  number  of  seams  stiffens  the  surface  and  helps  to  pre- 
vent buckles  and  rattling  in  stormy  weather.  For  a  flat-scam  roof,  the  edges  of 
the  sheets  are  turned  y2  in,  locked  together  and  well  soaked  with  solder.  The 
sheets  are  fastened  to  the  sheathing-boards  by  cleats  spaced  8  in  apart  and  locked 
in]the  seams.  Two  i-in  barbed  and  tinned-wire  nails  are  used  in  each  cleat.  No 
nails  should  be  driven  through  the  sheets.  The  seams  must  be  made  with  great 
care  and  sufficient  time  taken  to  properly  sweat  the  solder  into  the  seams.  Steep 
tin  roofs  should  be  made  with  standing  seams  and  with  28  by  20-in  sheets. 
The  sheets  are  first  single-seamed  or  double-seamed  and  usually  soldered  to- 
gether, preferably  end  to  end,  into  long  strips  that  reach  from  eaves  to  ridge. 
The  sloping  seams  are  composed  of  two  upstands,  interlocked  at  the  upper  edge, 
and  held  to  the  sheathing-boards  by  cleats.  The  standing  seams  are  usually  not 
soldered  but  simply  locked  together  with  the  cleats  folded  in  about  i  ft  apart. 
Nails  should  be  driven  into  the  cleats  only.  The  use  of  acid  in  soldering  the 
seams  of  a  tin  roof  should  be  carefully  avoided  as  acid  coming  in  contact  with  the 
bare  iron  on  the  cut  edges  and  corners,  where  the  sheets  are  folded  and  seamed 
together,  causes  rusting.  No  other  soldering-flux  but  good  rosin  should  ever  be 
used. 

Durability  of  Tin  Roofs.  A  tin  roof  of  good  material,  properly  put  on,  and 
kept  properly  painted,  will  last  from  forty  to  fifty  years,  or  longer.  All  traces 
of  rosin  left  on  the  roof  should  be  removed  as  soon  as  the  tin  is  laid  and  soldered, 
and  one  coat  of  paint  should  be  applied  promptly;  a  second  coat  should  follow 
two  weeks  after  the  first.  One  or  more  layers  of  felt  or  water-proof  paper  should 
be  placed  under  the  tin,  to  serve  as  a  cushion,  and  also  to  deaden  the  noise  pro- 
duced by  rain  striking  the  tin.  The  durability  of  tin  roofing,  and  especially  of 
tin  gutters,  valleys  and  flashings,  is  generally  increased  by  painting  the  tin  on 
the  back  before  laying.  An  excellent  paint  for  tin  roofs  is  composed  of  10  lb  of 
Venetian  red,  i  lb  of  red  lead  and  i  gal  of  pure  Unseed-oil. 

Maintenance  of  Tin  Roofs.  The  tin  roof  should  be  given  one  coat  of  paint 
after  it  is  laid  and  an  additional  coat  of  paint  at  four-year  or  five-year  intervals 
should  be  amply  sufficient  to  keep  its  upper  surface  in  first-class  condition  as 
long  as  the  building  stands.  With  each  painting  the  roof  is  fully  restored  to  its 
original  condition.  Graphite  and  tar  paints  should  be  avoided  on  tin  roofs. 
Metallic  brown,  Venetian  red,  red  oxide  or  red  lead,  only,  should  be  used  as 
pigments,  with  pure  linseed-oil.  Tinned  gutters  should  be  swept  clear  of  accu- 
mulations of  leaves,  dirt,  etc.,  and  if  water  has  a  tendency  to  lie  in  the  gutters 
they  should  be  painted  yearly. 

Number  of  Sheets  Required  to  a  Square.  For  flat-seam  roofing  a  sheet  of 
tin  14  by  20  in,  with  H-in  edges,  measures,  when  edged  or  folded,  13  by  19  in, 
or  247  sq  in;  but  its  covering  capacity  when  joined  to  other  sheets  on  the  roof  is 
only  12H  by  i8J^  in,  or  231.25  sq  in.  The  number  of  sheets  to  a  square,  there- 
fore, equals  14  400  divided  by  231.25  or  63,  and  an  area  of  i  000  sq  ft  requires  625 
sheets.  A  box  of  112  14  by  2c5-in  sheets  will  cover,  approximately,  180  sq  ft. 
Sheets  28  by  20  in,  when  edged  or  folded,  have  a  covering  capacity  of  490.25  sq  in, 
each.  To  cover  i  000  sq  ft  (10  squares)  requires  294  sheets.  For  standing- 
seam  roofing  the  locks  require  2^4  in  off  the  width  and  ij^  in  off  the  length  of 
the  sheet.  A  28  by  20-in  sheet,  with  the  seams  on  the  long  edges,  will  cover  463 
sq  in.     To  cover  i  000  sq  ft  requires  312  sheets. 

The   Cost*  of  Tin  Roofing  varies  from  $8  to  $12  per  square,  according  to  the 

grade  of  the  tin,  the  locality  and  nature  of  the  work  and  the  scale  of  wages. 

Standing-seam  roofs  cost  about  50  cts  a  square  less  than  flat-seam  roofs.     The 

cost,  when  14  by  20-in  sheets  are  used,  is  about  25%  more  than  for  28  by  20-in 

*  Variations  in  cost  must  be  ascertained  from  manufacturers'  lists. 


1590  Memoranda  on  Roofing  Part  3 

sheets,  owing  to  the  greater  number  of  seams;   hence,  more  tin,  solder,  cleats 
and  work  are  required. 

How  a  Tin  Roof  Should  he  Laid* 

The  Slope  of  the  Roof.  If  the  tin  is  laid  with  a  flat  seam  or  flat  lock,  the  roof 
should  have  an  incline  of  ^  in  or  more  to  i  ft.  If  laid  with  a  standing  seam,  there 
should  be  an  incline  of  not  less  than  2  in  to  i  ft.  Although  tin  is  used  on  roofs  of 
less  pitch  than  this  and  on  some  which  are  almost  flat,  a  good  pitch  is  desirable 
to  prevent  the  accumulation  of  water  and  dirt  in  shallow  puddles.  Gutters,  • 
valleys,  etc.,  should  have  sufficient  incline  to  prevent  water  from  standing  in 
them  or  backing  up  far  enough  to  reach  standing  seams.  Tongued  and  grooved 
sheathing-boards  of  well-seasoned  dry  lumber  are  recommended.  Narrow 
widths  are  preferable,  and  the  boards  should  be  free  from  holes,  and  of  even  thick- 
ness. A  new  tin  roof  should  never  be  laid  over  old  tin,  rotten  shingles,  or  tar 
roofs.  Sheathing-paper  is  not  necessary  where  the  boards  are  laid  as  specified 
above.  If  steam,  fumes,  or  gases  are  likely  to  reach  the  under  side  of  the  tin, 
some  good  water-proof  sheathing-paper,  such  as  black  Neponset  paper,  should  be 
used.  Tarred  paper  should  never  be  used.  No  nails  should  be  driven  through 
the  sheets. 

Flat-Seam  Tin  Roofing.  When  the  sheets  are  laid  singly,  they  should  be 
fastened  to  the  sheathing-boards  by  cleats,  using  three  to  each  sheet,  two  on  the 
long  side  and  one  on  the  short  side.  Two  i-in  barbed-wire  nails  should  be  used 
to  each  cleat.  If  the  tin  is  put  on  in  rolls  the  sheets  should  be  made  up  into  long 
lengths  in  the  shop,  and  the  cross-seams  locked  together  and  well  soaked  with 
solder.  They  should  be  edged  yi  in,  and  fastened  to  the  roof  with  cleats  spaced 
8  in  apart,  and  the  cleats  locked  into  the  seam  and  fastened  to  the  roof  with  two 
I -in  barbed-wire  nails  to  each  cleat. 

Standing-Seam  Tin  Roofing.  The  sheets  should  be  put  together  in  long 
lengths  in  the  shop,  and  the  cross-seams  locked  together  and  well  soaked  with 
solder.  They  should  be  applied  to  the  roof  the  narrow  way,  and  fastened  with 
cleats  spaced  i  ft  apart.  One  edge  of  the  course  is  turned  up  i  H  in  at  a  right 
angle,  and  the  cleats  are  installed.  The  adjoining  edge  of  the  next  course  is 
turned  up  i  Vi  in,  and  these  edges  are  locked,  turned  over  and  the  scam  flattened 
to  a  rounded  edge. 

Valleys  and  Gutters.  These  should  be  lined  with  IX  tin,  and  formed  with 
flat  seams,  the  sheets  being  applied  the  narrow  way.  It  is  important  to  see  that 
good  solder,  bearing  the  manufacturer's  name,  is  used,  that  it  is  guaranteed  one- 
half  tin  and  one-half  lead,  new  metals,  and  that  nothing  but  rosin  is  used  as  a 
flux.    The  solder  should  be  well  sweated  into  all  seams  and  joints. 

Painting.  All  painting  should  be  done  by  the  roofer.  The  tin  should  be 
painted  one  coat  on  the  under  side  before  it  is  applied  to  the  roof.  The  upper 
surface  of  the  tin  roof  should  be  carefully  cleanecf  of  all  rosin-spots,  dirt,  etc.,  and 
immediately  painted.  The  approved  paints  are  metallic  brown,  Venetian  red, 
red  oxide,  arid  red  lead,  mixed  with  pure  linseed-oil.  No  patent  drier  or  tur- 
pentine should  be  used.  All  coats  of  paint  should  be  applied  with  a  hand-brush, 
and  well  rubbed  on.  A  second  coat  should  be  applied  two  weeks  after  the  first 
and  a  third  coat  one  year  later. 

Caution.  No  unnecessary  walking  over  the  tin  roof,  or  use  of  it  for  storage  of 
materials,  should  be  allowed  at  any  time.     Workmen  should  wear  rubber-soled 

*  These  suggestions  are  in  accordance  with  the  standard  working  specifications  adopted 
by  the  National  Association  of  Sheet  Metal  Contractors. 


Covering  Capacity  of  Roofing-Tin 


1501 


shoes  or  overshoes  when  on  the  roof.     Wherever  the  slope  is  steep  enough  the  tin 
should  be  laid  with  standing  seams,  which  allow  for  expansion  and  contraction. 

Sizes,  Weights,  Etc.,  of  Roofing-Tin  * 

Roofing-tin  is  usually  furnished  in  two  sizes,  sheets  14  by  20  in  and  28  by  20  in, 
packed  112  sheets  to  the  box.  Target-and- Arrow  tia  is  furnished  in  three  thick- 
nesses: IC  thickness,  approximately  No.  30  gauge,  U.  S.  Standard;  IX  thickness, 
approximately  No.  28  gauge,  U.  S.  Standard;  2X  thickness,  approximately  No. 
27  gauge,  U.  S.  Standard,  etc.  Weight  per  100  sq  ft  laid  on  the  roof,  about  65  lb 
for  IC  thickness. 

Covering  Capacity  of  Roofing-Tin 

Flat-Seam  Tin  Roofing.  The  following  table  shows  the  quantity  of  14  by  20-in 
tin  required  to  cover  a  given  number  of  square  feet  with  flat-seam  tin  roofing.  A 
sheet  14  by  20  in  with  y2  in  edges  measures,  when  edged  or  folded,  13  by  19, 
or  247  sq  in,  but  its  covering  capacity  when  joined  to  other  sheets  on  the  roof 
is  only  i2i/i  by  18H  in,  or  231.25  sq  in.  In  the  following  table  each  fractional 
part  of  a  sheet  is  counted  a  full  sheet'. 


No.  of  square  feet . 
Sheets  required . . . 

100 
63 

no 
69 

120 
75 

130 

140 

150 

160 

170 
106 

180 
112 

190 
119 

200 
125 

81 

88 

94 

100 

No.  of  square  feet. 
Sheets  required . . . 

210 
131 

220 
137 

230 
144 

240 
150 

250 
156 

260 
162 

270 
169 

280 
175 

290 
i8i 

300 
187 

310 
193 

No.  of  square  feet. 
Sheets  required . .  . 

320 

200 

330 
206 

340 
212 

350 
218 

360 
224 

370 
231 

380 
237 

390 
243 

400 
249 

410 
256 

420 
262 

No.  of  square  feet . 
Sheets  required .  .  . 

430 
268 

440 
274 

4SO 
281 

460 
287 

470 
293 

480 
299 

490 
305 

500 
312 

510 
318 

520 
324 

630 
393 

530 
330 

640 
399 

No.  of  square  feet . 
Sheets  required . . . 

540 
337 

550 
343 

560 
349 

570 
355 

580 
362 

590 
368 

600 

610 
380 

620 
386 

No.  of  square  feet . 
Sheets  required .  .  . 

650 
405 

660 
411 

670 
418 

680 
424 

690 
430 

700 
436 

710 
442 

720 
448 

730 
455 

740 
461 

750 
467 

No.  of  square  feet . 
Sheets  retiuired .  . . 

760 

474 

770 
480 

780 
486 

790 
492 

800 
499 

810 
50s 

820 
511 

830 
517 

840 
523 

850 
530 

860 
536 

No.  of  square  feet . 
Sheets  required .  . . 

870 
542 

880 
548 

890 
554 

900 
561 

910 
567 

920 
573 

930 

579 

940 
586 

950 
592 

960 
598 

970 
604 

No.  of  square  feet . 
Sheets  required . .  . 

980 
610 

990 
617 

1000 
625 

A  box  of  112  sheets  14  by  20  in  laid  in  this  way  will  cover  180  sq  ft. 

Flat-Seam  Tin  Roofing.  The  following  table  shows  the  number  of  28  by  20-in 
sheets  required  to  cover  a  given  number  of  square  feet  with  flat-seam  tin  roofing. 
The  flat  seams  edged  V'  in  take  iH  in  off  the  length  and  width  of  the  sheet.  The 
covering  capacity  of  each  sheet  is,  therefore,  26y2  by  18^2  in,  or  490.25  sq  in.  In 
the  following  table  each  fractional  part  of  a  sheet  is  counted  a  full  sheet. 

■  •  The  following  tables  of  sizes,  weights,  covering  capacities  and  costs  are  adapted  from 
useful  data  compiled  for  the  use  of  sheet-metal  workers  by  th«  N.  &  G.  Taylor  Company, 
Philadelphia,  Pa. 


1592 


Memoranda  on  Roofing 


Part  3 


No.  of  square  feet . 
Sheets  required .  .  . 

lOO 

30 

110 
33 

120 
36 

130 
39 

140 
42 

150 
45 

160 
47 

170 

50 

180 
53 

190 
56 

200 
59 

No.  of  square  feet. 
Sheets  required .  .  . 

210 
62 

220 
65 

230 
68 

240 
71 

250 
74. 

260 

77 

270 
80 

280 

83 

290 
86 

300 
89 

310 
92 

No.  of  square  feet . 
Sheets  required .  . . 

320 
94 

330 
97 

340 
100 

350 
103 

360 
106 

370 
109 

380 
112 

390 

115 

400 
118 

410 
121 

420 
124 

No.  of  square  feet. 
Sheets  required .  .  . 

430. 
127 

440 
130 

133 

460 
136 

470 
139 

480 
141 

490 
144 

500. 
147 

510 
ISO 

520 
153 

530 
156 

No.  of  square  feet. 
Sheets  required .  . . 

540 
159 

550 
162 

560 
165 

570 
168 

580 
171 

590 
174 

600 
177 

610 

180 

620 

183 

630 

186 

640 
188 

No.  of  square  feet . 
Sheets  required . . . 

650 
191 

660 
194 

670 
197 

680 
200 

690 
203 

700 
206 

7T0 

209 

720 
212 

730 
215 

740 
218 

750 
221 

No.  of  square  feet . 
Sheets  required .  .  . 

760 
224 

770 
227 

780 
230 

790 
233 

800 
235 

8to 
238 

820 
241 

830 
244 

840 
247 

850 
250 

86c 
253 

No.  of  square  feet. 
Sheets  required .  .  . 

870 
256 

880 
259 

890 
262 

qoo 
265 

910 
268 

920 
271 

930 
274 

940 
277 

950 
280 

960 
282 

970 
285 

No.  of  square  feet . 
Sheets  required . .  . 

980 
288 

990 

291 

1000 
294 

A  box  of  112  sheets  28  by  20  in  laid  in  this  way  will  cover  381  sq  ft. 

Standing-Seam  Tin  Roofing.  The  following  table  shows  the  number  of  14  by 
20-in  sheets  required  to  cover  a  given  number  of  square  feet  with  standing-seam 
roofing.  The  standing  seams,  edged  iH  and  i^/i  in,  take  2%  in  off  the  width; 
and  the  flat  cross-seams,  edged  %  in,  take  i  \i  in  off  the  length  of  the  sheet.  The 
covering  capacity  of  each  sheet  is,  therefore,  iiH  by  18^6  in,  or  212.34  sq  in.  In 
the  following  table  each  fractional  part  of  a  sheet  is  counted  a  full  sheet. 


No.  of  square  feet. 
Sheets  required . .  . 

100 
68 

no 
75 

120 
82 

130 
89 

140 

95 

150 
102 

160 
109 

170 
116 

180 
123 

190 
129 

200 
136 

No.  of  square  feet. 
Sheets  required .  .  . 

210 
143 

220 
150 

230 
156 

240 
163 

250 
170 

260 
177 

270 
184 

280 
190 

290 
197 

300 
204 

310 
211 

No.  of  square  feet . 
Sheets  required .  .  . 

320 
218 

330 
224 

340 
231 

350 
238 

360 

245 

370 
251 

380 
258 

390 
265 

400 
271 

410 
•279 

420 
285 

No.  of  square  feet . 
Sheets  required .  .  , 

430 
292 

440 
299 

450 
306 

460 
312 

470 
319 

480 
326» 

490 
333 

Soo 
340 

510 
346 

520 
353 

530 
360 

No.  of  square  feet. 
Sheets  required . .  . 

540 
367 

550 
374 

560 
379 

570 
387 

580 
393 

590 

401 

600 

407 

610 
414 

620 
421 

630 
428 

640 
435 

No.  of  square  feet. 
Sheets  required .  .  . 

650 
441 

660 

447 

670 
455 

680 
462 

600 
468 

700 
475 

710 
482 

720 
489 

730 
495 

740 
501 

750 
509 

No.  of  square  feet. 
Sheets  required . . . 

760 
515 

770 
523 

780 
529 

790 
536 

800 
543 

810 
550 

820 
557 

830 
563 

840 
570 

850 
577 

860 
584 

No.  of  square  feet. 
Sheets  required .  . , 

870 
590 

880 
597 

890 
604 

QOO 
611 

910 
618 

920 
623 

930 
630 

940 
637 

950 
644 

960 
651 

970 
658 

No.  of  square  feet. 
Sheets  required . . . 

980 
66s 

990 
672 

1000 
679 

... 

... 
... 

A  box  of  112  sheets  14  by  20  in  laid  in  this  way  will  cover  165  sq  ft. 


Covering  Capacity  of  Roofing-Tin 


1593 


Standing-Seam  Tin  Roofing.  The  following  table  shows  the  number  of  28  by 
20-in  sheets  required  to  cover  a  given  number  of  square  feet  with  standing-seam 
roofing.  The  standing  seams  take  2%  in  off  the  width,  and  the  flat  cross-seams, 
edged  Vs  in,  take  iH  in  off  the  length  of  the  sheet.  The  covering  capacity  of 
each  sheet  is,  therefore,  26%  by  17 H  in,  or  463.59  sq  in.  In  the  following  table 
each  fractional  part  of  a  sheet  is  counted  a  full  sheet. 


No.  of  square  feet . 
Sheets  required .  .  . 

100 
32 

lie 
35 

120 
38 

130 
41 

140 
44 

ISO 
47 

160 
50 

170 
53 

180 
56 

190 
59 

200 
62 

No.  of  square  feet. 
Sheets  required . .  . 

210 
65 

220 
68 

230 
71 

240 
74 

250 

77 

260 
80 

270 
84 

280 
87 

290 
90 

300 
94 

310 

97 

No.  of  square  feet . 
Sheets  required .  .  . 

320 
100 

330 
103 

340 
106 

350 
109 

360 
112 

370 
115 

380 
118 

390 
121 

400 
125 

410 
128 

420 
131 

No.  of  square  feet. 
Sheets  required .  . . 

430 
134 

440 
137 

450 
141 

460 
144 

470 
147 

480 
150 

490 
153 

500 
156 

510 
159 

520 
162 

530 
165 

No.  of  square  feet. 
Sheets  required .  . . 

540 
168 

550 
171 

S6o 
174 

570 
177 

580 
180 

590 
184 

600 
187 

610 
190 

620 
193 

630 
196 

640 
199 

No.  of  square  feet. 
Sheets  required .  .  . 

650 

202 

660 
205 

670 
208 

680 
211 

690 
214 

700 
218 

710 
221 

720 
224 

730 
227 

740 
230 

750 
233 

No.  of  square  feet. 
Sheets  required .  .  . 

760 
236 

770 
239 

780 
242 

790 
245 

800 
249 

810 
252 

820 
255 

830 
258 

840 
261 

85c 
265 

860 
268 

No.  of  square  feet. 
Sheets  required .  .  . 

870 
271 

880 
274 

890 
277 

900 
280 

910 
283 

920 
286 

930 
289 

940 
292 

950 
296 

960 
299 

970 
302 

No.  of  square  feet. 
Sheets  required .  .  . 

980 
305 

990 
308 

... 

A  box  of  112  sheets  28  by  20  in  laid  in  this  way  will  cover  360  sq  ft. 

Laying  'the  Long  or  Short  Way.  Sheets  14  by  20  in  can  be  laid  either  the 
long  or  short  way.  The  best  roof  is  made  by  laying  the  sheets  the  14-in  way; 
similarly,  in  using  the  28  by  20-in  sheets,  they  should  always  be  laid  the  20-in 
way,  that  is,  with  the  short  dimension  crosswise. 

Cost  of  Roofing-Tin 
Cost  of  Tin  for*  Standing-Seam  Roofing 

Sheets  28  by  20  in.     Price  per  box  and  per  square  foot 


When  tin  costs 

■- 

per  box 

$11.00 

$11.50 

$12.00 

$12.50 

$13.00 

$13.50 

$14.00 

$14-50 

$15.00 

$15.50 

Standing-seam 
roofing  costs 
per  sq  ft 

0.0297 

0.0310 

0.0324 

0.0337 

0.0351 

0.0364 

0.0378 

0.0391 

0.0404 

0.0418 

When  tin  costs 

per  box.... .. 

16.00 

16.50 

17.00 

17.50 

18.00 

18.50 

19.00 

19.50 

20.00 

20 .  50 

Standing-seam 
roofing  costs 
per  sq  f t 

0.0432 

0.0446 

0.0459 

0.0473 

0.0486 

0.0500 

0.0513 

0.0526 

0.0540 

0.0553 

When  tin  costs 

per  box 

21.00 

21.50 

22.00 

22.50 

23.00 

23.50 

24.00 

24 -50 

25.00 

Standing-seam 
roofing  costs 
per  sq  ft 

0.0567 

0.0580 

0.0594 

0.0607 

0.0621 

0.0634 

0.0648 

0.0661 

0.0675 

The  above  estimates  do  not  include  cost  of  laying.  The  cost,  using  14  by  20-in  sheets, 
will  amount  to  about  25%  more  than  the  cost,  using  28  by  20-in  sheets,  owing  to  the 
greater  number  of  seams.     More  tin,  solder,  cleats  and  work  are  therefore  necessary. 


1594 


Memoranda  on  Roofing 


Tin  in  Rolls,  or  Gutter-Strips 

Number  of  sheets  required  per  linear  foot  for  20  and  28-in  widths 


Widths 

Widths 

Widths 

Hun- 

Widths 

Feet 

Feet 

Feet 

dred 

20 

28 

20 

28 

20 

28 

feet 

20 

28 

I 

I 

I 

3S 

If) 

23 

69 

31 

44 

2 

89 

128 

2 

I 

2 

36 

16 

23 

70 

32 

45 

3 

134 

192 

3 

2 

2 

37 

17 

24 

71 

32 

45 

4 

178 

256 

4 

2 

3 

38 

17 

24 

72 

32 

46 

5 

223 

320 

5 

3 

4 

39 

18 

25 

73 

33 

47 

6 

267 

384 

6 

3 

4 

40 

18 

26 

74 

33 

47 

7 

3T2 

444 

7 

4 

5 

41 

19 

27 

75 

34 

48 

8 

356 

512 

8 

4 

s 

42 

19 

27 

76 

34 

48 

9 

401 

576 

9 

4 

6 

43 

20 

28 

77 

35 

49 

10 

445 

64c 

10 

5 

7 

4; 

20 

28 

78 

35 

50 

II 

495 

704 

II 

5 

7 

4S 

20 

29 

79 

36 

SO 

12 

540 

768 

12 

6 

8 

46 

21 

2J 

80 

36 

SI 

13 

585 

832 

13 

6 

9 

47 

21 

30 

81 

36 

52 

14 

630 

896 

14 

7 

9 

48 

22 

31 

82 

37 

52 

15 

675 

060 

IS 

7 

10 

49 

22 

31 

83 

37 

53 

16 

720 

I  024 

16 

8 

II 

SO 

23 

32 

84 

38 

54 

17 

765 

I  088 

17 

8 

n 

SI 

23 

33 

85 

38 

54 

18 

810 

I  152 

18 

8 

12 

S2 

24 

33 

86 

39 

55 

19 

855 

I  216 

19 

9 

12 

S3 

24 

34 

87 

39 

55 

20 

900 

I  280 

20 

9 

13 

S4 

24 

34 

83 

40 

56 

21 

945 

1344 

21 
22 

10 
10 

14 
14 

ss 

25 

35 
36 

89 
90 

40 
40 

57 
57 

22 
23 

990 
1035 

1408 
I  472 

S6 

25 

23 

II 

IS 

S7 

25 

36 

91 

41 

58 

24 

I  oSo 

1536 

24 

II 

16 

S8 

26 

37 

92 

41 

59 

25 

1^35 

I  Geo 

25 

12 

16 

S9 

27 

33 

93 

42 

59 

26 

I  170 

1664 

26 

12 

17 

60 

27 

38 

94 

42 

60 

27 

I  215 

1738 

27 

12 

18 

61 

28 

39 

95 

43 

(n 

28 

1  2G0 

I  792 

2i 

13 

18 

62 

28 

40 

96 

43 

62 

29 

I  305 

1856 

29 

13 

19 

63 

28 

40 

97 

44 

62 

30 

I  350 

I  920 

30 

14 

19 

64 

29 

41 

98 

44 

63 

31 

I  395 

1984 

31 

14 

20 

65 

29 

41 

99 

44 

64 

32 

I  440 

2048 

32 

IS 

21 

66 

30 

42 

100 

45 

64 

33 

T  485 

2  112 

33 

IS 

21 

67 

30 

43 

34 

I  530 

2176 

34 

16 

22 

68 

31 

43 

35 

I  575 

2  240 

Cost  of  Tin  in  Rolls  or  Gutter-Strips 
Labor,  solder,  paint,  rosin  and  other  materials  not  included 
A  box  of  112  sheets  in  28-in  roll  will  cover  175  lin  ft 
A  box  of  112  sheets  in  20-in  roll  will  cover  248  lin  ft 
A  box  of  112  sheets  in  14-in  roll  will  over  350  lin  ft 
A  box  of  112  sheets  in  lo-in  roll  will  cover  496  Hn  ft 


Cost  per  box  (28  by  20  in) 

Cost  per  linear  foot,  28  in  wide. 
Cost  per  linear  foot,  20  in  wide. 


$10  00 
0.05714 
o . 04032 


$II.Od|    $12.00 

0.052^5,0.  o53-;6 
0.0443510.04838 


$13  00 
0.07426 
0.05241 


$14.00 
o . 07998 
0.05644 


Cost  per  box  (28  by  20  in) 

Cost  per  linear  foot,  28  in  wide, . ; . 
Cost  per  linear  foot,  20  in  wide. , , . 


$16  00 
0.09149 
d. 06450 


$17.00 
O.C17II 


Si8,oo 
0.10282 
d.^7256 


$19.00 
0.10853 
0.07659 


$20.00 
0.11424 
,©.68062 


Slag  and  Gravel  Roofing  1595 

Tin  in  Rolls.  For  the  convenience  of  roofers  and  for  rush-orders,  Target-and- 
Arrow  tin  is  put  up  in  rolls  14,  20  and  28  in  wide.  Each  roll  contains  108  sq  ft; 
(al^out  63  lin  ft,  28  by  20-in  sheets  laid  20  in  wide).  The  tin  is  painted  on  one 
or  both  sides,  as  wanted,  with  an  approved  metallic  brown  paint.  The  seams 
arc  carefully  soldered  by  hand,  good  100  to  100  solder  and  rosin  being  used  as 
a  tlux.       ^9|HH| 

'■^if^sm^  Slag  or  Gravel  Roofing 

The  Ordinary  Gravel  Roofing  over  boards  is  formed  by  first  covering  the 
surface  of  the  roof  with  dry  felt  (paper)  and  over  this  laying  three,  four,  or  five 
Jayers  of  tarred  or  asphaltic  felt  lapping  each  other  like  shingles,  so  that  only 
from  6  to  10  in  of  each  layer  are  exposed.  In  laying  roofs  over  concrete  the  dry 
felt  is  omitted,  a  mopping  of  pitch  is  placed  directly  on  the  concrete  and  the  first 
layer  of  the  felt  embedded  in  it. 

Flashing  against  walls,  chimneys,  curbs  of  skylights,  etc.,  is  done  by  turning 
the  felt  up  6  in  against  the  walls.  Over  this  is  laid  an  8-in  strip  with  half  its 
width  on  the  roof.  The  upper  edge  of  the  strip  and  of  the  several  layers  of  felt  is 
then  fastened  to  the  walls  by  nailing  wooden  strips  or  laths  over  the  felt  and  into 
the  walls.  Metal  flashings  to  protect  the  felt  are  better  than  the  wooden  stiipg 
and  should  be  used  when  possible.  At  the  eaves  and  on  all  exposed  edges, 
metal  gravel-stops  should  be  used. 

A  Better  Method  of  Slag  or  Gravel  Roofing  is  to  lay  two  plies  of  tarred  felt, 
lapping  each  other  17  in,  and  then  spreading  a  coat  of  pitch  over  the  entire  roof 4 
On  this  again  three  more  layers  of  felt  are  laid  and  then  coated  with  pitch,  into 
which  the  crushed  slag  or  screened  gravel  is  embedded. 

Specifications  for  Pitch-Slag  or  Gravel  Roofing.  The  following  specific 
cation-notes  *  describe  the  latter  method  more  in  detail  and  also  the  material^ 
that  should  be  used  to  secure  a  first-class  job.  These  roofs  are  most  efficient  and 
durable  on  comparatively  flat  inclines.  The  usual  built-up  roof  consists  of  suc- 
cessive layers  of  saturated  felt  cemented  together  and  surfaced  with  coal-tar 
pitch  or  asphalt,  into  which  is  embedded  the  gravel  or  slag.  Tile  is  also  used  as  a 
surfacing  material.  The  saturants  used  in  the  felt  are  generally  coal-tar  or 
asphalt-compounds. 

(i)  Specification  for  Pitch-Slag  or  Pitch-Gravel  Roofing  Over  Wooden 
Sheathing 

This  specification  should  not  be  used  when  the  roof-incline  exceeds  3  in  to  i  ft. 

Lay  one  thickness  of  sheathing-paper  or  unsaturated  felt  weighing  not  less 
than  5  lb  per  100  sq  ft,  lapping  the  sheets  at  least  i  in. 

Over  the  entire  surface  lay  two  plies  t  of  tarred  felt,  lapping  each  sheet  17  in 
over  the  preceding  one,  and  nail  as  often  as  is  necessary  to  hold  them  in  place 
until  the  remaining  felt  is  laid. 

Coat  the  entire  surface  uniformly  with  pitch. 

*  Condensed  and  adapted  from  specifications  published  by  the  Barrett  Manufacturing 
Company  and  known,  in  their  full  form,  as  "The  Barrett  Specifications,"  They  can  be 
obtained  from  the  manufacturers. 

t  In  the  Western  States  the  number  of  "plies"  is  construed  to  mean  the  total  num- 
ber of  layers,  including  dry  as  well  as  saturated  felt,  and  the  terms  3-ply,  S-ply,  etc.,  are 
hereinafter  used  on  that  basis.  In  the  Eastern  States,  3-ply,  5-ply,  etc.,  usually  refers 
to  the  number  of  layers  of  saturated  left;  The  total  number  of  layers  should  always  be 
specified  if  there  ia  any  doubt  as  .to  the  exact  meaning  of  the  term  as  used,  in  the  speci- 
ficatigns,     '"'  ^^^'^  tiOJuj  iu  iitnit^uj  mioiiau  >■  ]  13V0  bfiSiq  :        * 


1596 


Memoranda  on  Roofing 


Part  3 


Over  the  entire  surface  lay  three  plies  of  tarred  felt,  lapping  each  sheet  22  in 
over  the  preceding  one  and  mopping  with  pitch  the  full  22  in  on  each  sheet,  so 
that  in  no  place  felt  touches  felt.  Do  such  nailing  as  is  necessary  so  that  all  nails 
are  covered  by  not  less  than  two  plies  of  felt. 


Diagram  of   Gravel  or    Slag   Roofing   on 
Wooden  Sheathing 


Diagram  of   Gravel  or  Slag  Roofing  on 
Concrete  Base 


Spread  over  the  entire  surface  a  uniform  coating  of  pitch,  into  which,  while 
hot,  embed  not  less  than  400  lb  of  gravel  or  300  lb  of  slag  to  each  100  sq  ft.  The 
grains  of  the  gravel  or  slag  are  to  be  from  H  to  H  in  in  size,  and  dry  and  free  from 
dirt. 

The  roof  may  be  inspected  before  the  gravel  or  slag  is  applied,  by  cutting  a  slit 
not  less  than  3  ft  long  at  right-angles  to  the  direction  in  which  the  felt  is  laid. 
All  felt  and  pitch  is  to  bear  the  manufacturer's  label. 

(2)  Specification  for  Pitch-Slag  or  Pitch-Gravel  for  Roofing  over  Concrete 

This  specification  should  not  be  used  when  the  roof-incline  exceeds  3  in  to  the 
foot.  When  the  incline  exceeds  i  in  to  i  ft  the  concrete  must  permit  of  nailing  or 
nailing-strips  must  be  provided. 

Coat  the  concrete  uniformly  with  hot  pitch. 

Over  the  entire  surface  lay  two  plies  of  tarred  felt,  lapping  each  sheet  17  in 
over  the  preceding  one,  mopping  with  pitch  the  full  17  in  on  each  sheet,  so  that 
in  no  place  felt  touches  felt. 

Coat  the  entire  surface  uniformly  with  pitch. 

Over  the  entire  surface  lay  three  plies  of  tarred  felt,  lapping  each  sheet  22  in 
over  the  preceding  one  and  mopping  with  pitch  the  full  22  in  on  each  sheet,  so 
that  in  no  place  felt  touches  felt. 

Spread  over  the  entire  surface  a  uniform  coating  of  pitch,  into  which,  while 


Slag  and  Gravel  Roofing 


1597 


hot,  embed  not  less  than  400  lb  of  gravel  or  300  lb  of  slag  to  each  100  sq  ft.  The 
grains  of  the  gravel  or  slag  are  to  be  from  \i  to  H  in  in  size,  and  dry  and  free  from 
dirt. 

The  roof  may  be  inspected  before  the  gravel  or  slag  is  applied,  by  cutting  a  slit 
not  less  than  3  ft  long  at  right-angles  to  the  direction  in  which  the  felt  is  laid. 
All  felt  and  pitch  is  to  bear  the  manufacturer's  label. 

Notes  on  Slag  and  Gravel  Roofing.  The  difference  between  slag  and  gravel 
roofing  is  that  for  the  former  crushed  slag  is  used  instead  of  gravel.  The  greater 
the  number  of  plies  of  tarred  felt,  the  greater  the  amount  of  pitch  that  it  is  prac- 
tical to  use,  and  it  is  the  pitch  that  gives  life  to  the  roof.  As  there  are  several 
different  weights  and  qualities  of  tarred  felt,  a  specification  should  state  either 
the  minimum  weight  per  100  sq  ft,  single  thickness  (the  most  practical  weight  is 
from  14  to  16  lb),  or  some  known  quality,  such  as  Barrett's  "  Specification  Tarred 
Felt."  Felt  weighing  less  than  12  lb  per  100  sq  ft  is  not  economical  even  on  the 
cheaper  work.  To  comply  with  the  Barrett  specification  the  materials  neces- 
sary for  each  100  sq  ft  of  completed  roof  are  approximately  as  follows: 


Over  boards 


Material 


Over  concrete 


108  sq  ft 
80  to    8s  lb 
120  to  i6o  lb 
400  lb 
300  lb 


Sheathing-paper 

Specification  tarred  felt 

Specification-pitch 

Gravel 

Slag 


None 

80  to    8s  lb 
180  to  225  lb 
400  lb 
300  lb 


In  estimating  felt,  the  average  weight  is  practically  15  lb  per  100  sq  ft,  single 
thickness,  and  about  10%  additional  is  required  for  laps.  In  estimating  pitch 
the  weather-conditions  and  expertness  of  the  workmen  will  affect  the  amount 
necessary  for  the  moppings  and  for  a  proper  embedding  of  the  gravel  or  slag.  As 
there  are  several  qualities  of  pitch,  a  specification  should  either  specify  it  by 
name,  such  as  "Specification-Pitch"  or  "Straight-Run  Coal-Tar  Pitch,"  or  in 
specifying  asphalt-pitch,  the  brand  or  origin  should  be  plainly  defined.  The 
use  of  an  under-layer  of  sheathing-paper  next  to  board-sheathing  is  mainly  for 
the  purpose  of  preventing  any  pitch  which  might  penetrate  the  felt  from  cement- 
ing the  roofing  to  the  sheathing.  It  is  also  of  value  in  preventing  the  drying  out 
of  the  roof  from  belovv^  through  open  joints.  Where  a  less  expensive  roof  is  de- 
sired, four  plies  or  three  plies  of  saturated  felt  may  be  used.  With  the  four  plies 
there  should  be  used  from  90  to  100  lb  of  pitch  per  100  sq  ft  of  completed  roof; 
and  with  the  three  plies  from  70  to  80  lb  of  pitch. 

Durability  of  Slag  or  Gravel  Roofs.  These  roofs,  mentioned  in  the  pre- 
ceding paragraph,  will  last  from  five  to  ten  years,  or  even  longer,  depending  upon 
the  quaHty  of  the  materials  used  and  the  care  with  which  they  have  been  applied. 
Roofing  put  on  strictly  as  provided  for  in  the  standard  specifications  will  last 
twenty  years  or  more,  and  if  a  tile  surface  is  used,  instead  of  gravel  or  slag,  the 
roofing  will  last  as  long  as  the  structure  itself. 

Resistance  to  Fire,  Acid-Fumes,  Etc.  The  fire-resisting  properties  of  the 
slag  or  gravel  roof  are  due  principally  to  the  incombustible  material  on  the  sur- 
face. It  is  claimed  that  the  gravel  or  slag  tends  to  prevent  the  successive  layers 
of  felt  and  pitch  from  burning  and  the  whole  mass  has  a  blanketing  influence  on 
fires  originating  within  the  building.  Some  carefully  conducted  tests  seem  to 
indicate  that  gravel  roofing  protects  a  wooden  roof  better  than  tin.  The  general 
effect  of  a  fire  upon  gravel  roofing  is  to  soften  the  pitch  or  asphalt  in  the  roofing, 


1598  Memoranda  on  Roofing  Part  3 

to  burn  out  the  inflammable  oil  in  them  and  to  cause  the  residue  to  swell  and  form 
a  porous,  incombustible  coke.  This  type  of  roofing  is  not  attacked  by  corrosive 
gases  or  acid-fumes,  and  is  used  extensively  on  railroad-roundhouses  and  other 
structures  where  the  conditions  are  particularly  severe.  Coal-tar  or  tar-oil 
should  not  be  added  to  the  pitch  to  soften  it. 

Guarantee.     Roofers  generally  give  a  five-year  guarantee  with  gravel  roofs. 

Cost  *  of  Pitch-Slag  or  Gravel  Roofing'.  The  cost  of  this  type  of  roofing 
varies  greatly,  depending  on  the  location,  size  and  quality  of  the  work,  the  ex- 
tremes being  approximately  $2.50  and  $3.50  per  square  for  three-ply,  $3.50  and 
$4.50  per  square  for  four-ply,  and  $4.50  and  $7.00  per  square  for  five-ply  roofing-. 

Asphalt-Gravel  Roofing 

Asphalt-Gravel  or  Asphalt-Slag  Roofing  differs  from  coal-tar  roofing  princi- 
pally in  the  substitution  of  asphalt  or  asphaltic  cement  for  the  coal-tar  pitch,  for 
saturating  the  felt  as  well  as  for  mopping  and  surface-coating.  It  is  claimed  that 
the  oils  of  asphalt  do  not  evaporate  as  quickly  as  do  those  of  coal-tar  pitch  under 
ordinary  temperatures  and  that  therefore  the  flexibility  and  life  of  asphaltic  felts 
and  coatings  are  not  as  quickly  destroyed.  As. a  matter  of  fact,  asphalt  roofs  do 
not  always  last  longer  than  some  coal-tar  roofs,  but  the  chances  are  that  they 
will  last  fully  as  long  and  possibly  longer,  depending  upon  the  quality  of  the 
materials  and  the  workmanship.  The  asphalt  used  for  roofing  is  obtained  prin- 
cipally from  the  island  of  Trinidad. 

Specifications  for  Asphalt  Roofing,  f  The  following  specifications  were 
prepared  by  the  above-named  company  and  are  for  Warren's  heavy  standard 
Anchor-brand  roofing.  The  manner  of  laying  the  felting  differs  from  that  ordi- 
narily employed  for  coal-tar  roofing. 

(i)  Specification  for  Asphalt-Gravel  Roofing  Over  Wooden  Sheathing 

Cover  the  roof  with  two  thicknesses  of  Warren's  Composite  roofing-felt, 
manila-paper  side  down,  lapping  each  sheet  17  in  over  the  preceding  one,  and 
securing  with  nails  through  tin  discs  about  2y2  ft  apart. 

Over  the  entire  surface  of  the  Composite  felt  thus  laid,  mop  an  even  coating 
of  Warren's  Anchor  Brand  roofing-cement,  into  which,  while  hot,  lay  two 
thicknesses  of  Anchor  Brand  felt,  lapping  each  sheet  17  in  over  the  sheet 
preceding,  sticking  these  laps  the  full  width  with  hot  Anchor  cement  and  securing 
with  nails  through  tin  discs  not  more  than  20  in  apart. 

Over  the  entire  surface  of  the  felt  thus  prepared,  spread  an  even  coating  of  the 
cement,  covering  it  immediately  with  a  sufficient  body  of  well-screened,  dry 
gravel  or  crushed  slag. 

If  the  roofing  is  applied  in  cold  weather  the  gravel  or  slag  must  be  heated. 

Slag  only  should  be  used  if  the  incline  of  the  roof  exceeds  3  in  to  the  foot. 

All  layers  of  felt  must  be  turned  up  at  least  4  in  over  battlement-v/alls,  sky- 
light-curbs, or  any  projections  raised  above  the  roof. 

(2)  Specification  for  Asphalt-Gravel  Roofing  Over  Concrete 
The  concrete  foundation  is  to  be  smooth  and  perfectly  graded  to  carry  the 
water  to  the  outlets  or  gutters. 

Over  the  entire  surface  of  the  concrete  first  mop  a  smooth,  even  coating;:  of 
Eclipse  Asphalt  cement,  into  which,  while  hot,  lay  two  thicknesses  of  Warren's 
Anchor  Brand  roofing-felt,  lappmg  each  sheet  17  in  over  the  sheet  preceding. 

*  These  rvrices  have  advanced  and  the  manufacturers'  lists  must  be  consulted. 
tThe  asphalt -roofing  materials  manufactured  by  the  Warren  Chemical  tk  Manufac- 
turing Company  of  New  York   have  been   used  for   many  years  and  have  given  good 


Corrugated  Iron  and  Steel  Sheets  1599 

Mop  back  for  the  full  width  between  the  laps  of  the  felt  thus  laid,  with  War- 
ren's Anchor  Brand  roofing-cement. 

Ovci  the  entii-e  exposed  surface  of  the  felt  mop  an  even  coating  of  said  Anchor 
cement,  into  which,  while  hot,  lay  two  thicknesses  of  Anchor  Brand  felt,  lapping 
each  sheet  17  in  over  the  sheet  preceding,  and  sticking  these  laps  thoroughly  the 
full  width  with  hot  cement. 

Over  the  entire  surface  of  the  felt  thus  prepared,  spread  an  e.ven  coating  of  the 
cement,  covering  it  immediately  with  a  sufficient  body  of  well-screened,  dry 
gravel  or  crushed  slag. 

If  the  roofing  is  applied  in  cold  weather,  the  gravel  or  slag  must  be  heated. 

Slag  only  should  be  used  if  incline  of  roof  exceeds  3  in  to  the  foot.  On  steep 
surfaces  naihng-strips  should  be  provided  in  the  concrete,  unless  the  latter  is 
sufficiently  soft  to  admit  of  naiUng.  All  layers  of  felt  must  be  turned  up  at 
least  4  in  over  battlement-walls  and  skylight-curbs,  or  any  projections  raised 
above  the  roof. 

Cost  of  Asphalt-Gravel  or  Slag  Roofing.  Asphalt-gravel  roofing  costs  a 
little  more  than  pitch-gravel  roofing  of  the  same  grade.  (See  Cor^t  of  Pitch- 
Slag  or  Gravel  Roofing,  page  1598.) 

Roof-Incline.*  Asphalt-gravel  or  asphalt-slag  roofing  should  not  be  applied 
to  roofs  which  are  steep  enough  to  make  the  material  run  in  hot  weather.  The 
manufacturers  of  various  roofings  will  guarantee  the  permanency  of  their  roofings 
for  certain  maximum  slopes. 

Prepared  Roofing.  There  is  a  large  number  of  so-called  prepared  roofings 
or  READY  ROOFINGS,  which  are  made  by  cementing  together  two,  three,  or  more 
layers  of  saturated  felt  or  felt  and  burlap  and  then  coating  the  combination  either 
with  a  hard  solution  of  the  same  cementing  material,  or  with  hot  pitch  or  asphalt 
into  which  is  embedded  sand  or  fine  gravel.  These  roofings  are  commonly  put 
up  in  rolls  36  in  wide  and  are  applied  by  lapping  the  strips  2  in  with  a  coat  of 
cementing  material  between,  and  naiUng  every  2  or  3  in  with  tin-capped  roofing- 
nails.  A  sufficient  quantity  of  cement,  nails  and  tin  caps  is  packed  in  the  middle 
of  the  rolls.  The  particular  advantage  of  these  roofings  is  that  no  previous  expe- 
rience is  required  for  laying  them  and  no  kettles  are  required;  for  this  reason  they 
are  extensively  used  in  the  country,  and  on  railroad-shops,  factories,  and  mill- 
buildings.  In  cities  there  is  no  particular  advantage  in  using  them  except  for 
roofs  that  are  too  steep  for  coal-tar  pitch,  as  they  cost  on  the  roof  about  the  same 
as  good  gravel  roofing.  Many  of  these  prepared  roofings  are  as  durable  under  or- 
dinary conditions  as  the  light-weight  gravel  roofs.  In  Colorado,  however,  it  has 
been  found  that  they  are  badly  damaged  by  severe  hail-storms,  probably  owing 
to  the  lack  of  the  protecting  gravel.  For  roofs  having  a  rise  of  i  in  or  more  to 
the  foot,  these  roofings  make  economical  and  durable  roofs,  and  for  some  build- 
ings are  to  be  preferred  to  other  materials. 

Corrugated  Iron  and  Steel  Sheets 

Corrugated  Sheets  of  iron  and  steel  are  very  extensively  used  for  the  roofing 
and  siding  of  mills,  sheds,  grain-elevators  and  warehouses.  The  best  grades  of 
corrugated  sheets  are  now  made  of  double-refined  box-annealed  iron  or  steel.f 

*  The  Editor  has  been  notified  by  the  Warren  Chemical  &  Manufacturing  Company, 
New  York,  that  when  put  on  according  to  their  directions,  their  Anchor  Brand  roofing  has 
been  successfully  used  on  relatively  steep  surfaces  v/here  the  slope  was  as  high  as  9  in  to  the 
foot. 

t  It  is  claimed  that  "the  life  of  a  genuine  puddled-iron  sheet  when  exposed  only  to 
the  pure  air  and  natural  elc.nents  is  froiT>  five  to  eight  times  longer,  and  when  exposed  to 


1600 


Memoranda  on  Roofing 


Part  3 


The  corrugations  are  usually  made  lengthwise  of  the  sheet,  either  by  passing 
them  through  rolls  or  by  pressing  the  plain  sheets  in  a  press  made  to  give  the 
desired  corrugations.  It  is  claimed  that  the  latter  method  gives  the  more  per- 
fect and  uniform  corrugations.  The  weight  and  thickness  of  the  metal  is  rep- 
resented by  the  gauge-number  of  the  black  sheets  from  which  the  corrugated 
sheets  are  made.  The  standard  gauge*  for  sheet  iron  and  steel  in  this  country 
is  that  established  by  act  of  Congress,  March  3,  1893.    (See  page  402.) 

Gauges.  The  following  table  gives  the  weights  and  thicknesses  of  the  differ- 
ent gauges,  from  No.  7  to  No.  30,  for  flat  black  sheets.  The  gauge  extends 
from  No.  7-0,  H  in  thick,  up  to  No.  40,  0.005469  in  thick,  but  sheet  steel  is  not 
commonly  made  thinner  than  No.  30,  and  above  Ms  in,  the  thickness  is  gener- 
ally designated  by  fractions  of  an  inch.  Section  3  of  the  act  of  Congress  pro- 
vides that  in  the  practical  use  and  application  of  this  gauge,  a  variation  of 
2H%  either  way  may  be  allowed. 

United  States  Standard  Gauge  for  Sheet  Iron  and  Steel  * 


Num- 

Thicknesses 

Weights 

ber  of 

Approximate 

Approximate 

Weight  per 

Weight  per 

gauge 

thickness  in 

thickness  in 

square  foot 

square  foot 

fractions  of 

decimal  parts 

^n  ounces, 

in  pounds 

an  inch 

of  an  inch 

avoirdupois 

avoirdupois 

7 

3/i« 

0.1875 

120 

7.5 

8 

H64 

0.171875 

no 

6.875 

9 

H2 

0.15625 

100 

6.25 

10 

%4. 

0.140625 

90 

5-625 

II 

H 

0.125 

80 

5.0 

12 

7/64 

0.109375 

70 

4. 375 

13 

^A2 

0.0937s 

60 

3.75 

14 

%4 

0.078125 

50 

3.125 

IS 

%2% 

0.0703125 

45 

2.8125 

16 

Ma 

0.0625 

40 

2.5 

17 

Meo 

0.05625 

36 

2.25 

18 

\^o 

0.05 

32 

2.0 

19 

lUo 

0.04375 

28 

1-75 

20 

Ho 

0.0375 

24 

1.50 

21 

l»'^20 

0.034375 

22 

1.375 

22 

\i2 

0.0312s 

20 

1.25 

23 

^20 

0.028125 

18 

1. 125 

24 

Ho 

0.025 

16 

1.0 

25 

J^20 

0.021875 

14 

0.875 

26 

Meo 

0.01875 

12 

0.75 

27 

^Voio 

0.0171875 

II 

0.6875 

28 

\U 

0.015625 

10 

0.625 

29 

9^40 

0.014062s 

9 

0.5625 

30 

^60 

0.0125 

8 

0.5 

Galvanizing  the  Sheets  adds  approximately  2H  oz  per  sq  ft  to  the  above 
weights.  The  regular  sizes  of  the  corrugations  are  2\h,  iH,  %  and  M«  in, 
measured  from  center  to  center.     Besides  these  sizes,  5-in,  3-in  and  2-in  corru- 

sulphurous  and  other  gases  from  ten  to  twenty  times  longer,  than  a  sheet  of  steel  or  semi- 
steel  of  the  same  gauge,  or  a  light-gauge  sheet  made  from  pure  puddled  pig-iron;  and  that 
it  will  wear  longer  than  steel  sheets  of  the  heaviest  gauges,  or  galvanized  sheets  of  the 
same  gauge. " 

*  For  other  gauges,  see  pa^es  ^01,  402,  403,  1469, 1473, 1509,  isioan^  1513. 


Corrugated-Steel  Roofing 


1601 


gations  are  made  by  one  or  two  corrugating  companies.  Corrugated  sheets  are 
carried  in  stock  in  4-ft,  5-ft,  6-ft,  7-ft,  8-ft,  9-ft  and  lo-ft  lengths.  Sheets  can 
be  obtained  as  long  as  12  ft  at  a  cost  of  5%  extra.  The  8-ft  length,  however,  is 
most  commonly  used.  The  width  of  the  sheets,  as  a  rule,  is  24  in  between  cen- 
ters of  the  outer  corrugations,  so  that  the  covering  width  is  24  in  when  one 
corrugation  is  used  for  the  side  lap.  This  appHes  to  all  sizes  of  corrugations,  all 
though  one  or  two  mills  make  wider  sheets.  The  2-in,  2H-in  and  3 -in  corrugated 
sheets  are  made  in  all  gauges  from  No.  16  to  No.  28,  the  ij^i-in  corrugated  sheets 
from  No.  22  to  No.  28,  the  ^i-in  corrugated  sheets  from  No.  24  to  No.  28  and  the 
yiQ-'m  corrugated  sheets  in  Nos.  26,  27  and  28  only.  No.  28  gauge  is  the  one  com- 
monly used  for  all  purposes.  The  sheets  are  generally  painted  with  a  red  mineral 
paint  before  shipping  and  galvanized  sheets,  also,  can  be  obtained  if  desired. 
All  corrugated  sheets  are  sold  by  the  square  (100  sq  ft),  measuring  the  actual 
widths  and  lengths  of  the  corrugated  sheets. 


Corrugated-Steel  Roofing  * 

Useful  Data.     For  covering  roofs,  either  3-in,  23'i-in,  or  2-in  corrugations 
should  be  used,  the  2H-in  being  the  most  common  size.    The  thickness  or  gauge  • 
depends  upon  the  distance  between  the  supports  on  which  the  sheets  are  laid. 

Nos.  26  to  28  gauges  should  be  laid  on  close  sheathing,  or  strips  not  more 
than  from  i  to  2  ft  on  centers.  The  maximum  distances  between  supports  for 
other  gauges  should  be  as  follows:  t 

For  No.  24  gauge,  from  2  to  2H  ft,  center  to  center. 

For  Nos.  22  and  20  gauge,  from  2  to  3  ft,  center  to  center. 

For  No.  18  gauge,  from  4  to  s  ft,  center  to  center. 

For  No.  16  gauge,  s  to  6  ft,  center  to  center. 

The  least  pitch  which  should  be  given  to  roofs  that  are  to  be  covered  with 
corrugated  sheets  is  3  in  to  the  foot,  and  for  trussed  roofs  it  is  not  desirable  to 


Fig.  1.    Approved  Method  of  Laying  for  Side  Lap 

have  less  than  a  one-fourth  pitch  (6  in  to  the  foot).  When  laid  on  a  roof,  corru- 
gated sheets  should  have  a  lap  at  the  lower  end  of  from  3  to  6  in,  according  to 
the  pitch  of  the  roof.  For  a  H  pitch,  a  3-in  lap  is  used;  for  a  H  pitch,  a  4-in 
lap;  and  for  a  ^  pitch,  a  5-in  lap.  For  the  side  lap  it  is  recommended  that 
each  alternate  sheet  be  laid  upside  down  and  lapped  as  shown  in  Fig.  1.  By 
this  method,  when  water  is  blown  through  the  first  lap,  it  will  stop  and  not  pass 
the  half  lap,  but  run  down  and  out  at  the  end  of  the  sheet.  A  great  deal  of 
roofing,  however,  is  laid  as  in  Fig.  2.  In  applying  to  sheathing  or  wooden  strips, 
the  sheets  are  secured  by  nailing  through  the  tops  of  the  corrugations,  the  nails 
being  driven  through  every  alternate  corrugation  at  the  ends,  and  about  8  in 

*  Much  practical  information  regarding  the  use  of  corrugated  sheets  on  mill-build- 
ings, with  many  details,  is  contained  in  Steel  Mill  Buildings  and  in  the  Structural  En- 
gineers' Handbook,  by  Milo  S.  Ketchum. 

t  For  the  strength  of  corrugated  sheets,  see  the  books  above  mentioned. 


1602 


Memoranda  on  Roofing 


Part  3 


apart  at  the  sides.  When  applied  to  iron  or  steel  purlins,  the  side  laps  should 
extend  over  at  least  i^  corrugations,  and  the  sheets  should  be  riveted  together 
every  8  in  on  the  sides  and  at  every  alternate  corrugation  at  the  ends.  The 
Cincinnati  Corrugating  Company  makes  a  patent  edge-corrugation  which 
makes  a  tight  joint  with  a  lap  of  only  one  corrugation.     To  fasten  the  sheets  to 


Common  Method  of  Laying  for  Side  Lap 


the  purlins,  which  are  usually  steel  angles,  cleats  of  band-iron,  %  or  li  in  wide, 
may  be  passed  around  or  under  the  purlins  and  riveted  at  both  ends  to  .the 
sheets,  as  shown  in  Fig  3.  By  contracting  or  pressing  these  cleats  toward  the 
web,  a  tight,  secure  fastening  results,  which  allows  for  contraction  and  expansion 
of  the  sheets.     Cleats,  however,  are  generally  used  only  with  channel  or  Z-bar 


V\g.  3.     Sheets  Fastened  to  Angle- 
purlin  by  Band-iron  Cleats 


/ 


Sheets  Fastened  to  Angle-purlin 
by  Clinch-nails 


jDurlins.     For  angle-iron  purlins,  clinch-nails,  made  of  soft-iron  wire,  are  com- 
monly used,  as  shown  in  Fig.  4;   they  make  very  satisfactory  fastenings. 

The  following  table  shows  the  sizes  of  clinch-nails  to  be  used  with  different 
sizes  of  angle-purlins  and  also  the  number  of  nails  to  the  pound  in  each  instance: 


Purlin-angle^    ,  ^^^^.^ .^^j,.„ ......      2X^  in 

Lengths  of  nails. ».•*..,.        41 

Number  of  nails  peVy-^'^^  '*'  ' 


HXsin 

3HX3H  in 

4X4H  in 

5  m 

6  in 

7  m 

38 

33 

27 

.  ^.  ^^^,    .  , 

The  nails  should  be  placed  through  the  top  of  every  second  or  third  corruga- 
tion. At  the  eaves  of  the  building  and  along  the  edges  of  the  ventilators  special 
pains  should  be  taken  in  fastening  the  roofmg,  as  these  are  the  places  where  the 
force  of  the  wind  is  the  greatest  and  where  it  tends  to  strip  the  roofing  from  the 
purlins.  For  these  parts  of  the  roof  the  best  method  of  fastening  is  that  shown 
in  Fig.  5.  These  fastenings  consist  of  strips  of  sheet  iron  about  2  in  wider  than 
the  purlins,  made  of  No.  12  iron  and  riveted  to  the  purlins  with  ^4-in  rivets 
spaced  10  in  apart.  To  these  strips  the  corrugated  sheets  are  riveted,  every 
5  in  or  every  two  corrugates,  with  6-lb  rivets.  The  method  of  fastening  shown 
in  Fig.  6,  also,  answers  very  wdil  and  is  less  expensive. 


Corrugated  Siding 


1603 


In  ordering  corrugated  sheets  an  allowance  must  be  made  for  the  laps.     The 
following  table  gives  the  number  of  square  feet  necessary  to  cover  one  square  of 


Fig.  5.     Approved  Fastening 
for  Sheets  at  Eaves 


Fig.  6.    Alternate  Method  of 
Fastening  at  Eaves 


actual  surface,  using  sheets  8  ft  long.     If  shorter  sheets  are  used,  the  allowance 
must  be  slightly  increased. 

Number  of  Square  Feet  of  Corrugated  Sheets  to  Cover  loo  Square  Feet 
of  Roof 


End-laps 

I  in 

2  in 

3  in 

4  in 

5  in 

6  in 

Side  lap,  i  corrugation 

Side  lap,  ly^  corrugations 

Side  lap,  2  corrugations 

sqft 
no 
116 
123 

sqft 
III 
117 
124 

sqft 
112 
118 
125 

sqft 
113 
119 
126 

sqft 
114 
120 
127 

sqft 
115 
121 
128 

Approximate  Weights  in  Pounds  of  100  Square  Feet  of  2}i-ia.  Corrugated 
Sheets 


Gauge 

No.  28 

No.  27 

No.  26 

No.  24 

No.  22 

No.  20 

No.  18 

No.  16 

Painted.... 
Galvanized. 

69 
86 

77 
93 

84 
99 

III 
127 

138 

154 

165 
182 

220 
236 

275 
^91 

Anti-Condensation  Lining.  Wherever  corrugated  steel  is  laid  on  puriins 
with  no  sheathing  or  paper  underneath,  if  the  building  is  heated,  moisture  will 
invariably  collect  on  the  under  side,  and  if  the  air  in  the  building  is  warm  and 
humid,  considerable  dripping  will  result.  To  prevent  this  dripping,  it  is  neces- 
sary to  protect  the  under  side  of  the  corrugated  steel  with  paper  or  felt.  This 
may  be  done  by  first  stretching  poultry-netting  over  the  purlins,  from  eaves  to 
ridge,  and  wiring  the  strips  together  at  the  edges.  Over  this  should  be  laid  one 
thickness  of  asbestos  paper  and  one  or  two  layers  of  saturated  felt.  The  cor- 
rugated steel  may  then  be  fastened  to  the  purlins  in  the  usual  way.  The  side 
laps  may  be  secured  by  stove-bolts,  with  i  by  H  by  4-in  plate  washers  on  the 
under  side,  to  support  the  lining. 

Corrugated  Siding 

For  Siding,  either  the  2y2,  2,  or  iH-in  corrugations  are  used.  The  iH-in  size, 
however,  makes  the  best  appearance.  For  the  laps,  i  in  at  the  bottom  and  one 
corrugation  at  the  sides  are  sufficient. 

For  Sheds,  etc.,  the  sheets  may  be  nailed  to  cross-pieces  cut  in  between  the 
studs  horizontally  and  spaced  from  2  to  3  ft  apart,  the  studs  being  from  3  to  4  ft 


1604  Memoranda  on  Tiling  Part  3 

on  centers.  For  elevators,  either  cross-corrugated  sheets  or  sheets  not  more 
than  32  in  long  should  be  used.  The  nails  should  be  driven  in  the  trough  of 
each  alternate  corrugation,  2  in  above  the  lower  end  of  the  sheet,  which  will  be 
I  in  ABOVE  the  top  end  of  the  under  sheet.  This  allows  the  sheet  to  slide  i  in 
in  32  in  as  the  building  settles,  before  the  nail  will  strike  the  upper  end  of  the 
lower  sheet.    The  side  lap  should  not  be  nailed. 

Ceilings.  For  'the  ceilings  of  stores,  stables,  etc.,  fie  or  ^^-in  corrugated 
sheets  are  much  used;  and  the  construction  is  an  excellent  one  for  this 
purpose. 

Galvanized  Iron.  This  term  is  commonly  applied  to  all  galvanized  sheet 
metal.  Formerly  most  of  the  galvanized  sheets  had  a  steel  base,  but  since 
about  1906  a  nearly  pure  iron,  called  Toncan  Metal,  has  been  largely  used  for 
sheets  of  very  fine  quality.  Galvanized  sheets  come  in  lengths  of  6,  7  and  8  ft 
in  United  States  Gauge-Nos.  14,  16,  18,  20,  22,  24,  26,  27,  28  and  30,  and  in 
widths  of  24,  26,  28,  30  and  36  in  for  all  gauges  except  No.  30,  which  is  made  only 
in  widths  of  24,  26  and  28  in.  Sheets  of  No.  28  gauge  are  also  made  in  widths  of 
32  and  34  in.  The  widths  commonly  carried  in  stock  are  24,  28  and  30  in. 
Most  of  the  galvanized  iron  used  for  cornices  and  ornamental  work  is  No.  27 
gauge.     No.  28  is  sometimes  used  for  gutters  and  conductors. 

Copper  for  Roofs 

Method  of  Applying.  This  is  usually  in  2\i  by  5-ft  sheets,  making  iiVi 
sq  ft  and  weighing  from  10  to  14  lb  per  sheet.  It  is  laid  on  boards  to  which  it 
is  fastened  by  copper  cleats.  No  solder  is  employed,  as  it  is  in  tin  roofs,  in  the 
horizontal  joints,  and  the  horizontal  and  sloping  joints  are  made  by  simply  over- 
lapping and  bending  the  sheets.  The  horizontal  joints  are  locked  together  and 
then  tightly  flattened  down. 


MEMORANDA    ON    TttlNG 

Floor-Tiling  and  Wall-Tiling 

Tile  Floors  are  extensively  used  in  the  better  class  of  buildings,  and  par- 
ticularly in  those  portions  which  are  used  by  the  pubhc,  on  account  of  their  great 
durability,  sanitary  qualities  and  decorative  effects.  As  a  matter  of  fact,  a  good 
tile  floor  is  also  cheaper  in  the  long  run  than  a  wooden  floor  if  it  is  subject  to 
much  wear.  The  materials  used  for  tiling  floors  are  tiles  made  from  diff'erent 
grades  of  clay,  marble,  slate,  glass  and  rubber.  Of  these  probably  the  most 
durable  and  sanitary  are  the  vitreous  clay  tiles.  For  walls  and  wainscotings, 
glazed  tiles,  marbles  and  glass  are  extensively  used. 

Floor-Tiles.     The  following  include  some  of  the  principle  kinds  of  clay  tiles: 

(1)  Common  Encaustic  Tiles.  These  belong  to  the  cheapest  grades,  and  are 
made  of  naturally  colored  clays,  red,  buff,  gray,  chocolate  and  black.  These 
tiles  are  of  a  porous,  absorbent  nature  and  are  used  for  common  floors  where 
sanitary  requirements  are  not  exacting. 

(2)  Semivitreous  Tiles.  These  belong  to  a  somewhat  better  grade  than  the 
first  mentioned  and  are  less  porous  and  absorbent. 

(3)  Vitreous  Tiles.  These  are  the  hardest  tiles  known,  cannot  be  scratched 
by  steel  or  sand,  and  are  non-absorbent  and  thoroughly  aseptic.  They  are  used 
principally  for  floors  requiring  a  perfect  sanitary  condition  and  are  manufactured 
in  white,  blue,  gray,  green  and  pink  colors  of  great  delicacy. 


Classification  of  Tiles  1605 

(4)  Ceramic  Tiles  or  Ceramic  Roman  Mosaic.  This  material  is  made  of 
VITREOUS  clay  in  tesseral  pieces  representing  the  tesserae  of  the  Roman  mosaics. 
It  is  made  into  regular  tiles  ranging  from  yz  to  %-in  squares  and  also  in  hexagonal 
shapes  from  %  in  to  i  in  in  size.  A  rounded  lozenge  tile  is  also  manu- 
factured to  be  laid  in  tesseral  paving.  (See,  also,  Flooring  of  Mosaic,  Terrazzo, 
etc.,  page  1607.) 

The  material  itself  is  of  great  hardness  and  well  suited  for  work  of  a  monu- 
mental or  public  character.  The  even  and  regular  texture  of  the  tesserae  admits 
the  adoption  of  damask  designs  which  have  become  identified  and  associated 
with  this  material.  The  minuteness  of  the  tesserae  admits  of  a  great  range  in 
designing  and  the  following  of  the  architectural  lines.  The  ceramic  Roman 
mosaic  is  much  preferred  to  mosaic  consisting  of  natural  marbles,  because  of  the 
great  variety  in  colors  and  its  greater  durability.  The  vitreous-clay  tiles  are 
impervious  to  attacks  of  any  acids  contained  in  the  atmosphere,  while  marbles, 
especially,  are  subject  to  rapid  disintegration  caused  by  the  sulphuric  acid  con- 
tained in  the  smoke-laden  atmosphere  of  our  cities. 

(5)  Florentine  Mosaics  and  Flint  Tiles.  These  are  the  largest  and  heaviest 
tiles  manufactured  in  this  country.  They  are  either  plain  or  inlaid  and  are  in 
use  especially  in  ecclesiastic  work  on  account  of  their  relation  to  mediaeval 
application.  The  material  is  vitreous,  annealed  and  tougher  than  it  is  brittle. 
It  is  also  in  use  for  exterior  polychrome  work. 

(6)  Aseptic  Tiles.    These  are  large,  heavy  and  thoroughly  vitreous  tiles  used 
for  institute  work.     They  are  the  only  vitreous  tiles  of  large  size  made  in  this 
country.     As  the  tiles  are  large  and  generally  of  hexagonal  shape,  the  joint- 
spaces  are  reduced  to  a  minimum,  and  they  are,  therefore,  especially  adapted  ' 
for  hospitals,  operating-rooms  and  wards  for  contagious  diseases. 

Enameled  Tiles,  Wall-Tiles  and  Mantel-Tiles.  The  following  include 
some  of  the  enameled  tiles: 

(1)  White,  Wall-Tiles.  These  are  glazed  tiles  for  wainscots.  They  have 
a  white,  soft  body  and  a  surface  covered  with  a  clear  glaze.  The  brilliancy  of 
this  glaze  and  its  reflecting  properties  make  the  white  wall-tiles  especially  de- 
sirable for  dark  passages. 

(2)  Colored,  Glazed  or*  Enameled  Tiles.  These  tiles  are  about  the  same  as 
the  former  In  quality;  the  glaze  or  enamel,  however,  is  stained  with  metallic 
oxides,  which  produces  a  brilliant  decorative  effect. 

(3)  Dull-Satin,  etc.,  Finished,  Enameled  Tiles.  These  are  glazed  tiles  with 
a  DULL  or  BLIND  enamel-finish.  The  dull  finish  is  produced  either  by  sand- 
blasting or  by  devitrifying  enamels.  It  is  principally  used  for  quaint  decorative 
effects  in  mantel-work. 

(4)  Glazed  Roman  Mosaics.  This  is  a  type  of  enameled  tiling  which  has 
great  decorative  possibilities.  It  has  the  same  tesseral  texture  as  the  ceramic 
floor-tiles  and  is  readily  applied  to  wainscots  and  mantel-work. 

Setting  of  Tiles.  Clay  tiles  are  set  in  Portland-cement  mortar  as  a  rule, 
and  flooring  of  this  character  should  always  be  provided  with  a  substantial 
concrete  base.  Ceramic  mosaics  are  sometimes  laid  on  a  flexible  base.  With 
this  construction  wooden  floors  can  be  provided  with  tile  covering,  and  owing 
to  the  elasticity  and  lightness  of  the  material,  floors  in  elevators,  boats  and  other 
ambulant  structures  can  be  safely  tiled. 

Marble  Tiles,  from  9  to  12  in  square,  have  been  extensively  used  for  flooring, 
principally  on  account  of  their  decorative  effect.  None  of  the  marbles,  however, 
jg  as  hard  and. consequently  as  durable  as  the  vitreous  and  ceramic  tiles,  and 


160«  Memoranda  on  Tiling  Part  3 

from  all  practical  standpoints  the  marbles  do  not  make  as  good  floor-coverings. 
When  used,  they  should  be  iH  in  thick  and  not  over  12  in  square,  and  should  be 
bedded  in  cement  on  a  concrete  base.  Marbles  should  not  be  used  for  flooring 
in  hospitals,  as  they  yield  rapidly  to  the  usual  antiseptic  floor- washes. 

Slate,  although  non-absorbent  and  not  affected  even  by  dilute  mineral  acids, 
is  too  cold  and  dingy  to  commend  itself  for  floor-tiles,  but  because  it  is  conven- 
iently handled  in  large  slabs  it  is  valuable  as  a  cheap  base  and  as  a  cover  for 
wiring  and  pipe- trenches  in  the  floors.  As  these  often  follow  a  wall,  it  may  serve 
in  the  capacity  of  a  border  and  as  such  be  extended  around  the  floor-space. 
Slate  slabs  for  floors  should  be  about  iK  in  thick. 

Marbleithic  Tiles  or  Slabs  are  made  of  small  pieces  or  chips  of  marbles  of 
irregular  shapes,  set  in  a  backing  of  sand  and  Portland  cement.  After  the  ce- 
ment has  set,  the  top  surface  is  rubbed  until  it  becomes  flat  and  smooth.  Mar- 
bleithic resembles  mosaic  or  Terrazzo,  except  that  it  is  laid  in  the  form  of  tiles 
instead  of  being  put  down  on  the  floor  in  a  plastic  condition.  Much  objection  has 
been  made  to  Terrazzo  because  of  the  cracks  which  commonly  occur  in  it,  due 
to  the  sBght  settlements  which  are  unavoidable  in  a  new  building.  (See,  also, 
Flooring  of  Mosaic,  Terrazzo,  etc.,  page  1607.)  With  tile  floors  of  any  material 
the  joints  allow  for  any  slight  movement  of  the  floor-construction,  without 
causing  visible  cracks.  By  the  process  of  manufacture,  marbleithic  is  made 
much  harder  than  it  is  possible  to  make  mosaic  floors  that  are  laid  in  a  plastic 
condition,  so  that  they  have  a  much  better  wearing  surface.  Floors  of  this 
material  have  been  in  use  since  1895  and  show  little  if  any  wear.  Marbleithic 
tiles  are  made  of  various  colored  marbles  and  in  different  sizes,  shapes  and 
patterns,  so  that  a  great  variety  of  effects  may  be  produced.  Sanitary  coved 
bases,  stair-treads,  and  wainscotings,  also,  are  made  of  this  material. 

Cast-Glass  Tiles,  while  quite  resistant  to  a  blow  when  the  polish  is  un- 
broken, will  break  very  easily  when  the  surface  is  scratched.  All  glass  tiles 
should,  therefore,  be  very  thick  and  small  or  protected  by  metal  framing. 

Novus  Sanitary  Glass  *  is  a  sanitary  structural  glass  manufactured  in  all 
thicknesses  from  H  in  up  to  2  in  and  in  slabs  of  all  widths  and  lengths  up  to  100  in 
in  width  and  180  in  in  length.  It  is  made  in  various  colors  and  designs  and  in 
the  following  finishes:  natural-fire  finish,  hone,  semipolished  and  polishe^. 
It  can  be  worked  and  handled  the  same  as  marble,  it  is  readily  drilled  and  shaped 
to  accommodate  fixtures,  etc.,  and  is  very  handsome  in  appearance.  It  is  im- 
pervious to  discoloration  and  is  non-crazing.  These  qualities  make  it  especially 
desirable  for  floors,  wainscoting,  tables,  shelves,  etc.,  in  all  places  where  an  abso- 
lutely sanitary  condition  combined  with  a  handsome  appearance  is  required. 

Interlocking  Rubber  Tiling 

General  Description.  There  is  an  interlocking  rubber  tiling, f  which,  be- 
cause of  its  being  noiseless,  non-slippery,  and  more  comfortable  to  the  feet  than 
inelastic  substances,  has  met  with  great  favor  for  floors  in  banking-rooms, 
counting-rooms,  vestibules,  elevators,  stairs,  cafes,  libraries,  churches,  etc.  For 
elevators  it  is  one  of  the  most  durable  and  practical  floors  that  can  be  laid;' 
it  is  also  especially  and  peculiarly  adapted  for  floors  of  yachts  and  steamships. 
The  interlocking  feature  unites  the  tiles  into  a  smooth,  unbroken  sheet  of 
rubber,  unlimited  in  area.  The  tiles  do  not  pull  apart  or  come  up,  and  each 
being  distinct,  almost  any  color-scheme  can  be  employed,  the  tiles  bei»ng  made 
in  a  carefully  selected  variety  of  colors.     The  tiles  are  laid  directly  over  the 

•  Made  by  the  Penn-American  Plate  Glass  Company,  Pittsburgh,  Pa. 

I  M2^n\ifactured  by  the  I<Jew  Yorl^  Belting  ^pd  Packing  Compaoyi  New  York. 


Mosaic  Flooring.     Terazzo 


1607 


original  floor,  like  a  carpet,  except  that  they  are  not  fastened.  Experience  has 
shown  that  they  are  very  durable.  Each  tile  is  2%  in  square  and  %  in  thick; 
25.5  tiles  are  required  to  the  square  foot.  Rubber  nosing  for  stairs  is  made  to 
interlock  with  the  tiles. 

Cost  *  of  Different  Tiles 
Approximate  Cost.     The  following  prices  are  approximately  the  cost,  to  the 
trade,  at  the  factory.     To  these  should  l^e  added  the  freight  and  the  dealers' 
profits.     The  cost  of  laying  the  tiles  on  a  cement  base,  in  addition  to  the  cost 
of  the  riles,  should  not  exceed  25  cts  per  sq  ft. 


Floor-Tiles 


Kinds  of  tiles 


Common  encaustic  tiles,  unglazed 

Vitreous  tiles,  white . . ; 

Colors,  large  sizes 

Ceramic  tiles,  or  ceramic  Roman  mosaic 


Factory  price 
per  sq  ft 


IS  cts 
22 Ho  cts 
from  23  to  26  cts 
from  20  to  35  cts 


Wall-Tiles  and  Mantel-Tiles 


Kinds  of  tiles 


White  glazed  wall-tiles 

Colored  glazed  or  enameled  tiles '. 

Enameled  tiles,  dull  satin-finish 

Marbleithic,  from  45  cts,  upwards,  laid 
Hand-made  faience,  plain  colors 


Factory  price 
per  sq  ft 


23  cts 
35  cts 
sects 


trom  $0.60  to  $1 


Flooring  of  Mosaic,  Terrazzo,t  etc. 

Flooring  of  Mosaic  Work  is  largely  used.  (See,  also,  Ceramic  Tiles,  or 
Ceramic  Roman  Mosaic,  page  1605..  and  Marbleithic  Tiles,  page  1606.)  It  is 
composed  of  small  pieces  of  stone,  marble,  pottery  or  glass,  usually  laid  in  some 
ornamental  design  or  pattern.  A  bed  of  concrete  is  first  laid  and  the  small 
pieces  of  the  material  used  set  in  a  floating  of  cement  and  made  from  M2  to  i  in 
thick.  When  cubes  of  varicolored  marble  are  used,  pressed  into  the  cement 
mortar  it  is  called  Roman  Mosaic.  A  somewhat  cheaper  flooring  is  made  by 
spreading  marble  chips  of  irregular  shape  over  the  surface  of  the  cement, 
pressing  them  into  it  with  plasterers'  floats  and  rolling  them  with  iron  rollers. 
This  is  called  Terrazzo  Mosaic.  The  following  is  from  the  specifications  for 
the  new  Field  Museum,  Chicago,  III,  D.  H.  Burnham,  architects:  ''Filling 
under  terrazzo  shall  be  composed  i  part  cement,  2  parts  sand  and  4  parts  brick. 
Before  concrete  filling  commences  to  set  spread  a  3/4-in  weanng  surface  composed 
of  marble  chips  with  only  enough  neat  Portland  cement  to  firmly  umte  the 
nieces  Trowel  and  roll,  and  after  the  mortar  has  set,  rub  the  terrazzo  to  a 
smooth,  even  surface  and  wash  clean."  "Terrazzo  floors  in  the  East  cost  from 
20  to  30  cts  per  sq  ft,  contractor's  profit  included." t 

*  These  prices  have  advanced  and  the  manufacturers'  lists  must  be  consulted. 

t  See  article  on  Terrazzo  Floors,  by  C.  R.  Marsh,  in  Journal  of  the  Society  of  ConstruQ- 
tors  of  Federal  Buildings,  July ,19 14. 

X  Quoted  from  The  New  Estimator,  by  William  Arthur,  1914, 


1608  Asphaltum  Part  3 

ASPHALTUM 

Bitumen,  Asphaltum,  Asphalt.  "Bitumen  is  the  name  used  to  denote  a 
group  of  mineral  substances,  composed  of  different  hydrocarbons,  found  widely 
diffused  throughout  the  world  in  a  variety  of  forms  which  grade  from  thin  vola- 
tile liquids  to  thick  semifluids  and  soHds,  sometimes  in  a  free  or  pure  state,  but 
more  frequently  intermixed  with  or  saturating  different  kinds  of  inorganic  or 
organic  matter.  To  designate  the  condition  under  which  bitumen  is  found, 
different  names  are  employed;  thus  the  liquid  varieties  are  known  as  naphtha 
and  PETROLEUM,  the  semifluid  or  viscous  as  maltha  or  mineral  tar,  and  the 
solid  or  compact  as  asphaltum  or  asphalt.  "  *  • 

Asphaltum  is  found  in  extensive  beds  or  lake-like  deposits  on  both  continents; 
the  most  notable  of  these  are  the  pitch  lakes  on  the  island  of  Trinidad,  and  at 
Bermundez,  Venezuela.  It  is  also  found  saturating  the  limestone  and  sand- 
stone formations  in  certain  localities.  Deposits  of  very  nearly  pure  asphaltum 
are  found  in  Utah,  Mexico,  Cuba,  and  various  parts  of  the  United  States. 
Elaterite,  gilsonite  and  wurtzilite  are  varieties  of  very  nearly  pure  asphal- 
tum. 

Asphaltic  Roofing-Materials  are  manufactured  principally  from  Trinidad 
asphalt.  These  deposits  have  also  been  the  main  source  of  supply  for  the  as- 
phaltum used  in  street-paving  in  the  United  States. 

Rock-Asphalt.  The  term  rock-asphalt  is  commonly  used  to  designate  the 
material  obtained  from  the  bituminous  hmestone  deposits  at  Seyssel  and  Pyri- 
mont,  in  the  valley  of  the  Rhone,  France,  in  the  Val-de-Travers,  canton  of 
Neuchatel,  Switzerland,  and  at  Ragusa,  on  the  island  of  Sicily.  It  is  extensively 
employed  for  paving  purposes  throughout  Europe,  and  is  considered  to  make  a 
much  more  durable  pavement  than  can  be  made  with  asphaltum.  Rock- 
asphalt  is  prepared  for  shipment  in  two  forms:  (i)  compressed  asphalt  blocks, 
which  are  used  for  paving  in  much  the  same  way  as  stone  blocks,  and  (2)  mastic- 
asphalt,  which  is  put  up  in  cakes  of  varying  shape,  generally  bearing  the  manu- 
facturer's trade-mark. 

Mastic-Asphalt.  In  the  Eastern  States  mastic-asphalt  is  used  for  floors  of 
cellars,  stores,  breweries,  malt-houses,  hotel-kitchens,  stables,  laundries,  con- 
servatories, public  buildings,  carriage-factories,  sugar-refineries,  mills,  rinks,  etc., 
and  for  any  place  where  a  hard,  smooth,  clean,  dry,  fire-proof  and  water-proof, 
odorless  and  durable  covering  of  a  light  color  is  required,  either  in  the  basement 
or  upper  stories.  It  can  be  laid  over  cement  concrete,  brick,  or  wood,  in  one 
sheet  without  seams;  also  over  cement  concrete  for  roofs  for  fire-proof  buildings. 
For  dwelling-house  cellars,  especially  on  moist  or  filled  land,  this  material  is 
especially  adapted,  being  water-tight,  non-absorbent,  free  from  mold  or  dust, 
impervious  to  sewer-gases,  and  for  sanitarj'  purposes,  invaluable.  Mastic- 
asphalt  is  also  valuable  for  damp-courses  over  foundations,  and  for  covering 
vaults  and  arches  under  ground. 

Asphalt  Floors  and  Pavements.  For  floors  of  cellars,  courtyards,  etc., 
laid  on  the  ground,  a  base  of  cement  concrete  3  in  thick  should  first  be  laid;  and 
over  this  a  layer  of  asphalt  from  %  in  to  lYz  in  thick;  according  to  the  use  to 
which  it  is  to  be  put.  For  ordinary  cellar-floors,  the  asphalt  need  not  be  more 
than  %  in  thick;  for  yards  on  which  heavy  teams  are  to  drive,  it  should  be 
ly^  in  thick.  In  specifying  asphalt  pavement,  both  the  thickness  of  the  concrete 
and  of  the  asphalt  should  be  given;  it  should  also  be  remembered  that  asphalt 
pavement  does  not  include  the  concrete  foundation  unless  so  specified.    In 

*  Byroe,  Inspectors*  Pocket  Book. 


Mineral  Wool  1609 

laying  asphalt  over  planks  or  boards,  a  layer  of  stout,  dry,  but  not  tarred,  sheath- 
ing-paper  should  first  be  put  down  and  the  asphalt  laid  on  this.  Asphalt  floors 
for  stables  should  be  at  least  i  in  thick.  Architects  and  owners  desiring  to  em- 
ploy ROCK-ASPHALT  for  any  of  the  above  purposes  should  be  careful  to  secure  the 
genuine  Val-de-Travers,  Seyssel,  or  Sicilian  rock-asphalt,  as  there  are 
imitations  which  are  of  but  little  value. 

The  Bituminous  Sandstones  of  California  have  been  extensively  used  for 
paving  streets  in  Western  cities.  They  are  prepared  for  use  as  paving-materials 
by  crushing  to  powder.  With  this  powder  a  considerable  proportion  of  sand 
or  gravel  is  generally  mixed  and  the  mixture  heated  until  it  becomes  plastic;  it 
is  then  spread  over  the  roadways  and  compressed  by  roUing. 

MINERAL    WOOL 

Sources  of  Mineral  Wool.  There  are  at  least  two  kinds  of  mineral  wool 
made  in  this  country.  The  more  common  quality  is  made  by  mixing  certain 
kinds  of  stone  with  the  molten  slag  from  blast-furnaces  and  converting  the 
whole  mass  into  a  fibrous  state.  The  best  slag  for  the  purpose  is  that  which  is 
free  from  iron.  The  appearance  of  the  finished  product  is  much  like  that  of 
wool,  being  soft  and  fibrous,  but  in  no  other  respect  are  the  materials  alike. 
Mineral  wool  made  from  slag  appears  in  a  variety  of  colors,  principally  white, 
but  often  yellow  or  gray,  and  occasionally  quite  dark.  The  color,  however,  is 
said  to  be  no  indication  of  the  quality,  as  all  of  the  peculiar  properties  of  the 
material  are  present  in  equal  proportions  in  any  of  the  shades.  The  other  kind 
of  mineral  wool  is  known  as  rock-wool,  and  is  made  from  granite  rock  raised  to 
3  000°  F.  It  is  claimed  that  as  it  is  absolutely  free  from  sulphur,  it  is  the  only 
odorless  wool  manufactured.  It  has  been  approved  by  the  United  States  War 
Department.  It  has  the  same  general  appearance  as  that  made  from  slag,  and 
is  white  in  color. 

Nature  of  Mineral  Wool.  Both  of  these  materials  consist  of  a  mass  of  very 
fine,  pliant,  but  inelastic,  vitreous  fibers  interlacing  in  every  direction  and 
forming  an  innumerable  number  of  minute  air-cells.  Its  great  value  in  the  insu- 
lation and  protection  of  buildings  lies  in  the  number  of  air-cells  which  it  contains, 
its  consequent  non-conduction  of  heat,  and  its  fire-resisting  quahties.  In  wool 
made  from  common  slag,  92%  of  the  volume  consists  of  air  held  in  minute  cells, 
while  in  the  best  grade  the  proportion  of  air  reaches  as  high  as  96%.  This  con- 
fined air  makes  it  one  of  the  best,  if  not  the  best,  of  the  non-conductors  of  heat. 
Aside  from  these  qualities  it  is  very  durable  and  contains  nothing  that  can  decay 
or  become  musty.  Being  itself  incombustible  it  greatly  retards  the  burning  of 
wooden  floors  or  partitions  if  their  inner  spaces  are  filled  with  it. 

Uses  of  Mineral  Wool.  The  greatest  value  of  this  material  is  as  an  insula- 
tor of  heat,  but  it  is  also  a  valuable  non-conductor  of  sound.  It  is  the  general 
opinion,  however,  that  it  can  be  considered  only  as  a  muffler  of  the  sound- 
waves, for  there  seems  to  be  no  practical  way  in  which  it  can  be  used  so  as  to 
separate  entirely  the  floor  and  ceiling.  It  would  be  crushed  by  laying  floor- 
cleats  upon  it.  As  a  muffler  or  filling  between  the  beams,  however,  there  is 
probably  nothing  that  is  superior.  In  the  end,  then,  it  would  seem  that  the 
most  complete  insulation  from  sound,  without  separate  beams,  would  be  obtained 
by  FLOATING  the  flooring  on  some  material  like  Cabot's  Quilt  or  on  a  very  thick 
felt,  with  the  spaces  between  the  floor-cleats  filled  with  mineral  wool. 

Manner  of  Applying  Mineral  Wool.  Mineral  wool,  when  used  alone  as 
floor-deadening,  may  be  laid  on  boards  cut  in  between  the  joists,  or  on  top  of 
sheathing-lath  when  that  material  is  used.    The  wool  should  be  at  least  2  in 


1610  Mineral  Wool  Part  3 

thick.  Again,  mineral  wool  is  particularly  desirable  for  filling  the  spaces  between 
the  studs  of  outside  walls  and  partitions  and  between  the  rafters  of  roofs.  It 
may  be  used  to  great  advantage,  also,  in  partitions  around  bath-rooms  or  water- 
closets,  and  around  water-pipes  when  placed  in  partitions.  In  outside  walls 
and  attic  roofs,  as  a  protection  from  the  heat  of  summer  or  the  cold  of  winter, 
it  is  of  the  greatest  value.  By  lathing  the  under  side  of  the  rafters  with  sheath- 
ing-lath,  and  spreading  on  top  a  layer  of  2  or  3  in  of  mineral  or  rock-wool,  the 
comfort  of  the  room  is  greatly  increased.  Flat  roofs  over  inhabited  rooms  may 
be  covered  with  rough  boards  and  i^4-in  cleats  nailed  on  top,  the  spaces  filled 
with  wool,  and  the  roof-sheathing  then  nailed  to  the  cleats.  This  not  only 
greatly  increases  the  comfort  of  the  rooms,  but  greatly  retards  the  progress  of 
fire  from  the  outside.  When  insulating  against  heat,  nails  driven  through  the 
insulating  material  do  no  harm.  When  using  mineral  wool  in  floors  it  should  be 
packed  in  very  closely,  but  not  jammed  so  as  to  break  the  fibers,  which  are 
naturally  very  brittle.  In  partitions  it  is  packed  between  the  studs  and  laths, 
so  as  to  completely  fill  the  spaces,  the  wool  being  put  in  after  the  lathing  has 
reached  a  height  of  2  or  3  ft.  More  laths  are  then  put  on,  the  spaces  filled,  and 
so  on  to  the  top.  The  wool  should  not  be  dropped  from  any  considerable  height, 
as  the  breaking  up  of  the  fibers  destroys  the  insulating  q;ialities  of  the  material. 
In  fact  the  tendency  of  mineral  wool  to  settle  and  consolidate,  if  improperly  or 
too  loosely  packed,  is  the  only  drawback,  except  cost,  to  its  use  for  insulation. 
The  wool  behind  the  lathing  will  not  prevent  the  plaster  from  keying.  "■ 

Cost  of  Mineral  Wool.  Mineral  wool  is  sold  by  the  pound,  and  in  estimat- 
ing the  quantity  of  wool  required,  i  lb  per  sq  ft  of  filling,  i  in  thick,  should  be 
allowed  for  ordinary  wool  and  ^4  lb  for  selected  wool. 


Estimating  the  Cost  of  Buildings  1611 


ESTIMATING  THE  COBT  OF  BUILDINGS  * 

Cost  of  Buildings  per  Cubic  Foot.  The  method  of  cUBIC-foot  vai.uje3 
has  been  used  more  than  any  other  in  estimating  the  cost  of  any  proposed 
building,  before  the  plans  and  specifications  are  sufficiently  complete  for  tailing 
off  the  actual  quantities.  '*  Comparison  of  unit  costs  is  the  onlx  scientific 
criterion  by  which  to  judge  the  economic  merit  of  a  structure,  a  machine  or  a 
method  of  doing  work."  f  Two  buildings  in  the  same  city,  or  district  built 
in  the  same  style  and  for  the  same  purpose,  of  the  same  materials,  and  on  the 
same  scale  of  wages  and  prices  of  materials,  should  cost  the  same,  or  very  nearly 
the  same,  per  cubic  foot,  although  one  building  may  be  somewhat  larger  than  the 
other  and  of  different  shape.  It  therefore  follows  that  if  we  know  the  cost  per 
CUBIC  foot  of  different  classes  of  buildings,  in  different  localities,  we  can  approx- 
imate quite  closely  the  cost  of  any  proposed  building  by  multiplying  its  cubic 
contents  in  feet  by  the  known  cost  per  cubic  foot  of  a  similar  building  already 
built  in  that  locality. 

Size  of  Building  Proportioned  to  Cost  per  Cubic  Foot.  If  the  cost  of 
a  proposed  building  must  be  kept  absolutely  within  a  certain  sum,  the  size  of 
the  building  should  be  proportioned  so  that  the  cubic  contents  shall  not  ex- 
ceed the  quotient  obtained  by  dividing  the  amount  appropriated  by  the  average; 
cost  per  cubic  foot  of  similar  buildings.  Even  then  it  may  be  found,  wheiji 
the  bids  are  opened,  that  they  exceed  the  appropriajiion;  but  the  excess  is  ofteif 
a  relatively  small  percentage  of  the  total  cost  and  the  necessary  r/c4^<^U9^§  ^^^ 
be  made  without  altering  the  main  features  of  the  building. 

Methods  of  Computation.  In  estimating  the  cost  by  the  methop  of  cubic 
contents,  it  is  of  course  necessary  that  the  contents  be  computed  on  the  same 
basis,  in  both  the  proposed  building  and  the  one  already  built.  The  cubic 
contents  are  generally  computed  from  the  basement  or  cellar-floor,  to  the  aver- 
age height  of  a  flat  roof,  or,  if  there  is  a  pitched  roof,  the  finished  portion  of  the 
attic  is  included,  or  that  part  which  might  be  finished,  mere  air-spaces  and  open 
porches  not  being  included.  Vaults  and  areas  under  sidewalks,  etc.,  are  gen- 
erally included  as  part  of  the  basement.  All  measurements  are  to  the  outside 
f)i  the  walls  and  foundations.  The  estimated  cost  may  or  may  not  include  the 
fees  of  the  architect  and  other  experts. 

Other  Methods  of  Estimating  the  Cost  of  Buildings.  The  cost  of  build- 
ings, such  as  hospitals,  theaters,  schools,  churches,  barracks,  large  stables,  etc., 
is  sometimes  estimated  by  the  cost  per  bed,  sitting,  inmate,  etc.  Estimates 
are  also  based  upon  the  cost  per  square  foot  of  ground  occupied  or  of  all 
the  floor-space,  in  certain  types  of  buildings. 

*  The  editor  is  indebted  to  E.  S.  Hand  and  others  for  valuable  data  relating  to  this 
subject.  Readers  are  referred  to  the  Handbook  of  Cost  Data  for  Contractors  and 
Engineers,  by  H.  P.  GillettC:  The  New  Building  Estimator,  by  William  Arthur,  and  The 
Building  Estimator's  Reference  Book,  by  F.  R.  Walker.  Values  given  are  pre-war 
values  and  may  be  used  for  relative  costs. 

t  H.  P.  Gillette,  in  the  preface  to  his  Handbook  of  Cost  Data  for  Contractors  and 
Eagineers . 


1612  Estimating  tlie  Cost  of  Buildings  Part  3 

Data  *  on  Cubic-Foot  Values  as  a  Basis  for  Preliminary  Estimates 
'  of  Building  Costs 

Notes  on  Modifying  Conditions.  Buildings  of  a  given  type,  such  as  office- 
buildings  and  school-buildings,  when  similar  in  construction  and  finish  and  built 
under  similar  market-conditions  as  to  cost  of  labor  and  materials,  are  found  to 
be  nearly  identical  in  cubic-foot  costs.  The  buildings  of  any  such  type  do  not 
differ  widely  in  bulk,  and  this  is  always  very  considerable  when  compared  with 
such  structures  as  dwellings  and  small  business  buildings.  This  seems  only 
another  way  of  saying  that  similar  causes  produce  similar  effects,  but  it  goes  a 
step  farther  by  indicating  that  the  results  here  are  virtually  identical;  so  nearly 
so,  that  the  average  cubic-foot  cost  of  a  certain  kind  of  building  can  be  relied 
on  to  produce  an  estimate  within  from  3  to  5%  of  the  actual  cost  of  new  work  of 
the  same  kind  and  under  the  same  conditions.  Other  types  of  large  structures, 
such  as  public  buildings,  hotels,  churches  and  theaters,  are  less  subject  to  stand- 
ardization because  more  variable  in  equipment  and  finish.  This  is  true  also  of 
dwellings,  shops  and  other  small  structures  whose  lesser  bulk,  moreover,  renders 
even  less  possible  a  close  prediction  as  to  their  cost.  These  uncertainties  do  not, 
however,  warrant  the  rejection  of  the  cubic-foot-cost  method  for  preliminary 
estimating.  They  do  indicate  that  it  is  less  closely  approximate  for  some  types 
than  for  others.  But  the  degree  of  uncertainty  on  even  the  most  variable 
types  may  be  minimized  and  should  be  reduced  to  perhaps  10%  under  a  careful 
system  of  cost-computation.  Such  system  should  cover  a  considerable  number 
of  examples,  taking  account  of  all  factors  of  material  influence  upon  cost  in  each 
type,  and  must  follow  a  consistently  uniform  method  of  determining  cubic-foot 
values. 

The  Factors  Which  Influence  Cost  include  the  following. 

(i)  Prevailing  market  prices  of  labor  and  materials. 

(2)  Type  of  construction  employed,  depth  and  kind  of  foundations  and  exist- 

ence of  special  features  such  as  towers  or  domes. 

(3)  Finish:  external  facing  and  ornamentation;  internal  surfacing  and  deco- 

ration. 

(4)  Equipment:   {a)  number  and  complexity  of  heating,  lighting,  ventilating, 

sanitary,  elevator  and  other  systems;  (b)  extent  to  which  apparatus 
or  equipment,  such  as  laboratory-devices,  opera-chairs,  bank-counters, 
etc.,  is  provided  for  direct  use  of  occupants  of  building. 

(5)  Fees  of  architect  and  other  experts. 

(6)  Locality.     Costs  of  structures  of  a  given  type  will  vary  with  the  locality 

because  of  differing  standards  of  practice  and  building  laws,  availability 
of  building  materials,  labor,  etc. 

(7)  Other  items,  developing  in  the  experience  of  the  architect. 

The  Method  of  Determining  Cubage  may  either  simply  recognize  the 
geometrical  volume  of  the  building  or,  better,  may  employ  a  coefficient 
OF  value  for  any  part  whose  cost  varies  materially  from  the  average.  The 
latter  method  may  be  preferred  as  allowing  a  closer  calculation  of  variations 
from  known  examples.  For  instance,  an  unfinished  cellar  or  other  story. or  a 
small  light-court  would  cost  less  per  cubic  foot  than  the  remainder  of  the  build- 

*  The  data  on  this  page  and  page  1613  on  cubic -foot  values  are  quoted,  by  permis- 
sion, from  notes  relating  to  this  subject,  compiled  by  Professor  Warren  P.  Laird  from 
the  study  of  a  large  number  of  public  and  private  buildings  erected  in  widely  separated 
districts  of  the  United  States.  For  these  buildings  Professor  Laird  acted  as  the  profes- 
sional adviser  for  the  selection  of  the  architect,  and  in  all  cases  the  estimate  of  the  cost 
of  the  buildings  was  based  strictly  upon  a  total  number  of  cubic  feet  and  a  fixed  unit 
cost  per  cubic  foot. 


Unit  Costs  of  Buildings     -  1613 

ing,  while  a  tower  or  dome  of  finished  basement  containing,  also,  an  expensive 
mechanical  plant,  would  cost  more.  Foundations  sometimes  cost  so  much 
that  they  require  figuring  to  their  full  depths  as  though  the  finished  building 
were  carried  down  to  that  level. 

Cubic-Foot  Costs.  Subject  to  the  foregoing  considerations,  the  following 
data  on  fire-proof  l)uildings  were  average  pre-war  values.  These  unit  prices  no 
longer  prevail  as  labor  and  materials  have  in  some  cases  almost  doubled  in  cost 
since  the  war.  The  values  must  be  increased  from  50  to  100%,  depending  upon 
the  kind  of  building. 

Construction:  steel  and  terra-cotta,  stone  and  brick  facings,  complete  equip- 
ment  and  superior  grade  of  interior  finish: 

Office-buildings 32  to  35  '- '  ^ 

PubHc  buildings 40  to  45  ' 

School-buildings 20  to  25 

Construction:  reinforced  concrete;  facing,  common  brick;  equipment,  type 
usual  in  such  structures;   inside  finish,  the  simplest. 

Typepibiuing'   'V;    "         '    '       ^      ^^^^^^ 

Factories  f 14  to  16 

Lofts  t 15  to  18 


Table  for   Estimating    Roughly  the    Approximate  Cost  of  Some  Small 

Buildings  '     * 

Based  on  prices  for  labor  and  materials  in  1920.  The  cost  of  first-class  fire- 
proof buildings  is  greater  in  the  Western  and  Southern  States  than  in  the  Eastern 
States,  because  of  the  distance  from  the  great  steel  and  material-centers. 

Farm  and  Country  Property 

Cost  per 

cubic  foot, 

cents 

Dwellings,  frame;  small  box  house,  no  cornice 10 

DwelUngs,  frame;   shingle  roof,  small  cornice,  no  sash  weights,  plain.  12  to  14 

Dwellings,  brick;  same  class 16  to  18 

DwelUngs,  frame;    shingle  roof,  good  cornice,  sash  weights,  bHnds 

(good  house) 16  to  18 

Dwellings,  brick;  same  class  (good  house) 20  to  22 

Barns,  frame;  shingle  roof,  not  painted,  plain  finish 4  to    6 

Bams,  frame;  shingle  roof,  painted,  good  foundation 6  to    8 

Stores,  frame;  shingle  roof,  painted,  plain  finish 12  to  16 

Stores,  brick;  shingle  roof,  painted,  good  cornice,  well  finished 16  to  20 

Ordinary  frame  churches  and  school  houses;   country .  12  to  16 

*  These  pre-war  values  must  be  increased  from- 50%  to  100%,  depending  upon  the  kind 
of  building. 

t  If  such  subcontracts  as  plumbing,  heating,  lighting-fixtures,  elevators,  etc.,  are  not 
included,  of  course  these  figure?  were  reduced.  See  Cost  of  Reinforced-Concrete  Build- 
ings, page  1618: 


1614  Estimating  the  Cost  of  Buildings  Part  3 

Coss  per 

cubic  foot, 

cents 

Brick  churches  and  schoolhouses;  country i8  to  22 

If  the  roofs  are  slate  or  metal,  add  %  ct  per  cu  ft. 

City  and  Village  Property 

Dwellings,  frame;   shingle  roof,  pine  floors  and  finish,  no  bathroom 

or  furnace,  plain  finish  (good  house) 14  to  16 

Dwellings,  brick;  same  class j8  to  20 

Dwellings,  frame;    shingle  roof,  hard- wood  floor  in  hall  and  parlor, 

bath,  furnace,  and  fair  plumbing 18  to  20 

Dwellings,  brick;  same  class 18  to  23 

Dwellings,  frame;  shingle  roof,  hard-wood  in  first  story,  good  plumb- 
ing, furnace,  artistic  design,  some  interior  ornamentation,  well 

painted 22  to  26 

Dwellings,  brick;  with  good  plumbing,  bath,  hot  and  cold  water,  pine 
finish,  well  painted,  no  hard- wood  finish. 24  to  26 

Examples  of  Actual  Costs  of  Pre-war  Buildings  per  Cubic  Foot 

In  order  to  illustrate  the  subject  further,  examples  of  buildings  erected 
before  the  war  are  given.  The  lists  were  furnished  through  the  courtesy  of  the 
architects  of  the  buildings.  Such  lists  could  be  indefinitely  extended,  but  those 
submitted  are  deemed  sufficient  to  give  some  idea  of  the  similarities  and  varia- 
tions of  costs  based  upon  cubage.  With  the  exception  of  reinforced-concrete 
buildings,  it  is  probably  true  that  for  twenty  or  twenty-five  years  (1890  to  191 5) 
the  cost  of  buildings  increased,  with  some  variations  in  the  rate  of  increase,  at 
the  rate  of  about  i  %  per  year.  Costs  have  increased  since  the  war  from  50  to 
i®o%,  depending  upon  the  kind  of  building. 


Unit  Costs  of  Buildings 


1615 


Examples  of  the  Actual  Cost  of  Pre-war  Buildings  per  Cubic  Foot 
These  buildings  were  designed  by  Boring  &  Tilton 


Approx- 

Cost per 

Name  and  location  of  building 

Date 

Height  and  type 

imate 
cost 

cubic 
foot, 
cents 

Memorial  Hall,  Tome  Insti- 

1900 

Three  stories  and  base- 

$150 000 

16 

tute,  Port  Deposit,  Md. 

ment,  fire-proof 

West   Side   Branch   Library, 

1908 

One  story  and  basement. 

85  000 

17 

Cleveland,  Ohio 

non-fire-proof 

Stamford   Grammar  School, 

1908 

Two   stories   and   base- 

50000 

15 

Stamford,  Conn. 

ment,  non- fire-proof 

St.  Agatha's  School,  87th  St. 

1907 

Six  stories  and  basement. 

275000 

29 

and  West  End  Ave.,  New 

fire-proof 

York  City 

American    Seamen's    Friend 

1909 

Five  stories  and   base- 

200 000 

32 

Society,  Jane  and  West  Sts., 

ment,  fire-proof 

New  York  City 

Eastern      District      Branch 

1906- 

Six    stories    and    base- 

255000 

27 

Y.M.C.A.,Brooklyn,N.Y. 

1909 

ment,  fire-proof 

Tarry  town  Hospital,  Tarry- 

1910 

Two   stories   and   base- 

65 000 

26 

town,  N.  Y. 

ment,  non-fire-proof 

Blair  Hospital,  Huntingdon, 

1909 

Three  stories  and  base- 

90 000 

20 

Pa. 

ment,  fire-proof 

Elizabeth  Library,  Elizabeth, 

1912 

Three  stories  and  base- 

100 000 

35 

N.J. 

ment,  fire-proof 

Springfield  Library,  Spring- 

1908 

Two  stories,  mezzanine 

350000 

35 

field,  Mass. 

and  basement,  fire-proof 

Sioux    City    Library,    Sioux 

1912 

Two   stories   and   base- 

75000 

21 H 

City,  Iowa 

ment,  non-fire-proof 

521  Park  Avenue,  New  York 

1912 

Twelve  stories  and  base- 

350000 

45 

City 

ment,  fire-proof 

United     States     Immigrant 

1898 

Two   stories   and   base- 

625000 

n\^ 

Station,  Ellis  Island,  New 

ment,  fire-proof 

York  Harbor.    Main  build- 

ing 
Hospital  building 

1898 

Three  stories  and  base- 
ment, fire-proof 

150  000 

28 

Mount    St.    Mary's    College, 

1912 

Three  stories  and  base- 

250 000 

22 

Plainfield,  N.  J. 

ment,  fire-proof 

vitD  ??ToT  • 


1616  Estimating  the  Cost  of  Buildings 

These  buildings  were  designed  by  Palmer,  Hombostle^  &  Jones 


Part  3 


Name  and  location  of 
building 

Date 

Notes 

Cubic 

contents, 

cubic 

feet 

Approx- 
imate 
cost  * 

Cost*  per 
cubic 
foot, 
cents 

Oakland  City  Hall,  Oak- 
land, Cal. 

Allegheny  County  Sol- 
diers' Memorial,  Pitts- 
burgh, Pa. 

New  York  State  Educa- 
tion Building,  Albany, 
N.  Y. 

1914 
1911 
1912 

Based  on  all  con- 
tracts except  for 
lighting-fixtures 

2  999  442 
2  855  892 
II  281  691 

$1  400  000 

913  721 

3  744  521 

46^6 
32 

33H 

Original  contract 
completed,  Dec. 
1912 

These  buildings  were  designed  by  Robert  D.  Kohn 


Name  and  location  of 
building 


Date 


Height,  character  of  construction 
and  finish 


Hermitage     Hotel,     New 
York  City. 


Trades    School    Building, 
Manassas,  Va. 


Ethical   Culture   Meeting 
House. 


1907 


1910 


'.n-j-Ai 


1910 


Size  of  lot,  so  by  100  ft;  height,  150 
ft;  15  bedrooms  and  11  baths 
on  each  floor;  basement  and  sub- 
basement;  power,  electric  light 
and  refrigerating-plants;  complete 
kitchen-equipment;  brick  and 
limestone  exterior;    cement  floors. 

Main  wing,  50  by  100  ft,  two  and  one- 
half  stories;  shop-wing,  75  by  105 
.,.  ft,  one  story,  brick;  shops,  mill- 
1^., constructed  roof,  cement  floor; 
brick  exterior  throughout;  heating- 
plant  in  extension;  common  wood- 
en-floor construction,  tin  roof,  class- 
rooms plastered;   cheaply  built. 

Height,  100  ft;  basement,  assembly- 
room;  main  floor,  auditorium  for 
I  200  people;  two  stories  above  audi- 
torium, Sunday  school  and  offices; 
limestone  exterior;  fire-proof  con- 
struction; oak  finish. 


Cost  *  of  Some  Notable  Buildings  in  New  York  City.  Some  of  the  more 
prominent  buildings  in  the  Borough  of  Manhattan,  City  of  New  York,  are  in- 
cluded in  the  following  table.  For  all  these  structures  the  costs  per  cubic  foot 
are  given.  By  reason  of  its  height  the  Woolworth  Building  may  be  considered 
the  most  notable  of  the  list.  It  is  not  only  the  highest  building  in  New  York 
City  or  the  United  States,  but  in  tlie  world.  The  cubic  contents  total  nearly 
12  000000  cu  ft.  Its  foundations  are  carried  to  rock,  which  is  about  120  feet 
below  the  street-surface.  The  approximate  weight  of  its  steel  frame  is  23  000 
tons. 


Unit  Costs  of  New  York  Buildings 


1617 


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1618 


Estimating  the  Cost  of  Buildings 


Part  3 


The  Grand  Central  Station,  as  a  complete  terminal,  is  a  very  complex  struc- 
ture, but  there  is  a  distinct  part  which  contains  the  passenger-concourse  and  the 
waiting-rooms,  restaurant  and  other  parts  that  are  considered  necessary  to  care 
for  the  traflBc.  The  cubic  contents  of  this  part  total  about  14  000  000  cu  ft. 
Other  ])art5  of  the  building  are  not  considered  in  the  present  reference.  Some 
interesting  facts  as  to  the  main  station,  only,  are: 

Cost, *  about. .  .  i $8  000  000 

Ground-area  above  street-level,  square  feet 266  000 

Additional  station-facilities  under  street,  square  feet 80  000 

Floor-area  devoted  to  station-purposes,  square  feet i  188  000 

Cubic  contents,  about,  cubic  feet 32  857  800 

Steel  used  in  construction,  tons 35  767 

Weight  of  largest  girder  used,  tons 30 

Costs*  of  Pre-war  Reinforced-Concrete  Buildings. fi  In  judging  the  cost 
of  a  building  by  cubical  content  or  by  areas  of  floors  the  shape  of  the  build- 
ing in  plan  should  be  taken  into  consideration.  A  long,  narrow  building  will 
cost  more  per  cubic  or  sqliare  foot  than  one  more  nearly  square  in  plan;  and  in 
computing  costs  by  the  cubic-foot  or  square-foot  unit  prices  these  conditions 
as  well  as  the  judgment  and  experience  of  the  architect  or  engineer  who  makes 
the  estimates  affect  the  accuracy  of  the  results.  The  following  notes  quoted 
from  data  furnished  by  the  architects  and  engineers  of  the  buildings  mentioned 
include  useful  information  relating  to  costs  of  some  reinforced-concrete  buildings 
of  different  types,  erfccted  in  Philadelphia  and  vicinity  (1906-19 15). 

(1)  *  A  reinforced-concrete  building  of  the  factory-type,  erected  (i 914-15) 
in  the  City  of  Philadelphia.  It  is  a  concrete  cage,  with  no  brick  veneer,  four 
st  )ries  in  height,  no  basement,  size,  60  by  159  ft,  stair-shafts  and  elevator- 
shafts  projecting  beyond  the  building;  cubical  contents,  603  000  cu  ft.  The 
cost,  without  equipment,  was  7K  cts  per  cu  ft.  Drainage  is  included  in  this 
price,  but  no  plumbing,  heating^  lighting  or  elevators.  The  total  floor-area  of 
the  building  is  40  140  sq  ft  and  the  cost  per  square  foot  is  $1.1414.  This  is  built 
according  to  the  building  laws  of  Philadelphia. 

(2)  "A  mill-con.structed  building,  about  the  same  size  as  building  (i), 
recently  erected  in  a  manufacturing  town  forty  miles  from  Philadelphia.  It  is 
four  stories  in  height  and  has  a  part-basement,  a  wing  30  by  40  ft,  and  a  one- 
story  boiler-room  and  engine-room.  The  total  cubical  contents  are  524  160 
cu  ft,  and  the  cost,  6H  cts  per  cu  ft.  The  total  floor-area  is  37  gco  sq  ft,  and  the 
cost,  $0.85  H  per  sq  ft.  This  is  without  power^  heat,  or  light.  There  are  a  few 
plumbing-fixtures  in  this  building. 

"In  comparing  the  costs  of  the  two  buildings,  it  must  be  borne  in  mind  that 
one  is  located  forty  miles  from  Philadelphia,  and  was  not  erected  under  the 
rigid  building  laws  that  are  in  force  there.  It  is  usually  possible  to  erect  a 
building  of  any  type  at  less  expense  outside  of  Philadelphia  than  in  that  city 
and  this  can  probably  be  said  of  any  city  where  there  are  no  state  building  codes. 

(3)  "A  mill-constructed  building,  three  stories  in  height,  erected  in  1906 
in  Camden,  N.  J.,  and  having  575  044  cu  ft.  It  cost  7  cents  per  cu  ft.  It  has 
38  912  sq  ft  of  floor-area,  at  a  cost  of  $1.04  per  sq  ft.  This  price  is  without 
power,  heat,  Hght,  of  elevators,  but  includes  some  plumbing. 

(4)  "The  new  municipal  repair-shop  of  the  City  of  Philadelphia.  This  is  a 
reinforced-concrete  building  with  brick  veneer  of  an  ornamental  type,  and  cost 
9}^  cts  per  cu  ft  for  i  080  591  cu  ft  or  $1.74  per  sq  ft  for  57  323  sq  ft  of  total 

*  See  notes  on  costs  on  pa^  1614.     Prices  given  must  be  at  least  doubled  (1920). 
t  Valuable  data  on  ibis  subject  have  been  furnished  the  Editor  by  Ballinger  &  Perrot, 
the  architects  and  engineers  of  the  five  reinforced-cohcrete  buildings  described. 
1  See,  also,  page  1613. 


Division  of  Cost  of  Fire-Proof  Buildings  1619 

lloor-area.  This  is  without  plumbing,  power,  heat,  light,  or  elevators.  The 
relatively  high  cost  per  square  foot  for  this  building  is  due  to  the  fact  that  the 
crane  run-way  takes  up  a  considerable  portion  of  the  building,  so  that  a  floor 
is  omitted  where  the  crane  is  placed,  and  the  floor-area  accordingly  reduced. 

(5)  "The  new  building  for  the  Automobile  Club  of  Philadelphia.  This  is 
a  three-story  building,  of  reinforccd-concrete  cage-construction,  and  contains 
I  341  966  cu  ft,  at  a  cost  of  10%  cts  per  cu  ft.  The  total  floor-area  is  90  602 
sq  ft,  costing  $1.54  per  sq  ft.  This  is  without  power,  heat,  light,  or  any  equip- 
ment, but  includes  plumbing.  The  shape  of  this  building  favors  economy  o( 
construction,  as  it  is  nearly  square  in  plan." 

In  summing  up  the  conclusions  arrived  at  in  regard  to  the  average  costs  of 
reinforced  buildings,  E.  G.  Perrot  states  *  that  the  cost  can  best  be  considered 
by  classifying  them  under  three  general  heads: 

(i)  Warehouses  and  manufactories.     Cost,  from  8  to  11  cts  per  cu  ft. 

(2)  Stores  and  loft-buildings.     Cost,  frorh  11  to  17  cts  per  cu  ft. 

(3)  Miscellaneous  buildings,  such  as  school-houses,  hospitals,  etc.  Cost  from 
15  to  20  cts  per  cu  ft. 

Cost   of   Mills   and  Factories  Built   on  the  Slow-Burning   Principle. 

For  data  relating  to  total  and  unit  costs  of  buildings  of  this  type,  see  Chapter 
XXII,  pages  802  to  810., 

Percentages  of  Cost  of  Items  of  Construction  in  Fire-Proof  Buildings 

The  tables  t  on  the  following  six  pages  show,  on  pages  1620  to  1625,  the 
DIVISION  OF  THE  COSTS  of  fire-proof  buildings  among  the  different  materials  and 
parts  of  the  construction,  the  data  having  been  furnished  the  compiler  hy 
architects  and  builders  in  the  cities  mentioned  in  the  tables.  Each  column  of 
values  in  the  tables  gives  the  data  for  an  individual  building,  except  the  values 
for  New  York  City,  in  the  second,  third  and  fifth  columns,  which  show  the 
averages  for  a  large  numl^cr  of  buildings.  The  tables  on  the  first  four  pages 
include  only  buildings  approximating  closely  the  standard  specifications  of  the 
National  Board  of  Fire  Underwriters.  The  tables  show  that  the  foundations 
and  steel  frames,  the  Only  parts  little  damaged  in  conflagrations,  represent, 
approximately,  only  25%  of  the  entire  sound  value  of  a  building.  For  examplci 
in  the  tables  on  the  first  four  pages,  the  average  cost  of  all  the  foundations  is 
8%,  while  the  average  cost  of  the  steel  frames  is  17.88%.  The  tables  show, 
also,  on  pages  1624  and  1625  the  percentages  of  cost  of  the  classified  items  of 
construction  of  eight  buildings  damaged  by  the  Baltimore  conflagration  (1904)} 
the  averages  of  these  eight  buildings  being  given  in  the  last  column. 

*  See  "Comparative  Costs  of  Reinforced  Concrete  Buildings,"  by  E.  G.  Perrot,  in 
Proceedings  of  the  National  Association  of  Cement  Users,  Vol.  V,  1909.  See,  also,  notes 
on  costs  on  page  1614. 

t  The  tables  on  the  first  four  pages  were  compiled  by  F.  J.  T.  Stewart,  Continental 
Insurance  Company,  and  those  on  the  last  two  pages  by  the  Baltimore  Committee  of 
the  National  Board  of  Fire  Underwriters.  All  are  reproduced,  by  permission,  from  J.  K. 
Freitag's  Fire  Prevention  and  Fire  Protection.  Those  parts  of  the  Baltimore  tables 
which  gave  the  proportion  of  fire-damage  to  sound  value  of  the  various  items  have  been 
omitted  as  this  article  of  the  Pocket-Book  deals  more  especially  with  original  costs. 


1620 


Estimating  the  Cost  of  Buildings 


Part  3 


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Division  of  Cost  of  Fire-t*roof  Buildings 


1621 


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1622 


Estimating  the  Cost  of  Buildings 


Part 


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Division  of  Cost  of  Fire-Proof  Buildings 


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1624 


Estimating  the  Cost  of  Buildings 


Part 


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^Division  of  Cost  of  Fire-Proof  Buildings 


1625 


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1626 


Estimating  the  Cost  of  Buildings 


Part  3 


Costs  *  of  Different  Kinds  of  Work  per  Cubic  Foot  of  Building 

Some  estimates  f  have  been  made  by  F.  W.  Fitzpatrick  showing  the  propor- 
tionate COST  OF  THE  DIFFERENT  BRANCHES  OF  WORK  which  gO  tO  make  Up  3 

completed  building.  Believing  that  these  data  will  be  found  useful  in  making 
up  approximate  estimates,  Mr.  Kidder  obtained  permission  to  use  them  in  the 
Pocket-Book.  The  following  figures  represent  the  actual  cost  of  a  ten-stor^ 
OFFICE-BUILDING,  6o  by  130  ft  in  plan,  built  in  the  Middle  West,  a  first-class 
fire-proof  structure,  with  two  street-fronts  faced  with  granite  and  resting  on  a 
pile  foundation. 


Kind  of  work 

Per  cubic 
foot  of 
entire 

building, 
cents 

Kind  of  work 

Per  cubic 
foot  of 
entire 

building, 
cents 

Foundations 

1% 

2 

Ms 

Heating ; 

iH 

Steel  framing 

Plumbing  .   . 

Vi 

Granite  and  all  masoni-y .  . 
Cornice,    roofs    and    sky- 
lights  

Elevators 

I 

Stairs,    scenic    structural 
framing,  "making  ends 
meet,"       lamp-fixtures, 
etc.        What  might  be 
called  a  fair  amount  for 
"  contingencies  "         in 
such  a  building,  includ- 
ing lesser  items  net  men- 
tioned here  but  grouped 
together 

Fire-proof  floors 

Partitions,  tile 

All  plastering  and  stucco. . 
Elevator-fronts  and  all  oir- 

namental  metal  work 

Marble  work 

Hardware 

Joiners'  work 

42^20 

Glass 

Architect's  fee 

!•% 

Painting  and  varnishing. . . 
Electric  wiring 

Total 

34M2 

The  Chicago  post-office  building,  containing  12  000000  cu  ft  and  of  monu- 
mental character  and  finish,  cost,  *  in  some  of  its  items,  as  follows: 


Kind  of  work 


Foundations 

Steel  framing 

Granite  and  masonry 

Fire-proof  floors 

Plaster,   plain   and   orna- 
mental   


Per  cubic 
foot  of 
entire 

building, 
cents 


i94 

2\^ 

13H 


m 


Kind  of  work 


Ornamental  metalwork 

Marble 

Plumbing 

Heating 


Per  cubic 
foot  of 
entire 

building, 
cents 


2H 
1% 


It  will  be  noticed  that  the  relative  cost  of  several  .of  these  items  is  the  same 
•^.s  in  the  office-building.     The  total  cost  *  of  this  building  was  42^  cts  per  cu  ft. 
*  These  pre-war  figures  must  be  increased  from  50%  to  100%. 
t  Published  in  "  Fireproof^'^Mfrchj  1903, 


Cost  of  Buildings  per  Square  Foot  iSSt 

Cost  *  of  Buildings  per  Square  Foot 

One-Story  Buildings  of  Large  Area,  such  as  exposition-buildings,  etc., 
may  be  estimated  almost  as  accurately  by  the  square  foot  of  ground  covered  as 
by  the  cubic  foot  of  building,  as  there  are  few  or  no  interior  partitions,  and  usu- 
ally no  plastering  or  interior  finish. 

Iron  and  Steel  Buildings.  "Roughly  speaking,  the  cost  of  one-story  iron 
and  steel  buildings,  complete,  is,  for  sheds  and  storage-houses,  from  40  to  60  cts 
per  sq  ft  of  ground,  and  for  such  buildings  as  machine-shops,  foundries,  and 
electric-light  plants,  that  are  provided  with  traveling  cranes,  the  cost  is  from  60 
to  90  cts  per  sq  ft  of  ground  covered."  f 

Structural  Steel.  For  estimates  of  cost  of  structural  steel  for  buildings, 
see  pages  1204  to  1207. 

Wooden  and  Brick  Mills  and  Warehouses.  See  Chapter  XXII,  pages 
802  to  810. 

Exposition-Buildings.  The  cost  t  of  the  World's  Fair  buildings  (Chicago, 
1893)  per  square  foot  of  ground  covered,  including  sculpture  and  decoration, 
was  as  follows: 

Manufactures  and  Liberal  Arts  Building $1 .39 

Transportation  Building i .  08 

Electricity  Building i .  69 

Machinery  Hall 2.12 

Agricultural  Building i .  44 

Administration  Building 9.18 

Horticultural  Building i .  41 

Mines  and  Mining  Building i  .04 

Fisheries  Building 2.35 

Forestry  Building 0.75 

Cost*  of  Structures  for  the  St.  Louis  Exposition  (1904).  The  following 
figures  were  issued  by  Isaac  S.  Taylor,  at  that  time  Director  of  Works,  of  the 


Building 


Art 

Two  Art  Pavilions,  each 

Art  Building  Annex 

Government  Building 

Government  Fisheries 

Mines  and  Metallurgy 

Liberal  Arts 

Education  and  Social  Economy . . 

Manufactures 

Electricity 

Varied  Industries 

Machinery 

Steam,  Gas  and  Fuel 

Transportation • . 

Horticulture 

Agriculture 

Forestry,  Fish  and  Game 

Festival  Hall 


Dimensions, 

Area, 

Total  cost 

Cost. 

ft 

acres 

sq  ft 

161X346 
144X423 

1.42  1 
3.i4i 

S967  833.90 

$5.45 

106X150 

0.41 

39388.99 

2.48 

200X736 

3.86 

328980.00 

2.23 

136X136 

0.42 

45  000.00 

2.43 

525X750 

9.08 

488848.50 

1.24 

525X750 

8.80 

471  820.95 

1.20 

525X758 

7.70 

323950.75 

0.81 

525X1  200 

13.47 

711  510.00 

1. 13 

525X758 

6.67 

408531.57 

1.03 

525X1  200 

10.28 

704067.96 

1.12 

525X1  000 

51.48 

509  110.50 

0.97 

301X326^^ 

2.25 

135  480.00 

1.38 

525X1  300 

15.70 

674853.42 

0.99 

374X782 

5.42 

225342.27 

0.77 

500X1  600 

18.62 

520491.07 

0.58 

300X600 

4.07 

168883.38 

0.94 

195  in  diam- 

1 

eter,  exclusive 

?     109 

215899.00 

of  annex 

) 

eased  from  50^ 

I  to  100%. 

fH.  G 

.Tyrell.^ 

1628  Estimating  the  Cost  of  Buildings  Part  3 

World's  Fair,  showing  the  area  and  cost  of  the  principal  exhibition-buildings. 
The  total  area  of  twenty-two  buildings  was  123.51  acres,  and  the  total  cost 
$6  939  992.26.  The  cost  was  for  the  bare  buildings,  and  did  not  include  sculp- 
tural or  other  decorations,  or  the  architects'  compensation. 

Recent  Exposition  Buildings.  The  cost  of  buildings  of  this  character, 
erected  since  1904,  shows  a  pretty  general  increase  up  to  19 14,  with  occasional 
variations  in  the  rate  of  change,  of  from  i  to  2%  per  year.  Increase  since  1914 
would  be  from  50  to  100%. 

Cost  *  of  United  States  Government  Buildings.  There  was  published  in 
1900,  by  the  United  States  Treasury  Department,  a  history  of  the  public 
buildings  of  the  United  States,  giving  their  cost,  and  in  1902,  there  was  pub- 
lished t  a  list  of  287  buildings,  giving  the  cost  per  cubic  foot,  the  material 
used  for  the  walls  and  the  date  of  erection.  There  was  also  published,  in  1910, 
by  the  Committee  on  Public  Buildings  and  Grounds  of  the  United  States  Senate, 
a  list  of  sites  and  plans  for  pul^lic  buildings,  giving  data  of  much  value  in  regard 
to  the  cost  of  public  buildings,  their  cubical  contents  and  their  cost  per  cubic 
foot,  including  buildings  erected  from  1816  to  1910.  "As  a  rule,  these  buildings 
have  cost  more  per  cubic  foot  than  private  buildings,  so  that  their  cost  cannot 
always  be  used  as  a  guide,  except  for  government  buildings."  | 

Unit  Prices  *  per  Cubic  Foot  for  Recent  Government  Buildings  of  the 
Same  Type.§  The  data  included  in  the  following  paragraphs  relate  to  federal 
buildings  erected  before  or  in  process  of  construction  in  19 14.  They  are  of 
certain  fixed  types  and  in  different  parts  of  the  United  States.  The  buildings 
are  post-office  buildings  and  the  location,  brief  description  of  the  general  con- 
struction, ground-area  covered,  cubical  contents  and  comparative  rates  per 
cubic  foot  are  given.  The  buildings  are  grouped  under  five  different  types,  and 
the  VARIATIONS  IN  COSTS  PER  CUBIC  fOot  of  similar  or  identical  buildings  in  each 
type,  located  in  different  sections  of  the  country,  are  shown.  Following  these 
five  types  is  a  list  of  buildings  of  various  .sizes  and  descriptions  showing  the 
variations  in  the  cubic-foot  rates.  The  conclusions  arrived  at  and  summarized 
at  the  end  of  the  lists,  include  a  table  which  shows  what  was  considered  by  the 
office  of  the  Supervising  Architect  to  be  a  fair  difference  in  cost  of  buildings 
OF  THE  SAME  TYPE  in  different  sections  of  the  United  States.  It  wns  con.sidered, 
also,  by  that  office,  that  the  method  of  estimating  the  cost  of  buildings  by  a 
CUBIC-FOOT  unit  PRICE  is  productive  of  very  uncertain  results,  inasmuch  as 
there  are  many  variable  conditions  entering  into  the  construction  of  buildings 
located  in  different  localities.  The  principal  items  affecting  the  cost  of  similar 
types  of  buildings  are: 

(i)  Labor;    rates  and  efficiency. 

(2)  Materials;   quality  and  freight-rates. 

(3)  Season;   time  of  year  when  building  is  constructed. 

(4)  Contractors;  finances,  abihty,  equipment,  overhead  expenses  and  margin 
of  profit  desired. 

*  Pre-war  figures  must  be  increased  from  50%  to  100%. 

t  Published  in  the  Architects'  and  Builders'  Magazine,  Aug.,  1902,  and  in  the  Inland 
Architect,  April,  1902, 

t  F.  E.  Kidder,  in  previous  editions  of  the  Pocket-Book. 

§  The  information  relating  to  the  cost  of  recent  government  buildings  of  certain  types 
was  furnished  by  J.  W.  Ginder,  Superintendent  of  the  Computing  Division,  Office  of 
the  Supervising  Architect,  by  permission  of  Mr,  O.  Wenderoth,  the  Supervising  Archi- 
tect, throui^h  whose  courtesy  and  valuable  assistance  the  editor  is  able  to  present  the 
data  referred  to.  The  editor  regrets  that  limited  space  prevents  the  reproduction  of  a 
carefully  prepared  and  most  interesting  series  of  photographs  of  the  plans,  elevations 
and  sections  of  the  government  buildings,  the  costs  of  which  per  cubic  foot  are  here 
discussed. 


Cost  of  Government  Buildings 


1629 


(c)  Location;  as  to  supply-centers,  distance  from  railroads,  and  facilities  for 
handling  mtaerials. 

Variations  in  Unit  Costs  *  of  Identical  Buildings  in  Different  Localities 
In  order  to  compare  the  costs  of  identical  buildings,  with  slight  modification 
only,  the  following  are  given  as  examples,  to  show  the  variance  in  different 
localities. 

Type  I.  Post-office  buildings  at  Grenada,  Miss.,  Bennettsville,  S.  C.,  Cov- 
ington, Tenn.,  and  Burhngton,  N.  J. 

Description.  Main  building,  two  stories  and  basement;  rear  projection,  one 
story  and  basement;  non-fire-proof  construction  throughout;  brick  facing;  stone 
trim;  wooden  cornice;  slate-covered  gable  roof,  with  dormers  over  two-story 
portion,  and  flat,  composition  roof  over  one-story  portion. 


Area  and  contents 


Ground-area 

Cubical  contents . 


3  825  sq  ft 
138  210  cu  ft 


Rate  per  cubic  foot  * 


Location 


Grenada,  Miss 

Covington,  Tenn. . 
Bennettsville,  S.  C, 
Burlington,  N.  J... 


Non-fire-proof 


$0,322 
0.31S 
0.304 
0.293 


First  floor, 
fire-proof 


$0,327 
o  324 
0.309 
0.298 


,  and 


Type  2.     Post-office  buildings  at  Winchester,  Tenn.,  McPherson,  Kan., 
Longview,  Tex.  .      .  , 

Description.  Main  building,  two  stories;  rear  projection,  one  story;  partly 
excavated  basement;  non-fire-proof  construction  throughout;  brick  facing; 
stone  trim;  wooden  cornice  and  pilasters  at  front  entrance;  slate-covered  gable 
roof  with  dormers  over  two-story  portion,  and  flat,  composition  roof  over  one- 
story  portion. 


Area  and  contents 

3  825  sq  ft 
138  210  cu  ft 

Cubical  contents 

Rate  per  cubic  foot  * 

,                                      Location 

Non-fire-proof 

First  floor, 
fire-proof 

$0,344 
0.346 
0.332 

$0,350 
0.351 
0.337 

.♦  These  pre-war  figures  must  be  increased  from  50  to  100%. 


1630 


Estimating  the  Cost  of  Buildings 


Part  3 


Type  3.     Post-office  buildings  at  Cookeville,  Teiin.,  and  Jackson,  Ky. 

Description.  Three-story-and-basement  building;  stone-faced  to  top  of 
course  over  water-table;  selected,  common-brick  facing  and  ornamental  terra- 
cotta trim;  composition  and  slate  roof  and  non-fire-proof  construction,  except 
the  first  floor. 


Area  and  contents 

Ground-area 

4  942  sq  ft 
290  300  cu  ft 

Cubical  contents     

Rate  per  cubic  foot  * 

Cookeville,  Tenn                           

So. 275 
0.269 

Jackson,  Ky 

Type  4.  Post-ofTice  buildings  at  Garden  City,  Kan.,  and  Lake  City,  Minn, 
(identical  buildings). 

Description.  One-story-and-basement,  brick-faced  building,  with  stone  water- 
table  course  and  trimmings  and  ornamental  terra-cotta  cornice,  architrave  and 
parapet-coping;  non-fire-proof  construction,  except  the  first  floor;  composition 
roof. 


Area  and  contents 

Ground-area 

3  888  sq  ft 
141  456  cu  ft 

Cubical  contents 

Rate  per  cubic  foot  * 

Garden  City,  Kan 

$0,405 
0.341 

Lake  City,  Minn 

Type  5.     Post-office  buildings  at  Abilene,  Kan.,  and  Bellefontaine,  Ohio. 
Description.     One  story  and  basement;    stone  facing;    granite  steps,  etc.; 
tin  roof;  fire-proof  construction,  except  roof. 


Area  and  contents 

Ground-area         

5  000  sq  ft 
183  000  cu  ft 

Cubical  contents 

Rate  per  cubic  foot  * 

Abilene   Kan                                              

$0,359 
0.367 

Bellefontaine,  Ohio 

Buildings  of  Various  Sizes  and  Descriptions.  The  following  li.st  is  for 
buildings  of  various  sizes  and  descriptions  throughout  the  country  and  shows 
the  variance  in  the  cubic- foot  rate. 

*  These  pre-war  figures  must  be  increased  from  50  to  100%. 


Cost  of  Government  Buildings 


1631 


Post-office  building  at  New  Rochelle,  N.  Y.  ,  ,  * 

Description.     This  building  is  of  an  irregular  plan;   two-story  and  basement; 

•enter  pavilion;   sides  and  rear  one-story  and  basement;   clearstory  over  work- 

•oom;  stone  facing  to  first-floor  level;  brick  facing  above  this  point,  with  terra- 

:otta'trim  and  cornice;   composition  roof;   fire-proof  construction. 


_ 


Ground-area 

Cubical  contents 

Rate  per  cubic  foot  *  . 


7  512  sq  ft 
258  900  cu  ft 
$0,259 


Post-office  building  at  Mobile,  Ala. 

Description.  Front  portion,  two  stories,  and  rear  portion,  one  story  over 
workroom  Only  a  small  portion  of  basement  excavated  for  heating-plant. 
Main  building  faced  with  limestone  and  rear  second  story  portion  with  orna- 
mental terra-cotta.  Fire-proof  construction;  long  and  short  spans  and  con- 
crete joists  with  terra-cotta  fillers;   copper  deck  and  Spamsh-tile  roofs. 


Ground-area 

Cubical  contents 

Rate  per  cubic  foot  * . 


18  054  sq  ft 
670  476  cu  ft 
$0,341 


Post-ofhce  building  at  Muskogee,  Okla. 

Description.     A   four-story-and-basement    building, 
floor  line,  stone-faced  above  (except  in  interior  court,  which  is  brick) 
cotta  cresting  at  roof;    copper  roofing  and  fire-proof  construction  throughout. 
Both  standard  types  of  concrete  and  terra-cotta  floor-co^nstruction,     M.n,. 
mental  in  design.      Corinthian  colonnade  at  entrance, 
lamp-standards.     Six  flights  of  marble  stairs, 
very  ornamental  plaster-work  in  lobby  and  court-room. 


Granite  to  the  first- 

terra- 

jhout. 

Monu- 

Eight  heavy  bronze 

Entire  lobby  of  marble,  and 


Ground-area 

Cubical  contents 

Rate  per  cubic  foot  *. 


20  400  sq  ft 
I  326  612  cu  ft 

$0.43 


Post-office  building  at  New  Bedford,  Mass. 

Description.     One    story,    basement    and    mezzanine 
ce^t^d  portion;    granite  facing,  except  ^l-story    w^^^^^^^^^^ 
cotta;    main  roof  of  composition;    clearstory  roof  of  copper, 
struction. 


vith    clearstory   over 


fire-proof  con- 


Ground-area 

Cubical  contents 

Rate  per  cubic  foot  * . 


27  750  sq  ft 
I  080  690  cu  ft 
$0,323 


Pnqt  office  building  at  Newark,  Ohio. 

Dccript  on  Two-story,  basement  and  unfinished  attic  The  workroom  ex- 
tendtthrough  two  stories.  Offices  in  second  story  over  ba  ance  of  bu.ldmg. 
Firrnroof  construction  throughout.  Terra-cotta  floors,  ce.lmgs  roo  s,  parti- 
fion?furri.g  etc  Exterior  faced  with  pink  granite  to  the  first-floor  level  and 
rhwhte  marble  above,  including  cornice,  parapet  etc  Flat  t."  roof;  bron.^ 
Grille,  at  first  and  second-story  windows  on  front  of  bu.ldmg  Cast-iron  grilles 
!  first  story  and  basement-windows  on  sides  and  rear;  bron.e-faced  post- 
offict  iree7  desks,  revolving  doors,  vestibules,  etc.,  and  drawn-bronze  covered 
f  hes  wTnd^w-fra^es,  doors,  etc.,  in  lobby.  Caen-^stone  cormce  and  coSered 
ceiling  in  lobby.    Bronze  and  marble  stairs  to  second  story. 

♦  These  nre-war  figures  must  be  increased  rrom  so  to  100%. 


1632 


Estimating  the  Cost  of  Buildings 


Part  c 


Ground-area         ..... 

6  912  sq  ft 
369  640  cu  ft 
$0,487 

Cubical  contents 

Rate  per  cubic  foot  * 

Post-office  building  at  Mi  not,  N.  D. 

Description.  Three-story-and-basement  building;  fire-proof,  except  roof 
which  is  plank  on  steel  beams;  stone  facing  to  second-story  window-sills;  bricl 
lacing  above,  with  stone  cornice,  parapet-coping,  etc. 


Oround-area         .    .       

6  700  sq  ft 
427  300  cu  ft 
$0,328 

Cubical  contents 

Rate  per  cubic  foot  * 

Post-office  building  at  McAlester,  Okla. 

Description.  Three  stories  and  basement;  fire-proof,  except  roof;  terra 
cotta  floors,  etc.;  suspended  ceilings;  stone  facing  to  second-floor  level;  bricl 
facing  above,  with  stone  trim;   cornice  and  balustrade;   tin  roof. 


Ground-area 

7  482  sq  ft 
394  765  cu  ft 
$0.38 

Cubical  contents 

Rate  per  cubic  foot  * 

Post-ofiice  building  at  North  Tonawanda,  N.  Y. 

Description.  The  building  has  two  stories  and  basement;  granite  to  th( 
first-floor  line;  brick-faced  above  with  stone  trimming  and  slate  roof;  fire-proo 
construction  to  and  including  the  second  floor. 


Ground-area 

5  475  sq  ft 
276  320  cu  ft 
$0,289 

Cubical  contents 

Rate  per  cubic  foot  *    . 

Conclusions  Regarding  Variations  in  Unit  Costs.  In  the  foregoing 
unit  costs,  the  approach-work,  such  as  walks,  platforms,  terraces,  etc.,  is  in 
eluded.  This,  in  some  cases,  is  quite  expensive,  and  is  generally  from  5  to  lO/^ 
of  the  entire  cost  of  the  building.  In  federal  buildings,  there  are  many  require 
ments  not  met  with  in  the  ordinary  mercantile  buildings,  and  the  permanent 
character  of  the  building  necessitates  all  materials,  workmanship  and  construe 
tion  to  be  of  the  very  best  in  each  case.  This  is  guaranteed  by  iron-clad  speci- 
fications, long-time  guarantees  for  several  items  of  the  work,  and  persona 
government  inspection.  The  office  of  the  supervising  architect  has  deter- 
mined that  the  rel.ative  increase  in  cost  of  buildings  throughout  the  country 
over  the  cost  in  the  Mississippi  Valley  district  was  about  as  follows,  taking  the 
Mississippi  Valley  district,  as  a  base,  at  100%,  and  the  labor  and  market-con- 
ditions which  prevailed  in  October,  19 14. 


! 

Per  cent 

Mississippi  Valley  district .     ... 

100 
no 
H5 
100 
130 
120 

125 

New  England  (except  Maine) 

Maine                   .   .         .    . 

Southern  States 

Northwest  Mountain  district 

Southwest  Mountain  district 

Pacific  Coast '. 

*  These  pre-war  figures  must  be  increased  from  50  to  100%. 


Cost  of  Government  Buildings  1633 

In  the  grouping  of  districts,  the  Mississippi  Valley  district  is  intended  to 
cover  the  Middle  States  as  far  east  as  Ohio  and  Pennsylvania,  and  the  states, 
generally,  bordering  on  the  western  bank  of  the  Mississippi  River.  This  is 
found  to  be  a  part  of  the  country  in  which  the  lowest  prices  have  been  ob- 
tained. The  other  districts  represent  the  approximate  greater  cost  for  buildings 
over  that  in  the  Mississippi  Valley  or  Middle  States,  and  is  intended  to  repre- 
sent the  DIFFERENCE  IN  COST  AT  ANY  TIME;  but  is  not  intended  to  represent 
the  diiTerence  in  cost  at  different  periods. 

Illustration  of  Variation  in  Cost  *  of  Buildings  of  Identical  Area  and 
Contents.  The  following  notes  are  taken  from  photographs  of  drawings, and 
from  data  accompanying  them.f  The  drawings  were  for  a  Post-Office  build- 
ing at  Menomonie,  Wis.  This  building  contains  4  770  sq  ft  of  ground-area, 
and  the  cubical  contents  are  147  570  cu  ft.  The  contract  was  awarded  (19 13) 
for  $45  380,  or  at  the  rate  of  $0,308  per  cu  ft.  It  is  a  one-story-and-basement 
building,  faced  with  brick,  with  stone  water-table,  brick  parapet  and  tin  and 
composition  roof.  The  first  floor,  only,  is  fire-proof.  Proposals  were  opened 
(19 14)  for  a  Post-Office  building  at  Uvalde,  Tex.  This  building,  except  for 
some  slight  modifications,  is  as  nearly  like  the  Menomonie  building  as  it  is 
possible  to  make  it  without  using  the  same  drawings.  The  ground-area  of  the 
Uvalde  building  is  4  672  sq  ft  and  the  cubical  contents,  151  875  cu  ft.  The  work 
in  connection  with  the  approaches  is  practically  the  same  as  that  at  Menomonie. 
If  these  buildings  had  been  erected  in  the  same  town,  it  does  not  appear  that 
there  would  have  been  any  difference  in  the  costs,  but  the  lowest  proposal 
received  for  the  Uvalde  building  was  $56  400,  or  at  the  rate  of  $0,371  per  cu  ft. 
A  comparison  of  the  amounts  for  these  two  buildings  further  illustrates  the 
unreliability  of  any  universal  appHcation  of  the  cubic-foot  rate  in  determining 
the  costs  of  buildings,  and  also  shows  that  the  difference  in  cost  of  construction 
of  buildings  in  different  sections  of  the  country  varies  considerably. 

Cost  per  Cubic  Foot  of  Some  Important  Federal  Buildings.  The  follow- 
ing tabulations  contain  additional  unit  costs  and  other  data  for  public  buildings. 

Cost  *  per  Cubic  Foot  of  Some  Important  Federal  Buildings. 


Location  and  building 


New  York,  N.  Y.,  Custom-House  (completed  1908) 

Cleveland,  Ohio,  Post-Office,  Custom-House  and  Court-House.  ..... 

San  Francioco,  Cal.,  New  Post-Office  and  Court-House   (completed 

1906) 

Denver,  Col.,  new  Mint  (completed  1905) 

San  Francisco,  Cal.,  Subtreasury  Building  (estimated) 

Baltimore,  Md.,  new  Custom-House  (completed  1908) 

Washington,  D.  C,  Senate  Office-Building 

Salt  Lake  City,  Utah,  Post-Office  (completed  1905) : 

Indianapolis,  Ind.,  new  Post-Office  (completed  1906) 

Philadelphia,  Pa.,  new  Mint  (completed  1901) 

Washington,  D.  C,  National  Museum  Building 

Washington,  D.  C,  Agricultural  Buildings  (portions  completed) 

Washington,  D.  C,  House  Office-Building 


Cost  per 

cubic  foot, 

cents  • 


74 
68 

66 
65 
60 
55 
50 
47 
46 
45 
43 
40 
36 


*  These  pre-war  figures  must  be  increased  from  50  to  100%. 

t  These  photographs  of  plans,  elevations  and  sections,  together  with  many  others,  and 
accompanying  explanations  and  data,  were  furnished  the  editor  by  J.  W.  Cinder,  Super- 
intendent of  the  Computing  Division,  Office  of  the  Supervising  Architect,  by  permission 
of  Mr.  O.  Wenderoth,  the  Supervising  Architect  (1914),  and  have  been  of  great  assistance 
in  the  nresentation  of  notes  on  the  costs  of  buildings. 


1634  Estimating  the  Cost  of  Buildings  Part  3 

Cost  *  per  Cubic  Foot  and  per  Square  Foot  of  Some  New  Public  Buildings  t 


Location 

Facing 

Cost 

Contents, 
cuft 

Area, 
sqft 

Cost           ] 

Cuft 

Sqft 

Bangor,  Me 

Granite 

Marble 

Stone 

Limestone 

Brick 

Limestone 

Granite 

$271  297 
288800 
132  702 
95200 
81532 
116  689 
295051 

793  720 
576000 
377668 

256  210 

256  210 

448300 

I  080  000 

15600 
II  000 
II  000 
6470 
6470 
9984 
21  732 

$0,342 
0.500 
0.350 
0.373 
0.318 
0.360 
0.300 

$17-40 
26.20 
12.00 
14.80 
12.60 
11.70 
13.50 

Augusta,  Ga 

South  Chicago,  111 

Long  Branch,  N.  J 

Plymouth,  Mass 

Piqua,  Ohio 

New  Bedford,  Mass.  . . 

Depreciation  of  Buildings  | 

Discounts  from  Values  of  New  Buildings.  The  figures  given  on  the  pre- 
ceding pages  are  for  new  buildings.  To  ascertain  their  value  at  any  time  sub- 
sequent to  their  erection,  a  discount  from  the  value  when  new  should  be  made 
as  follows: 

Per  cent  per  year 

Brick,  occupied  by  owner i      to  1  ^ 

Brick,  occupied  by  tenant iH  to  ij^^ 

Frame,  occupied  by  owner 2      to  2}-^ 

Frame,  occupied  by  tenant 2»'i  to  3 

If  built  of  long-leaf  yellow  pine,  or  of  spruce  from  the  New  England  States, 
add  from  20  to  30%,  or  if  of  short-leaf  yellow  pine,  add  from  40  to  50%  to  these 
values.  If  of  redwood  or  cedar  from  the  Pacific  Coast,  use  about  one-half 
these  estimates,  which  are  for  white  pine  or  white  pine  with  oak  framing-timbers. 
These  figures  for  depreciation  are  to  include  buildings  in  which  ordinary  repairs 
have  been  made.  If  extraordinary  repairs  have  been  made,  the  discount  should 
not  be  so  heavy.  Good  judgment  must  be  used  in  estimating  the  amount  of 
depreciation  in  buildings. 

The  Depreciation  of  Mill-Buildings.  The  annual  depreciation  of  a  mill- 
building  of  slow-burning  construction  varies  from  i  to  iyi%,  while  the  de- 
preciation of  a  reinforced-concrete  factory-building  is  relatively  much  less, 
since  it  is  confined  entirely  to  such  details  as  windows,  doors,  roofing,  etc. 

The  Wear  and  Tear  of  Building  Materials.  At  the  tenth  annual  meeting 
of  the  Fire  Underwriters'  Association  of  the  Northwest,  held  at  Chicago  in 
September,  1879,  Mr.  A.  W.  Spalding  read  a  paper  on  the  wear  and  tear  of 
building  materials  and  tabulated  the  results  of  his  investigations  in  the  follow- 
ing form: 

*  These  pre-war  figures  must  be  increased  from  50  to  100%. 

t  Reproduced,  by  permission,  from  the  Journal  of  the  Society  of  Constructors  of 
Federal  Buildings,  September,  1914,  through  the  courtesy  of  C.  R.  Marsh,  Editor  of 
Publications  of  the  Society  of  Constructors  of  Federal  Buildings.  This  Journal,  published 
monthly,  contains  data  of  much  interest  to  architects  and  builders. 

X  From  Tiffany's  Estimate  of  Depreciation,  used  by  the  United  States  Government. 


Quantity  System  of  Estimating 


1635 


Material  in  building 


Brick 

Plastering 

Painting,  outside... 

Painting,  inside 

Shingles 

Cornices 

Weather-boarding.  . 

Sheathing 

Flooring 

Doors,  complete. . . . 
Windows,  complete. 
Stairs  and  newels. . . 

Bases 

Inside  blinds 

Building  hardware. 
Piazzas  and  porches 
Outside  blinds.  . 
Sills  and   first-floor 

joists 

Dimension-lumber 


These  figures  represent  the  averages  deduced  from  the  replies  made  by  eighty- 
three  competent  builders  unconnected  with  fire-insurance  compames  m  twenty- 
seven  cities  and  towns  of  the  eleven  Western  States. 

THE  QUANTITY  SYSTEM  * 

Explanation  of  the  System.  The  quantity  system  is  not,  as  some  persons 
have  supposed,  merely  the  taking  off  of  a  list  of  items  by  one  person  probably 
with  uncertain  accuracy,  for  some  other  person's  use.  It  means  the  careful 
measurement  by  a  disinterested  expert  specially  trained  in  this  kmd  of  work, 
that  is  a  quantity  surveyor.  This  specialist  proceeds  in  a  manner  quite 
different  from  that  of  the  average  contractor.  He  follows  a  certain  recognized 
order  and  system  in  taking  off  quantities,  abstracting  and  billing,  with  a  view 
to  eliminating  errors.  He  uses  certain  uniform  standards  of  measurements  and 
expressions  well  understood  by  bidders.  His  checking  and  rechecking  methods 
to  ensure  accuracy  must  be  studied  to  be  appreciated  by  those  to  whom  the 
quantity  system  is  unknown.  A  record  is  kept  of  every  item,  however  small, 
having  a  money-value.  These  items  are  classified  and  arranged,  each  under 
its  proper  trade  or  department,  in  methodical  order.     Guess-work  methods 

*  The  quantity  "system"  which  is  not  merely  a  survey  of  items,  has  been  systematically 
advocated  since  1891  by  G.  Alexander  Wright,  A.I.A.,  354  Pine  Street,  San  Francisco 
who  is  the  founder  of  the  movement  to  adapt  the  Quantity  System  to  American  building 
nractice  It  has  attracted  much  attention  among  contractors,  architects,  and  engineers. 
In  course  of  time  this  system  of  estimating  must  be  adopted,  as  it  stands  for  a  square 
deal  between  owner  and  contractor.  The  movement  in  aid  of  this  work  is  purely  a 
voluntary  one,  an  honest  effort  to  bring  about  better  methods. 


1636  Quantity  System  of  Estimating  Part  3 

are  unknown  to  the  quantity  surveyor,  while  his  accuracy  and  attention  to  even 
small  details  is  worthy  of  comment.  Every  l^idder  figures  from  a  copy  of  the 
surveyor's  quantities  furnished  to  each  one,  with  (if  desired)  the  plans  and 
specifications.  The  surveyor  who  does  this  work  is  a  professional  man  similar 
to  the  engineer  or  the  architect.  He  should,  in  fact,  have,  and  he  usually  has 
had,  experience  in  these  professions,  and  in  addition,  a  practical  experience 
acquired  in  the  field  in  actual  contact  with  and  superintendence  of  construction- 
work. 

Method  of  Procedure.  Such  a  surveyor,  in  taking  off  quantities  from  an 
architect's  or  engineer's  drawings,  readily  detects  any  discrepancies  due  to  hasty 
preparation  or  other  cause.  The  attention  of  the  architect  or  engineer  is  called 
to  such  matters  by  the  quantity  surveyor,  as  he  goes  on  with  his  work.  De- 
tected in  this  way,  all  uncertainties  are  at  once  corrected  and  adjusted,  so 
that  by  the  time  the  drawings  and  specifications  reach  contractors,  everything 
has  been  made  plain  and  accurate  and  the  possibility  of  error  in  quantities 
can  therefore  be  disregarded.  The  resulting  document,  the  bill  of  quantities, 
is  then  either  printed  or  otherwise  reproduced,  and  a  facsimile  copy  supplied 
free  of  cost  to  each  bidder  who  inserts  his  unit  price  opposite  each  item  and 
in  an  hour  or  two  foots  up  the  money-cost  in  dollars  and  cents.  This  is  really 
all  that  a  contractor  should  be  expected  to  do  (for  nothing).  The  bill  of 
QUANTITIES  contains  everything  the  contractor  is  called  upon  to  perform  or 
furnish,  in  order  to  complete  his  contract.  In  short,  the  bid  becomes  a  pro- 
posal to  do  a  certain  fixed  quantity  of  work,  no  more  and  no  less.  This  then, 
briefly,  is  the  main  underlying  principle  of  the  quantity  system:  a  definite 
quantity  of  work  for  a  definite  price,  and  the  elimination  of  every  condition 
which  now  compels  bidders  to  take  chances. 

The  Present  Unsatisfactory  Conditions.  Most  architects  are  familiar 
with  the  wasteful,  unsatisfactory  methods  followed  to-day.  They  injure  both 
parties  to  a  contract  because  of  bidders'  mistakes  in  figuring,  accuracy  being 
so  often  sacrificed  for  speed.  While  wonderful  strides  in  methods  of  construc- 
tion have  been  made,  no  attention  has  been  given  to  standardizing  methods 
of  measuring  builders'  work,  and  so  both  owner  and  contractor  suffer.  As  a 
result  of  the  movement  in  aid  of  better  methods  (initiated  in  San  Francisco 
in  1 891)  more  conservatism,  and  a  closer  adherence  to  business  principles  are 
being  preferred  in  place  of  gambling  methods  of  estimating.  Architects  or 
engineers  who  now  permit  an  unduly  low  bidder  to  take  a  contract  are  courting 
trouble  every  time. 

Use  of  the  Quantity  System  in  Other  Countries.  The  principle  of  pay- 
ment by  measurement  is  based  upon  equity  and  square  dealing.  On  large  work 
it  is  used  in  England,  Ireland,  Scotland,  France,  Germany,  Austraha,  and 
South  Africa,  and  to  some  extent  in  the  United  States  and  Canada.  It  is  a 
significant  fact,  that  in  no  instance  in  which  this  measurement  system  has 
been  once  established,  has  it  ever  been  abandoned  for  the  former  haphazard 
methods. 

Advantages  Claimed  for  the  Quantity  System.  The  following  are  the 
advantages  claimed  for  the  system: 

(i)  An  immense  saving  of  time  and  money  now  wasted  by  bidders;  all 
doing  the  same  thing,  going  over  the  same  ground,  and  each  arriving  at  a 
different  result. 

(2)  Safer  bids,  as  the  work  to  be  performed  is  clearly  written  out  in  the 
^ill  of  quantities,  which  can  be  the  essence  of  the  contract.  • 


Quantity  System  of  Estimating  1637 

(3)  No  expense  to  the  bidder;  the  owner  pays  for  the  quantities  knowingly, 
The  owners  pay  now,  but  this  fact  is  not  brought  to  their  attention,  and  it 
(lots  not  occur  to  them.  The  percentage  added  to  a  bidder's  net  cost  is  not 
all  profit,  a  certain  portion  being  absorbed  in  overhead  charges,  inchiding  cost 
of  estimating,  which,  of  course,  is  ultimately  borne  by  owners. 

(4)  Saving  of  disputes  arising  from  ambiguities,  oversights,  and  even  errors, 
.ill  ( ausing  extra  claims  more  or  less  just,  but  usually  vexatious,  and  sometimes 
embarrassing. 

(5)  Better  opportunities  for  the  competent  bidder,  as  the  bidders  all  work 
up  and  price  from  the  same  basis. 

(6)  Better  work  and  greater  harmony.  If  no  part  of  the  work  is  omitted 
there  is  less  reason  to  skin  the  work,  a  proceeding  which  produces  friction,  or 
worse. 

(7)  Misunderstandings  are  reduced.  The  bill  of  quantities  states  clearly 
what  is  intended,  and  is  a  sort  of  clearing-house  for  the  drawings  and  specifica- 
tions. 

(8)  Neither  party  can  obtain  an  advantage  over  the  other  on  quantity  or 
description  of  work. 

(9)  No  disputes  with  subbidders,  it  being  clearly  stated  what  each  trade  is 
to  furnish. 

(10)  Contractors  have  no  figuring  of  quantities  to  do  and  can  therefore 
devote  more  time  to  buildings  in  hand  and  save  profits  now  lost  for  want  of 
their  personal  supervision. 

(11)  Fewer  inferior  contractors  as  lowest  bidders. 

(12)  Fewer  extras,  which  are  usually  a  trouble  to  all  concerned. 

(13)  The  architect  or  engineer  has  the  assistance  by  collaboration  of  the 
professional  quantity  surveyor,  who  is  available,  also,  for  preliminary  figures. 
This  advance-information,  now  so  often  furnished  by  a  prospective  bidder, 
creates  undesirable  obligations. 

(14)  No  change  or  reorganizing  of  architects'  offices  is  entailed.  Much 
detail-work  now  involved  in  receiving  bids  could  be  taken  care  of  in  the 
quantity  surveyor's  office. 

(15)  The  drawings  and  specifications  having  been  previously  made  as  com- 
plete as  possible,  subsequent  inconvenience  to  contractors  and  foremen  on  the 
job,  and  inquiries  at  the  architects'  offices  for  explanations  become  unneces- 
sary. The  BILL  OF  QUANTITIES  gives  detailed  information  which  cannot  be  well 
given  by  drawings. 

Adaptation  to  American  Practice.  In  the  United  States  any  such  uni- 
versal system  must  conform  to  American  needs  and  sentiment,  and  be  a  prac- 
tical system.  For  many  reasons  it  would  be  unpractical  to  follow  the  English 
practice.  The  principles  it  stands  for  can,  however,  be  accepted  and  applied 
anywhere  with  great  advantage. 


DIMENSIONS    AND    DATA  USEFUL    IN    THE    PREPARA- 
TION OF  ARCHITECTS'   DRAWINGS  AND 
SPECIFICATIONS* 

Dimensions  for  Furniture.  For  the  convenience  of  draughtsmen  when 
designing  furniture  or  providing  space  for  a  special  article  the  following  dimen- 
sions are  given:  f 

*  See,  also,  the  additional  tables  with  more  detailed  and  classified  lists, 
t  Many  of  these  dimensions  were  first  contributed  to  the  American  Architect  of  NQ' 
Vf^ber  IP,  1894,  by  Alvin  C.  Nye. 


1638  Dimensions  and  Data 


Parfl 


a-L  IS, 
t  size^ 

'1 

ingB 


Chuirs  ai4d  Seats.  The  average  figures  taken  from  a  variety  of  good  < 
are:  Height  of  the  seat  above  the  floor,  i8  in;  depth  of  the  seat,  19  in;  the  tof*' 
of  the  back  above  the  floor,  sS  in..  Usually  the  seat  increases  in  depth  as  it 
decreases  in  height,  while  the  back  is  higher  and  slopes  more.  Twenty  inches 
inside  is  a  comfortable  depth  for  a  seat  of  moderate  size.  Chair-arms  are  about 
9  in  above  the  seat.  The  slope  of  the  back  should  not  be  more  than  one-fifth 
the  depth  of  the  seat.     A  lounge  is  6  ft  long  and  about  30  in  wide. 

Tables  vary  in  shape  and  size  almost  as  much  as  chairs.  Writing-tables  and 
dining-tables  are  made  2  ft  5  in  high,  and  the  type  of  sideboard  called  a  carving- 
table  is  made  3  ft  high  to  the  principal  shelf;  but  tables  for  general  use  are  '2  ft 
6  in  high.  Dining-tables  are  made  from  3  ft  6  in  to  4  ft  wide  and  to  extend 
from  12  ft  to  16  ft  by  means  of  slides  within  the  frame.  This  frame  should  not 
be  so  deep  as  to  interfere  with  the  knees  of  any  one  sitting  at  the  table;  that  is, 
there  must  be  about  2  ft  clear  space  between  it  and  the  floor.  The  smallest  siz^ 
practicable  for  the  knee-holes  of  desks  and  library-tables  is  2  ft  high  by  i  ft  2 
wide,  the  width  to  be  increased  as  much  as  possible. 

Bedsteads  are  classed  as  single,  three-quarters,  and  double.  A  singli 
bed  is  from  3  to  4  ft  wide  inside;  a  three-quarter  bed,  from  4  ft  to  4  ft  6  in; 
a  double  bed,  5  ft.  Bedsteads  are  from  6  ft  6  in  to  6  ft  8  in  long  inside.  Foot- 
boards are  from  2  ft  6  in  to  3  ft  6  in  and  headboards  from  5  ft  to  6  ft  6  in  high. 
Single  beds  for  dormitories  are  often  made  only  2  ft  8  in  wide. 

Bureaus  vary  in  shape  and  size  to  such  an  extent  that  it  is  almost  impossible 
to  say  that  any  dimension  is  fixed.     Convenient  sizes  are:   body,  3  ft  5  in  wid 
T  ft  6  in  deep  and  2  ft  6  in  high;  or  4  ft  wide,  i  ft  8  in  deep  and  3  ft  high. 

Commodes  are  i  ft  6  in  square  on  the  top  atid  2  ft  6  in  high. 

Chiffoniers  ace  about  3  ft  wide,  i  ft  8  in  deep  and  4  ft  4  in  high. 

Cheval-Glasses  are  made,  if  large,  6  ft  4  in  high  and  3  ft  2  in  wide.  If  small, 
5  ft  high  and  i  ft  8  in  wide.     If  medium,  5  ft  6  in  high  and  2  ft  wide. 

Wash-Stands  of  large  sizes  are  3  ft  long,  i  ft  6  in  wide  and  2  ft  7  in  high.  Small 
sizes  are  from  2  ft  4  in  to  2  ft  8  in  long. 

Wardrobes  may  be  8  ft  high,  2  ft  deep  and  4  ft  6  in  wide;   or  6  ft  9  in 
I  ft  5  in  deep  and  3  ft  wide. 

Sideboards  may  be  from  4  to  6  ft  long  and  from  20  in  to  2  ft  2  in  deep. 

Upright  Pianos  vary  from  4  ft  10  in  to  5  ft  6  in  in  length,  from  4  to  4  ft  ^| 
in  height  and  are  about  2  ft  4  in  deep  over  all. 

Miniature  and  Baby-Grand  Pianos  vary  from  5  ft  10  in  to  6  ft  in  length,  an3 
are  about  4  ft  10  in  in  width. 

Parlor-Grand  Pianos  vary  from  5H  ft  to  6  ft  10  in  in  length,  and  are  about 
4  ft  10  in  in  width. 

Concert-Grand  Pianos  are  about  8  ft  10  in  in  length  and  5  ft  in  width. 

Billiard-Tables  (Collender),  4  by  8  ft,  4  ft  2  in  by  9  ft  and  5  by  10  ft. 
of  room  required  13  by  17  ft,  14  by  18  ft  and  15  by  20  ft,  respectively. 

Classified  Tables  *  of  Furniture-Dimensions.    The  following  more 
tailed  and  classified  tables  of  average  dimensions  of  furniture  are  added  to  those 
already  given  and  are  taken  from  recent  data  furnished  by  manufacturers  of 

*  These  additional  tables  were  compiled  by  E.  S.  Hand,  and  much  of  this  data  in  the 
several  editions  of  the  Pocket-Book  has  been  taken,  by  permission,  from  the  valuable 
treatise  on  Furniture  Designing  and  Draughting,  by  A.  C.  Nye,  ^^1 


i 


Dimensions  of  Tables  and  Chairs 


1639 


furniture.  While  some  of  these  measurements  vary  sHghtly  from  the  dimen- 
sions given  in  the  preceding  paragraphs  they  represent  average  dimensions  of 
furniture  as  made  at  the  present  time. 

Dimensions  of  Tables 


Kind  of  table 


Bedroom-table . 
Bedi-oom-table . 

Bijou-table 

Carving-table .  . 
Dressing-table . 
Extension  table 
Extension  table 
Library-table... 
Library-table . . . 
Library-table . . . 
Library-table . . . 

Tea-table 


Length        Width        Height         Remarks 


30 
42 
36 
66 
54 
51 
42 
54 
60 
13 
18 
23 
30 


66 
54 
41 
27 
34 
36 
13 
18 
17 
23 


29 
30 
30 
36 
30 
30 
30 
30 
29 
29 
29 
20 
24 
29 
18 


Commode 


Round 
Square 
Oval 


Round 
Square 
Upper  shelf 
Lower  shelf 


All  dimensions  are  in  inches.    Heights  are  from  the  floor. 
Dimensions  of  Chairs 


Kind  of  chair 


Bedroom-chair 

Baby's  high  chair  *.. 

Check-chair  f 

Chip-chair 

Chip-chair 

Dining-chair 

Dining-chair 

Dining-chair 

Dining-chair 

Easy  chair , 

Easy  chair  f 

Hepplewhite  chair. . . 

Parlor-chair  I 

Parlor-chair  f 

Parlor-chair  f 

Parlor-chair  § 

Piano-bench. 

Reception-chair  li  . . . 

Rocking-chair 

Roundabout  chair. . 

Rubens  chair 

Slipper-chair 


Height 


17 
17 
18 


19 

18 

17 

17 

18 

16K2 

14 

18 

18 

20 

17 

16 

18 


Seat-width, 


Front      Back 


16 

14 
29 


24 
19 
19 
20 
33 
27 


26K2 


23y. 
18 

18 


25 

17V2 

17 

22 

17 

17 

15 

28 

25 

17 

193-^ 
21 

22  H 
13 

19 

20  H 
18 

17^2 

15 


Depth, 
outside 


17 

13K2 

2^y2 

17 

17% 

22 

19 

18 

IS 

241 
27  K2 
17 
mi 

18  u 
26 1/2 
19 
15 

21 

18 

IS 

17 


Back 


Height    Slope 


34 
37 

44 

39 

38 

45 

43 

38'/^ 

36 

43 

41 

34^/^ 

36 

29 

37 


30 
41 

29l/i2 

40 
28 


2K2 
2 

1K2 


5 

6K2 


Arms, 
height 
from 
floor 


26K2 


21 
26 
27 

25H 

25 
23 


24 

2SH 


*  Foot  rest  12  in  above  floor,     t  Overstuffed.  t  French  cane  seat  and  back. 

§  Wooden  arm  and  back.  II   Upholstered  seat.     H  Depth  mside. 

All  dimensions  are  in  inches.     Heights  are  from  the  floor.    The  slope  of  the  back  is  meas- 
ured at  the  seat-lavel  to  a  pe-oendicular  through  the  highest  pomt  of  the  back. 


1640 


Dimensions  and  Data 


Part  3 


Dimensions  of  Sofas 


Kind  of  sofa 


Small 

Extra  large . . . 
Ordinary  sofa 

Lounge 

Lounge. 


Height 


i8 
16. 
IS 
17 
17 


Seat-width 


Front      Back 


43 
78 
54 
68 
57 


40 
76 
51 


Depth, 
outside 


Back 


36 

24 
28 
29 


Height     Slope 


32  H 

29 

34 

35 

23 


5^^ 

2 1/2 


Arms, 
height 
from 
floor 


24 
25 
24 
29 
34 


All  dimensions  are  in  inches.     Heights  are  from  the  floor.     The  slope  of  the  back  is 
measured  at  the  seat-level  to  a  perpendicular  through  the  highest  point  of  the  back. 

Dimensions  of  Case-Work 


Kind  of  case-work 

Body 

Remarks 

Width 

Depth 

Height 

Bureau 

45 
51 
48 
54 
60 
60 
39 
36 
25 
16 
84 
36 
54 

20'/^ 

23 

22 
20 
33 
32 

20 
20 

"16' 
32 
19 
24 

37  >  2 

36K2 

42 

42 

44 

48 

51 

65 

31 

30 

69 

96 

Bureau 

Bureau 

Bookkeeper's  desk 

Bookkeeper's  desk 

Chiffonier 

Deck,  II  in;  slope,  22  in 

Chiffonier 

Cheval-glass 

Commode 

Sideboard 

Wardrobe 

Wardrobe 

All  dimensions  are  in  inches.     Heights  are  from  the  floor.     The  slope  of  the  back  is  meas- 
ured at  the  seat-level  to  a  perpendicular  through  the  highest  point  of  the  back. 


Dimensions  of  Bedsteads 


Kind  of  bed 

Inside 

Heights 

Height, 
Width,      bottom 
side  rail      of  side 
rail 

Length 

Width 

Foot 

Head 

Single  bed 

Single  bed 

Double  bed 

Double  bed 

78 
78 
78 
78 

42 
42 

56 

40 
41 
42 
36 

62 
60 
63 
67 

gy>             9K2 

10  10 

11  10V2 
13                 9V2 

All  dimensions  are  in  inches.     Heights  are  from  the  floor. 

Dimensions  of  Plumbing-Fixtures.  Enameled-Iron  Bath-Tubs.  Standard 
sizes  for  roll-rim  baths  with  sloping  ends  are:  nominal  lengths,  4  ft,  4V2  ft,  5  ft, 
SH  ft  and  6  ft;  width  over  all,  from  30  to  34  in.  Specially  narrow  tubs  are  made 
from  25  to  29  in  wide.  The  actual  length  over  rim  is  usually  i  or  2  in  more 
than  the  nominal  length,  and  2  in  will  include  an  ordinary  overflow-pipe. 


Dimensions  of  Plumbing-Fixtures  1641 

Wash-Basins.  Crockery  basins,  to  go  with  marble  slabs,  are  made  round 
and  oval.  Round  bowls  are  made  lo,  12,  13,  14  and  16  in  in  diam,  measured 
from  the  outside  of  the  rim.  Oval  bowls,  14  by  17  in,  15  by  19  in  and  16  by  21 
in.     The  12  and  14-in  rounds  and  15  by  19-in  oval,  are  commonly  used. 

Marble  Basin-Slabs  may  be  20  by  24  in,  20  by  30  in,  22  by  28  in,  or  24  by  30  in, 
the  last  being  a  very  common  size.  They  can  be  made  any  size,  to  order.  They 
should  be  iV4  in  thick,  countersunk  on  top,  and  should  have  molded  edges  where 
exposed. 

Corner-Slabs  are  commonly  made  21  by  21  in  and  24  by  24  in.  Marble  backs 
are  usually  8  or  10  in  high,  and  sometimes  12  in. 

Enameled-Iron  Wash-Basins  or  Lavatories  made  in  one  piece:  common  sizes 
are  16  by  20  in,  11  by  14-in  basin;  18  by  21-in,  11  by  15  in  basin;  18  by  24  in, 
12  by  15-in  basin;  back,  10}'^  in  high.  The  smallest-sized  wash-basin  is  13  in 
wide  at  the  back. 

Corner-Basins,  i2y2  by  12I/2  in,  12-in  round  basin;  15  by  15  in,  11  by  14-in 
basin;  16  by  16  in,  11  by  14-iiTbasin;  19  by  19  in,  11  by  15-in  basin.  The  stand- 
ard height  of  wash-basins  is  2  ft  6  in  from  the  floor. 

Foot-Baths,  enameled  iron,  roll-rim,  are  22yz  by  19  in;  width,  including 
fittings,  I  ft  II  in;   height  17  in;   depth  inside,  11  in. 

Seat-Baths,  enameled  iron,  average  about  32  in  long  over  fittings,  and  27  in 
wide. 

Water-Closets.  The  dimensions  of  water-closet  bowls  vary  considerably, 
the  following  being  about  an  average:  width  of  bowl  over  all,  13  in;  depth  from 
wah  to  front  of  seat,  23  in;  height  from  floor  to  seat,  17  in;  width  of  seat,  from 
15  to  16  in.  Closets  with  low-down  tanks  measure  about  28  in  from  front  of 
seat  to  wall.  The  distance  from  center  of  outlet-opening  to  the  walls,  or  the 
ROi'GHiNG-iN  dimensions,  are  given  in  manufacturers'  catalogues,  as  they  vary 
with  difierent  closets.  The  smaflest  space  permissible  for  water-closet  compart- 
ments, where  doors  open  out,  is  2  ft  4  in  by  4  ft.  If  the  doors  open  in,  the  com- 
partment should  be  3  by  5  ft. 

Closet-Ranges,  used  in  schools  and  factories,  are  made  24,  27  and  30  in, 
center  to  center  of  partitions.  For  graded  schools,  24  in  is  ample,  and  for 
factories,  27  in.  The  range  usually  occupies  a  space  28  in  in  depth,  if  set  against 
a  wall. 

Urinal-Stalls  should  be  from  24  to  27  in,  center  to  center  of  partitions;  depth 
of  partitions,  20  or  22  in;  of  ends,  2  ft;  of  bottom  slab,  2  ft;  height  of  partitions, 
from  4  ft  6  in  to  5  ft  6  in. 

Kitchen-Sinks  of  cast  iron  are  made  in  a  great  variety  of  sizes,  those  most 
commonly  used  being  16  by  24  in,  18  by  30  in,  18  by  36  in,  20  by  30  in  and  20  by 
36;  24  by  50  in  is  the  largest  size  for  enameled  sinks.  Th^  depth  inside,  for 
the  sizes  given,  is  6  in.  Plain  cast-iron  sinks  are  made  as  large  as  32  by  56  in,  or 
28  by  78  in.     Steel  sinks  are  made  in  all  of  the  above  sizes  up  to  20  by  40  in. 

Porcelain  Sinks.  Common  sizes  of  porcelain  sinks  are  20  by  30  in,  23  by  36  in 
and  24  by  42  in. 

Cast-iron  Slop-Sinks,  common  sizes,  are  16  by  16  in,  16  by  20  in,  18  by  22  in 
and  20  by  24  in;    12  in  deep. 

Copper  Pantry-Sinks.  Common  sizes  are  12  by  18  in,  14  by  20  in  and  16  by 
24  in. 

Laundry-Tubs  of  slate  or  soapstone  are  commonly  made  2  ft  wide  over  all, 
and  16  in  deep.     Lengths  over  all,  two-part  tubs,  4  ft  and  4  ft   6  in;  three- 


1642  Dimensions  and  Data  Part  3 

part  tubs,  6  ft,  6  ft  6  in  and  7  ft.  Earthen  and  porcelain  tubs  come  separately, 
and  are  connected  as  required.  The  dimensions  of  each  tub  are  2  ft  or  2  ft 
'jy2  in  in  length,  2  ft  iVz  in  in  width  and  15  in  in  depth,  inside.  The  length 
required  for  two  2-ft  tubs  is  4  ft  i  in;  for  three  tubs,  6  ft  2  in;  and  for  four  tubs, 
8  ft  3  in.  WoltT's  roll-rim  enameled-iron  wash-tubs  are  55  in.  over  all,  for  two 
tubs,  and  82  in  for  three  tubs. 

Range-Boilers  are  12  in  diameter  for  30-gal,  14  in  for  40-gal,  16  in  for  52- 
gal  and  63-gal,  22  in  for  loo-gal  and  120-gal  boilers. 

Dimensions  of  Carriages.     Covered  Buggy  (Goddard).     Length  over  all, 
14  ft;  width,  5  ft;  height,  7  ft  4  in.     Will  turn  in  space  from  14  to  20  ft  square, 
according  to  skill. 

Coupe.     Length  over  all,  18  ft;  width,  6  ft;  height,  6  ft  6  in. 

Buggy  (Piano-Box).     Length  over  all,  14  ft;  width,  4  ft  10  in. 

Landau.  Length  over  all,  19  ft  6  in;  width,  6  ft  3  in;  height,  6  ft  3  in;  length 
of  pole,  8  ft  o  in. 

Stanhope  Gig,  Two  Wheels.  Length  over  all,  10  ft  6  in;  width,  5  ft  8  in; 
height,  7  ft  6  in. 

Victoria.  Length,  without  pole,  9  ft  6  in;  length  of  pole,  8  ft;  width  over 
all,  5  ft  4  in. 

Light  Brougham.  Length,  without  pole  or  shaft,  9  to  11  ft;  width  over  all, 
5  ft  4  in;   height,  6  ft  4  in. 

Automobiles.     Length,  from  m  to  19  (average  16)  ft;  width,  6  ft;  height,  7  ft. 

Dimensions  and  Weight  of  Fire-Engines.  From  measurements  of  differ- 
ent fire-engines  belonging  to  the  city  .of  Boston,  it  was  found  that  the  greatest 
length,  including  pole,  was  22  ft  6  in.  The  widths  varied  from  5  ft  to  5  ft  11  in, 
the  average  height  being  8  ft  8  in.  The  average  weight  (computed  from  29 
engines),  8  000  lb;  the  greatest  weight,  9  420  lb  and  the  least,  4  780  lb. 

Dimensions  and  Weight  of  Hose-Carriages.  Extreme  length  with  horse, 
19  ft  6  in,  without  horse,  17  ft  6  in;  width,  from  5  ft  9  in  to  7  ft;  height,  from  6  ft 
8  in  to  7  ft;  average  weight  (computed  from  11  carriages),  2  943  lb;  greatest 
weight,  3  500;   least  weighs  2  120. 

Dimensions  and  Weight  of  Ladder- Wagons.  Length  of  truck,  33  ft; 
total  length,  with  ladders  on,  45  ft;  width,  6  ft  2  irt;  average  weight  (com- 
puted from  12  wagons),  6  660  lb;  greatest  weight,  8  800;   least,  4  350. 

Dimensions  of  Locomotives  and  Cars.  The  dimensions  of  locomotives 
and  freight-cars  vary  considerably,  but  the  following  will  cover  those  in  com- 
mon use: 

Locomotives.  From  15  ft  4  in  to  15  ft  10  in  to  top  of  stack  from  top  of  rail; 
extreme  width  o^  cab,  10  ft  2  in.  Doors  to  admit  locomotives  should  be  from 
12  to  13  ft  wide  and  18  ft  high. 

Furniture-Cars  are  14  ft  i  in,  from  top  of  track  to  top  of  brake-staff;  floor, 
3  ft  8  in  from  track;  extreme  width,  9  ft  10  in. 

Stock-Cars,  13  ft  5  in,  from  top  of  track  to  top  of  brake-staff;  floor,  4  ft  from 
track;   extreme  width,  9  ft  8  in. 

Refrigerator-Cars,  14  ft  6  in,  from  top  of  track  to  top  of  brake-staff;  floor,  4  ft 
from  track;   extreme  width,  9  ft  7  in. 

Ordinary  Freight-Cars  are  about  13  ft  high  to  top  of  brake-staff  and  9  ft  4  in 
in  extreme  width.  The  height  of  floor  of  freight-cars  varies  from  3  ft  8  in  to  4 
ft  above  top  of  track  for  standard-gauge,  and  from  3  ft  to  3  ft  6  in  for  nar- 
row-gauge cars.     Standard-gauge,  5  ft  S^  in. 


Dimensions  of  Bowling-Alleys  1643 

Passenger-Coaches  vary  from  14  to  16  ft  in  height  and  from  10  to  11  ft  in 
width.  Doors  to  admit  cars  should  give  at  least  12  in  clearance  on  each  side, 
and  2  ft  overhead. 

Street  Trolley-Cars  are  about  8  ft  6  in  wide  for  the  car  proper,  and  the  steps 
project  about  8  in.  Height  from  track  to  top  of  coach,  11  ft  6  in;  the  trolley- 
stand  is  18  in  higlier.  The  length  varies,  up  to  42  ft.  Trucks  for  a  41  ft  6  in 
car  are  about  24  ft  apart.  Wheel-bases,  4  ft  center  to  center.  Radius  of  short- 
est curve  in  Denver,  Colo.,  35  ft  to  midway  between  rails.  The  gauge  of  a  rail- 
road track  is  the  distance  between  the  inner  sides  of  the  heads  of  tine  two  rails. 
The  standard  or  broau  gauge  is  4  ft  8^2  in;  standard  narrow  gauge,  3  it  3]^^  in. 

Capacity  of  Freight-Cars.  Car-Loads.  The  capacity  of  freight-cars,  and 
the  minimum  car-loads,  vary  so  greatly  that  no  accurate  general  information 
can  be  given.  For  heavy  freight,  25  tons  is  an  average  load;  for  light  freight, 
from  12  to  15  tons;  for  household  goods,  10  tons  is  about  the  minimum;  for 
lime,  15  tons  is  about  a  minimum  load;  for  cement,  20  tons.  The  minimum 
car-load,  to  obtain  car-load  rates,  varies  with  different  roads,  and  also  with  the 
rate  made;  a  low  rate  is  usually  made  on  the  basis  of  a  big  load.  Thirty  tons 
is  a  good  load  for  heavy  freight,  and  40  tons  is  about  the  maximum,*  except  for 
special  cars. 

Miscellaneous  Dimensions.  Horse-Stalls.  Width,  from  3  ft  10  in  to  4  ft 
or  else  5  ft  or  over;  length,  9  ft.  The  width  should  never  be  between  4  ft  and 
5  ft.  as  a  horse  is  liable  to  cast  himself. 

Dimensions  of  Standard  Bowling-Alleys.*  For  one  pair  of  alleys:  Room 
necessary,  83  ft  over  all;  li  ft  6  in  wide,  60  ft  from  foul-line  to  head  pin,  3  ft 
for  pins  to  back  of  alley,  4  ft  for  pin-pit,.  8  in  deep  in  front,  6  in  in  back;  alleys^ 
of  maple  flooring,  should  extend  on  and  beyond  the  foul-line  12  ft,  and  then 
4  ft  more,  making  a  i6-ft  approach  to  the  foul-line  for  the  player  to  run  to  deliver 
the  ball.  For  one  alley:  Same  length,  8s  ft;  width,  6  ft  3H  in;  closer  dimen- 
sions; beds  42  in,  gutters  9  in,  division-pieces  2%  in,  ball-return  9%  in. 

In  In 

One  alley:    Ball-return 9%  One  pair  of  alleys:  Ball-return  9% 

First-division  piece 2%  First-division  piece 2% 

Gutter . ." 9  Gutter 9 

Bed 42  Bed 42 

Gutter 9  Gutter 9 

Second-division  piece 2%  Second-division  piece 2% 

6  ft  sVi  in  *=     7SH  6  ft  3H  in  =  7SH 

To  the  75 H  in  of  the  pair  of  alleys,  should  be  added 

Gutter 9 

Bed 42 

Gutter 9 

Third-division  piece 2% 

138 

Additional  room  should  be  provided  for  the  bowlers  and  spectators  as  these 
dimensions  are  for  the  alleys  only. 

Dimensions  of  Drawings  for  Patents   (United  States).     10  by   15   in,   with 
border-line  i  in  inside  all  around. 
*  Dimensions  furnished  by  The  Brunswick-Balke-Collender  Company,  New  York  City. 


1644  Dimensions  and  Data  Part  3 

Dimensions  of  a  Barrel.  Diameter  of  head,  17  in;  diameter  at  bung,  19  in; 
length,  28  in;   volume,  7  680  cu  in. 

Miscellaneous  Memoranda.  Weight  of  Men  and  Women.  The  average 
weight  per  person  of  twenty  thousand  men  and  women  weighed  at  Boston,  Mass., 
in  1864,  was,  men,  141^^2  lb;  women,  1 24)^2  lb. 

Wooden  Flagpoles.  For  a  flagpole,  extending  from  30  to  60  ft  above  the 
roof,  the  following  proportions  give  satisfactory  results:  The  diameter  at  the 
roof  should  be  lio  .the  height  above  the  roof,  and  the  top  diameter  one-half  the 
lower.  To  profile  the  pole,  divide  the  height  into  quarters;  make  the  diameter 
at  the  first  quarter  above  the  roof,  fifteen-sixteenths  of  the  lower  diameter; 
at  the  second  quarter,  seven-eighths,  and  at  the  third  quarter,  three-quarters 
the  lower  diameter.* 

Steel  Flagpoles,  t  The  Department  of  Education,  City  of  New  York,  has 
abandoned  the  use  of  wooden  flagpoles  and  is  using  steel  flagpoles.  For  an 
ordinary  building,  60  ft  in  height  above  the  curb,  a  pole  4SV2  ft  in  height  is  used, 
which  is  sufficient  for  the  tackle  of  a  large  or  post-flag,  for  the  reason  that  roof- 
parapets  are  very  low.  Each  pole  is  required  to  be  fitted  complete  with  a  cast- 
iron,  galvanized,  revolving  truck,  mounted  on  crucible-steel  pins,  the  cap  be- 
neath it,  also,  being  of  galvanized  iron.  The  truck  is  fitted  with  two  4^4-in 
bronze  sheaves  on  Tobin-bronze  pins,  surmounted  with  an  8-in  20-oz  copper 
ball,  acid-cleaned  and  painted  with  four  coats  of  the  best  English  weather-proof 
sizing,  and  covered  with  XXXX  leaf-gold.  One  or  more  field-joints  are  per- 
mitted in  the  length  of  the  pole,  which  are  determined  according  to  standard 
details,  the  bands  being  secured  to  the  male  tube,  and  both  edges  of  the  inner 
band  and  the  shoe  being  machine-beveled  to  insure  a  perfect  fit.  The  female 
tube  is  drilled  and  secured  to  the  male  shoe  with  tap-screws  of  sufl5cient  strength 
to  carry  the  upper  section  of  the  pole,  and  the  ends  of  the  screws  are  upset. 
The  exposed  ends  of  the  female  tube  are  chamfered  and  caulked  tight.  A  steel 
collar  or  band,  to  receive  the  copper  flashing,  is  secured  to  the  pole  and  braced 
just  above  the  roof-lines. 

Dimensions  of  Schoolrooms,  Boston  Schools. t  The  sizes  of  the  rooms  in 
the  Boston  school-houses,  as  adopted  by  the  school  board,  are,  for  grammar- 
schools,  28  by  32  ft  in  plan  by  13  ft  6  in  in  height;  for  primary  schools,  24  by 
32  by  12  ft.  This  accommodates  56  scholars  per  room,  in  each  grade,  allowing 
216  cu  ft  per  scholar  in  the  grammar  schools,  and  165  cu  ft  in  the  primary  grade. 
A  width  of  27  ft  is  very  satisfactory  for  schoolrooms,  and  is  commonly  adopted 
because  it  permits  of  the  use  of  28-ft  joists,  without  waste. 

Heights  of  Blackboards  in  Schoolrooms. |  The  heights  from  floor  to  top 
of  chalk-rail  should  be  about  as  follows: 

For  third  and  fourth  grades,     chalk-rail 2  ft  i  in  from  floor 

For  fifth  grade,  chalk-rail 2  ft  2H  in  from  floor 

For  sixth  grade,  chalk-rail 2  ft  4  in  from  floor 

For  seventh  and  eighth  grades,  chalk-rail 2  ft  6  in  from  floor 

Slate  blackboards  are  made  3  ft  6  in,  4  ft  and  4  ft  6  in  high,  4  ft  being  a  very 
common  and  satisfactory  height. 

*  The  Building  Trades  Pocketbook. 

t  From  data  compiled  by  E.  S.  Hand  from  notes  furnished  by  C.  B.  J.  Snyder,  Super- 
intendent of  School  Buildings,  New  York  City. 
X  F.  E.  Kidder,  in  previous  editions. 


Dimensions  of  School-Furniture 


1645 


Sizes  of  Seats  and  Desks  for  Schools  and  Academies  * 


Space  occupied 

Nuniber  of 

Age  of  scholar 

Height  of  seat 

Height  of  desk 

by  desk  and 

desk 

or  chair 

(next  scholar) 

seat  (back  to 
back) 

years 

in 

in 

ft        in 

0 

i6  to  i8 

i6% 

29^/i 

2           9 

I 

14  to  i6 

I5H 

28 

2           9 

2 

12  to  14 

15  K2 

27K2 

2            8 

3 

10  to  12 

i4'/i 

26V^2 

2            7 

4 

8  to  10 

iM 

25H 

2            5 

5 

7  to    8 

121/4 

24 

2            4 

6 

6  to    7 

ii'/i 

22V2 

2            3 

7 

5  to    6 

101/2 

21 

2            2 

4  to    5 

■     9K2 

19 

2            0 

Desks  for  two  scholars  are  3  ft  10  in  long,  and  for  a  single  scholar,  2  ft  long. 
Aisles  are  from  2  ft  to  2  ft  4  in  wide,  according  to  age  of  scholars  and  size  of  room. 

Additional  Dataj  on  School-Houses 

Sizes  of  Rooms.  The  Department  of  Education,  New  York  City,  has  adopted, 
for  the  dimensions  of  the  schoolrooms,  the  German  standard  of  22  by  30  ft  in 
plan  by  14  ft  in  height,  with  unilateral  lighting.  These  dimensions  are  used  for 
all  grades  of  elementary  schools,  the  sittings  being  on  the  basis  of  15  sq  ft  of 
floor-space  per  pupil.  Good  light  cannot  be  had  on  desks  which  are  placed  at  a 
greater  distance  from  the  windows  than  one  and  one-half  times  the  height  of  the 
top  of  the  upper  sash  from  the  floor. 

Sizes  of  Seats  and  Desks  for  Elementary  and  High  Schools 


Space  §  occupied 

Nunil^er  of 
desk 

Age  of  scholar 

Height  X  of  seat 
or  chair 

Height  X  of  desk 

by  desk  and 
seat  (back  to 

back) 

years 

in 

in 

in 

0 

f    16  to  18 

17 

31 

32 

I 

14  to  16 

16 

30 

32 

2 

12  to  14 

IS 

28 

31 

3 

ID  to  12 

14 

26 

30 

4 

8  to  ID 

13 

24 

29}-^ 

5 

7  to    8 

12 

23 

27 

6 

6  to    7 

II 

22 

27 

7 

5  to    6 

10 

20  H 

26 

Blackboards.  For  first  and  second-year  scholars  the  chalk-rail  is  placed  2  ft 
from  the  floor,  and  the  boards  are  4  ft  high.     This  allows  the  smaller  children 

*  F.  E.  Kidder,  in  previous  editions. 

t  From  cLata  compiled  by  E.  S.  Hand  from  notes  furnished  by  C.  B.  J.  Snyder,  Super- 
intendent of  School  Buildings,  New  York  City. 

X  Heights  are  measured  as  follows:  From  the  floor  to  the  top  of  ink-well  strips  of 
desks,  and  from  floor  to  top  of  front  edge  of  seats,  and  should  not  vary  more  than  H  »n 
from  the  heights  given  in  this  table. 

Aisles  have  a  minimum  width  of  18  in  for  the  lower  grades  and  22  in  for  the  upper 
grades. 

§  If  chairs  are  used,  this  distance  must  be  increased  from  lYz  to  2  in. 


Dimensions  and  Data 


Part  3 


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Table  of  Treads  and  Risers 


1647 


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1648  Dimensions  and  Data  Part  3 

to  use  the  lower  portion.  The  upper  part  of  the  surface  is  at  a  height  convenient 
for  the  use  of  the  teacher,  there  being  much  display-work  employed  in  the  lower 
grades.  For  scholars  in  grades  from  the  third  to  the  eighth  year,  inclusive,  and 
for  high  schools  the  chalk-rail  is  placed  2y2  ft  from  the  floor  and  the  boards  are 
3  ft  6  in  in  height. 

Doors  and  Stairways.  Wardrobes  should  be  entered  from  the  classrooms 
only.  Classroom-doors  should  open  into  the  rooms,  so  as  to  afford  the  teacher 
control  in  case  of  panic.  All  exit-doors  should  open  out.  All  stairways  should 
be  shut  off  from  corridors  by  means  of  self-closing  doors,  which,  together  with 
the  stairways  and  the  enclosures,  should  be  of  lire-proof  materials.  Stairways 
should  be  of  sufficient  number  to  permit  of  the  building  being  vacated  within 
three  minutes  from  the  time  a  signal  is  given.  This  can  be  effected  by  allowing 
a  lineir  width  of  4  ft  for  the  first  50  persons  and  12  in  additional  for  each  100 
persons  in  excess  thereof.  No  stairway  is  to  be  less  than  4  ft  nor  more  than 
5  ft  in  width.  Exits  should  be  planned  so  as  to  provide  15  lin  ft  for  the  first  500 
persons  and  6  in  additional  for  each  100  persons  in  excess  thereof.  No  stairway 
should  have  more  than  15  steps  in  any  one  flight,  changes  in  direction  being 
effected  by  a  square  platform  and  no  winders  being  used.  No  stair-door  or 
exit-door  should  open  out  over  a  step.  Platforms  are  to  be  provided  for  such 
doors  and  are  to  extend  at  least  i  ft  beyond  the  edge  of  the  door  when  standing 
©pen. 

Stairs,*  The  rise  of  a  stair  is  the  height  from  the  top  of  one  step  to  the  top 
of  the  next.  The  total  rise  is  the  height  from  floor  to  floor.  The  run  is  the 
horizontal  distance  from  the  face  of  one  riser  to  the  face  of  the  next.  Risers 
are  the  upright  boards  or  other  materials  forming  the  faces  of  the  steps,  and 
the  treads  are  the  horizontal  pieces  or  surfaces  on  which  the  feet  tread. 
Treads  are  usually  from  \M  to  1^4  in  wider  than  the  run,  on  account  of  the 
NOSING.  The  height  of  an  individual  riser  or  the  rise  of  any  stairs  is  found 
by  dividing  the  total  rise  by  the  number  of  risers.  The  run  of  the  stairs 
may  be  flxed  at  will  unless  the  space  is  cramped,  but  to  secure  a  comfortable 
stair  the  run  must  bear  a  certain  relation  to  the  rise. 

Rules  for  Dimensions  of  Treads  and  Risers.  For  ordinary  use  a  rise  of  from 
7  to  7'/2  in  makes  a  very  comfortable  flight  of  stairs.  For  schools  and  for 
stairs  used  by  children  the  rise  should  not  exceed  6  in.  Stairs  having  a  rise 
greater  than  7^/4  in  are  steep.  The  width  of  the  run  should  be  determined  by 
the  height  of  the  rise;  the  less  the  rise  the  greater  should  be  the  run,  and  vice- 
versa.     Several  rules  have  been  given  for  proportioning  the  run  to  the  rise: 

(i)  The  sum  of  the  rise  and  run  should  be  equal  to  from  17  to  \^y1  in. 

(2)  The  sum  of  two  risers  and  a  tread  should  not  be  less  than  24  nor  more 
than  25  in. 

(3)  The  product  of  the  rise  and  run  should  not  be  less  than  70  nor  more 
than  75. 

These  rules  apply  only  to  stairs  with  nosings.  Stone  stairs  without  nosings 
should  have  at  least  12-in  treads  for  adults.     (See  Tables,  pages  1646-7.) 

Height  of  Hand-Rail.  In  dwellings,  hotels,  apartments,  etc.,  the  height  of 
the  rail  should  be  about  2  ft  6  in  above  the  tread,  on  a  line  with  the  face  of  the 
riser.  For  grand  staircases  the  height  may  be  reduced  to  2  ft  4  in.  On  steep 
stairs  the  height  should  be  from  2  ft  7  in  to  2  ft  9  in.  The  rail  should  also  be 
raised  over  winders.  On  landings,  the  height  of  the  rail  should  be  equal  to  the 
height  of  the  stair-rail,  measured  at  the  center  of  the  tread,  the  usual  height  in 
residences  being  from  2  ft  8  in  to  2  ft  10  in. 

*  This  subject  is  quite  fully  treated  in  Building  Construction  and  Superintendence, 
Part  II,  Carpenters'  Work,  by  F.  E.  Kidder. 


Sash- Cords 


1649 


Sash-Cords.*  Until  a  few  years  ago,  linen  or  cotton  cord  only  was  used  for 
connecting  weights  with  the  sashes  of  double-hung  windows,  and  cord  is  still 
more  extensively  used  than  either  riblx)ns  or  chains.  For  windows  of  ordinary 
size  a  good  brand  of  cord  will  wear  for  a  long  time,  and  this  material  will  prob- 
ably never  be  entirely  displaced  by  metal.  "Tests  made  at  the  Massachusetts 
Institute  of  Technology  show  that  cords  wear  much  longer  than  chains,  though 
they  have  less  tensile  strength.  Cords  should  be  smooth  and  round,  so  that  each 
strand  bears  its  part  of  the  stress,  and  well  glazed,  so  that  they  have  a  smooth 
surface  aiid  consequently  less  wear  from  friction  with  the  wheel  of  the  pulley." 
It  has  been  found  that  cord  can  be  braided  too  hard  for  durability,  yet  if  it  is 
braided  so  as  to  be  very  flexible  it  may  be  so  soft  that  it  will  stretch  and  cause 
great  annoyance  by  permitting  the  weight  to  hit  the  bottom  of  the  weight-box. 
The  architect,  however,  shjuld  always  specify  the  particular  brand  and  size 
of  cord  to  be  used,  and  also  the  diameter  of  the  pulley.  Among  the  leading 
brands  of  sash-cord  at  present  are  the  Samson  Spot,!  and  the  Silver  Lake  A. J 
These  brands  are  superior  to  the  ordinary  braided  cords,  which  are  made  from 
inferior  yarns  to  meet  the  jobbers'  requirements  for  price.  In  addition  to  other 
most  excellent  qualities,  the  Samson  cord  offers  an  additional  advantage  that 
architects  will  appreciate;  it  has  a  colored  strand  woven  through  it,  which  shows 
in  spots  on  the  surface  and  thus  enables  one  to  tell  at  a  glance  that  no  other  cord 
has  been  substituted.  The  Silver  Lake  A  sash-cord  has  the  name  Silver  Lake  A 
branded  on  every  foot  of  cord;  but  unless  the  letter  A  accompanies  the  name  a 
second  grade  of  cord  is  denoted.  The  marking  of  the  cord  by  color,  or  any 
other  device,  does  not  alter  the  quality  of  the  cord.  Special  marks  may  be 
applied  to  inferior  cords  as  well  as  to  the  best.  The  following  numbers  should 
be  specihed  for  the  different  weights  of  sash- weights: 


Relative  Sizes  of  Sash-Cords,  Weights  and  Piilleys 


Size-number 

Diameter  in  inches. . . . 

Feet  per  pound 

Suitable      for     weights      in 

pounds  up  to 

Minimum  diameter  in  inches 

of  pulley  allowable  . . 


6 

7 

8 

9 

10 

12 

3/i6 

li2 

H 

%2 

Me 

H 

66 

55 

44 

36 

27 

20 

5 

12 

20 

30 

40 

50 

iH 

1% 

2 

2H 

2^/^ 

3 

For  hanging*  sashes  weighing  over  40  lb,  only  the  largest  size  of  Samson  c 
Silver  Lake  A  cord,  or  some  form  of  sash-chain  or  sash-ribbon,  should  be  used, 
and  the  pulleys  should  be  selected  to  fit  the  cord  or  chain.  A  guarantee  that  the 
cord  will  last  at  least  twenty  years  may  be  had  from  either  of  the  manufacturers 
mentioned  above.  The  Samson  wire-center  sash-cord  has  recently  been  put  on 
the  market.  This  is  really  a  metal  sash-cord  protected  by  a  braided-cotton  sur- 
face which  acts  as  a  noiseless  cushion.  It  is  claimed  that  it  harmonizes  with  the 
window-finish  and  that  it  has  greater  durability  than  other  sash-cords  or  metal 
devices.  (See  record  of  tests  made  at  Massachusetts  Institute  of  Technology, 
page  165 1.)  The  standard  color  is  that  of  dark  mahogany,  but  this  cord  is 
made  to  order  for  large  buildings  in  other  colors  to  match  the  finish. 

*  The  following  notes,  relating  to  Sash-Cords,  Sash-Chains,  Sash-Ribbons,  Sash- 
Weights  and  Sash-Balances,  are  condensed  and  revised  from  articles  by  Professor  Thomas 
Nolan,  in  Kidder's  Building  Construction  and  Superintendence,  Part  II,  Carpenters' 
Work. 

t  Manufactured  by  the  Samson  Cordage  Works,  Boston,  Mass. 

I  Manufactured  by  the  Silver  Lake  Company,  Boston,  Mass. 


1650  Dimensions  and  Data  Part  3 

Sash- Chains.  Of  several  styles  of  sash-chains  on  the  market,  the  style  most 
largely  used  is  the  flat-link  chain.*  This  chain  is  made  either  of  steel,  or  of  bronze 
composed  of  95%  copper  and  5%  of  tin.  For  suspending  very  heavy  sashes, 
doors  and  gates,  a  cable-chain  has  been  extensively  used.  Star  f  sash-chain  is 
made  of  bronze-metal.  The  manufacturers  of  the  Norris  sash-pulley  claim  that 
a  riveted  chain  that  has  joints  only  one  way  is  almost  sure  to  break  when  even 
slightly  twisted,  and  that  it  is  better  to  use  two  chains  of  the  link-pattern  run- 
ning side  by  side  over  the  same  pulley.  The  strongest  sash-chains  are  of  steel, 
made  rust-proof  by  the  hot-galvanizing  process,  and  electro-copperplated  to 
give  a  bronze  finish;  and  of  a  bronze-mixture  which  looks  like  copper,  but  is 
tougher  and  harder.  One  firm  J  claims  that  its  galvanized-steel  sash-chain  is 
from  II  to  45%  stronger  than  any  bronze  or  copper  sash-chain  and  that  it  will 
resist  fire  for  a  much  longer  period.  The  tensile  strength  of  their  chain  varies 
from  475  to  850  lb,  according  to  the  weight  used. 

Sash-Ribbons.  These  are  now  also  extensively  used  in  hanging  the  sashes  of 
the  better  class  of  buildings.  The  ribbons  are  made  of  steel  and  aluminum- 
bronze  or  of  some  mixture  of  aluminum,  and  in  %,  Yz,  ^^,  ^4  and  %-m.  widths. 
They  are  claimed  to  be  practically  indestructible,  but  according  to  one  series  of 
tests  it  would  appear  that  in  some  cases  they  do  not  wear  as  long  as  sash-cords 
or  sash-chains.  Some  people  object  that  the  ribbons  snap  against  the  pulley- 
stiles,  when  the  sash  is  raised  or  lowered,  and  thus  make  considerable  noise. 
The  %-m  ribbon  may  be  used  for  a  sash  weighing  up  to  100  lb  and  requiring 
50-lb  weights.  For  a  window  6  ft  10  in  high  and  3  ft  wide,  glazed  with  plate  glass, 
the  ribbons  with  attachments  cost  about  75  cts.  Sash-ribbons  are  now  manu- 
factured by  a  number  of  firms  who  also  make  the  necessary  attachments  for 
weight  and  sash.  For  the  best  working  of  windows  hung  with  ribbons,  pulleys 
«f  the  following  sizes  should  be  used: 


For  sashes  weighing  not  over  40  lb,  2  in 
For  sashes  weighing  not  over  60  lb,  2]i  in 
For  sashes  weighing  not  over  100  lb,  2y>  in 
For  sashes  weighing  not  over  150  lb,  3  in 
For  sashes  weighing  not  over  250  lb,  zVi  in 
For  sashes  weighing  not  over  300  lb,  4  in 
For  sashes  weighing  not  over  350  lb,  ^Yi  in 


Comparative  Strength  of  Sash-Cords  and  Chains.  The  comparative  strength 
and  durability  of  sash-cords  and  chains  have  been  determined  by  careful  tests, 
but  there  is  a  great  variation  in  both  cases,  due  partly  to  variation  in  mate- 
rial, but  principally  to  the  relative  sizes  of  the  chain  and  pulley  or  cord  and 
pulley.  The  cords  or  chains  may  be  too  light  for  the  weights  used,  or  the 
pulleys  too  small  in  diameter  to  carry  the  cord  without  undue  bending.  The 
pulleys  may  also  have  too  narrow  a  groove  or  an  uneven  groove  with  sharp 
edges  which  cut  the  cords.  The  larger  the  diameter  of  the  pulley,  the  longer 
the  wear. 

Tests  §  on  Wire-Center  Sash-Cord  and  Bronze  Sash-Chains.  The  cord 
tested  was  size  No.  8,  Y\-m  diam,  Samson  solid  braided  cotton  cord  with  steel- 

*  One  type  of  this  kind  of  sash-chain  is  manufactured  by  the  Bridgeport  Chain  Com- 
pany, Bridgeport,  Conn.  , 

t  Manufactured  by  the  U.  T.  Hungerford  Brass  &  Copper  Company,  New  York  City. 

X  The  Oneida  Community,  Ltd.,  Oneida,  N.  Y. 

§  Made  at  the  Massachusetts  Institute  of  Technology,  May,  1914,  by  Professor  E.  F. 
Miller. 


Sash-Cords,  Chains  and  Weights 


1651 


wire  cable  center,  He  in  in  diam.  The  chains  tested  were  of  two  different 
makes  of  bronze,  size  No.  2,  purchased  in  the  open  market  as  typical  bronze 
sash-chains,  each  recommended  by  a  reputable  dealer  as  the  proper  chain,  for 
use  with  a  25-lb  window-weight.  The  tests  for  the  better  of  the  two  chains  are 
those  given.  Durability-tests  were  made  by  raising  and  lowering  a  25-lb 
weight  over  a  2-in  pulley,  each  movement  corresponding  to  once  opening  and 
shutting  a  window.  The  cord  was  tested  over  the  regular  round  grooved 
pulley  ordinarily  used  for  cords,  and  the  chains  were  tested  over  the  combina- 
tion grooved  pulley  usually  furnished  for  sash-chains.  For  the  fire-tests  the 
cords  or  chains  were  hung  through  an  asbestos  box  in  which  a  Buflsen  flame 
under  pressure  was  applied  to  all  alike,  the  temperature  being  about  2  200°  F. 
A  25-lb  weight  was  attached  in  each  case  to  keep  the  cord  or  chain  under  the 
same  tension.  The  wire-center  cord  took  about  twice  as  long  to  burn  through 
and  wore  about  seventeen  times  as  long  as  the  bronze  chain. 


Tests  on  Wire-Center  Sash-Cord  and  Bronze  Sash-Chain 


Durability-tests 

Fire-tests 

Number  of  lifts  before  breaking 

Length  of  time  before  parting 

Bronze  chain 

Samson  wire- 
center  cord 

Bronze  chain, 
sec 

Samson  wire- 
center  cord, 
sec 

34  944 
37486 
37381 
32948 
40  356 
31  234 
40  790 
27874 

Average  35  377 

6S9  892 
592  559 
632  230 
594  114 
631  286 
577  154 
504  032 
637  796 

Average  603  633 

42.5 
40 
39 
32 

78.S 
75.5 

77 
75 

Average  38.4 

Average  76.5 

Weights  of  Sashes  and  Glass.  In  figuring  the  weights  of  windows,  the 
weight  of  the  glass  may  be  taken  at  3V2  lb  per  sq  ft  for  plate  glass,  iH  lb  for 
double-strength  glass  and  i  lb  for  single-strength  glass.  For  the  weight  of  the 
wooden  sash,  add  together  the  height  and  width,  in  feet,  of  each  sash,  and  mul- 
tiply by  2.1  for  2H-in  sash,  by  1%  for  iM-in  sash  and  by  i}i  for  i^6-in  sash. 
These  values  are  sufficiently  accurate  for  determining  the  size  of  sash-cords 
and  pulleys,  but  the  weights  should  be  determined  by  weighing  each  sash  after 
it  is  glazed,  as  the  weight  of  the  glass  varies  considerably. 

Iron  Sash-Weights.  The  weights  ordinarily  used  for  balancing  windows  are 
made  of  cast  iron,  in  the  form  of  solid  cylinders  from  1%  to  2%  in  in  diameter,  and 
from  7 1'^  to  31  in  long,  with  an  eye  cast  in  the  upper  end  of  each.  The  lengths 
vary  with  the  weights,  which  are  from  2  to  25  lb.  Flat  weights,  which  usually 
are  calbd  for  in  the  Philadelphia  and  some  other  markets,  are  from  6  to  34^/^  in 
long,  from  2  to  30  lb  in  weight,  and  from  iH  by  1%  to  iH  by  2%  in  in  cross- 
section.  In  ordering  sash-weights  the  number  of  pounds  of  each  weight,  and 
the  sections  and  lengths  of  the  boxes  in  which  the  weights  will  work,  should  be 
given.  Ordinary  weights  have  very  rough  eyes  for  the  sash-cords.  There  are 
a  few  manufacturers  in  the  East  who  make  weights  with  a  patent  eye  that  will 


1652  Dimensions  and  Data  Part  3 

not  cut  the  cord.  A  sectional  sash-weight*  made  with  a  well-designed  hooking- 
device  which  has  given  satisfaction,  is  said  to  be  one  of  the  best  on  the  market. 
Usually  from  three  to  six  sections  are  required  on  each  side  to  balance  a  sash 
properly.  If  the  hooking-device  fails  near  the  top  the  upper  sash  cannot  be 
closed  and  if  at  the  bottom  the  window  cannot  be  opened.  It  is  then  necessary 
to  open  the  weight-box  and  rehang  the  sections  before  the  window  can  be  oper- 
ated. In  theory,  sectional  weights  are  ideal;  in  practice,  however,  they  are 
not  considered  as  satisfactory  as  solid  weights.  The  Brown  f  sectional  weights 
are  made  2^  by  2>H  in  and  in  weights  of  6,  7,  8,  9  and  10  lb.  They  are  made 
of  both  cast-iron  and  lead.  It  frequently  occurs  after  a  contract  is  let,  that  the 
glass  is  changed  from  double-thick  to  plate  or  prism  glass.  This  means  increased 
weight;  but  the  length  of  the  sash-weight  cannot  be  increased  and  it,  therefore, 
becomes  necessary  to  increase  the  area  of  its  cross-section.  If  the  weight-box 
is  detailed  to  take  the  regular  round  sash-weight,  its  general  construction  will 
be  such  that  it  will  take  a  2-in  round  sash-weight,  but  not  a  2-in  square  sash- 
weight.  This  difficulty  can  be  avoided  by  a  little  thought  at  the  start.  An 
added  depth  of  K  in  in  the  weight-box  permits  the  use  of  a  rqptangular  cast-iron 
sash- weight.  The  Sanborn  sectional  sash- weight  i  is  intended  for  use  in  large 
buildings  of  heavy  construction.  Because  of  the  lack  of  uniformity  in  the 
weight  of  plate  glass  the  required  weights  of  sash-weights  cannot  be  accurately 
determined  previous  to  the  hanging  of  the  sashes.  By  the  use  of  a  sectional 
sash-weight,  combinations  of  units  can  be  made  up  to  suit  the  requirements. 
The  units  are  made  square  or  rectangular  in  section  in  order  to  secure  a  max- 
imum weight  with  a  minimum  length.  An  opening  of  12  in  in  the  side  of  the 
pocket  is  sufficient  for  hanging  the  largest  unit.  These  units  are  manufactured 
in  standard  sizes  to  meet  the  general  conditions  found  in  the  building  trades. 

Lead  Sash-Weights.  It  often  happens  that  for  wide  and  low  windows  the 
weights  if  of  iron  would  be  so  long  that  they  would  touch  the  bottom  of  the 
pocket  before  the  bottom  sash  was  fully  raised.  Iri  such  cases  lead  weights  are 
usually  resorted  to,  lead  being  80%  heavier  than  cast  iron.  By  casting  the 
weights  square  in  section,  whether  of  iron  or  lead,  a  considerable  saving  can  be 
made  in  the  lengths.  One  sash-weight  manufacturer!  makes  a  specialty  of 
compressed-lead  sash-weights,  with  wrought  and  malleable-iron  fastenings, 
centered  so  that  the  weights  hang  perfectly  plumb;  and  when  lead  weights  are 
necessary  the  architect  will  do  well  to  specify  the  weights  made  by  this  com- 
pany. These  weights  are  made  under  hydrauHc  pressure,  by  which  greater 
smoothness,  solidity  and  density  of  metal  is  secured  than  is  possible  by  the 
casting-process.  A  wrought-iron  rod  is  run  through  the  center,  to  which  are 
securely  attached  the  malleable-iron  fittings.  In  hanging  the  sashes  the  weights 
for  the  upper  sash  should  be  about  y2  lb  heavier  than  the  sash,  and  for  the  lower 
sash,  y2  lb  lighter. 

Sash-Balances.  Within  a  comparatively  few  years  several  devices  have 
been  patented  for  balancing  sashes  by  means  of  springs  instead  of  weights,  but 
the  author  believes  that  only  one  type,  known  as  the  sash-balance,  has  proved 
a  practical  success.  The  sash-balance  consists  of  a  drum  on  which  the  ribbon 
is  wound,  and  which  contains  a  coiled-steel  clock-spring,  immersed  in  oil;  the 
spring  sustains  the  weight  of  the  sash.  The  common  type  very  much  resembles 
in  outward  appearance  the  ordinary  sash-pulley,  and  is  applied  in  practically 
the  same  way;  the  ribbons,  which  are  made  usually  of  aluminum-bronze,  are 

*  Manufactured  by  E.  E.  Brown  &  Company,  Philadelphia,  Pa. 

t  Manufactured  by  E.  E.  Brown  &  Company,  Philadelphia,  Pa. 

t  Manufactured  by  the  Lidgerwood  Manufacturing  Company,  New  York  City. 

§  Raymond  Lead  Company,  Chicago,  III. 


Seating-Space  in  Churches  and  Theaters"  1653 

attached  to  the  sashes  in  the  same  manner  as  cords  when  weights  are  used. 
While  the  sash-balance  in  its  best  form  works  very  satisfactorily,  it  will  probably 
never  entirely  supplant  the  weight  and  axle-pulley  for  ordinary  windows.  There 
are  many  windows,  however,  for  which  sufficient  pocket-room  for  weights  cannot 
be  obtained  without  spoiling  the  effect  desired  or  narrowing  the  glass,  as  in  some 
bay  windows,  or  where  it  is  undesirable  to  break  the  frame  into  the  brick  jamb. 
In  such  cases  the  sash-balance  is  almost  invaluable.  For  hanging  the  glass 
doors  of  show-cases,  sash-balances  are  usually  preferable  to  weights.  Sash- 
balances  are  made  in  both  side  and  top-patterns,  but  the  former  are  recommended 
wherever  there  is  room  at  the  side  of  the  frame  for  the  depth  of  mortise  required. 
For  windows  of  the  sizes  usually  found  in  residences,  the  depth  of  the  sash- 
balance  measured  from  the  face  of  the  pulley-stile  will  vary  from  3  to  4  in; 
this  can  be  provided  for  usually  by  cutting  a  hole,  if  necessary,  in  the  masonry 
or  studding  back  of  the  frame.  As  sash-balances  require  only  a  plank  frame, 
the  consequent  reduction  in  the  cost  of  the  frame  offsets  the  extra  cost  of  the 
balance.  In  remodeling  old  buildings  which  have  plank  frames  without  weights, 
sash- balances  are  found  to  be  a  great  convenience,  since  they  can  easily  be  in- 
serted in  the  old  frames.  An  advantage  which  all  spring-balances  possess  is 
that  they  act  most  strongly  when  the  sash  is  down,  and  so  enable  one  to  raise 
a  binding  window  more  readily  than  if  it  were  hung  with  weights;  while  when 
the  sash  is  up  the  springs  barely  suffice  to  hold  it  in  position,  and  do  not  offer 
resistance  to  drawing  it  down.  Of  the  various  sash-balances  on  the  market,  the 
Pullman*  and  the  Caldwell f  are  the  most  extensively  used,  and  are  undoubtedly 
reliable.  The  Pullman  Unit  sash-balance  has  been  on  the  market  many  years 
and  has  proved  satisfactory.  These  balances  are  now  made  with  uniform-size 
face-plates  for  the  various  weights  of  sash  with  which  they  are  to  be  used, -and 
thus  make  it  possible  to  have  all  mortises  for  the  balances  cut  at  the  mill,  as  is 
now  done  for  the  regular  cord-pulleys.  The  Caldwell  sash-balance,  both  top 
and  side-types,  is  much  used  by  the  United  States  Post  Office  and  Navy  Depart- 
ments. It  is  used  also  by  the  leading  car-builders.  The  springs  are  made  of 
high-grade  cold-rolled  tempered-steel  wire,  a  material  similar  to  that  used  for 
clock-springs.  The  manufacturers  guarantee  these  sash-balances  for  from  ten 
to  fifteen  years. 

Seating-Space  in  Churches  and  Theaters.  The  minimum  spacing  for 
pews,  back  to  back,  is  30  in.  This  spacing  is  fairly  comfortable  for  occupants, 
but  is  a  little  cramped  for  persons  passing  by  others  into  or  out  of  the  pews. 
A  spacing  of  32  in  is  to  be  preferred,  and  if  there  is  abundance  of  room,  the  spac- 
ing may  be  made  ss  ii^-  Anything  over  33  in  is  a  waste  of  room.  A  space  of 
18  in  in  the  length  of  the  pew  is  considered  a  sitting. t 

Opera  or  Theater-Chairs  are  made  19,  20,  21  and  22  in  wide,  center  to  center 
of  arms,  and  in  arranging  them  in  rows  where  the  aisles  converge,  the  ends  are 
brought  to  a  line  on  the  aisles  by  using  a  few  chairs  that  are  either  narrower  or 
wider  than  the  standard  width.  For  churches,  a  standard  width  of  20  in  is 
the  least  that  is  desirable.  For  theaters,  21  or  22-in  chairs  are  commonly  used 
in  the  parquet,  20  or  21-in  in  the  dress-circle,  and  20  and  19-in  in  balcony  and 
gallery,  although  there  is  no  accepted  rule  in  this  respect.  On  account  of  the 
seat-lifting,  opera  or  theater-chairs  may  be  comfortably  spaced  31  in,  back  to 
back,  and  this  is  the  usual  spacing  in  halls  and  churches.  In  theaters  the 
chairs  are  usually  set  on  steps.  In  the  upper  gallery  these  steps  should  not  be 
more  than  30  in  wide;  in  the  balcony  they  are  usually  made  either  30  or  31  in 

*  Manufactured  by  the  Pullman  Manufacturing  Company,  Rochester,  N.  Y. 
t  Manufactured  by  the  Caldwell  Manufacturing  Company,  Rochester,  N.  Y. 
X  For  dimensions  of  pew-bodies  see  page  48  of  Churches  and  Chapels,  by  F,  E.  Kidder, 


1654 


Dimensions  and  Data 


Part  3 


wide,  and  in  the  parquet,  31  or  32  in  wide.  As  a  rule  the  higher- priced  scats 
arc  more  commodious  than  the  lower-priced. 

Estimating  Sealing  Capacity.  The  actual  seating  capacity  of  theaters  and 
audience-rooms  can  be  determined  only  by  drawing  the  seats  to  an  accurate 
scale,  on  the  floor-plan,  and  then  counting  the  number  of  chairs,  or  measuring 
the  linear  feet  of  pews. 

Approximate  Seating  Capacity.  For  approximate  purposes  the  seating  capac- 
ity or  required  size  of  room  may  be  determined  by  allowing  from  7  to  8  sq  ft 
to  each  seat,  or  sitting,  when  on  a  curve,  and  from  6  to  7  sq  ft  to  each  sitting 
when  in  straight  rows,  the  smaller  number  being  used  only  for  large  rooms. 
This  allows  for  aisles  and  pulpit-platform.  For  small  concert-halls  and  narrow 
rectangular  rooms,  6  sq  ft  per  sitting  will  usually  be  sufficient  allowance,  pro- 
vided only  that  the  actual  floor-space  utilized  for  seats  and  aisles  is  considered. 

Seating  Capacity  of  Several  of  the  Older  Cathedrals,  Churches,  Theaters 
and  Opera-Houses  * 


European  Cathedrals  and  Churches 
Estimating  that  one  person  occupies  an  area  of  19.7  inches  square  f 


St.  Peter's,  Rome 

Milan  Cathedral 

St.  Paul's,  Rome 

St.  Paul's,  London 

St.  Petronio's,  Bologna 

Florence  Cathedral 

Antwerp  Cathedral 

St.  Sophia's,  Constantinople, 
St.  John  Lateran,  Rome. . . . 


54  000 
37  000 
32  000 
25  600 
24  400 
24300 
24  000 
23  000 
22  900 


Notre  Dame,  Paris 

Pisa  Cathedral 

St.  Stephen's,  Vienna 

St.  Dominic's,  Bologna 

St.  Peter's,  Bologna 

Cathedral  of  Sienna 

St.  Mark's,  Venice 

Spurgeon's      Tabernacle, 
London 


21  000 
13  000 
12  400 
12  000 
II  400 
II  000 
7  000 

7  000 


European  Theaters  and  Opera-Houses 


Carlo  Felice,  Genoa 

Opera-House,  Munich 

Alexander,  St.  Petersburg.  . 

San  Carlo,  Naples 

Imperial,  St.  Petersburg  — 

La  Scala,  Milan 

Academy  of  Paris 


2560 

2370 

2332 

2240 

2  160 

2  113 

2092 

Drury  Lane,  London 

Covent  Garden,  London. 

Opera  House,  Berlin 

Adelphi,  London 

Lancaster,  London 

Globe,  London 


1948 
3000 
1636 
2300 
I  850 
I  100 


Some  Early  American  Theaters  and  Opera-Houses,  outside  of  New  York 


The  Auditorium,  Chicago.  .^ 
Academy    of    Music,    Phila- 
delphia  

Boston  Theater,  Boston 


3124 
3000 


Castle   Square   Theater, 
Boston 


Gaiety  Theater,  Boston. .  .  j 
Grand    Opera-House,    Cin- 


I  600  to 
I  800 

nearly 
3000 

I  736 


*  The  table  following  this  one  gives  the  seating  capacities  of  theaters  in  use  in  1914  in 
some  of  the  boroughs  of  New  York  City.  The  above  table  of  seating  capacities  of  some 
of  the  earlier  churches  and  theaters  is  retained  for  purposes  of  comparison.  So  many 
important  structures  of  these  types  have  been  erected  in.  recent  years  in  the  larger  cities  of 
the  world,  or  are  now  in  process  of  erection,  that  it  has  been  found  impossible  to  make 
any  list  that  would  be  and  would  remain,  for  any  length  of  time,  complete. 

t  See  note  on  page  1655. 


Seating  Capacity  of  New  York  Theaters 
Seating  Capacity  of  New  York  Theaters  (1914) 


1655 


Boroughs  of  Manhattan  and  the  Bronx 


Name 


Academy  of  Music 

Alhambra 

American 

American,  Roof 

Astor 

Belasco 

Berkley  Lyceum 

Bijou 

Broadway 

Bronx 

Carnegie  Hall 

Carnegie  Lyceum 

Casino 

Century 

Century,  Roof 

Circle 

City 

Clinton  Street  (Odeon) . . . 

George  M.  Cohan 

Colonial 

Columbia 

Comedy • 

Criterion '. . 

Daly's 

Delancy  Street 

Foxes  (Dewey) 

86th  Street 

Eltinge 

Empire 

Family 

Fifth  Avenue  (Proctor's) . 

14th  Street 

48th  Street  (Brady's) 

Fulton 


Seating 
capacity 


2653 

1389 

1683 

I  134 

I  137 

984 

416 

814 

1  776 
1764 

2  632 
640 

1465 
2  078 
I  150 

1  684 

2  289 
904 

I  072 

I  541 

131S 

696 

916 

1074 

I  242 

I  310 

1436 

89s 

I  099 

687 

I  204 

I  255 

969 

662 


Name 


Gaiety 

Garden 

Garrick 

Globe 

Gotham 

Grand 

Grand  Opera-HoUse 

Greeley  Square  (Loew's) 

Harlem  Casino 

Harlem  Opera-House 

Harris 

Herald  Square 

Hippodrome 

Hudson 

Hurtigand  Seamon's  (Music- 

Hall) 

Illington 

Irving  Place 

Keith's  Union  Square 

Kessler's  2nd  Avenue 

Kessler's  2nd  Avenue,  Roof. 

Knickerbocker 

Lafayette 

Liberty 

Lincoln  Square 

Lipzin 

Little 

Longacre 

Loew's  Fifth  Avenue 

Loew's  7th  Avenue 

Loew's  National 

Lyceum 

Lyric* 

Madison  Square  Garden . .  . . 


Seating 
capacity 


I  090 
844 
I  194 
I  626 
1888 
2093 


1393 
847 
I  160 
4588 
1077 

1093 

* 

1079 
I  080 
1803 
734 
I  351 
I  042 

I  2H 
1547 

I  030 

299 

« 

964 
I  626 
2333 

957 
I  452 
3366 


*  Data  not  furnished. 


Note  Regarding  Unit  Area  for  Seating  Capacity.  The  unit  area  given  in  the 
table  on  page  1654  appears  in  the  former  editions  of  this  book  and  seems  to  be 
too  small.  The  original  authority  for  the  data  cannot  be  determmed.  A  more 
reasonable  minimum  area  would  be  about  23^2  inches  square,  or  about  18  by  30 
iji,  or  540  sq  in,  or  about  3.8  sq  ft.     Editor. 


1656 


Dimensions  and  Data 


Seating  Capacity  of  New  York  Theaters   (1914)    (Continued) 

Boroughs  of  Manhattan  and  the  Bronx 


Name 


Madison  Sq  Garden,  Roof.. 

Manhattan  Opera-House 

Maxine  Elliott 

Metropolis 

Metropolitan  Opera-House. . 

McKinley  Square 

Miner's  Bowery , 

Miner's  Bronx  (Acme) 

Miner's  8th  Avenue 

Minsky 

Moulin  Rouge 

Murray  Hill 

Mount  Morris 

Nemo 

New  Amsterdam 

New  Amsterdam,  Roof. . . . 
New  York  Theater,  Roof. . 

Olympic 

ii6th  Street 

Odeon  145th  Street 

Park 

People's 

Philipps 

Plaza 

Playhouse 


Seating 

capacity 

700 

3200 

904 

I  ISO 

330s 

I  500 

I  168 

1798 

I  178 

1866 

I  61S 

I  224 

* 

941 

I  618 

610 

1337 

745 

I  743 

904 

I  513 

1693 

* 

1544 

879 

Name 


Proctor's  23rd  Street 

Proctor's  58th  Street 

Proctor's  125th  Street 

Prospect 

Republic 

Richmond 

Riverside 

Savoy 

Star 

St.  Nicholas 

Thalia 

Third  Avenue  (Keeney's) . . . 

39th  Street 

Tremont 

Victoria. 

Victoria,  Roof 

Wadsworth 

Wallack's 

Washington 

Weber's 

West  End 

Weber  and  Field  Music-Hall 

Winter  Garden 

Yorkville 


Seating 
capacity 


■  Data  not  furnished. 


Borough  of  Brooklyn 


Academy  of  Music . . . 

Amphion 

Bijou 

Broadway 

Bushwick 

Casino 

Columbia 

Comedy 

Crescent 

DeKalb 

Empire 

Fifth  Avenue 

Folly 

Fulton 

Gayety 

Gotham 

Grand  Opera-House. 
Greenpoint 


2  200 

I  589 

I  562 

I  969 

•2228 

ISO3 

1673 

I  123 

I  610 

2232 

I  740 

I  063 

I  840 

1492 

1455 

958 

I  515 

I  776 

Jones 

Liberty 

Linden 

Lyceum 

Lyric 

Majestic 

Myrtle 

New  Montauk. 

Novelty 

Olympic 

Orpheum 

Oxford 

Payton's 

Prospect  Hall . . 

Royal 

Shubert's 

Star 


Dimensions  of  Theaters  and  Opera-Houses 


1657 


Dimensions  of  Some  Theaters  and  Opera-Houses  ** 

The  following  are  the  dimensions,  in  feet,  of  some  of  the  earlier  theaters  in  this  country 
and  in  Europe. 


Name  and  location 


Auditorium 


Proscenium- 
opening 


Stage 


Alexander,  St.  Petersburg. . 

,  Berlin 

La  Scala,  Milan 

San  Carlo,  Naples 

Grand,  Bordeaux 

Salle  Lepeletier,  Paris 

Covent  Garden,  London. .  . 

Drury  Lane,  London 

Boston,  Boston 

Academy  of  Music,  New 
York 

Academy  of  Music,  Phila- 
delphia  

Globe,  Boston 

Museum,  Boston 

Metropolitan  Opera-House, 
New  York  § 

The  Auditorium,  Chicago. . 

Empire,  New  York 

Knickerbocker,  New  York. 

Garrick,  New  York 

Fifth  Avenue,  New  York.. 

American,  New  York 

Proctor's  Pleasure  Palace, 
New  York 

Hudson,  New  York 

Grand  Opera-House,  Cin- 
cinnati  

Castle  Square,  Bostonll 

Gaiety,  Boston 


69 

70% 

'74K2 

67I4 

67 

79K2 
77 


66 
79 
52 

74K2 

67 

69 

85!/^ 
80% 


58 


47?^3t 


7ot 


34  II 
30 


75 
92 
86 
66 
80 
78 
86 
48 
87 

83 

90 
62 
68 

100 
no 

67 

40 

71 K2 

80 

77-K 

70 
67  H 

67 
68 
60 


72 
38 
46 

73 

70 
30 

65'/2 

28'/^ 

35 

43H 

40 
302^i 

41 

45^/2 
42 


73H 


Notes  on  Theater-Dimensions.ft  "The  utmost  distance  from  the  front  of 
the  stage  to  the  rear  ought  not  to  exceed  75  ft,  or  the  limit  the  voice  is  capable 
of  expanding  in  a  lateral  direction." 

"Measured  from  the  curtain-line,  the  San  Carlo  Theater  in  Naples  is  73  ft;  the 


*  From  the  curtain  or  back  line  of  proscenium  opening, 
t  Measured  from  stage  to  center  of  ceiling. 
j  To  the  "gridiron"  or  rigging-loft. 
§  As  remodeled  in  1893. 
II   Can  be  enlarged  to  40  by  40  ft. 

II  The  plan  of  this  theater  is  in  the  shape  of  a  horseshoe. 

**  See  footnote  with  table  of  Seating  Capacities  of  Churches,  Theaters,  etc.,  page  1654, 
in  regard  to  data  relating  to  recently  constructed  buildings  of  these  types.  . 

tt  From  The  Planning  and  Construction  of  American  Theaters,  by  Wm.  H.  Birkmir*. 


1658 


Dimensions  and  Data 


Part  3 


theater  at  Bologna,  74  ft.  Of  the  London  theaters,  the  Adelphi  is  74  ft,  Covent 
Garden  80  ft,  the  Gaiety  53  ft  6  in,  Lancaster  58  ft  4  in,  Marylebone  74  ft  and 
the  Globe  47  ft  6  in." 

1  The  width  of  the  ideal  theater,  between  inside  walls,  should  be  from  70  to 
75  ft,  and  "the  ceiling  should  be  from  55  to  65,  or  even  70  ft  above  the  stage- 
level." 

"The^depth  of  the  parquet-floor  at  the  orchestra-rail  is  governed  by  the 
stage-level,  and  is  generally  from  3  ft  6  in  to  4  ft  3  in  below  the  stage.  A  depth 
of  3  ft  9  in  is  a  good  height,  as  it  fixes  the  eye  of  the  spectator  5  in  above  the 
stage-level." 

"The  height  of  the  stage,  that  is,  from  the  floor  to  the  bottom  of  the  'gridiron' 
or  rigging-loft,  should  be  2  or  3  ft  over  twice  the  height  of  proscenium-opening, 
in  order  that  the  fire-curtain  may  be  raised  the  full  height  of  the  opening." 
There  should  be  a  height  of  7  ft  above  the  gridiron  to  enable  the  fly-men  to  adjust 
their  ropes  with  facility. 

Proportioning  Gutters  and  Conductors  to  the  Roof-Surface.  The  size 
of  gutters  and  down-spouts  and  their  distance  apart  for  roofs  of  mill-buildings 
with  a  H  pitch  and  of  different  spans  are  shown  in  the  following  table:  * 


One-half  roof-span,  in  feet 

Size  of  gutter',  in  inches 

Size  of  down-spouts,  in  inches.  . 
Spacing  of  down-spouts,  in  feet. 


10 

20 

30 

40 

50 

60. 

70 

80 

5 

5 

6 

6 

7 

7 

8 

8 

3 

3 

4 

4 

5 

5 

6 

6 

50 

SO 

50 

50 

40 

40 

40 

40 

The  specifications  of  the  American  Bridge  Company  provide  as  follows  foi 
the  size  of  gutters  and  conductors:  f 


Span  of  roof 

Gutters 

Conductors 

Up  to    so  ft 
From  so    to    70  ft 
From  70    to  100  ft 

6  in 

7  in 
Sin 

4  in  every  40  ft 

5  in  every  40  ft 
5  in  every  40  ft 

Hanging  gutters  should  ha^  e  a  slope  of  about  i  in  in  every  16  ft. 

"The  Produce  Exchange  Building  in  New  York  City,  with  a  roof-area  of 
three-fourths  of  an  acre,  roughly  speaking,  has  twelve  leaders,  each  about  5  in 
in  diameter.  The  roof,  which  is  paved  with  fire-brick,  is  graded  with  slopes  of 
perhaps  one  in  fifty  toward  the  points  at  which  the  leader-openings  are  placed, 
most  of  these  draining-surfaces  being  about  40  by  70  ft  each.  The  provision 
here  made  is  equivalent  to  about  i  sq  in  of  leader-opening  to  140  sq  ft  of  roof- 
surface.  On  the  Sioane  Building,  at  19th  Street  and  Broadway,  New  York 
City;  with  a  roof-area  of  18  000  or  20  000  sq  ft,  sloping  one  in  twenty-five,  there 
are  two  leaders,  each  about  6  in  in  diameter,  and  a  third  rectangular  leader, 
4  by  6  in  in  cross-section.  This  gives  an  allowance  of  240  sq  ft  of  surface  to  the 
square  inch  of  leader-opening,  while  on  the  Massachusetts  Hospital  Life  Insur- 
ance Company's  Building  and  the  Hemenway  Building,  in  Boston,  the  proportion 
is  only  from  60  to  70  sq  ft  to  the  square  inch  of  opening. "  J 

*  H.  G.  Tyrrell. 

t  M.  S.  Ketchum. 

i  Dwight  Potter  in  The  Technology  Quarterly, 


Elevator-Service  in  Buildings  1659 

ELEVATOR-SERVICE  IN  BUILDINGS* 

General  Considerations.  An  efBcient  elevator-service  may  be  obtained  by 
machines  of  any  one  of  several  types,  the  choice  of  the  one  decided  upon  for  any 
building  depending  upon  varying  conditions.  The  following  is  a  general  classi- 
fication of  elevators  (see,  also,  page  1668): 

1.  Hydraulic  elevators: 

(i)  Vertical,  geared  hydraulic  type. 

(2)  Horizontal,  geared  hydraulic  type. 

(3)  Direct-lift  plunger-type. 

(4)  Inverted  (high  pressure)  plunger-type. 

2.  Electric  elevators: 

(i)  Drum-type. 

(2)  Worm-gear  traction-type. 

(3)  Helical-gear  type. 

(4)  Gearless,  traction-type. 

(a)  Direct-drive  (one-to-one)  type. 

(b)  Two-to-one  type. 

In  addition  to  these,  there  are  also  the  belt-driven  type  of  elevators,  and  the 
HAND-POWER  elevators.  The  belt-driven  type  may  be  either  single-belt  or 
DOUBLE-BELT  driven,  the  former  being  used  with  a  reversible  motor  and  the 
latter  where  driving-power  is  taken  from  a  line-shaft.  In  view  of  varying  and 
sometimes  conflicting  claims  of  competing  manufacturers,  the  architect's  de- 
cision must  be  governed  by  impartial  engineering  judgment  rendered  after  a 
careful  study  of  the  problem  in  each  case. 

Geared  Versus  Gearless  Types  of  Elevators.  (See,  also,  page  1669.) 
There  has  been  much  discussion  regarding  the  merits  and  demerits  of  geared 
and  gearless  machines  for  elevators  and  the  efficiency  and  future  of  each. 
Manufacturers  of  gearless  traction-machines  have  claimed  that  the  use  of  the 
heHcal  gear,  for  example,  for  elevator-machines,  being  a  relatively  recent  devel- 
opment, has  not  extended  over  a  sufficient  length  of  time  to  permit  of  extensive 
or  definite  data;  that  they  are  used  for  different  and  less  severe  service  than 
that  for  which  the  gearless  traction-machines  are  employed;  and  that  they  can- 
not rival  the  gearless  traction-machines  from  the  standpoint  of  efficiency.  On 
the  other  hand,  the  manufacturers  of  helical-gear  elevator-machines  claim  that 
gears  have  been  in  successful  use  for  many  years,  the  substitution  of  helical 
gears  for  worm-gears  being  the  only  difference  made  in  the  application  to  their 
type  of  elevators;  that  the  helical-gear  elevators  installed  in  some  of  the  highest 
office-buildings  are  doing  as  much  work  as  any  gearless  traction-machines;  and 
that  the  mechanical  efficiency  of  the  helical-gear  machines  is  only  a  little  below 
that  of  the  gearless  traction  the  electrical  efficiency  under  local  or  ordinary 
running  conditions,  greater,  and  the  car-mile  consumption  in  kilowatt-hours,  less. 

Questions  of  Cost  and  Efficiency  of  Elevators.  The  principal  demerit 
of  elevator-machines  of  the  gearless  type  is  their  relatively  high  first  cost,  al- 
though even  that  is  much  lower  than  the  initial  cost  of  elevators  of  the  plunger- 
type.  The  use  of  any  gear,  whether  of  the  helical,  worm  or  spur-type,  is,  in  the 
opinion  of  many  engineers,  to  be  recommended  only  for  the  purpose  of  obtaining 

*  The  matter  relating  to  elevators  and  elevator-service  is  condensed  and  adapted  by 
permission,  from  data  furnished  by  various  engineers  and  manufacturers,  and  papers 
by  the  Otis  Elevator  Company,  New  York  City;  The  H.  J.  Reedy  Company,  Cincinnati, 
Ohio;  R.  P.  Bolton  of  The  R.  P.  Bolton  Company,  Consulting  Engineers,  New  York, 
and  author  of  "  Elevator  Service";  C  E.  Knox,  Consulting  Engineer,  New  York;  M.  W. 
Ehrlich,  Consulting  Engineer,  New  York;  and  others, 


1660  Elevator-Service  in  Buildings  Part  3 

a  higher-speed  motor,  because  a  higher-speed  motor  costs  less  than  a  low-speed 
motor.  The  heHcal  gear  is  generally  considered  a  more  efficient  type  of  gear 
than  the  worm-gear  and  has  a  deserved  place  in  the  development  of  the  eleva- 
tor-industry. The  helical-geared  traction-elevators  will  undoubtedly  be  ex- 
tensively used,  for  the  reason  that,  even  if  they  are  not  considered  b>  some 
engineers  to  be  as  good  in  some  details  as  machines  of  the  gearless,  traction- 
type,  they  are  less  expensive.  It  is  undoubtedly  true,  however,  that  the  intro- 
duction of  any  gear  means  some  los5  in  power,  and  it  is  claimed  that  tests  show 
that  low-speed  motors  can  be  designed  which  arc  in  every  way  as  efficient  as 
high-speed  motors.  The  data  and  statements  in  the  following  paragraphs  relat- 
ing to  elevator-service  in  buildings  are  presented  as  useful  aids  to  architects,  and 
include  some  opinions  and  conclusions  which  are  to  be  accepted  or  modified  in 
the  light  of  constant  additions  to  engineering  knowledge. 

A.    General  Conditions  Affecting  the  Requirements  of  Specifications 
for  Elevator-Service  * 

Electric  Versus  Hydraulic  Elevators.  The  question  of  the  type  of  eleva- 
tors, whether  electric  or  hydraulic,  is  best  determined  by  the  local  conditions,  or 
the  special  conditions  which  exist  in  every  plant.  The  relation  of  the  elevator- 
equipment  to  the  entire  mechanical  equipment  should  be  carefully  considered, 
and  should  be  decided  only  after  mature  deliberation  and  consultation  with 
unprejudiced  engineers  and  elevator-manufacturers.  At  the  present  time  (19 14) 
about  90%  of  the  elevators  being  installed  are  electric,  and  this  includes  all 
types  of  buildings  from  the  small  one  with  but  one  elevator  to  the  tall  sky- 
scrapers of  the  big  cities.  The  electric  equipment  recommends  itself,  for  while 
it  has  all  of  the  safety-features  of  the  hydraulic  equipment,  it  is  a  more  flexible 
system,  is  more  adaptable  to  all  kinds  of  conditions,  and  requires  much  less  space. 
The  question  of  space  is  a  particularly  important  consideration  in  office-buildings. 
Furthermore,  the  control-system  is  more  automatic,  the  acceleration  and  retarda- 
tion of  the  car  can  be  made  more  rapid,  and  the  stops  more  accurate;  the  effi- 
ciency, also,  is  higher  and  in  most  cases  the  cost  of  operation  lower.  (See,  also, 
paragraph  on  Comparison  of  Merits  of  Electric,  Traction  and  Hydraulic,  Plunger- 
Elevators,  page  1670.) 

Location  of  Hoistways  and  Machinery-Room.  The  location  of  the  hoist- 
ways  is  rather  a  matter  for  the  good  judgment  of  the  architect.  In  the  larger 
equipment  all  elevators  serving  one  portion  of  the  building  and  for  the  same 
character  of  service,  should  be  placed  in  one  bank  and  not  distributed  or  sepa- 
rate 1.  Thus,  all  express-elevators  should  be  together  and  in  one  bank,  as  should, 
also,  the  locals.  The  hoistways  should  be  so  placed  that  the  entrances,  in  all 
stories,  are  on  the  same  side  of  the  car.  In  some  of  the  larger  cities,  two  en- 
trances for  a  passenger-car  are  not  permitted,  unless  the  doors  ca  1  be  controlled 
by  the  attendant  without  leaving  the  operating-device.  The  machinery-room 
should  be  well  ventilated,  light  and  clean  as  possible,  in  order  that  the  machinery 
may  be  given  proper  attention.  This  room  should  also  be  largo  enough  to  make 
iihe  machines  readily  accessible  for  repairs  and  inspection.  Where  the  machines 
have  heavy  parts,  which  it  may  be  necessary  to  remove  from  time  to  time  for 
repairs,  it  is  advisable  to  locate  a  trolley-beam  with  hand-hoist  above  them  to 
facilitate  the  handling  of  these  parts. 

*  The  Otis  Elevator  Company,  New  York,  has  been  of  assistance  in  furnishing  much 
of  the  engineering  data  of  Section  A,  of  this  article  on  elevators.  Among  other  details 
it  considers  especially  those  conditions  which  should  be  considered  and  made  definite 
by  the  architect  preliminary  to  the  preparation  of  the  elevator-specifications.  The 
paragraphs  of  Section  A  sliould  be  read  in  connection  with  those  of  Section  B,  page  1667, 
and  the  data  compared. 


Number  and  Size  of  Elevators 


1661 


Number  and  Sizes  of  Elevators.  (See,  also,  pages  1673  and  1675.)  The 
number  and  sizes  of  elevators  are  governed  by  the  following  considerations:  (i) 
the  character  of  the  building,  (2)  the  height  of  the  building,  (3)  the  rentable 
area,  (4)  the  time-intervals  between  the  departures  of  cars,  (5)  the  number  of 
stories  to  be  served,  (6)  the  average  number  and  length  of  stops  per  trip,  (7) 
the  speed  of  the  elevators  and  (8)  the  type  of  elevators  used.  No  iron-clad 
rules  can  be  given  for  all  types  of  buildings,  but  the  larger  office- buildings, 
loft-buildings  or  light-manufacturing  buildings  have  been  sufficiently  regular 
in  design  to  warrant  same  general  rules,  based  upon  experience;  even  in  these 
cases,  however,  the  governing  conditions  vary  with  the  size  of  the  building. 
One  of  the  most  essential  requirements  for  a  satisfactory  plant  is  quick  ser- 
vice and  in  first-class  office-buildings  the  intervals  between  cars  should  not 
exceed  30  seconds.  The  number  of  stories  to  be  served  by  a  car  should  be  a 
consideration.  For  example,  in  a  fifteen-story  building,  assuming  that  stops  are 
made  at  80%  of  the  stories  for  one  passenger  each,  and  allowing  2  sq  ft  for  each 
passenger,  and  4  sq  ft  for  the  operator,  the  car  should  have  an  inside  area  of 
about  28  sq  ft.  In  order  to  facilitate  unloading  and  thus  increase  the  efficiency 
of  the  system,  it  is  desirable  to  have  the  width  of  the  car  greater  than  the  depth. 
In  the  above  case,  a  car  with  outside  dimensions  of  about  6  ft  wide  by  5  ft  deep 
would  give  the  best  results,  showing  a  difference  of  from  15  to  20%  between  tho 
depth  and  width.  In  specifying  the  equipment,  it  is  better  to  call  for  several 
moderate-sized  cars  and  a  high  speed,  than  for  a  few  large  cars  of  slower  spee({ 
and  larger  capacities.  Thus,  three  cars,  each  carrying  one-third  of  all  the  passen- 
gers, are  better  than  two  cars,  each  carrying  one-half,  as  the  service  is  increased 
by  making  the  period  between  cars  less.  As  the  elevator-service  largely  deter- 
mines the  success  of  a  building,  it  is  of  vital  importance  that  a  sufficient  number 
of  elevators  be  installed  to  handle  the  regular  traffic,  as  well  as  emergency-con- 
ditions in  case  of  a  shut-down.  To  illustrate  what  is  considered  the  proper 
proportion  of  passenger-elevators  for  buildings  of  various  heights,  the  following 
table  is  given,  based  upon  a  rentable  area  of  8  000  sq  ft  per  story  and  125  sq  ft 
per  person.  This  table  shows  the  various  combinations  for  elevators  with  a 
speed  of  from  400  to  500  ft  and  of  600  ft  per  min  for  buildings  of  from  10  to 
30  stories  above  the  ground. 

Table  Showing  Number  of  Elevators  Required 


Number 
of  stories 

Express 

600  ft  per 

min 

Local 

600  ft 

per  min 

Express 

600  ft  per 

min 

Local 

500  ft 

per  min 

Express 

500  ft  per 

min 

Local 

400  ft 

per  min 

10 
12 
15 
18 

18 

20 
20 

25 
30 

4 
5 
6 

7 

I  to  II 
5 

All  locals 

8 
I  to  12 

5 
I  to  IS 

6 
I  to  18 

7 

S 
5 
7 
8 

I  to  ID 
5 

5 

6 

7 

8 
(-  500  ft    ^ 
per  min 
|i  ton 

Express  to  11 
5 

j 

Express  to  10 
5 

! 

Express  to  11 

s 

f 

Express  to  12 

5 
Express  to  15 

6 
Express  to  18 

7 

i 

Express  to  11 

5 
Express  to  14 

6 
Express  to  17 

7 

I  to  11 

5 
I  to  14 

6 
I  to  17 

7 

Express  to  12 

6 
Express  to  15 

7 
Express  to  18 

8 

I  to  12 

6 
I  to  15 

7 
I  to  18 

8 

1662  Elevator- Service  in  Buildings  Part  3 

Buildings  equipped  with  both  local  and  express-service  should  have  the  same 
number  of  elevators  for  each  class  of  service.  In  the  case  of  the  twenty-five 
story  building  for  600  ft-per-min  speed,  it  is  to  be  noted  that  the  local  elevators 
are  shown  serving  from  the  first  to  fifteenth  story,  whereas  the  express-elevators 
serve  from  the  fifteenth  to  the  twenty-fifth  story.  The  express-elevators  can- 
not serve  as  many  stories  as  the  locals  on  account  of  the  extra  time  consumed  in 
the  run  to  the  first  express-landing.  With  the  distribution  as  shown,  the  service 
for  all  stories  is  about  equal,  and  both  express-elevators  and  local  elevators 
operate  on  about  the  same  schedule.  In  the  fourth  and  fifth  columns  are 
shown  what  is  considered  the  best  arrangement  with  the  express-elevators 
operating  at  a  6cx3  and  the  locals  at  a  500  ft-per-min  speed.  Upon  comparison 
with  the  second  and  third  columns,  it  will  be  noted  that  the  express-elevators 
are  to  serve  one  additional  story.  This  is  due  to  the  difference  in  si3eed  between 
the  express-elevators  and  local  elevators  and  is.  done  so  that  the  schedule  may 
still  remain  the  same  for  both.  (See,  also,  paragraph  on  the  Local  and  Express 
Round-Trip  Time,  page  1675.) 

Loads  and  Speeds.  The  sizes  of  the  machines  or  hoisting-apparatus  are 
determined  by  the  loads  and  speeds.  The  loads  for  passenger-cars  should  be 
figured  on  a  basis  of  75  lb  per  sq  ft  of  inside  area  of  platform.  The  speed  is  a 
very  important  factor,  as  the  foregoing  indicates.  This  is  usually  limited  by 
local  ordinances,  and  in  New  York  City,  cars  stopping  at  all  stories  are  not  per- 
mitted to  exceed  a  speed  of  500  ft  per  min.  For  express-service,  in  that  portion 
of  the  shaft  where  no  stop  is  made,  a  speed  of  700  ft  per  min  is  allowed.  This 
NO-STOP  DISTANCE  must  be  at  least  80  ft  or. more.  The  best  companies  for  ele- 
vator-insurance will  not  permit  electric-drum  elevators  for  a  speed  much  over 
400  ft  per  min,  whereas  the  gearless,  traction-drive  type  and  the  hydraulic  types 
are  approved  up  to  the  limits,  as  noted  above.  In  hydraulic  plants  it  is  necessary 
to  specify  the  number  of  round  trips  per  hour  for  the  entire  elevator-equipment. 
This  is  required  in  order  to  determine  an  adequate  pumpin^-plant. 

Hoistways.  The  hoistways  should  be  finished  to  plumb-line  dimensions,  so 
that  the  car  running  on  guide-rails  set  to  plumb-line  will  at  all  points  have  the 
same  clearance.  Supports  should  be  provided  adjacent  to  the  hoistway  for  the 
overhead  beams  at  a  distance,  if  possible,  of  at  least  4  ft  from  the  top  of  car- 
frame  when  the  platform  is  flush  with  the  top  landing.  This  distance  should 
be  increased  where  possible  so  that  the  car  will  have  ample  clearance,  thus 
preventing  accidents  due  to  striking  the  overhead  work,  in  case  it  should  run 
past  the  top  landing.  The  minimum  clearances  between  the  top  of  the  car- 
frame  and  the  overhead  apparatus  are  usually  limited  by  the  local  building  regu- 
lations, and  these  should  be  consulted.  In  the  case  of  the  elevators  operating 
at  a  speed  greater  than  350  ft  per  min,  the  distance  given  above  would  probably 
have  to  be  increased  in  order  to  comply  with  these  regulations.  A  pit  should  be 
provided  at  the  bottom  of  the  shaft.  This  should  be  at  least  3  ft  deep,  and  as 
is  the  case  with  the  overhead  clearances,  the  depth  is  usually  regulated  by  the 
building  regulations,  in  accordance  with  the  speed  of  the  elevator.  Wherever 
possible,  the  hoistways  should  be  so  planned  that  the  main  guide-rails  may  be 
placed  at  the  sides  of  the  car.  Supports  should  be  provided  at  all  the  floors  for 
these  rails,  and  where  the  distance  between  floors  is  greater,  than  12  ft,  inter- 
mediate supports  should  be  provided.  The  distance  from  the  supports  for  the 
overhead  beams,  to  the  penthouse  or  skylight-roof,  varies  with  the  type  of  in- 
stallation, but  can  be  accurately  obtained  from  the  elevator-manufacturer. 

Protection  of  Counterweights.  In  New  York  City  the  Bureau  of  Buildings 
requires  that  where  the  counterweights  run  in  the  same  shaft  as  the  car,  they 
must  be  protected  with  a  substantial  screen  of  iron  from  the  top  of  the  rail  to  a 


Specifications  for  Elevator-Installation  1GG3 

point  15  ft  below,  except  where  the  plunger-type  or  traction-type  elevator  is 
used. 

Building  Laws  Governing  Elevator-Installation.  The  Bureau  of  Build- 
ings, Borough  of  Manhattan,  New  York  City,  issued  regulations  *  governing 
the  construction,  inspection  and  operation  of  all  types  of  elevators,  and  the 
special  attention  of  all  architects  is  called  to  them,  as  they  are  not  only  obligatory 
there,  but  are  excellent  guides  to  practice  at  all  times.  The  foregoing  paragraphs 
are  intended  to  give  an  idea  of  what  the  architect  must  consider  and  provide 
in  a  building  for  the  reception  of  the  elevator-apparatus,  and  what  he  must 
determine  in  order  to  enable  the  manufacturer  to  intelligently  design  and  lay 
out  his  machinery. 

Standard  Designs  and  Special  Apparatus.  The  specifying  of  apparatus 
of  special  construction  is,  as  a  rule,  not  to  be  recommended.  Standard  designs 
should  be  used  as  much  as  possible,  as  (i)  they  are  more  apt  to  be  well  designed, 
tested  and  built,  (2)  they  are  undoubtedly  less  expensive,  both  in  initial  cost 
and  maintenance  and  (3)  repair-parts  may  be  more  easily  and  quickly  obtained 
and  at  less  cost. 

Specifications  for  Elevator-Installation.  The  specifications  should  include 
data  included  in  the  following  classification. 

(i)  Kinds  of  service  and  number  of  elevators  of  each  service. 

(2)  Maximum  load  wanted. 

(3)  Maximum  speed. 

(4)  Load  with  maximum  speed. 

(5)  Maximum  number  of  round  trips  per  hour  for  each  elevator. 

(6)  Method  of  control.     For   electric  elevators,  car-switch  control  should 

be  used  for  passenger-service  and  for  all  elevators  for  a  speed  over 
150  ft  per  min. 

(7)  Size  of  hoistways  and  area  of  car-platforms. 

(8)  Travel  of  car-pkitform  in  feet,  number  of  car-landings,  and  number  of 

openings  at  each  landing. 

(9)  System  used.     If  electric,  direct  or  alternating  current,  the  voltage  and, 

also,  the  phase  of  cycles  for  alternating  current  should  be  given.  If 
hydraulic,  the  steam-pressure  or  electric  current  characteristics  for 
the  pump-motors  or  the  water-pressure,  if  the  purchaser  provides  the 
pumps,  tanks  or  other  source  of  water-pressure  supply. 

(10)  A  sketch-elevation  showing  landings,  supports  for  overhead  beams,  space 

for  the  overhead  sheaves,  and  runbys  at  top  and  bottom;  a  sketch-plan 
showing  size  and  shape  of  hoistways,  entrances,  position  of  car  and 
counterweight,  guide-rails,  and  location  of  space  available  for  machines, 
pumps,  tanks,  etc.,  with  reference  to  hoistways. 

(11)  Car  and  counterweight  guide-rails,  whether  of  wood  or  steel. 

(12)  Supports  for  fastening  the  rails,  character  of  these  supports,  and  where 

and  how  located. 

(13)  Value  of  finished  car  or  cage,  that  is,  the  specified  amount  to  be  allowed 

for  each,  the  design  being  subject  to  the  approval  of  the  architect. 

(14)  Number  and  size  of  ropes,  if  not  left  to  the  judgment  of  the  elevator- 

contractor.  The  largest  sheaves  possible  should  always  be  required, 
as  this  factor  determines  largely  the  life  of  the  ropes. 

(15)  System  of  signals,  that  is,  (a)  annunciators  in  the  cars  with  push-buttons 

at  the  landings,  {b)  up  and  down  signals  in  the  cars,  with  up  and-DOWN 
buttons  at  the  landings,  so  arranged  that  a  car  going  up  receives  only 

*  Published  in  the  Record  and  Guide,  July  29th,  191 1. 


1664       ^  Elevator-Service  in  Buildings  Part  3 

UP  signals,  and  a  car  going  down  receives  only  down  signals,  each 
signal  being  automatically  reset  b}'^  the  first  car  stopping  at  the  story 
from  which  the  signal  is  given.  This  system  adds  greatly  to  the 
efficiency  of  a  battery  of  elevators,  as  it  avoids  the  confusion  of  more 
than  one  car  answering  a  signal,  or  a  car  going  in  one  direction  stopping 
for  a  passenger  going  in  the  opposite  direction.  The  number  of 
stories  at  which  each  car  is  to  land  should  always  be  specified. 
(i6)  Indicators.  Whether  at  the  ground-fioor  only,  for  the  information  of 
the  starter  regarding  the  position  of  the  cars,  or  at  all  floors.  Indi- 
cators are  unnecessary  with  the  automatic  signals  last  described,  except 
at  the  ground-floor,  as  there  is  at  each  floor  an  up  and  down  signal  to 
show  the  first  available  car  in  either  direction. 

(17)  Source  of  power.     It  should  be  specified  whether  the  connections  will  be 

brought  to  the  elevator-apparatus  by  the  purchaser  or  by  the  ele- 
vator-contractor. If  by  the  latter,  a  sketch  should  be  made  showing 
the  distance,  and  for  the  electric  system  the  specifications  should  state 
whether  the  wiring  is  to  be  open,  that  is,  on  cleats,  in  moldings,  or  in 
conduits;  the  sizes  of  wire,  and  the  switches,  cut-outs,  etc.  For  an 
hydraulic  system,  the  size  of  pipe  for  steam-supply  should  be  given. 
The  sizes  of  water-piping  should  be  left  to  the  elevator-contractor  and 
he  should  be  held  responsible  for  them.  Also,  in  the  case  of  an  hy- 
draulic system  operating  from  street-mains,  the  specifications  should 
state  by  whom  the  piping  is  to  be  done  and  who  is  to  furnish  the  water- 
meter. 

(18)  Pumps  and  tanks  in  hydraulic  plants.     These  should  be  furnished  by  the 

contractor.  The  specifications  should  state  whether  the  capacity  is 
to  be  just  ample  J;o  do  the  work,  or  whether  there  is  to  be  a  reserve- 
capacity,  with  reserve-units,  to  provide  against  interference  with  the 
service  in  case  of  accident  to  a  pump  or  tank,  or  for  future  elevators; 
but  the  sizes  and  design  should  be  left  to  the  judgment  of  a  responsible 
elevator-contractor, 

(19)  Foundations  for  the  machine,  whether  they  are  to  be  provided  by  the 

purchaser  or  by  the  contractor. 

(20)  Miscellaneous.     Gratings  underneath  the  overhead  work,  pitpans,  paint- 

ing in  addition  to  the  standard  factory-finish  and  all  items  not  men- 
tioned above  are  generally  furnished  by  tlie  purchaser  under  separate 
contracts,  but  this  should  be  clearly  set  forth  in  the  elevator-specifi- 
cations. 

Safety-Devices  for  Elevators.  (See,  also,  page  1672.)  The  question  of 
safety-devices  cannot  be  too  carefully  considered  for  all  elevators,  and  for 
passenger-elevators  in  particular  only  the  best  and  most  thoroughly  tested 
apparatus  should  be  installed.  Each  car  should  be  equipped  with  the  me- 
chanical device  designed  to  grip  the  rails  and  stop  the  car  in  case  it  exceeds  a 
predetermined  maximum  descending-speed,  either  from  breaking  of  the  cables 
or  from  any  other  causes.  This  safety-device  should  be  mounted  upon  the 
car-frame  beneath  the  platform,  and  should  be  operated  by  means  of  a  speed- 
governor  located  overhead.  For  speeds  above  150  ft  per  min,  this  gripping  of 
the  rails  should  be  done  gradually.  In  New  York  City  the  instantaneous  stop- 
ping is  not  allowed  above  a  speed  of  100  ft  per  min.  A  switch  for  emergency- 
use  should  be  placed  in  the  car  of  electric  elevators.  The  opening  of  this 
switch  should  stop  the  car  immediately  and  independently  of  the  regular  oper- 
ating-device. All  electric^ elevator-machines  should  be  equipped  with  an  electric 
brake.    This  brake  should  be  automatically  applied  when  the  car  stops  or  when 


Geatless  Traction-Elevators 


1665 


the  current-supply  is  interrupted.  The  brake  should  be  released  electrically  and 
applied  by  means  of  spring-pressure.  Automatic  limits  should  be  placed  at 
the  top  and  bottom  of  the  hoistway,  to  automatically  slow  down  and  stop  tha 
car  at  the  limits  of  travel,  independently  of  the  operator. 

Gearless  Traction-Elevators.*  Among  the  more  recent  developments  of 
the  elevator  industry  is  the  electric,  gearless,  traction-elevator  (Figs.  1  and  2). 
(See,  also,  Fig.  5.)  The  designing  of  an  efficient  slow- 
speed  motor  made  it  practical  to  build  a  traction-machine 
with  the  driving-sheave  mounted  directly  upon  the  arma- 
ture-shaft, thus  eliminating  the  use  of 
gears  to  reduce  to  the  desired  car- 
speed.  This  gearless  machine  is  used 
for  speeds  from  250  ft  per  min  and 
above.  The  manufacturers  of  this 
type  of  machine  claim  that  it  is  the 
outcome  of  a  general  tendency  toward 
simplicity  in  design  with  efficiency  in 
operation.  The  machines  are  gener- 
ally located  over  the  hatchway.  The 
car  is  supported  by  cables  which  lead 
from  the  car  directly  over  the  driving- 
sheave,  with  overhead  installation, 
then  partially  around  the  auxiliary 
idler  or  leading-sheave  and  again  over 
the  driving-sheave  to  the  counter- 
weight. With  this  arrangement  a 
complete  turn  around  the  driving- 
sheave  and  the  idler-sheave  is  ob- 
tained, giving  sufficient  tractive  effort 
to  drive  the  car.  The  machine  being 
placed  overhead,  the  cables  can  lead 
directly  to  the  car  and  counter- 
weights; and  as  this  allows  the  cables 
to  bend  in  the  same  direction,  it  is  claimed  by  the  manufacturers  that 
it  is  an  advantage  and  that  the  life  of  the  cables  is  appreciably  lengthened. 
Special  hitches  are  used  for  connections  to  the  car  and  counterweight  to 
counteract  the  twisting  effort  due  to  the  reaving  of  the  cables.  As  soon 
as  cither  the  car  or  counterweight  is  obstructed,  the  tension  in  the  cables  is 
decreased  and  consequently  the  tractive  effort  reduced.  This  arrangement, 
it  is  claimed,  brings  either  the  car  or  counterweight  to  rest  and  prevents 
running  by  the  limits  of  travel,  and  into  the  overhead  beams,  should  either 
member  land  on  the  buffers  at  the  bottom  of  the  shaft.  Underneath  both  car 
and  counterweight  are  placed  oil-buffers  designed  to  bring  the  car  or  counter- 
weight to  rest  at  the  limits  of  travel,  from  full  speed.  At  the  top  and  bottom 
of  the  hatchway  the  car  is  stopped  automatically  by  a  scries  of  electric  switches. 
The  operation  of  these  switches  is  so  timed  that  the  car  is  brought  to  a  smooth 
and  gradual  stop.  The  slow-speed  shunt-motor,  with  its  control,  makes  a  flex- 
ible system.  The  acceleration  and  retardation  may  be  arranged  to  suit  the 
particular  service-requirements.  For  speeds  below  450  ft  per  min,  it  is  the  prac- 
tice to  obtain  the  slow  speed  by  passing  the  cables  around  sheaves  mounted  in 

*  For  full  and  valuable  data  relating  to  the  relative  advantages  of  the  helical-gear 
elevators  as  compared  with  those  of  the  traction-type,  see  papers  published  by  the  H.  J. 
Reedy  Company,  Cincinnati,  Ohio,  and  others  advocating  the  geared  machines.    Editor. 


/ 


Fig. 


Compensating 

Cables 
1.     Roping   for 
to    I    Traction- 
machine 


Cojxnterweight  L 
Compensating 
Cables 
Fig.    2.    Roping  for 
2    to    I    Traction- 
machine 


1666 


Elevator-Service  in  Buildings 


Part  3 


the  cross-head  of  the  car  and  of  the  counterweight,  and  anchoring  the  ends  of 
the  cables  at  the  top  of  the  hoistway.  These  sheaves,  with  their  ball  bearings, 
are  specially  made  to  withstand  the  heavy  service  to  which  they  are  subjected. 
In  addition  to  the  above  details,  elevators  of  this  type  should  be  provided  with 
all  of  the  regular  safety-devices  used  with  passenger-elevators. 

Electric  Elevators  with  Push-Button  Control.  One  of  the  most  ingenious 
and  serviceable  developments  in  the  elevator-industry  is  that  of  the  automatic 
electric  elevator  with  push-button  control.  In  New  York  City  this  type  of 
elevator  is  permitted  only  in  residences,  but  in  other  cities  it  is  used  in  apart- 
ments/hospitals, and  other  places  where  the  service  is  very  light  and  intermittent, 
and  it  is  desired  to  dispense  with  an  attendant.  In  the  design  of  these  elevators 
it  has  been  the  aim  to  provide  all  safety-devices  and  appliances  to  make  the  in- 
stallation absolutely  safe,  so  that  the  elevators  may  be  operated  even  by  a  child 
alone,  without  danger.  In  each  story  is  located  a  button,  similar  in  appearance 
to  the  ordinary  signal-button,  and  the  passenger,  by  pressing  this,  may  call  the 
car,  if  it  is  unoccupied  or  not  in  use,  to  any  story.  The  car  comes  to  the  story 
at  which  it  is  required,  and  stops  automatically.  When  it  comes  to  rest  in  this 
story,  the  entrance-door  to  the  hoistway  is  automatically  unlocked,  and  it  is 
then  possible  for  the  passenger  to  open  the  door  and  the  car-gate,  and  enter  the 


Fi?.  3.     Standard  Hatchway  and  Car-     Fig.  4.     Standard  Hatchway  and  Car- 
platiorm.     Side-guides  platform.     Corner-guides 


car.  The  hoistway-gates  and  the  car-gate  are  so  arranged  that  the  machine  is 
inoperative  until  both  are  tightly  closed.  The  hoistway-doors  can  be  opened 
from  a  hall,  only  when  the  car  is  at  the  landing  of  that  particular  hall.  In  the 
car  is  a  bank  of  buttons  corresponding  to  the  various  stories  served,  and  also 
a  stop-button  or  emergency-button.  After  entering  the  car,  and  closing  the 
hatchway-door  and  the  car-gate,  the  passenger  can  push  the  button  in  the 
car  corresponding  to  the  story  to  which  he  desires  to  go.  The  car  will  proceed 
to  the  designated  story  and  stop  automatically.  Should  the  passenger  desire, 
for  any  reason,  to  stop  the  car  at  any  point  of  its  travel,  he  can  do  so  by  pushing 
the  stop  or  pmergency-button.  The  car  is  in  the  complete  control  of  the  pas- 
senger, as,  after  the  initial  operation  of  calling  or  sending  it  to  a  landing,  its 
further  operation  cannot  be  interfered  with  until  after  both  the  hatchway-door 
and  the  car-gate  are  opened  and  closed.  This  means  that  no  other  person  can 
call  the  car  until  after  the  passenger  has  reached  the  desired  landing,  left  the 
car,  and  closed  the  gate  and  door.  In  some  equipments  for  elevators  of  this  type, 
the  device  for  releasing  the  door-lock  is  prevented  from  operating  while  the  car 
is  in  motion.    This  is  a  very  desirable  safety-feature,  as  otherwise  each  lock 


Electric-Elevator  Service  1667 

is  temporarily  released  as  the  car  passes  up  or  down  the  hoistway,  and  a  person 
on  a  landing  can  open  the  door  during  the  momentary  period  that  it  is  unlocked. 
In  some  cases  the  gate  on  the  car  is  omitted;  but  this  is  a  very  dangerous  prac- 
tice and  should  not  be  permitted.  Elevators  of  this  type  are  designed  for  oper- 
ation with  direct  current  or  alternating  current,  and  single  or  multiphase 
circuits.  Single  phase  should  be  avoided,  if  possible,  and  before  deciding  upon 
this  type  of  current,  the  consent  of  the  electric  power  company  should  be  ob- 
tained for  placing  upon  their  lines  a  motor  with  the  heavy  inrush  of  current 
required  at  starting. 

Standard  Relations  of  Hatchway,  Platform  and  Car-Sizes.  (See,  also, 
page  1675.)  In  Figs.  3  and  4  are  shown  some  typical  elevator  layouts  for 
electric  installations,  with  side  and  corner-posts  and  steel  construction.  (See, 
also.  Fig.  7.)  The  clearances  shown  are  for  elevators  traveling  at  a  speed  of 
450  ft  per  min  or  more,  and  may  be  reduced  about  i  Vz  in  for  elevators  of  slower 
speed.  Some  of  the  minimum  dimensions  given,  with  Figs.  3  and  4  vary  slightly 
from  those  given  with  Fig.  7  and  in  Table  D,  page  1676,  but  agree  in  the  essen- 
tial requirements. 

B.    Electric,  Passenger-Elevator  Systems  * 

Elevator-Development.  The  object  in  view  in  presenting  this  material  is 
not  to  discuss  all  the  details  of  elevator-construction  or  the  mechanical  features, 
but  to  outline  the  results  of  a  study  in  connection  with  the  economic  division  of 
passenger-elevators  and  an  efficient  elevator-service  for  the  traffic  of  the  modera 
commercial  or  distinct  type  of  office-building.  The  requirement  of  such  build- 
ings is  a  very  ample  and  adequate  elevator-service,  not  only  because  the  mon- 
etary value  of  the  building  may  otherwise  be  affected,  but  in  time  of  necessity, 
as  during  a  fire  or  other  panic,  the  occupants  must  be  readily  brought  to  safety. 
During  the  early  development  of  the  sky-scraper  the  necessity  for  a  proper 
elevator-service  was  partly  overlooked,  and  perhaps  not  altogether  realized,  for 
some  of  the  older  buildings  suffer  from  a  lack  of  traveling-facilities,  resulting 
in  an  inconvenience  to  the  many  occupants.  The  tenants  of  the  upper  stories 
are  therefore  obliged  to  wait  on  the  up  trip  of  the  elevator,  and  the  people  occu- 
pying the  lower  portion  of  the  building  are  left  behind  on  the  down  trip. 

The  Extensive  Use  of  Elevators.  To  fully  indicate  the  extensive  use  to 
which  the  elevator  has  been  adopted  for  passenger  traffic  in  large  cities,  the  in- 
stance of  the  Borough  of  Manhattan  of  New  York  City  is  given.  There  were 
in  19 14  about  10  000  machines  in  service,  twice  the  number  that  were  in  oper- 
ation in  1904,  and  these  were  divided  among  the  different  classes  of  buildings 
approximately  as  follows: 

5  000  elevators  in  office-buildings  over  10  stories  high. 
I  500  elevators  in  office-buildings  under  10  stories  high. 

500  elevators  In  loft-buildings. 

700  elevators  in  residences. 

800  elevators  in  apartment-houses. 

500  elevators  in  department  and  other  stores. 
I  000  elevators  in  hotels,  clubs,  institutions,  etc. 

*  The  matter  in  Section  B  of  this  article  on  Elevators  is,  by  permission,  condensed 
and  adapted  from  data  contained  in  papers  by  M.  W.  Ehrlich,  consulting  engineer.  The 
papers  first  appeared  in  the  Aprii,  May  and  June,  1914,  issues  of  Electrical  Engineering, 
and  afterwards  were  published  in  condensed  form  in  Lefax,  by  the  Standard  Corpora- 
tion of  Philadelphia.  Section  B  includes  a  brief  outline  of  elevator-development,  some 
economic  considerations  and  some  installation-data,  and  the  paragraphs  of  this  Section 
should  be  read  in  connection  with  those  of  Section  A,  page  1580,  and  the  data  compared. 


1668 


Elevator- Service  in  Buildings 


Part  3 


Besides  these  passenger-cars,  the  buildings  requiring  freight-service  involved 
an  additional  lo  ooo  machines. 

Two  Common  Types  of  Elevators.  In  modern  elevator-practice  there 
are  but  two  comm3n  types  of  successful  machines  in  use,  the  hydraulic  and  elec- 
tric elevators.     These  may  both  be  subdivided  in  the  classification  according 

^^/'TcL Motor  and 
'^^~^.    Driving  Sheave 

Idler  Sheave 


U' 


Counter 
weight 


Elevator- car 


GEARLESS.TRACTION, ELECTRIC 

OVERHEAD-DRIVE 


Counter 
weight 
Idler  Sheave  1 

Motor  and 
\V^   Driving  Sheavo 

WORM-GEAR,  ELECTRIC 

BASEMENT- DRIVE 


^^ 


CyKnder 


^Pressure  Tank 

Casing 


Pump 


— I        ]  Discharge -Tank 
VERTICAL  CYLINDER.HYDRAULIC  DIRECT-ACTING.PLUNGER 

Fig.  5.    Some  Types  and  Varieties  of  Elevators 

to  the  mode  of  drive  or  operation  and  the  transmission  of  ix)wer,  thereby  showing 
an  apparent  variety  of  elevators.  The  machine  of  the  hydraulic  type  may  be 
of  the  vertical-cylinder  pattern  or  of  the  plunger-type,  while  the  electrical  appa- 
ratus may  be  of  the  drum,  worm-gear  or  gearless  traction-type.  Some  of  the 
types  and  varieties  are  illustrated  in  Fig.  5.  (See,  also,  Figs.  1  and  2,  page  1665, 
and  general  classification  on  page  1659.) 

A  Short  Historical  Account  of  the  Development   of  the  Commercial 
Passenger-Elevator  brings  one  back  a  little  more  than  half  a  century  to  the 


Traction  and  Geared  Elevators  1669 

introduction  of  the  first  steam-elevator.  This  fjorm  of  drive  was  soon  replaced 
by  the  water-balance  type  of  hydraulic  elevator,  which,  even  though  a  faster 
machine,  proved  to  be,  in  operation,  quite  dangerous.  P'or  a  number  of  years 
this  type  enjoyed  the  distinction  of  being  the  only  high-speed  apparatus  until 
the  advent  of  the  vertical-cylinder  hydraulic  elevator,  about  twenty 
years  later.  Running-speeds  as  high  as  400  ft  per  min  were  readily  attained, 
and  on  account  of  the  ease  in  handling  and  the  safety  in  operation,  these  ele- 
vators soon  gained  favor  and  were  the  only  types  of  machines  installed  in  the 
then  tall  buildings.  The  electric  drum-machine  made  its  first  appearance  in 
New  York  during  the  year  1889,  and  owing  to  the  merits  of  this  new  system, 
the  electric  machine  soon  established  itself  as  a  successful  competitor  with  the 
hydraulic  type.  The  only  obstacle  remaining  was  to  overcome  the  slower 
speed,  and  this  brought  out  the  Sprague  long-screw  electric  elevator. 
Elevators  of  this  type  proved  quite  costly  to  maintain  and  operate,  but  on 
account  of  their  possibilities  of  speed  and  high  rise,  were  installed  in  several 
tall  structures.  These  different  types  of  elevators  helped  considerably  in  the 
development  of  the  sky-scraper  buildings,  and  as  further  building  projects 
brought  on  an  extension  in  height,  a  hitherto  unknown  condition  of  passenger- 
elevator  service  had  to  be  met.  About  the  year  1900  the  direct- acting 
PLUNGER  hydraulic  ELEVATOR  was  introduced  to  fulfil  this  increasing  demand 
of  continued  high  rise  with  high, speed.  The  inherent  safety  in  operation  and 
the  relatively  high  economy  allowed  for  no  doubt  as  to  the  possibilities  of  the 
PLUNGER,  but  after  several  years,  experience  painted  out  that  the  advantages 
of  the  hydraulic  plunger-elevator  were  somewhat  limited  in  certain  directions, 
and  only  under  conditions  of  a  rise  not  exceeding  150  ft  could  the  character- 
istics of  the  safe  and  economical  plunger-elevator  be  maintained. 

Traction  and  Geared  Elevators.  (See,  also,  page  1659.)  Recent  experi- 
ments conducted  to  perfect  an  electric  elevator  that  would  meet  the  growing 
requirements  of  heavy  passenger  traffic  in  the  newest  form  of  tall  office-build- 
ings have  resulted  in  the  production  of  what  is  now  commercially  known  as  the 
ONE-TO-ONE,  or  GEARLESS  TRACTION-ELEVATOR.  Among  the  earliest  New  York 
installations  of  this  type  of  electric  elevator  may  be  named  those  in  the  Singer 
Building  and  Tower,  and  later  those  in  the  Metropolitan  Building  and  Tower, 
while  the  latest  developments  include  the  Woolworth  and  the  Equitable  Build- 
ings. The  apparatus  used  in  the  Municipal  Building  is  one  in  which  the 
machines  are  an  adaptation  of  the  usual  double-worm-and-gear  drive  between 
a  relatively  high-speed  motor  and  a  cable-drum,  a  double  set  of  intermeshing 
spur-gears  being  employed  between  the  two  gear-shafts.  In  summarizing,  it 
might  be  well  to  mention  that  the  commercial  or  useful  life  of  an  elevator  and 
its  combined  mechanisms  seldom  exceeds  fifteen  years,  and  that  where  remod- 
eling has  been  resorted  to,  the  electric  drum  and  worm-gear  traction  have 
usually  been  substituted  for  the  hydraulic  type  in  buildings  not  exceeding 
from  twelve  to  sixteen  stories  in  height;  and  that  in  higher  structures  the 
gearless  traction-elevator  or  its  modification  in  the  form  of  an  electric  two- 
to-one  traction-elevator  has  been  resorted  to. 

Safety  of  Electric  and  Hydraulic  Elevators.  (See  page  1664.)  It  is 
true,  however,  that  both  the  electric  and  hydraulic  types  of  elevators  have 
been  perfected  to  a  state  of  high  efficiency,  and  they  may,  therefore,  be  used 
with  entire  safety.  Of  the  hydrauHc  types  it  may  be  said  that  the  plunger- 
elevators  are  inherently  safer  than  those  which  are  suspended,  or  than  even  the 
more  modern  electric  traction-elevators;  but  it  cannot  be  denied  that  the  many 
refinements  and  improved  appliances  attached  to  elevators  of  the  various  electric 
types  have  made  the  latter  as  reliable  as  hydraulic  machines  designed  according 


1670 


Elevator- Service  in  Buildings 


Part  3 


to  best  practice.  It  is  claimed  that  the  electric  traction-elevator  is  relatively 
free  from  the  element  of  danger  because  of  the  improved  methods  of  power- 
transmission  and  the  peculiar  form  of  windings  used  for  the  drive. 

Comparison  of  Merits  of  Electric,  Traction,  and  Hydraulic  Plunger- 
Elevators.     In  narrowing  down  the  question  as  to  the  merits  of  the  electric 

TRACTION-ELEVATOR   and   of   the   HYDRAULIC   PLUNGER-ELEVATOR   for   passeugcr- 

service  in  tall  office-buildings  of  to-day,  it  might  be  well  to  note  that  the  new 
elevator-installations,  almost  without  exception,  have  favored  the  electric. 
Not  only  is  the  cost  of  installing  the  traction-machine  from  25  to  35%  less  than 
that  of  the  plunger-type,  but  the  room  occupied  by  the  driving-machinery  is 
reduced  to  a  minimum,  and,  as  a  matter  of  fact,  may  be  placed  at  the  head  and 
directly  over  the  elevator-shaft.  If  no  local  supply  of  electricity  is  available  on 
the  premises,  the  public  source  may  be  resorted  to.  The  difficulty  with  the 
plunger-elevator  for  high-rise,  high-speed  work  lies  in  the  requirement  for  mov- 
ing the  mass  of  water  and  the  massive  plunger  proper,  and  as  this  immense 
weight  cannot  be  readily  and  smoothly  stopped,  the  result  is  a  sluggishness  in 
starting  and  stopping.  At  any  rate,  it  remains  an  open  question  as  to  whether 
the  economic  values  attached  to  modern  buildings  would  favor  the  installation 
of  the  plunger-elevator,  with  its  accompanying  pumping-plant,  which  neces- 
sarily occupies  considerable  floor-space.  The  choice,  therefore,  would  tend  to 
favor  the  high-rise,  high-speed  electric  traction-elevator  for  passenger- 
service.  (See,  also,  paragraph  on  Electric  Versus  Hydraulic  Elevators,  page 
1660.) 


Table  A.    Relative  Operating-Costs  of  Elevators 


Costs 


Per  cent  of  rentals 

Cents  per  car-mile . 

Dollars  per  car  per 
annum 

Per  cent  of  all  oper- 
ating-costs   


Office-building 


25 


7.2 

22 


1850 


6.8 


I  680 


II. 3 


6.5 
19 

I  600 


Loft-building       Apartment-house 


23.8 


II. o    18.015.4 


6.5 
19 


14.8 


6.2 
18 


14.0 


560 
13-6 


6.0 
18 


5-5 
17 

480 


53 
16 


10.6 


Relative  Operating-Costs  of  Elevators.  The  figures  given  in  Table  A 
may  prove  of  interest  in  pointing  out  the  relatively  higher  operating-costs  of  the 
different  electric  types  over  the  vertical-cylinder  hydraulic  and  plunger- 
elevators.  The  values  given  represent  only  the  cost  of  labor,  power,  repairs 
and  supplies.  By  a  close  perusal  of  the  amounts  listed,  it  will  be  confirmed 
that  the  economies  of  the  plunger  cannot  be  utilized  beneficially  in  tall  office- 
buildings,  on  account  of  the  mechanical  difficulties,  and  in  other  types  of  smaller 
buildings,  allowing  for  a  low  rise,  the  installation  cost  becomes  exorbitant.  If 
the  relatively  high  first  cost  of  this  type  of  machine  were  taken  into  considera- 
tion, with  an  addition  for  the  extra  cost  in  building-construction  necessary  for 
the  space  occupied  by  the  pump  and  tank-equipment,  the  total  expenditure  on 
the  whole  would  show  no  great  favor  either  way.  In  explaining  the  values 
given  in  Table  A,  it  should  be  understood  that  the  figures  are  computed  on  a 
basis  of  actual  records  of  several  buildings  that  have  been  brought  to  the  writer's 


Power-Diagrams 


1671 


notice.  The  general  method  of  comparing  records  in  business  buildings  is  to 
compare  the  costs  with  the  total  annual  income  or  rental.  The  total  oper- 
ating-costs include  the  expense  in  the  mechanical,  electrical  and  building 
departments,  covering  all  costs  of  labor  and  material  for  the  maintenance  of  the 
different  divisions  of  service.  Therefore  the  annual  cost  of  operating  an  ele- 
vator-system is  given  as  a  percentage  of  the  gross  rentals  received,  and  is 
further  stated  as  a  percentage  of  the  total  operating-expenditure  of  the  build- 
ings under  consideration.  The  average  cost  in  cents  per  car-mile  traversed  is 
also  given,  together  with  the  average  annual  cost  in  dollars  to  pay  for  the 
labor  of  operating  and  repairing,  the  necessary  power,  and  the  material  and 
supplies  required  per  single  elevator. 

Economic  Considerations.  The  efficient  operation  of  an  elevator-system 
does  not  rest  altogether  on  the  economic  division  and  disposition  of  the  cars,  as 
the  human  element  becomes  one  of  the  main  factors.  It  is  self-evident,  there- 
fore, that  the  service  of  an  elevator  is  limited  not  only  by  the  different  classes  of 
passengers  entering,  riding  and  leaving  the  conveyance,  but  by  the  experience 
of  the  hallman  or  starter  and  his  ability  to  understand  the  demands  of  the 
traffic  and  the  personal  peculiarities  of  the  elevator-operators. 

Time-Schedules.  It  is  now  common  practice  to  dispatch  the  various  ma- 
chines of  an  elevator-system  on  a  predetermined  time-schedule,  thus  avoiding 
to  a  great  extent  any  confusion  or  overcrowding  that  would  otherwise  arise. 
It  has  been  well  established  that  the  travel  of  elevators  under  consecutive-trip 
schedule-operation  allows  for  a  hi::;hly  efficient  service,  not  only  in  the  handling 
of  the  traffic,  but  in  the  demand  for  power,  which  is  thereby  reduced  to  a  min- 


Tiuie  in  SeconUs.  Up-Trip  Time  in  Seconds. Down- Xrip 

Ca)  Operation  of  one  car 


" 

1^ 

^ 

> 

/ 

l\ 

B 

/ 

7 

V. 

r       y'^ 

,"(1     1 

,            r 

\.y     .sr 

i  ^ 

-:^;#%";4^7--^c^ 

f-WS..;-;,:, 

-/^N 

^•^I^KJ  '[ 

-^^^^M 

1        ■'      * 

r±:"'::  "■■::: 

1" ±   - 

Scale  of  Time  in  Seconds  per  Round  Trip 
(b)   Operation  of  a  bank  of  elevators 
Fig.  6.     Recorded  Current-consumption  of  Gearless  Traction-elevators 


Power-Diagrams.  The  Power-diagrams  (Fig.  6)  point  to  the  effect  of  a 
poor  and  a  proper  service  under  different  conditions.  The  upper  curve  (a)  was 
taken  under  test-conditions  and  represents  the  operation  of  one  elevator.  The 
load  in  the  single  car  is  approximately  eciual  to  the  designed  machine-balance, 
both  on  the  up  and  down  trips,  and  the  number  of  stops  corresponds  to  the 
average  per  car  per  mile  under  actual  service  in  office-buildings.  This  diagram 
is  given  mainly  to  allow  for  a  proper  understanding  of  the  combined  curve  (b), 
showing  the  actual  round-trip  operation  of  a  bank  of  elevators  in  one  of  the  New 
York  sky-scraper  buildings  at  an  early-morning  hour.  The  full  or  solid-line 
curve  shows  an  excessive  power-demand  due  to  an  inconsistent  schedule,  the 


1672  Elevator-Service  in  Buildings  Part  3 

cars  having  been  dispatched  by  a  starter  who  may  be  identified  as  A",  while  the 
dotted  or  broken-line  curve  shows  the  more  expert  handling  under  the  consecutive 
trips  by  starter  Y,  the  same  operators  running  the  cars  in  each  case. 

Safety-Appliances.  (See,  also,  page  1664.)  To  minimize  the  many  acci- 
dents in  elevator-practice,  a  safety-lock  is  recommended,  so  attached  that  it 
will  not  permit  the  elevator  to  leave  a  landing  until  the  gate  has  been  locked.  ; 
Accidents  are  seldom,  if  ever,  due  to  the  faulty  behavior  of  the  elevator  proper, 
but  sometimes  the  breaking  of  suspension-ropes,  as  recorded  by  a  relatively  few 
cases,  will  result  in  a  serious  accident.  The  most  frequent  cause  of  accidents 
connected  with  the  operation  of  elevators,  is  that  due  directly  to  the  negli- 
gence of  the  operator  in  handling  the  doors  or  elevator-gates,  and  this  may  be 
avoided  by  the  installation  of  the  safety-locks  above  recommended.  So  far 
as  has  been  practically  demonstrated,  many  of  the  safety-appHances  on  the 
older  installations  designed  to  stop  a  falling  elevator  have  usually  failed  to  act; 
but  the  improved  wedge-type  of  jaw-safety,  actuated  bj^  a  speed-governor 
and  attached  to  the  more  recent  installations,  usually  acts  when  the  elevator 
exceeds  its  normal  running-speed.  This  generally  occurs  when  the  designed  or 
safe-distance  limit  has  been  passed,  and  the  jar  occasioned  by  the  final  stopping 
of  the  car  is  not  altogether  a  pleasant  experience.  The  serious  injuries  and 
fatalities  due  to  the  falling  of  an  elevator  are  proportionately  small  when  com- 
pared with  the  entire  list,  and  amount  to  about  20%  of  the  total,  whereas  the 
loss  of  life  caused  by  open  and  unlocked  gates  in  elevator-practice  today 
accounts  for  the  remaining  80%,  The  only  safety-device,  therefore,  that  may 
be  called  useful,  as  it  eliminates  the  personal  element,  is  a  safety-lock.  Of 
the  several  automatic  devices  now  available  for  this  provision  of  safety,  all  de- 
serve merit;  and  while  some  are  purely  mechanical,  others  are  actuated  elec- 
trically, and  only  by  the  installation  of  such  automatic  locks  will  unnecessary 
elevator-accidents  be  avoided. 

Signal-Systems.  A  signal-system  is  essential  to  an  efficient  service.  Auto- 
matic electric-light  indicators  at  the  different  landings,  with  a  mechanical 
indicator  on  the  ground-floor  or  street-landing,  will  be  found  highly  efficient 
even  though  not  the  simplest.  Briefly  described,  the  system  is  composed  of  a 
dynamotor  supplying  current  for  the  magnets,  push-buttons  and  lamps.  At 
each  landing  one  or  more  sets  of  push-buttons  are  arranged  for  both  the  up  and 
DOWN  signal,  and  over  each  elevator-gate  two  lamps  of  different  color,  one  over 
another,  to  indicate  the  direction  of  car-travel;  and  each  elevator-car  is  also 
provided  with  a  signal-lamp  and  a  transfer-switch  or  push-button.  A  mechan- 
ical indicator  on  the  main  landing  informs  the  starter  as  to  the  location  of  the 
different  elevators,  and  thereby  aids  him  in  exercising  full  discretion  as  to  when 
to  dispatch  the  next  car.  The  general  system  operates  in  a  manner  approxi- 
mately as  follows:  When  a  push-button  is  pressed  for  either  direction  in  any 
story,  it  actuates  a  magnet  corresponding  to  that  story,  which  iji  turn  signals 
to  the  operator  in  any  approaching  car,  thereby  indicating  a  waiting  passenger; 
and,  according  to  the  movement  of  the  elevator,  further  contact  is  made  with 
the  outside  signal-lamps  at  that  story  showing  to  the  waiting  person  the  car 
approaching  that  floor.  In  a  properly  proportioned  elevator-system  the  trans- 
fer-switch is  seldom  used,  but  in  buildings  in  which  the  travel  becomes  overtaxed 
during  the  rush-hours,  and  when  an  approaching  car  is  filled  to  its  capacity, 
the  operator  may  press  the  transfer-button  and  thereby  signal  the  car  following. 

Traffic-Capacity  of  Elevators.  The  traffic-capacity  of  an  elevator,  or 
its  passenger  accommodations  must  necessarily  be  of  such  proportions  as  to 
handle  the  travel  of  the  tenants  of  the  building  and  also  of  their  visitors  and  in- 
sure a  proper  working  schedule.    From  a  study  of  existing  systems  in  which  the 


Formulas  for  Elevator- Service  1673 

elevator-service  is  considered  adequate,  it  is  found  that  the  questions  of  build- 
ing-occupancy as  related  to  building-area  and  elevator  traffic-capacity 
may  be  combined  into  a  consideration  of  a  proper  unit  area  for  the  elevator. 
In  regard  to  the  determination  of  the  maximum  traffic-capacity  of  a  passenger- 
elevator,  experience  shows  that  an  average  weight  of  140  lb  may  be  allowed  for 
each  passenger,  and  as  each  size  of  car  has  its  corresponding  load  at  the  rated 
speed,  the  total  load  divided  by  140  gives  the  maximum  number  of  passengers  an 
elevator  can  accommodate  at  its  designed  speed.  In  another  simple  computa- 
tion for  this  result,  an  allowance  of  2  sq  ft  of  car  is  made  for  each  passenger.  The 
maximum  capacity  of  an  elevator  may  be  of  interest  in  computing  the  time  re- 
quired to  empty  a  building  in  case  of  emergency;  but  when  a  car  of  proper  unit 
area  is  installed,  this  condition  is  taken  care  of.  Tests  have  shown  that  the 
average  passenger  traffic  of  an  elevator-system  bears  a  definite  relation  to 
the  tenancy  of  the  building,  and  to  the  maximum  travel,  the  result  being  that 
expressed  in  Formula  (6). 

Number  of  Elevators.  (See,  also,  page  1661.)  Modern  practice  tends  to 
show  that  the  number  of  elevators  required  for  any  office-building  is  really 
governed  by  the  physical  aspects  and  conditions  of  that  building.  Wherever  it 
is  not  practicable  to  use  a  car  of  large  area,  the  number  required  will  certainly 
be  in  excess  of  that  necessary  when  large  cars  are  used.  It  is  not  advisable, 
therefore,  to  base  any  conclusions  on  the  number  of  cars  to  adequately  satisfy 
a  certain  condition,  unless  the  unit  area  of  the  car  is  considered. 

Local  and  Express-Elevators.  Another  important  consideration  is  the 
division  so  common  in  high-class  office-buildings,  namely,  the  proper  service  of 
LOCAL  and  EXPRESS-elevators. 

Formulas  for  Elevator-Service.  The  formulas  given  below  are  well  sub- 
stantiated, and  give  economical  service-conditions  based  on  existing  systems  in 
the  larger  cities  of  the  United  States.  By  these  formulas  the  number  of  eleva- 
tors required,  the  division  of  service,  and  their  operation  may  be  determined. 

E  =  74/24000  (i) 

f=n/2-{-2  (2) 

Te  =  (25/5  4-  5/100)  n  and  Tl  =  (25/5  -h  //lo)  n  (3) 

Me  =  2  w/7  Te  and  Ml  =  2  n/l  Tl  (4) 

Ce=  115  n/100  Te  and  Cl=  115  n/ioo  Tl  (5) 

pe  =  $00/ Te  and  pi  =  300/ Tl  (6) 

The  notations  in  the  formulas  are: 

E  =  number  of  elevators  required 
A  =  square  feet  of  gross  building-area  served 
/  =  story  at  which  express-run  terminates 
n  =  total  number  of  stories  served 
s  =  speed  of  elevator,  in  feet  per  minute 
Tl  =  local  round-trip  time,  in  minutes 
Te  =  express  round-trip  time,  in  minutes 
Ml  =  miles  traveled  per  hour  by  local 
Me  =  miles  traveled  per  hour  by  express 
CI  =  current  consumed  per  hour  by  local,  in  kilowatt-hours 
Ce  =  current  consumed  per  hour  by  express,  in  kilowatt-hours 
pi  =  passengers  carried  per  hour  by  local,  one  way,  up  or  down 
pe  =  passengers  carried  per  hour  by  express,  one  way,  up  or  down 

The  figures  in  Table  B  represent  the  average  load  and  speed-combinations 
for  various  heights  of  buildings,  together  with  the  usual  area  of  the  elevator- 


1074 


Elevator-Service  in  Buildings 


Part  3 


CAR  consistent  with  the  standard  sizes  manufactured,  and  should  be  used  as  a 
basis  for  selecting  the  proper  unit  areas  in  connection  with  l^onnula  (i).  Tho 
many  factors  entering  into  the  operation  of  an  elevator  would  affect  tho  current- 
consumption  to  a  considerable  extent,  as  may  be  seen  in  Fig.  0,  previously  ex- 
plained. But  Formula  (5)  agrees  with  modern  service  under  average  operating- 
conditions. 


Table  B.    Unit  Area,  Load  and  Speed-Combinations 


Number 
of  stories 

Car-area, 
sqft 

Load, 
lb 

Speed, 
ft  per  min 

8  to  13 
14  to  22 
23  to  30 

25 

30 
40 

I  700 
2000 
3000 

250  to  350 
350  to  600 
400  to  600 

Table  C.    Elevator-Installation  Data 


I                              2 

3 

4         1         5                  6         1       .    7 

Building 

Number  of  elevator?  required 

Number 
of  stories 

Gross  area, 
sqft 

Total 

car-area, 

sqft 

Cars 
at  25 
sqft 

Cars 
at  30 
sqft* 

Cars 
at  40 
sqft 

By 
Formula  (i) 

8 
10 
12 
14 
16 
18 
20 
25 
30 

80  000 
100  000 
120  000 
210  000 
240  000 
270000 
300000 
375000 
800  000 

89 
III 
133 
262 
300 
337 
375 
577 
I  221 

4 
4 
5 
II 
12 

14 

4 

4 

5 

9 

10 

II 

13 

16 

33 

9 
10 
II 
13 

19 
40 

15 

10 
15 

30 

Number 
of  stories 

8                        9 

10           1           II 

12 

Round  trip  time  in  minutes 

/.or 

express-run, 

in  stories 

Tl  at  350  ft 
per  min 

Tl  at  500  ft 
per  min 

Teat  500  ft 
.  per  min 

Te  at  600  ft 
per  min 

8 
10 
12 
14 
16 
18 
20 
25 
30 

1.3 
1-7 
2.0 
2.4 
2.7 



2.1 

2.4 
2.7 
3  0 

1.6 
1.8 
2.0 
2.5 
3  0 

10 
II 
12 
15 

TT 

1.8 
2.3 

2    T 

Hatchways  and  Car-Platforms 


X675 


Installation-Data.  In  order  to  facilitate  the  ready  understanding  of  the 
various  formulas  given,  Table  C,  embodying  the  computations,  is  presented. 
The  various  headings  included  are  numbered  in  respective  order  from  i  to  i2,l 
so  that  an  explanation  of  the  items  considered  will  not  be  confusing.  Under' 
column  I  is  listed  the  heights  of  buildings,  with  the  assumed  floor-areas,  extend-! 
ing  the  full  height  of  the  structure,  given  in  column  2.  In  column  3  are  listed 
the  actual  square  feet  of  car-area  now  provided  in  many  buildings  of  similar 
floor-space  and  with  an  adequate  service.  This  is  intended  as  a  guide  where 
the  considerations  in  planning  the  building  have  included  a  means  of  accom- 
modating the  standard-sized  elevators  most  suitable  for  that  building  and  where 
serious  attention  has  been  given  to  the  disposition  of  the  cars.  But,  on  the 
other  hand,  the  values  listed  may  also  be  used  to  advantage  in  proportioning 
the  number  of  elevators  required  under  any  conditions,  and  where  the  physi- 
cal aspect  of  the  building  does  not  allow  for  an  economic  disposition  of  the} 
elevators.  Any  conservative  unit  area  best  suited  to  the  conditions  may  then 
be  allotted  for  each  car,  and  the  numl^er  of  elevators  then  determined.  Col- 
umns 4,  5  and  6  give  the  numbers  of  cars  for  various  standard  unit  areas,  while 
the  values  in  column  7  are  computed  by  Formula  (i). 

The  Local  and  Express  Round-Trip  Time  for  different  running-speeds 
is  given  in  columns  8,  9,  10  and  11  of  Table  C,  and  the  value  for  /  as  given 
in  Formula  (2)  is  given  in  column  12.  It  will  be  noticed  that  in  columns  8 
and  9  the  time  occupied  in  traversing  the  heights  of  buildings  exceeding  eighteen 
stories  is  slightly  more  than  would  actually  prove  economical.  It  might  be  well, 
therefore,  to  point  out  that  the  speeds  of  local  elevators  for  high  buildings  might 
be  increased  to  advantage;  but  whether  the  service  is  local  or  express,  it  is  not 
advisable  to  exceed  a  speed-rate  of  600  ft  per  min.  In  order  to  rectify  this  con- 
dition, under  the  speeds  considered,  the  numl:)er  of  express-elevators  must  then 
be  more  than  half  the  total  number  in  the  system,  and  a  subdivision  of  express- 
service  proper  is  also  necessary.  (See,  also,  Table  Showing  Number  of  Eleva- 
tors Required  and  notes  following,  page  166 1.) 

Sizes  of  Hatchways  and  Car-Platforms.  (See,  also,  page  166 1.)  The 
sizes  of  elevator-car  p'atforms  and  hatchways  of  unit  areas  heretofore  con- 


HW- 


////////////////////////^^/////,       /2;^^^^^^^ 


^.^ 


^5^^^^^^^^^^^^^ 
^ 


>HD 


B 

Fig.  7.  Typical  Layouts  for  Elevator-hatchways  and  Car-platforms 
sidered  are  shown  in  the  following  diagrams  (Fig.  7)  illustrating  three  typical 
forms  of  modern  installations  with  steel  guide-rails.  (See,  also,  Figs.  3  and  4.) 
The  gate  or  door-opening  may  be  either  right-hand  or  left-hand,  as  best  suited 
to  planning,  structural,  or  other  conditions.  The  clear  inside  dimensions  of  the 
necessary  hatchway  are  given,  and  also  the  clearances  required  between  this  and 
the  car.  Some  of  the  minimum  dimensions  given  with  Fig.  7  and  in  Table  D 
vairy  slightly  from  those  given  with  Figs.  3  and  4,  page  1666,  but  agree  in  the 


1676  Elevator-Service  in  Buildings  Part  3 

Table  D.     Sizes  of  Elevator-Car  Platforms  and  Hatchways 


Dimensions 

Area  of  car-platform 

25  sq  ft 
ft         in 

30  sq  ft 
ft         in 

40  sq  ft 
ft         in 

PF= inside  width  of  car 

6  p 

4  3 

2  3 

3  9 

7  0 
7        4 
7        3 

5  I 

4  9 

5  2 

6  3 
4        9 
2          3 

4  0 

7  3 
7         7 
7        6 

5  7 
5        3 
5        8 

7  o 

5  9 
2         3 
4        9 

8  0 
8        4 
8        3 

6  7 
6        3 
6        8 

D  =  inside  depth  of  car 

0= space  for  operator 

G  =  gate-opening 

//  W=  hatch-width,  car  A 

car  B 

car  C 

II D  =  hatch-depth,  car  A 

car  B 

car  C.                      .      . 

90 

/ 

1 

/ 

1 

/^ 

/ 

/ 

7 

i^^5 

it 

vV 

/ 

/ 

/ 

/ 

80 

/ 

Vl 

1 

fl 

V 

/•«; 

/ 

/ 

/ 

/ 

1 

7 

h 

rj 

f 

/ 

/ 

70 

/ 

1 1 

'/ 

// 

/ 

^% 

¥ 

/ 

/ 

// 

/  / 

' 

/I 

/ 

/ 

^. 

/ 

u 

% 
o60 

1 

/ 

'h 

1/ 

/ 

/ 

/ 

7 

/ 

t-  50 

1 

1 

// 

m 

A 

/ 

/ 

/ 

c 

f 

>/" 

/ 

/ 

/ 

/ 

/ 

i 

i 

O 

o  40 

1 

I 

V, 

// 

/ 

/ 

/ 

/ 

4> 

} 

1 , 

// 

// 

/ 

/ 

/ 

/^ 

m 

/ 

1 

m 

/ 

// 

/ 

/' 

\ 

/ 

<S^ 

sy^ 

30 

9^1 

// 

1  li 

'/ 

Z 

/ 

/ 

/ 

^ 

.^^ 

1^ 

i 

//// 

'/ 

V 

/ 

/ 

/ 

V 

y 

A 

■0^ 

5>^ 

20 
15 

§ 

k 

// 

/ 

/ 

y' 

y^ 

y^ 

'//. 

/. 

y 

/ 

X 

^ 

-^ 

j^ 

^j^ 

y. 

-"/ 

^ 

^ 

^^ 

^ 

100     150     200  :300  400  500 

Speed  of  Machine.  Feet  per  Miixute 
Fig.  8.    Motor-sizes  for  Electric  Elevators 


600 


Mail-Chutes 


1677 


Size  of  Motor.  It  is  often  helpful  to  be  informed  as  to  the  size  of  motor  re- 
quired for  an  installation,  and  the  diagram  (Fig.  8)  may  be  used  for  this  purpose. 
For  .sake  of  illustration  in  the  use  of  the  diagram,  a  speed  of  400  ft  per  min  is 
assumed,  with  a  combined  load  of  2  500  lb.  Following  the  line  marked  with  an 
arrow  from  the  speed  of  400  ft,  the  point  of  intersection  is  then  at  2  500  lb.  From 
this  point  follow  the  line  as  indicated  to  the  scale  of  motor-sizes,  and  the  result 
is  about  40  horse-power. 


Table  E. 

Current-Consumption 

Motor-size 

Starting- 
current 

Running- 
current 

20  horse-power 
40  horse-power 
60  horse-power 

102  amperes 
202  amperes 
292  amperes 

74  amperes 
147  amperes 
213  amperes 

Current-Consumption.  Table  E  gives  the  current-consumption  of  motor- 
sizes  common  in  elevator-practice.  The  figures  are  for  direct-current  motors 
operating  at  230  volts  and  are  based  on  the  results  of  tests. 

Electric  Feeders.  To  aid  in  the  selection  of  well-proportioned  electric 
FEEDERS  for  clcvator-motors,  Table  F  is  given.  The  figures  are  for  230-volt, 
direct-current  machines. 

Table  F.     Wire  and  Conduit-Sizes  for  Electric  Elevators,  2-Wire,  230-Volt, 
Direct-Current  Systems 


Wire 

Max- 

Conduit 

Motor- 

imum 
run  or 
distance 

Under- 

Trade 

Inside 

Outside 

h.p. 

Size  of  each 
wire 

carrying 
capacity, 

for  2% 

drop, 

ft 

size  for 
2  wires 

diam- 
eter, 
in 

diam- 
eter, 
in 

amperes 

15 

No.              3 

80 

154 

iKi 

1.38 

1.66 

20 

No.              I 

100 

174 

1^/2 

1. 61 

1.90 

25 

No.             0 

125 

186 

iVz 

1. 61 

1.90 

30 

No.            00 

150 

198 

2 

2.06 

2.37 

35 

No.               ODD 

175 

212 

2 

2.06 

2.37 

40 

No.        0000 

225 

226 

2 

2.06 

2.37 

45 

No.        0000 

225 

226 

2 

2.06 

2.37 

50 

300000      cm.* 

275 

248 

2\^ 

2.46 

2.87 

55 

300  000       cm.* 

275 

248 

2H 

2.46 

2.87 

60 

400  000       cm.* 

325 

272 

3 

3.06 

3.50 

•  Circular  mils. 


MAIL-CHUTES 

General  Description.  This  system  of  mailing  letters  by  means  of  a  specially 
constructed  chute  connected  with  the  receiving-box  at  the  bottom,  has  come 
into  such  general  use  in  public  buildings,  office-buildings,  apartment-houses 
^nd  hotels,  that  the  restrictions  affecting  the  same  and  what  is  required  in  the 
way  of  preparaLion  should  be  known  to  architects.  The  system  is  installed  by 
the  patentees,  under  regulations  of  the  Post-Office  Department  governing  itg 


1078 


Mail-Chutes 


Part  3 


coMstruction  and  location,  and  for  this  reason  it  is  well  to  consult  the  makers* 
before  permanently  locating  the  apparatus  on  the  plans.  It  may  be  placed  in 
any  building  of  more  than  one  story,  used  by  the  public,  where  there  is  a  free 
delivery  and  collection-service,  in  the  discretion  of  the  local  postmaster,  subject 
to  whose  approval  the  contracts  are  made. 

The  Chute  and  Receiving-Box.  The  chute  is  required  to  be  made  with  a 
removable  front  and  a  continuous,  rigid,  vertical  support  is  absolutely  necessary. 
It  must  be  of  metal,  its  front  must  be  of  plate  glass,  and  it  mu;  t  bear  the  insignia 
prescribed  by  the  department;  and  the  whole  apparatus,  when  erected  and  the 
Government  lock  put  on  the  box,  passes  under  the  exclusive  care  and  control 
of  the  Post-Office  Department,  and  the  chutes  become  a  part  of  the  receiving- 
boxes.  These  boxes  may  be  of  various  patterns  and  highly  ornamented  and  are 
furnished  by  the  makers  in  connection  with  the  chutes.  The  work  of  preparing 
a  rigid  support  for  the  chute  and  cutting  and  finishing  the  openings  in  the  floors 
is  of  the  utmost  importance,  and  details  showing  the  usual  arrangements  are 
always  given. 

Preparatory  Work.  The  requirements  for  what  the  manufacturers  call 
PREPARATORY  WORK  include  a  flat,  vertical,  continuous  surface  not  less  than 


W//////////^///////yM  LineTof 


Fig.  1.    Wooden  Support  for  Mail-chute 


'Elevator-Screen'-Nv. 


Fig.  2.    Steel  Support  for  Mail-chute 


Elevator-Screen-^ ' 


S>%'- 


I2V2XX' 

n  .Angles    ... 


Floor- 
Thimble 


Fig.  3. 


Alternate  Steel  Support  for  Mail- 
chute 


Fig.  4.  Preparatory 
Work  Complete  for 
Mail-chute 


io>^  in  wide,  extending  from  the  floor  of  the  ground-story  to  a  point  4  ft  6  in 
above  the  finished  floor  in  the  top  story,  and  an  opening  in  each  floor  directly 
in  front  of  and  centered  upon  this  surface.  These  openings  are  neatly  finished, 
and  their  size  and  shape  determined  by  setting  in  them  thimbles  of  iron  which 

♦  The  Cutler  Mail  Chute  Company,  Rochester,  N.  Y. 


Refrigerators  1679 

are  furnished  and  delivered  by  the  patentees,  as  part  of  their  contract.  In 
ordinary  installations  a  casing  of  wood,  suitably  molded  and  finished  to  match 
the  trim  of  the  building,  answers  every  purpose.  Such  a  casing  is  shown  in  plan. 
Fig.  1,  with  the  opening  finished  by  the  iron  thimble.  In  buildings,  or  some- 
times in  a  few  stories,  where  a  more  elaborate  finish  is  desired,  marble  is  sub- 
stituted for  wood,  the  form  and  construction  of  the  casing  being  adapted  to  the 
material,  but  of  course  without  disturbing  the  size  and  form  of  the  front  surface. 
Steel  angles  are  used  where  the  use  of  wood  is  objected  to,  or  where  it  is  necessary 
to  run  the  chute  in  front  of  an  elevator-screen,  or  in  other  locations  where  a  solid 
wall  is  not  available  to  support  the  casing.  Steel  square-root  angles,  2  by  2  by 
H  in  in  section,  are  generally  used,  and  set  as  in  Fig.  2,  but  sometimes,  where 
it  is  desirable  to  fill  up  the  space  between  them  and  the  elevator-screen,  they  are 
reversed,  as  in  Fig.  3.  The  angles  are  usually  bolted  to  the  beams,  and  in  any 
case  must  be  straightened  so  that  they  are  without  twists  or  kinks,  and  the  sur- 
face which  receives  the  mail-chute  plumb  and  flush  in  all  stories.  Fig.  4  gives 
a  general  view  of  the  mail-chute  casings  and  floor-openings  ready  to  receive  the 
chutes  themselves.  This  work  of  preparing  the  building,  except  the  cutting  or 
leaving  ready  the  necessary  openings  in  the  floors,  is  now  usually  included  in  the 
mail-chute  contract,  as  it  has  been  found  for  many  reasons  undesirable  to  sepa- 
rate it.  The  necessary  openings  in  floors,  and  all  patching  around  such  open- 
ings, should  be  included  in  the  mason's  or  other  proper  specifications. 

Essential  Points  to  be  remembered  are  (i)  that  no  bends  or  offsets  can  be 
made,  a  vertical  fall  being  absolutely  essential,  and  (2)  that  the  entire  apparatus 
must  be  exposed  to  view  and  must  be  accessible,  that  is,  it  is  not  permitted  to 
extend  the  work  behind  an  elevator-screen  or  partition  or  through  any  part  of 
the  building  except  a  public  corridor. 

REFRIGERATORS  * 

General  Requirements.  The  following  information  is  given  as  a  guide  to 
architects  in  providing  for  refrigerators  in  large  residences,  hotels,  clubs,  hospitals 
and  other  institutions.  Consultation  with  a  reliable  refrigerator-builder,  how- 
ever, is  always  desirable  before  deciding  upon  spaces  to  be  occupied  by  refriger- 
ators, refrigerating-rooms,  etc.,  as  a  satisfactory  refrigerator  cannot  be  adapted 
to  a  badly  proportioned  space.  (See,  also,  Design  of  Refrigerators,  under 
Mechanical  Refrigeration,  page  1691.) 

Residence-Refrigerators.  Care  should  be  taken  to  select  a  refrigerator 
which  is  simple  in  operation  and  easily  cleansed,  as  modern  sanitary  science  has 
traced  much  illness  to  faulty  refrigeration.  Thorough  insulation  is  an  important 
feature  in  a  refrigerator,  as  upon  this  depends  economy  in  the  use  of  ice  and  the 
securing  and  maintaining  of  the  low  temperature  necessary  to  the  proper  preser- 
vation of  food.  Fig.  1  shows  a  kitchen-refrigerator  for  use  of  families  of  ordi- 
nary size.  The  ice-compartment  is  located  in  the  middle  division.  The  depth 
should  not  be  more  than  3  ft  nor  less  than  2  ft,  and  the  height  may  vary  from 
4  ft  6  in  to  7  ft.  The  length  of  the  front  largely  determines  the  capacity  and 
should  range  from  about  4  to  7  ft.  Fig.  1  shows,  also,  a  most  satisfactory  method 
of  accomplishing  the  outside-icing  feature  which  consists  of  a  double  outside 
icing-door  complete,  with  frame  and  jamb.  This  is  provided  by  the  refrigerator- 
builder  to  fit  the  rough  opening  furnished  by  the  owner  in  the  outside  wall  of 

*  Valuable  data  and  the  drawings  relating  to  this  subject  were  furnished  the  author  and 
editor  by  The  Jewett  Refrigerator  'Company,  Buflfalo,  N.  Y.  Practical  data  were  furnished, 
also,  by  The  Brunswick-Balke-Collender  Company,  New  York  City.  There  are  numer- 
ous other  reliable  firms  whose  refrigerator-work  has  the  highest  reputation. 


1680 


Refngerators 


Part  3 


the  building.  With  this  method  a  minimum  outside  opening  is  required  to 
furnish  a  maximum  inside  opening  for  ice.  The  drain-pipes  should  be  as  short 
and  straight  as  possible  and  should  be  readily  detachable  for  cleansing  pur- 
poses. The  drain  should  be  properly  trapped  in  the  floor  of  the  refrigerator  and 
carried  through  the  floor  of  the  building,  discharging  over  the  plumber's  open 

connection    as   shown  in    the 
elevation  of  Fig.  1. 

Fig.  2  shows  a  refrigerator  for 
use  in  a  butler's  pantry  where 
economy  of  space  is  important. 
The  ice-compartment  is  of 
galvanized  steel  throughout 
and  is  removable  for  con- 
venience in  filling  as  it  slides 
on  roller-bearing  runways. 
When  the  ice-compartment  is 
replaced  in  position  the  out- 
side door  closes  over  it.  The 
adjoining  storage-compart- 
ment is  generally  fitted  with 
one  removable  shelf,  below 
which  is  a  bottle-rack  for 
horizontally  placed  bottles  and 
a  space  for  standing  bottles. 
The  depth  should  be  about  2 
ft  and  the  height  2  ft  8  in, 
under  counter-top.  The  length 
of  the  front  determines  the 
capacity,  but  it  should  never 
be  less  than  3  ft.  For  a  double 
refrigerator  with  a  central  ice- 
compartment  and  storage-com- 
partments at  either  side,  5  ft  is 
a  convenient  length.  The  ex- 
terior finish  and  hardware 
should  correspond  with  the 
adjacent  trim.  The  most 
sanitary  and  attractive  interior 
finishfor  storage-compart- 
ments consists  of  white  plate  glass  for  the  walls  and  ceilings  and  tile  for  the 
flooring.  The  usual  complement  of  refrigerators  for  use  in  ordinary  families 
ronsist«i  of  one  adjacent  to  the  kitchen  and  one  in  the  butler's  pantry.  For 
large  families  the  number  could  be  the  same  with  the  capacity  greater. 

Refrigerators  for  Hotels,  Clubs,  Etc.  Mechanical  refrigeration  has 
largely  superseded  ice  as  a  cooling-agent  where  the  refrigerator-equipment  con- 
sists of  several  units,  as  in  hotels,  clubs  and  institutions.  (See,  also.  Mechan- 
ical Refrigeration,  page  169 1.)  The  arrangement  of  refrigerators  is  similar  to 
that  employed  where  ice  is  used,  as  the  refrigerating-coils  are  often  contained  in 
compartments  corresponding  to  ice-compartments;  the  alternative  method  is 
to  .place  the  coils  against  walls  of  storage-compartments.  Refrigerating-coils 
are  generally  of  i}4-in  pipe,  the  length  of  coil  depending  upon  the  temperature 
required.     Fig.  3  shows  a  practical  layout   for-  the  working-department  of  a 

*  The  Jewett  Refrigerator  Company. 


KITCHEN 
PANTRY 


PLAN 


Fig.  1.*    Kitchen-refrigerator  for  Small  Family 


Refrigerators  for  Hotels,  Clubs  and  Hospitals 


1681 


ELEVATION 
Removable 
Ice-compartment 
on  Roller-bearing 
Runways-^ 


good-sized  club,  and  illustrates  the  proper  complement  of  mechanically  cooled 
refrigerators,  together  with  adjacent  operating-equipment.  No.  i,  a  store-room 
refrigerator,  has  the  front  arranged  in  one  full-height  door  and  is  fitted  with  three 
tiers  of  shelves  throughout.  No.  2,  a  meat-refrigerator,  is  also  accessible  through 
a  full-height  door  and  is  fitted  with  shelves  and  meat-racks.  No.  3,  a  broiler 
and  fish-refrigerator,  has  the  front 
arranged  in  two  doors,  each  door 
opening  onto  a  series  of  six  galvanized 
sheet-steel  pans  sliding  on  self-sus- 
taining roller-bearing  runways.  No. 
4,  a  serving-pantry  refrigerator,  is 
subdivided  by  an  insulated  partition 
into  three  separate  and  distinct  com- 
partments, those  at  the  left  and  right 
being  each  accessible  through  two 
doors,  while  the  middle  compartment 
is  accessible  through  one  door,  below 
which  is  a  series  of  four  drawers 
sliding  on  self-sustaining  roller-bearing 
runways.  The  doors  open  onto  re- 
movable shelves  throughout.  No.  5, 
an  ice-cream  refrigerator,  occupies  a 
position  in  the  serving-pantry  counter 
and  has  the  top  arranged  in  one  lift- 
off cover.  Its  interior  fittings  consist 
of  three  20-quart  porcelain-lined  ice- 
cream jars  and  one  glace-frame  for 
fancy  forms  of  ice-cream.  No.  6,  a 
pastry-refrigerator,  has  the  front  ar- 
ranged in  four  doors,  two  upper  doors 
opening  onto  removable  shelving,  and 
two  lower  doors  onto  pastry-pans 
sliding  on  angle-iron  runways.  No. 
7,  a  bar-refrigerator,  is  subdivided  by 
an  insulated  partition  into  two  sepa- 
rate and  distinct  compartments,  each 

accessible  through  four  doors.  The  upper  doors  open  onto  three  tiers 
removable  shelves  for  standing  bottles,  while  the  lower  doors  open  onto  five 
tiers  of  racks  arranged  specially  for  horizontal  bottles.  The  equipment 
described  above  will  also  satisfactorily  cover  the  requirements  of  a  moderate-sized 
hotel. 

Refrigerators  for  Hospitals.  The  usual  complement  of  refrigerators  for 
small  hospitals  consists  of  one  large  storage-refrigerator,  one  refrigerator  for 
the  chef's  use  in  or  neat  the  kitchen,  one  for  milk  and  butter  and  one  iron-lmed 
chest  for  broken  ice.  For  large  hospitals  the  same  number  with  increased  ca- 
pacity and  with  the  addition  of  small  diet-kitchen  refrigerators,  and  possibly  a 
mortuary-refrigerator  for  two  or  three  bodies,  will  meet  the  requirements. 

The  Height  of  Large  Refrigerators  for  hotels,  clubs  and  institutions,  to  be 
entered  through  full-height  doors,  should  be  from  10  to  12  ft,  if  equipped  with 
overhead  ice  or  coil-compartments;  with  side  ice-compartments  or  coils  placed 
against  walls,  the  height  should  be  7  ft  6  in  or  8  ft.    The  smaller  refrigerators, 

*  Tht  Jewett  Refrigerator  Company 


Cupboards 


Cupboards 


BUTLER'S  PANTRY 

PLAN 

Fig.  2.*    Refrigerator  for  Butler's  Pantry 


of 


1682 


Refrigerators 

Private  Dining-Room 


Enclosed 
Porch 


Main  .Dinlng-Koom 
Fig.  3.*    Plan  of  Refrigerators  for  Large  Club-house 
*  The  Jewett  Refrigerator  Company. 


Mortuary- Refrigerators 


1683 


I    /^SyCement 
TT^f     Platform 


ELEVATION 


accessible  through  half-height  doors,  hinged  covers,  drawers,  etc.,  should  be 
placed  on  a  3-in  sanitary  cement  platform  finished  with  cove  to  floor  of  building. 
These  refrigerators  should  not  be  higher  than  6  ft  6  in  unless  provided  with  over- 
head ice  or  coil-compartments,  in 
which  case  the  height  should  be  from 
8  to  9  ft. 

Insulation.  (See,  also.  The  Value 
of  Good  Insulation,  page  i6qo.) 
Refrigerators  in  modern  hotels,  clubs, 
institutions,  etc.,  are  insulated  with 
Government-standard  corkboard,  the 
large  refrigerators  being  constructed 
of  4-in  cork  throughout,  in  two  courses 
of  2  in  thickness,  and  with  all  joints 
broken.  Cork  is  applied  to  adjacent 
walls  of  a  building  with  Portland 
cement,  H  in  thick,  and  this  cement 
is  used,  also,  in  applying  the  inner 
course  of  cork  to  the  outer  course  in 
walls,  partitions  and  ceilings.  All 
cork  in  the  flooring  is  asphalted 
water-tight.  Interior  finish  may  be 
of  Portland  cement  throughout  or  of 
galvanized  sheets  on  walls  and  ceil- 
ings and  of  Portland  cement  on  floors. 
Or  the  walls  and  ceilings  may  be  of 
f  used-on  porcelain  or  white  plate  glass, 
and  the  floors  of  tile,  all  depending 
upon  the  grade  and  character  of  the 
building  to  be  equipped.  The  in- 
sulation of  smaller  refrigerators  con- 
sists of  (1)  an  exterior  course  of  ^^-in 
tongued  and  grooved  lumber,  (2)  twa 
courses  of  water-proof  insulating- 
paper  and  (3)  a  3-in  thickness  of 
sheet  cork  in  two  ij^^-in  courses,  all 
joints  being  broken.  To  this  insula- 
tion is  applied  the  interior  lining. 

Mortuary-Refrigerators.  Mor- 
tuary-refrigerators should  be  cooled 
by  mechanical  refrigeration,  the  coils 
being  placed  longitudinally  on  both 
sides  of  the  mortuary-trays.  Fig.  4 
illustrates  a  mortuary-refrigerator  for 
three  bodies.  This  may  be  used  as  a 
unit  in  designing  mortuary-refrigera- 
tors of  larger  capacity,  or  the  height 
may  be  reduced  to  5  ft  and  the 
bodies  placed  in  two  instead  of  three 


PLAN 
Fig.  4.*    Mortuary-rctrigerator 


horizontal  tiers.  Mortuary-refrigerators  sometimes  have  both  fronts  finished 
and  equipped  with  doors  so  that  bodies  are  accessible  for  identification  or 
examination  from  both  fronts. 

*  The  Jcwett  Refrigerator  Company. 


16S4 


Mechanical  Refrigeration 


Part  3 


MECHANICAL    REFRIGERATION* 

A  Brief   Description  of   Methods  in  Common  Use  for  Producing  and 
Applying  Refrigeration,  with  Special  Reference  to  Small  Plants 

A  British  Thermal  Unit,  (Btu),  is  the  quantity  of  heat  required  to  raise 
the  temperature  of  i  lb  of  water  i°  F.  Heat  used  in  this  way,  that  is,  to  raise 
the  temperature  of  water  or  other  substance,  is  said  to  be  present  in  that  sub- 
stance as  SENSIBLE  HEAT,  or,  in  other  words,  beat,  the  presence  of  which  we  can 
feel,  or  sense. 

The  Heat  of  Liquefaction,  or  so-called  latent  heat  of  liquefaction 
of  a  mass  of  ice,  is  the  amount  of  heat  it  will  absorb  in  melting.  One  pound  of 
ice  at  32°  F.  will  absorb  144  Btu  in  melting  to  water  at  32°  F.  Heat  coming 
into  a  cake  of  ice  is  thus  absorbed  in  melting  the  ice  and  becomes  what  is  known 
as  latent  heat,  or  heat  absorbed  without  any  rise  in  temperature.  If  the  ice 
is  at  a  lower  temperature  than  32°  F.,  or  if  the  water  resulting  from  the  melting 
rises  above  32°  F.,  additional  heat  will  be  absorbed  as  sensible  heat. 

The  Specific  Heat  of  a  substance  is  the  ratio  of  the  quantity  of  heat  required 
to  raise  the  temperature  of  a  certain  weight  of  the  substance  one  degree  to 
that  required  to  raise  the  same  weight  of  water  from  62°  to  63°  F. 

The  Heat  of  Vaporization  of  water  or  of  any  other  liquid  is  the  amount  of 
heat  it  will  absorb  in  vaporizing,  in  evaporating  from  a  liquid  to  a  gas,  or  will 
give  out  in  returning  from  the  gaseous  to  the  liquid  state. 

Transfer  of  Heat  occurs  in  three  ways:  (i)  by  convection,  (2)  by  radiation 
,  and  (3)  by  conduction.  For  instance,  if  particles  of  air  in  a  refrigerator  ad- 
jacent to  a  source  of  heat  become  warmed  they  circulate  and  distribute  the  heat 
by  convection  through  the  refrigerator-box.  Heat  will  pass  from  a  warm  sub- 
stance, as  from  the  filament  of  an  incandescent  lamp,  out  into  the  box  by 
RADIATION.     Heat  will  enter  the  box  through  the  walls  by  conduction. 

Heat-Transmission.  When  the  temperatures  on  opposite  sides  of  any  sur- 
face, as  for  instance,  a  wall,  are  unequal,  heat  will  pass  by  conduction  through 
the  material  from  the  warmer  to  the  cooler  side.  The  rate  of  this  movement  is 
the  RATE  OF  heat-transmission  and  is  stated  in  terms  of  the  quantity  of  heat 
called  (Btu)  which  will  pass  through  i  sq  ft  of  surface  in  24  hours,  per  degree 
temperature-difference  between  the  two  sides  of  the  wall. 

Some  Advantages  Claimed  for  Mechanical  Refrigeration. 
(i)  Lower  temperatures  can  be  obtained  with  refrigcrating-machines  than 
with  ice. 

(2)  The  inconvenience  of  handling  ice  is  avoided. 

(3)  There  is  no  accumulation  of   slime  in  the  refrigerators  as  from  the 

melting  of  even  the  best, ice. 

(4)  Refrigerators   cooled   mechanically   are   dryer   than   ice-cooled   boxes 

because  the  moisture  is  frozen  out  of  the  air  and  deposited  on  the 
cooling  surfaces. 

(5)  There  is  generally  a  better  air-circulation,  resulting  in  a  more  uniform 

temperature  and  dryer  atmosphere  throughout  the  compartment. 

(6)  With  proper  design  of  refrigerator  and  refrigeratirig-machine  any  de- 

sired  temperature  can  be  obtained. 

(7)  Refrigeration  produced  mechanically  is  oftei^  p^eaper  than  refrigeration 

produced  by  melting  ice.     (See  page  1695.) 

*  CompUed  and  adapted,  by  permission,  frqm  data  included  in  a  paper  by  R.  F.  Massa, 
See,  also,  Refrigerators,  pages  1679  to  1683, 


Types  of  Refrigerating-Ma chines  1685 

Operation  of  Refrigerating-Machines.  In  almost  all  methods  of  producing 
cold,  advantage  is  taken  of  the  fact  that  when  a  liquid  evaporates  it  usually  cools 
both  itself  and  its  surroundings,  and  changes  into  a  gas  or  vapor.  There  are 
several  liquids  which  are  easily  made  to  evaporate  and  produce  this  cooling 
effect,  and  were  it  not  for  their  cost,  refrigeration  could  be  very  simply  produced 
by  supplying  a  steady  stream  of  the  hquid  and  allowing  the  vapor  or  gas  evapo- 
rated to  escape  into  the  atmosphere.  A  refrigerating-machine  is  practically  an 
apparatus  for  saving  this  gas  which  has  evaporated  and  returning  it  to  its  liquid 
form  to  be  used  over  again.  In  this  process  of  recovery  and  condensation  the 
gas  gives  out  the  heat  which  it  has  previously  absorbed  in  evaporating.  This 
heat  is  carried  away  by  flowing  water,  which,  in  absorbing  the  heat,  rises  in 
-temperature. 

Types  of  Refrigerating-Machines.  In  the  (i)  compression-type  of  re- 
frigel-ating-machines  the  recovery  of  the  gas  is  elTected  by  drawing  it  away  from 
the  point  where  it  has  been  evaporated  and  pumping  it  under  increased  pressure 
into  a  chamber  where  it  gives  out  its  heat  to  the  water-cooled  walls  of  the 
chamber  and  returns  to  the  liquid  state  ready  to  be  used  over  again.  In  the 
(2)  ABSORPTION-TYPE  of  refrigerating-machines  ammonia  is  generally  used  and 
the  recovery  of  the  gas  is  elTected  by  bringing  it  into  contact  with  water  with 
which  it  unites  chemically.  The  solution  thus  formed  is  pumped  into  another 
chamber,  and  heat  is  applied  to  drive  off  the  ammonia-gas  which  is  then  condensed 
under  high  pressure.  It  is  now  ready  to  be  reevaporated  and  reproduce  its  cool- 
ing effect.  In  all  cases  of  large  units,  and  in  all  cases  of  either  large  or  small 
units  where  exhaust-steam  is  available  in  sufficient  quantities,  absorption  re- 
frigerating-machines are  very  economical. 

Liquids  Used  in  Refrigerating-Machines.  A  number  of  liquids  have  been 
used  in  refrigerating-machines,  the  ones  commonly  employed  being  (i)  am- 
monia, (2)  carbon  dioxide  and  (3)  sulphur  dioxide.  Various  practical 
considerations  determine  which  is  to  be  used  in  any  particular  design  of  machine. 
With  (i)  ammonia  the  advantage  is  the  lower  working  pressures,  from  15  to 
300  lb  per  sq  in,  which  are  easy  to  deal  with.  An  advantage  over  carbon  dioxide 
is  that  leaks  are  very  easily  located.  Ammonia-fumes,  however,  are  offensive 
and  sometimes  dangerous  in  case  of  a  break.  With  (2)  carbon  dioxide  the 
advantage  is  in  its  inoffensive  odor.  Its  disadvantages  are  the  high  pressure  at 
which  it  works,  from  300  to  i  200  lb  per  sq  in,  the  relative  difficulty  of  holding 
these  pressures  and  of  finding  small  leaks,  owing  to  its  slight  odor  and  chemical 
inactivity.  With  (3)  sulphur  dioxide  the  advantage  is  its  comparatively  low 
working  pressure,  which  is  not  above  75  lb  per  sq  in.  Its  great  disadvantage  is 
that  with  moisture  it  forms  an  acid  which  rapidly  corrodes  the  apparatus.  At 
one  time  this  disadvantage  was  fatal,  since  with  the  old-type  machines,  air  and 
moisture  were  constantly  being  drawn  into  the  system  more  or  less  rapidly  and 
mixed  with  the  sulphur  dioxide.  This  difficulty  has  recently  been  overcome  in 
some  modern  types  of  machines  *  in  which  the  refrigerant  is  hermetically  sealed 
in  the  machine  and  chemical  action,  therefore,  prevented. 

Rating  of  Refrigerating-Machines.  A  i-TON  refrigerating-machine  is  a 
machine  which,  if  operated  for  24  hours, -will  absorb  the  amount  of  heat  which 
I  ton  of  ice  would  absorb  in  melting.  If  the  machine  is  operated  a  shorter  time 
per  day,  a  less  amount  of  heat  will  of  course  be  absorbed,  and  in  order  to  main- 
tain the  temxperature  during  the  period  when  the  machine  is  not  running,  some 

*  The  Audiffren  Refrigerating-Machine,  a  small  machine  intended  for  domestic  uses 
and  sold  by  the  H.  W.  Johns-Manville  Company,  New  York.  There  are  many  other 
reliable  firms  making  refrigerating-machines  of  other  distinct  types,  and  the  architect 
should  look  carefully  into  the  merits  and  claims  of  each  when  called  upon  to  specify  them. 


1G86  Mechanical  Refrigeration  t*art  3 

means  must  be  adopted  for  storing  cold.  (See  paragraph  below.)  Ref  rigerating- 
machines  are  sometimes  rated  in  terms  of  ice-making  capacity,  that  is,  in  terms 
of  the  amount  of  ice  the  machine  will  make  in  24  hours.  This  is  always  less  than 
the  refrigerating  capacity  because  some  refrigerating  effect  is  required  to  cool 
the  water  down  to  32°  F.  before  the  freezing  can  begin,  and  the  ice  is  usually 
cooled  several  degrees  below*32°  F.,  which  requires  a  still  greater  capacity.  There 
is  also  some  flow  of  heat  into  the  apparatus.  These  elements  vary  considerably 
so  that  from  some  points  of  view  ice-making  capacity  might  be  considered  an 
unsatisfactory  method  of  rating  some  refrigerating-machines. 

Applying  the  Cold.  According  to  one  classification  there  are  three  common 
systems  of  applying  the  cold.  These  are,  (i)  the  direct-expansion  system, 
(2)  the  brine-system  and  (3)  the  cold-air  system. 

(i)  In  the  direct-expansion  system  the  refrigerant  is  evaporated  in  coils 
of  pipe  placed  directly  in  the  room  to  be  cooled. 

(2)  In  the  brine-system  the  refrigerant  is  used  to  cool  brine,  which  is  then 
circulated  through  coils  of  pipe  in  the  room  to  be  cooled. 

(3)  In  the  COLD-AIR  system  a  current  of  air  is  chilled  by  passing  it  over  coils 
of  pipe  cooled  directly  by  the  evaporating  refrigerant,  or  by  brine,  or  by 
passing  it  through  a  spray  of  cold  brine;  and  this  chilled  air  is  then  passed  into 
the  room  and  circulated  back  to  the  cooling-coils,  the  whole  operation  being 
repeated  indefinitely. 

All  of  these  systems  have  their  advantages  and  disadvantages.  While  the 
brine-system  is  a  little  more  expensive  to  operate  in  large  plants,  the  temper- 
ature is  more  easily  controlled  than  with  the  direct-expansion  system,  and  in 
practice  in  small  plants  it  is  found  as  economical  in  operation  in  spite  of  its 
theoretical  disadvantage.  Furthermore,  in  case  of  any  breakdown  in  the  ma- 
chine, the  temperature  can  be  held  for  a  time  by  circulating  the  brine  until  it 
becomes  too  warm  to  be  of  use,  whereas  with  direct  expansion  the  temperature 
will  begin  to  rise  immediately  upon  the  stopping  of  the  machine.  The  cold-air 
system  is  not  as  applicable  where  any  drying  of  the  goods  stored  would  be  harm- 
ful and  there  is  some  risk  of  carrying  fire  in  the  air-passages.  It  is  much  used, 
nevertheless,  for  such  service  as  chocolate-dipping  rooms,  ice-cream  hardening, 
fur-storages,  etc. 

Storage  of  Cold.  When  temperatures  are  to  be  maintained  while  the  refrig- 
erating-machine  is  shut  down,  cold  must  be  stored.  In  the  brine-system  this 
is  effected  by  cooling  a  comparatively  large  body  of  brine  which  warms  slowly 
as  it  is  circulated.  Where  the  brine-circulating  pump  as  well  as  the  machine 
must  be  stopped,  so-called  pressure-tanks  may  be  placed  in  the  piping- 
system  in  the  room  being  cooled;  the  mass  of  brine  in  these  tanks  absorbs  the 
heat  and  helps  to  maintain  an  approximately  even  temperature.  Where  the 
direct-expansion  system  is  used,  a  part  of  the  cooling-coils  may  be  immersed  in 
a  tank  of  brine  placed  in  the  room  and  the  remainder  of  the  coils  arranged  for 
the  direct  cooling  of  the  room.  In  some  places  the  spaces  avfiilable  will  not 
permit  the  use  of  brine-storage  tanks.  In  cases  of  this  kind  smaller  tanks  may 
be  used  and  filled  with  water,  or  a  weak  brine  which  will  freeze  at  a  tempera- 
ture a  little  below  32°  F.  Since  i  lb 'of  ice  in  melting  will  absorb  144  Btu  and 
1  lb  of  brine  rising  in  temperature,  say  26^,  will  absorb  only  from  14  to  16  Btu, 
the  saving  of  space  is  apparent.  It  must  be  absolutely  certain  that  the  refrig- 
erant reaches  the  tank  first  at  the  bottom  and  that  the  air  to  be  cooled  reaches 
it  first  at  the  top  so  that  the  ice  in  forming  shall  not  bulge  or  burst  the  tank. 
If  the  congealing  mass  were  to  freeze  from  the  top  down  the  tank  would  be 
strained  and  finally  leak,  because  of  the  expansion  of  the  ice  in  freezing.  An- 
other fact  to  be  considered  is  that  where  water,  only,  is  frozen,  a  resulting  high 


Description  of  Refrigerating-Machines  1687 

temperature  may  be  olitaincd  in  the  refrigerator,  since  the  brine  must  be 
warmer  than  the  ice  in  order  to  melt  it,  and  the  refrigerator  just  that  much 
warmer,  or  warmer  than  an  ice-cooled  box.  In  calculating  the  proper  sizes  of 
tanks  for  storing  brine,  it  should  be  remembered  that,  usually,  the  period  during 
which  the  machine  is  shut  down  coincides  with  the  period  during  which  the 
demand  for  refrigeration  in  the  box  is  the  least.  The  amount  of  heat  to  be 
absorbed  is  usually  only  that  entering  through  the  insulation,  as  the  doors  are 
shut  and  no  food  is  put  in  or  removed. 

Description  of  Refrigerating-Machines.  As  explained  in  the  preceding 
paragraphs  refrigerating-machincs  may  be  divided  generally  into  two  classes, 
(i)  the  COMPRESSION-TYPE  and  (2)  the  absorption-type. 

(i)  The  Compression-Type  of  Refrigerating-Machines  may  be  subdivided  as 
follows: 

(a)  The  open  type  of  machine,  which  is  made  both  vertical  and  horizontal, 
and  both  single  and  double-acting,  that  is,  compressing  the  gas  at  one  end  or 
at  both  ends  of  the  cylinder,  {b)  The  partially  enclosed  type  of  machine,  in 
which  all  the  moving  parts  of  the  compressor  proper  are  enclosed  within  the  frame 
of  the  compressor,  except  the  fly-wheel  and  the  main  shaft  which  enters  the 
frame  of  the  machine  through  a  stuffing-box.  Such  valves,  also,  as  are  required 
in  the  system  are  exposed,  (c)  The  wholly  enclosed  type  of  machine,*  in  which 
all  of  the  working  parts  are  enclosed  in  a  hermetically  sealed  container. 

(a)  One  advantage  of  the  open  type  of  machine  is  that  any  lack  of  adjustment 
due  to  wear  can  be  readily  corrected;  so  that,  with  proper  attention,  it  gives 
excellent  results.  For  large  installations  this  is  considered  by  many  to  be  a 
most  efficient  type  of  machine. 

(b)  The  enclosed  type  of  machine  resulted  from  the  effort  to  reduce  the  amount 
of  attention  required  by  the  open  machine,  to  cheapen  its  construction  and  to 
reduce  the  possibility  of  trouble  from  inexpert  tampering.  An  objection  to 
machines  of  this  type  is  that  when  adjustments  have  to  be  made  the  working 
parts  are  relatively  inaccessible. 

(c)  With  the  wholly  enclosed  type  of  machine  it  is  claimed  that  the  loss  of 
the  refrigerant  is  prevented  by  the  hermetical  sealing  of  the  apparatus,  and  that 
the  working  parts,  being  completely  enclosed,  are  protected  from  deterioration 
due  to  outside  causes  or  tampering. 

(2)  The  Absorption-Type  of  Refrigerating-Machines  are  of  two  kinds,  differ- 
ing principally  in  the  .proportioning  of  the  parts.  In  the  one  machine  high-pres- 
sure steam  is  used;  in  the  other  the  proportions  are  such  that  low-pressure 
or  exhaust-steam  may  be  used.  Where  exhaust-steam  is  available  machines 
of  this  type  are  found  to  be  very  economical,  and  this  is  true,  also,  for  all  large 
units  whether  or  not  exhaust-steam  is  used.  Full  descriptions  of  these  machines 
with  detailed  plans  and  layouts  may  be  obtained  from  the  various  manufacturers. 

Calculations  for  the  Capacity  of  a  Refrigerating-Machine.  Heat  enters 
the  refrigerated  compartments,  (i)  through  the  walls,  (2)  with  warm  goods,  (3) 
by  the  interchange  of  the  outside  air  when  doors  are  opened  and  by  air-leaks, 
since  the  cooled  air  is  the  heavier  and  immediately  flows  out  when  a  door  is 
opened,  (4)  from  lights  or  from  the  heat  of  the  bodies  of  workers,  and  (5) 
from  any  change  of  state  occurring  in  the  goods,  such  as  freezing,  fermenting, 
etc.  In  large  rooms  these  various  sources  of  heat  should  be  analyzed  sepa- 
rately. In  small  refrigerators,  as  in  hotels,  kitchens,  dwellings,  etc.,  a  rough 
rule,  quite  as  accurate  as  a  more  elaborate  analysis,  allows  a  certain  number  of 
Btu  per  cubic  foot  of  refrigerated  space  per  24  hours.     This  amount  varies 

?  Referred  to  on  page  1685. 


1688  Mechanical  Refrigeration  Part  3 

with  the  character  and  location  of  the  box,  the  nature  of  its  insulation,  the  tem- 
peratures desired  and  so  on.  It  will  be  seen  that  the  insulation,  while  of  great 
importance,  is  not  by  any  means  the  only  important  factor  in  this  class  of 
boxes.  For  domestic  refrigerators  in  which  a  temperature  of  from  35  to  50°  F. 
is  maintained,  soo  Btu  per  cu  ft  of  refrigerator  per  24  hours  should  be  allowed. 
For  boxes  in  hotel  or  restaurant-kitchens,  600  Btu,  or  even  900  Btu  in  ex- 
treme cases  and  where  low  temperatures  are  required,  should  be  allowed.  For 
butchers'  coolers  or  large  storage-boxes  in  hotels,  etc.,  from  2cx>  to  250  Btu  per 
cu  ft  per  24  hours  should  be  allowed.  A  check  on  the  above  figures  for  the 
large  type  of  box  is  the  following:  *  "When  the  exact  conditions  under  which 
cold-storage  rooms  are  to  be  operated  are  known,  namely,  the  size  and  shape  of 
the  rooms,  the  quality  of  the  insulation,  the  kind  and  quantity  of  goods  to  be 
handled  per  day  and  the  temperatures  at  which  they  are  received  and  at  which 
they  are  to  be  held,  the  amount  of  refrigeration  required  can  be  estimated  very 
closely  by  the  following  rule:  (i)  Calculate  the  exact  area  of  exposed  surface 
in  the  walls,  floor  and  ceiling  of  the  room  in  square  feet,  multiply  the  total  num- 
ber of  square  feet  by  the  number  given  in  the  table  for  the  required  tempera- 
ture and  divide  the  product  by  288  000.  (2)  Multiply  the  amount  of  goods, 
in  pounds,  to  be  stored  per  day  by  the  number  of  degrees  of  heat  to  be  extracted 
by  the  specific  heat  of  the  goods,  and  divide  by  288  000.  This  will  give  the 
amount  of  refrigeration,  in  tons  per  day,  necessary  to  maintain  the  tempera- 
ture required  for  the  goods.  (3)  Add  these  two  amounts  together.  The  total 
will  be  the  amount  of  refrigeration,  in  tons  per  day,  required  to  maintain  the 
temperature  required  for  the  goods  and  for  the  room.  (4)  If  the  goods  are 
to  be  frozen,  the  latent  heat  of  freezing  should  be  added  to  the  number  of 
Btu  to  be  extracted." 


For  rooms  containing  less  than  i  000  cu  ft 

If  maintained  at    0°  F.  multiply  the  exposed  surface  by 

t  775 

If  maintained  at    5°  F.  multiply  the  exposed  surface  by 

710 

If  maintained  at  10°  F.  multiply  the  exposed  surface  by 

535 

If  maintained  at  20°  F.  multiply  the  exposed  surface  by 

3^5 

If  maintained  at  32°  F.  multiply  the  exposed  surface  by 

265 

If  maintained  at  36°  F.  multiply  the  exposed  surface  by 

180 

For  rooms  containing  from  i  000  to  10  000  cu  ft 

If  maintained  at   0°  F.  multiply  the  exposed  surface  by  ] 

250 

If  maintained  at    5°  F.  multiply  the  exposed  surface  by 

600 

If  maintained  at  10°  F.  multiply  the  exposed  surface  by 

300 

If  maintained  at  20°  F.  multiply  the  exposed  surface  by.. 

190 

If  maintained  at  32°  F.  multiply  the  exposed  surface  by 

160 

If  maintained  at  36°  F.  multiply  the  exposed  surface  by 

125 

For  rooms  containing  more  than  10  cxx)  cu  ft 

If  maintained  at    0°  F.  multiply  the  exposed  surface  by  ] 

100 

If  maintained  at    5°  F.  multiply  the  exposed  surface  by 

550 

If  maintained  at  10°  F.  multiply  the  exposed  surface  by 

275 

If  maintained  at  20°  F.  multiply  the  exposed  surface  by 

180 

If  maintained  at  32°  F.  multiply  the  exposed  surface  by 

140 

If  maintained  at  36°  F.  multiply  the  exposed  surface  by 

no 

*  Taken  from  Levey's  Refrigeration  Memoranda,  page  41. 


Capacities  of  Refrigerating-Machines  1689 

With  small  machines  it  is  necessary  to  allow  a  greater  capacity  of  machine 
for  a  given  size  of  box  than  with  large  machines,  since,  with  the  latter,  one  can 
always  throw  a  large  part  of  the  machine-capacity  to  any  given  box  where 
special  need  may  exist;  whereas  to  do  this  with  the  small  machine  would  almost 
certainly  rob  some  other  box,  if  indeed  there  happened  to  be  another  box.  It  is 
never  possible  to  determine  with  mathematical  certainty  exactly  how  much 
refrigeration  is  required  for  a  given  case.  It  is  best  to  allow  for  this  fact  and 
to  be  sure  the  machine  is  amply  large.  Where  an  existing  ice-cooled  box  is  to 
be  cooled  mechanically  one  check  upon  the  size  of  the  machine  required  is  the 
amount  of  ice  used.  This  check  is  more  apt  than  any  other,  however,  to  lead 
to  erroneous  conclusions  unless  the  figures  are  properly  analyzed. 

Another    Method  of    Determining    the  Capacity  of    a   Refrigerating-Machine. 

The  following  is  a  method  that  gives  good  results,  except  that  allowance  may  be 
made  in  the  larger  boxes  and  where  brine-storage  tanks  are  provided  in  the  box 
for  the  steadying  effect  of  the  mass  of  cold  brine: 

(i)  The  ice-consumption  for  the  hottest  month  of  the  year  should  be  deter- 
mined.    This  will  give  the  average  ice-consumption  for  that  month. 

(2)  The  average  temperature  that  is  maintained  in  the  box  with  ice  should 
then  be  accurately  determined.  This  will  usually  be  from  55  to  65°  F.  It  will 
commonly  be  stated  to  be  anywhere  from  40  to  45°  F.,  but  these  temperatures 
are  seldom  obtained.  Even  if  they  are,  with  a  full  ice-chamber  and  the  box 
closed  for  long  periods  the  average  will  be  above  these  figures.  Unless,  there- 
fore, there  is  positive  assurance  to  the  contrary,  from  55  to  60°  F.  should  be 
considered  the  average  temperatures. 

(3)  A  calculation  should  then  be  made  of  the  heat-inflow  through  the  insula- 
tion, with  a  temperature  of  55°  F.  in  the  box  and  with  the  average  summer 
temperature  outside.  The  difference  between  the  heat-inflow  through  the 
insulation  and  the  total  heat  actually  absorbed  by  the  melting  of  the  ice  is  the 
amount  entering  the  box  from  other  sources  than  through  the  insulation.  This 
access  of  heat  ordinarily  occurs  during  the  hours  of  daytime  only,  that  is,  when 
the  box  is  being  opened,  since  at  night  the  box  will  remain  closed.  A  machine 
of  sufficient  capacity  to  produce  the  temperature  actually  obtained  with  ice 
must,  therefore,  be  of  larger  rated  capacity  than  that  indicated  by  the  actual 
ice-consumption;  and  how  much  larger  it  should  be  can  be  determined  by  this 
method. 

(4)  A  further  fact  which  it  is  claimed  should  be  taken  into  account  m  deter- 
mining the  proper  size  of  a  machine  is  that  temperatures  obtainable  with  ice 
are  often  unsatisfactory.  If  they  were  always  satisfactory  one  reason  for  put- 
ting in  cooling-machinery  would  be  done  away  with.  Where  55°  F.  is  obtained 
with  ice,  from  35  to  45°  F.  will  be  required  with  mechanical  cooling  and  the 
machine-size  must  be  further  increased  in  the  ratio  of  the  temperature-differ- 
ences between  average  summer  temperatures  and  35°  F.,  and  average  summer 
temperatures  and  55°  F.  .  ,     ,         /-  1  j 

(5)  The  cooling-machine  if  installed  in  accordance  with  these  figures  would 
handle  average-weather  conditions  but  would  not  be  adequate  for  extreme 
hot-weather  conditions,  the  most  important  conditions  to  be  met  by  cooling- 
machinery.  It  is  necessary,  therefore,  to  further  increase  the  size  of  the  machine 
in  the  ratio  of  the  difference  in  temperature  between  maximum  summer  tem- 
perature and  35°  F.,  and  average  summer  temperature  and  35°  F. 

(6)  A  further  allowance  should  be  considered,  namely,  the  fact  that  in  many 
cases  for  one  reason  or  another,  it  is  not  possible,  or  else  not  desirable,  to  oper- 
ate the  machine  except  during  certain  periods  of  the  day,  and  the  machine-size 
must  be  increased  as  much  as  may  be  required  to  take  care  of  these  conditions. 


1690  Mechanical  Refrigeration  Part  3 

f 

^  (7)  If  the  machine  is  not  placed  directly  at  the  box  to  be  cooled,  allowance 
must  be  made  for  the  heat-inflow  into  the  insulated  brine-mains.  The  amount 
of  heat  entering  from  this  source  is  often  of  considerable  importance,  particu- 
larly with  small  machines.  The  table  below  gives  heat  transmissions  for  cork 
pipe-covering  and  some  other  materials. 

Water  and  Milk-Cooling.  Mechanical  refrigeration  as  apphed  to  cooling 
Water  and  milk  differs  in  one  respect  from  other  classes  of  refrigerating-work. 
A  relatively  intense  quantity  of  cooling  effect  is  called  for  in  a  brief  interval 
of  time.  For  instance,  in  a  drinking-water  system  the  heaviest  requirements 
may  come  at  the  noon-hour.  In  a  bakery,  also,  the  demand  for  chilled  water 
will  be  intermittent,  a  large  quantity  of  water  being  required  for  the  dough- 
mixing.  In  dairy- work  the  milk  must  be  cooled  very  rapidly  to  check  the 
development  of  bacteria  which  grow  with  incredible  rapidity  within  the  tem- 
perature-rangc  of  from  no  to  50°  F.  To  install  a  large  enough  refrigerating- 
machine  to  produce  the  required  cooHng  effect  as  it  is  needed  would  in  most 
cases  call  for  a  very  large  machine.  This  is  overcome  by  using  a  smaller 
machine  and  allowing  it  to  operate  for  a  longer  time,  say  throughout  the 
day,  storing  the  refrigerating  effect  produced  by  cooling  a  large  body  of  brine, 
or  melting  the  ice  as  rapidly  as  may  be  required.  For  instance,  if  50  cans 
of  milk,  of  40  qts  each,  are  to  be  cooled  from  a  temperature  of  from,  say,  75 
to  35°  F.,  in  I  hour,  the  refrigcjation  required  will  be  50  cans  times  40  qts  times 
2  lb  per  qt  times  (75°  F.  —  35°  F.),  which  eciuals  320000  Btu.  Milk  is  treated 
in  the  calculation  as  having  the  same  specific  heat  as  water,  since  water  forms 
so  large  a  percentage  of  its  total  weight.  This  amount  of  refrigeration  pro- 
duced by  a  machine  running  12  hours  per  day  would  require  the  machine  to 
absorb  320000  Btu  divided  by  12,  or  26  000  Btu  per  hour.  The  quantity  of 
brine  necessary  to  store  the  cooling  effect  may  be  calculated  closely  enough  for 
practical  purposes  by  using  the  following  approximate  figures.  The  specific 
heat  of  brine  is  0.75.  The  weight  of  the  brine  is  9  lb  per  gallon.  The  permis- 
sible temperature-range  of  the  brine  dei^cnds  upon  the  conditions  and  may  be 
from,  say,  30  to  15°  F.,  or  lower.  In  other  words,  the  temperature  to  which 
the  brine  can  be  permitted  to  rise  is  limited  to  the  temperature  it  must  produce 
in  the  room  or  in  the  substance  being  cooled,  and  the  temperature  to  which 
the  brine  can  be  cooled  in  storing  cold  is  limited  by  the  decrease  in  economy  of 
the  rcf rigerating-machine  at  the  low,  temperatures. 

The  Value  of  Good  Insulation.  (See,  also,  Insulation,  page  1683 )  The 
importance  of  good  insulation  cannot  be  too  strongly  emphasized.  A  cold- 
storage  room  or  refrigerator  and  its  contents  may  be  cooled  by  ice  or  mechani- 
cal means,  but  unless  the  walls  are  adequately  insulated,  the  demand  caused 
by  the  inflow  of  heat  through  the  poor  insulation  may  be  more  than  the  ice- 
supply  or  refrigerating-machine  can  meet  to  maintain  the  required  tempera- 
ture. The  almost  universal  standard  of  insulation  for  cold-storage  rooms  is  a 
4-in  thickness  of  pure-cork  sheet.  The  following  table  shows  the  heat  trans- 
mitted through  I  in  in  thickness  of  each  of  the  substances,  per  square  foot  of 
exposed  surface  per  degree  difference  in  temperature  j>er  24  hours. 


Pure-cork  sheets 6.4  Btu 

Hair-felt 7-3  Btu 

Impregnated  cork  boards 8.5  Btu 

Rock-wool  blocks 8 . o  Btu 

Waterproofing  lith-blocks ' 8.5  Btu 

SprUce,  clear  and  dry 16 . o  Btu 

White  oak 26.0  Btu 


\ 


Design  of  Refrigerator  1691 

Design  of  Refrigerators.  Disposition  of  Cooling-Surfaces.  (See,  also, 
subject  of  Refrigerators,  page  1679.)  No  attempt  need  be  made  to  describe  all 
of  the  many  arrangements  of  refrigerated  compartments  that  are  to  be  found  in 
service.  The  intention  is  to  point  out  some  of  the  more  important  things  to 
be  considered  in  determining  upon  the  design  of  a  box.  It  is  desirable  in  a 
refrigerator  to  produce  not  only  a  low  temperature,  but  a  relatively  dry  atmos- 
phere. 

Cooling-Surface  and  Temperature.  Securing  the  low  temperature  is  merely 
a  question  of  supplying  sufficient  cooling-surface  to  produce  the  desired  results 
with  the  temperature  available  in  the  refrigerant.  The  amount  of  surface 
required  is  influenced  by  the  arrangement  of  the  box,  that  is,  whether  or  not 
the  air  passes  freely  or  sluggishly  over  the  surface,  whether  the  cooling-surface 
is  placed  on  the  ceiling  or  walls  of  the  compartment  or  in  a  loft  and,  if  the  latter 
arrangement  is  used,  whether  or  not  the  air-passages  are  of  proper  size  and  the 
circulation  between  the  loft  and  the  compartment  sufficient. 

Dryness  of  Atmosphere  and  Temperature.  To  secure  a  box  of  satisfactory 
dryness  it  is  necessary  to  have  a  relatively  low  temperature  in  the  refrigerant. 
The  air  which  passes  over  the  cooling-surfaces  is  practically  in  a  saturated  con- 
dition when  it  leaves  them.  If  it  is  to  be  dry  at  the  temperature  required  in 
the  box,  it  must  have  been,  necessarily,  cooled  well  below  the  box-temperature. 
For  instance,  in  a  box,  the  temperature  of  which  is  maintained  at  35°  F.,  the 
brine  should  be  run  at  a  temperature  of  from  about  20°  to  25°  F.  It  is  further 
desirable  to  so  locate  the  cooHng-surface  that  frost  in  melting  will  pass  out  of 
the  box  quickly  and  not  remain  to  be  reabsorbed  by  the  air  in  the  box. 

Arrangements  of  Cooling~Surface&.  There  are  several  common  arrangements 
of  cooling-surfaces  in  refrigerators.  Sometimes  the  coils  are  arranged  overhead, 
but  directly  in  the  compartment  to  be  cooled.  This  is  one  of  the  efficient  ways 
in  which  a  cooling-surface  can  be  arranged,  so  far  as  the  cooling  effect  alone  is 
concerned.  It  is  not,  in  general,  a  good  arrangement,  however,  since  frost 
melting  from  the  coils  drips  on  the  goods.  In  another  arrangement  the  cooling- 
surfaces  are  on  the  wall.  This  is  preferable  to  the  ceiling-arrangement,  as  far 
as  the  dripping  is  concerned.  The  objection  to  it  is  that  goods  placed  close  to 
the  walls  are  apt  to  be  overchilled,  while  goods  nearer  the  center  of  the  com- 
partment are  not  cooled  quickly  enough.  It  also  wastes  floor-space,  because 
packing  goods  close  to  the  coils  is  not  practicable  on  account  of  possible  over- 
chilling  and  also  on  account  of  the  liability  of  retarding  the  air-circulation.  The 
wall-arrangement  for  cooling-surfaces  is,  nevertheless,  often  the  most  practica- 
ble method.  Another  method  involves  a  modified  form  of  wall-coil  arrangement 
in  which  a  brine-storage  tank  is  used  to  assist  in  maintaining  the  temperature 
when  the  machine  is  shut  down.  A  further  modification  is  often  introduced, 
in  which  a  partition  or  baffle-plate  is  used  in  front  of  the  coils.  The  best  types 
of  box-arrangement  are  those  in  which  the  cooling-surface  is  separated  from  the 
storage-space  and  is  so  arranged  as  to  secure  an  active  circulation  of  the  air 
over  the  coils  and  through  the  compartments.  In  all  of  these  plans  the  one 
requirement  calling  for  the  .greatest  care  is  that  the  air-passages  shall  be  as 
direct  as  possible  and  of  ample  size.  The  force  causing  the  air  to  circulate, 
namely,  the  difference  in  weight  due  to  differences  in  temperature  and  density 
between  the  column  of  air  in  the  coil-compartment  and  that  in  the  storage- 
compartment,  is  so  extremely  small  that  any  slight  interference  is  a  serious 
matter.  An  extra  turn  in  the  passage  or  a  slight  reduction  in  the  size  of  the 
passage  will  produce  a  marked  effect.  A  good  rule  to  follow  is  to  make  the 
passage  as  large  as  it  can  be  made  without  allowing  any  drip  to  reach  the 
storage-compartment.    This  will  work  out  in  many  cases  to  show  a  ratio  of 


1692  Mechanical  Refrigeration  Part  3 

I  to  8  or  9  between  the  area  of  the  passage  and  the  floor-area  of  the  compart- 
ment; but  even  i  to  6  is  just  that  much  better  if  it  can  be  secured.  The  matter 
of  proportioning  the  size  of  the  air-passages  is  of  much  less  importance  where 
the  air  is  circulated  by  fans.  Forced  circulation  is  not  usual,  however,  except 
in  large  storage-refrigerators,  and  no  attempt  will  be  made  here  to  consider  it. 
One  precaution  that  must  be  taken  in  arranging  the  cooUng-surface,  especially 
in  small  and  frequently  opened  boxes,  is  the  avoidance  of  any  undue  cooling  of 
walls  or  ceilings  that  are  exposed  to  currents  of  warm  air  when  the  door  is 
opened.  Moisture  from  the  incoming  air  deposits  on  these  surfaces  and  causes 
the  offensive  so-called  sweating  of  the  box.  This  is  most  often  seen  on  the 
storage-compartment  side  of  uninsulated  coil-compartment  floors  or  partitions, 
and  also  occurs  on  walls  or  ceihngs  where  the  cooling-pipes  are  set  very  close  to 
these  surfaces.  The  obvious  and  effective  cure  is  to  insulate  the  partitions 
between  coil-compartments  and  storage-compartments  and  keep  cooling-sur- 
faces well  away  from  walls  or  ceilings,  from  3  to  8  in,  depending  upon  the  tem- 
perature of  the  brine. 

Incidental  Notes  on  Refrigerators.  Drawers.  In  restaurant-kitchens 
and  elsewhere  it  is  sometimes  convenient  to  have  a  box  fitted  with  a  number 
of  refrigerated  drawers.  The  heat-leakage  through  the  many  joints,  through 
shdes  which  are  invariably  only  partially  closed,  and  through  the  poor  insula- 
tion of  the  drawers,  is  very  great.  Where  it  is  at  all  possible  to  do  so,  it  is 
best  to  arrange  an  insulated  door  covering  the  entire  drawer-space. 

Anterooms.  In  storage-rooms  of  medium  to  large  size  the  air-interchange 
due  to  opening  doors  is  reduced  to  a  minimum  by  arranging  an  anteroom  or 
entry  which,  after  it  is  entered,  has  its  outer  door  closed  before  the  door  to  the 
storage-room  proper  is  opened.  Where  two  rooms  are  side  by  side,  it  is  often 
possible  to  reduce  the  interchange  of  air  by  treating  the  one  room  as  an  ante- 
room of  the  other,  having  but  one  door  to  the  outside  air. 

Doors.'  Special  note  should  be  made  as  to  the  design  of  doors  for  refrigerated 
rooms  or  boxes.  There  is  a  common  idea  that  a  refrigerator-door  should  be 
beveled.  As  a  matter  of  fact  no  more  certain  means  of  ensuring  air-leakage 
could  be  devised.  A  perfectly  fitted  beveled  door,  hung  accurately  in  place, 
could  perhaps  be  made  tight  in  the  beginning.  This  door  in  service  at  once 
begins  to  sag,  since  a  refrigerator-door  is  always  heavy.  It  immediately  be- 
comes impossible  to  force  it  to  a  tight  seat  and  continuous  leakage  of  air  begins. 
A  refrigerator-compartment  door  is  most  readily  made  tight  by  having  a  flat 
surface  on  the  door  come  up  against  a  corresponding  surface  on  the  frame,  with 
a  soft  gasket  of  some  kind  between  them.  There  are  several  well  made  re- 
frigerator-doors on  the  market  at  prices  low  enough  to  make  it  doubtful  economy 
to  attempt  the  home-made  article. 

Arrangement  of  Brine-Mains.  In  laying  out  mains  to  carry  brine  from  the 
refrigerating-machine  to  the  refrigerator,  there  are  a  few  simple  points  to  be 
cared  for.  For  the  convenience  of  the  pipe-covering  man,  the  flow  and  return 
lines  should  be  placed  far  enough  apart  so  that  he  can  get  his  covering  onto 
each  pipe  without  cutting  it  to  pieces,  or  else  they  should  come  close  together 
so  as  to  be  covered  together.  A  common  difficulty  experienced  in  brine-sys- 
tems of  refrigeration,  where  the  cooling-coils  in  several  compartments  are  fed 
from  the  same  main,  is  that  when  the  adjustment  of  the  valve  controlling  the 
flow  of  brine  through  one  coil  is  changed,  it  upsets  the  adjustment  of  the  whole 
system.  This  is  due  to  too  small  mains  or  too  small  a  pump,  or  both.  A 
similar  action  is  observed  when  the  opening  of  a  faucet  on  a  water-pipe  checks 
the  flow  from  other  open  faucets  on  the  line.    The  ideal  cross-section  area  of 


Calculations  for  Cooling- Surfaces 


1693 


the  brine-mains  is  as  nearly  as  possible  equal  to  the  combined  cross-section 
area  of  the  coils  which  they  serve  at  any  one  time.  Even  with  this  proportion, 
however,  it  is  not  possible  to  absolutely  ensure  that  the  lower  coils  will  not  rob 
the  upper  ones,  or  even  drain  them  completely  in  some  systems  of  piping.  A 
most  effective,  even  if  somewhat  expensive  method  of  overcoming  this  diffi- 
culty, is  by  the  addition  of  a  third  main.  In  this  arrangement  it  is  not  possible 
for  one  coil  to  rob  another  to  the  point  of  draining  it. 

Calculations  for  the  Necessary  Amount  of  Cooling-Surfaces.  No 
hard  and  fast  rule  can  be  given  regarding  the  proper  amount  of  coohng-surface 
for  compartments  of  various  sizes,  since  the  design  and  arrangement  of  the 
cooling-surface  and  the  freedom  with  which  the  air  circulates  over  it  greatly 
affect  the  amount  required.  As  a  general  guide,  however,  and  where  the  con- 
ditions are  such  as  to  permit  a  good  circulation  of  the  air,  the  following  formula 
will  give  good  results.  It  will  be  understood,  of  course,  that  the  refrigeration 
required  in  the  given  room  has  been  determined  as  previously  indicated. 
The  cooling-surface  required,  in  square  feet,  per  ton  of  refrigeration  equals 
4  7oo/(r—  t)  in  which  T  is  the  temperature  desired  in  the  compartment,  and  i 
the  average  temperature  of  the  brine. 


Approved  Cold-Storage  Temperatures 


Articles  stored 


Degrees 
Fahrenheit 


Beef 

Lamb  and  mutton •  • 

Hogs 

Veal 

M'eats,  in  pickle  or  brine 

Butter,  must  be  kept  separate  from  other  goods 

Eggs 

Cheese 

Lard 

Poultry,  to  freeze 

Poultry,  when  frozen 

Game,  to  freeze 

Game,  when  frozen 

Fish,  retail  fish-counters  should  be  cooled  with   ice  rather  than 

mechanically 

Oysters 

Beer 

Wines 

Cider 

Fruits 

Vegetables • 

Canned  goods 

Flour  and  meal 

Furs 

Brine  for  ice-cream  freezing 

Ice-cream,  air-hardening 

Ice-cream,  serving-temperature 


36  to  40 
32  to  36 
29  to  32 

34  to  36 

35  to  40 
oto38 

29  to  32 

32  to  34 
38  to  40 

5  to  10 
25  to  28 

5  to  10 
25  to  28 

25  to  28 

33  to  45 
33  to  42 
40  to  45 

30  to  40 

33  to  36 

34  to  40 
38  to  40 
40 

25  to  32 
5  to  10 
S 

14  to  16 


Ice-Making.     If  the  following  facts  of  physics  are  kept  in  mind  in  consider- 
ing methods  of  making  ice  the  results  obtainable  may  be  understood  or  pre- 


1694  Mechanical  Refrigeration  Part  3 

(i)  Chemically  pure  water  will  freeze  solid  and  clear. 

(2)  Water  containing  impurities  in  solution  tends  in  freezing  to  force  these 

impurities  out  of  solution.  The  slower  the  process  of  freezing  the 
more  completely  is  the  purification  effected. 

(3)  Ice  forming  in  still  water  sends  out  long  slender  crystals  which  increase 

in  number  and  size,  forming  a  meshwork  that  gradually  becomes  a 
solid  mass. 

(4)  Agitation  of  water  during  freezing  aids  in  the  separation  of  impurities 

and  therefore  in  forming  solid,  clear  ice. 

(5)  Practically  all  natural  waters  contain  more  or  less  organic  or  inorganic 

material  in  solution  and  invariably  contain  air  in  solution.  These 
substances  are,  therefore,  frozen  out  of  solution  and  tend  to  cause  the 
ice  formed  to  be  opaque,  the  lighter  substances  tending  to  rise  and 
collect  near  the  surfaice,  and  the  heavier  ones  tending  to  sink. 

(6)  The  rate  of  freezing  of  ice  decreases  as  the  thickness  already  formed 

increases,  so  that  the  time  required  to  freeze  increases  as  the  square 
of  the  thickness  to  be  frozen.     In  the  formation  of  natural  ice  the 
freezing  is  from  the  top  down  and  impurities  frozen  out  of  solution  fall. 
This  and  the  motion  of  the  water,  especially  in  quiet  running  streams, 
tends  to  make  naturally  frozen  ice  transparent.     American  manufac- 
turers of  ice  have  always  tried  to  duplicate  this  clearness- 
Methods  of  Ice-Making.    The  method  first  adopted  in  this  country  was  the 
one  in  which  distilled  water  was  used.     From  a  sanitary  point  of  view  such 
ice  would  be  theoretically  ideal.     Practical  difiicultics  make  it  almost  impos- 
sible to  secure  pure  ice  in  this  way.     Some  of  these  difl5culties  are: 

(i)  Removal  of  oil  from  the  distilled  water,  this  oil  being  picked  up  as  the 
steam  passes  through  the  cylinder  of  the  engine.  It  is  difficult  to 
remove  organic  oil  which  is  present  in  the  lubricant. 

(2)  Assurance  that  the  filters  are  in  proper  shape,  an  assurance  often  impos- 

sible to  obtain  since  this  apparatus  is  ordinarily  used  the  season  through 
without  overhauling. 

(3)  Possibility  of  contamination  in  the  storage-tank  where  the  distilled  water 

is  held  and  usually  precooled  to  as  near  32°  F.  as  possible,  before 
passing  to  the  freezing-cans,  thus  saving  time  in  the  freezing  process 
in  the  tank. 

(4)  Possible  contamination  from  handling  the  cans  and  the  wooden  covers 

over  them.  These  covers  form  the  top  of  the  freezing-tank  in  which 
the  cans  of  water  are  immersed  in  cold  brine  for  freezing  and  are 
tramped  over  by  the  ice-harvester  with  the  consequent  possibility  of 
dirt  getting  into  the  cans. 

A  second  system  of  ice-making  in  common  use  in  this  country  is  the  plate 
system.  In  this  process  the  ice  is  formed  on  vertical  steel  plates.  Natural 
or  raw  water  is  used  and  the  bath  is  agitated  by  various  methods.  The  re- 
sulting ice  is  very  clear  and  dense.  In  this  system  when  the  ice  is  formed  to 
the  desired  thickness,  usually  about  12-  in,  it  is  loosened  from  the  freezing- 
plate  by  various  thawing-arrangements  in  different  forms  of  the  apparatus. 
The  ice-plates,  often  9  by  16  ft  by  12  in  in  thickness,  are  lifted  from  the  tanks 
by  overhead  cranes  and  carried  to  a  table  where  they  are  cut  to  commercial 
sizes.  While  the  plate  process  is  usually  very  slow  on  account  of  the  fact 
that  the  freezing  is  from  one  side  only,  it  is  largely  used  and  lends  itself  to  great 
economy  in  steam-consumption,  whereas  in  the  old-style  distilled-water  ice- 
•  making  plant  the  amount  of  steam  required  to  make  the  ice  was  more  than  an 


Tower-Clocks  1695 

economical  engine  would  use  and  it  was  not  possible  to  obtain  fuel-economy. 
One  modified  form  of  this  system,  now  coming  into  considerable  favor,  is 
aiiaiiged  so  that  stationary  CANS  are  filled  with  raw  water  and  kept  agitated 
l)y  compressed  air  bubbling  up  through  it.  When  the  freezing  has  progressed 
somewhat  the  remaining  water  is  drawn  off  and  replaced  by  fresh  water,  thus 
removing  the  greater  part  of  the  impurities  that  have  been  frozen  out  of  solu- 
l  ion.  Various  other  modifications  of  these  two  systems  of  ice-making  have  been 
and  are  being  developed.  All  of  them  depend,  however,  upon  the  series  of 
pli\sical  facts  stated  in  the  preceding  paragraphs,  and  the  results  may  be 
analyzed  by  reference  to  them. 

Relative  Economy  of  Producing  Refrigeration  Mechanically  and  by 
Ice.  (i)  In  determining  the  cost  of  refrigeration  by  ice,  account  must 
1)1'  taken  not  only  of  the  cost  of  the  ice  but  of  melting,  of  the  uncertain  ice- 
harvest,  of  the  amount  of  ice  left  over  at  the  end  of  the  season  and  of  that 
ffo/cn  together  in  the  storage  and,  therefore,  practically  useless.  Regarding 
the  melting,  it  may  run  anywhere  up  to  50%  of  the  total  ice-harvest.  The 
<iuantity  left  over  at  the  end  of  the  season  is,  of  course,  so  variable  that  it  is 
imi)()ssible  to  estimate  it,  this  being  purely  a  matter  of  chance.  In  many 
cases,  however,  it  is  a  very  large  item.  The  loss  by  the  ice  freezing  together 
in  the  storage  can  be  reduced  to  a  very  small  amount  where  the  ice  is  properly 
packed  with  distance-strips  between  the  ice-cakes.  Proper  packing  is  much 
more  readily  carried  out,  however,  where  artificial  ice  is  stored  than  where 
natural  ice  is  held,  and  a  mechanically  cooled  ice-storage  is  less  subject  to  this 
difficulty,  since  the  temperature  is,  of  course,  constantly  held  below  the  melting- 
point  of  ice.  (2)  The  total  cost  of  refrigeration  produced  mechanically 
includes  the  cost  of  power,  water,  oil,  refrigerant  (usually  ammonia),  labor 
and  attendance,  and  interest  and  depreciation  on  the  investment.  The  figures 
on  these  items  vary  between  wide  limits.  The  following  figures,  however,  will 
be  of  interest.  Care  should  be  taken  in  drawing  conclusions  from  them  as  to 
cost  in  prospective  installations.  These  figures  are  from  the  annual  cost  of  an 
ice-manufacturing  company  having  a  capacity  of  i  500  tons  per  day  in  plants 
ranging  in  size  from  50  to  100  tons  per  day  each. 

Coal 40  cts  per  ton  of  ice  produced. 

Labor 50  cts  per  ton  of  ice  produced. 

Ammonia , 10  cts  per  ton  of  ice  produced. 

Water 5  cts  per  ton  of  ice  produced. 

Waste,  power,  oil,  etc 10  cts  per  ton  of  ice  produced. 

Total $1.15  per  ton  of  ice  produced. 

TOWER-CLOCKS  * 

Rule  for  Diameter  of  Dials.  "To  look  well  and  show  plainly,  dials  should 
be  I  ft  in  diameter  for  every  10  ft  of  elevation  and  should  set  out  flush  with  or 
close  to  the  line  of  the  building  or  tower."  t 

Dimensions  of  Some  Large  Clock-Faces.  Colgate's  Factory,  Jersey 
City,  N.  J.  The  diameter  of  the  dial  is  40  ft.  The  minute-hand  is  20  ft  long 
and  2  ft  II  in  in  extreme  width,  and  the  hour-hand  is  15  ft  long  and  3  ft  10  in 
in  extreme  width.  The  minute-hand  weighs  640  lb  and  the  hour-hand  500  lb. 
This  is  the  largest  clock  in  the  world. 

*  For  a  description  of  the  requirements  of  installation  of  tower-clocks,  see  page  154 
of  "Churches  and  Chapels,"  by  F.  E.  Kidder. 
t  Seth  Thomas  Clock  Company,  New  York, 


1696  Library  Book-Stacks  Part  3 

Bromo-Scltzer  Building,  Baltimore,  Md.  The  dials  are  24  ft  in  diameter. 
The  minute-hand  is  12  ft  7  in  and  the  hour-hand  9  ft  8  in  from  tip  to  tip.  The 
minute-hand  weighs  175  lb,  the  hour-hand  145  lb. 

Daniels-Fisher  Building,  Denver,  Colo.  The  dials  are  15  ft  6  in  in  diameter. 
The  minute-hand  is  7  ft  10  in  and  the  hour-hand  5  ft  7  in  long. 

Maryland  Casualty  Building,  Baltimore,  Md.  The  dials  are  17  ft  in  diam- 
eter.    The  minute-hand  is  8  ft  4  in  and  the  hour-hand  5  ft  1 1  in  long. 

Elgin  Watch  Company's  Factory,  Elgin,  111.  The  dials  are  14  ft  6  in  in  diam- 
eter.    The  minute-hand  is  7  ft  4  in  and  the  hour-hand  5  ft  4  in  long. 

Tower-clock,  Station  of  the  Central  Railroad  of  New  Jersey,  at  Communi- 
paw,  N.  J.  The  diameter  of  the  single  dial  is  14  ft  3  in;  the  minute-hand  is 
7  ft  long  and  weighs  40  lb;  the  hour-hand  is  5  ft  long  and  weighs  28  lb.  The 
motive  power  is  furnished  by  a  weight  of  700  lb,  hung  from  a  ^^-in  steel  cable. 

Four-dial  clock.  Produce  Exchange  Building,  New  York.  The  diameter  of 
each  dial  is  12  ft  6  in. 

Four-dial  clock,  Chronicle  Tower,*  San  Francisco,  Cal.  The  diameter  of  each 
dial  is  16  ft  6  in;  length  of  minute-hands,  8  ft;  length  of  hour-hands,  5  ft  6  in. 
The  mechanism  of  the  clock  is  6  ft  i  in  high  and  weighs  3  000  lb. 

Pneumatic  clock,  City  Hall  and  Court-House,  Minneapolis,  Minn.  The  dials 
are  23  ft  4  in  in  diameter. 

LIBRARY  BOOK-STACKS 

The  Stack-Work  in  General.  The  stack-room  of  a  library  is  usually  cut 
off  by  fire-proof  doors  from  the  rest  of  the  building.  The  customary  practice 
among  architects  is  to  make  the  stack-work  a  separate  contract  and  have  the 
general  contractor  turn  the  stack-room  over  to  the  stack-contractor  with  fin- 
ished floors,  walls  and  ceilings.  The  stacks,  made  entirely  of  incombustible 
materials,  are  then  built  as  an  independent  structure. 

Book-Ranges.  The  book-ranges  are  usually  double-faced  and  are  placed 
in  parallel  rows  with  aisles  between.  The  minimum  aisle-width  is  about  2  ft 
4  in.  Radial  ranges  waste  space  and  are  costly.  Single-faced  ranges  are 
relatively  more  expensive  than  double-faced  ranges. 

Tiers.  All  stacks  are  divided  in  their  height  into  tiers  by  deck-floors  in 
order  that  all  shelves  may  be  easily  reached.  The  regular  tier-height  is  7  ft 
or  7  ft  6  in. 

Deck-Floors.  Deck-floors  are  composed  of  slabs  of  H-in  rough  plate 
glass  or  iH-in  white  marble,  supported  on  steel  framework.  A  long,  narrow 
opening  or  deck-slit  is  left  between  the  edge  of  each  deck-floor  and  the  face  of 
each  range  to  allow  proper  ventilation  of  the  stack-tiers.  The  net  thickness 
from  top  of  deck  to  bottom  of  steel  framework  is  from  3M  to  3%  in  for  ordinary 
spans.     The  deck-floors  are  carried  by  the  shelf-supports. 

Vertical  Communication.  Continuous  flights  of  stairs  of  simple  design 
and  construction  are  placed  at  central  points.  Books  are  moved  up  and  down 
by  means  of  dumb-waiters  operated  by  hand,  for  short  runs,  or  by  electric 
power  controlled  by  push-buttons. 

Shelf-Supports.  The  shelf-supports  are  made  in  various  ways,  differing 
with  each  manufacturer.  In  the  best  construction  they  extend  the  full  width 
of  the  shelves  so  as  to  hold  up  the  shelves  and  books  without  the  use  of  any 
projecting  brackets.  They  are  made  of  sufficient  strength  to  carry  the  com- 
bined loads  of  books,  deck-floors  and  superimposed  stack-tiers.    They  should 

*  Destroyed  in  the  earthquake  and  fire. 


Classical  Moldings  1697 

provide  for  a  uniform  shelf -adjustment  at  intervals  of  about  i  in.  Compact- 
ness is  important.  Open-work  shelf-supports  promote  proper  lighting  and 
ventilation. 

Shelves.  In  each  tier  of  regular  height  there  are  usually  six  rows  of  adjust- 
able shelves  and  one  row  of  fixed  shelves.  Shelves  are  generully  8  or  lo  in  wide 
and  3  ft  long.  Other  sizes  are  supplied  if  necessary.  The  adjustable  shelves 
are  made  of  solid  plates  of  sheet  steel  or  of  parallel  bars  with  spaces  between. 
The  fixed  shelves  are  placed  about  2  in  above  each  floor-level.  They  are  made 
of  solid  plates  of  steel  to  form  dust-stops,  fire-stops  and  water-stops  between  the 
tiers. 

Finish.  The  adjustable  shelves  are  always  completely  finished  with  baked 
enamel  before  delivery.  The  fixed  parts,  also,  of  the  stack-construction  may 
be  finished  at  the  shop  with  baked  enamel,  or  preferably  with  air-drying  enamel, 
after  erection  at  the  building,  so  as  to  permit  repair. 

Lighting.  Electric-light  wires  arc  carried  in  metal  conduits  supported  by 
the.  steel  framework  of  the  deck-floors.  Lights  of  16  candle-power  are  spaced 
about  6  ft  apart  in  range-aisles  and  12  ft  apart  in  main  aisles. 

Heating.  Indirect  radiation  is  best  for  books.  The  lower  tiers,  only,  of  a 
stack  should  be  heated,  to  prevent  the  upper  tiers  from  becoming  too  warm. 

Ventilation.  Large  stacks  are  usually  ventilated  artificially  to  prevent  the 
^ntry  of  dust  and  outside  air  through  open  windows.  In  the  Library  of  Con- 
gress, in  Washington,  D.C.,  fresh,  filtered  and  tempered  air  is  forced  in  at  the 
bottom  tier,  finds  its  way  up  through  the  stack  by  means  of  the  deck-slits  and 
is  drawn  out  at  the  top  tier. 

Weights.  The  shelves  and  shelf -supports  *  weigh  from  7  to  10  lb  per  cu  ft 
of  book-range.  Books  weigh  about  20  or  25  lb  per  cu  ft  of  book-range.  The 
steel  deck-floor  framing  weighs  from  4  to  6  lb  per  sq  ft  of  gross  area  of  deck- 
floor.  Marble  floor-slabs,  rV4  in  thick,  weigh  about  20  lb  per  sq  ft,  and  %  in 
rough,  plate-glass  slabs,  about  10  lb  per  sq  ft  of  net  area. 

Book-Capacities.  Book-capacities  per  linear  foot  of  shelf  may  be  figured  on 
the  following  basis:  law-books,  5  volumes;  reference  books,  6  volumes;  scien- 
tific books,  7  volumes;  general  literature,  from  8  to  10  volumes.  The  average 
in  the  Library  of  Congress  is  Syz  volumes  per  linear  foot.  An  ordinary  stack- 
tier,  7  shelves  high  with  double-faced  ranges  16  in  deep  (or  8-in  shelves)  and 
aisles  32  in  wide,  with  a  reasonable  allowance  made  for  cross-aisles,  stairways, 
etc,  will  contain  about  22  volumes  per  sq  ft  of  gross  area. 

Cost.  The  cost  in  the  United  States  of  library-stacks  of  standard  construc- 
tion varies  from  50  cts  to  $1  or  more  per  linear  foot  of  shelving.  Economy  is 
secured  by  following  established  standards  while  special  designs  increase  the  cost. 

CLASSICAL    MOLDINGS 

Moldings  are  so  called  because  they  are  of  the  same  shape  throughout  their 
length  as  though  the  whole  had  been  cast  in  the  same  mold  or  form.  The  regu- 
lar moldings,  as  found  in  remains  of  classic  architecture,  are  eight  in  number, 
as  shown  in  the  accompanying  iUustration,  and  are  known  by  the  following 
names:  The  last  two  are  commonly  called,  also,  ogee  moldings.  Some  of  these 
terms  are  derived  thus:  fillet,  from  the  French  word  fil,  a  thread;  astragal, 
from  ASTRAGALOS,  a  bone  of  the  heel,  or  the  curvature  of  the  heel;  bead,  because 
this  molding,  when  properly  carved,  resembles  a  string  of  beads;  torus,  or  tore, 

*  As  made  by  The  Snead  &  Co.  Iron  Works,  Jersey  City,  N.  J. 


1698  Classical  Orders  Part  2 

the  Greek  for  ro{>c,  which  it  resembles  when  on  the  base  of  a  column;  scotia^ 
from  SKOTiA,  darkness,  because  of  the  strong  shadow  cast  in  its  hollow,  and  which 
is  increased  by  the  projection  of  the  torus  above  it;  ovolo,  from  ovum,  an  egg, 
which  this  member  resembles  when  carved,  as  in  the  Ionic  capital;  cavetto, 
from  CAVus,  hollow;  cymatium,  from 

Annulet,  iand,  ciucturl.  fillet.       AatL«.  or  bei  KUMATON,  a  WaVC. 


3       [^ 


""^^''"^^^"^^^  Characteristics    of    Moldings. 

None  of  these  moldings  is  pecuHar  to 
any  one  of  the  orders  of  architecture; 
and  although  each  has  its  appropriate 
use,  it  is  by  no  means  confined  to  any 
certain  position  in  an  assemljlage  of 

OtoIo,  quarter-round,  or  echinus.    Cavetto,  cove,  or  hollow.  moldiugS.       The   USC    of   tllC    fillet    and 

also  of  the  astragal  and  torus,  which 
resemble  ropes,  is  to  bind  the  parts. 
The  ovolo  and  cyma-reversa  are  strong 


C7   XT 


Cjmatium,orcyma-re.ta.     i-^verte^cymatium,  or  ^t    their   uppcr   extremities,   and  are 

therefore  used  to  support  projecting 
parts  above  them.  The  cy ma-recta  and  cavetto,  being  weak  at  their  upper 
extremities,  are  not  used  as  supporters,  but  are  placed  uppermost  to  cover  and 
shelter  the  upper  parts.  The  scotia  is  introduced  in  the  base  of  a  column  to 
separate  the  upper  and  lower  torus,  and  to  produce  a  pleasing  variety  and 
relief.  The  form  of  the  bead  and  that  of  the  torus  are  the  same;  the  reason 
for  giving  distinct  names  to  them  is  that  the  torus,  in  every  order,  is  always 
considerably  larger  than  the  bead  and  is  placed  among  the  base-moldings, 
whereas  the  bead  is  never  placed  there,  but  on  the  capital  or  entablature. 
•The  torus,  also,  is  seldom  carved,  whereas  the  bead  is;  and  while  the  torus, 
among  the  Greeks,  was  frequently  elliptical  in  its  form,  the  bead  retains  its 
circular  shape.  While  the  scotia  is  the  reverse  of  the  torus,  the  cavetto  is  the 
reverse  of  the  ovolo,  and  the  cyma-recta  and  cyma-reversa  are  combinations 
of  the  ovolo  and  cavetto. 


THE    CLASSICAL    ORDERS* 

Origin  of  the  Orders.  "In  the  classical  styles  several  varieties  of  column 
and  entablature  are  in  use.  These  are  called  the  orders.  Each  order  comprises 
a  COLUMN  with  a  base,  shaft  and  capital,  with  or  without  a  pedestal,  with  its 
BASE,  DIE  and  CAP,  and  is  crowned  by  an  entablature,  consisting  of  architrave, 
FRIEZE  and  CORNICE.  The  entablature  is  generally  about  one-fourth  as  high  as 
the  column,  and  the  pedestal  one-third,  more  or  less.  Among  the  Greeks  the 
forms  used  by  the  Doric  race,  which  inhabited  Greece  itself  and  had  colonies  in 
Sicily  and  Italy,  were  much  unlike  those  of  the  Ionic  race,  which  inhabited  the 
western  coast  of  Asia  Minor,  and  whose  art  was  greatly  influenced  by  that  of 
Assyria  and  Persia.  Besides  the  Ionic  and  Doric  styles,  the  Romans  devised 
a  third,  which  employed  brackets,  called  modillions,  in  the  cornice,  and  was 
much  more  elaborate  than  either  of  them;  this  they  called  the  Corinthian. 
They  used  also  a  simple  Doric  called  the  Tuscan,  and  a  cross  between  the 
Corinthian  and  Ionic  called  the  composite.     These  are  the  five  orders.     The 

*  The  paragraphs  in  quotation-marks  are  taken  from  The  American  Vignola  by  Pro- 
fessor W.  R.  Ware,  by  permission  of  the  owners  of  the  copyright,  the  International  Text- 
book Company,  Scranton,  Pa.,  proprietors  of  the  International  Correspondence  Schools. 
The  engravings  were  made  especially  for  this  book,  and  correspond  with  the  original 
drawings  prepared  by  Giacorao  Barozzi  da  Vignola. 


Tuscan,  Doric  and  Tonic  Orders 


1699 


ancient  examples  vary  much  among  themselves  and  diftcr  in  different  places, 
and  in  modern  times  still  further  varieties  are  found  in  Italy,  Spain,  France, 
Germany  and  England.  The  best  known  and  most  admired  forms  for  the  orders 
are  those  worked  out  by  Giacomo  Barozzi  da  Vignola  in  the  sixteenth  century 
from  the  study  of  ancient 
examples." 

The  Tuscan  Order. 
"The  distinguishing 
characteristic  of  the  Tus- 
can ORDER  (Fig.  1)  is 
simplicity.  Any  forms 
of  pedestal,  column  and 
entablature  that  show 
but  few  moldings,  and 
those  plain,  are  con- 
sidered to  be  Tuscan." 

The  Doric  Order. 
"The  distinguishing 
characteristics  of  the 
Doric  order  are  fea- 
tures in  the  frieze  and 
in  the  bed-mold  above 
it  called  triglyphs  and 
MUTULES,  which  are  sup- 
posed to  be  derived  from 
the  ends  of  beams  and 
rafters  in  a  primitive 
wooden  construction 
with  large  beams.  Un- 
der each  triglyph,  and 
beneath  the  taenia  which 
crowns  the  architrave,  is 
a  little  fillet  called  the 
REGULA.  Under  the 
regula  are  six  long  drops, 
called  GUTT^,  which  are 
sometimes  conical,  some- 
times pyramidal.  There 
are  also  either  eighteen 
or  thirty-six  short  cylin- 
drical guttai  under  the 
soffit  of  each  mutule. 
The  guttai  are  supposed 
to  represent  the  heads  of 
wooden  pins,  or  treenails. 
Two  different  Doric  cor- 

Dices  are  in  use,  the  mutulary  with  bracket  and  the  denticulated  with  dentils, 
the  principal  difference  being  in  the  bed-mold."  The  order  shown  in  Fig.  2 
has  the  denticulated  cornice. 

The  Ionic  Order.  "The  prototypes  of  the  Ionic  order  (Fig.  3)  are  to  be 
found  in  Persia,  Assyria,  and  Asia  Minor.  It  is  characterized  by  bands  in  the 
architrave  and  dentils  in  the  bed-mold,  both  of  which  are  held  to  represent 
small  sticks  laid  together  to  form  a  beam  or  a  roof.     But  the  most  conspicuous 


Dimensions  are  in  24thK  of  Diameter, 

Fig.  1.    The  Tuscan  Order 


1700 


Classical  Orders 


Part  3 


and  distinctive  feature  is  the  scrolls  which  decorate  the  capital  of  the  column. 
These  have  no  structural  significance,  and  are  purely  decorative  forms  derived 
from  Assyria  and  Egypt.  Originally  the  Ionic  order  had  no  frieze  and  no 
ECHINUS  in  the  capital.     These  were  borrowed  from  the  Doric  order,  and,  in 


X 


T    II 


U-iuuuaiuuuTxi 

r— t^ T . 


I                                I     > 
,k- :lrD^2i 


Dimensions  are  in  2iths  of  Diameter 
Fig.  2.    The  Doric  Order 

like  manner,  the  dentils  and  bands  in  the  Doric  were  borrowed  from  the  Ionic. 
The  Ionic  frieze  was  introduced  in  order  to  afford  a  place  for  sculpture,  and  was 
called  by  the  Greeks  the  zoophorous,  or  figure-bearer.  The  typical  Ionic  base 
is  considered  to  consist  mainly  of  a  scotia,  as  in  some  Greek  examples.  It  is 
common,  however,  to  use  instead  what  is  called  the  Attic  base,  consisting  of  a 


Ionic  Order 


1701 


^ ^i^p jz;j 

Plmeusions  are  ia  24ths  of  Diameter. 

Fig.  3.    The  Ionic  Order 


1702  Classical  Orders  Part  3 

SCOTIA  and  two  fillets  between  two  large  toruses,  mounted  on  a  plinth,  the 
whole  half  a  diameter  high.  The  plinth  occupies  the  lower  third,  or  one-sixth 
of  a  diameter.  Vignola  adopted  for  his  Ionic  order  a  modification  of  the  Attic 
base,  substituting  for  the  single  large  scotia  two  small  ones,  separated  by  one 
or  two  beads  and  fillets,  and  omitting  the  lower  torus. "  This  is  the  base  shown 
in  Fig.  3.  "The  Ionic  frieze  is  plain,  except  for  the  sculpture  upon  it.  It 
sometimes  has  a  curved  outline,  as  if  ready  to  be  carved,  and  is  then  said  to  be 
PULViNATED,  from  pulvinar,  a  bolster,  which  it  much  resembles.  The  shaft 
of  the  column  is  ornamented  with  twenty-four  FLUTmos,  semicircular  in  section, 
which  are  separated  not  by  an  arris,  but  by  a  fillet  of  about  one-fourth  their 
width.     This  makes  the  llutings  only  about  two-thirds  as  wide  as  the  Doric 

channels,    or    about    one-ninth   of   a 
\       !        ',  diameter,  instead  of  one-sixth." 

\     l\      ;  To   Describe   the  Ionic   Volute. 

\    I  \      I  There  are  several   methods  of  doing 

^^_Juj>l  this,  the  simplest  being  by  means  of 

/^ /'''^  ^v  |\  centers  found  as  shown  by  the  diagram 

/__h^_l_\_xA^     \  i"  Fig.  4.     First  locate  the  center  of 

---/■-/^p^^4A--^^5\^\  the   EYE    M  D    vertically   below    the 

""//^^■"^"t^vj^  \J  point    A,   Fig.  3.     Then   describe   a 

f\    1  1^3^^^^^-'----/  circle  with  a  diameter  equal  to  Ms  D, 

\^\'/rT~''"    8^7,7^7  ^^  ^^''"^  ^^^  ^y^-     Inside  of  this  circle 

\  ^\  f'^~~~/*    /  inscribe  a  square  at  45  degrees  to  a 

\s!  \^  I  /     'y  horizontal ;    then   draw  the  axes   1-3 

_i^^jr-N/l-'^■"'^  and  2-4,  and  divide  each  of  these  into 

'    J   I  six  equal  parts.     Then  with  the  point 

I    !   !  I  as  a  center,  and  a  radius  extending 

'    '  to  /!,  Fig.  3,  draw  a  quarter-circle  to 

Fig.  4.    The  Ionic  Volute  line  1-2  produced,  with  2  as  a  center, 

continue  the  curve  until  it  intersects 

2-3  produced,  and  so  on.     The  centers  for  the  outer  curve  of  the  volute  are  at 

the  points  i,  2,  3,  4,  5,  6,  etc.     For  the  centers  for  the  inner  curve,  start  with  a 

point  one-third  the  way  from  i  to  5,  then  a  point  one-third  the  way  from  2  to  6, 

and  so  on. 

The  Corinthian  Order.  "The  three  distinguishing  characteristics  of  the 
Corinthian  order  (Fig.  5)  are  a  tall,  bell-shaped  capital,  a  series  of  small 
brackets  called  modillions,  which  support  the  .cornice  instead  of  mutules,  in 
addition  to  the  dentils,  and  a  general  richness  of  detail  which  is  enhanced  bv 
the  use  of  the  acanthus  leaf  in  both  capitals  and  modillions.  Here,  again,  the 
Attic  base  is  commonly  used,  but  sometimes,  especially  in  large  columns,  a 
base  is  used  which  resembles  Vignola's  Ionic  base,  except  that  it  has  two  beads 
between  the  scotias  instead  of  one,  and  also  a  lower  torus.  The  shaft  i^ 
fluted  like  the  Ionic  shaft,  with  twenty-four  semicircular  flutings,  but  the^ 
are  sometimes  filled  with  a  convex  molding  or  carle  to  a  third  of  their  height. 
Almost  all  the  buildings  erected  by  the  Romans  employ  the  Corinthian  order." 
The  Composite  Order.  "The  composite  order  is  a  heavier  Corinthian, 
just  as  the  Tuscan  is  a  simplified  Doric.  The  chief  proportions  are  the  same  as 
in  the  Corinthian  order,  but  the  details  are  fewer  and  larger.  It  owes  its  name 
to  the  CAPITAL,  in  which  the  two  lower  rows  of  leaves  and  the  caulicoli  are 
the  same  as  in  the  Corinthian.  But  the  caulicoli  carry  only  a  stunted  leaf-bud, 
and  the  upper  row  of  leaves  and  the  sixteen  volutins  are  replaced  by  the  large 
echinus,  scrolls  and  astragal  of  a  complete  Ionic  capital.  Vignola's  com- 
posite entablature  differs  from  his  Ionic  chiefly  in  the  shape  and  size  of  the 


Corinthian  Order 


1703 


(H%- 


r~\ 

%' 

dL- 

-■ 

7- 

"  J 

--- 

- 

D 

=  21 

v^ 

- 

- 

I 

I 

k 

I 


1- 


t_.J J 


Dimensions  are  in  24ths  of  Diameter 
THE  CORINTHIAN  ORDER 

E«.  5.    The  Corinthian  Order 


1704 


Lightning-Conductors 


Part  3 


DENTILS.    They  are  larger,  and  are  more  nearly  square  in  elevation,  being  one- 
fifth  of  a  diameter  high  and  one-sixth  wide,  the  interdentil  being  one-twelfth, 

and  they  are  set  one-fourth  of 
a  diameter  apart,  on  centers. 
The  composite  capital  is  em- 
ployed in  the  Arch  of  Titus  in 
Rome,  and  elsewhere,  with  a 
Corinthian  entablature,  and  the 
BLOCK  CORNICE  occurs  in  the  so- 
called  FRONTISPIECE  of  Nero, 
as  well  as  in  the  temple  at 
Athens,  in  connection  with  a 
Corinthian  capital." 

Egyptian  Style.*  The  archi- 
tecture of  the  ancient  Egj^'ptians 
is  characterized  by  boldness  of 
outline,  solidity,  and  grandeur. 
The  principal  features  of  the 
Egyptian  style  of  architecture 
are:  uniformity  of  plan,  never 
deviating  from  right  lines  and 
angles;  thick  walls,  having  the 
outer  surface  slightly  deviating 
inwardly  from  the  perpendicular; 
the  whole  building  low;  roof  flat, 
composed  of  stones  reaching  in 
one  piece  from  pier  to  pier, 
these  being  supported  by  enor- 
mous columns,  very  stout  in 
proportion  to  their  height;  the 
shaft  sometimes  polygonal,  hav- 
ing no  base,  but  with  a  great 
variety  of  handsome  capitals, 
the  foliage  of  these  being  of  the 
palm,  lotus  and  other  leaves; 
entablatures  having  simply 
an  ARCHITRAVE,  crowned  with  a 
huge  CAVETTO  ornamented  with 
sculpture;  and  the  intercolum- 
NiATiON,  very  narrow,  usually 
1 1/2  diameters  and  seldom  ex- 
ceeding 2  3^2.  A  great  dissimi- 
larity exists  in  the  proportions, 
forms  and  general  features  of  Egyptian  columns.  For  practical  use  the  column 
shown  in  Fig.  6  may  be  taken  as  a  standard  of  the  Egyptian  style. 


Fig.  6.     An  Egyptian  Order.     Diameter  Divided 
into  Sixty  Parts 


LIGHTNING-CONDUCTORS 

Rules  for  the  Erection  of  Lightning-Conductors.  The  following  rules 
for  the  erection  of  lightning-conductors  were  issued  in  1882  by  the  Department  of 
Explosives  of  the  English  Home  Office  to  the  occupiers  of  all  factories  and  maga-: 

'  From  The  American  House  Carpenter,  by  R.  G.  Hatfield. 


Lightning-Conductors  1705 

zines  for  explosives,  and  to  those  local  and  police  authorities  upon  whom  de- 
volves the  inspection  of  stores  of  explosives: 

(i)  Material  of  Rod.  Copper,  weighing  not  less  than  6  oz  per  ft  run,  the 
{electrical  conductivity  of  which  is  not  less  than  90%  of  that  of  pure  copper, 
[either  in  the  form  of  rod,  tape,  or  rope  of  stout  wires,  no  individual  wire  being 
less  than  No.  12,  Birmingham  Wire-Gauge  (0.109  in)  the  English  standard 
wire-gauge.  Iron  may  be  used,  but  should  not  weigh  less  than  2H  lb  per  foot 
of  run. 

(2)  Joints.  Every  joint,  besides  being  well  cleaned  and  screwed,  scarfed, 
or  riveted,  should  be  thoroughly  soldered. 

(3)  Form  of  Points.  The  point  of  the  upper  terminal  *  of  the  conductor 
should  not  have  an  angle  sharper  than  90°.  A  foot  below  the  extreme  point  a 
coi)[)cr  ring  should  be  screwed  and  soldered  on  to  the  upper  terminal,  in  which 
ring  should  be  fixed  three  or  four  sharp  copper  points,  each  about  6  in  long, 
it  is  desirable  that  these  points  should  be  so  platinized,  gilded,  or  nickel-plated 
as  to  resist  oxidation. 

(4)  Number  and  Height  of  Upper  Terminals.  The  number  of  conductors  or 
upper  terminals  required  will  depend  upon  the  size  of  the  building,  the  material 
of  which  it  is  constructed,  and  the  comparative  height  above  ground  of  the 
several  parts.  No  general  rule  can  be  given  for  this,  except  that  it  may  be 
as>umed  that  the  space  protected  by  the  conductor  is,  as  a  rule,  a  cone,  the 
radius  of  whose  base  is  equal  to  the  height  of  the  conductor  from  the  ground. 

(5)  Curvature.  The  rod  should  not  be  bent  abruptly  around  sharp  corners. 
In  no  case  should  the  length  of  a  curve  be  more  than  half  as  long  again  as  its 
chord.  A  hole  should  be  drilled  in  string-courses  or  other  projecting  masonry, 
when  possible,  to  allow  the  rod  to  pass  freely  through  it. 

(6)  Insulators.  The  conductor  should  not  be  kept  from  the  building  by 
glass  or  other  insulators,  but  attached  to  it  by  fastenings  of  the  same  metal  as 
that  of  the  conductor  itself. 

(7)  Fixing.  Conductors  should  preferentially  be  taken  down  the  side  of 
the  building  which  is  most  exposed  to  rain.  They  should  be*  held  firmly,  but 
the  holdfasts  should  not  be  driven  in  so  tightly  as  to  pinch  the  conductor  or 
prevent  contraction  and  expansion  due  to  change  of  temperature. 

.  (8)  Other  Metalwork.  All  metallic  spouts,  gutters,  iron  doors,  and  other 
masses  of  metal  about  the  building  should  be  electrically  connected  with  the- 
conductor. 

(9)  Earth-Connection.  It  is  most  desirable  that,  whenever  possible,  the 
lower  extremity  of  the  conductor  should  be  buried  in  permanently  damp  soil. 
Hence,  proximity  to  rain-water  pipes  and  to  drains  or  other  water  is  desirable. 
It  is  a  very  good  plan  to  bifurcate  the  conductor  close  below  the  surface  of  the 
ground,  and  to  adopt  two  of  the  following  methods  for  securing  the  escape  oi 
the  lightning  into  the  earth:  (a)  A  strip  of  copper  tape  may  be  led  from  the 
bottom  of  the  rod  to  a  gas  or  water-main  (not  merely  to  a  leaden  p'pe),  if  such 
exist  near  enough,  and  be  soldered  to  it;  (6)  a  tape  .may  be  solderea  to  a  sheet 
of  copper,  3  by  3  ft  by  Me  in  thick,  buried  in  permanently  wet  earth  and  sur- 
rounded by  cinders  or  coke;  (c)  many  yards  of  copper  tape  may  be  laid  in  a 
trench  filled  with  coke,  having  not  less  than  18  sq  ft  of  copper  exposed. 

(10)  Protection  from  Theft,  etc.  In  places  where  there  is  any  likelihood  of 
the  copper  being  stolen  or  injured,  it  should  be  protected  by  being  enclosed 

*  The  upper  terminal  is  that  portion  of  the  conductor  which  is  between  the  top  of  the 
edifice  and  the  point  of  the  conductor. 


1706  Lightning-Conductors  Part  3 

in  an  iron  gas-pipe,  reaching  lo  ft  (if  there  is  room)  above  ground  and  some 
distance  into  the  ground. 

(ii)  Painting.  Iron  conductors,  galvanized  or  not,  should  be  painted.  It  is 
optional  with  copper  ones. 

(12)  Inspection.  When  the  conductor  is  finally  fixed  it  should  in  all  cases 
be  examined  and  tested  by  a  qualified  person,  and  this  should  be  done  in  the 
case  of  new  buildings  after  all  work  on  them  is  finished.  Periodical  examina- 
tion and  testing,  should  opportunities  offer,  are  also  very  desirable,  especially 
when  iron  earth-connections  are  employed. 

Lightning-Protection  for  High  Chimneys.  The  following  is  a  descrip- 
tion of  the  system  of  lightning-protection  *  for  the  radial-brick  chimney-stack, 
350  ft  in  height,  for  the  plant  of  the  St.  Joseph  Lead  Company,  Herculaneum, 
Mo. 

Conductor.  The  conductor  used  is  of  commercially  pure  copper.  No.  1 1,  Brown 
&  Sharpe  gauge,  in  the  form  of  a  cable,  consisting  of  twenty-eight  wires,  seven 
strands,  four  wires  to  the  strand,  and  %  in  in  diameter,  230  552  circular  mils. 
The  vertical  conductors  are  of  continuous  lengths  from  the  top  of  the  chimney 
to  and  into  the  ground.  A  circuit-conductor  is  placed  5  ft  below  the  top  of 
the  chimney  and  connected  to  each  down-conductor  by  a  12-in  two-way  splice. 

Points.  The  air-terminals  are  eight  in  number  equally  spaced  around  the 
top  of  the  chimney,  and  consist  of  solid,  copper  bars  i  in  in  diam  and  10  ft  in 
length,  the  upper  12  in  tapering  to  a  point  and  covered  with  a  12-in  thimble  of 
genuine  platinum.  Air-terminals  extend  5  ft  above  the  top  of  the  stack  and 
the  lower  end  of  each  copper  bar  is  set  in  a  heavy  copper  T  coupler,  which  con- 
nects the  same  into  the  circuit-conductor.  Each  rod  is  held  in  place  by  heavy 
anchor-fasteners,  bolted  from  the  inside  of  the  stack.  These  anchors  are  en- 
cased in  copper  tubes  set  in  the  solid  masonry. 

Grounding.  At  a  point  below  the  ground-level  and  at  the  chimney-line, 
the  conductor  is  carried  in  a  downward  course  from  the  chimney,  in  a  trench 
bedded  in  charcoal,  to  a  point  5  ft  outside  the  foundation-line.  An  additional 
conductor  is  spliced  into  the  main  cable  at  this  point,  forming  a  Y  with 
branches  terminating  15  ft  apart.  Two  well-holes  are  bored  to  a  depth  of  ap- 
proximately 20  ft  into  permanent  moisture.  The  end  of  each  Y  conductor  is 
electrically  soldered  into  perforated,  copper  reservoirs  4^/2  in  in  diam  and  28  in 
in  length,  and  filled  with  pea-size  charcoal.  The  effect  of  the  reservoir  is  to 
give  the  required  amount  of  surface-contact  with  the  earth  and  to  insure  per- 
manent moisture  through  the  charcoal  by  capillary  attraction.  Each  main 
conductor  is  thus  grounded  in  two  places  instead  of  in  one  place. 

Lead  Covering.  To  preserve  the  conductor  system  against  decomposition 
in  ozone,  in  which  sulphuric  or  other  acid  gases  may  exist,  all  of  the  conductor 
system  at  the  top,  and  to  a  point  75  ft  below  the  top  of  the  chimney  is  covered 
with  lead  H  in  in  thickness.  Exception  is  made  to  the  platinum-covered  12-in 
top  of  each  rod,  which  requires  no  lead  covering.  Where  splices  are  made  and 
anchor-fasteners  set,  the  whole  is  covered  with  lead  sleeves  or  hoods  thoroughly 
wiped  and  hermetically  sealed.  Connections  of  point-bar  T's  etc.,  are  all 
soldered,  lead-covered  and  sealed.  Practical  experience  seems  to  show  that 
all  lightning-conductor  systems  on  chimneys  should  be  lead-covered  and 
hermetically  sealed  to  a  point,  approximately  25  ft  downward  from  the  top,  to 
protect  the  copper  against  decomposition,  not  necessarily  as  thick  as  on  this 
chimney,  but,  say,  He  in,  the  thickness  being  determined  by  the  size  and  usage 

•  Installed  by  the  Ajax  Conductor  and  Manufacturing  Compauy,  Chicago,  IlL 


Automatic  Telephones  for  Intercommunicating  Service       1707 

of  the  stack.  It  has  been  found  that  in  from  three  to  five  years  there  is  a  de- 
cided honeycombing  of  the  copper,  through  the  action  of  the  sulphuric  and 
other  acid  gases.  It  has  often  been  necessary  to  replace  points,  sections  of  cable, 
etc.,  entirely  eaten  away  from  this  cause. 


INTERPHONES.     AUTOMATIC  TELEPHONES  FOE 
INTERCOMMUNICATING  SERVICE 

Description.  The  interphone  system  is  an  application  of  the  telephone  for 
interior  use.  It  is  an  automatic,  intercommunicating  system,  requiring  neither 
switchboard  nor  operator,  and  being  self-contained  within  the  walls  of  the  estab- 
lishment for  whose  benefit  it  has  been  installed. 

Advantages.  In  brief,  the  advantages  of  such  a  system  are  these:  (i)  the 
mere  pressing  of  a  button  gives  a  person  telephone-connection  with  any  desired 
party,  without  the  loss  of  time  involved  in  first  calling  up  a  third  party;  (2)  re- 
course to  directory  or  information  bureau  is  made  unnecessary  through  the  use 
of  labels,  properly  inscribed,  on  the  face  of  the  instrument;  (3)  no  maintenance- 
expense  is  involved,  and  the  system,  consequently,  is  as  inexpensive  to  operate 
as  an  electric  door-bell;  (4)  the  wiring-arrangement  is  such  that  the  system  ma^ 
be  provided  for  when  the  original  plans  for  a  new  building  are  being  drawn  up, 
and  in  this  respect  it  does  not  differ  much  from  a  system  of  electric  lights  or 
plumbing. 

The  Use  of  Interphones  in  residences,  schools,  hospitals,  factories,  mills, 
offices,  stores  and  clubs  is  constantly  increasing.  The  same  general  features 
apply  to  all  of  these  types  of  installations,  and  in  practically  every  case  it  is 
the  simplicity  of  the  system  that  especially  recommends  it  for  service.  The 
interphone  usually  fits  in  where  formerly  call-bells,  speaking-tubes,  messenger 
service  and  other  inadequate  methods  were  the  rule.  The  interphone  field  of 
service  is  in  the  estabhshmcnt  whose  needs  call  for  from  four  to  thirty-two 
telephone-stations.  When  there  are  more  than  thirty-two  the  installation  of  a 
private  telephone-exchange,  with  a  switchboard,  is  better  practice. 

Types  of  Interphones.  There  are  several  types  of  interphones  for  varying 
degrees  of  service. 

(i)  The  most  familiar  instrument  is  a  wall-interphone,  of  the  non-flush 
TYPE.  The  telephone  is  of  metal,  with  connecting  buttons,  labels,  bells,  mouth- 
piece, hook  and  receiver,  all  mounted  on  its  face.  This  instrument  is  to  be  at- 
tached directly  to  the  wall. 

(2)  The  FLUSH  TYPE  resembles  the  first-mentioned  type  in  every  particular 
but  the  one  implied  in  its  title.  The  instrument  is  mounted  into  the  wall,  with 
its  face  flush  with  the  rest  of  the  wall-surface.  These  two  instruments  are  most 
popular  for  installation  in  club-halhvays,  in  stores  and  factories,  in  residences, 
and  in  all  places  where  wall-telephones  would  ordinarily  be  used.  Busy  offices 
and  stores  often  employ  variations  of  types  (i)  and  (2)  and  use  a  desk-set,  a 
separate  instrument  taking  care  of  the  connecting  buttons  and  labels,  or  a  hand- 
set. 

(3)  The  DESK-STAND  telephone  is  of  the  type  often  used  for  local  and  long- 
distance service.  Connected  with  it  is  a  metal  box  containing  the  rows  of 
buttons  and  labels,  each  label  being  opposite  the  button  through  which  is  se- 
cured connection  with  the  corresponding  station.  The  telephone  in  this  case 
stands  on  the  desk,  and  the  key-box  is  conveniently  close  at  hand,  either  on  the 
desk  or  on  the  wall. 


1708  Vacuum-Cleaning  Part  3 

(4)  Some  prefer  for  this  service  the  hand-set,  with  the  receiver  and  trans- 
mitter in  one  piece.  This  is  a  convenient,  compact  instrument,  well  fitted  for 
use  in  an  office. 

(5)  From  two  to  six  instruments  of  still  another  type  make  up  a  party-line 
INTERPHONE  SYSTEM.  Here  there  are  no  connecting  buttons,  the  principle  in- 
volved being  the  same  as  that  of  the  elementary,  farmers'  Hne.  This  makes  a 
convenient  private-line  system  for  a  small  residence,  and  is  appropriate  for  a 
house-to-garage  circuit. 

Variations  from  Standard  Types.  There  are  systems  with  variations  from 
the  standard  types.  Many  schools  are  using  a  combination  of  interphones  of 
type  (i)  or  (2)  with  (5).  In  the  principal's  office  is  an  instrument  of  type 
(i)  or  (2)  with  a  connecting  button  for  each  outside  station,  while  the  class- 
room-telephones are  all  of  type  (5).  With  this  system  the  principal  can  at 
any  time  call  up  any  teacher;  but  a  teacher  can  call  up  another  classroom 
only  through  the  medium  of  this  master-station,  which  acts  as  a  sort  of  ex- 
change. The  advantages  of  this  arrangement  for  a  school  are  obvious.  In  a 
hospital  the  instruments  are  usually  placed  outside  of  the  more  important 
operating-rooms  and  wards  and  in  the  offices  and  reception-rooms. 

Wiring  and  Batteries.  All  wiring  is  enclosed  in  cables.  Energy  is  obtained 
from  dry  cells.  The  only  maintenance-expense  connected  with  an  interphone 
system  is  the  occasional  renewal  of  these  batteries^. 

VACUUM-CLEANING 

General  Description.  Vacuum-cleaners  are  appliances  which  have  come 
into  use  during  recent  years  and  which  are  for  the  purpose  of  removing  dirt 
and  dust  from  rooms  of  buildings,  cars,  steamships,  etc.,  or  from  furniture, 
carpets,  curtains,  or  other  interior  fittings.  The  dust  and  dirt  are  removed  by 
suction  and  the  apparatus  consists  of  an  air-pump  which  is  arranged  to  draw 
the  air  and  the  dirt  or  dust  contained  in  it  through  pipe  and  nozzle.  This 
nozzle  is  drawn  or  passed  over  the  surfaces  which  are  to  be  cleaned.  Screens 
of  musUn  or  other  appropriate  cloth  are  used  to  separate  by  filtration  the  dust 
and  dirt  which  are  borne  along  with  the  stream  of  air;  and  in  some  types  of 
apparatus  this  process  is  assisted  by  what  are  called  baffle-plates  which  are  added 
to  make  the  heavier  particles  of  dust  drop  by  their  own  weight  to  the  lower 
part  of  the  receptacle  placed  to  receive  them.  About  the  year  1890  compressed 
air  was  used  for  the  first  time  in  railroad-cars  for  purposes  of  cleaning  and  dust- 
removal.  There  were  serious  objections  to  this  method  of  cleaning,  however, 
as  it  was  found  that  the  jets  of  compressed  air  blew  out  the  dust  and  dirt  in  such 
a  way  that  it  was  difficult  to  arrange  for  their  collection  and  retention;  the 
principle  of  suction  was  consequently  introduced  to  overcome  these  difiiculties. 

Types  of  Vacuum-Cleaners.  The  machines  belonging  to  the  earliest  types 
usually  consist  of  a  pump,  the  motor-power  of  which  is  cither  a  gas-engine  or  an 
electric  motor,  the  machines  being  portable.  They  can  be  moved  about  from 
one  building  to  another  as  occasion  demands.  Cleaners  of  the  next  type  intro- 
duced involve  an  installation  in  the  basement  or  lower  part  of  a  building  and  a 
fixed  and  permanent  position.  From  the  central  plant  pipes  art*  run  to  various 
rooms  and  apartments  and  are  fitted  in  such  rooms  or  apartments  or  in  adjacent 
halls  or  corridors,  with  valves  to  which  are  attached  the  hose  with  the  cleaning- 
appliances  at  the  end.  In  some  cases  this  vacuum-arrangement  is  combined 
with  another  for  washing  floors,  the  secondary  system  including  a  second  set  of 
pipes  from  a  tank  filled  with  soap  and  water.  Compressed  air  is  employed  to 
spray  the  latter  over  the  floor,  and  both  dirt  and  water  are  finally  removed 


Waterproofing  for  Foundations  1709 

'Ugh  pipes  to  the  street-sewers.  A  portable  tank  is  used  for  the  soap  and 
rv.  Vacuum-cleaners  of  a  third  type  consist  of  small  machines  which  take 
place  of  the  brooms  and  dusters  or  are  used  in  connection  with  them.  They 
now  very  generally  used  and  may  be  driven  by  an  electric  motor,  by  foot,  or 
■  and.  These  last-mentioned,  smaller,  portable  cleaners  are  used  for  many 
r  purposes  than  the  ordinary  cleaning  of  rooms  and  furniture. 
etails  and  Specifications  for  Vacuum-Cleaning  Installations.  Com- 
'  plans  and  specifications  for  the  installation  of  a  vacuum-cleaning  plant  for 
ilding  may  be  obtained  from  any  of  the  numerous  manufacturers  making 
I  apparatus  and  taking  contracts  to  put  it  in  place.  There  are  several  types 
uichines  and  systems  of  installation  and  detailed  descriptions  would  exceed 
limits  of  space  in  this  handbook. 

WATERPROOFING   FOR    FOUNDATIONS* 

The  Waterproofing  of  Substructure  Work  is,  comparatively  speaking,  a 

]iiv)dcrn  branch  of  engineering.  It  is  only  within  recimt  years  that  it  has  become 
accessary  to  construct  deep  basements  for  buildings.  In  the  past,  the  more 
imoortant  structures,  such  as  cathedrals,  capitols,  state-buildings  and  the  like, 
were  usually  built  upon  high  ground,  and  water  was  prevented  from  entering 
ih--  basements  of  such  buildings  by  means  of  drainage.  Waterproofing,  as  we 
know  it,  was  generally  unnecessary.  With  the  advent  of  the  so-called  sky- 
I !  )ers,  however,  requiring  large  mechanical  plants,  deep  basements  became 
an  actual  necessity,  and  as  these  basements  are  usually  carried  below  ground- 
water level,  and  in  many  instances  below  tide-level,  the  question  became  one  of 
utmost  importance.  Like  almost  every  detail  of  a  modern  building,  water- 
proofing is  a  specialty.  Each  building  presents  its  own  problems,  and  the  safest 
plan  is  to  leave  the  solution  of  these  problems  to  some  one  expert  in  the  knowledge 
of  waterproofing  who  has  made  it  a  special  study  and  knows  how  best  to  over- 
come the  existing  difficulties.  It  may  be  laid  down  as  an  invariable  rule  that, 
where  conditions  are  at  all  serious,  the  owner  or  the  general  contractor  will 
save  money  in  the  long  run  if  he  employs  the  services  of  an  expert  waterproofer 
to  place  his  waterproofiug-seal,  regardless  of  the  method  he  wishes  to  use. 

Pressure-Resistance  Versus  Waterproofing.  In  waterproofing  large  base- 
ments where  actual  pressure  exists,  it  is  a  question  for  the  engineer  to  decide 
whether  it  is  more  economical  to  attempt  to  secure  an  absolute  pressure-job 
or  a  WATER-PROOF  JOB  in  connection  with  a  drainage  system.  As  a  general 
rule,  it  may  be  stated  that  where  a  building  is  generating  its  own  power,  it  is 
more  economical  to  use  a  drainage  system  with  an  open  sump  than  to  construct 
a  pressure-cellar,  the  cost  of  pumping  being  much  less  than  the  interest  charges 
on  the  cost  of  a  floor-slab  sufficiently  strong  to  withstand  the  pressure. 

Waterproofing  Concrete  Foundations.  The  three  following  subdivisions 
of  this  subject,  discussing  the  causes  of  permeability  of  concrete,  the  addition  of 
substances  to  render  it  more  water-proof,  and  the  treatment  of  its  surfaces  to 
make  it  less  permeable,  embody  the  conclusions  of  Committee  D-8  of  the  Amer- 
ican Society  for  Testing  Materials,  f  This  committee,  since  its  organization  in 
1 90s  has,  through  laboratory-tests  and  experiments,  together  with  examinations 
of  work  during  construction  and  after  completion,  4s  well  as  the  study  of  liter^ 
ature  on  the  subject,  sought  to  secure  sufficient  information  to  enable  it  to  for- 

*  For  foundations  in  general,  see  Chapter  II. 

tThis  article,  to  the  middle  of  page  1713,  is  the  substance  of  a  Report  submitted  to 
the  American  Society  for  Testmg  Materials  at  its  meeting,  June  24-28,  19 13.  This 
society  has  (1920)  no  Standard  Specifications  for  Waterproofing,  but  published  in  1918 
ftmr  Tentative  Soecificatioris  on  this  subject. 


1710  Waterproofing  for  Foundations  Part  3 

miilate  definite  methods  for  securing  water-proof  concrete  structures.  The  work 
of  the  committee  was  compHcated  by  reason  of  the  facts  that  there  seemed  to  be 
so  httle  concordance  between  results  of  tests  obtained  under  laboratory-condi- 
tions and  in  the  field  and  that  it  was  necessary  to  extend  its  investigations  over 
a  period  of  years  in  order  to  determine  the  permanency  of  the  action  noted.  The 
committee  reported  that  while  it  had  not  been  able  to  arrive  at  sufficiently  definite 
conclusions  to  enable  it  to  formulate  specifications  for  the  making  of  concrete 
structures  water-proof  or  for  materials  to  be  used  in  such  work,  it  had  reached 
certain  general  conclusions  which  might  be  of  assistance  to  the  constructor  in 
securing  the  desired  result  of  impermeable  concrete.  Early  in  the  investigation, 
the  work  was  found  to  subdivide  naturally  into  three  branches,  and  the  con^ 
elusions  reached  will  be  grouped  in  order  under  these  subdivisions,  which  are: 

(i)  The  determination  of  causes  of  the  permeability  of  concrete  as  usually 
made  from  mixtures  of  Portland  cement,  sand  and  stone,  or  other  coarse  aggre- 
gate, in  proportions  of  from  i  of  cement,  2  of  sand  and  4  of  stone,  to  i  of 
cement,  3  of  sand  and  6  of  stone,  and  the  best  methods  of  avoiding  these 
causes.  V 

(2)  The  rendering  of  concrete  more  water-proof  by  adding  to  ordinary  mix- 
tures of  cement,  sand  and  stone,  other  substances  which,  either  by  their  void- 
filling  or  repellent  action,  would  tend  to  make  the  concrete  less  permeable. 

(3)  The  treatment  of  exposed  surfaces  after  the  concrete  or  mortar  has  been 
put  in  place  and  hardened  more  or  less,  either  by  penetrative,  void-filling  or 
repellent  liquids,  making  the  concrete  itself  less  permeable;  or  by  extraneous 
protective  coatings,  preventing  water  from  having  access  to  the  concrete. 

Considering  these  several  subdivisions  separately  and  in  the  order  named,  the 
committee  arrives  at  the  following  conclusions: 

(i)  Causes  of  Permeability  of  Concrete.  In  the  laboratory  and  under  test- 
conditions  where  properly  graded  and  sized  coarse  and  fine  aggregates  are 
used,  in  mixtures  ranging  from  i  of  cement,  2  of  sand  and  4  of  stone,  to  i  of  ce- 
ment, 3  of  sand  and  6  of  stone,  impermeable  concrete  can  invariably  be  pro- 
duced. Even  with  sand  of  poor  granulometric  composition,  with  mixtures  as 
rich  as  i  of  cement,  2  of  sand  and  4  of  stone,  permeable  concrete  is  seldom,  if 
ever,  found  and  is  a  rare  occurrence  with  mixtures  of  i  of  cement,  3  of  sand 
and  6  of  stone.  But  the  fact  remains,  nevertheless,  that  the  reverse  often  ob- 
tains in  actual  construction,  permeable  concretes  being  encountered  even  with 
mixtures  of  i  of  cement,  2  of  sand  and  4  of  stone  and  are  of  frequent  occurrence 
where  the  quantity  of  the  aggregate  is  increased.  This  the  committee  attributes 
to: 

(a)  Defective  workmanship,  resulting  from  improper  proportioning,  lack  of 
thorough  mixing,  separation  of  the  coarse  aggregate  from  the  fine  aggregate  and 
cement  in  transporting  and  placing  the  mixed  concrete,  lack  of  density  through 
insuflicient  tamping  or  spading,  improper  bonding  of  work-joints,  etc. 

(b)  The  use  of  imperfectly  sized  and  graded  aggregates. 

(c)  The  use  of  excessive  water,  causing  shrinkage-cracks  and  formation  of 
laitance-seams. 

(d)  The  lack  of  proper  provision  to  take  care  of  expansion  and  contraction, 
causing  subsequent  cracking. 

Theoretically,  none  of  these  conditions  should  prevail  in  properly  designed  and 
supervised  work,  and  they  are  avoided  in  the  laboratory  and  in  the  field,  under 
test-conditions,  where  speed  of  construction  and  cost  are  negligible  items,  instead 
of  being  governing  features  as  they  must  be  in  actual  construction.  Properly 
graded  sands  and  coarse  aggregates  are  rarely,  if  ever,  found  in  nature  in  sufficient 
quantities  to  be  available  for  large  construction,  and  the  effect  of  poorly  graded 


Waterproofing  for  Foundations  1711 

aggregates  in  producing  permeable  concrete  is  aggravated  by  poor  and  inefficient 
field-work.  Even  if  the  added  expense  of  screening  and  remixing  tlie  aggre- 
gates could  be  afforded,  so  as  to  secure  proper  granulometric  composition  to 
give  the  density  required  to  make  untreated  concretes  impermeable,  it  is  seem- 
ingly often  a  commercial  impossibility  on  large  construction  to  obtain  work- 
manship, even  approximating  that  found  in  laboratory- work. 

(2)  Addition  of  Foreign  Substances  to  Cement  Before  or  During  Mixture.  The 
committee  finds  that  in  consequence  of  the  conditions  outlined  above,  sub- 
stances calculated  to  make  the  concrete  more  impermeable,  either  incorporated 
in  the  cement  or  added  to  the  concrete  during  mixing,  are  often  used.  This 
has  resulted  in  the  development  and  placing  on  the  market  of  numerous  patented 
or  proprietary  waterproofing-compounds,  the  composition  of  which  is  more  or 
less  of  a  trade-secret.  While  it  has  been  impossible  for  the  committee  to  test  all 
of  the  special  waterproofing-compounds  being  placed  on  the  market,  it  has 
investigated  a  sufficient  number  of  these,  as  well  as  the  use  of  certain  very  finely 
divided,  naturally  occurring  or  readily  obtainable  commercial  mineral  products, 
such  as  finely  ground  sand,  colloidal  clays,  hydrated  lime,  etc.,  to  form  a  general 
idea  of  the  value  of  the  different  types.     The  committee  finds: 

(k)  That  the  majority  of  patented  and  proprietary  integral  compounds  tested 
have  little  or  no  immediate  or  permanent  effect  on  the  permeability  of  concrete 
and  that  some  of  these  even  have  an  injurious  effect  on  the  strength  of  mortar 
and  concrete  in  which  they  are  incorporated. 

(b)  That  the  permanent  effect  of  such  integral  waterproofing-additions,  if 
dependent  on  the  action  of  organic  compounds,  is  very  doubtful. 

(c)  That  in  view  of  their  possible  effect,  not  only  upon  the  early  strength, 
but  also  upon  the  durability  of  concrete  after  considerable  periods,  no  integral 
waterproofing-material  should  be  used  unless  it  has  been  subjected  to  long-time 
practical  tests  under  proper  observation  to  demonstrate  its  value,  and  unless 
its  ingredients  and  the  proportion  in  which  they  are  present  are  known. 

(d)°That  in  general,  more  desirable  results  are  obtainable  from  inert  com- 
pounds acting  mechanically,  than  from  active  chemical  compounds  whose 
efficiency  depends  on  change  of  form  through  chemical  action  after  addition  to 
the  concrete.  ,         u  i 

(e)  That  void-filling  substances  are  more  to  be  relied  upon  than  those  wliose 
value  depends  on  repellent  action. 

(f)  That,  assuming  average  quality  in  sizing  of  the  aggregates  and  reasonably 
good  workmanship  in  the  mixing  and  placing  of  the  concretes,  the  addition  ot 
from  10  to  20%  of  very  finely  divided  void-filling  mineral  substances  may  be 
expected  to  result  in  the  production  of  concrete  which,  under  ordinary  conditions 
of  exposure  will  be  found  impermeable,  provided  the  work-joints  are  properly 
bonded,  and  cracks  do  not  develop  on  drying,  or  through  change  m  volume  dus 
to  atmospheric  changes,  or  by  settlement. 

(3)  External  Treatment.      While  external  treatment  of   concrete  would  not 
be  necessary  if  the  concrete  itself,  either  naturally  or  by  the  addition  of  wat^er- 
prfing-material,  was  impermeable  to  water,  it  has  ^een  ^ound  m  pra^^^^^^^^ 
in  large  construction,  no  matter  how  carefully  the  concrete  itself  has  been  made^ 
cracks  are  apt  to  develop,  due  to  shrinkage  in  drying  out,  ^^^^^^'^^^^^^^^^^ 
tion  under  change  of  temperature  and  moisture-content    and  t«  se^^^^^^^ 
ment      It  is   therefore,  often  advisable  in  important  construction  to  anticipate 
Xrovide'for  the  possible  occurrence  of  such  cracks  by  external^t^^^^^^^^ 
with  a  protective  coating.     Such  coating  must  be  sufficiently  ^i^f  ^  ^^^^^^^^^ 
to  Drevent  the  cracks  extending  through  the  coating  itself.     The  application  ot 
merel7  penetrative  void-filling  liquid  washes  will  not  prevent  the  passage  of 


1712  Waterproofing  for  Foundations  Part  3 

water  due  to  cracking  of  the  concrete.     The  committee  has,  therefore,  consid- 
ered surface-treatment  under  two  heads: 

(a)  Penetrative  void-iiiHng  Hquid  washes. 

(b)  Protective  coatings,  including  all  surface-applications  intended  to  prevent 
water  coming  in  contact  with  the  concrete. 

Penetrative  Washes.  While  some  penetrative  washes  may  be  efficient  in 
rendering  concrete  water-proof  for  limited  periods,  their  efficienci^  may  decrease 
with  time  and  it  may  be  necessary  to  repeat  such  treatment.  Some  of  these 
washes  may  be  objectionable,  due  to  discoloring  the  surface  to  which  they  are 
applied.  The  committee,  therefore,  believes  that  the  first  effort  should  be  made 
to  secure  a  concrete  that  is  impermeable  in  itself  and  that  penetrative  void- 
filling  washes  should  only  be  resorted  to  as  a  corrective  measure. 

Protective  Coatings.  While  protective  extraneous  bituminous  or  asphaltic 
coatings  are  unnecessary,  so  far  as  the  major  portion  of  the  surface  of  the  con- 
crete is  concerned,  provided  the  concrete,  either  in  itself  or  through  the  addition 
of  integral  compounds,  is  made  impermeable,  they  are  valuable  as  a  protection 
where  cracks  develop  in  a  structure.  It  is  therefore  recommended  that  a  com- 
bination of  inert  void-filling  substances  and  extraneous  waterproofing  be  adopted 
in  especially  difficult  or  important  work. 

Bituminous  or  Asphaltic  Coatings.  Considering  the  use  of  bitum.inous  or 
asphaltic  coatings,  the  committee  finds: 

(a)  That  such  protective  coatings  are  often  subject  to  more  or  les.^  deteriora- 
tion with  time,  and  may  be  attacked  by  injurious  vapors  or  deleterious  substances 
in  solution  in  the  water  coming  in  contact  with  them. 

(b)  That  the  most  effective  method  for  applying  such  protection  is  either  the  ■ 
Z2tting  of  a. course  of  impervious  brick  dipped  in  bituminous  material  into  a  solid 
^ed  of  bituminous  material,  or  the  application  of  a  sufficient  number  of  layers  of 
satisfactory  membranous  material  cemented  together  with  hot  bitumen. 

(c)  That  their  durability  and  efficiency  are  very  largely  dependent  on  the  care 
with  which  they  are  applied.  Such  care  refers  particularly  to  proper  cleanhig 
and  preparation  of  the  concrete  to  insure  as  dry  a  surface  as  possible  before  appli- 
cation of  the  protective  covering,  the  lapping  of  all  joints  of  the  meinbranous  * 
layers,  and  their  thorough  coating  with  the  protective  material.  The  use  of 
this  method  of  protection  is  further  desirable  because  proper  bituminous  cover- 
ings offer  resistance  to  stray  electrical  currents,  the  possible  attack  from  which 
is  referred  to  in  succeeding  paragraphs. 

Rich  Mixtures.     So  far,  the  committee  has  considered  only  concretes  of  the 
usual  proportions,  namely,  those  ranging  from  i  of  cement,  2  of  sand  and  4  of 
stone,  to  I  of  cement,  3  of  sand  and  6  of  stone.     It  has  been  suggested  that  im- 
permeable concretes  could  be  assured  by  using  mixtures  considerably  richer  in 
cement.     While  such  practice  would  probably  result  in  an  immediate  imperme- 
able concrete,  it  is  believed  by  many  that  the  advantage  is  only  temporary,  as 
richer  concretes  are  more  subject  to  check-cracking  and  are  less  constant  in 
volume  under  changes  of  conditions  of  temperature,  moisture,  etc.     Therefci   . 
the  use  of  more  cement  in  mass-concrete  would  cause  increased  cracking,  unk 
some  means  of  controlling  the  expansion  and  contraction  is  discovered.     Wi: 
reinforced  concretes  the  objection  is  not  so  great,  as  the  tendency  to  crackii 
is  more  or  less  counteracted  by  the  reinforcement. 

Fine  Flour  Mixtures.     It  has  also  been  suggested  that  the  presence  in  the    : 
cement  of  a  larger  percentage  of  very  fine  flour  might  result  in  the  production  of 
u  denser  and  more  impermeable  concrete,  through  the  formation  of  a  larger 
timount  of  colloidal  gels.     Neither  of  these  suggestions  has  been  especially  in- 
vestigated by  the  committee.    Both  appeal  to  the  committee,  however,  for  the 


Waterproofing  for  Foundations  1713 

reason  that  they  substitute  active  cementitious  substances  for  the  largely 'in- 
active void-filUiig  materials  previously  recommended,  thus  increeteing  the  strength 
of  the  concrete. 

Character  of  Workmanship.  In  conclusion,  the  committee  would  point  out 
that  no  addition  of  waterproofing-compounds  or  substances  can  be  relied  upon 
to  completely  counteract  the  effect  o/  bad  workmanship,  and  that  the  produc- 
tion of  impermeable  concrete  can  only  be  hoped  for  where  there  is  determined 
insistence  on  good  workmanship. 

Saline  Waters.  Electrical  Action.  The  production  of  impermeable  concrete 
has  assumed  greater  importance  since  the  appointment  of  this  committee, 
owing  to  the  well-known  injurious  action  of  saline  or  alkaline  waters  and  to  the 
suggested  possible  effect  of  the  moisture  in  concrete  occasioning  or  aggravating 
electrical  action  from  stray  currents.  Originally,  the  question  of  waterproofing 
involved  mainly  the  physical  troubles  resulting  from  water  passing  through 
concrete  without  any  special  consideration  of  its  effect  on  its  durabiUty,  other 
than  a  gradual  leacliing  out  of  the  cement.  Recent  developments  suggest  the 
possibility  that,  owing  to  the  increased  conductivity  of  damp  concrete  to  elec- 
trical currents,  such  currents,  if  present,  may  so  affect  damp  concrete  as  to  seri- 
ously lessen  its  integrity;  and  this  possibility  further  emphasizes  the  importance 
of  the  recommendation  that  no  waterproofing-compound  of  unknown  chemical 
composition  be  added  to  concrete,  as  recent  tests  seem  to  show  that  the  action  of 
electrical  currents  is  aggravated  by  the  presence  of  certain  solutions. 

Waterproofing  by  External  Linings  of  Brick,  Tar,  or  Asphalt,  and  Felt, 
The  oldest  method  of  waterproofing  is  the  one  involving  the  use  of  a  tar-and-felt 
or  asphalt-and-felt  seal  (Fig.  1).  This  consists  of  building  first  a  supporting 
wall  arid  a  supporting  concrete  slab  to  hold  the  seal.  On  the  floors,  this  slab 
is  usually  composed  of  concrete,  4  in  thick.  The  walls  are  generally  of  brick 
from  4  to  8  in  thick,  but  occasionally  4-in  terra-cotta  tiles  are  used.  Upon  this 
base  a  swabbing  of  tar  or  asphalt  is  placed  and  before  this  has  become  cold  or 
set,  one  thickness  of  paper,  saturated  with  coal-tar,  is  laid.  This  paper  receives 
a  swabbing  of  coal-tar  and  asphalt  and  another  layer  of  paper  is  placed,  the 
operation  being  continued  until  there  are  three  or  more  layers  of  paper  with 
four  or  more  swabbings  of  tli^  tar  or  asphalt.  For  damp-proof  work,  three  layers 
of  paper  with  four  swabbings  of  tar  are  usually  sufficient.  For  waterproofing- 
work  not  less  than  five  and  usually  six  layers  of  paper  with  from  six  to  seven 
swabbings  of  tar  are  used.  The  main  walls  of  the  structure  are  then  built  against 
the  wall-waterproofing,  and  after  these  are  in  place,  the  main  concrete  basement- 
floor  is  laid  immediately  on  top  of  the  floor-seal,  the  idea  being  to  form  a  con- 
tinuous water-proof  seal  enveloping  the  entire  basement  below  grade.^  The 
difficulties  of  this  system  consist  chiefly  in  securing  perfect  laps  at  all  points  in 
the  work,  and  unless  extreme  care  is  used  and  unless  there  is  perfect  cooperation 
between  the  waterproofer  and  the  mason-contractor,  there  is  apt  to  be  a  break 
somewhere  in  the  seal,  usually  where  the  wall-waterprooflng  is  supposed  to  be 
joined  to  the  floor-work.  The  disadvantages  of  this  system  are  due  to  the  fact 
that  the  seal  is  not  permanent  in  all  soils  as  the  subsurface  water  frequently 
contains  acids  which  destroy  the  seal.  Then  again,  the  seal  may  be  easily 
punctured  by  the  mas6n-contractor  in  building  his  wall  against  it  or  in  laying 
the  concrete  floor  upon  the  flat  work.  The  chief  disadvantage,  however,  is  that 
the  waterproofing- seal  is  invariably  buried  behind  a  mass  of  masonry,  either 
brick  or  concrete,  which  means  that  should  there  be  a  leak,  due  to  either  care- 
lessness or  accident,  through  the  waterproofing-seal,  it  is  frequently  impossible 
to  stop  it.  It  not  infrequently  happens  that  when  a  leak  has  developed  in  tar- 
and-felt  work,  the  actual  presence  of  the  water  does  not  show  opposite  the  leak, 


1714 


Waterproofing  for  Foundations 


Part  3 


but  following  some  line  of  least  resistance,  appears  from  50  to  100  ft,  or  more, 
away  from  where  the  actual  damage  causing  the  leak  occurs.  In  actual  water- 
proofing work  it  is  seldom  attempted  to  secure  a  bottle-tight  job  with  tar  and 
felt.  Instead,  some  system  of  drainage  is  installed  beneath  the  water-proof 
seal  which  is  on  the  floors  of  the  building,  and  the  water  is  conducted  through  tile 


Brick  wall 

4  in. 

Tile  blocks 

A  in. 

Waterproofing 

JS^in. 

Bricks 

lin. 

Concrete 

30  in. 

Furring  and  plaster 
Total  thickness  of  wall 

4  in. 

465^  in. 

Total  thickness  of  floor 

16  In. 

Fig.  1.*     Felt-Waterproofing  for  Foundations 


or  other  pipes  to  some  central  sump  from  which  it  is  mechanically  pumped  to 
a  sewer.  The  purpose  of  the  waterproofing  in  this  case,  therefore,  is  to  con- 
centrate or  drive  the  water  to  this  sump.  For  shallow  cellars  and  especially 
dampproofing-work,  this  tar-and-felt  method  is  the  most  economical  and  most 
frequently  employed. 

Waterproofing  by  Coating  with  Water-Proof  Cement.  For  deep  and 
difficult  work  a  comparatively  new  method  of  waterproofing  is  often  used 
(Fig.  2).  This  consists  of  placing  a  coating  of  water-proof  cement  upon  the 
interior  surface  of  the  exterior  walls  of  the  building  and  over  the  upper  surface 
of  the  concrete  floor-slab  in  the  basement  or  subbasement.  Fig.  3  shows  a 
foundation  for  an  engine,  the  concrete  being  waterproofed  as  shown.  The  pit 
is  made  somewhat  larger  than  the  foundation,  the  extra  space  being  filled  in 
with  cinders,  dry  bricks  or  terra-cotta  blocks,  which  may  be  readily  removed 
to  allow  access  to  the  bed-plate  bolts  for  which  hand-holes  have  been  cast  in 
the  concrete,  thus  permitting  the  complete  removal  of  the  engine.     The  figure 

*  Reproduced,  by  permission,  from  a  pamphlet  published  by  The  Waterproofing  Com- 
pany. New  York,  and  showing  the  greater  thickness  of  walls  and  floor  required  for  the 
outside-surface  brick -and-felt  method  of  waterproofing  as  compared  with  the  inside- 
surface  waterproof -cement  coating.  Taken  from  design  for  waterproofing  in  a  prominent 
New  York  building.     See,  also,  Fig.  2. 


Waterproofing  for  Foundations  1715 

shows  a  2-in  sand  cushion  and  a  2-in  layer  of  planks  under  the  engine-foundation. 
This  is  not  a  part  of  the  waterproofing  but  is  put  in  to  prevent  the  communica- 
tion of^  vibration.  Fig  4  shows  rcinforced-concrete  floors  for  an  engine-room 
and  boiler-room,  the  concrete  slab  being  12  in  thick  under  the  former  and  24  in 


Concrete  wall 

30  in. 

Waterproofing 

^irx. 

Total  thickness  of  wall 

30X  in. 

Total  thickness  of  floor 

11  in. 

Fig.  2.*     Cement  Waterproofing  for  Foundations 

thick  under  the  latter.  Both  floors  are  covered  with  a  i-in  course  of  water-proof 
cement.  The  reinforcement  is  put  in  as  shown  and  in  sizes  and  spacing  as 
follows: 


i2-in  slab 

24-in  slab 

Rods  in  two  courses 

Rods  in  three  courses 

Lower  rods,  4  in  on  centers,  6  in  from 

Lowest  rods,  3  in  on  centers,  12  in  from 

surface 

surface 

Upper  rods,  6  in  on  centers,  2  in  from 

Intermediate  rods,  3  in  on  centers,  7  in 

surface 

from  surface 

For  five  rods,  total  area  of  cross-section 

Upper  rods,  6  in  on  centers,  2  in  from 

is  0.703  sq  in;    per  square  foot  of  sur- 

surface - 

face,  2.39  lb 

For  ten  rods,  total  area  of  cross-section. 

1.4  sq  in;  per  square  foot  of  surface. 

4.78  lb 

*  From  a  pamphlet  published  by  The  Waterproofing  Company,  New  York,  and  show- 
ing reduced  total  thickness  of  walls  and  floor  required  for  the  inside-surface  water-proof 
cement  method  of  waterproofing.  Taken  from  design  for  waterproofing  of  the  same 
building  shown  in  Fig.  1.     The  walls  and  floors  were  put  in  place  in  the  monolithic  form. 


1716 


Waterproofing  for  Foundations 


Part  3 


There  are  many  compounds.advertised  to  make  cement  or  concrete  water-proof. 
Besides  these,  there  are  water-proof  cements  manufactured  by  secret  processes 
and  applied  by  companies  that  make  a  specialty  of  waterproofing.  Some  of 
the  many  waterproofing-compounds  have  merit;    but  the  main  factors  of    a 


Fig.  3.*    Engine-foundation  with  Water-proof  Cement 

successful  job  of  waterproofing  are  the  skill  and  experience  of  the  waterproofers 
who  do  the  work.  It  is  claimed  that  to  apply  cement  waterproofing  so  as  to 
obtain  efficient  results  requires  more  skill  than  to  apply  a  tar-and-felt  seal;  but 
a  cement  waterproofing,  once  properly  applied,  seems  to  possess  some  advantages 


Fig.  4.*    Reinforced-concrete  Floor  with  Water-proof  Cement 


over  the  older  method  of  tar  and  felt.  One  advantage  is  that  the  waterproofing 
is  accessible,  and  that  if  any  leaks  develop,  they  are  apparent  and  can  be  readily 
and  economically  repaired  by  cutting  out  the  old  waterproofing  and  placing 
a  new  coating  where  the  damage  exists.  Another  advantage  claimed  is  that 
cement  waterproofing  is  generally  permanent  and  not  damaged  by  the  ordinary 

*  Reproduced  by  permission  of  The  Waterproofing  Company,  New  York. 


Force  of  the  Wind  1717 

acids  found  in  solution  with  water  in  soil.  By  the  cement  method  the  cost  of 
the  brick  supporting  walls  and  the  concrete  supporting  slab  is  eliminated  as  is 
also  the  corresponding  cost  of  the  necessary  excavation  for  them;  and  finally, 
the  waterproofing  on  the  floor  serves  the  double  purpose  of  waterproofing  and 
wearing-surface,  thus  saving  the  cost  of  the  cement  finish  usually  found  in 
basements  and  subbasements.  One  of  the  disadvantages  of  cement  water- 
proofing is  that  the  material  is  rigid  and  is  fractured  by  any  settlement  of  the 
building  or  contraction  in  the  concrete  upon  which  it  is  placed.  Experience  has 
shown,  however,  that  settlement-cracks  usually  take  place  before  the  water- 
proofing contractor  has  left  the  building  and  that  there  is  little  or  no  trouble 
from  these  causes  after  his  work  is  completed.  Contraction-cracks  in  concrete, 
however,  seem  to  develop  at  any  time  within  twenty-four  months  after  concrete 
has  been  placed.  In  order  to  prevent  these  cracks,  users  of  the  cement  water- 
proofing have  adopted  a  system  of  reinforcement  in  the  concrete,  and  it  is  claimed 
that  this  reinforcement  is,  in  the  long  run,  an  economy,  as  it  permits  of  less  con- 
crete and  gives  a  better  and  stronger  floor  or  wall.  On  brick  and  stone  walls 
no  trouble  is  experienced  from  contraction  and  expansion. .  It  should  be  re- 
membered that  this  work  is  all  below  grade  where  contraction  and  expansion 
are  reduced  to  a  minimum,  regardless  of  the  materials  used. 

Waterproofing  by  Adding  Substances  to  Cement.  This  is  another 
method  of  waterproofing  now  being  advocated  by  some.  If  this  method  could 
always  be  made  efficient,  it  would  be  highly  advantageous.  It  is  claimed  by 
the  manufacturers  of  these  compounds  that  in  order  to  secure  a  water-proof 
basement,  for  example,  a  certain  percentage  of  the  compound  is  to  be  mixed 
with  the  cement  before  it  is  incorporated  in  the  concrete.  The  opponents  of 
this  method  claim,  however,  that  it  is  impossible  to  construct  a  basement  in 
this  way  without  incurring  the  danger  of  serious  leaks  at  the  joinings  of  one 
day's  work  with  that  of  another;  that  leakage  at  these  points  of  cleavage  may 
be  increased  by  the  use  of  waterproofing-compounds;  and  that  their  principal 
merit  is  that  they  produce  a  very  dense  mass  of  concrete.  It  is  always  difficult 
to  bond  old  concrete  to  new,  and  if  concrete  is  made  water-proof,  or,  in  other 
words,  nonabsorbent,  the  difficulty  of  joining  new  concrete  to  a  nonabsorbent 
mass  of  old  concrete  is  increased.  This  method  is  effective,  however,  and  is  to 
be  recommended  in  work  which  can  be  carried  on  without  interruption,  such,  for 
instance,  as  small  elevator-pits  or  small  swimming-pools,  where  the  concrete 
can  be  started  in  the  morning  and  completed  by  night  or  before  any  part  of  the 
work  has  had  time  to  attain  its  initial  set. 

FORCE    OF    THE    WIND 

Relation  Between  the  Pressure  and  Velocity  of  Wind.  According  to 
experiments  made  in  1890  or  thereabouts,  by  C.  F.  Marvin,  United  States 
Signal  Service,  the  relation  between  wind-pressure  and  velocity  is  given  very 
accurately  by  the  formula  p  =  0.004  V'-,  where  p  is  the  pressure  in  pounds  per 
square  foot  on  a  flat  surface  normal  to  the  direction  of  the  wind,  and  V  the 
velocity  of  the  wind  in  miles  per  hour.  Smeaton  considered  the  pressure  as 
equal  to  0.005  F^.  The  following  table,  based  on  Marvin's  formula,*  is  quoted 
by  Turneaure  and  Ketchum.f 

*  If  Marvin's  formula  is  written  p  =  0.0032  V^  the  values  in  this  table  will  be  slightly 
changed.  See  Chapter  XXVII,  pages  1052  and  1053;  Chapter  XXX,  page  1199;  and  also 
page  1394.  The  formula  used  by  the  United  States  Signal  Service  is  />  =  0.004  V^-  The 
true  pressure  is  probably  somewhere  between  0.005  V'^  and  0.004  V-,  near  the  former  for 
very  low  velocities  and  near  the  latter  for  high  velocities. 

t  See,  also.  Trautwine's  Pocket-Book,  page  321. 


1718 

Copies  of  Tracings                                  PaiiH 
Table  Showing  the  Force  of  the  Wind                                H 

Miles  per 
hour 

Feet  per 
minute 

Feet  per 
second 

Force,  in 
pounds,  per 
square  foot 

Description 

I 

2 

,      3 
4 
5 

10 

IS 

20 
25 
30     . 

35 

40 
45 
SO 
60 
70 
80 
100 

88 
176 
264 
352 
440 
880 
1  320 

1  760 

2  200 
2  640 
3080 
3520 
3960 
4400 
5280 
6160 
7040 
8800 

1.47 
2.93 
4.40 
5.87 
7.33 
14.67 
22.0 
29-3 
26.6 
44.0 
51.3 
58.6 
66.0 
73.3 
88.0 
102.7 
117. 3 
146.6 

0.004 
0.014  / 
0.036  j 
0.064  ( 
0.1      i 
0.4      ( 
0.9      j 
1.6      / 
2.5      ( 

3.6  j 

4.9   j 

6.4      I 
8.1      ( 

10. 0 

14.4      j 

19.6      ( 

25.6 

40.0      ( 

Hardly  perceptible 
Just  perceptible 

Gentle  breeze 

Pleasant  breeze 

Brisk  gale 

High  wind 

Very  high  wind 
Storm 
Great  storm 

Ilurricane 

COPIES    OF    TRACINGS 

Blue-Prints  from  Tracings.  The  following  directions  *  cover  the  whole 
ground.  The  sensitized  paper  can  be  procured,  all  prepared,  at  stores  where 
artists'  materials  are  sold,  so  that  the  process  of  preparing  the  paper  by  means 
of  chemicals  can  then  be  omitted.     The  materials  required  are  as  follows: 

(i)  A  board  a  Httle  larger  than  the  tracing  to  be  copied.  The  drawing- 
board  on  which  the  drawing  and  tracing  are  made  can  always  be  used. 

(2)  Two  or  three  thicknesses  of  flannel  or  other  soft  white  cloth,  which  is  to 
be  smoothly  tacked  to  the  board  to  form  a  smooth  surface,  on  which  to  lay  the 
sensitized  paper  and  tracing  while  printing. 

(3)  A  plate  of  common  double-thick  window-glass,  of  good  quality,  slightly 
larger  than  the  tracing  to  be  copied.  The  function  of  the  glass  is  to  keep  the 
tracing  and  sensitized  paper  closely  and  smoothly  pressed  together  while 
printing. 

(4)  The  chemicals  for  sensitizing  the  paper.  These  consist  simply  of  equal 
parts,  by  weight,  of  citrate  of  iron  and  ammonia,  and  red  prussiate  of-  potash 
and  can  be  obtained  at  any  drug-store.  The  price  should  not  be  over  8  or 
10  cts  per  ounce  for  each. 

(5)  A  stone  or  yellow-glass  bottle  to  keep  the  solution  of  the  above  chemicals 
in.  If  there  is  but  little  copying  to  do,  an  ordinary  glass  bottle  will  do,  and  the 
solution  can  be  freshly  made  whenever  it  is  wanted  for  immediate  use. 

(6)  A  shallow  earthen  dish  in  which  to  place  the  solution  when  using  it.     A 
*  common  dinner-plate  is  as  good  as  anything  for  this  purpose. 

(7)  A  soft  paste-brush,  about  4  in  wide. 

(8)  Plenty  of  cold  water  in  which  to  wash  the  copies  after  they  have  been 
exposed  to  the  sunlight.  The  outlet  of  an  ordinary  sink  may  be  closed  by 
placing  a  piece  of  paper  over  it  with  a  weight  on  top  to  keep  the  paper  down, 
and  the  sink  filled  with  water,  if  the  sink  is  large  enough  to  lay  the  copy  in. 

*  Taken  from  The  Locomotive. 


Blue-Prints  and  Black-Line  Prints  1719 

If  it  is  not,  it  is  better  to  make  a  water-tight  box  5  or  6  in  deep,  and  6  in  wider 
and  longer  than  the  drawing  to  be  copied. 

(9)  A  good  quality  of  white  book-paper. 

The  following  directions  are  to  be  followed: 

Dissolve  the  chemicals  in  cold  water  in  these  proportions:  i  oz  of  citrate  of 
iron  and  ammonia;  i  oz  of  red  prussiate  of  potash;  and  8  oz  of  water.  They 
may  all  be  put  into  a  bottle  together  and  shaken  up.  Ten  minutes  will  suffice 
to  dissolve  them. 

Lay  a  sheet  qf  the  paper  to  be  sensitized  on  a  smooth  table  or  board,  pour  a 
little  of  the  solution  into  the  earthen  dish  or  plate,  and  apply  a  good  even  coat- 
ling  of  it  to  the  paper  with  the  brush.  Then  tack  the  paper  to  a  board  by  two 
adjacent  corners,  and  set  it  in  a  dark  place  to  dry.  One  hour  is  sufficient  for 
'the  drying.  Place  the  paper,  with  its  sensitized  side  up,  on  the  board  on  which 
ycu  have  smoothly  tacked  the  white  flannel  cloth;  lay  the  tracing  to  be  copied 
on  top  of  it;  on  top  of  all  lay  the  glass  plate,  being  careful  that  paper  and  tracing 
arc  Ijoth  smooth  and  in  perfect  contact  with  each  other,  and  lay  the  whole 
thing  out  in  the  sunlight.  Between  eleven  and  two  o'clock  in  the  summer-time, 
on  a  clear  day,  from  6  to  10  minutes  will  be  sufficiently  long  to  expose  it;  at 
otficr  seasons  a  longer  time  will  be  required.  If  the  location  does  not  admit 
of  direct  sunlight,  the  printing  may  be  done  in  the  shade,  or  even  on  a  cloudy 
day;  but  from  1  to  2y2  hours  will  be  required  for  exposure.  A  httle  experience 
will  soon  enable  any  one  to  judge  of  the  proper  time  for  exposure  on  different 
cia\s.  After  exposure,  place  the  print  in  the  sink  or  trough  of  water  before 
nuMitioned,  and  wash  thoroughly,  letting  it  soak  from  3  to  5  minutes.  Upon 
ininicrsion  in  the  water,  the  drawing,  hardly  visible  before,  will  appear  in  clear 
wltite  lines  on  a  dark-blue  ground.  After  washing,  tack  up  against  the  wall, 
jr  other  convenient  place,  by  the  corners,  to  dry.  This  finishes  the  operation, 
which  is  very  simple  and  thorough.  After  the  copy  is  dry,  it  can  be  written  on 
witli  a  common  pen  and  a  solution  of  common  soda,  which  makes  a  white  line. 

Alternate  Recipe  for  Making  Blue-Prints.  The  following  is  an  alternative 
recipe  to  the  one  given  above.  The  paper  should  be  prepared  by  floating  it 
lor  one  minute  in  a  solution  of  ferricyanide  of  potassium  (red  prussiate  of  potash), 
I  <»z,  and  water,  5  oz.  It  should  then  be  dried  in  a  dark  room,  afterwards  ex- 
)o-td  beneath  the  negative  until  the  dark  shades  have  assumed  a  deep  blue 
oK-r,  and  immersed  in  a  solution  of  water,  2  oz,  and  bichloride  of  mercury,  i  gr. 
Ilu;  print  should  be  washed,  immersed  in  a  hot  solution  of  oxalic  acid,  4  drm, 
md  water,  4  oz,  washed  again  and  dried.  Where  a  copy  of  a  drawing  is  to  be 
iuide  the  prepared  paper  is  placed,  sensitive  side  uppermost,  on  a  flat  board 
a)\  cred  with  two  or  three  thicknesses  of  blanket  or  its  equivalent.  A  tracing 
)f  the  drawing  is  made,  laid  on  the  sensitized  paper  and  held  in  place  by  a  sheet 
'f  ^Mass  clamped  to  the  board.  The  sensitized  paper  is  exposed  to  the  sunlight 
roni  4  to  10  minutes  or  to  a  clear  sky  from  20  to  30  minutes  and  then  removed, 
vashed  and  dried.  The  only  requisite  as  to  paper  is  that  it  must  stand  wash- 
ng.     Prepared  paper  may  be  purchased. 

Black-Line  Copies  from  Tracings.*   The  directions  for  making  the  sensitiz- 

ng  solution  used  in  this  process  are  as  follows:  Dissolve  separately,  gum  arabic, 
3  <h-,  in  17  oz  water;  tartaric  acid,  13  dr,  in  6  oz,6  dr  water;  persulphate  of  iron, 
^  dr,  in  6  oz  6  dr  of  water.  Pour  the  third  solution  into  the  second,  stir  thor- 
'ut^hly,  and  then  pour  the  resulting  mixture  into  the  first,  the  stirring  being 
ontinued.  When  the  mixture  is  complete,  add  slowly,  still  stirring,  3  fl  oz  and 
;  drm  of  liquid  perchloride  of  iron;  filter  into  a  bottle  and  keep  in  the  dark. 
/sc  a  strong  well-sized  paper,  apply  a  thin,  smooth  coat  of  the  solution  with  a 
arL'c  brush  or  sor)nge,  and  then  dry  in  a  dark  room  with  moderate  heat.  The 
*  inhere  is  as  yet  no  known  recipe  resulting  in  jet-black  lines. 


1720  Horse-Power,  Pulleys,  Belting  atid  Shafting  Part  i 

paper  should  be  yellowish  in  tint  and  will  not  keep  long.  Place  the  tracing 
made  with  very  black  ink,  in  the  printing-frame,  the  drawing  being  in  clos( 
contact  with  the  glass,  and  place  over  it  the  sensitized  paper,  with  the  preparec 
side  in  contact  with  the  back  of  the  tracing.  After  an  exposure  of  lo  or  i: 
minutes,  the  print  should  show  a  yellow  drawing  on  a  white  ground.  Taki 
the  print  from  the  frame  and  float  for  a  minute,  face  down,  in  a  developini 
bath  of  gallic  acid,  or  tannin,  from  31  to  46  gr;  oxalic  acid,  iH  gr;  and  water 
34  oz.  Then  plungd  it  in  clear  water,  rinse  well  and  dry.  The  orange-yellov 
lines  will  be  changed  into  a  purplish-black. 

Brown-Line  Copies  from  Tracings.  The  directions  for  making  the  sensitiz 
ing  solution  used  in  thii  process  are  as  follows:  Dissolve  gelatine,  6  gr;  water 
r  oz;  swell  in  cold  water,  give  water-bath  and  add  tartaric  acid,  8  oz;  silve 
nitrate,  9  gr;  and  ammonia  citrate  of  iron,  40  gr.  Filter  in  a  subdued  light 
Print  in  a  bright  light  until  slightly  darker  than  ordinary  printing-out  paper 
wash  for  5  minutes;  immerse  in  a  2V2%  solution  of  Itypo  until  desired  color  ii 
obtained;  and  wash  and  dry.  Blue-prints  may  be  turned  to  a  rich-browr 
color  by  immersing  in  a  solution  of  caustic  soda  the  size  of  a  bean  dissolved  ir 
5  oz  of  water,  until  the  blue  has  changed  to  orange-yellow.  They  are  ther 
washed  thoroughly,  immersed  in  a  bath  of  water  in  which  has  been  dissolvec 
a  heaping  teaspoonful  of  tannic  acid,  rinsed  in  clear  water  and  dried.  Papei 
may  be  sized  for  brown-prints  by  soaking  it  in  a  mixture  of  90  gr  of  arrowrooi 
and  5  oz  of  cold  water,  rubbed  into  a  cream  and  mixed  with  20  gr  of  glucose  anc 
5  oz  of  hot  water.  The  mixture  should  be  boiled  2  minutes  and  then  permittee 
to  cool  before  use. 

HORSE-POWER,*  PULLEYS,   GEARS,  BELTING 
AND    SHAFTING 

Horse-Power.  A  horse  can  travel  400  yd  at  a  walk  in  4!^^  min,  at  a  trot  ir 
2  min,  and  at  a  gallop  in  i  min;  he  occupies  at  a  picket  3  ft  by  9  ft;  and  hi: 
average  weight  is  i  000  lb.  An  average  horse  carrying  225  lb  can  trave 
25  miles  in  a  day  of  8  hr.  A  draught-horse  can  draw  i  600  lb  23  miles  a  day 
weight  of  carriage  included.  In  a  horse-mill  a  horse  moves  at  the  rate  of  3  fl 
in  a  second.     The  diameter  of  the  track  should  not  be  less  than  25  ft. 

A  Horse-Power,  in  Machinery,  is  estimated  at  33  000  lb,  raised  i  ft  in  £ 
minute;  but  as  a  horse  can  exert  that  force  but  6  hr  a  day,  one  machinery 
horse-power  is  equivalent  to  that  of  four  horses. 

Rules  to  Determine  the  Size  and  Speed  of  Pulleys  or  Gears.  The 
driving-pulley  is  called  the  driver,  and  the  driven  pulley  the  driven.  If  the 
number  of  teeth  in  the  gears  are  used  instead  of  the  diameter,  in  these  calcula- 
tions, number  of  teeth  must  be  substituted  wherever  diameter  occurs. 

(i)  To  Find  the  Diameter  of  the  Driver,  the  diameter  of  the  driven  and  its 
revolutions,  and  also  revolutions  of  driver,  being  given.  Multiply  the  diametei 
of  the  driven  by  its  revolutions,  and  divide  the  product  by  the  revolutions  oi 
the  driver;   the  quotient  will  give  the  diameter  of  the  driver. 

(2)  To  Find  the  Diameter  of  the  Driven,  the  revolutions  of  the  driven,  also  the 
diameter  and  revolutions  of  the  driver,  being  given.  Multiply  the  diameter  of 
the  driver  by  its  revolutions,  and  divide  the  product  by.  the  revolutions  of 
the  driven;   the  quotient  will  give  the  diameter  of  the  driven. 

(3)  To  Find  the  Revolutions  of  the  Driver,  the  diameter  and  revolutions  of 
the  driven,  also  the  diameter  of  the  driver,  being  given.     Multiply  the  diametei 

*  See,  also,  pages  1274  and  1397. 


Horse-Power,  Pulleys,  Belting  and  Shafting  1721 

of  the  driven  by  its  revolutions,  and  divide  the  product  by  the  diameter  of  the 
driver;  the  quotient  will  give  the  revolutions  of  the' driver. 

(4)  To  Find  the  Revolutions  of  the  Driven,  the  diameter  and  revolutions  of 
the  driver,  also  the  diameter  of  the  driven,  being  given.  Multiply  the  diameter 
of  the  driver  by  its  revolutions,  and  divide  the  product  by  the  diameter  of  the 
driven;  the  quotient  will  give  the  revolutions  of  the  driven. 

Horse-Power  Transmitted  by  Belting.  The  efficiency  of  belting  to  trans- 
mit power,  or  to  turn  a  wheel  or  pulley,  depends  upon  the  width  and  thickness 
of  the  belt,  the  arc-contact  with  the  pulley,  the  position  of  the  belt,  whether 
horizontal,  vertical,  or  at  an  angle,  and  the  velocity.  The  greater  the  velocity 
and  the  thicker  the  belt,  the  more  power  it  will  transmit.  A  belt  running  ver- 
tically or  inclined  will  transmit  less  power  than  one  running  horizontally,  but 
in  figuring  the  horse-power  capacity  of  belting  only  the  velocity,  width  and 
thickness  of  belt  are  usually  considered,  it  being  assumed  that  the  pulleys  are 
of  proper  size  and  located  so  that  the  belt  will  be  nearly  horizontal.  Belts  are 
commonly  assumed  to  be  of  leather,  unless  otherwise  designated.  The  term 
SINGLE  BELT  is  used  to  designate  a  belt  made  of  a  single  thickness  of  cowhide 
leather.  A  double  belt  is  made  by  cementing  and  riveting  together  two 
thicknesses  of  leather.  There  is  no  standard  thickness  for  either  single  or  double 
belts. 

Rules.  Many  rules  have  been  given  for  determining  the  horse-power  that 
belting  will  transmit.*     Those  commonly  used  are: 

(i)  For  Single  Belts.  Multiply  the  width,  in  inches,  by  the  velocity  in  feet 
per  minute  and  divide  by  i  000. 

(2)  For  Double  Belts.  Multiply  the  width  by  the  velocity  and  divide  by  700. 
The  answer  is  the  number  of  horse-powers. 

Some  authorities  give  divisors  of  800  and  733  for  single  belts,  and  550  and  513 
for  double  belts.  For  the  velocity  of  the  belt  multiply  the  number  of  revolutions 
per  minute  of  either  pulley  by  the  circumference  of  that  pulley. 

Notes  on  Belting.  For  continuous  use  a  double  belt  is  the  most  economical 
in  the  long  run,  except  on  very  small  pulleys  or  for  very  light  duty.  Triplex 
and  quadruple  belts  are  sometimes  used  for  very  heavy  duty,  but  such  belts  are 
not  commonly  carried  in  stock.  Single  belts  should  always  be  used  with  the 
hair-side  next  the  pulley.  The  belt-speed  for  maximum  economy  should  be 
from  4  000  to  4  500  ft  per  minute.  Idler-pulleys  work  most  satisfactorily 
when  located  on  the  slack  side  of  the  belt  about  one-quarter  way  from  the  driv- 
ing-pulley. Belts  are  more  durable  and  work  more  satisfactorily  when  made 
narrow  and  thick  than  when  made  wide  and  thin.  As  belts  increase  in  width 
they  should  also  be  made  thicker.  For  dynamo-work  or  electric  motors  the 
ends  of  the  belt  should  be  fastened  together  by  splicing  and  cementing  instead 
of  by  lacing.  For  all  other  cases  the  ends  are  fastened  by  hooks  or  lacing. 
Belts  should  be  cleaned  and  greased  every  5  to  6  months. 

Distance  from  Center  to  Center  of  Shafts.*  In  locating  shafts  that  are 
to  be  connected  with  each  other  by  belts,  care  should  be  taken  to  separate  them 
by  a  proper  distance.  This  distance  should  be  such  as  to  allow  a  gentle  sag  to 
the  belt  when  in  motion. 

Rule.  A  general  rule  may  be  stated  thus:  Where  narrow  belts  are  to  be  run 
over  small  pulleys,  15  ft  is  a  good  average,  the  belt  having  a  sag  of  from  ili  to 
2  in.  The  minimum  distance  between  shafts  is  about  10  ft.  For  larger  belts, 
working  on  larger  pulleys,  a  distance  of  from  20  to  25  ft  does  well,  with  a  sag 

•  For  a  discussion  of  belting,  belt-dressing,  care  of  belting,  shafting,  etc.,  see  Kent's 
Mechanical  Engineers'  Pocket-Book. 


1722 


Horse-Power,  Pulleys,  Belting  and  Shafting 


Part  3 


of  from  2^^  to  4  in.  For  main  belts,  working  on  very  large  pulleys,  the  distance 
should  be  from  25  to  30  ft,  the  belts  working  well  with  a  sag  of  from  4  to  5  in. 
If  too  great  a  distance  is  attempted,  the  belt  will  have  an  unsteady  flapping 
motion,  which  will  destroy  both  the  belt  and  the  machinery. 

Arrangement  of  Belts  and  Pulleys.*  If  possible  to  avoid  it,  connected 
shafts  should  never  be  placed  one  directly  over  the  other,  as  in  such  case  the 
belt  must  be  kept  very  tight  to  do  the  work.  For  this  purpose  belts  should  be 
carefully  selected  of  well-stretched  leather.  It  is  desirable  that  the  angle  of 
the  belt  with  the  floor  should  not  exceed  45°.  It  is  i^lso  desirable  to  locate  the 
shafting  and  machinery  so  that  belts  will  run  off  from  each  shaft  in  opposite 
directions,  as  this  arrangement  will  relieve  the  bearings  from  the  friction  that 
would  result  if  all  pulled  one  way  on  the  shaft.  If  possible,  machinery  should 
be  so  placed  that  the  direction  of  the  belt-motion  will  be  from  the  top  of  the 
driving  to  the  top  of  the  driven  pulley,  so  that  the  sag  will  increase  the  arc  of 
contact.  The  pulley  should  be  a  little  wider  than  the  belt  required  for  the 
work,  and  should  have  a  crowning  face,  except  where  the  belt  is  to  be  shifted. 
The  motion  of  driving  should  run  with  and  not  against  the  laps  of  the 
belts. 

Rubber  Belts  are  cheaper  than  leather  belts  and  should  always  be  used  in 
wet  places,  but  for  ordinary  use  in  dry  places  they  are  not  as  durable  as  leather 
belts.  They  should  always  be  kept  free  from  grease  or  animal  oils.  If  they  slip, 
their  inside  surfaces  should  be  moistened  with  boiled  linseed-oil.  Some  fine 
chalk,  sprinkled  on  over  the  oil,  will  help  the  belt. 

Rule  for  Finding  the  Lengths  of  Belts.  Add  the  diameter  of  the  two 
pulleys  together,  multiply  by  s^,  divide  the  product  by  2,  add  to  the  quotient 
twice  the  distance  between  the  center  of  the  shafts,  and  the  sum  will  be  the 
required  length. 


The  Horse-Power  that  Shafting  will  Transmit 


Revolutions  per 

minute 

Diameter  01  snait 

100 

ISO 

200 

250 

300 

350 

in 

i6th 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H^ 

0 

15 

1.2 

1.7 

2.4 

3.1 

3.6 

4.3 

sW 

I 

3 

2.4 

3.7 

4.9 

6.1 

7  3 

8.5 

9.7 

I 

7 

4.3 

6.4 

8.S 

10. 5 

12.7 

14.8 

16.9 

I 

II 

6.7 

10. 1 

13.4 

16.7 

20.1 ' 

23.4 

26.8 

I 

15 

10. 0 

iS.o 

20.0 

25.0 

30.0 

35.0 

40.0 

2 

3 

14.3 

21.4 

28.5 

35.6 

42.7 

49.8 

57.0 

2 

7 

19s 

293 

39.0 

48.7 

58. s 

68.2 

78.0 

2 

II 

26.0 

39- 0 

S2.0 

65.0 

78.0 

87.0 

104.0 

2 

IS 

33.8 

SO. 6 

67. S 

84.4 

101.3 

118. 2 

135.0 

3 

3 

43.0 

64.4 

85.8 

107.3 

128.7 

150.3 

171. 6 

3 

7 

53.6 

79-4 

107.2 

134.0 

1.S8.8 

187.6 

214.4 

3 

II 

6S.9 

97.9 

121. 8 

164.8 

19s.  7 

230.7 

243-6 

3 

IS 

80.0 

120.0 

160.0 

200.0 

240.0 

280.0 

320.0 

4 

7 

113. 9 

170.8 

227.8 

284.7 

341.7 

398.6 

455.6 

4 

IS 

IS6.3 

234.4 

312.5 

390.6 

468.7 

546.8 

625.0 

*  See  Keat's  Mechanical  Engineers'  Pocket-Book.. 


Chain-Blocks,  Hoists,  Hooks,  Etc. 
CHALN-BLOCKS,  HOISTS,  HOOKS,  ETC. 


1723 


General  Description.  These  are  portable  hoisting-devices  which  enable  one 
man  to  raise  a  very  heavy  load  and  which  sustain  the  load  at  any  point.  In 
general,  they  resemble  pulleys  operated  by  chains.  Since  the  invention  of  the 
differential  pulley-block  by  T.  A.  Weston,  about  the  year  1863,  chain-blocks 
have  come  into  very  general  use  for  economical  hoisting,  particularly  where  it  is 
desired  to  hold  the  load  at  any  point.     Chain-blocks  are  of  three  general  classes: 

(i)  The  Differential  Block.  This  Is  the  original  and  the  simplest  and  cheap- 
est form  of  self-sustaining  pulley; 

(2)  The  Screw-Block  or  Worm-Geared  Block.  Of  these,  the  Yale  &  Towne 
duplex  block  is  the  most  efficient  type; 

(3)  The  Triplex  Block.     This  is  spur-geared. 

Differential  and  worm-geared  blocks  of  all  kinds  depend  upon  friction  to  pre- 
vent the  load  from  running  down.  In  the  triplex  block  a  separate  device  is 
introduced  which  automatically  holds  the  load  safely,  and  yet  enables  it  to  be 
lowered  with  slight  effort  and  at  high  velocity  but  without  acceleration  or  danger. 
This  is  the  most  efficient  of  all  chain-blocks,  and  the  most  economical  wherever 
quick  work  is  wanted  and  economy  in  time  and  labor  sought.  For  information 
as  to  the  kind  of  block  best  adapted  to  any  particular  service,  the  manufacturers 
should  be  consulted.  The  following  data  on  the  power  and  efficiency  of  chain- 
blocks  were  supplied  by  the  Yale  &  Towne  Manufacturing  Company. 

Power  and  Efficiency  of  Chain-Hoists.  The  table  below  gives  the  work 
to  be  done  by  the  operator  at  the  hand-puUing  chain  with  each  size  of  the  various 
kinds  of  chain-blocks  in  lifting  the  stated  capacity,  that  is,  the  amount  of  work 
or  pulling  required  to  hft  this  load  one  foot  by  stating  the  force  exerted  in 
pounds  and  the  distance  in  feet  of  operating-chains  to  be  pulled.  The  product 
of  these  two  factors  determines  the  efficiency  of  the  block  and  the  ease  and  speed 
of  hoisting.  The  12,  16,  and  20-ton-capacity  chain-blocks  have  each  two  hand- 
chains. 

Work  Done  by  Operator  with  Chain-Blocks 


Capacity , 
tons 

Triplex 

spur-geared, 

lb      ft 

Duplex 

worm-geared, 

lb      ft 

Differential 
lb     ft 

Yz 

I 

2 
3 

4 

5 

6 

8 
10 
12 
16 
20 

62  X  21 
82  X  31 
iicX  35 
120X  42 
114X  69 
124 X  84 
1 10X126 
130X126 
135X168 
140X210 
130X126 
135X168 
140X210 

68  X  40 
87  X  59 
94X  80 
115X  93 
132X126 
142X155 
145X195 
145X252 
160X310 
160X390 

122X24 
216X30 
246X36 
308X42 
557X38 



The  capacities  are  given  in  tons.  The  figures  give  the  number  of  feet  to 
be  operated  on  each  hand-chain.  A  man  cannot  pull  more  than  his  own 
weight  on  the  operating  chains,  and  can  pull  faster  in  proportion  as  the  pull 
required  is  lighter.  The  maximum  pull  usually  required  of  one  man  is  82  lb, 
and  he  will  do  more  work  with  less  fatigue  if  the  hand-chain  pull  is  not  over 


1724 


Chain-Blocks,  Hoists  and  Hooks 


Part  3 


40  lb,  because  he  can  then  pull  the  chain  hand  over  hand  a  little  more  than  twice 
as  fast  as  he  could  when  pulling  twice  as  hard.  When  the  hand-chain  pull  is 
less  than  20  lb  the  speed  of  hoisting  an  equal  load  is  diminished,  because  the  man 
is  tired  by  moving  his  arms  too  rapidly,  and  cannot  do  as  much  work  as  with  a 
heavier  pull.  The  best  result  is  obtained  by  using  a  chain-block  which  has 
a  capacity  of  double  the  usual  load.  The  operator  then  wjrks  to  the  best  ad- 
vantage with  average  loads,  and  occasional  heavy  loads  are  easily  har.dled  with- 
out overstraining  either  the  operator  or  the  chain-block,  which  shoukl  never  be' 

used  beyond  its  capacity  for  fcir  of  stretch- 
ing the  chain  so  that  it  will  not  work 
smoothly. 

Proportions  of  Hooks.*  For  economy 
of  manufacture  hooks  of  different  sizes  are 
made  from  some  regular  commercial  sizes 
of  round  iron.  The  basis,  or  ini  ial  point,' 
in  each  case  is,  therefore,  the  size  of  the 
iron  of  which  the  hook  is  t^  be  mcde,  and 
it  is  indicated  by  the  dimension  A  in  the 
diagram.  The  dimension  D  is  arbitrarily 
assumed.  The  other  dimensions,  as  given 
by  the  formulas,  are  those  which,  while 
preserving  a  proper  bearing  face  on  the 
interior  of  the  hook  for  the  ropes  or  chains 
which  may  be  passed  througli  it,  -give  the 
•  greatest    resistance    to    spreading    and    to 

ultimate  rupture  which  the  amount  of 
material  in  the  original  bar  admits  of.  The  symbol  A  is  used  in  the  formukus 
to  indicate  the  nominal  capacity  of  the  hook  in  tons  of  2  000  lb.  The  formulas 
which  determine  the  lines  of  the  other  parts  of  the  hooks  of  the  several  sizes  are 
as  follows,  all  the  measurements  being  expressed  in  inches: 


Z)  =  o.5A    fi.25 
E  =  0.64  A-f  1.60 
F  =  0.33  A +  0.85 
H=  1.08  A 
I  =  1.33^ 
J  =  1.20^ 
K  =1.13  A 


O  =  0.3.63  A  +  0.66 
Q  =  0.64  A+  i-6o 
L=  1.0s  A 
M  =  0.50^4 
iV  =  0.85  5 -0.16 
U  =  0.866  A 


Example.     To  find  the  dimension  D,  for  a  2-ton  hook.     The  formula  is: 
Z?  =  o.5  A+  1.25 

and  as  A  =  2,  the  dimension  D  by  the  formula  is  found  to  be  2K1  in.  The  dimen- 
sions A,  are  necessarily  based  upon  the  ordinary  merchant  sizes  of  round  iron. 
The  sizes  which  it  has  been  found  best  to  select  are  the  following: 

Capacities  of  hooks  \i    H     Hi        i^/i  3      2      45      6      8  10    tons 

Dimensional Ys  ^He  %  iHe   iH  iH  iH  2  2]-!   214  2^i       3M  inches 

The  formulas  which  give  the  sections  of  the  hook  at  the  several  points  are 
all  expressed  in  terms  of  A,  and  can  therefore  be  readily  ascertained  by  refer- 
ence to  the  foregoing  scale. 

*  By  Henry  R.  Towne,  in  his  Treatise  on  Cranes,  which  includes  the  results  of  an  ex- 
tensive exnf  n'mpnfnl  nnri  maihemntirnl  invesflpntmn. 


Bells 


1725 


iBxainple.    To  find  the  dimension  /,  in  a  2-(on  hook.    The  formula  is 

and  for  a  2-tqn  hook,  A  =  i%  in.     Therefore  /,  in  a  2-lon  hook,  is  found  to  be 
ii'Mfi  in. 

Manner  of  Failure  of  Hooks.  Experiment  has  shown  that  hooks  made 
according  to  the  above  formulas  will  give  way  first  by  the  opening  of  the  jaw, 
which,  hov/ever,  will  not  occur  except  with  a  load  much  in  excess  of  the  nominal 
capacity  of  the  hook.  This  yielding  of  the  hook  when  overloaded  becomes  a 
source  of  safety,  as  it  constitutes  a  signal  of  danger  which  cannot  easily  be  over- 
looked, and  which  must  proceed  to  a  considerable  length  before  rupture  occurs 
and  the  load  is  droi)ped.  A  comparison  of  these  hooks  with  most  of  those  in 
ordinary  use  shows  that  the  latter  are,  as  a  rule,  badly  proportioned,  and  fre- 
quently dangerously  weak. 

BELLS 

Dimensions  and  Weights  of  Church-Bells 

Manufactured  by  Meneely  Bell  Company,  Troy,  N.  Y. 


Bells 

Mountings 

Weights. 

Medium 
tones 

Diameters, 

Sizes  of  frames, 
outside, 

Diameters  of 
wheels. 

lb 

in 

in 

ft        in 

400 

D 

27 

42X42 

4        4 

450 

CJ 

28 

42X42 

4        4 

500 

c  . 

29 

45X47 

4        4 

550 

c 

30 

45X47 

4        4 

600 

B 

31 

45X47 

4        9 

700 

B 

33 

48X48 

5        6 

800 

Bb 

34 

48X54 

5        6 

.900. 

A 

36 

54X54 

5        9 

I  000 

A 

37 

54X54 

5        9 

I  100 

A 

38 

54X59 

5        9 

I  200 

Ab 

39 

56X59 

6        3 

I  300 

Ab 

40 

56X59 

^     i 

I  400 

G 

41 

60X60 

6     6        •; 

I  500 

G 

42 

60X60 

6        6 

I  600 

G 

43 

60X60 

6        6 

I  800 

FJ 

45 

65X68 

7 

2  000 

F 

46 

65X68 

7 

2  100 

F 

47 

65X68 

7 

2300 

E 

49 

70X72 

7        6 

2500 

E 

50 

70X72 

7        6 

2800 

Eb 

51 

74X78 

8 

3  000 

Eb 

53 

74X78 

8 

3  500 

D 

56 

74X78 

8        6 

4  000 

cj      •• 

58 

78X81 

'          ^                     i 

4500 

c 

61 

•      78X81 

9                     1 

5000 

c 

63 

84X84 

9                    i 

'            5  500 

B 

65 

84X84 

9 

6000 

Bb 

67 

84X84 

9        6 

6  500 

Bb 

68 

90X90 

9        6 

7  000* 

Bb 

69 

101X90 

9        6 

*  A  notable  example  of  a  7  000-Ib  bell  is  the  large  bell  of  the  peal  in  the  tower  of  the 
Metropolitan  Life  Insurance  Building,  in  New  York. 
The  actual  weights  usually  exceed  the  patterns,  noted  above,  from  2  to  3%  • 


1726 


Bells 


Meneely  School-Bells 


Bells 

Mountings 

Weights, 

Diameters, 

Sizes  of  frames, 
outside, 

lb 

in 

ft  in         ft  in 

100 

17 

26X28 

125 

iSVz 

26X28 

150 

19K2 

26X28 

200 

21  Ki 

28X30 

250 

23 

30X32 

300 

24H 

30X34 

350 

26 

30X34 

Sizes  of  Rope  for  Bells 

Diameter,  in 

For  hells  of  less  than  500  lb i/i 

For  bells  of  500  to  800  lb % 

For  bells  of  800  to  i  800  lb , •>4 

For  bells  above  i  800  lb ^i  to  i 

The  Largest  Bells  in  the  World  * 


Actual 

Diam- 

Sound-bow 

Names  and  locations 

Date 

vibra- 

Key- 

eter, 

Weight. 

of  bells 

cast 

note 

lb 

tion 

in 

Inches 

Stroke 

Moscow,  T7.ar  Kolokol  f- 

1733 

74 

D 

272 

23 

0.84 

443  772 

Burmah,   Mingoon 

94 

Ft 

203? 

16? 

0.80 

201  600 

Moscow,  St.  Ivan's 

1819 

105 

Gi 

185 

14.75 

0.80 

127  350 

Pekin,  Great  Bell 

156 

120  000 

Burmah,  Maha  Ganda. . 

125 

B 

155 

12. 5 

0.80 

95000 

Nishni  Novgorod.  ...:.. 

125 

B 

151 

12 

0.80 

69664 

Moscow,  Church  of  Re- 

deemer  

1879 

141 

ct 

136.3? 

10.6 

0.80 

60  736 

Nankin,  China 

112 

45000 

London,  St.  Paul's 

1881 

157 

Ej 

114.25 

8.75 

0.76 

42000 

Olmutz,  Bohemia 

157 

E(7 

121 

9.125 

0.75 

40320 

Vienna,  Austria 

1711 

157 

Eb 

118 

9.5 

0.80 

40  200 

Westminster,  London — 

1856 

166 

E 

113. 5 

9-375 

0.83 

35620 

Erfurt,  Saxony   

1487 

176 

F 

103.6 

g.75 

0  75 

30  800 

Notre  Dame,  Paris 

1680 

166 

E 

103 

7.5 

0.73 

28670 

Montreal,  Canada 

1847 

176 

P 

103 

7.8 

0.76 

28560 

York,  England 

1845 

187 

n 

100 

8 

0.80 

24  080 

St.  Peter's,  Rome 

1786 

187 

Fit 

97.25 

7-5 

0.77 

18  000 

Great  Tom,  Oxford 

1680 

210 

Git 

84. 

6.125 

0.73 

17  024 

Cologne,  Germany 

1477 

.   198 

G 

95 

7.2 

0.75 

16  016 

Brussels,  Belgium 

210 

Git 

95.81 

7.75 

0.71 

15848 

State-house,  Philadelphia 

i87S 

198 

G 

88 

6.375 

0.73 

13  000 

Lincoln,  England 

1834 

210 

Git 

82.85 

6 

0.73 

12096 

St.  Paul's,  London 

1716 

222 

A 

81 

6.08 

0.75 

II  500 

Exeter  England 

1675 

210 

Git 

76 

5 

0  66 

10  080 

Old  Lincoln,  England. . . 

1610 

249 

B 

75. 5 

5.94 

0.78 

9  856 

Westminster^  London.... 

i8S7 

249 

B 

72 

5.75 

0.79 

8960   ^ 

*  John  W.  Nystrom,  in  the  Journal  of  the  Franklin  Institute,  Philadelphia. 
t  This  bell  is  fractured  and  has  not  been  rung  for  many  years. 


Circular  of  Advice  on  Professional  Practice  1727 

SYMBOLS  FOR  THE  APOSTLES  AND  SAINTS 

From  the  constant  occurrence  of  symbols  in  the  edifices  of  the  Middle  Ages 
and  many  of  the  cathedrals  of  the  present  day,  the  following  list  of  symbols,  as 
commonly  attached  to  the  apostles  and  saints,  may  be  found  useful: 

Holy  Apostles 

St.  Peter.     Bears  a  key,  or  two  keys  with  different  wards. 

St.  Andrew.    Leans  on  a  cross  so  called  from  him;  called  by  heralds  the  saltire. 

St.  John  the  Evangelist.     With  a  chalice,  in  which  is  a  winged  serpent.     When 

this  symbol  is  used,  the  eagle,  another  symbol  of  him,  is  never  given. 
St.  Bartholomew.     With  a  flaying-knife. 

St.  James  the  Less.     A  fuller's  staff  bearing  a  small  square  banner.    ■ 
St.  James  the  Greater.     A  pilgrim's  staff,  hat  and  escalop-shell. 
St.  Thomas.     An  arrow,  or  with  a  long  staff. 
St.  Simon.     A  long  saw. 
St.  Jude.     A  club. 
St.  Matthias.     A  hatchet. 

St.  Philip.    Leans  on  a  spear  or  has  a  long  cross  in  the  shape  of  a  T. 
St.  Matthew.     A  knife  or  dagger. 
St.  Mark.     A  winged  lion. 
St.  Luke.    A  bull. 
St.  John.     An  eagle. 

St.  Paul.     An  elevated  sword,  or  two  swords  in  saltire. 
St.  John  the  Baptist.     An  Agnus  Dei. 
St.  Stephen.     With  stones  in  his  lap. 

Saints 

St.  Agnes.     A  lamb  at  her  feet. 

St.  Cecilia.     With  an  organ. 

St.  Clement.     With  an  anchor. 

St.  David.     Preaching  on  a  hill. 

St.  Denis.     With  his  head  in  his  hands. 

St.  George.     With  the  dragon. 

St.  Nicholas.     With  three  naked  children  in  a  tub,  in  the  end  whereof  rests  his 

pastoral  staff. 
St.  Vincent.     On  the  rack. 

CIRCULAR  OF  ADVICE  RELATIVE  TO  PRINCIPLES 
OF    PROFESSIONAL  PRACTICE  AND   THE 
CANONS  OF  ETHICS,  BY  THE  AMERI- 
CAN INSTITUTE  OF  ARCHITECTS  * 

■    A  Circular  of  Advice 

Introductory.  The  American  Institute  of  Architects,  seeking  to  maintain  a 
high  standard  of  practice  and  conduct  on  the  part  of  its  members  as  a  safeguard 
of  the  important  financial,  technical  and  esthetic  interests  entrusted  to  them, 
offers  the  following  advice  relative  to  professional  practice:  The  profession  of 
architecture  calls  for  men  of  the  highest  integrity,  business  capacity  and  artistic 

*The  American  Institute  of  Architects,  Document  No.  141,  Washington,  D.  C, 
April  29,  1919.  Reprinted  by  permission.  This  circular  relates  to  the  principles  of 
professional  practice  and  the  canons  of  ethics. 


1728  Circular  of  Advice  on  Professional  Practice  Part  3 

ability.  The  architect  is  entrusted  with  financial  undertakings  in  which  his 
honesty  of  purpose  must  be  above  suspicion;  he  acts  as  professional  adviser  to 
his  client  and  his  advice  must  be  absolutely  disinterested;  he  is  charged  with 
the  exerdse  of  judicial  functions  as  between  client  and  contractors  and  must 
act  with  entire  impartiahty;  he  has  moral  responsibilities  to  his  professionil 
associates  and  sabordinates;  finally,  he  is  .engaged  in  a  profession  which  carries 
with  it  grave  responsibility  to  the  public.  These  duties  and  responsibilities 
cannot  be  properly  discharged  unless  his  motives,  conduct  and  ability  are  sujh 
as  to  command  respect  and  confidence.  No  set  of  rules  can  be  framed  which 
will  particularize  all  the  duties  of  th2  architect  in  his  various  relations  to  his 
clients,  to  contractors,  to  his  professional  brethren,  and  to  the  public.  The 
following  principles  should,  however,  govern  the  conduct  of  members  of  the  pro- 
fession and  should  serve  as  a  guide  in  circumstances  other  than  those  enumer- 
ated: 

(i)  On  the  Architect's  Status.  The  architect's  relation  to  his  client  is 
primarily  that  of  professional  adviser;  this  relation  continues  throughout 
the  entire  course  of  his  service.  When,  however,  a  contract  has  been  executed 
between  his  client  and  a  contractor  by  the  terms  of  which  the  architect  becomes 
the  official  Interpreter  of  its  conditions  and  the  judge  of  its  performance,  an 
additional  relation  is  created  under  which  it  is  incumbent  upon  the  arcliitect 
to  side  neither  with  client  nor  contractor,  but  to  use  his  powers  under  the  con- 
tract to  enforce  its  faithful  performance  by  both  parties.  The  fact  that  the 
architect's  payment  com^s  from  tha  client  does  not  invalidate  his  obligation  to 
act  with  impartiahty  to  both  parties. 

(2)  On  Preliminary  Drawings  and  Estimates.  The  architect  at  the  out- 
set should  impress  upon  the  client  the  importance  of  su'iicient  time  for  the 
preparation  of  drawings  and  sp3cifications.  It  is  the  duty  of  the  architect  to 
make  or  secure  preliminary  estimates  when  requested,  but  he  should  acquaint 
the  client  with  their  conditional  character  and  inform  him.  that  complete  and 
final  figures  can  be  had  only  from  complete  and  final  drawings  and  specifications. 
If  an  unconditional  limit  of  cost  be  imposed  before  such  drawings  arc  m;ide  and 
estimated,  the  architect  must  be  free  to  make  such  adjustments  as  seem  to  him 
necessary.  Since  the  architect  should  assume  no  responsibility  that  may  pre- 
vent him  from  giving  his  client  disinterested  advice,  he  should  not,  by  bond  or 
otherwise,  guarantee  any  estimate  or  contract. 

(3)  On  Superintendence  and  Expert  Services.  On  all  work  except  the 
simplest,  It  is  to  the  interest  of  the  owner  to  employ  a  superintendent  or  clerk 
OF  THE  WORKS.  In  many  engkieering  problems  and  in  certain  specialized  esthetic 
problems,  it  is  to  his  interest  to  have  the  services  of  special  experts  and  the 
architect  should  so  inform  him.  The  experience  and  special  knowledge  of  the 
architect  make  it  to  the  advantage  of  the  owner  that  these  persons,  although 
paid  by  the  owner,  should  be  selected  by  the  architect  under  whose  direction  they 
are  to  work.  . 

(4)  On  the  Architect's  Charges.  The  Schedule  of  Charges  of  the 
American  Institute  of  Architects  is  recognized  as  a  proper  minimum  of  payment. 
The  locality  or  the  nature  of  the  work,  the  quality  of  services  to  be  rendered, 
the  skill  of  the  practitioner  or  other  circumstances  frequently  justify  a  higher 
charge  than  that  indicated  by  the  schedule. 

(5)  On  Payment  for  Expert  Service.  The  architect  when  retained  as  an 
EXPERT,  whether  in  connection  with  competitions  or  otherwise,  should  receive 
a  compensation  proportionate  to  the  responsibUity  and  difficulty  of  the  service. 
Nq  duty  of  the  arcliitect  is  more  exacting  than  such  service,  and  the  honor  of 


Circular  of  Advice  on  Professional  Practice  1729 

the  profession  is  involved  in  it.,    Under  no  circumstances  should  experts  know- 
ingly name  prices  in  competition  with  each  other. 

(6)  On  Selection  of  Bidders  or  Contractors.  The  architect  should  advise 
the  client  in  the  selection  of  bidders  and  in  the  award  of  the  contract.  In 
advising  that  none  but  trustworthy  bidders  be  invited  and  that  the  award  be 
made  only  to  contractors  who  are  rehable  and  competent,  the  architect  protects 
the  interests  of  his  client. . 

(7)  On  Duties  to  the  Contractor.  As  the  architect  decides  whether  or 
not  the  intent  of  his  plans  and  specifications  is  properly  carried  out,  he  should 
take  special  care  to  see  that  these  drawings  and  specifications  are  complete  and 
accurate,  and  he  should  never  call  upon  the  contractor  to  make  good  oversights 
or  errors  in  them  nor  attempt  to  shirk  responsibility  by  indefinite  clauses  in  the 
contract  or  specifications. 

(8)  On  Engaging  in  the  Building  Trades.  The  architect  should  not  directly 
or  indirectly  engage  in  any  of  the  building  trades.  If  he  has  any  financial 
interest  in  an}^  building  material  or  device,  he  should  not  specify  or  use  it  without 
the  knowledge  and  approval  of  his  chent. 

(9)  On  Accepting  Commissions  or  Favors.  The  architect  should  not 
receive  any  commission  or  any  su])stantial  service  from  a  contractor  or  from 
any  interested  person  other  than  his  client. 

(10)  On  Encouraging  Good  Workmanship.  The  large  powers  with  which 
the  architect  is  invested  should  be  used  with  judgment.  While  he  must  con- 
demn bad  work,  he  should  commend  good  work.  Intelligent  initiative  on  the 
part  of  craftsnen  and  workmen  should  be  recognized  and  encouraged  and  the 
architect  should  make  evident  his  appreciation  of  the  dignity  of  the  artisan's 
fltnction. 

(11)  On  Offering  Services  Gratuitously.  The  seeking  out  of  a  possible 
client  and  the  offering  to  him  of  professional  services  on  approval  and  without 
compensation,  unless  warranted  by  personal  or  previous  business  relations, 
t-cnds  to  lower  the  dignity  and  standing  of  the  profession  and  is  to  be  condemned. 

(i?)  On  Advertising.  PubUcity  of  the  standards,  aims  and  progress  of  the 
profession,  both  in  general  and  as  exemphfied  by  individual  achievement,  is 
ei^sential.  Advertising  of  the  individual,  meaning  self-laudatory  publicity 
procured  by  the  person  advertised  or  with  his  consent,  tends  to  defeat  its  own 
ends  as  to  the  individual  as  well  as  to  lower  the  dignity  of  the  profession,  and  is 
to  be  deplored. 

(13)  On  Signing  Buildings  and  Use  of  Titles.  The  unobtrusive  signature 
OF  BUILDINGS  after  completion  is  desirable.  The  placing  of  the  architect's 
NA\rE  ON  A  building  DURING  CONSTRUCTION  serves  a  legitimate  purpose  for 
public  information,  but  it  is  to  be  deplored  if  done  obtrusively  for  individual 
publicity.  The  use  of  initials  designating  membership  in  the  Institute  is 
desirable  in  all  professional  relationships,  in  order  to  promote  a  general  under- 
standing of  the  Institute  and  its  standards  through  a  knowledge  of  its  members 
and  their  professional  activities.  Upon  the  members  devolves  the  responsibility 
to  associate  the  symbols  of  the  Institute  with  acts  representative  of  the  highest 
standards  of  professional  practice. 

fi4^  On  Competitions.  An  architect  should  not  take  part  in  a  competition 
as  a  compf.titor  or  juror  unless  the  competition  is  to  be  conducted  according 
to  the  !)est  practice  and  usage  of  the  profession,  as  evidenced  by  its  havmg 
received  the  approval  of  the  Institute,  nor  should  he  continue  to  act  as  pro- 
fession \l  a-dviser  after  it  has  been  determined  that  the  program  cannot  be  so 


X730  The  Canons  of  Ethics  Part  3 

drawn  as  to  receive  such  approval.  When  an  architect  has  been  authorized  to 
submit  sketches  for  a  given  project,  no  other  architect  should  submit  sketches 
for  it  until  the  owner  has  taken  definite  action  on  the  first  sketches,  since,  as 
far  as  the  second  architect  is  concerned,  a  competition  is  thus  established. 
Except  as  an  authorized  competitor,  an  architect  may  not  attempt  to  secure 
work  for  which  a  competition  has  been  instituted.  He  may  not  attempt  to 
influence  the  award  in  a  competition  in  which  he  has  submitted  drawings.  He 
may  not  accept  the  commission  to  do  the  work  for  which  a  comf>etition  has  been 
instituted  if  he  has  acted  in  an  advisory  capacity  either  in  drawing  the  program 
or  in  making  the  award. 

(15)  On  Injuring  Others.  An  architect  should  not  falsely  or  maliciously 
injure,  directly  or  indirectly,  the  professional  reputation,  prospects  or  business 
of  a  fellow  architect. 

(16)  On  Undertaking  the  Work  of  Others.  An  architect  should  not  under- 
take a  commission  while  the  claim  for  compensation  or  damages  or  both,  of 
an  architect  previously  employed  and  whose  employment  has  been  terminated 
remains  unsatisfied,  unless  such  claim  has  been  referred  to  arbitration  or  issue 
has  been  joined  at  law;  or  unless  the  architect  previously  employed  neglects 
to  press  his  claim  legally;  nor  should  he  attempt  to  supplant  a  fellow  architect 
after  definite  steps  have  been  taken  toward  his  employment. 

(17)  On  Duties  to  Students  and  Draughtsmen.  The  architect  should 
advise  and  assist  those  who  intend  making  architecture  their  career.  If  the 
beginner  must  get  his  training  solely  in  the  office  of  an  architect,  the  latter  should 
assist  him  to  the  best  of  his  ability  by  instruction  and  advice.  An  architect 
should  urge  his  draughtsmen  to  avail  themselves  of  educational  opportunities. 
He  should,  as  far  as  practicable,  give  encouragement  to  all  worthy  agencies  and 
institutions  for  architectural  education.  While  a  thorough  technical  prepar- 
ation is  essential  for  the  practice  of  architecture,  architects  cannot  too  strongly 
insist  that  it  should  rest  upon  a  broad  foundation  of  general  culture. 

(18)  On  Duties  to  the  Public  and  to  Building  Authorities.  An  archi- 
tect should  be  mindful  of  the  pubHc  welfare  and  should  participate  in  those 
movements  for  public  betterment  in  which  his  special  training  and  experience 
quality  him  to  act.  He  should  not,  even  under  his  client's  instructions,  engage 
in  or  encourage  any  practices  contrary  to  law  or  hostile  to  the  pubUc  interest; 
fo*-  as  he  is  not  obliged  to  accept  a  given  piece  of  work,  he  cannot,  by  urging  that 
he  has  but  followed  his  client's  instructions,  escape  the  condemnation  attaching 
to  his  acts.  An  architect  should  support  all  public  officials  who  have  charge 
of  building  in  the  rightful  performance  of  their  legal  duties.  He  should  care- 
fully comply  with  all  l^uilding  laws  and  regulations,  and  if  any  such  appear  to 
him  unwise  or  unfair,  he  should  endeavor  to  have  them  altered. 

(19)  On  Professional  Qualifications.  The  public  has  the  right  to  expect 
that  he  who  bears  the  title  of  architect  has  the  knowledge  and  abiUty  needed 
for  the  proper  invention,  illustration  and  supervision  of  all  building  operations 
which  he  may  undertake.  Such  quaUfications  alone  justify  the  assumption  of 
the  title  of  architect. 

The  Canons  of  Ethics  * 

The  following  Canons  are  Adopted  by  The  American  Institute  of 
Architects  as  a  general  guide,  yet  the  enumeration  of  particular  duties  should 

*  Adopted,  December  14-16,  1909.  Revised,  December  10-12,  191 2.  Revised,  April 
2«,  1918. 


Circular  of  Advice  on  Professional  Practice  1731 

not  be  construed  as  a  denial  of  the  existence  of  others  equally  important  although 
not  specially  mentioned.  It  should  also  be  noted  that  the  several  sections 
indicate  offenses  of  greatly  varying  degrees  of  gravity.  It  is  unprofessional  for 
an  architect 

(i)  To  engage  directly  or  indirectly  in  any  of  the  building  or  decorative  trades. 

(2)  To  guarantee  an  estimate  or  contract  by  bond  or  otherwise. 

(3)  To  accept  any  commission  or  substantial  service  from  a  contractor  or 
from  any  interested  party  other  than  the  owner. 

(4)  To  take  part  in  any  competition  which  has  not  received  the  approval  of 
the  Institute  or  to  continue  to  act  as  professional  adviser  after  it  has  been  de- 
termined that  the  program  cannot  be  so  drawn  as  to  receive  such  approval. 

(s)  To  attempt  in  any  way,  except  as  a  duly  authorized  competitor,  to 
secure  work  for  which  a  competition  is  in  progress. 

(6)  To  attempt  to  influence,  either  directly  or  indirectly,  the  award  of  a  com- 
petition in  which  he  is  a  competitor. 

(7)  To  accept  the  commission  to  do  the  work  for  which  a  competition  has  been 
instituted  if  he  has  acted  in  an  advisory  capacity,  either  in  drawing  the  pro- 
gram or  in  making  the  award. 

(8)  To  injure  falsely  or  maliciously,  directly  or  indirectly,  the  professional 
reputation,  prospects,  or  business  of  a  fellow  architect. 

(9)  To  undertake  a  commission  while  the  claim  for  compensation,  or  damages, 
or  both,  of  an  arcliitect  previously  employed  and  whose  employment  has  been 
terminated  remains  unsatisfied,  until  such  claim  has  been  referred  to  arbitration 
or  issue  has  been  joined  at  law,  or  unless  the  architect  previously  employed 
neglects  to  press  his  claim  legally. 

(10)  To  attempt  to  supplant  a  fellow  architect  after  definite  steps  have  been 
taken  toward  his  employment,  that  is,  by  submitting  sketches  for  a  project  for 
which  another  architect  has  been  authorized  to  submit  sketches. 

(ii)  To  compete  knowingly  with  a  fellow  architect  for  employment  on  the 
basis  of  professional  charges. 

Professional  Practice  of  Architects.     Details  of  Service  to  be  Rendered 
and  Schedule  of  Proper  Minimum  Charges  * 

(i)  The  architect's  professional  services  consist  of  the  necessary  conferences, 
the  preparation  of  preliminary  studies,  working  drawings,  specifications,  large- 
scale  and  full-size  detail  drawings;  the  drafting  of  forms  of  proposals  and 
contracts;  the  issuance  of  certificates  of  payment;  the  keeping  of  accounts,  the 
general  administration  of  the  business  and  supervision  of  the  work,  for  which, 
except  as  hereinafter  mentioned,  the  minimum  charge,  based  upon  the  total 
cost  of  the  work  t  complete,  is  6  per  cent. 

(2)  On  residential  work,  alterations  to  existing  buildings,  monuments,  furni- 
ture, decorative  and  cabinetwork  and  landscape-architecture,  it  is  proper  to 
make  a  higher  charge  than  above  indicated. 

*As  adopted  at  the  Washington,  D.  C,  Convention,  December  15-17,  1908,  and 
as  revised  in  form  at  the  Minneapolis  convention,  December  6-8,  1916. 

t  The  words  "the  cost  of  the  work,"  as  used  in  Articles  (i)  and  (9)  hereof,  are  ordinarily 
to  be  interpreted  as  meaning  the  total  of  the  contract-sums  incurred  for  the  execution  of 
the  work,  not  including  architect's  and  engineer's  fees  or  the  salary  of  the  clerk  of  the 
works,  but  in  certain  rare  cases,  that  is,  when  labor  or  material  is  furnished  by  the  owner 
below' its  market  cost  or  when  old  materials  are  reused,  the  cost  of  the  work  is  to  be 
interpreted  as  the  cost  of  all  materials  and  labor  necessary  to  complete  the  work,  as 
such  cost  would  have  been  if  all  materials  had  been  new  and  if  all  labor  had  been  fully 
paid  at  market  prices  current  when  the  work  was  ordered,  plus  contractor's  profits  and 
exuensps 


1732  Schedule  of  Charges  Part  3 

(3)  The  architect  is  entitled  to  compensation  for  articles  purchased  under 
his  direction,  even  though  not  designed  by  him. 

(4)  Where  the  architect  is  not  otherwise  retained,  consultation-fees  for  pro- 
fessional advice  are  to  be  paid  in  proportion  to  the  importance  of  the  question 
involved  and  services  rendered. 

(5)  The  architect  is  to  be  reimbursed  for  the  costs  of  transportation  and 
living  incurred  by  him  and  his  assistants  while  traveling  in  discharge  of  duties 
connected  with  the  work,  and  the  costs  of  the  services  of  heating,  ventilating, 
mechanical,  and  electrical  engineers. 

(6)  The  rate  of  percentage  arising  from  Articles  (i)  and  (2)  hereof,  that  is, 
the  basic  rate,  applies  when  all  of  the  work  is  let  under  one  contract.  Should 
the  owner  determine  to  have  certain  portions  of  the  work  executed  under 
separate  contracts,  as  the  architect's  burden  of  service,  expense,  and  responsi- 
bility is  thereby  increased,  the  rate  in  connection  with  such  portions  of  the  work 
is  greater  (usually  by  4  per  cent)  than  the  basic  rate.  Should  the  owner  deter- 
mine to  have  substantially  the  entire  work  executed  under  separate  contracts, 
then  such  higher  rate  applies  to  the  entire  work.  In  any  event,  however,  the 
basic  rate,  without  increase,  applies  to  contracts  for  any  portions  of  the  work 
on  which  the  owner  reimburses  the  engineer's  fees  to  the  architect. 

(7)  If,  after  a  definite  scheme  has  been  approved,  the  owner  makes  a  decision 
which,  for  its  proper  execution,  involves  extra  services  and  expense  for  changes 
in  or  additions  to  the  drawings,  specifications,  or  other  documents;  or  if  a  con- 
tract be  let  by  cost  of  labor  and  materials  plus  a  percentage  or  fixed  sum;  or  if 
the  architect  be  put  to  labor  or  expense  b\'  delays  caused  by  the  owner  or  a  con- 
tractor, or  Ijy  the  delinquency  or  insolvency  of  either,  or  as  a  result  of  damage  by 
fire,  he  is  to  be  equitably  paid  for  such  extra  service  and  expense. 

(8)  Should  the  execution  of  any  work  designed  or  specified  by  the  architect 
or  any  part  of  such  work  be  abandoned  or  suspended,  the  architect  is  to  be  paid 
in  accordance  with  or  in  proportion  to  the  terms  of  Article  (9)  of  this  Schedule 
for  the  service  rendered  on  account  of  it,  up  to  the  time  of  such  abandonment  or 
suspension. 

(9)  Whether  the  work  be  executed  or  whether  its  execution  be  suspended  or 
abandoned  in  part  or  whole,  payments  to  the  architect  on  his  fee  are  subject 
to  the  provisions  of  Articles  (7)  and  (8),  made  as  follows:  Upon  completion 
of  the  preliminary  studies,  a  sum  equal  to  20  per  cent  of  the  basic  rate  computed 
upon  a  reasonable  estimated  cost.  Upon  completion  of  specifications  and  gen- 
eral working  drawings  (exclusive  of  details)  a  sum  sufiicient  to  increase  pay- 
ments on  the  fee  to  sixty  per  cent  of  the  rate  or  rates  of  commission  agreed  upon, 
as  influenced  by  Article  (6),  computed  upon  a  reasonable  cost  estimated  on 
such  completed  specifications  and  drawings,  or  if  bids  have  been  received, 
then  computed  upon  the  lowest  bona-fide  bid  or  bids.  From  time  to  time 
during  the  execution  of  work  and  in  proportion  to  the  amount  of  service  ren- 
dered by  the  architect,  payments  are  made  until  the  aggregate  of  all  payments 
made  on  account  of  the  fee  under  this  Article  reaches  a  sum  equal  to  the  rate 
or  rates  of  commission  agreed  upon  as  influenced  by  Article  (6),  computed  upon 
the  final  cost  of  the  work.  Payments  to  the  architect,  other  than  those  on  his 
fee,  fall  due  from  time  to  time  as  his  work  is  done  or  as  costs  are  incurred.  No 
deduction  is  made  from  the  architect  s  fee  on  account  of  penalty,  liquidated 
damages  or  other  sums  withheld  from  payments  to  contractors. 

(10)  The  owner  is  to  furnish  the  architect  with  a, complete  and  accurate 
survey  of  the  building-site,  giving  the  grades  and  Hnes  of  streets,  pavements 
and  adjoining  properties;  the  rights,  restrictions,  easements,  boundaries  and 
contours  of  the  building-site,  and  full  information  as  to  sewer,  water,  gas  and 


Architectural  Competitions  1733 

electrical  service.     The  owner  is  to  pay  for  borings  or  test-pits  and  for  chemical 
mechanical  or  other  tests,  when  required. 

(ii)  The  architect  endeavors  to  guard  the  owner  against  defects  and  de- 
ficiencies in  the  work  of  contractors,  but  he  does  not  guarantee  the  performance 
of  their  contracts.  The  supervision  of  an  architect  is  to  be  distinguished  from 
the  continuous  personal  superintendence  to  ]je  obtained  by  the  employment 
of  a  clerk  of  the  works.  When  authorized  by  the  owner,  a  clerk  of  the  works, 
acceptable  to  both  owner  and  architect,  is  to  be  engaged  by  the  architect  at  a 
salary  satisfactory  to  the  owner  and  paid  by  the  owner,  upon  presentation  of 
the  architect's  monthly  certificates. 

(12)  When  requested  to  do  so,  the  architect,  makes  or  procures  preUminary 
estimates  on  the  cost  of  the  work  and  he  endeavors  to  keep  the  actual  cost  of 
the  work  as  low  as  may  be  consistent  with  the  purpose  of  the  building  and  with 
proper  workmanship  and  material,  but  no  such  estimate  can  be  regarded  as 
other  than  an  approximation. 

(13)  Drawings  and  specifications,  as  instruments  of  service,  are  the  property 
of  the  architect,  whether  the  work  for  which  they  are  made  be  executed  or  not. 

ARCHITECTURAL  COMPETITIONS  * 

This  Circular  of  Advice  furnishes  information  as  to  the  best  methods  of 
conducting  architectural  competitions  and  states  the  conditions  which  are  pre- 
requisite to  participation  in  them  by  members  of  The  American  Institute  of 
Architects.  It  does  not  apply  to  competitions  for  work  to  he  erected  elsewhere 
than  in  the  United  States,  its  territories  and  possessions. 

The  Attitude  of  The  American  Institute  of  Architects  to  Competitions. 
Since  its  foundation,  more  than  sixty  years  ago  (1857),  The  American  Institute 
of  Architects  has  given  much  attention  to  the  conduct  of  architectural  cx)M- 
PETiTiONS.  These  contests,  instituted  when  the  direct  selection  of  an  architect 
could  not  be  made,  were  for  many  years  conducted  without  proper  regulation 
and  often  in  disregard  of  the  interests  both  of  the  owner  aiad  of  the  competitors. 
The  owner,  totally  unfamiliar  with  the  intricacies  of  the  subject,  assumed,  with- 
out skilled  assistance,  to  prepare  the  programme,  laying  down,  or  more  frequently 
ignoring,  rules  to  govern  procedure.  With  the  growth  of  the  countr\',  the  in- 
crease in  expenditures  for  pubHc  and  private  buildings,  and  the  increase  in  the 
number  of  architects,  all  the  evils  of  ill-regulated  competitions  became  more 
marked.  Programmes  varied  from  loose  and  careless  forms,  difficult  to  under- 
stand and  often  open  to  the  suspicion  that  only  the  initiated  knew  what  they 
meant,  to  over-elaborate  ones  necessitating  useless  study  of  details  and  needless 
drawings.  Those  instituting  the  competition  often  had  no  legal  authority  to  pay 
any  competitors,  still  less  to  employ  the  winner.  There  was  great  economic 
waste,  the  total  cost  of  participation  exceeding  the  total  net  profit  accruing  to  the 
profession  from  work  secured  through  competitions.  Architects  have  learned 
that  the  outcome  of  a  competition,  unless  governed  by  well-defined  agreements, 
is  largely  a  matter  of  chance.     The  owner  has,  to  be  sure,  a  choice  of  designs,  but 

*The  American  Institute  of  Architects,  Document  114.  Reprinted  by  permission. 
Authorized  by  the  43d  annual  convention  at  Washington,  D.  C,  December  14-16,  1909; 
issued  March  30,  1910,  amended  June  10,  1910;  and  January  3,  1911;  ratified  by  the 
44th  annual  convention  at  San  Francisco,  January  16-21,  1911;  reaffirmed  by  the  45th 
annual  convention  at  Washington,  D.  C;  amended  January  3,  1912,  as  authorized  by 
the  convention;  amended  December  9,  191 2,  and  ratified  hy  the  46th  annual  convention 
at  Washington,  D.  C,  December  10-12,  191 2;  amended  December  2,  1913,  and  ratified 
by  the  47th  annual  convention  at  New  Orleans,  La.,  December  3-5,  1913;  amended  and 
ratified  by  the  48th  annual  convention  at  Washington,  D.  C,  December  2-4,  1914. 


1734  Architectural  Competitions  Pa^^ 

he  is  no  more  likely  to  make  the  wisest  selection  or  to  obtain  the  best  building 
than  if  he  selects  his  architect  directly,  guided  by  the  results  previously  achieved 
by  the  men  he  is  considering.  When  a  competition  is  necessary  or  desirabb 
it  should  be  of  such  form  as  to  establish  equitable  relations  between  the  owner 
and  the  competitors.     To  insure  this: 

(i)  The  REQUIREMENTS  should  be  clear  and  definite,  and  the  statement  of 
them,  since  it  must  be  in  technical  terms,  should  be  drawn  by  one  familiar  mih 
such  terms. 

(2)  The  COMPETENCY  of  all  competing  should  be  assured.  The  drawings  sub- 
mitted in  a  competition  are  evidence,  only  in  part,  of  the  ability  of  the  architect 
to  execute  the  building.  The  owner,  for  his  own  protection,  should  admit  to 
the  competition  only  those  to  whom  he  would  be  willing  to  entrust  the  work; 
that  is,  to  men  of  know^n  honesty  and  competence. 

(3)  The  AGREEMENT  between  the  owner  and  the  competitors  should  be 
definite,  as  becomes  a  plain  statement  of  business  relations. 

(4)  The  JUDGMENT  should  be  based  on  knowledge,  and  since  ideas  presented 
in  the  form  of  drawings  are  intelligible  only  to  a  trained  mind,  judgment  should 
not  be  rendered  until  the  owner  has  received  competent  technical  advice  as  to 
the  merits  of  those  ideas. 

To  sum  up:  To  insure  the  best  results,  a  competition  should  have  (i)  a  clear 
programme,  (2)  competent  competitors,  (3)  a  business  agreement,  (4)  a  fair 
judgment. 

Fifteen  years  ago  many  competitions  had  none  of  these  provisions  and  few 
had  all  of  them.  The  commonest  form  of  competition  was  one  that  was 
open  to  all,  had  a  programme  prepared  by  a  layman,  was  judged  by  the  owner 
without  professional  assistance,  contained  no  agreement,  and  made  no  provision 
to  eliminate  the  incompetent.  All  this  demanded  correction.  The  Institute, 
seeking  a  means  of  reform,  perceived  at  once  that  its  relation  to  the  owner  could 
be  only  an  advisory  one.  It  might  advise  him  how  to  hold  a  competition, 
but  it  could  go  no  further.  To  architects  in  general  the  Institute  could 
scarcely  presume  to  offer  even  its  advice,  but  being  a  professional  body 
charged  with  maintaining  ethical  standards  among  its  own  members,  its  duty 
was  to  see  that  they  did  not  take  part  in  competitions  that  fell  below  a  reason- 
able standard. 

It  was,  therefore,  voted  in  convention  of  the  Institute  that  members  should 
be  free  to  take  part  in  competitions  only  when  their  terms  had  received  the 
APPROVAL  OF  THE  INSTITUTE.  Thereupon  the  Institute  fully  stated  the  prin- 
ciples which  should  govern  competitions  and  defined  the  conditions  prerequisite 
to  the  giving  of  its  approval.  These  are  contained  in  the  Circular  of  Advice 
here  following,  which  is  intended  as  a  guide  to  all  who  are  interested  in  com- 
petitions. Committees  of  the  Institute  throughout  the  country  are  authorized 
to  give  its  approval  to  competitions  when  properly  conducted,  but  unless  a 
programme  has  received  such  approval  members  of  the  Institute  do  not  accept 
a  position  as  competitor  or  juror,  nor  does  a  member  continue  to  act  as  profes- 
sional adviser  after  it  becomes  evident  that  the  owner  will  not  permit  his 
programme  to  be  brought  into  harmony  with  the  principles  approved  by  the 
Institute. 

The  position  thus  taken  by  the  Institute  is  by  no  means  an  arbitrary  one,  since 
it  governs  the  action  of  none  but  its  own  members.  To  the  owner  its  service 
has  been  of  great  value  in  giving  him  information  and  useful  advice  and  in  saving 
him  from  the  delays,  cost  and  disappointment  incident  to  the  amateur  conduct 
of  a  competition.  The  owner  who  disregards  the  standard  set  by  the  Institute 
finds  it  increasingly  difficult  to  get  men  of  standing  in  the  profession  to  enter. 
He  who  raises  his  programme  to  that  standard  has  no  difficulty  in  securing  the 


Architectural  Competitions  1735 

services  of  architects  of  the  greatest  ability.  Even  in  the  few  years  since  the 
Institute  first  made  its  firm  stand  against  the  abuses  of  competitions,  the  effect 
of  that  action  has  been  far  greater  than  could  have  been  foreseen.  It  has  not 
altogether  eliminated  ill-regulated  competitions,  but  it  has  greatly  reduced  their 
number,  and  it  is  safe  to  say  that  no  competition  of  prime  importance  is  now 
conducted  except  in  accordance  with  the  principles  stated  in  the  following  Cir- 
cular OF  Advice: 

A  Circular  of  Advice  and  Information  Relative  to  the  Conduct  of 
Architectural  Competitions 

Competitions  are  instituted  to  enable  the  owner  *  to  choose  an  architect 
through  comparison  of  the  designs  submitted.  The  American  Institute  of  Archi- 
tects, believing  that  the  interests  of  both  owner  and  competitors  are  best  served 
by  fair  and  equitable  agreements  between  them,  issues  this  circular  as  a  state- 
ment OF  the  principles  which  should  underlie  such  agreements.  The  Institute 
does  not  assume  to  dictate  the  owner's  course  in  conducting  competitions,  but 
aims  to  assist  him  by  advising  the  adoption  of  such  methods  as  experience  has 
proved  to  be  just  and  wise.  So  important,  however,  does  the  adoption  of  such 
methods  appear  to  architects  that  members  of  the  Institute  do  not  take  part  in 
competitions  except  under  conditions  based  on  this  circular  and  specifically  set 
forth  in  Articles  (i6)  and  (i8). 

(i)  On  Competitions  in  General.  A  competition  exists  when  two  or  more 
architects  prepare  sketches  at  the  same  time  for  the  same  project,  but  no  archi- 
tect who  prepares  drawings  for  comparison  in  problems  of  an  altruistic  or  edu- 
cational nature,  where  the  problem  does  not  involve  a  definite  proposed  building 
operation,  shall  be  held  as  having  taken  part  in  a  competition,  within  the  mean- 
ing of  this  circular  of  advice. 

(2)  On  the  Employment  of  a  Professional  Adviser.  No  competition 
shall  be  instituted  without  the  aid  of  a  competent  adviser.  He  should  be  an 
architect  of  the  highest  standing  and  his  selection  should  be  the  owner's  first 
step.  He  must  be  chosen  with  the  greatest  care,  as  the  success  of  the  competition 
will  depend  largely  upon  his  experience  and  abiUty.  The  expert's  advice  is 
of  great  value  to  the  owner,  for  example,  in  so  drawing  the  programme  as  to 
safeguard  him  against  the  employment  of  an  architect  who  submits  a  design 
largely  exceeding  in  cost  of  execution  the  sum  at  his  disposal,  and  in  helping  him 
to  avoid  the  disappointment,  embarrassment  and  litigation  which  so  often  result 
from  competitions  conducted  without  expert  technical  advice.  The  duties 
OF  the  expert  are  to  advise  those  who  hold  the  competition  as  to  its  form  and 
terms,  to  draw  up  the  programme,  to  advise  in  choosing  the  competitors,  to 
answer  their  questions,  and  to  conduct  the  competition. 

(3)  On  the  Forms  of  Competition.     The  following  forms  of  competition 

are  recognized:  .  u       c       w 

Limited.  In  this  form,  participation  is  limited  to  a  certam  number  of  archi- 
tects whose  names  should  be  stated  in  the  programme  and  to  any  one  of  whom 
the  owner  is  wiUing  to  entrust  the  work.  In  a  limited  competition  the  com- 
petitors may  be  chosen  (a)  from  among  architects  whose  ability  is  so  evident 
that  no  formal  inquiry  into  their  qualifications  is  needed,  or  (b)  from  among 
architects  who  make  application  accompanied  by  evidence  of  their  education 
and  experience.  The  Hmited  form  has  the  advantage  that  the  owner  and  the 
professional  adviser  may  meet  competitors  and  discuss  the  terms  of  the  com- 

*  The  person,  corporation  or  other  entity  instituting?  a  competition,  whether  acting 
directly  or  through  representatives,  is  heroin  called  the  owner. 


1736  Architectural  Competitions  Part  3 

petition  with  them  before  the  issuance  of  the  programme      Form  (a)  is  the 
simplest  and  most  direct  form  of  competition. 

Open.  The  Institute  believes  that  a  competition  open  to  all  who  wish  to 
participate  without  regard  to  their  qualifications  is  detrimental  to  the  interests 
alike  of  owner  and  of  architects.  It  will,  therefore,  give  its  approval  to  that  form 
only  when  conducted  in  two  stages,  since  by  that  means  alone  it  is  possible  to 
insure  anonymity  of  submission  while  safeguarding  the  owner's  interests  against 
the  selection  as  winner  of  a  person  lacking  the  qualifications  set  forth  in  Article 
(4)  hereof.  In  this  form  there  is  a  first  stage  open  to  all,  in  which  the  com- 
petitive drawings  are  of  the  slightest  nature,  involving  only  the  fundamental 
ideas  of  the  solution.  These  drawings  are  accompanied  by  evidence  of  the  com- 
petitor's education  and  experience.  From  the  first  stage  a  small  number  who 
have  thus  demonstrated  their  competence  to  design  the  work  and  to  carry  it 
successfully  into  execution  are  chosen  to  take  part  in  a  final  and  strictly  anony- 
mous stage  involving  competitive  drawings  of  the  type  indicated  in  Article  (8) 
hereof. 

(4)  On  the  Qualification  of  Competitors.  The  interests  of  the  owner 
may  be  seriously  prejudiced  by  admitting  to  a  limited  competition  or  to  the 
second  stage  of  an  open  competition  any  architect  who  has  not  established  to 
the  satisfaction  of  the  owner  his.  competence  to  design  and  execute  the  work. 
It  is  sometimes  urged  that  by  admitting  all  who  wish  to  take  part  some  unknown 
but  brilliant  designer  may  be  found.  If  the  object  of  a  competition  were  a  set 
of  sketches,  such  reasoning  might  be  valid.  But  sketches  give  no  evidence  that 
their  author  has  the  matured  artistic  ability  to  fulfil  their  promise,  or  that  he 
has  the  technical  knowledge  necessary  to  control  the  design  of  the  highly  com- 
plex structure  and  equipment  of  a  modern  building,  or  that  he  has  executive 
ability  for  large  afifairs,  or  the  force  to  compel  the  proper  execution  of  contracts. 
Attempts  have  often  been  made  to  defend  the  owner's  interests  by  associating 
an  architect  of  ability  with  one  lacking  in  experience.  These  have  generally 
resulted  in  failure.  As  the  owner  should  feel  bound,  not  only  legally,  but  in 
point  of  honor,  to  retain  as  his  architect  the  competitor  to  whom  the  award  is 
made,  it  is  essential  that  the  competitors  in  a  limited  competition,  or  in  the 
second  stage  of  an  open  competition,  should  be  selected  with  the  greatest  care  in 
consultation  with  the  professional  adviser,  and  that  there  should  be  included 
among  them  only  architects  in  whose  ability  and  integrity  the  ov/ner  has  abso- 
lute confidence,  and  to  any  one  of  whom  he  is  willing  to  entrust  the  work. 

(5)  On  the  Number  of  Competitors.  Experience  has  demonstrated  that 
the  admission  of  many  competitors  is  detrimental  to  the  success  of  a  competi- 
tion. When  there  are  many,  each  knows  that  he  has  but  a  slight  chance  of 
success,  and  he  is  therefore  less  aroused  to  his  best  effort  than  when  there  are  but 
a  few.  As  the  owner  is  interested  only  in  the  best  result,  he  is  ill-advised  to 
sacrifice  quality  for  quantity. 

(6)  On  Anonymity  of  Competitors.  Absolute  and  efifective  anonymity 
is  a  necessary  condition  of  a  fair  and  unbiased  competition.  The  signing  of 
DRAWINGS  should  not  be  permitted  nor  should  they  bear  any  motto,  device  or 
distinguishing  mark.  Drawings  and  the  accompanying  sealed  envelopes  con- 
taining their  authors'  names  should  be  numbered  upon  receipt,  the  envelopes 
remaining  unopened  until  after  the  award. 

(7)  On  the  Cost  of  the  Proposed  Work.  No  statement  of  the  intended 
cost  of  the  work  should  be  made  unless  it  has  been  ascertained  that  the  work 
as  described  in  the  programme  can  be  properly  executed  within  the  sum  named. 
Jn  general  it  is  wiser  to  limit  the  cubic  contents  of  the  building  than  to  state  a 


Architectural  Competitions  1737 

limit  of  cost.  The  programme  slioiild  neither  require  nor  permit  competitors 
to  furnish  their  own  or  builders'  estimates  of  the  cost  of  executing  the  work  in 
accordance  with  their  designs.  Such  estimates  are  singularly  unreliable.  If 
the  cubage  be  properly  limited  they  are  unnecessary. 

(8)  On  the  Jury  of  Award.  To  insure  a  wise  and  just  award  and  to  pro- 
tect the  interests  of  both  the  owner  and  the  competitors,  the  competitive  draw- 
ings should  be  submitted  to  a  jury  sj  chosen  as  to  secure  expert  knowledge  and 
freedom  from  personal  bias.  Such  a  jury  thoroughly  understands  and  can 
explain  the  intent  of  the  drawings.  It  discovers  from  them  their  authors' 
skill  in  design,  arrangement  and  construction.  Because  of  its  trained  judgment 
its  advice  as  to  the  merits  of  the  designs  submitted  is  of  the  highest  value  to  the 
owner.  The  jury  must  consist  of  at  least  three  members,  one  of  whom  must, 
and  a  majority  of  whom  should,  be  PRACTicmo  architects.  One  or  more 
members  of  the  jury  may  be  chosen  by  the  competitors.  It  is  the  duty  of  the 
JURY  to  study  carefully  the  programme  and  all  conditions  relating  to  the  problem 
and  the  competition  before  examining  the  designs  submitted;  to  refuse  to  make 
or  recommend  an  award  in  favor  of  the  author  of  any  design  that  does  not  fulfil 
the  conditions  distinctly  stated  as  mandatory  in  the  programme;  to  give  ample 
time  to  the  careful  study  of  the  designs;  and  to  render  a  decision  only  after 
mature  consideration.  The  jury  should  see  to  it  that  a  copy  of  its  report  reaches 
every  competitor.  The  professional  adviser  should  not  be  a  member  of  the 
jury,  as  his  judgment  is  apt  to  be  influenced  by  his  previous  study  of  the  problem. 

(9)  On  the  Competitive  Drawings.  The  purpose  of  an  architectural  com- 
petition is  not  to  secure  fully  developed  plans,  but  such  evidence  of  skill  in  treat- 
ing the  essential  elements  of  the  problem  as  will  assist  in  the  selection  of  an 
ARCHITECT.  The  drawings  should,  therefore,  be  as  few  in  number  and  as  simple 
in  character  as  will  express  the  general  design  of  the  building.  A  jury  of  experts 
does  not  need  elaborate  drawings. 

(10)  On  the  Programme.  The  programme  should  contain  rules  for  the 
conduct  of  the  competition,  instructions  for  competitors  and  the  jury,  and  t;he 
agreement  between  the  owner  and  the  competitors.  Uniform  conditions  for  all 
competitors  are  fundamental  to  the  proper  conduct  of  competitions.  Lengthy 
programmes  and  detailed  instructions  as  to  the  desired  accommodations  should 
be  avoided  as  they  confuse  the  problem  and  hamper  the  competitors.  The 
problem  should  be  stated  broadly.  Its  solutions  should  be  left  to  the  competi- 
tors. A  distinction  should  be  clearly  drawn  between  the  mandatory  and  the 
ADVISORY  provisions  of  the  programme,  that  is,  between  those  which,  if  not  met, 
preclude  an  award  in  favor  of  the  author  of  a  design  so  failing,  and  those  which 
are  merely  optional  or  of  a  suggestive  character.  The  mandatory  requirements 
should  be  set  forth  in  such  a  way  that  they  cannot  fail  to  be  recognized  as  such. 
They  should  be  as  few  as  possible,  and  should  relate  only  to  matters  which 
cannot  be  left  to  the  discretion  of  the  competitors.  It  is  difficult  to  summarize 
briefly  the  progranime,  but  it  should  at  least: 

(a)  Name  the  ov/ner  of  the  structure  forming  the  subject  of  the  competition, 
and  state  whether  the  owner  institutes  the  competition  personally  or  through 
representatives;  if  the  latter,  name  the  representatives,  state  how  their  author- 
ity is  derived,  and  define  its  scope. 

(b)  State  the  kind  of  competition  to  be  instituted,  and  in  limited  conipetitions 
name  the  competitors;  or  in  open  competitions,  if  the  competition  is  limited 
geographically  or  otherwise,  state  the  limits. 

(c)  Fix  a  time  and  place  for  the  receipt  of  the  designs.  The  time  should  not 
be  altered  except  with  the  unanimous  consent  of  the  competitors. 

(d)  Furnish  exact  information  as  to  the  site. 


1738  Architectural  Competitions  Part 


(e)  State  the  desired  accommodation,  avoicling  detail. 

(f)  State  the  cost  if  it  be  fixed  or,  better,  Hmit  the  cubic  co-ntents. 

(g)  Fix  uniform  requirements  for  the  drawings,  giving  the  number,  the  sc; 
or  scales,  and  the  method  of  rendering. 

(h)  Forbid  the  submission  of  more  than  one  design  by  any  one  competitor. 

(i)  Provide  a  method  for  insuring  anonymity  of  submission. 

(j)  Name  the  members  of  the  jury  or  provide  for  their  selection.  Define 
their  powers  and  duties.  If  for  legal  reasons  the  jury  may  not  make  the  final 
award,  state  such  reasons  and  in  whom  such  power  is  vested. 

(k)  Provide  that  no  award  shall  be  made  in  favor  of  any  design  until  the  jury 
shall  have  certified  that  it  does  not  violate  any  mandatory  requirement  of  the 
programme. 

(1)  Provide  that  during  the,  competition  there  shall  be  no  communication 
relative  to  it  between  any  competitor  and  the  owner,  his  representatives,  or  any 
member  of  the  jury,  and  that  any  communication  with  the  professional  adviser 
shall  be  in  writing.  Provide  also  that  any  information,  whether  in  answer  to 
such  communications  or  not,  shall  be  given  in  writing  simultaneously  to  all 
competitors.     Set  a  date  after  which  no  questions  will  be  answered. 

(m)  State  the  number  and  amount  of  payments  to  competitors. 

(n)  Provide  that  the  professional  adviser  shall  send  a  report  of  the  competi- 
tion to  each  competitor,  including  therein  the  report  of  the  jury. 

(o)  Provide  that  no  drawing  shall  be  exhibited  or  made  public  until  after  the 
award  of  the  jury. 

(p)  Provide  for  the  return  of  unsuccessful  drawings  to  their  respective  authors 
within  a  reasonable  time. 

(q)  Provide  that  nothing  original  in  any  of  the  unsuccessful  designs  shall  be 
used  without  consent  of,  and  compensation  to,  the  author  of  the  design  in  which 
it  appears. 

(r)  Include  the  contract  between  the  owner  and  the  competitors. 

(s)  Include  the  contract  between  the  owner  and  the  architect  receiving  the 
award. 

(ii)  On  the  Agreement.  An  owner  who  institutes  a  competition  assumes 
a  moral  obligation  to  retain  one  of  the  competitors  as  his  architect.  In  order 
that  architects  invited  to  compete  may  determine  whether  they  will  take  part 
it  is  essential  that  they  should  know  the  terms  upon  which  the  winner  will  be 
employed;  and  it  is  of  the  utmost  importance  to  the  owner  that  those  terms 
should  be  so  clearly  defined  that  no  disagreement  as  to  their  meaning  can  arise 
after  the  award  is  made.  Unless  they  be  so  defined,  delay  is  likely  to  occur  and 
disagreements  to  arise  at  a  time  when  a  complete  understanding  between  owner 
and  architect  is  most  important  for  the  welfare  of  the  work.  Therefore,  there 
must  be  included  in  the  programme  a  form  which  guarantees  the  appointment 
of  one  of  the  competitors  as  architect  and  provides  an  agreement  operative 
up^n  that  appointment,  defining  his  employment  m  terms  consonant  with  the 
best  practice.  This  must  conform  in  all  fundamental  respects  to  the  typical 
form  of  agreement  appended  to  this  circular. 

(12)  On  Payments  to  Unsuccessful  Competitors.  In  a  limited  com- 
petition and  in  the  second  stage  of  an  open  competition  each  competitor, 
except  the  winner,  should  be  paid  for  his  services. 

(13)  On  Legality  of  Procedure.  It  is  highly  important  tliat  each  step 
taken  in  coiiaecLijii  with  a  co.npelition  and  every  provision  of  the  jorogramrae 
should  be  in  consonance  with  law.  Those  charged  with  holding  the  competition 
should  know  and  state  their  authjrity.  If  they  are  not  empowered  to  Ijind  their 
principal  by  contracts  with  the  competitors,  they  should  seek  and  receive  such 


Architectural  Competitions  1739 

authority  before  issuing  an  invitation.  If  authority  cannot  legally  be  granted 
to  the  jury  to  make  the  award,  that  fact  should  be  stated,  and  the  body  named 
in  which  such  authority  is  vested. 

(14)  On  the  Conduct  of  the  Owner.  In  order  to  maintain  absolute 
impartiahty  toward  all  competitors,  the  owner,  his  representatives  and  all  con- 
nected with  the  enterprise  should,  as  soon  as  a  professional  adviser  has  been 
appointed,  refrain  from  holding  any  communication  in  regard  to  the  matter 
with  any  architect  except  the  adviser  or  the  jurors.  The  meeting  with  com- 
petitors described  in  Article  (3)  is  of  course  an  exception. 

(15)  On  the  Conduct  of  Architects.  An  architect  should  not  attempt 
in  any  way,  except  as  a  duly  authorized  competitor,  to  secure  work  for  which  a 
competition  is  in  progress,  nor  should  he  attempt  to  influence,  either  directly 
or  indirectly,  the  award  in  a  competition  in  which  he  is  a  competitor.  An  archi- 
tect should  not  accept  the  commission  to  do  the  work  for  which  a  competition 
has  been  instituted  if  he  has  acted  in  an  advisory  capacity,  either  in  drawing  the 
programme  or  making  the  award.  An  architect  should  not  submit  in  competi- 
tion a  design  which  has  not  been  produced  in  his  own  office  or  under  his  own 
direction.  No  competitor  should  enter  into  association  with  another  architect, 
except  with  the  consent  of  the  owner.  If  such  associates  should  win  the  com- 
petition, their  association  should  continue  until  the  completion  of  the  work 
thus  won.  During  the  competition,  no  competitor  should  hold  any  communi- 
cation relative  to  it  with  the  owner,  his  representatives  or  any  member  of  the 
jury,  nor  should  he  hold  any  communication  with  the  professional  adviser,  except 
it  be  in  writing.  When  an  architect  has  been  authorized  to  submit  sketches 
for  a  given  project,  no  other  architect  should  submit  sketches  for  it  until  thf? 
owner  has  taken  definite  action  on  the  first  sketches,  since,  as  far  as  the  second 
architect  is  concerned,  a  competition  is  thus  established. 

(16)  On  the  Participation  of  Members  of  the  Institute.  Members  of 
The  American  Institute  of  Architects  do  not  take  part  as  competitors  or  jurors 
in  any  competition  the  programme  of  which  has  not  received  the  formal  approval 
of  the  Institute,  nor  does  a  member  continue  to  act  as  professional  adviser  after 
it  has  been  determined  that  the  programme  cannot  be  so  drawn  as  to  receive 
such  approval. 

(17)  Committees.  In  order  that  the  advice  of  the  Institute  may  be  given 
to  those  who  seek  it  and  that  its  approval  may  be  given  to  programmes  in  con- 
sonance with  its  principles,  the  Institute  maintains  the  following  committees: 

(a)  The  Standing  Committee  on  Competitions,  representing  the  Institute 
in  its  relation  to  competitions  generally.  This  committee  advises  the  subcom- 
mittees and  directs  their  work  and  they  report  to  it.  . 

(b)  A  subcommittee  for  the  territory  of  each  chapter,  representmg  the 
Institute  in  its  relation  to  competitions  for  work  to  be  erected  within  such 

The  president  of  the  chapter  is  ex-officio  chairman  of  the  subcommittee, 
the  other  members  of  which  he  appoints.  The  subcommittees  derive  their 
authority  from  the  Institute  and  not  from  the  chapters.  An  appeal  from  the 
decision  of  a  subcommittee  may  be  made  to  the  standing  committee  The 
standing  committee  may  approve,  modify  or  annul  the  decision  of  a  subcom- 
mittee. 

(iS)  The  Institute's  Approval  of  the  Programme.  The  approval  of  the 
Institute  is  not  given  to  a  programme  unless  it  meets  the  following  essential 
conditions: 

(a)  That  there  be  a  professional  adviser.  .,.  j  .     a  .-  1    /  ^ 

(b)  That  the  competition  be  of  one  of  the  forms  described  m  Article  (3). 


1740  Arcjiitectural  Competitions  Part  3 

(c)  That  the  programme  contain  an  Agreemknt  and  Conditions  of  Con- 
tract between  architect  and  owner  in  conformity  with  those  printed  in  the 
Appendix  of  this  circular,  that  it  include  no  provision  at  variance  therewith, 
that  it  ontain  terms  of  payments  in  accord  with  good  practice,  and  that  it  spe- 
cifically set  forth  the  nature  of  expert  engineering  services  for  which  the  architect 
will  be  reimbursed. 

(d)  That  the  programme  make  provision  for  a  jury  of  at  least  three  persons. 

(e)  That  the  programme  conform  in  all  particulars  to  the  spirit  of  this  cir- 
cular. 

When  the  programme  meets  the  above  essential  conditions,  the  approval  of 
the  Institute  may  be  given  to  it  by  the  subcommittee  for  the  territory  in  which 
the  work  is  to  be  erected,  or  if  there  be  no  subcommittee  for  that  territory,  then 
by  the  standing  committee  on  competitions.  If,  for  legal  or  other  reasons,  the 
standing  committee  deem  that  deviations  from  the  essential  conditions  are 
justified,  it  may  give  the  approval  of  the  Institute  to  a  programme  containing 
such  deviations.  Power  to  give  approval  in  such  cases  is,  however,  vested  only 
in  the  standing  committee.  The  professional  adviser,  when  duly  authorized 
in  writing  by  the  proper  committee,  may  print  the  Institute's  approval  as 
a  part  of  the  programme  or  otherwise  communicate  it  to  those  invited  to 
compete. 

^  Typical  Form  of  Agreement  between  Owner  and  Competitors 

In  consideration  of  the  submission  of  drawings  in  this  competition  (here  insert 
the  name  of  the  owner  or  of  the  body  duly  authorized  to  enter  into  contracts 
on  behalf  of  the  owner),  hereinafter  called  the  owner,  agrees  with  the  competi- 
tors jointly  and  severally  that  the  owner  will,  within days  of  the  date 

set  for  the  submission  of  drawings,  make  an  award  of  the  commission  to  design 
and  supervise  the  work  forming  the  subject  of  this  competition  to  one  of  those 
competitors  who  submit  drawings  in  consonance  with  the  mandatory  require- 
ments of  this  programme,  and  will  thereupon  pay  him,  on  account  of  his  services 
as  architect,  one-tenth  of  his  total  estimated  fee  as  stated  below.  And  further, 
in  consideration  of  the  submission  of  drawings  as  aforesaid  and  the  mutual 
promis3s  enumerated  in  the  subjoined  Conditions  of  Contract  between 
Architect  and  Owner,  the  owner  agrees  and  each  competitor  agrees,  if  the 
award  be  made  in  his  favor,  immediately  to  enter  into  a  contract  containing  all 
the  Conditions  here  following,  and  until  such  contract  is  executed  to  be  bound 
by  the  said  Conditions. 

Conditions  of  Contract  between  Architect  and  Owner 

Article  I.    Duties  of  the  Architect 

(x)  Design.  The  architect  is  to  design  the  entire  building  and  its  immediate 
surroundings  and  is  to  design  or  direct  the  design  of  its  constructive,  engineering 
and  decorative  work  and  its  fixed  equipment  and,  if  further  retained,  its  movable 
furniture  and  the  treatment  of  the  remainder  of  its  grounds. 

(2)  Drawings  and  Specifications.  The  architect  is  to  make  such  revision 
of  his  competitive  scheme  as  may  be  necessary  to  complete  the  preliminary 
studies;  and  he  is  to  provide  drawings  and  specifications  necessary  for  the  con- 
duct of  the  work.  All  such  instruments  of  service  are  and  remain  the  property 
of  the  architect. 

(3)  Administration.  The  architect  is  to  prepare  or  advise  as  to  all  forms 
connected  with  the  making  of  proposals  and  contracts,  to  issue  all  certificates 


Architectural  Competitions  1741 

•f  payment,  to  keep  proper  accounts  and  generally  to  discharge  the  necessary 
administrative  duties  connected  with  the  work. 

(4)  Supervision.  The  architect  is  to  supervise  the  execution  of  all  the  work 
committed  to  his  control. 

Article  II.    Duties  of  the  Owner 

(i)  Payments.     The  owner  is  to  pay  the  architect  for  his  services  a  sum 

e<^l^a^  to per  cent  *  upon  the  cost  of  the  work.     (The  times  and  amounts 

of  payments  should  be  here  stated.)  f 

(2)  Reimbursements.  The  owner  is  to  reimburse  the  architect,  from  time 
to  time,  the  amount  of  expenses  necessarily  incurred  by  him  or  his  deputies 
while  traveling  in  the  discharge  of  duties  connected  with  the  work. 

(3)  Service  of  Engineers.  The  owner  is  to  reimburse  the  architect  the  cost 
of  the  services  of  such  engineers  for  heating,  mechanical  and  electrical  work  as 
are  specifically  provided  for  in  each  programme.  The  selection  of  such  engineers 
and  their  compensation  shall  be  subject  to  the  approval  of  the  owner. 

(4)  Information,  Clerk  of  the  Works,  etc.  The  owner  is  to  give  all  in- 
formation as  to  his  requirements;  to  pay  for  all  necessary  surveys,  borings  and 
tests,  and  for  the  continuous  services  of  a  clerk  of  the  works,  whose  competence 
is  approved  by  the  architect. 

Standard  Form  of  Competition- Programme  J 

The  following  standard  form  of  Competition-programme,  prepared  by  The 
American  Institute  of  Architects,  contains  those  provisions  which  the  Institute 
considers  essential  to  the  fair  and  equitable  conduct  of  a  competition.  The 
Institute  in  no  way  assumes  or  attempts  to  dictate  an  Owner's  course  in  con- 
ducting a  competition;  it  claims  only  the  right  to  control  its  own  members,  and 
having  found  by  experience  the  danger  to  the  interests  of  both  Owner  and 
Competitor  from  a  competition  in  which  such  provisions  are  lacking,  it  per- 
mits no  member  to  take  part  in  any  competition  which  does  not  meet  those 
essential  conditions,  and  the  programme  of  which  has  not  been  specifically 
approved.  A  competition  should  be  of  such  form  as  to  establish  equitable  rela- 
tions betv/een  the  Owner  and  the  Competitor.  To  insure  this,  the  require- 
ments should  be  clear  and  definite;  the  competency  of  the  Competitors  should 
be  assured;  the  agreement  between  the  Owner  and  Competitors  should  be 
definite,  as  becomes  a  plain  statement  of  business  relations;  and  the  judgment 
should  be  based  on  expert  knowledge.  The  following  programme  will,  if  adhered 
to,  be  duly  approved  by  the  Institute  Subcommittees  on  Competitions  for 
the  various  chapters  of  the  Institute,  and  by  the  Standing  Committee  on 
Competitions  of  the  Institute. 

*  The  percentage  inserted  should  be  in  accord  with  good  practice. 

t  Good  practice  has  established  the  payments  on  account  as  follows:  Upon  completion 
of  the  preliminary  studies  one-fifth  of  the  total  estimated  fee  less  the  previous  payment; 
upon  completion  of  contract-drawings  and  specifications  two-fifths  additional  of  such  fee; 
for  other  drawings,  for  supervision  and  for  administration,  the  remainder  of  the  fee, 
from  time  to  time,  in  proportion  to  the  progress  of  the  work. 

JAs  authorized  by  the  48th  annual  convention,  1914.  The  American  Institute  of 
Architects,  Document,  Series  A,  No.  115,  Washington,  D,  C.,  January,  1918.  Reprinted 
by  permission. 


1742  .  Architectural  Compotitivons  Part  3 

Programme  of  Competition  for 

(Insert  name  of  proposed  building) 
NOTE.     Throughout  this  programme  the  word  Owner  is  used  to  indicate  either  the 
owner  in  person,  or  those  to  whom  he  has  delegated  his  powers. 

PART   I 

(i)  Proposed  Building.     The 

(Insert  name  of  owner) 

proposes  to  erect  a  new 

(Insert  name  of  building) 

on  the  site  at 

(Insert  location) 

(2)  Authority.    The 

(Insert  name  of  owner) 

has  (delegated  to > 

(Insert  name  or  names  of  individuals) 
authority  to  select  an  architect  to  prepare  the  plans  for,  and  supervise  thfe 
erection  of  the  building. 

NOTE.  If  authority  for  the  erection  of  the  proposed  building  is  granted  by  act  of 
legislature,  ordinance,  etc.,  it  is  desirable  to  make  clear  the  source  of  such  authority. 

(3)  Architectural  Adviser.  The  Owner  has  appointed  as  his  expert  Pro- 
fessional Adviser 

(Insert  name  and  address  of  adviser) 
to  prepare  this  programme  and  to  act  as  his  Adviser  in  the  conduct  of  this 
competition. 

NOTE.  No  competition  shall  be  instituted  without  the  aid  of  a  competent  adviser. 
He  should  be  an  architect  of  the  highest  standing  and  his  selection  should  be  the  Owner's 
first  step.  He  should  be  chosen  with  the  greatest  care,  as  the  success  of  the  competition 
will  depend  largely  upon  his  experience  and  ability.  The  duties  of  the  expert  are  to 
advise  those  who  hold  the  competition  in  regard  to  its  form  and  terms,  to  draw  up  the 
programme,  to  advise  in  choosing  the  Competitors,  to  answer  inquiries  from  Competitors 
and  in  general  to  direct  the  competition. 

(4)  Competitors.     Participation  in  this  competition  is  limited 

(A),  to  the  following  architects: 

(Insert  names  of  invited  competitors) 

and  ^^^  ^^  ^^^^  architects  as  shall  have  made  application  on  or  before 

(Insert  date) 
accompanied  by  evidence  of  their  education  and  experience,  satisfactory  to  the 
Owner  and  the  Professional  Adviser.     It  is  agreed  that  the  names  of  all 
those  admitted  to  the  competition  shall  be  made  public  on  or  before 

(Insert  date) 
The  Owner  agrees  that  he  will  admit  no  one  as  a  Competitor  to  whom  he 
k  not  willing  to  award  the  commission  to  erect  the  building,  in  case  of  his  success 
in  the  competition. 


Architectural  Competitions  1743 

(5)  Tury  of  Award.  The  Owner  agrees  that  there  will  be  a  Jtjry  of  Award 
{A)  which  will  consist  of  the  following  members: 

(Insert  names  of  jury) 

Or  (B)  which  will  consist  of members.     Of  these,  the  Owner 

(Insert  number) 

has  appointed  the  following: 

and 

(Insert  names  of  those  so  selected) 
the  Competitors  will  select  the  remaining  members  of  the  Jury. 

NOTE.  To  insure  a  just  and  wise  award  and  to  protect  the  interests  of  both  the 
Owner  and  the  Competitors,  the  drawings  should  be  submitted  to  a  Jury  chosen  to 
secure  expert  knowledge  and  freedom  from  personal*  bias.  The  Jury  shall  consist  of  at 
least  three  members,  one  of  whom  must,  and  the  majority  of  whom  should,  be  practicing 
architects,  for  example,  a  layman  and  an  architect  selected  by  the  Owner  or  the  Building 
Committee,  and  an  architect  selected  by  the  Competitors.  For  work  of  great  impor- 
tance it  is  desirable  to  increase  the  size  of  the  Jury,  adding  to  it  architects  and  specially 
qualified  laymen.  Some  of  the  advantages  of  a  Jury  so  constituted  are  that  it  thoroughly 
understands  and  can  explain  the  intent  of  the  drawings,  and  discovers  from  them  their 
author's  skill  in  design,  arrangement  and  construction.  Because  of  its  expert  knowledge, 
its  judgment  on  the  merits  of  the  designs  submitted  is  of  the  highest  value  to  the  Owner. 
The  adaption  of  the  recommendation  that  the  architectural  members  of  the  Jury  be  in 
the  majority,  is  not  necessarily  a  cause  of  expense,  for  the  reason  that  in  order  to  insure 
the  proper  conduct  of  competitions,  many  architects  of  standing  are  willing,  if  the  occasion 
warrants,  to  serve  as  Jurors  without  payment,  other  than  actual  expenses.  It  is  cus- 
tomary and  desirable  that  the  Competitors  should  elect  one  or  more  of  the  architectural 
members  of  the  Jury.  It  is  not  advisable  that  the  Professional  Adviser,  who  has 
drawn  up  the  programme,  be  permitted  to  vote  as  a  member  of  the  Jury,  although  he 
may  with  advantage  take  part  in  the  deUberations  of  the  Jury. 

(6)  Authority  of  Jury.  The  Owner  agrees  that  the  Jury  above  named,  or 
selected  as  above  provided,  will  have  authority  to  make  the  award  and  that  its 
decision  in  the  matter  shall  be  final.  Moreover,  this  Jury  will  make  an  award 
to  one  of  those  taking  part  in  this  competition,  unless  no  design  is  submitted 
which  fulfils  the  mandatory  requirements  of  this  programme.  The  Owner 
further  agrees  to  employ  as  architect  for  the  work  as  more  fully  set  forth  herein- 
after, the  author  of  the  design  selected  by  the  Jury  as  its  first  choice. 

NOTE.  If,  under  the  law,  authority  to  make  the  award  cannot  be  delegated  to  the 
Jury,  the  following  form  should  be  substituted  for  Section  (6): 

The  Owner  agrees  that  the  Jury  above  named  or  selected  as  above  provided,  will 
select  the  design  which  appears  to  it  to  be  the  most  meritorious  and  make  a  written  report 
to  the  Owner,  designating  it  by  number.  The  Owner  will  then  consider  this  design 
and  the  report  of  the  Jury  and  will  thereupon,  without  learning  the  identity  of  the  Com- 
petitors, select  as  the  winner  of  the  competition  the  author  of  the  design  selected  by 
the  Jury,  unless  in  his  judgment  there  be  cause  to  depart  from  such  selection,  in  which 
case  he  will,  still  without  learning  the  identity  of  the  Competitors,  select  one  of  the  other 
designs  submitted  in  competition.  The  Owner  further  agrees  that  he  will  pay  to  the 
author  of  the  design  designated  as  most  meritorious  by  the  Jury,  in  case  he  should  not 

be  appointed  Architect  of  the  building,  a  prize  of  $ 

(State  amount  of  prize) 

The  opening  of  the  envelope  containing  the  name  of  the  author  of  the  design  selected 
by  the  Owner  will  automatically  close  the  contract  between  him  and  the  Owner,  printed 
as  Part  III  hereof. 

(7)  Examination  of  Designs  and  Award.  The  Professional  Adviser  will 
examine  the  designs  to  ascertain  whether  they  comply  with  the  mandatory  re-. 


quirements  of  the  programme,  and  will  report  to  the  Jury  any  instance  of  failure 
to  comply  with  these  mandatory  requirements.  The  Owner  further  agrees 
that  the  Jury  will  satisfy  itself  of  the  accuracy  of  the  report  of  the  Professional 
Adviser,  and  will  place  out  of  competition  and  make  no  award  to  any  design 
which  does  not  comply  with  these  mandatory  requirements.  The  Jury  will 
carefully  study  the  programme  and  any  modifications  thereof,  which  may  have 
been  made  through  communications  (see  Section  (12)),  and  will  then  consider  the 
remaining  designs,  holding  at  least  two  sessions  on  separate  days,  and  consider- 
ing at  each  session  all  the  drawings  in  competition,  and  will  make  the  award, 
and  the  classification  of  prize-winners,  if  prizes  are  given,  by  secret  ballot,  and 
by  majority  vote,  before  opening  the  envelopes  which  contain  the  names  of  the 
Competitors.  In  making  the  award  the  Jury  will  thereby  affirm  that  it  has 
made  no  effort  to  learn  the  identity  of  the  various  Competitors,  and  that  it  has 
remained  in  ignorance  of  such  identity  until  after  the  award  was  made.  The 
opening  of  the  envelope  containing  the  name  of  the  author  of  the  selected  design, 
will  automatically  close  the  contract  between  him  and  the  Owner,  printed  as 
Part  III  hereof. 

(8)  Report  of  the  Jury.  The  Jury  will  make  a  full  report  which  will  state 
its  reasons  for  the  selection  of  the  winning  design  and  its  reason  for  the  classifica- 
tion of  the  designs  placed  next  in  order  of  merit,  and  a  copy  of  this  report,  accom- 
panied by  the  names  of  prize-winners,  if  prizes  are  given,  will  be  sent  by  the 
Professional  Adviser  to  each  Competitor.  Immediately  upon  the  opening 
of  the  envelopes,  the  Professional  Adviser  will  notify  all  Competitors,  by 
wire,  of  the  result  of  the  competition. 

(9)  Compensation  to  Competitors.  The  Owner  agrees  to  pay  to  the  suc- 
cessful competitor  within  ten  days  of  the  judgment,  on  account  of  his  fee  for 
services  as  architect,  one-tenth  of  his  total  estimated  fee. 

In  full  discharge  of  his  obligation  to  them  (in  case  prizes  or  fees  are  ofifered), 
the  Owner  agrees: 

(A)  To  pay  the  following  prizes  to  those  ranked  by  the  Jury  next  to  the  suc- 
cessful design:    To  the  design  placed  second  $ ,  to  the  design  placed 

third  $ ,  to  the  design  placed  fourth  $ ,  to  the  design  placed 

fifth  $ ,  etc.,  within  ten  days  of  the  judgment,  or 

(B)  To  pay  to  each  of  the  Competitors  invited  to  take  part  in  this  competi- 
tion, other  than  the  successful  Competitor,  a  fee  of  $ within  ten  days 

of  the  judgment. 

(10)  Exhibition  of  Drawings.  It  is  agreed  that  no  drawings  shall  be  ex- 
hibited or  made  public  until  after  the  award  of  the  Jury.  There  will  be  a  public 
exhibition  of  all  drawings  after  the  judgment,  and  all  drawings,  except  those 
of  the  successful  competitor,  will  be  returned  to  their  authors  at  the  close 
thereof. 

(11)  Use  of  Features  of  Unsuccessful  Designs.  Nothing  original  in 
the  unsuccessful  designs  shall  be  used  without  consent  of,  or  compensation 
to,  the  author  of  the  design  in  which  it  appears.  In  case  the  Owner  de  ires 
to  make  use  of  any  individual  feature  of  an  unsuccessful  design,  the  same  may 
be  obtained  by  adequate  compensation  to  the  designer,  the  amount  of  such 
compensation  to  be  determined  in  consultation  with  the  author  and  the  Pro- 
fessional Adviser. 

(12)  Communications.  (Mandatory.)  If  any  Competitor  desires  infor- 
mation of  any  kind  whatever  in  regard  to  the  competitition,  or  the  programme, 
he  shall  ask  for  this  information  by  anonymous  letter  addressed  to  the  Pro- 
fessional Adviser,  and  in  no  other  way,  and  a  copy  of  this  letter  and  the 


-^  Architectural  Competitions  1745 

answer  thereto  will  be  sent  simultaneously  to  each  Competitor,  but  no  re- 
quest received  after 

(Insert  date) 
will  be  answered. 

(13)  Anonymity  of  Drawings.  (Mandatory.)  The  drawings  to  be  sub- 
mitted shall  bear  no  name  or  mark  which  could  serve  as  a  means  of  identification, 
nor  shall  any  such  name  or  mark  appear  upon  the  wrapper  of  the  drawings,  nor 
shall  any  Competitor  directly  or  indirectly  reveal  the  identity  of  his  designs, 
or  hold  communication  regarding  the  competition  with  the  Owner  or  with  any 
member  of  the  Building  Committee  or  of  the  Jury,  or  with  the  Professional 
Adviser,  except  as  provided  for  under  Communications.  It  is  understood  that 
in  submitting  a  design,  each  Competitor  thereby  affirms  thart  he  has  complied 
with  the  foregoing  provisions  in  regard  to  anonymity  and  agrees  that  any  vio- 
lation of  them  renders  null  and  void  this  agreement  and  any  agreement  arising 
from  it.  With  each  set  of  drawings  must  be  enclosed  a  plain,  opaque,  sealed 
envelope  without  any  superscription  or  mark  of  any  kind,  same  containing  the 
name  and  address  of  the  Competitor.  These  envelopes  shall  be  opened  by  the 
Professional  Adviser  after  the  final  selection  has  been  made,  and  preferably 
in  the  presence  of  the  Jury. 

(14)  Delivery  of  Drawings.  (Mandatory.)  The  drawings  submitted  in 
this  competition  shall  be  securely  wrapped,  addressed  to  the  Professional  Ad- 
viser at 

. in  plain  lettering  and 

(Insert  address  for  delivery  of  drawings) 
with  no  other  lettering  thereon,  and  delivered  at  this  address  not  later  than 

(Insert  date  and  hour) 
In  case  drawings  are  sent  by  express,  they  may  be  delivered  to  an  express  com- 
pany at  the  above  date  and  hour,  in  which  case  the  express  company's  receipt, 
bearing  date  and  hour,  shall  be  mailed  immediately  to  the  Professional  Ad- 
viser as  evidence  of  delivery. 

PART  II 

(15)  Site.     The  site  of  the  building  is  as  follows 

(Insert  description  of  site,  and  provide  topographical  map  giving  dimensions,  grades,  etc.) 

NOTE.  The  site  should  be  carefully  described  and  a  survey  of  the  property  should  be 
attached  and  included  as  part  of  the  programme.  Conditions  pertaining  to  the  site  and 
to  neighboring  buildings  frequently  become  determining  factors  in  a  design.  Photo- 
graphs showing  surrounding  buildings  and  landscape-conditions  may  with  advantage  be 
included. 

(16)  Cost.  (Mandatory.)  For  the  purpose  of  this  competition  the  cost  of 
the  building  shall  be  figured  at cts  per  cu  ft,  and  the  total  thereof 

(Insert  number) 

figured  on  this  basis  shall  not  exceed 

(Insert  limit  of  cost) 

(17)  Cubage.  (Mandatory.)  Cubage  shall  be  so  computed  as  to  show  as 
exactly  as  possible  the  actual  volume  of  the  building,  calculated  from  the  finished 
level  or  levels  of  the  lowest  floor  to  the  highest  points  of  tlTe  roofs,  and  contamed 
within  the  outside  surfaces  of  the  walls.  Pilasters,  cornices,  balconies  and  other 
similar  projections  shall  not  be  included.  Porticos  with  engaged  columns  and 
similar  projections  shall  be  taken  as  solids  and  figured  to  the  outer  face  of  the 
columns.    When  columns  are  free-standing,  one-half  of  the  volume  of  the  Dorti- 


1746  Architectural  Competitions  Partfl 

cos  shall  be  taken.  There  shall  also  be  included  in  the  cubage  the  actual  volume 
of  all  parapets,  towers,  lanterns,  dormers,  vaults,  and  other  features  adding  to 
the  bulk  of  the  building,  also  the  actual  volume  of  exterior  steps  above  grade. 
Light-wells  of  an  area  of  loss  than  400  sq  ft  shall  not  be  deducted.  In  calculat- 
ing cubage,  account  shall  be  taken  of  variations  in  the  exterior  wall-surface,  as 
for  example,  the  projection  of  a  basement-story  beyond  the  general  line  of  the 
building.  A  figured  diagram  showing  method  adopted  in  cubing  shall  accom- 
pany each  set  of  drawings. 

(18)  Drawings.  (Mandatory.)  The  drawings  submitted  shall  be  made 
according  to  the  following  hst,  at  the  scale  given,  and  rendered  as  noted;  and 
no  other  drawings  than  these  shall  be  submitted: 

(Insert  list,  scale  and  method  of  rendering) 

NOTE.  The  drawings  submitted  should  be  the  least  number  necessary  to  set  forth 
clearly  the  solution  of  the  problem,  and  the  scale  of  these  drawings  the  smallest  com- 
patible with  the  requirement  that  the  intention  of  each  Competitor  be  made  clear  to  an 
expert  Jury.  Where  the  number  and  scale  of  drawings  is  reduced  to  the  minimum,  and 
simple  methods  of  rendering  imposed,  the  Competitors  are  enabled  to  devote  their  time 
and  energy  to  the  study  of  the  problem,  which  is  the  serious  business  of  a  competition, 
instead  of  upon  draughtsmanship  and  rendering,  which  when  carried  beyond  a  certain 
point,  are  of  no  value  whatever  in  determining  the  fitness  of  the  Competitors  to  handle 
the  work  of  erecting  the  building,  for  which  the  competition  is  being  held. 

PART  III 

Agreement  between  Owner  and  Competitors 

In  consideration  of  the  submission  of  drawings  in  this  competition,  and  the 
mutual  promises  enumerated  in  the  subjoined  Conditions  of  Contract  be- 
tween Architect  and  Owner  the  Owner  agrees,  and  each  Competitor  agrees 
if  the  aw.ird  be  made  in  his  favor,  immediately  to  enter  into  a  contract  contain- 
ing all  the  Conditions  here  following,  and  until  such  contract  is  executed,  to  be 
bound  by  the  said  Conditions. 

Conditions  of  Contract  between  Architect  and  Owner 

Duties  of  the  Architect 

(i)  Design.  The  architect  is  to  design  the  entire  building  and  its  imme- 
diate surroundings  and  is  to  design  or  direct  the  design  of  its  constructive, 
engineering  and  decorative  work  and  its  fixed  equipment  and,  if  further  re- 
tained, its  movable  furniture  and  the  treatment  of  the  remainder  of  its  grounds.' 

(2)  Drawings  and  Specifications.  The  architect  is  to  make  such  revision 
of  his  competitive  scheme  as  may  be  necessary  to  complete  the  preliminary 
studies;  and  he  is  to  provide  drawings  and  specifications  necessary  for  the  con- 
duct of  the  work.  All  such  instruments  of  service  are  and  remain  the  prop- 
erty, of  the  architect. 

(3)  Administration.  The  architect  is  to  prepare  or  advise  as  to  all  forms 
connected  with  the  making  of  proposals  aud  contracts,  to  issue  all  certificates 
of  payment,  to  keep  proper  accounts  and  generally  to  discharge  the  necessary 
aiiministrative  duties  connected  with  the  work. 

(4)  Supervision.  The  architect  is  to  supervise  the  execution  of  all  the 
work  committed  to  his  control. 


Architect  uru.1  Competitions  1747 

Duties  of  the  Owner 

(5)  Payments.  The  Owner  is  to  pay  the  architect  for  his  services  a 
sum  equal  to per  cent  upon  the  cost  of  the  work. 

NOTE.  The  percentage  inserted  should  be  in  accord  with  good  practice.  The  times 
and  amounts  of  payments  should  be  here  stated.  Good  practice  has  established  the 
payments  on  account  as  follows:  Upon  completion  of  the  ,preliminary  studies  one-fifth 
of  Hie  total  estimated  fee  less  the  previous  payment;  upon  completion  of  contract-drawings 
ar.d  specifications  two-fifths  additional  of  sucK  fee;  for  other  drawings,  for  supervision 
and  for  administration,  the  remainder  of  the  fee,  from  time  to  time,  as  the  work  progresses. 

(6)  Reimbursements.  The  Owner  is  to  reimburse  the  architect  from  time 
to  lime,  the  amount  of  expenses  necessarily  incurred  by  him  or  his  deputies 
while  traveling  in  the  discharge  of  duties  connected  with  the  work. 

(7)  Service  of  Engineers.    The  Owner  is  to  reimburse  the  architect, 

the  cost  of  the  services  of  engineers  for 

(Insert  nature  of  \v6rk  for  which  the  Owner  agrees  that  engineers  shall  be  employed  at 
his  expense) 

The  selection  of  such  engineers  and  their  compensation  shall  be  subject  to 
the  approval  of  the  Owner. 

(8)  Information,  Clerk  of  the  Works,  Etc.  The  Owner  is  to  give  all  in- 
formation as  to  his  requirements;  to  pay  for  all  necessary''  surveys,  borings  and 
tests,  and  for  the  continuous  services  of  a  clerk  of  the  works  whose  competence 
is  approved  by  the  architect. 

PART   IV 

Requirements  of  the  Building 

NOTE.  For  the  same  reason  that  elaborate  drawings  are  undesirable,  it  is  advisable 
to  avoid  hngthy  and  detailed  instructions  as  to  the  desired  accomniodations,  as  they 
confuse  the  problem  and  hamper  the  Competitors;  and  the  Owner  loses  thereby  the 
benefit  he  might  gain  in  allowing  the  Competitors  freedom  to  develop  solutions  which 
they  would  not  otherwise  be  at  liberty  to  suggest.  It  should  be  borne  in  mind  that  either 
the  cost  of  the  building,  as  determined  by  its  cubical  contents,  should  be  fixed,  or  the 
requirements  of  the  Owner  in  regard  to  the  design,  materials  of  construction,  dimensions 
of  rooms,  etc.,  should  be  fixed,  but  not  both.  If,  on  the  one  hand,  the  cubical  contents 
and  cost  is  fixed,  it  should  be  stated  that  the  requirements  of  the  Owner  must  be  adhered 
to  as  closely  as  possible  by  Competitors;  if,  on  the  other  hand,  the  requirements  of  the 
Owner  are  definitely  fixed,  it  may  be  stated  that  the  cubical  contents  of  each  design, 
while  not  limited,  will  be  taken  into  consideration  in  making  the  award.  In  case  the 
sizes  of  certain  rooms,  etc.,  are  definitely  fixed,  the  word  Mandatory  should  be  placed 
at  the  head  of  the  paragraph  referring  to  these  rooms. 

Here  should  follow  a  list  of  rooms  required,  together  with  sizes  and  other  data 
which  apply  to  the  building  under  consideration. 


1748  Standard  Documents  Part  C 

THE  STANDARD  DOCUMENTS  OF  THE  AMERICAN 
INSTITUTE   OF  ARCHITECTS* 

Introductory  Notes.  This  introductory  paragraph  is  from  an  article  t  by  R. 
Clipston  Sturgis,  President  of  The  American  Institute  of  Architects.  "  For  many 
years  builders'  and  owners  have  commonly  used  an  agreement  recognized  as  in- 
adequate and  imperfect,  and  one  apt  to  lead  to  serious  misunderstandings,  if  not 
to  legal  diflGiculties.  Architects  entrusted  with  important  work  and  its  accom- 
panying responsibilities  have  endeavored  to  have  agreements  drawn  which  would 
adequately  safeguard  the  interests  involved.  When,  some  nine  years  ago  (1907), 
the  Institute  attempted  to  prepare  a  new  standard  agreement,  it  found  already 
in  use  a  considerable  number  of  forms  prepared  by  architects,  differing  in  detail 
but  agreeing  in  one  main  point.  This  one  point  was  that  the  contract  and  the 
conditions  of  the  contract  should  be  treated  as  two  branches  of  the  same  agree- 
ment, not  as  one  document,  nor  yet  as  two.  The  contract  was  to  be  as  brief  as 
possible,  stating  simply  what  the  obligation  was.  The  conditions  of  the  contract, 
complicated  and  involved,  yet  essential  to  the  contract,  were  of  necessity  com- 
paratively lengthy.  The  most  difficult  part  of  the  work,  surveying  the  field  and 
breaking  out  the  way,  was  done  by  the  Committees  on  Contracts  and  Specifica- 
tions during  the  years  1906  to  191 1,  and  resulted  in  the  first  edition  of  the 
STANDARD  DOCUMENTS,  pubHshed  in  1911.  At  that  time  some  thought  the  prob- 
lem solved;  others  thought  it  but  an  important  step  forward;  which  latter  proved 
to  be  the  fact.  These  first  documents,  excellent  as  they  were  as  text-books,  were 
not  suitable  for  everyday  use.  The  Institute  again  took  up  the  problem,  this 
time  with  the  definite  aim  to  produce  a  document  which  should  entirely  replace 
the  uniform  agreement  when  the  contract  for  its  publication  expired  in  May, 
19 1 5.  This  has  been  done  and  the  carefully  studied  agreement  and  condi- 
tions OF  THE  contract  presented  to  the  convention  in  December,  19 14,  have 
been  further  studied  and  improved  and  are  now  (19 15)  on  the  market  for  general 
use.  In  the  final  study  between  January  and  May,  1915,  the  Institute  had  the 
advantages  of  cooperation  with  representatives  of  many  of  the  building  trades 
and  the  advice  of  counsel  representing  the  Institute  and  counsel  representing 
the  building  trades.  The  document,  like  its  predecessor,  will  now  come  to  the 
test  of  actual  use.  It  will  prove  to  be  imperfect  and  revised  sections  will  be 
necessary,  but  it  is  believed  to  be  in  the  main  a  fair  and  comprehensive  agree- 
ment and  one  that  is  practical  and  fit  for  general  use.  Architects  everywhere 
are  urged  to  use  and  test  this  form,  and  criticism  from  owners  and  builders  will 
be  gladly  received  and  considered.  In  addition  to  this  most  important  docu- 
ment the  committee  has  prepared  and  the  Institute  has  published  a  form  of 
BOND,  a  LETTER  OF  ACCEPTANCE  by  a  Contractor  of  a  sub-contractor's  bid,  and  an 
agreement  between  a  contractor  and  sub-contractor.  Many  architects  who  have 
done  work  on  which  a  bond  has  been  required  have  been  surprised  at  the  ease 
with  which  the  obligations  of  the  bond  could  be  evaded.  In  most  cases,  because 
someone,  architect,  contractor,  or  owner,  had  invalidated  the  bond.  The  new 
form  of  bond  is  prepared  for  insuring,  as  far  as  possible,  that  the  bonding  com- 
pany shall  discharge  its  obligations  and  protect  the  owner  who  pays  for  this 
protection.  The  letter  from  contractor  to  sub-contractor  is  intended  to 
provide  a  simple  form  whereby  the  mutual  obhgations  of  the  two  shall  be  clearly 
defined.  The  agreement  between  contractor  and  sub-gontractor  accom- 
plishes the  same  purpose  in  a  somewhat  more  formal  way." 

*  Third  Edition,  copyrighted  by  The  American  Institute  of  Architects,  1915-1918,  and 
inserted  here  by  permission. 

t  Published  in  the  Journal  of  The  American  Institute  of  Architects,  June,  1915. 


Standard  Documents  1749 

The  Development  of  the  Standard  Documents.  In  the  year  1887  The 
American  Institute  of  Architects,  the  Western  Association  of  Architects  and  the 
National  Association  of  Builders,  thinking  it  desirable  to  estabhsh  better  practice 
in  the  matter  of  building  contracts,  undertook  the  preparation  of  a  form  of  con- 
tract satisfactory  to  all.  Under  the  name  of  the  uniform  contract  this  form 
attained  wide  acceptance  and  has  been  long  in  use.  About  the  year  1907,  feeling 
that  practice  had  advanced  to  a  point  no  longer  fully  reflected  by  the  uniform 
CONTRACT,  the  Institute  undertook  a  general  study  of  the  subject  with  a  view 
to  developing  a  form  of  contract  clear  in  thought,  equitable,  applicable  to  work 
of  almost  all  classes,  binding  in  law  and  a  standard  of  good  practice.  The  work 
was  entrusted  to  the  Standing  Committee  on  Contracts  and  Specifications,  who 
spent  four  years  on  it,  studying  the  uniform  contract  and  forms  in  use  by  some 
thirty  well-known  architects,  and  submitted  various  drafts  for  criticism  to  the 
chapters  of  the  Institute  and  to  engineers,  contractors  and  architects  throughout 
the  country.  The  documents  were  prepared  under  the  advice  of  Francis  Fisher 
Kane,  counsel  for  the  Institute,  and  Ernest  Eidlitz,  and  with  the  able  and  careful 
criticism  of  Professor  Samuel  Williston  of  the  Harvard  Law  School,  and  with  the 
assistance  of  James  W.  Pryor,  in  their  editing.  The  Institute  gave  its  approval 
to  the  work  in  191 1.  The  Standing  Committee  on  Contracts  and  Specifications, 
during  the  preparation  of  the  first  edition  of  the  standard  forms,  consisted  of 
Grosvenor  Atterbury,  Chairman;  Allen  B.  Pond,  Secretary;  Frank  Miles  Day» 
William  A.  Boring,  Frank  C.  Baldwin,  Frank  W.  Ferguson,  Alfred  Stone  and 
G.  L.  Heins.  Criticisms  of  the  first  edition  of  the  documents  were  invited  by 
the  Institute  and  during  the  year  19 13  a  group  of  architects  and  builders  in  Bos- 
ton, known  as  the  Joint  Committee  of  the  Boston  Society  of  Architects,  and  of 
the  Master  Builders'  Association,  gaVe  much  sincere  study  to  the  subject.  At 
the  same  time  the  National  Association  of  Builders'  Exchange  offered  a  detailed 
criticism  of  the  documents. 

In  19 1 4  the  Institute  instructed  its  Standing  Committee  on  Contracts  and 
Specifications  to  undertake  a  general  revision  with  a  view  to  making  the  con- 
ditions simpler  in  wording  and  more  equitable.  The  committee  was  empowered 
to  hold  conferences  with  organizations  so  desiring.  Subcommittees  for  the  terri- 
tory of  the  several  chapters  of  the  Institute  were  appointed  and  collaborated  with 
the  standing  committee.  The  Boston  group  presented  its  ideas  in  the  form  of  an 
entirely  new  draft  which  proved  of  high  value  and  its  Chairman,  W.  Stanley 
Parker,  was  present  with  the  Standing  Committee  at  nearly  all  its  meetings. 
The  Committee  had  a  joint  meeting  with  representatives  of  the  National  Asso- 
ciation of  Builders'  Exchanges  and  thereafter  the  counsel  of  the  Association, 
W.  B.  King,  and  the  counsel  of  the  Institute,  Louis  Barcroft  Runk,  collabo- 
rated most  effectively  with  the  committee.  The  general  conditions  were 
entirely  rewritten  and  in  response  to  the  strong  desire  of  contractors  and  subcon- 
tractors, the  principle  of  general  arbitration,  subject  to  limitations  in  the 
documents,  was  adopted,  and  provisions  relative  to  the  relations  of  the  con- 
tractor and  his  subcontractors  were  included  in  the  documents.  After  much 
study,  conference  and  criticism,  a  draft  of  the  second  edition  was  issued  by 
authority  of  the  Institute,  April  i,  19 15.  During  the  revision  of  the  documents, 
the  Standing  Committee  on  Contracts  and  Specifications  consisted  of  Frank 
Miles  Day,  Chairman;  Allen  B.  Pond,  Sullivan  W.  Jones,  Clarence  A.  Martin, 
Norman  M.  Isham,  Octavius  Morgan,  Thomas  Nolan,  A.  O.  Elzner,  M.  B. 
Medary,  Jr.,  Jos.'  Evans  Sperry,  Frank  W.  Ferguson  and  Samuel  Stone. 

The  Construction  of  the  Standard  Documents.  An  agreement,  and 
drawings  and  specifications  are  the  necessary  parts  of  a  building  contract. 
Many  conditions  of  a  general  character  may  be  placed  at  will  in  the  agreement 


1750  Standard  Documents  Part  3 

or  in  the  specifications.  It  is,  however,  wise  to  assemble  them  in  a  single 
document  and,  since  they  have  as  much  bearing  on  the  drawings  as  on  the 
SPKCiFicATiONS,  and  even  more  on  the  business  relations  of  the  contracting 
parties,  they  are  properly  called  the  general  conditions  of  the  contract. 

As   the   AGREEMENT,    GENERAL  CONDITIONS,   DRAWINGS   and   SPECIFICATIONS   are 

the  constituent  elements  of  the  contract  and  are  acknov/ledged  as  such  in  the 
Agreement,  they  are  correctly  termed  the  contract  documents.  Statements 
made  in  any  one  of  them  are  just  as  binding  as  if  made  in  the  agreement.  The 
Institute's  forms,  although  intended  for  use  in  actual  practice,  should  also  be 
regarded  as  a  code  of  reference  representing  the  judgment  of  the  Institute  as  to ' 
what  constitutes  good  practice  and  as  such  they  may  be  drawn  upon  by  archi- 
tects in  improving  their  own  forms.  Although  the  forms  are  suited  for  use  in 
connection  with  a  single  or  general  contract,  they  are  equally  applicable  to  an 
operation  conducted  under  separate  contracts. 

Titles  of  the  Standard  Contract  Documents.*  The  new  standard  con- 
tract DOCUiffiNTS  of  The  American  Institute  of  Architects  are  now  on  salef  by 
dealers  in  office  and  drafting-supphes  in  all  the  large  cities  of  the  country, 
and  replace  the  old  uniform  contract.  The  following  are  the  titles  of  the 
standard  documents:  a.  i.  form  of  agreement  and  a.  2.  general 
Conditions  of  the  Contract.  B.  Bond  of  suretyship.  C.  Form  of 
Subcontract.  D.  Letter  of  Acceptance  of  Subcontractor's  Proposal. 
A  cover  in  heavy  paper  with  valuable  explanatory  notes  is  sent  without  charge 
with  each  complete  set  of  the  documents.  These  documents  have  received 
the  full  approval  of  the  Institute,  through  its  conventions,  board  of  directors 
and  officers.  They  are  the  outcome  of  nine  years  of  continuous  work,  by  a 
Standing  Committee  on  Contracts  and  Specifications.  This  committee,  com- 
prising some  of  the  ablest  American  architects,  was  assisted  by  the  Institute's 
thirty-nine  chapters;  advised  by  eminent  legal  specialists  in  contract  law  and 
aided  by  representatives  of  the  Building  and  Trade  Associations  of  the  United 
States.     The  Standard  Documents  have  received  the  formal  approval  of  the 

*  Third  Edition,  copyrighted  by  the  American  Institute  of  Architects. 

t  Notice  to  Architects,  Builders  and  Contractors.  The  contract  forms  may  be 
obtained  singly  or  in  lots  from  the  local  dealers.  If  your  dealer  cannot  supply  you  send 
your  order  and  his  name  to  The  Executive  Secretary,  A.  I.  A.,  The  Octagon,  Washington, 
D.  C.  All  orders  must  include  the  necessary  remittance  irrespective  of  A.  I.  A.  member- 
ship and  irrespective  of  commercial  standing  of  purchaser.  The  Institute  has  adopted 
these  CASH  terms,  from  which  no  exception  will  be  made  to  anybody,  in  order  to  reduce 
cost  of  accountancy  and  thereby  reduce  expense  to  the  user.  Remittances  may  be  by 
check,  money-order,  cash,  or  stamps. 

Prices  for  Single  Copies:  Agreement  and  General  Conditions  in  cover,  $0.14;  General 
Conditions  without  Agreement,  $0.10;  Agreement  without  General  Conditions,  $0.03; 
Bond  of  Suretyship,  $0.02;  Form  of  Subcontract,  $0.03;  Letter  of  Acce{)tance  of  Sub- 
contractor's Proposal,  $0.02;  Cover  (heavy  paper,  with  valuable  notes),  $0.01;  Com- 
plete set  in  cover,  $0.20.     A  Trial  set  will  be  delivered  upon  receipt  of  ten  2-ceut  stamps. 

Prices  for  Quantities  and  Discounts  to  Architects,  Builders  and  Contractors. 
Orders  for  quantities  are  subject  to  the  following  discounts  (which  are  also  given  by  all 
dealers) : 

Five  per  cent  on  lots  of  100  (one  kind  or  assorted);  10%  on  lots  of  500  (one  kind  or 
assorted);  15%  on  lots  of  i  000  (one  kind  or  assorted).  As  these  documents  are  printed 
on  sheets,  8 H  by  11  ins,  and  in  large  quantities,  they  cannot  be  supplied  with  any  indi- 
vidual names  or  printing  different  from  the  standard  forms.  The  Institute  does  not 
wish  to  encourage  the  use  of  the  agreement  with  general  conditions  other  than  those 
endorsed  by  it,  but  on  request  will  sell  the  agreements  separate  from  tlic  standard 
GENERAL  CONDITIONS  at  3  cts  each. 


Standard  Documents  1751 

National  Association  of  Builders'  Exchanges,  the  National  Association  of  Master 
Plumbers,  the  National  Association  of  Sheet  Metal  Contractors  of  the  United 
States,  the  National  lilectrical  Contractors'  Association  of  the  United  States, 
the  National  Association  of  Marble  Dealers,  the  Building  Granite  Quarries 
Association,  the  Building  Trades  Employers'  Association  of  the  City  of  New 
York,  and  the  Heating  and  Piping  Contractors'  National  Association. 


A.  I.     THE    STANDARD    FORM     OF    AGREEMENT    BETWEEN 
CONTRACTOR    AND    OWNER* 

ISSUED  BY  THE  AMERICAN  INSTITUTE  OF  ARCtllTECTS  t 

This  form  has  been  approved  by  the  National  Association  of  Builders'  Exchanges,  The 
National  Association  of  Master  Plumbers,  the  National  Association  of  Sheet  Metal 
Contractors  of  the  Utiited  States,  the  National  Electrical  Contractors'  Association  of 
the  United  States,  the  National  Association  of  Marble  Dealers,  the  Building  Granite 
Quarries  Association,  the  Building  Trades  Employers'  Association  of  the  City  of  New 
York,  and  the  Heating  and  Piping  Contractors'  National  Association. 

THIRD  EDITION,  COPYRIGHT   1915-1918,  BY  THE  AMERICAN  INSTITUTE  OF  ARCHI- 
TECTS, THE  OCTAGON,  WASHINGTON,  D.  C.     THIS  FORM  IS  TO  BE  USED  ONLY 
WITH    THE    STANDARD    GENERAL    CONDITIONS    OF    THE    CONTRACT 

THIS  AGREEMENT,  made  the 

day  of in  the  year  Nineteen  Hundred  and 

by  and  between (Two  blank  lines)  t 

hereinafter  called  the  Contractor,  and (Two  blank  lines) 

hereinafter  called  the  Owner 

WITNESSETH,  that  the  Contractor  and  the  Owner  for  the  considerations 
hereinafter  named  agree  as  follows: 

Article  i .  The  Contractor  agrees  to  provide  all  the  materials  and  to  perform 
all  the  work  shown  on  the  Drawings  and  described  in  the  Specifications  entitled 

(Here  insert  the  caption  descriptive  of  the  work  as  used  in  the  Proposal,  General  Con- 
ditions, Specifications,  and  upon  the  Drawings.) 
(Five  blank  lines) 

prepared  by (Two  blank  lines) 

acting  as,  and  in  these  Contract  Documents  entitled  the  Architect,  and  to  do 
everything  required  by  the  General  Conditions  of  the  Contract,  the  Specifica- 
tions and  the  Drawings. 

Article  2.  The  Contractor  agrees  that  the  work  under  this  Contract  shall 
be  substantially  completed. 

(Here  insert  the  date  or  dates  of  completion,  and  stipulations  as  to  liquidated 

damages  if  any.) 

(Eight  blank  lines) 

Article  3.  The  Owner  agrees  to  pay  the  Contractor  in  current  funds  for  the 
performance  of  the  Contract. 

($ )     subject 

to  additions  and  deductions  as  provided  in  the  General  Conditions  of  the  Con- 

*  Published  by  permission  of  The  American  Institute  of  Architects, 
t  For  use  when  a  stipulated  sum  forms  the  basis  of  payment. 

t  Dotted  lines,  as  indicated,  are  in  the  standard  documents  and  are  omitted  here  to 
save  space. 


1752  Standard  Documents  Part  S 

tract  and  to  make  payments  on  account  thereof  as  provided  therein,  as  follows 

On  or  about  the day  of  each  month 

per  cent  of  the  value,  proportionate  to  the  amount  of  the  Contract,  of  laboi 

and  materials  incorporated  in  the  work 

up  to  the  first  day  of  that  month  as  estimated 

by  the  Architect,  less  the  aggregate  of  previous  payments.     On  substantia' 
completion  of  the  entice  work,  a  sum  sufficient  to  increase  the  total  payment; 

to per  cent  of  the  contract  price,  and 

days  thereafter,  provided  the  work  be  fully  completed  and  th( 

Contract  fully  performed,  the  balance  due  under  the  Contract. 
(Five  blank  lines) 

Article  4.  The  Contractor  and  the  Owner  agree  that  the  General  Condition; 
of  the  Contract,  the  Specifications  and  the  Drawings,  together  with  this  Agree 
ment,  form  the  Contract,  and  that  they  are  as  fully  a  part  of  the  Contract  as  ij 
hereto  attached  or  herein  repeated;  and  that  the  following  is  an  exact  enumera- 
tion of  the  Specifications  and  Drawings: 
(Thirty-five  blank  lines) 

The  Contractor  and  the  Owner  for  themselves,  their  successors,  executors 
administrators  and  assigns,  hereby  agree  to  the  full  performance  of  the  covenant; 
herein  contained. 

IN  WITNESS  WHEREOF  they  have  executed  this  agreement,  the  day  anc 
year  first  above  written. 


A.     2.     THE  GENERAL  CONDITIONS  OF  THE  CONTRACT  * 

STANDARD   FORM   OF  THE  AMERICAN   INSTITUTE  OF 
ARCHITECTS 

This  form  has  been  approved  by  the  National  Association  of  Builders'  Exchanges,  The 
National  Association  of  Master  Plumbers,  the  National  Association  of  Sheet  Metal 
Contractors  of  the  United  States,  the  National  Electrical  Contractors'  Association  of  the 
United  States,  the  National  Association  of  Marble  Dealers,  the  Building  Granite  Quarries 
Association,  the  Building  Trades  Employers'  Association  of  the  City  of  New  York, 
and  the  Heating  and  Piping  Contractors'  National  Association. 

THIRD  EDITION,  COPYRIGHT   1915-1918,  BY  THK  AMERICAN  INSTITUTE  OF 
ARCHITECTS,  THE  OCTAGON,   WASHINGTON,  D.  C. 

Index  to  the  Articles  of  t!ie  General  Conditions 


I. 

Definitions. 

8. 

Samples. 

2. 

Documents. 

9- 

The  Architect's  Status. 

3>. 

Details  and  Instructions. 

10. 

The  Architect's  Decisions. 

4- 

Copies  Furnished. 

II. 

Foreman,  Supervision. 

%. 

Shop  Drawings. 

12. 

Materials.  Appliances,  Employees. 

6. 

Drawings  on  the  Work. 

13- 

Inspection  of  Work. 

7- 

Ownership  of  Drawings. 

14. 

Correction  Befoxe  Final  Payment. 

•Published  by  permission  of  The  American  Institute  of  Architects. 


Standard  Documents 


1753 


32.  Use  of  Premises. 

33.  Cleaning  Up. 

34.  Cutting,  Patching  and  Digging. 

35.  Delays. 

36.  Owner's  Right  to  Do  Work. 

37.  Owner's  Right  to  Terminate  Contract. 

38.  Contractor's    Right    to  Stop  Work  or 

Terminate  Contract. 

39.  Damages. 

40.  Mutual  Responsibility  of  Contractors. 

41.  Separate  Contracts. 
Assignment. 
Subcontracts. 

Relations  of  Contractor  and  Subcon- 
tractor. 

Arbitration. 


42. 
43- 
44. 


45- 


5.  Deductions  for  Uncorrected  Work. 

6.  Correction  After  Final  Payment. 

7.  Protection  of  Work  and  Property. 
:8.  Emergencies. 

:9.  Contractor's  LiabilHty  Insurance. 
>o.  Owner's  Liability  Insurance. 

Fire  Insurance. 
!2.  Guaranty  Bonds. 
>3.  Cash  Allowances. 
!4.  Changes  in  the  Work. 
!5.  Claims  for  Extras. 
>6.  Applications  for  Payments. 
17.  Certificates  and  Payments. 
>8.  Payments  Withheld. 
>9.  Liens. 

JO.  Permits  and  Regulations. 
.  Royalties  and  Patents. 

Art.  I.     Principles  and  Definitions. 

(a)  The  Contract  Documents  consist  of  the  Agreement,  the  General  Con- 
iitions  of  the  Contract,  the  Drawings  and  Specifications,  including  all  modi- 
ications  thereof  incorporated  in  the  documents  before  their  execution.  These 
iorm  the  Contract. 

(b)  The  Owner,  the  Contractor  and  the  Architect  are  those  named  as  such  in 
the  Agreement.  They  are  treated  throughout  the  Contract  Documents  as  if 
each  were  of  the  singular  number  and  masculine  gender. 

(c)  The  term  Subcontractor,  as  employed  herein,  includes  only  those  having 
a  direct  contract  with  the  Contractor  and  it  includes  one  who  furnishes  material 
worked  to  a  special  design  according  to  the  plans  or  specifications  of  this  work, 
but  does  not  include  one  who  merely  furnishes  material  not  so  worked. 

(d)  Written  notice  shall  be  deemed  to  have  been  duly  served  if  delivered  in 
person  to  the  individual  or  to  <i  member  of  the  firm  or  to  an  officer  of  the  corpora- 
tion for  whom  it  is  intended,  or  if  delivered  at  or  mailed  to  the  last  business 
address  known  to  him  who  gives  the  notice. 

(e)  The  term  "work"  of  the  Contractor  or  Subcontractor  mcludes  labor  or 
materials  or  both. 

(f)  All  time-limits  stated  in  the  Contract  Dccum.ents  are  of  the  essence  ot 

the  contract.  ,  ..         r  ^1  • 

(g)  The  law  of  the  place  of  building  shall  govern  the  construction  of  this 

contract. 

Art  2.  Execution,  Correlation  and  Intent  of  Documents.  The  Con- 
tract Documents  shall  be  signed  in  duplicate  by  the  Owner  and  Contractor.  In 
case  of  failure  to  sign  the  General  Conditions,  Drawings  or  Specifications  the 
Architect  shall  identify  them.  The  Contract  Documents  are  complementary, 
and  what  is  called  for  by  any  one  shall  be  as  binding  as  if  called  for  by  al^ 
The  intention  of  the  documents  is  to  include  all  labor  and  materials  reasonably 
necessary  for  the  proper  execution  of  the  work.  It  is  not  intended, 
however,  that  materials  or  work  not  covered  by  or  proper  y  inferable  from  any 
heading,  branch,  class  or  trade  of  the  specifications  shall  be  supp  led  unless 
distinctly  so  noted  on  the  drawings.  Materials  or  work  described  in  words 
which  so  applied  have  a  well-known  technical  or  trade  meaning  shall  be  held 
to  refer  to  such  recognized  standards. 

Art  %  Detail  Drawings  and  Instructions.  The  Architect  shall  furnish, 
with  reasonable  promptness,  additional  instructions,  by  means  of  drawings  or 
otherwise,  necessary  for  the  proper  execution  of  the  work.     All  such  drawings. 


1754  Standard  Documents  Part  3 

and  instructions  shall  be  consistent  with  the  Contract  Documents,  true  develop- 
ments thereof,  and  reasonably  inferable  thereform.  The  work  shall  be  executed 
in  conformity  therewith  and  the  Contractor  shall  do  no  work  without  proper 
drawings  and  instructions.  In  giving  such  additional  instructions,  the  Architect 
shall  have  authority  to  make  minor  changes  in  the  work,  not  involving  extra 
costs,  and  not  inconsistent  with  the  purposes  of  the  building.  The  Contractor 
and  the  Architect,  if  either  so  requests,  shall  jointly  prepare  a  schedule,  subject 
to  change  from  time  to  time  in  accordance  with  the  progress  of  the  work, 
fixing  the  latest  dates  at  which  the  various  detail  drawings  will  be  required, 
and  the  Architect  shall  furnish  them  in  accordance  with  that  schedule.  Under 
like  conditions,  a  schedule  shall  be  prepared,  fixing  dates  for  the  submission 
of  shop  drawings,  for  the  beginning  of  manufacture  and  installation  of  materials 
and  for  the  completion  of  the  various  parts  of  the  work. 

Art.  4.  Copies  Furnished.  Unless  otherwise  provided  in  the  Contract 
Documents  the  Architect  will  furnish  to  the  Contractor,  free  of  charge,  all 
copies  of  drawings  and  specifications  reasonably  necessary  for  the  execution  of 
the  work. 

Art.  5.  Shop  Drawitigs.  The  Contractor  shall  submit,  with  such  prompt- 
ness as  to  cause  no  delay  in  his  own  work  or  in  that  of  any  other  contractor, 
two  copies  of  all  shop  or  setting  drawings  and  schedules  required  for  the  work 
of  the  various  trades  and  the  Architect  shall  pass  upon  them  with  reasonable 
promptness.  The  Contractor  shall  make  any  corrections  required  by  the 
Architect,  file  with  him  two  corrected  copies  and  furnish  such  copies  as  may 
be  needed.  The  Architect's  approval  of  such  drawings  or  schedules  shall  not 
relieve  the  Contractor  from  responsibility  for  deviations  from  drawings  or 
specifications,  unless  he  has  in  writing  called  the  Architect's  attention  to  such 
deviations  at  the  time  of  submission,  nor  shall  it  relieve  him  from  responsibility 
for  errors  of  any  sort  in  shop  drawings  or  schedules. 

Art.  6.  Drawings  and  Specifications  on  the  Work.  The  Contractor  shall 
keep  one  copy  of  all  drawings  and  specifications  on  the  work,  in  good  order, 
available  to  the  Architect  and  to  his  representatives. 

Art.  7.  Ownership  of  Drawings  and  Models.  All  drawings,  specifications 
and  copies  thereof  furnished  by  the  Architect  are  his  property.  They  arc  not 
to  be  used  on  other  work  and,  with  the  exception  of  the  signed  contract-set, 
are  to  be  returned  to  him  on  request,  at  the  completion  of  the  work.  All 
models  are  the  property  of  the  Owner. 

Art.  8.  Samples.  The  Contractor  shall  furnish  for  approval  all  samples  as 
directed.     The  work  shall  be  in  strict  accordance  with  approved  samples. 

Art.  9.  The  Architect's  Status.  The  Architect  shall  have  general  super- 
vision and  direction  of  the  work.  He  is  the  agent  of  the  Owner,  only  to  the  ex- 
tent provided  in  the  Contract  Documents  and  when  in  special  instances  he  is 
authorized  by  the  Owner  so  to  act,  and  in  such  instances  he  shall,  upon  request, 
show  the  Contractor  written  authority.  He  has  authority  to  stop  the  work 
whenever  such  stoppage  may  be  necessary  to  insure  the  proper  execution  of  the 
Contract.  As  the  Architect  is,  in  the  first  instance,  the  interpreter  of  the 
Contract  and  the  judge  of  its  performance,  he  shall  side  neither  with  the  Owner 
or  with  the  Contractor,  but  shall  use  his  powers  under  the  Contract  to  enforce 
its  faithful  performance  by  both.  In  case  of  the  termination  of  the  employ- 
ment of  the  Architect,  the  Owner  shall  appoint  a  capable  and  reputable  Architect, 
whose  status  under  the  contract  shall  be  that  of  the  former  Architect. 

Art.  10.  The  Architect's  Decisions.  The  Architect  shall,  within  a  reason- 
able time,  make  decisions  on  all  claims  of  the  Owner  or  Contractor  and  on  all 


Standard  Documents  1755 

other  matters  relating  to  the  execution  and  progress  of  the  work  or  the  interpre- 
tation of  the  Contract  Documents.  The  Architect's  decisions,  in  matters  rehiting 
to  artistic  effect,  shall  be  final,  if  within  the  terms  of  the  Contract  Documents. 
Except  as  above  or  as  otherwise  expressly  provided  in  these  General  Conditions 
or  in  the  specifications,  all  the  Architect's  decisions  are  subject  to  arbitration. 

Art.  II.  Foreman,  Supervision.  The  Contractor  shall  keep  on  the  work  a 
competent  foreman  and  any  necessary  assistants,  all  satisfactory  to  the 
Architect.  The  foreman  shall  not  be  changed  except  with  the  consent  of  the 
Architect,  unless  the  foreman  proves  to  be  unsatisfactory  to  the  Contractor 
and  ceases  to  be  in  his  employ.  The  foreman  shall  represent  the  Contractor 
in  his  absence  and  all  directions  given  to  him  shall  be  as  binding  as  if  given  to 
the  Contractor.  Important  directions  shall  be  confirmed  in  writing  to  the  Con- 
tractor. Other  directions  shall  be  so  confirmed  on  written  request  in  each 
case.  The  Contractor  shall  give  efficient  supervision  to  the  work,  using  his  best 
skill  and  attention.'  He  shall  carefully  study  and  compare  all  drawings,  specifi- 
cations and  other  instructions  and  shall  at  once  report  to  the  Archit  3ct  any  error, 
inconsistency,  or  omission  which  he  may  discover. 

Art.  12.  Materials,  Appliances,  Employees.  Unless  otherwise  stipulated, 
the  Contractor  shall  provide  and  pay  for  all  materials,  labor,  water,  tools,  equip- 
ment, light  and  power  necessary  for  the  execution  of  the  work.  Unless  other- 
wise specified,  all  materials  shall  be  new  and  both  workmanship  and  materials 
shall  be  of  good  quality.  The  Contractor  shall,  if  required,  furnish  satisfactory 
evidence  as  to  the  kind  and  quality  of  materials.  The  Contractor  shall  not 
employ  on  the  work  any  unfit  person  or  any  one  not  skilled  in  the  work  assigned 
to  him. 

Art.  13.  Inspection  of  Work.  The  Owner,  the  Architect  and  their  repre- 
sentatives shall  at  all  times  have  access  to  the  work  wherever  it  is  in  preparation 
or  progress  and  the  Contractor  shall  provide  proper  facilities  for  such  access  and 
for  inspection.  If  the  specifications,  the  Architect's  instructions,  laws,  ordi- 
nances or  any  public  authority  require  any  work  to  be  specially  tested  or 
approved,  the  Contractor  shall  give  the  Architect  timely  notice  of  its  readiness 
for  inspection,  and  if  the  inspection  is  by  another  authority  than  the  Architect, 
of  the  date  fixed  for  such  inspection.  Inspections  by  the  Architect  shall  be 
promptly  made.  If  any  such  work  should  be  covered  up  without  approval  or 
consent  of  the  Architect,  it  must,  if  required  by  the  Architect,  be  uncovered 
for  examination  at  the  Contractor's  expense.  Reexamination  of  questioned 
work  may  be  ordered  by  the  Architect.  If  such  work  be  found  in  accordance 
with  the  contract,  the  Owner  shall  pay  the  cost  of  reexamination  and  replace- 
ment. If  such  work  be  found  not  in  accordance  with  the  contract,  through  the 
fault  of  the  Contractor,  the  Contractor  shall  pay  such  cost,  unless  he  shall  show 
that  the  defect  in  the  work  was  caused  by  another  contractor,  and  in  that 
event  the  Owner  shall  pay  such  cost. 

Art.  14.  Correction  of  Work  Before  Final  Payment.  The  Contractor 
shall  promptly  remove  from  the  premises  all  materials  condemned  by  the 
Architect  as  failing  to  conform  to  the  Contract,  whether  incorporated  in  the 
work  or  not,  and  the  Contractor  shall  promptly  replace  and  re-execute  his  own 
work  in  accordance  with  the  Contract  and  without  expense  to  the  Owner  and 
shall  bear  the  expense  of  making  good  all  work  of  other  contractors  destroyed 
or  damaged  by  such  removal  or  replacement.  If  the  Contractor  does  not 
remove  such  condemned  work  and  materials  within  a  reasonable  time,  fixed  by 
written  notice,  the  Owner  may  remove  them  and  may  store  the  material  at 
the  expense  of  the  Contractor.     If  the  Contractor  does  not  pay  the  expense 


1756  Standard  Documents  Part  3 

of  such  removal  within  five  days  thereafter,  the  Owner  may,  upon  ten-days' 
written  notice,  sell  such  materials  at  auction  or  at  private  sale  and  shall 
account  for  the  net  proceeds  thereof,  after  deducting  all  the  cost  and  expenses 
that  should  have  been  borne  by  the  Contractor. 

Art.  15.  Deductions  for  Uncorrected  Work.  If  the  Architect  and 
Owner  deem  it  inexpedient  to  correct  work  injured  or  not  done  in  accordance 
with  the  Contract,  the  difference  in  value  together  with  a  fair  allowance  for 
damage  shall  be  deducted. 

Art.  16.  Correction  of  Work  After  Final  Payment.  Neither  the  final  cer- 
tificate nor  payment  nor  any  provision  in  the  Contract  Documents  shall  relieve 
the  Contractor  of  responsibihty  for  negligence  or  faulty  materials  or  workman- 
ship and  he  shall  remedy  any  defects  due  thereto  and  pay  for  any  damagt  to 
other  work  resulting  therefrom,  which  shall  appear  within  a  period  of  two  years 
from  the  time  of  installation.  The  Owner  shall  give  notice  of  observed  defects 
with  reasonable  promptness.  All  questions  arising  under  this  Article  shall 
be  decided  under  Articles  10  and  45. 

Art.  17.  Protection  of  Work  and  Property.  The  Contractor  shall  con- 
tinuously maintain  adequate  protection  of  all  his  work  from  damage  and  shall 
protect  the  Owner's  property  from  injury  arising  in  connection  with  this  Con- 
tract. He  shall  make  good  any  such  damage  or  injury,  except  such  as  may  be 
directly  due  to  errors  in  the  Contract  Documents.  He  shall  adequately  protect 
adjacent  property  as  provided  by  law  and  the  Contract  Documents. 

Art.  18.  Emergencies.  In  an  emergency  afi"ecting  the  safety  of  life  or  of  the 
structure  or  of  adjoining  property,  not  considered  by  the  Contractor  as  within 
the  provisions  of  Article  17,  then  the  Contractor,  without  special  instruction  or 
authorization  from  the  Architect  or  Owner,  is  hereby  permitted  to  act,  at  his 
discretion,  to  prevent  such  threatened  loss  or  injury  and  he  shall  so  act,  without 
appeal,  if  so  instructed  or  authorized.  Any  compensation  claimed  to  be  due  to 
him  therefor  shall  be  determined  under  Articles  10  and  45  regardless  of  the 
limitations  in  Article  25  and  in  the  second  paragraph  of  Article  24. 

Art.  19.  Contractor's  Liability  Insurance.  The  Contractor  shall  main- 
tain such  insurance  as  will  protect  him  from  claims  under  workmen's  compensa- 
tion acts  and  from  any  other  claims  for  damages  for  personal  injury,  including 
death,  which  may  arise  from  operations  under  this  contract,  whether  such 
operations  be  by  himself  or  by  any  subcontractor'or  anyone  directly  or  indirectly 
employed  by  either  of  them.  Certificates  of  such  insurance  shall  be  filed  with 
the  Owner,  if  he  so  require,  and  shall  be  subject  to  his  approval  for  adequacy 
of  protection. 

Art.  20.  Owner's  Liability  Insurance.  The  Owner  shall  maintain  such 
insurance  as  will  protect  him  from  his  contingent  liability  for  damages  for 
personal  injury,  including  death,  which  may  arise  from  operations  under  this 
Contract. 

Art.  21.  Fire  Insurance.  The  Owner  shall  effect  and  maintain  fire  insur- 
ance upon  the  entire  structure  on  which  the  work  of  this  contract  is  to  be  done 
and  upon  all  materials,  in  or  adjacent  thereto  and  intended  for  use  thereon, 
to  at  least  eighty  p>er  cent  of  the  insurable  value  thereof.  The  loss,  if  any, 
is  to  be  made  adjustable  with  and  payable  to  the  Owner  as  Trustee  for  whom 
it  may  concern.  All  policies  shall  be  open  to  inspection  by  the  Contractor. 
If  the  Owner  fails  to  show  them  on  request  or  if  he  fails  to  effect  or  maintain 
insurance  as  above,  the  Contractor  may  insure  his  own  interest  and  charge 
the  cost  thereof  to  the  Owner.     If  the  Contractor  is  damaged  by  failure  of  the 


Standard  Documents  1757 

Owner  to  maintain  such  insurance,  he  may  recover  under  Art.  39.  If  required 
in  writing  by  any  party  in  interest,  the  Owner  as  Trustee  shall,  upon  the 
occun:ence  of  loss,  give  bond  for  the  proper  performance  of  his  duties.  He  shall 
deposit  any  money  received  from  insurance  in  an  account  separate  from  all  his 
other  funds  and  he  shall  distribute  it  in  accordance  with  such  agreement  as  the 
parties  in  interest  may  reach,  or  under  an  award  of  arbitrators  appointed,  one  by 
the  Owner,  another  by  joint  action  of  the  other  parties  in  interest,  all  other 
procedure  being  in  accordance  with  Art.  45.  If  after  loss  no  special  agreement  is 
made,  replacement  of  injured  work  shall  be  ordered  under  Art.  24.  The  Trustee 
shall  have  power  to  adjust  and  settle  any  loss  with  the  insurers  unless  one 
of  the  contractors  interested  shall  object  in  writing  within  three  working  days 
of  the  occurrence  of  loss  and  thereupon  arbitrators  shall  be  chosen  as  above. 
The  Trustee  shall  in  that  case  make  settlement  with  the  insurers  in  accordance 
with  the  directions.of  such  arbitrators,  who  shall  also,  if  distribution  by  arbitra- 
tion is  required,  direct  such  distribution. 

Art.  22.  Guaranty  Bonds.  The  Owner  shall  have  the  right  to  require 
the  Contractor  to  give  bond  covering  the  faithful  performance  of  the  contract 
and  the  payment  of  all  obligations  arising  thereunder,  in  such  form  as  the  Owner 
may  prescribe  and  with  such  sureties  as  he  may  approve.  If. such  bond  is 
required  by  instructions  given  previous  to  the  receipt  of  bids,  the  premium 
shall  be  paid  by  the  Contractor;  if  subsequent  thereto,  it  shall  be  paid  by  the 
Owner. 

Art.  23.  Cash  Allowances.  The  Contractor  shall  include  in  the  contract 
sum  all  allowances  named  in  the  Contract  Documents  and  shall  cause  the  work 
so  covered  to  be  done  by  such  contractors  and  for  such  sums  as  the  Architect 
may  direct,  the  contract  sum  being  adjusted  in  conformity  therewith.  The 
Contractor  declares  that  the  contract  sum  includes  such  sums  for  expenses  and 
profit  on  account  of  cash  allowances,  as  he  deems  proper.  No  demand  for 
expenses  or  profit  other  than  those  included  in  the  contract  sum  shall  be  allowed. 
The  Contractor  shall  not  be  required  to  employ  for  any  such  work  persons 
against  whom  he  has  a  reasonable  objection. 

Art.  24.  Changes  in  the  Work.  The  Owner,  without  invalidating  the 
contract,  may  make  changes  by  altering,  adding  to  or  deducting  from  the  work, 
the  contract  sum  being  adjusted  accordingly.  All  such  work  shall  be  executed 
under  the  conditions  of  the  original  contract  except  that  any  claim  for  extension 
of  time  caused  thereby  shall  be  adjusted  at  the  time  of  ordering  such  change. 

Except  as  provided  in  Articles  3,  9  and  18,  no  change  shall  be  made  unless  m 
pursuance  of  a  written  order  from  the  Owner  signed  or  countersigned  by  the 
Architect,  or  a  written  order  from  the  Architect  stating  that  the  Owner  has 
authorized  the  change,  and  no  claim  for  an  addition  to  the  contract  sum  shall 
be  valid  unless  so  ordered. 

The  value  of  any  such  change  shall  be  determined  in  one  or  more  of  the 
following  ways: 

(a)  By  estimate  and  acceptance  in  a  lump  sum. 

(b)  By  unit  prices  named  in  the  contract  or  subsequently  agreed  upon. 

(c)  By  cost  and  percentage  or  by  cost  and  a  fixed  fee. 

(d)  If  none  of  the  above  methods  is  agreed  upon,  the  Contractor,  provided 
he  receive  an  order  as  above,  shall  proceed  with  the  work,  no  appeal  to  arbitra- 
tion being  allowed  from  such  order  to  proceed. 

In  cases  (c)  and  (d),  the  Contractor  shall  keep  and  present  in  such  form  a? 
the  Architect  may  direct,  a  correct  account  of  the  net  cost  of  labor  and  mate- 
rials  together  with  vouchers.     In  any  case,  the  Architect  shall  certify  to  the 


1758  Standard  Documents  Part  3 

amount,  including  a  reasonable  profit,  due  to  the  Contractor.  Pending  final 
determination  of  value,  payments  on  account  of  changes  shall  be  made  on  the 
Architect's  certificate. 

Art.  25.  Claims  for  Extras.  If  the  Contractor  claims  that  any  instruc- 
tions, by  drawings  or  otherwise,  involve  extra  cost  under  this  contract,  he  shall 
give  the  Architect  written  notice  thereof  before  proceeding  to  execute  the  work 
and,  in  any  event,  within  tw^o  weeks  of  receiving  such  instructions,  and  the 
procedure  shall  then  be  as  provided  in  Art.  24.  No  such  claim  shall  be  valid 
unless  so  made. 

Art.  26.  Applications  for  Payments.  The  Contractor  shall  submit  to  the 
Architect  an  application  for  each  payment  and,  if  required,  receipts  or  other 
vouchers  showing  his  payments  for  materials  and  labor  as  required  by  Article  44. 
If  payments  are  made  on  valuation  of  work  done,  such  application  shall  be 
submitted  at  least  ten  days  before  each  payment  falls  due,  and,  if  required, 
the  Contractor  shall  before  the  first  application,  submit  to  the  Architect  a 
schedule  of  values  of  the  various  parts  of  the  work,  including  quantities,  aggre- 
gating the  total  sum  of  the  contract,  divided  so  as  to  facilitate  payments  to 
subcontractors  in  accordance  with  Article  44  (e),  made  out  in  such  form,  and, 
if  reciuired,  supported  by  evidence  as  to  its  correctness,  as  the  Architect  may 
direct.  This  schedule  when  approved  by  the  Architect j  shall  be  used  as  a 
basis  for  certificates  of  payment,  unless  it  be  found  to  be  in  error.  In  applying 
for  payments,  the  Contractor  shall  submit  a  statement  based  upon  this  schedule 
and,  if  required,  itemized  in  such  form,  and  supported  by  such  evidence,  as  the 
Architect  may  direct,  showing  his  right  to  the  payment  claimed. 

Art.  27.  Certificates  and  Payments.  If  the  Contractor  has  made  applica- 
tion as  above,  the  Architect  shall,  not  later  than  the  date  when  each  payment 
falls  due,  issue  to  the  Contractor  a  certificate  for  such  amount  as  he  decides 
to  be  properly  due.  No  certificate  issued  nor  payment  made  to  the  Contractor, 
nor  partial  or  entire  use  or  occupancj^  of  the  work  by  the  Owner  shall  be  an 
acceptance  of  any  work  or  materials  not  in  accordance  with  this  contract.  The 
making  and  acceptance  of  the  final  payment  shall  constitute  a  waiver  of  all 
claims  ])y  the  Owner,  otherwise  than  under  Articles  16  and  29  of  these  con- 
ditions or  under  requirement  of  the  specifications,  ai^d  of  all  claims  by  the 
Contractor,  except  those  previously  made  and  still  unsettled.  Should  the 
Owner  fail  to  pay  the  sum  named  in  any  certificate  of  the  Architect  or  in  any 
award  by  arbitration,  upon  demand  when  due,  the  Contractor  shall  receive,  in 
addition  to  the  sum  named  in  the  certificate,  interest  thereon  at  the  legal  rate 
in  force  at  the  place  of  building. 

Art.  28.  Payments  Withheld.  The  Architect  may  withhold  or,  on  account 
of  sulisequently  discovered  evidence,  nullify  the  whole  or  a  part  of  any  certificate 
for  payment  to  such  extent  as  may  be  necessary  to  protect  the  Owner  from 
loss  on  account  of: 

(a)  Defective  work  not  remedied. 

(b)  Claims  filed  or  reasonable  evidence  indicating  probable  fifing  of  claims. 

(c)  Failure  of  the  Contractor  to  make  payments  properly  to  subcontractors 
or  for  material  or  labor. 

(d)  A  reasonable  doubt  that  the  contract  can  be  completed  for  the  balance 
then  unpaid. 

(e)  Damage  to  another  contractor  under  Article  40. 

•  When  all  the  alcove  grcimds  are  removed  certificates  shall  at  once  be  issued 
for  amounts  withheld  because  of  them. 

Art.  29.  Liens.     Neither  the  final  payment  nor  any  part  of  the  retained 


Standard  Documents  1759 

percentage  shall  become  due  until  the  Contractor,  if  required,  shall  deliver  to 
the  Owner  a  complete  release  of  all  liens  arising  out  of  this  contract,  or  receipts 
in  full  in  lieu  thereof  and,  if  required  in  either  case,  dn  affidavit  that  so  far 
as  he  has  knowledge  or  information  the  releases  and  receipts  include  all  the 
labor  and  material  for  which  a  lien  could  be  filed;  but  the  Contractor  may, 
if  any  subcontractor  refuses  to  furnish  a  release  or  receipt  in  full,  furnish  a 
bond  satisfactory  to  the  Owner,  to  indemnify  him  against  any  claim  by  lien  or 
otherwise.  If  any  lien  or  claim  remain  unsatisfied  after  all  payments  are 
made,  the  Contractor  shall  refund  to  the  Owner  all  moneys  that  the  latter 
may  be  compelled  to  pay  in  discharging  such  lien  or  claim,  including  all  costs 
and  a  reasonable  attorney's  fee. 

Art.  30.  Permits  and^Regulations.  The  Contractor  shall  obtain  and  pay 
for  all  permits  and  Hcenses,  but  not  permanent  easements,  and  shall  give  all 
notices,  pay  all  fees,  and  comply  with  all  laws,  ordinances,  rules  and  regulations 
bearing  on  the  work,  as  drawn  and  specified.  If  the  Contractor  observes  that 
drawings  and  specifications  are  at  variance  therewith,  he  shall  promptly  notify 
the  Architect  in  writing,  and  any  necessary  changes  shall  be  adjusted  under 
Art.  24.  If  the  contractor  performs  any  work  knowing  it  to  be  con- 
trary to  such  laws,  ordinances,  rules  and  regulations,  and  without  such  notice  to 
the  Architect,  he  shall  bear  all  costs  arising  thereform. 

Art.  31.  Royalties  and  Patents.  The  Contractor  shall  pay  all  royalties 
and  Hcense  fees.  He  shall  defend  all  suits  or  claims  for  infringement 
of  any  patent  rights  and  shall  save  the  Owner  harmless  from  loss  on 
account  thereof,  except  that  the  Owner  shall  be  responsible  for  all  such  loss 
when  the  product  of  a  particular  manufacturer  or  manufacturers  is  specified; 
but  if  the  Contractor  has  information  that  the  article  specified  is  an  infringe- 
ment of  a  patent  he  shall  be  responsible  for  such  loss  unless  he  promptly  gives 
such  information  to  the  Architect  or  Owner. 

Art.  32.  Use  of  Premises.  The  Contractor  shall  confine  his  apparatus, 
the  storage  of  materials  and  the  operations  of  his  workmen  to  Hmits  indicated 
by  law,  ordinances,  permits,  or  directions  of  the  Architect  and  shall  not  unreason- 
ably encumber  the  premises  with  his  materials.  The  Contractor  shall  not  load 
or  permit  any  part  of  the  structure  to  be  loaded  with  a  weight  that  will  endanger 
its  safety.  The  Contractor  shall  enforce  the  Architect's  instructions  regarding 
signs,  advertisements,  fires  and  smoking. 

Art.  33.  Cleaning  l^.  The  Contractor  shall  at  all  times  keep  the  premises 
free  from  accumulations  of  waste  material  or  rubbish  caused  by  his  employees 
or  work  and  at  the  completion  of  the  work  he  shall  remove  all  his  rubbish  from 
and  about  the  building  and  all  his  tools,  scaffolding  and  surplus  materials,  and 
shall  leave  his  work  "broom  clean"  or  its  equivalent,  unless  more  exactly 
specified.  In  case  of  dispute  the  Owner  may  remove  the  rubbish  and  charge 
the  cost  to  the  several  contractors  as  the  Architect  shall  determine  to  be  just. 

Art  34  Cutting,  Patching  and  Digging.  The  Contractor  shall. do  all 
cuttin-  fitting,  or  patching  of  his  work  that  may  be  required  to  make  its  several 
parts  come  together  properly  and  fit  it  to  receive  or  be  received  by  work  of  other 
contractors  shown  upon,  or  reasonably  implied  by,  the  Drawings  and  Specifica- 
tions for  the  completed  structure,  and  he  shall  make  good  after  them,  as  the 
Architect  may  direct.  Any  cost  caused  by  defective  or  ill-timed  work  shall  be 
borne  by  the  party  responsible  therefor.  The  Contractor  shall  not  endanger 
any  work  by  cutting,  digging,  or  otherwiseand  shall  not  cut  or  alter  the  work 
of  any  other  contractor,  save  with  the  consent  of  the  Architect-. 

Art.  35.  Delays.     If  the  Contractor  is  delayed  in  the  completion  of  the  work 


1760  Standard  Documents  Part  3 

by  any  act  or  neglect  of  the  Owner  or  the  Architect,  or  of  any  employee  of  either, 
or  by  any  other  contractor  employed  by  the  Owner,  or  by  changes  ordered  in  the 
work,  or  by  strikes,  lockouts,  fire,  vmusual  delay  by  common  carriers,  unavoid- 
able casualties,  Or  any  causes  beyond  the  Contractor's  control,  or  by  delay 
authorized  by  the  Architect  pending  arbitration,  or  by  any  cause  which  the 
Architect  shall  decide  to  justify  the  delay,  then  the  time  of  completion  shall 
be  extended  for  such  reasonable  time  as  the  Architect  may  decide.  No  such 
extension  shall  be  made  for  delay  occurring  more  than  seven  days  before  claim 
therefor  is  made  in  writing  to  the  Architect.  In  the  case  of  a  continuing  cause 
of  delay,  only  one  claim  is  necessary.  If  no  schedule  is  made  under  Art.  3, 
no  claim  for  delay  shall  be  allowed  on  account  of  failure  to  furnish  drawings 
until  two  weeks  after  demand  for  such  drawings  and  not  then  unless  such 
claim  be  reasonable.  This  article  does  not  exclude"  the  recovery  of  damages 
for  delay  by  either  party  under  Article  39  or  other  provisions  in  the  Contract 
Documents. 

Art.  36.  Owner's  Right  to  Do  Work.  If  the  Contractor  should  neglect 
to  prosecute  the  work  properly  or  fail  to  perform  any  provision  of  this  contract, 
the  Owner,  after  three-days'  written  notice  to  the  Contractor,  may,  without 
prejudice  to  any  other  remedy  he  may  have,  make  good  such  deficiencies  and 
may  deduct  the  cost  thereof  from  the  payment  then  or  thereafter  due  the 
Contractor;  provided,  however,  that  the  Architect  shall  approve  both  such 
action  and  the  amount  charged  to  the  Contractor. 

Art.  37.  Owner's  Right  to  Terminate  Contract.  If  the  Contractor  should 
be  adjudged  a  bankrupt,  or  if  he  should  make  a  general  assignment  for  the  benefit 
of  his  creditors,  or  if  a  receiver  should  be  appointed  on  account  of  his  insolvency, 
or  if  he  should,  except  in  cases  recited  in  Article  35,  persistently  or  repeatedly 
refuse  or  fail  to  supply  enough  properly  skilled  workmen  or  proper  materials,  or 
if  he  should  fail  to  make  prompt  payment  to  subcontractors  or  for  material  or 
labor,  or  persistently  disregard  laws,  ordinances  or  the  instructions  of  the  Archi- 
tect, or  otherwise  be  guilty  of  a  substantial  violation  of  any  provision  of  the  con- 
tract, then  the  Owner,  upon  the  certificate  of  the  Architect  that  sufficient  cause 
exists  to  justify  such  action,  may,  without  prejudice  to  any  other  right  or  remedy 
and  after  giving  the  Contractor  seven-days'  written  notice,  terminate  the 
employment  of  the  Contractor  and  take  possession  of  the  premises  and  of  all 
materials,  tools  and  apphances  thereon  and  fmish  the  work  by  whatever  method 
he  may  deem  expedi.^nt.  In  such  case  the  Contractor  shall  not  be  entitled  to 
receive  any  further  payment  until  the  work  is  finished.  If  the  unpaid  balance 
of  the  contract  price  shall  exceed  the  expense  of  finishing  the  work,  including 
compensation  to  the  Architect  for  his  additional  services,  such  excess  shall  be 
paid  to  the  Contractor.  If  such  expense  shall  exceed  such  unpaid  balance,  the 
Contractor  shall  pay  the  difference  to  tiie  Owner.  The  expense  incurred  by 
the  Owner  as  herein  provided,  and  the  damage  incurred  through  the  Con- 
tractor's default,  shall  be  certified  by  the  Architect. 

Art.  38.  Contractor's  Right  to  Stop  Work  or  Terminate  Contract.  If 
the  work  should  be  stopped  under  an  order  of  any  court,  or  other  public 
authority,  for  a  period  of  three  months,  through  no  act  or  fault  of  the  Con- 
tractor or  of  any  one  employed  by  him,  or  if  the  Owner  should  fail  to  pay  to 
the  Contractor,  within  seven  days  of  its  maturity  and  presentation,  any  sum 
certified  by  the  Architect  or  awarded  by  arbitrators,  then  the  Contractor  may, 
upon  three-days'  written  notice  to  the  Owner  and  the  Architect,  stop  work  or 
terminate  this  contract ^and  recover  from  the  Owner  payment  for  all  work  exe- 
cuted and  any  loss  sustained  upon  any  plant  or  material  and  reasonable  profit 
&nd  damages, 


Standard  Documents  I76l 

Art.  39.  Damages.  If  either  party  to  this  contract  should  suffer  damage  in 
any  manner  because  of  any  wrongful  act  or  neglect  of  the  other  party  or 
of  any  one  employed  by  him,  then  he  shall  -be  reimbursed  by  the  other  party 
for  such  damage.  Claims  under  this  clause  shall  be  made  in  writing  to  the 
party  liable  within  a  reasonable  time  of  the  first  observance  of  such  damage 
and  not  later  than  the  time  of  final  payment,  except  in  case  of  claims  under 
Article  16,  and  shall  be  adjusted  by  agreement  or  arbitration. 

Art.  40.  Mutual  Responsibility  of  Contractors.  Should  the  Contractor 
cause  damage  to  any  other  contractor  on  the  work,  the  Contractor  agrees,  upon 
due  notice,  to  settle  with  such  person  by  agreement  or  arbitration,  if  he 
will  so  settle.  If  such  other  contractor  sues  the  Owner  on  account  of 
any  damage  alleged  to  have  been  so  sustained,  the  Owner  shall  notify  the 
Contractor,  who  shall  defend  such  proceedings  at  the  Owner's  expense  and, 
if  any  judgment  against  the  Owner  arise  therefrom,  the  Contractor  shall  pay 
or  satisfy  it  and  pay  all  costs  incurred  by  the  Owner. 

Art.  41.  Separate  Contracts.  The  Owner  reserves  the  right  to  let  other 
contracts  in  connection  with  this  work.  The  Contractor  shall  afford  other  con- 
tractors reasonable  opportunity  for  the  introduction  and  storage  of  their  mate- 
rials and  the  execution  of  their  work  and  shall  properly  connect  and  coordinate 
his  work  with  theirs.  If  any  part  of  the  Contractor's  work  depends  for  proper 
execution  or  results  upon  the  work  of  any  other  contractor,  the  Contractor  shall 
ins})ect  and  promptly  report  to  the  Architect  any  defects  in  such  work  that 
render  it  unsuitable  for  such  proper  execution  and  results.  His  failure  so  to 
inspect  and  report  shall  constitute  an  acceptance  of  the  other  contractor's  work 
as  iU  and  proper  for  the  reception  of  his  work,  except  as  to  defects  which  may 
d('\  clop  in  the  other  contractor's  work  after  the  execution  of  his  work.  To 
insure  the  proper  execution  of  his  subsequent  work  the  Contractor  shall  measure 
work  already  in  place  and  shall  at  once  report  to  the  Architect  any  discrepancy 
between  the  executed  work  and  the  drawings. 

Art.  42.  Assignment.  Neither  party  to  the  Contract  shall  assign  the  con- 
trai  t  without  the  written  consent  of  the  other,  nor  shall  the  Contractor  assign 
an>-  moneys  due  or  to  become  due  to  him  hereunder,  without  the  previous 
written  consent  of  the  Owner. 

Art.  43.  Subcontracts.  The  Contractor  shall,  as  soon  as  practicable  after 
thi;  signing  of  the  contract,  notify  the  Architect  in  writing  of  the  names  of 
sill) contractors  proposed  for  the  principal  parts  of  the  work  and  for  such  others 
as  the  Architect  may  direct  and  shall  not  employ  any  that  the  Architect  may 
within  a  reasonable  time  object  to  as  incompetent  or  unfit.  If  the  Contractor 
has  submitted,  before  signing  the  contract,  a  list  of  subcontractors  and  the. 
change  of  any  name  on  such  list  is  required  or  permitted  after  signature  of 
agreement,  the  contract  price  shall  be  increased  or  diminished  by  the  difference 
between  the  two  bids.  The  Architect  shall,  on  request,  furnish  to  any  subcon- 
tractor, wherever  practicable,  evidence  of  the  amounts  certified  to  on  his 
account.  The  Contractor  agrees  that  he  is  as  fully  responsible  to  the  Owner 
for  the  acts  or  omissions  of  his  subcontractors  and  of  persons  either  directly  or 
indirectly  employed  by  them,  as  he  is  for  the  acts  and  omissions  of  persons  di- 
rectly employed  by  him.  Nothing  contained  in  the  Contract  Documents  shall 
create  any  contractual  relation  between  any  subcontractor  and  the  Owner. 

Art.  44.  Relations  of  Contractor  and  Subcontractor.  The  Contractor, 
agrees  to  bind  every  subcontractor  and  every  subcontractor  agrees  to  be  bound, 
by  the  terms  of  the  General  Conditions,  Drawings  and  Specifications,  as  far  as 
applicable  to  his  work,  including  the  following  provisions  of  this  Article,  unless 


1762  Standard  Documents  Part  3 

specifically  noted  to  the  contrary  in  a  subcontract  approved  in  writing  as 
adequate  by  the  Owner  or  Architect.  This  does  not  apply  to  minor  sub- 
contracts. 

The  Subcontractor  agrees: 

(a)  To  be  bound  to  the  Contractor  by  the  terms  of  the  General  Conditions, 
Drawings  and  Specifications  and  to  assume  toward  him  all  the  obligations  and 
responsibihties  that  he,  by  those  documents,  assumes  toward  the  Owner. 

(b)  To  submit  to  the  Contractor  applications  for  payment  in  such  reasonable 
time  as  to  enable  the  Contractor  to  apply  for  payment  under  Article  26  of  the 
General  Conditions. 

(c)  To  make  all  claims  for  extras,  for  extensions  of  time  and  for  damages  for 
delays  or  otherwise,  to  the  Contractor  in  the  manner  provided  in  the  General 
Conditions  for  like  claims  by  the  Contractor  upon  the  Owner,  except  that  the 

.  time  for  making  claims  for  extra  cost  as  under  Article  25  of  the  General  Condi- 
tions is  one  week. 

The  Contractor  agrees: 

(d)  To  be  bound  to  the  Subcontractor  by  all  the  obligations  that  the  Owner 
assumes  to  the  Contractor  under  the  General  Conditions,  Drawings  and  Specifi- 
cations and  by  all  the  provisions  thereof  affording  remedies  and  redress  to  the 
Contractor  from  the  Owner. 

(e)  To  pay  the  Subcontractor,  upon  the  issuance  of  certificates,  if  issued  under 
the  schedule  of  values  described  in  Article  26  of  the  General  Conditions,  the 
amount  allowed  to  the  Contractor  on  account  of  the  Subcontractor's  work  to 
the  extent  of  the  Subcontractor's  interest  therein. 

(f )  To  pay  the  Subcontractor,  upon  the  issuance  of  certificates,  if  issued  other- 
wise than  as  in  (e),  so  that  at  all  times  his  total  payments  shall  be  as  large  in 
proportion  to  the  value  of  the  work  done  by  him  as  the  total  amount  certified  ta 
the  Contractor  is  to  the  value  of  the  work  done  by  him. 

(g)  To  pay  the  Subcontractor  to  such  extent  as  may  be  provided  by  the 
Contract  Documents  or  the  subcontract,  if  either  of  these  provides  for  earlier 
or  brger  payments  than  the  above. 

(h)  To  pay  the  Subcontractor  on  demand  for  his  work  or  materials  as  far  as 
executed  and  fixed  in  place,  less  the  retained  percentage,  at  the  time  the  certifi- 
cate should  issue,  even  though  the  Architect  fails  to  issue  it  for  any  cause  not 
the  fault  of  the  Subcontractor. 

(j)  To  pay  the  Subcontractor  a  just  share  of  any  fire-insurance  money  received 
by  him,  the  Contractor,  under  Article  21  of  the  General  Conditions. 

(k)  To  make  no  demand  for  liquidated  damages  or  penalty  for  delay  in  any 
sum  in  excess  of  such  amount  as  may  ))e  specifically  named  in  the  subcontract. 

(1)  That  no  claim  for  services  rendered  or  materials  furnished  by  the  Con- 
tractor to  the  Subcontractor  shall  be  valid  unless  written  notice  thereof  is  given 
by  the  Contractor  to  the  Subcontractor  during  the  first  ten  days  of  the  calendar 
month  following  that  in  which  the  claim  originated. 

(m)  To  give  the  Subcontractor  an  opportunity  to  be  present  and  to  submit 
evidence  in  any  arbitration  involving  his  rights. 

(n)  To  name  as  arbitrator  under  Article  45  of  the  General  Conditions  the 
person  nominated  by  the  Subcontractor,  if  the  sole  cause  of  dispute  is  the  work, 
materials,  rights,  or  responsibilities  of  the  Subcontractor;  or,  if  of  the  Sub- 
contractor and  an}-  other  subcontractor  jointly,  to  name  as  such  arbitrator  the 
person  upon  whom  they  agree. 

The  Contractor  and  the  Subcontractor  agree  that: 

(o)  .In  the  matter  of  arlntration,  their  rights  and  obligations  and  all  procedure 
shall  be  analogous  to  those  set  forth  in  Article  45  of  the  General  Conditions. 


Standard  Documents  17G3 

Nothing  in  this  Article  shall  create  any  obligation  on  the  part  of  the  Owner 
to  pay  to  or  to  see  to  the  payment  of  any  sums  to  any  Subcontractor. 

Art.  45.  Arbitration.  Subject  to  the  provisions  of  Article  10,  all  questions 
in  dispute  under  this  contract  shall  be  submitted  to  arbitration  at  the  choice 
of  cither  party  to  the  dispute.  The  Contractor  agrees  to  push  the  work  vigor- 
ously during  arbitration  proceedings.  The  demand  for  arbitration  shall  be 
filed  in  writing  with  the  Architect,  in  the  case  of  an  appead  from  his  decision, 
within  ten  days  of  its  receipt  and  in  any  other  case  within  a  reasonable  time 
after  cause  thereof  and  in  no  case  later  than  the  time  of  final  payment,  except 
as  to  questions  arising  under  Article  t6.  If  the  Architect  fails  to  make  a 
decision  within  a  reasonable  time,  an  appeal  to  arbitration  may  be  taken  as 
if  his  decision  had  been  rendered  against  the  party  appealing.  No  one  shall 
be  nominated  or  act  as  an  arbitrator  who  is  any  way  financially  interested 
in  this  contract  or  in  the  business  affairs  of  either  the  Owner,  Contractor  or 
Architect.  The  general  procedure  shall  conform  to  the  laws  of  the  State  in 
which  the  work  is  to  be  erected.  Unless  otherwise  pfovided  by  such  laws, 
the  parties  may  agree  upon  one  arbitrator;  otherwise  there  shall  be  three, 
one  named,  in  writing,  by  each  party  to  this  contract,  to  the  other  party  and 
to  the  Architect,  and  the  third  chosen  by  these  two  arbitrators,  or  if  they  fail 
to  select  a  third  within  ten  days,  then  he  shall  he  chosen  by  the  presiding  officer 
if  the  Bar  Association  nearest  to  the  location  of  the  work.  Should  the  party 
demanding  arbitration  fail  to  name  an  arbitrator  within  ten  days  of  his  demand 
his  right  to  arl)itration  shall  lapse.  Should  the  other  party  fail  to  choose  an 
arbitrator  within  said  ten  days,  then  such  presiding  officer  shall  appoint  such 
arbitrator.  Should  either  party  refuse  or  neglect  to  supply  the  arbitrators  with 
any  papers  or  information  demanded  in  writing,  the  arbitrators  are  empowered 
by  both  parties  to  proceed  ex  parte.  The  arbitrators  shall  act  with  promptness. 
If  there  be  one  arbitrator  his  decision  shall  be  binding;  if  three  the  decision 
of  any  two  shall  be  binding.  Such  decision  shall  be  a  condition  precedent  to 
any  right"  of  legal  action,  and  wherever  permitted  Ijy  law  it  may  be  filed  in 
Court  to  carry  it  into  effect.  The  arbitrators,  if  they  deem  that  the  case 
demands  it,  are  authorized  to  award  to  the  party  whose  contention  is  sustained 
such  sums  as  they  shall  deem  proper  for  the  time,  expense  and  trouble  incident 
to  the  appeal  and,  if  the  appeal  was  taken  without  reasonable  cause,  damages 
for  delay.  The  arbitrators  shall  fix  their  own  compensation,  unless  otherwise 
provided  by  agreement,  and  shall  assess  the  costs  and  charges  of  the  arbitration 
upon  either  or  both  parties.  The  award  of  the  arbitrators  must  be  in  writmg 
and,  if  in  writing,  it  shall  not  be  open  to  objection  on  account  of  the  form  of 
the  proceedings  or  the  award,  unless  otherwise  provided  by  the  laws  of  the 
State  in  which  the  work  is  to  be  erected.  In  the  event  of  such  laws  providmg 
on  any  matter  covered  by  this  article  otherwise  than  as  hereinbefore  specified, 
the  method  of  procedure  throughout  and  the  legal  effect  of  the  award  shaU 
be  wholly  in  accordance  with  the  said  State  laws  it  being  intended  hc^reby  to 
lay  down  a  principle  of  action  to  be  followed,  leaving  its  bcal  apphcation  to  be 
adapted  to  the  legal  requirements  of  the  place  in  which  the  work  is  to  be  erected. 

B    THE  STANDARD  FORM  OF  BOND  * 

•"  "■ "  =sr  r-r.:  »=  »  -  == ""  °' 

*  Published  by  permission  of  The  American  Institute  of  Architects. 


1764  Standard  Documents  Part  3 

Contractors  of  the  United  States,  the  National  Electrical  Contractors'  Association  of 
the  United  States,  the  National  Association  of  Marble  Dealers,  the  Building  Granite 
Quarries  Association,  the  Building  Trades  Employers'  Association  of  the  City  of  New 
York,  and  the  Heating  and  Piping  Contractors'  National  Association. 

COPYRIGHT    19 1 5    BY   THE   AMERICAN   JNSTITUTE    OF   ARCHITECTS,    THE    OCTAGON, 
WASHINGTON,    D.   C. 

KNOW  ALL  MEN:  That  we 

(Here  insert  the  name  and  address  or  legal  title  of  the  Contractor.) 

(Two  blank  lines)* 

hereinafter  called  the  Principal,  and 

[l^Here  insert  the  name  and  address  or  legal  title  of  one  or  more  sureties.) 

(Two  blank  lines) and 

(Two  blank  lines) and 

hereinafter  called  the  Surety  or  Sureties,  are  held  and  firmly  bound  unto 

(Here  insert  the  name  and  address  or  legal  title  of  the  Owner.) 

"; (Two  blank  lines) 

hereinafter  called  the  Owner,  in  the  sum  of 

(Two  blank  lines) ($ ) 

for  the  payment  whereof  of  the  Principal  and  the  Surety  or  Sureties  bind  them- 
selves, their  heirs,  executors,  admini.strators,  succes.sors  and  assigns  jointly  and 
severally,  firmly,  by  these  presents. 

Whereas,   the  Principal  has,  by  means  of  a  written  Agreement,  dated 

entered  into  a  contract  with  the  Owner  for 

(Two  blank  lines) 

a  copy  of  which  Agreement  is  by  reference  made  a  part  hereof: 

Now,  Therefore,  the  Condition  of  this  Obligation  "is  such  that  if  the  Principal 
shall  faithfully  perform  the  Contract  on  his  part,  and  satisfy  all  claims  and 
demands,  incurred  for  the  same,  and  shall  fully  indemnify  and  save  harmless  the 
Owner  from  all  cost  and  damage  which  he  may  suffer  by  reason  of  failure  so  to 
do,  and  shall  fully  reimburse  and  repay  the  Owner  all  outlay  and  expense  which 
the  Owner  may  incur  in  making  good  any  such  default,  and  shall  pay  all  per- 
sons who  have  contracts  directly  with  the  Principal  for  labor  or  materials,  then 
this  obligation  shall  be  null  and  void;  otherwise  it  shall  remain  in  full  force 
and  effect. 

Provided,  however,  that  no  suit,  action  or  proceeding  by  reason  of  any  default 

whatever  shall  be  brought  on  this  bond  after months   from 

the  day  oh  which  the  final  jpayment  under  the  Contract  falls  due. 

And  Provided,  that  any  alterations  which  may  be  made  in  the  terms  of  the 
Contract,  or  in  the  work  to  be  done  under  it,  or  the  giving  by  the  Owner  of  any 
extension  of  time  for  the  performance  of  the  Contract,  or  any  other  forbearance 
on  the  part  of  either  the  Owner  or  the  Principal  to  the  other  shall  not  in  any  way 
release  the  Principal  and  the  Surety  or  Sureties,  or  either  or  any  of  them,  their 
heirs,  executors,  administrators,  successors,  or  assigns  from  their  liability  here- 
under, notice  to  the  Surety  or  Sureties  of  any  such  alteration,  extension,  or  for-r 
bearance  being  hereby  waived. 

Signed  and  Sealed  this day  of 

In  Presence  of 


(Repeated  three  times)  }  as  to  (Repeated  three  times) 

"  Dotted  lines,  as  indicated,  are  in  the  standard  documents  and  are  omitted  here  to 


I 


Standard  Documents  1765 

C.  THE  STANDARD  FORM  OP  AGREEMENT   BETWEEN  CON- 
TRACTOR AND  SUBCONTRACTOR  * 

OK    I'SE   IN  CONNECTION  WITH  THE  THIRD  EDITION  OF  THE  STANDARD  FORM  OF 
AGREEMENT  AND  GENERAL  CONDITIONS  OF  THE  CONTRACT 

This  form  has  been  approved  by  the  National  Association  of  Builders'  Exchanges,  The 
iNjational.  Association  of  Master  Plumbers,  the  National  Association  of  Sheet  Metal 
;"ontractors  of  the  United  States,  the  National  Electrical  Contractors'  Association  of 
he  United  States,  the  National  Association  of  Marble  Dealers,  the  Building  Granite 
Quarries  Association,  the  Building  Trades  Employers'  Association  of  the  City  of  New 
ii^ork,  and  the  Heating  and  Piping  Contractors'  National  Association. 

COPYRIGHT  19 1 5  BY  THE  AMERICAN  INSTITUTE  OF  ARCHITECTS,  THE 
OCTAGON,  WASHINGTON,  D.  C 

THIS  AGREEMENT,  made  this. day  of 19. . 

)y  and  between .  . . ., heroinafter  called 

he  Subcontractor  and 

lereinafter  called  the  Contractor. 

WITNESSETH,    That  the  Subcontractor  and  Contractor  for  the  considera- 

ions  hereinafter  named  agree  as  follows: 

Section  i.     The  Subcontractor  agrees  to  furnish  all  material  and  perform  all 

rork  as  described  in  Section  2  hereof  for (Here  name  the  kind  of  building). . . . 

(Blank  lines) '■ 

or ...  .^ (Here  insert  the  name  of  the  Owner) • 

_\ (Blank  lines) 

lereinafter  called  the  Owner,  at (Here  insert  the  location  of  the  work.). . . . 

(Blank  lines) 

accordance  with  the  General  Conditions  of  the  Contract  between  the  Owner 
tnd  the  Contractor,  and  in  accordance  with  the  Drawings  and  the  Specifications 

)repared  by hereinafter  called  the  Architect,  all  of 

vhich  General  Conditions,  Drawings  and  Specifications  signed  by  the  parties 
hereto  or  identified  by  the  Architect,  form  a  part  of  a  Contract  between  the 

:ontractor  and  the  Owner  dated i9-  •    and  hereby  become  a 

)art  of  this  Contract. 

Section  2.  The  Subcontractor  and  the  Contractor  agr:e  that  the  materials 
:o  be  furnished  and  work  to  be  done  by  the  Subcontractor  are  (Here  )nsert  a 
)recise  description  of  the  work,  preferably  by  reference  to  the  numbers  of  the  Drawmgs 
md  the  pages  of  the  Specifications.) 

(Blank  lines) * 

Section  3.     The  Subcontractor  agrees  to  complete  the  several  portions  and 
Lhe  whole  of  the  work  herein  sublet  by  the  time  or  times  following: .  ......... 

(Here  insert  the  dates  or  date  and  if  there  be  liquidated  damages  state  them.). . . . 

.  (Blank  lines) 

Section  4.  The  Contractor  agrees  to  pay  the  Subcontractor  for  the  perform- 
ance of  his  work  the  sum  of     (Blank  line).  .     ...  ■  •  •  ••($ ■-> 

in  current  funds,  subject  to  additions  and  deductions  for  changes  as  may  be 
agreed  upon,  and  to  make  payments  on  account  thereof  in  accordance  with 
Section  5  hereof. 

Section  5.  The  Contractor  and  Subcontractor  agree  to  be  bound  by  the 
terms  of  the  General  Conditions,  Drawings  and  Specifications  as  far  as  apphcable 
to  this  subcontract,  and  also  by  the  foUowing  provisions:! 

;  isi  ^rrsissitfo^src:^^^  ^n ... ... ... 

exception  of  references  to  other  articles,     See  page  1761,  _ 


1766                                   Standard  Documents                               Part  3 
Section  6 


.  (One  page  of  blank  lines)  . 


Finally.  The  Subcontractor  and  Contractor,  for  themselves,  their  heir., 
successors,  executors,  administrators  and  assigns,  do  hereby  agree  to  the  full 
performance  of  the  covenants  herein  contained. 

IN  WITNESS  WHEREOF  tliey  have  hereunto  set  their  hands  the  day  and 
date  first  above  written. 

In  Presence  of 


Suhcontr  actor. 
Contractor. 

D.  STANDARD  FORM  OF  ACCEPTANCE  OF  SUBCONTRACTOR'S 
PROPOSAL  * 

FOR  USE   IN  CONNECTION  WITH   THE  THIRD  EDITION  OF  THE  STANDARD  FORM  OF 
AGREEMENT  AND  GENERAL  CONDITIONS  OF  THE  CONTRACT 

This  form  has  been  approved  by  the  National  Association  of  Builders'  Exchanges,  The 
National  Association  of  Master  Plumbers,  the  National  Association  of  Sheet  Metal 
Contractors  of  the  United  States,  the  National  Electrical  Contractors'  Association  of 
the  United  States,  the  National  Association  of  Marble  Dealers,  the  Building  Granite 
Quarries  Association,  the  Building  Trades  Employers'  Association  of  the  City  of  New 
York,  and  the  Heating  and  Piping  Contractors'  National  Association. 

COPYRIGHT  19 1 5  BY  THE  AMERICAN  INSTITUTE  OF  ARCHITECTS,  THE 
OCTAGON,    WASHINGTON,   D.  C. 

Dear  Sir:  Having  entered  into  a  contract  with  (Here  insert  the  name  and  ad- 
dress or  corporate  title  of  the  Owner. ) 

(Blank  line) 

for  the  erection  of   (Here  insert  the  kind  of  work  and  the  place  at  which  it  is  to  be 

erected. ) 

(Blank  line) 

in  accordance  with  plans  and  specifications  prepared  by   (Here  insert  the  name 

and  address  of  the  Architect.) ." . . 

(Blank  line) 

and  in  accordance  Vi  ith  the  General  Conditions  of  the  Contract  prefixed  to  the 
specifications,  the  undersigned  hereby  accepts  your  proposal  of  (Here  insert  date.) 

to  provide  all  the  materials  and  do  all  the  work  of  (Here  insert  the  kind  of  work 
to  be  done,  as  plumbing,  roofing,  etc.,  accurately  describing  by  number,  page,  etc.,  the 

drawings  and  specifications  governing  such  work.) 

(Blank  lines) 

The  Undersigned  agrees  to  pay  you  in  current  funds  for  the  faithful  perform- 
ance of  the  subcontract  established  by  this  acceptance  of  your  proposal  the  sura 

of .^ ($ 

Our  relations  in  respect  of  this  subcontract  are  to  be  governed  by  the  plans 
and  specifications  named  above,  by  the  General  Conditions  of  the  Contract  as 
far  as  applicable  to  the  work  thus  sublet  and  especially  by  Article  44  of  those 
conditions  printed  on  the;  reverse  hereof,  t 

Very  truly  yours, 

•Published  by  permission  of  The  American  Institute  of  Architects, 
t  Article  44  of  the  Cieneral  Conditions  of  the  Contract  is  printcfl  in  full  on  the  reverse 
side  of  the  Institute's  standard  form.     See  page  1761. 


Official  Institute  Documents  of  a  Permanent  Nature        17G7 

The  Subcontractor  entering  into  this  agreement  should  be  sure  that  not 
merely  the  above  Article  44,  but  the  full  text  of  the  General  Conditions  of  the 
Contract  as  signed  by  the  Owner  and  Contractor  is  known  to  him,  since  such 
full  text,  though  not  herein  repeated,  is  binding  on  him. 

OFFICIAL  INSTITUTE  DOCUMENTS  OF  A  PERMA- 
NENT NATURE  PUBLISHED   (1921)  BY  THE 
AMERICAN  INSTITUTE  OF  ARCHITECTS. 
TITLES  AND  PRICES 

The  Journal  of  the  American  Institute  of  Architects,  monthly,  50  cts; 

yearly,  to  A.  I.  A.  members $3 .  50 

Yearly,  to  non-Institute  members 5 .00 

The  Monograph  on  the  Octagon  (Thirty  Drawings,  12  X  18,  Photographs 

and  Text) 12 .  50 

The  Standard  Contract  Documents: 

Agreement  and  General  Conditions  in  Cover 14 

General  Conditions  without  Agreement 10 

Agreement  without  General  Conditions 03 

Bond  of  Suretyship .02 

Form  of  Subcontract 03 

Letter  of  Acceptance  of  Subcontractor's  Proposal 02 

Cover  (heavy  paper,  with  valuable  notes) 01 

Complete  set  in  Cover 20 

The  Standard  Form  of  Agreement  between  Owner  and  Architect  (Per- 
centage Basis) 03 

A  Circular  of  Information  on  the  Fee-Plus-Cost  System  of  Charges Free 

(Explanatory   of   Owner-Architect   Agreement   on  Fee-Plus-Cost 
Basis) 
A  Form  of  Agreement  between  Owner  and  Architect   (Fee-Plus-Cost 

System) $0.03 

A  Form  of  Agreement  between  Owner  and  Contractor  (Cost-Plus-Fee 

Basis) 05 

Circular  of  Information  Relative  to  Cost-Plus-Fee  System  of  Contracting       Free 

(Explanatory  of  Contractor-Owner  Agreement) 
A  Circular  of  Advice  and  Information  Relative  to  the  Conduct  of  Archi- 
tectural Competitions Free 

Standard  Form  of  Competition-Programme $0.08 

Proceedings  of  the  Convention ^J^^ 

Annuary  to  Institute  Members J*^^ 

To  Commercial  Firms $5.00 

Circular  of  Information  Concerning  Requirements  for  Institute  Member- 
ship      Free 

Circular  of  Information  Concerning  Requirements  for  Chapter  Associate- 

,  .  Free 

ship Pj.ee 

Constitution  and  By-laws „ 

Standard  Form  of  Chapter  Constitution  and  By-laws.  .  . .  .^. .  • ..  •.•.••     ^ree 
A  Circular  of  Advice  Relative  to  Principles  of  Professional  Practice,  The     ^^^^ 

Canon  of  Ethics $0  02 

Schedule  of  Proper  Minimum  Charges V :    "  ^V  \ir' ^4^  \. Fr*.#» 

Circular  Relative  to  the  Size  and  Character  of  Advertising  Matter Free 


176S  Regulation  of  Practice  of  Architecture  by  State  Legislation  Part  3 

Model  Registratwn  Law Free 

List  of  Institute  Documents Free 

For  the  convenience  of  the  members  of  the  Institute,  and  the  profession 
generally,  who  use  in  .their  practice,  by  reference  or  otherwise,  the  various 
official  documents  of  the  American  Institute  of  Architects,  the  above  schedule 
of  Titles  and  Prices  is  issued.  On  single  copies  of  pamphlet-documents  postage 
will  be  prepaid,  otherwise  not.  The  prices  quoted  in  practically  every  case 
are  to  cover  the  actual  cost  of  printing  and  handling.  The  Institute  has  no 
desire  to  make  a  profit  on  documents  issued  primarily  for  the  benefit  of  the 
profession.  For  distinctly  educational  work,  and  for  Chapter-work,  no  charge 
will  be  made  for  small  quantities  of  documents,  except  for  postage.  Requests 
of  this  kind  should  come  through  the  Chapter-Secretary  or  a  Committee- 
Chairman.  Communications  and  remittances  should  be  sent  to  the  Executive 
Secretary,  The  Octagon  House,  Washington,  D.  C.  All  orders  are  filled  on 
the  day  received. 


REGULATION    OF  THE  PRACTICE    OF   ARCHITEC- 
TURE   BY    STATE    LEGISLATION* 

States  Having  Registration  Laws  (1920).  Sixteen  States  have  registra- 
tion or  license  laws  (1920)  affecting  the  practice  of  architecture,  as  follows: 
California,  Colorado,  Florida,  Georgia,  Idaho,  IlUnois,  Louisiana,  Michigan, 
Montana,  New  Jersey,  New  York,  North  Carolina,  North  Dakota,  Oregon, 
Pennsylvania,  South  Carolina,  Utah,  Virginia,  Washington,  and  Wisconsin. 

Laws  are  pending  (1921)  in  Indiana,  Iowa,  and  Minnesota!. 

Theory  of  Registration  Laws.  The  reason  for  the  regulation  of  archi- 
tectural PRACTICE  BY  LAW  is  the  fact  that  men  improperly  qualified  to 
practice  can  otherwise,  at  will,  assume  the  title  of  architect  and  impose  upon 
the  public,  thereby  discrediting  the  profession.  In  some  States  and  in  Canada 
it  seems  evident  that  legislation  was  enacted  for  protection  of  local  architects 
against  encroachment  on  the  part  of  non-resident  architects.  Such  a  motive 
is  unworthy  of  the  profession,  whose  efforts  through  legislation  should  be  to 
encourage  design  of  higher  artistic  quahty  and  to  insure  safe  construction. 
Some  laws,  like  the  first  one  formulated  (Illinois  1897),  are  license  laws  in  that 
they  tax  every  architect.  Other  laws,  that  in  New  York,  for  example,  called 
registration  laws,  undertake  to  issue  certificates  only  to  those  qualified  to 
practice.  Registration  laws  should  not  in  a  retroactive  way  attempt  to  deprive 
those  of  their  right  who,  by  virtue  of  having  been  in  bona-fide  practice  when 
the  law  was  enacted,  have  the  legal  right  to  continue  in  such  practice,  S'ubject 
to  the  effect  of  pubHc  sentiment  which  may  be  created  against  non-registered 
architects,  and  subject  also  to  responsibihties  imposed  by  building  ordinances 
requiring  safe  construction.  The  theory  of  the  registration  law  is  that 
an  architect  should  attain  to  a  certain  minimum  general  education,  a  certain 
minimum  technical  education,  plus  a  certain  minimum  of  practical  experience, 
before  beginning  practice  on  his  own  account.  That  theory  is  carried  into 
effect  by  requiring  under  penalty  that  no  person  may  assume  the  title  architect 
whether  he  is  a  new  practitioner,  or  an  experienced  practitioner  from  without 
the  State,  without  first  estabhshing  his  qualifications  and  receiving  a  certificate 
authorizing  him  to  use  that  title.     The  new  york  state  law,  printed  here- 

*  This  matter  was  prepared  by  D.  Everett  Waid,  President  of  the  New  York  State 
Board  of  Examiners  and  Registration  of  Architects  (term  expires,  1922). 


Registration  of  Architects.     New  York  State  17G9 

with,  is  typical  of  recent  laws  which  attempt  to  embody  this  theory.  References 
here  are  made  to  this  law  and  the  notation  also  that  the  American  Institute 
of  Architects  is  prepared  to  cooperate  with  any  persons  interested  who  desire 
to  improve  upon  the  laws  already  passed  when  trying  to  secure  in  other  States 
such  legislation  as  will  tend  to  raise  the  standard  of  quaUfications  of  architects. 
Such  legislation  will  certainly  achieve  its  highest  end  if  looked  upon  as  educa- 
tional in  purpose.  Incidentally  it  may  be  remarked  that  the  best  interests  of 
all  will  be  conserved  if  earnest  efforts  are  made  toward  a  common  standard 
which  will  encourage  reciprocal  relations  among  the  States.  An  architect 
who  has  demonstrated  his  quahfications  by  passing  a  proper  examination  in 
one  State  should  not  be  harassed  by  repetitions  of  the  test  in  other  States 
in  which  he  may  choose  to  practice. 

Standards  of  Education..  The  general  education  required  under  the 
New  York  law  is  the  completion  of  a  high-school  course,  or  equivalent  thereof; 
also  the  satisfactory  completion  of  such  courses  in  mathematics,  history,  and 
one  modern  language,  as  are  included  in  two  years  of  an  approved  institution 
granting  the  degree  of  A.B.  Five  years'  practical  experi];:nce  in  the  office 
of  a  reputable  architect,  beginning  after  the  high-school  course,  is  required 
before  a  candidate  can  take  the  technical  examination  conducted  by  the 
Board  of  Examiners.  This  technical  examination  is  not  required  of  graduates 
of  recognized  schools  of  architecture  who  shall  have  had,  also,  three  years'  prac- 
tical experience. 

Administration  of  Registration  Laws.  In  New  York  State,  architects 
are  admitted  to  practice  by  the  Regents  of  the  University  of  the  State,  who 
administer  the  law  through  a  Board  of  Examiners  and  Registration  of 
Architects.  In  other  States,  the  Boards  of  Examiners  are  appointed  by  the 
Governors. 

Application  for  Certificates.  AppUcation-blanks  and  information  regard- 
ing admittance  to  practice,  dates  of  examinations,  etc.,  can  be  obtained  by 
addressing  the  Board  of  Examiners  and  Registration  of  Architects,  Education 
Building,  Albany,  N.  Y.  In  other  States,  such  inquiries  may  be  addressed 
to  the  Secretary  of  State. 

Model  Registration  Law.  Those  interested  in  state  legislation  regu- 
lating  THE   practice   OF   ARCHITECTURE   AND   THE  EDUCATION  OF  ARCHITECTS 

may  secure  copies  of  a  bill  issued  to  serve  as  a  basic  model  which,  with  suitable 
modifications,  may  be  enacted  in  any  State.  Address  the  Secretary,  American 
Institute  of  Architects,  The  Octagon  House,  Washington,  D.  C. 

REGISTRATION    OF    ARCHITECTS   IN  THE   STATE   OF   NEW 
YORK* 

The  law  in  relation  to  the  practice  of  architecture  and  the  rules  of  the 
State  Board  of  Examiners  and  Registration  of  Architects  approved 
by  the  Regents  of  The  University  of  the  State  of  New  York 

The  Assistant  Commissioner  and  Director  of  Professional  Education  is  in 
charge  of  universities,  colleges,  professional  and  technical  schools,  the  execution 
of  the  laws  concerning  the  professions,  and  the  relations  and  chartering  of 
institutions.  All  correspondence  relating  to  the  issuance  of  certificates,  the 
details  of  licensing  examinations,  and  admissions  to  the  practice  of  architecture 

*  The  form  of  the  law  itself  and  of  the  State  official  documents,  with  the  exception  of 
the  type,  are  inserted  as  enacted  and  printed,  without  further  editing. 


1770  Registration  of  i\rcliitccts.    New  York  State  Part  3 

should  be  addressed  to  the  Director  of  the  Examinations  and  Inspections 
Division,  Albany,  N.  Y. 

REGISTERED  ARCHITECTS 

General  business  law  (L.  1909,  Ch.  25)  Chapter  20  of  the  consolidated  laws, 
became  a  law  February  17,  1909 

Article  7-A,  Registered  Architects 

Became  a  law  April  28, 19 15  (Laws  of  1915,  Chapter  454).   As  amended  by  Laws  of  1918, 
Chapter  77. 

Section  77.    Registered  Architects. 

Section  78.     Board  of  Examiners. 

Section  79.     Qualifications.     Examinations.     Fees. 

Section  79a.  Certificates. 

Section  79b.  Violation  of  Article. 

77.  Registered  Architects.  Any  person  residing  in  or  having  a  place  of 
business  in  the  State,  who,  before  this  article  takes  effect,  shall  not  have  been 
engaged  in  the  practice  of  architecture  in  New  York  State,  under  the  title 
of  architect,  shall,  before  being  styled  or  known  as  an  architect,  secure  a  cer- 
tificate of  his  qualification  to  practice  under  the  title  of  architect,  as  provided 
by  this  article.  Any  person  who  shall  have  been  engaged  in  the  practice  of 
architecture  under  the  title  of  architect,  before  this  article  takes  effect,  may  ■ 
secure  such  certificate,  in  the  manner  provided  by  this  article.  Any  person 
having  a  certificate  pursuant  to  this  article  may  be  styled  or  known  as  a  regis- 
tered architect.  No  other  person  shall  assume  such  title  or  use  the  abbreviation 
R.  A.,  or  any  other  words,  letters  or  figures  to  indicate  that  the  person  using 
the  same  is  a  registered  architect;  but  this  article  shall  not  be  construed  to 
prevent  persons  other  than  architects  frorn  filing  applications  for  building 
permits  or  obtaining  such  permits. 

78.  Board  of  Examiners  and  Registration.  There  shall  be  a  State  Board 
of  Examiners  and  Registration  of.  Architects,  who,  and  their  successors,  shall 
be  appointed  by  and  hold  during  the  pleasure  of  the  Board  of  Regents  of  The 
University  of  the  State,  and  who,  subject  to  the  approval  and  to  the  rules  of 
the  Regents,  may  make  rules  for  the  examination  and  registration  of  candidates 
for  the  certificates  provided  for  by  this  article.  Such  board  of  examiners  shall 
be  composed  of  five  architects,  who  have  been  in  active  practice  in  the  State 
of  New  York  for  not  less  than  ten  years,  previous  to  their  appointment,  selected 
by  the  Regents.  Such  examiners  shall  be  entitled  to  such  compensation  for 
their  services  under  this  article  as  the  Board  of  Regents  shall  determine,  not 
exceeding  in  the  aggregate  the  amount  of  fees  collected  from  applicants  for 
certificates. 

79.  XJualification.  Examination.  Fees.  Any  citizen  of  the  United 
States,  or  any  person  who  has  duly  declared  his  intention  of  becoming  such 
citizen,  being  at  least  twenty-one  years  of  age  and  of  good  moral  characteri 
may  apply  for  examination  or  certificate  of  registration  under  this  article,  but 
before  securing  such  certificate  shall  submit  satisfactory  evidence  of  having 
satisfactorily  completed  the  course  in  high  school  approved  by  the  Regenti 
of  the  University  or  the  equivalent  thereof  and  subsequent  thereto  of  havini 
satisfactorily  completed  such  courses  in  mathematics,  history  and  one  moderi 
language,  as  are  included  in  the  first  two  years  in  an  institution  approved  b] 
the  Regents,  conferring  the  degree  of  bachelor  of  arts.     Such  candidate  shall  h 


Registration  of  Architects.     New  York  State  1771 

addition  submit  satisfactory  evidence  of  at  least  five  years'  practical  experience 
in  the  office  or  offices  of  a  reputable  architect  or  architects,  commencing  after 
the  completion  of  the  high  school  course.  The  board  of  examiners  may  accept 
satisfactory  diplomas  or  certificates  from  approved  institutions  covering  the 
course  required  for  examination.  Upon  complying  with  the  above  require- 
ments, the  applicant  shall  satisfactorily  pass  an  examination  in  such  technical 
and  professional  courses  as  are  established  by  the  board  of  examiners.  The 
board  of  examiners  in  lieu  of  examinations  may  accept  satisfactory  evidence 
of  any  one  of  the  quahfications  set  forth  under  subdivisions  i  and  2  of  this 
section. 

1.  A  diploma  of  graduation  or  satisfactory  certificate  from  an  architectural 
college  or  school  approved  by  the  Regents,  together  with  at  least  three  years' 
practical  experience  in  the  office  or  offices  of  a  reputal^le  architect  or  architects; 
but  the  three  years'  experience  shall  be  counted  only  as  beginning  at  the  com- 
pletion of  the  course  leading  to  the  diploma  or  certificate;  the  State  Board  of 
Examiners  and  Registration  of  Architects  may  require  applicants  under  this 
subdivision  to  furnish  satisfactory  evidence  of  knowledge  of  professional  prac- 
tice; 

2.  Registration  or  certification  as  an  architect  in  another  state  or  country, 
where  the  qualifications  required  for  the  same  are  equal  to  those  required  in 
this  State; 

3.  The  board  of  examiners  in  lieu  of  all  examinations  shall  accept  satisfactory 
evidence  as  to  the  applicant's  character,  competency  and  qualifications,  and 
that  he  has  been  continuously  engaged  in  the  practice  of  architecture  for  more 
than  two  years  next  prior  to  the  date  when  this  article  shall  take  effect,  or  that 
he  has  been  actually  engaged  in  the  practice  of  architecture  on  his  own  account 
or  as  a  member  of  a  reputable  firm  or  association  for  more  than  one  year  prior 
to  the  date  when  this  article  shall  take  effect;  providing  the  apphcation  for 
such  certification  shall  be  made  on  or  before  January  i,  19 18.  Any  architect 
who  has  lawfully  practiced  architecture  for  a  period  of  more  than  ten  years 
without  the  State  shall  be  required  to  take  only  a  practical  examination,  which 
shall  be  of  the  nature  to  be  determined  by  the  State  Board  of  Examiners  and 
Registration  of  Architects.  Every  person  applying  for  examination  or  certifi- 
cate of  registration  under  this  article  shall  pay  a  fee  of  twenty-five  dollars  to 
the  Board  of  Regents. 

79a.  Certificates,  i.  The  result  of  every  examination,  or  other  evidence 
of  quahfication,  as  provided  by  this  article,  shall  be  reported  to  the  Board  of 
Regents  by  the  board  of  examiners,  and  a  record  of  the  same  shall  be  kept 
by  the  Board  of  Regents,  and  such  board  shall,  unless  deemed  otherwise  advis- 
able, issue  a  certificate  of  registration  to  every  person  certified  by  the  board 
of  examiners  as  having  passed  such  examination  or  as  being  otherwise  qualified 
to  be  entitled  to  receive  the  same. 

2.  Every  person  securing  such  certificates  shall  register  in  the  office  of  the 
county  clerk  of  the  county  in  which  he  maintains  a  place  of  business,  in  a  book 
kept  by  the  clerk  for  such  purpose,  his  name,  residence,  place  and  date  of  birth 
and  post  office  address,  source,  number  and  date  of  his  certificate  of  registration 
to  practice  architecture  and  the  date  of  such  registration,  which  registration 
he  shall  be  entitled  to  make  only  upon  showing  to  the  county  clerk  his  certificate 
of  registration  and  making  an  affidavit  of  the  above  facts,  and  that  he  is  the 
identical  person  named  in  the  certificate;  that  before  receiving  the  same  he 
complied  with  all  of  the  preliminary  requirements  of  this  article  and  the  rules 
of  the  Regents  and  the  board  of  examiners  as  to  the  terms  and  the  amount 
of  c^tudy  and  examination;    that  no  money  other  than  the  fees  prescribed  by 


1772  Registration  of  Architects.     New  York  State  Part  3 

this  article  and  such  rules  was  paid  directly  or  indirectly  for  such  registration, 
and  that  no  fraud,  misrepresentation  or  mistake  in  material  regard  was  em- 
Jjloyed  or  occurred  in  order  that  such  certificate  should  be  made,  which  affidavit 
shall  be  preserved  in  a  bound  volume  by  the  county  clerk.  The  county  clerk 
shall  indorse  or  stamp  on  the  back  of  the  certificate  the  date  and  his  name 
preceded  by  the  words  '*  registered  as  authority  to  practice  as  a  registered 

architect,  in  the  clerk's  office  of county";    and  shall 

issue  to  each  person  duly  registering  and  making  such  affidavit  a  certificate 
of  registration  in  his  county  which  shall  include  a  transcript  of  the  registration. 
Such  transcript  and  the  certificate  of  registration  may  be  offered  as  presump- 
tive evidence  in  all  courts  of  the  facts  stated  therein.  The  county  clerk's 
fee  for  taking  such  registration  and  affidavit  and  issuing  such  certificate  shall 
be  one  dollar.  Any  person  who,  having  lawfully  registered  as  aforesaid,  shall 
thereafter  change  his  name  in  any  lawful  manner,  shall  register  the  new  name 
with  a  marginal  note  of  the  former  name,  and  shall  note  upon  the  margin  of 
the  former  registration  the  fact  of  such  change  and  a  cross-reference  to  the  new 
registration.  A  county  clerk  who  knowingly  shall  make  or  suffer  to  be  made 
upon  the  book  of  registry  of  architects  kept  in  his  office  any  other  entry  than 
is  provided  for  in  this  article  shall  be  guilty  of  a  misdemeanor. 

3.  An  architect  having  duly  registered  to  practice  as  a  registered  architect  in 
one  county  and  removing  his  practice  or  a  part  thereof  to  another  county  or 
regularly  engaging  in  practice  or  opening  an  office  in  another  county,  shall  show 
or  send,  by  registered  mail,  to  the  clerk  of  such  other  county,  his  certificate 
of  registration.  If  such  certificate  clearly  shows  that  the  original  registration 
was  duly  issued  Under  seal  l:)y  the  Board  of  Regents,  the  clerk  shall  thereupon 
register  the  applicant  in  the  latter  county  on  receipt  of  a  fee  of  25  cents  and 
shall  stamp  or  indorse  on  such  certificate  the  date  and  his  name,  preceded  by 

the  words  "Registered  also  in county,"  and  return 

the  certificate  to  the  applicant. 

4.  The  Board  of  Regents  may  revoke  any  certificate,  if  such  action  be  recom- 
mended by  the  board  of  examiners,  after  thirty  days'  written  notice  to  the 
holder  thereof  and  after  a  hearing  before  the  board  of  examiners,  upon  proof 
that  such  certificate  has  been  obtained  by  fraud  or  misrepresentation,  or  upon 
proof  that  the  holder  of  such  certificate  has  been  guilty  of  felony  in  connection 
with  the  practice  of  architecture. 

79b.  Violation  of  Article.  Any  violation  of  this  article  shall  be  a  mis- 
demeanor, punishable  for  the  first  offense  by  a  fine  of  not  less  than  fifty  and 
not  more  than  one  hundred  dollars,  and  for  a  subsequent  offense  by  a  fine 
of  not  less  than  two  hundred  nor  more  than  five  hundred  dollars,  or  imprison- 
ment for  not  more  than  one  year,  or  both. 

SYNOPSIS  OF  SUBJECTS  ON  WHICH  EXAMINATIONS  ARE  BASED  • 

The  examinations  of  applicants  for  certificates  shall  be  based  on  the  four 
following  subjects  or  groups: 

a.  History  of  Architecture.  The  candidate  shall  give  evidence  in  the 
examination  that  he  understands  the  essentials  that  give  character  to  the 
various  historic  styles  of  architecture  by  clear  descriptive  analyses  of  plan, 
construction,  general  expression  and  ornament.  Questions  will  be  asked 
relating  to: 

(i)  Architecture  in  various  countries. 

*  Taken  from  the  Rules  of  the  New  York  State  Board  of  Examiners  and  Registration 
of  Architects. 


Registration  of  Architects.     New  York  State  J773 

(2)  Styles  and  orders.     Sketches  and  names  of  examples. 

(3)  Sculpture  and  painting  and  color  as  applied  to  architecture. 

(4)  Furniture  and  decoration. 

b.  Architectural  Composition.  The  candidate  shall  give  evidence  that 
he  understands  the  broad  principles  underlying  the  subject  of  architectural 
plannmg  by  the  application  of  the  same  to  specific  problems  stated  in  the 
examination.  The  social,  economic  and  physical  requirements  of  several 
architectural  problems  will  be  outlined  and  the  candidate  will  be  asked  to 
state  the  principal  considerations  that  would  guide  him  in  the  choice  of  an 
arrangement  of  plan  that  would  most  adequately  express  and  fulfill  the  con- 
ditions suggested.  Small  sketches  will  be  required  to  illustrate  the  application 
of  the  principles  involved.     Questions  will  refer  to: 

(i)  Principles  of  Planning:  Problems  in  planning  individual  buildings, 
groups  and  towns;  illustrations  may  "be  asked  to  show  how  plans  may  be 
influenced  by  considerations,  esthetic,  structural,  and  as  to  kinds  of  materials, 
and  modifications  of  plan  due  to  considerations  of  occupancy  and  of  fire  pre- 
vention both  for  fireproof  and  non-fireproof  buildings. 

(2)  Esthetic  Design:  Original  examples  will  be  required  illustrating  prin- 
ciples involved  in  the  solution  of  practical  problems  and  the  relation  of  plan 
to  elevation. 

c.  Architectural  Engineering.  In  this  examination  the  candidate  shall 
give  evidence  that  he  has  a  thorough  understanding  of  the  appropriate  use 
of  the  various  materials  used  in  buildings.  He  will  be  required  also  to  solve 
certain  technical  problems  siich  as  the  calculation  of  the  proper  economic 
dimensions  of  various  structural  members  common  to  buildings,  in  the  several 
materials  noted.  Candidates  will  not  be  required  to  make  complicated  calcu- 
lations, and  the  use  of  handbooks  will  be  permitted.  Questions  will  be  asked 
as  to  the  knowledge  of  these  subjects  that  an  architect  should  possess  in  order 
properly  to  advise  his  clients  and  to  design  or  to  direct  the  designing  of  suitable 
mechanical  equipment  for  buildings  of  different  classes.  Questions  will  be  asked 
relating  to: 

(i)  Structural  Design: 

Column,  girder,  joist  and  truss  designs. 

Wind  bracing  for  buildings  of  different  classes. 

Various  types  of  foundations  and  conditions  under  which  their  use  is  advisable. 

Various  kinds  of  bottom  met  with  in  ordinary  practice  and  unit  loads  allowable 
under  foundations  in  each  case. 

Different  types  of  concrete  floor  slab  construction  in  common  use. 

Structural  design  as  affected  by  fire  and  resistive  quaUties  of  different  build- 
ing materials. 

(2)  Use  of  Materials: 

Strength  of  materials,  durability  and  considerations  of  wear  and  repair. 
Esthetic  reasons  for  use  of  different  materials. 

(3)  Heating  and  Ventilating: 

Various  systems  and  reasons  for  and  against  use  under  specific  conditions. 
Important  features  of  design  that  should  be  specified. 

(4)  Electric  Equipment:    General  questions  rather  than  technical. 
Various  kinds  of  current  and  considerations  involved. 

Kinds  of  wiring  and  insulation;   methods  and  materials. 

Light  distribution.  .  u     •    1 

Lighting   fixtures;    esthetic   and   practical   design;     important   mechanical 

details. 


1774  Registration  of  Architects.     New  York  State  Part  3 

Generators,  motors,  storage  batteries,  and  advice  to  clients  regarding  the 
same. 

Independent  power  plant  considerations. 

(5)  Plumbing  and  Fire  Protection  Equipment: 
Supply  and  waste  systems. 

Kinds  of  material  for  piping  and  reasons  for  use. 

Kinds  of  materials  for  fixtures. 

Sewage  disposal  plants  and  considerations  involved. 

Water  supply,  different  systems  and  considerations  of  supply  and  filtration. 

Sprinklers  and  other  fire  protection  equipment. 

(6)  Elevators: 
Types  of  elevators. 

Arrangement  and  location  of  elevators. 

d.  Architectural  Practice.  In  this  examination  the  candidate  shall  give 
evidence  that  he  understands  the  moral  and  the  legal  responsibilities  of  the 
architect  in  the  proper  performance  of  his  duties  as  such.  He  will  be  required 
to  outline  or  draft  clauses  of  contracts  between  owner  and  architect  and  to 
state  specifically  the  content  of  the  clauses  included  in  the  contract  between 
owner  and  contractor  which  are  incorporated  for  the  purpose  of  defining  the 
architect's  authority  and  responsibility  to  both  parties  of  the  contract.  Each 
candidate  will  be  required  to  show  that  he  understands  the  major  provisions 
of  state,  county  and  municipal  building  laws  and  ordinances  and  how  the  same 
affect  the  different  classes  of  buildings.  He  shall  be  able  also  to  cite  the  com- 
petent authority  under  whose  jurisdiction  permits  for  the  erection  and  occupancy 
of  various  types  of  buildings  must  be  obtained.  Questions  will  be  asked  relat- 
ing to: 

(i)  Business  and  Professional  Functions  of  Architects: 

Professional  relation  of  clients  and  contractors. 

Essential  provisions  in  contract  between  architect  and  his  client. 

When  the  architect  is  disinterested  arbitrator,  and  when  he  properly  may  act 
as  an  agent. 

Relation  of  architects  to  each  other  in  ordinary  practice,  in  association,  and 
in  consultation,  and  when  one  architect  displaces  another  on  a  given  piece  of 
work. 

Sources  and  kinds  of  compensation  for  architect's  services. 

Responsibilities  of  architects  and  methods  of  conducting  their  business. 

Scope  of  architect's  work,  esthetic  and  structural. 

When  expert's  services  should  be  advised. 

Scope  of  architect's  work,  administrative  business,  and  legal  contracts, 
arbitrations,  court  evidence,  contractors  in  default,  when  counsel  of  client's 
lawyer  should  be  advised. 

(2)  Building  Laws: 

State,  county  and  municipal  laws,  ordinances  and  regulations,  and  how 
they  affect  different  classes  of  buildings. 

Filing  drawings  and  specifications  and  obtaining  permits. 

(3)  Contracts: 

Drawings,  specifications  and  agreement  as  essential  parts  of  the  customary 
contract  between  owner  and  builder. 

Variations  in  kinds  and  forms  of  agreements  and  contracts. 

Definition  of  architect's  authority. 

Provisions  as  to  bids,  letting  contracts,  unit  prices,  requisitions,  certificatl 
and  payments. 

Insurance:  fire,  liability,  compensation. 


1 


Registration  of  Schools  of  Architecture  1775 

Bonding  contractors. 

(4)  Specifications: 

General  conditions,  purp  -ises  and  scope. 
Scope  and  purposes  and  limitations  of  general  clauses. 
Principles  which  should  he  observed  in  writing  specifications. 
Right  and  wrong  methods  of  specifying  qualities  of  materials  and  workman- 
ship. 

(5)  Drawings: 

Purposes,  use  and  limitations  of  preliminary  drawings. 
Essentials  which  should  be  embodied  in  contract  drawings. 
Purposes  and  limitations  of  detail  and  other  working  drawings  which  are 
not  contract  drawings. 


REGISTRATION  OF  SCHOOLS  OF  ARCHITECTURE  • 

A  school  of  architecture  may  be  registered  as  maintaining  a  satisfactory 
standard  and  may  be  legally  incorporated.  Incorporation  by  the  Regents  will 
be  made  on  formal  appHcation  and  inspection  by  the  Department  which  show 
that  the  school  possesses  the  minimum  requirements. 

Application.  An  educational  institution  desiring  admission  to  or  incor- 
poration or  registration  by  the  University  must  file  a  written  application  giving 
the  information  requested  in  the  form  prescribed  by  the  Commissioner  of 
Education.  A  form  will  be  mailed  on  application  to  the  Assistant  Commissioner 
for  Higher  Education.  Such  application  must  be  on  file  in  the  Education 
Department  at  least  10  days  before  the  meeting  of  the  Regents  at  which  action 
thereon  is  to  be  taken. 

Accrediting.  Institutions  unable  to  meet  the  standards  required  by  the 
Regents  for  registration  in  fall  shall  be  accredited  by  the  Department  for  one 
or  more  years  of  professional  training  as  they  meet  the  requirements  for  admission 
and  for  professional  training  set  by  the  Regents  standards. 

Recognition  Accorded  Accredited  Professional  Schools.  Professional 
schools  registered  by  the  Regents  shall  give  the  work  of  accredited  institutions 
no  higher  recognition  than  that  accorded  such  institutions  in  the  Department's 
accredited  Ust,  viz.:  (1)  The  successful  completion  of  a  four-year  course  in  a 
professional  school  accredited  by  the  Department  for  three  years  shall  be 
accorded  three  years'  recognition  only;  (2)  the  successful  completion  of  a 
three- year  course  in  a  professional  school  accredited  by  the  Department  for 
two  years  shall  be  accorded  two  years'  recognition  only;  (3)  the  successful 
completion  of  a  two-year  course  in  a  professional  school  accredited  by  the 
Department  for  one  year  shall  be  accorded  one  year's  recognition  only.  A 
registered  school  may  refuse  to  accord  an  accredited  institution  the  recognition 
given  it  by  the  Department  but  it  may  not  give  it  any  higher  recogmtion. 

Comity  of  Action  in  the  Transfer  of  Students  from  One  Professional 
School  to  Another.  The  Department  does  not  consider  a  course  in  a  school 
of  architecture  satisfactory  if  more  than  two  conditions,  one  major  of  100  hours 
and  one  minor  of  50  hours,  are  allowed  students  for  promotion  from  one  year  s 
class  to  the  next. 

*  T^oton  from  thp  Rulcs  of  thc  Ncw  Yofk  State  Board  of  Examiners  and  Registration 
of  ATctTectrls  —  U  be  added  to  the  accredited  lists,  these  Usts  must  be 
revised  from  time  to  time. 


1776  Regents'  Rules.     Schools  of  Architecture  Part  3 

REGENTS'  RULES 
Schools  of  Architecture  * 

440.  Definitions.  School  of  Architecture  means  any  college  or  school 
of  architecture,  or  school,  department  or  course  of  architecture  in  a  college 
or  university,  whatever  the  corporate  title. 

441.  Requirements.  A  School  of  Architecture,  legally  incorporated, 
may  be  registered  as  maintaining  proper  standards.  It  must  afford  satis- 
factory instruction  in  such  technical  and  professional  courses  as  are  established 
by  the  board  of  examiners,  for  admission  to  the  examinations  in  the  history 
of  architecture,  architectural  composition,  architectural  engineering  and  archi- 
tectural practice. 

442.  General  Education.  A.  Preliminary.  For  admission  to  a  school 
of  architecture,  evidence  shall  be  required  showing  the  satisfactory  completion 
of  a  four-year  course  in  a  secondary  school  approved  by  the  Board  of  Regents, 
or  the  equivalent,  72  counts  in  the  academic  examinations.  B.  Higher. 
For  admission  to  the  examinations  for  the  certificate  of  R.  A.  evidence  shall 
be  required  of  such  courses  in  mathematics,  history  and  modern  languages  as 
?ire  included  in  the  first  two  years  of  the  curriculum  leading  to  the  degree  of 
bachelor  in  arts,  or  the  equivalent,  graduation  from  a  junior  college  approved 
by  the  Board  of  Regents. 

SCHOOLS  OF  THE  UNITED   STATES  AND   CANADA  REGISTERED 
OR  ACCREDITED.!     JUNE,    (1918) 

Alphabetically  Arranged  by  States 

United  States 

California.  Registered:  School  of  Architecture,  University  of  California, 
Berkeley.     (Graduate  course,  one  or  two  years.) 

District  of  Columbia.  Registered:  Department  of  Architecture,  George 
Washington  University,  Washington.     (Course,  four  years.) 

Georgia.  Registered:  Department  of  Architecture,  Georgia  School  of 
Technology,  Atlanta.     (Course,  four  years.) 

Illinois.  Registered:  Chicago  School  of  Architecture,  Armour  Institute  of 
Technology,  Chicago.     (Course,  four  years.) 

Department  of  Architecture,  University  of  Ilhonis,  Urbana.  (Course,  four 
years.) 

Indiana.  Registered:  College  of  Architecture,  University  of  Notre  Dame, 
Notre  Dame.     (Course,  four  years.) 

Department  of  Architectural  Engineering,  Rose  Polytechnic  Institute,  Terre 
Haute.     (Course,  four  years.) 

Kansas.  Department  of  Architecture,  Kansas  State  Agricultural  College, 
Manhattan.     (Course,  four  years.) 

Department  of  Architectural  Engineering,  University  of  Kansas,  Lawrence. 
(Course,  four  years.) 

•  Taken  from  the  Rules  of  the  New  York  State  Board  of  Examiners  and  Registration 
of  Architects.  As  schools  may  be  added  to  the  accredited  lists,  these  lists  must  be 
revised  from  time  to  time. 

t  This  is  the  list  of  Schools  or  Departments  of  Architecture  in  the  United  States  and 
Canada,  registered  or  accredited  by  the  New  York  State  Board  of  Examiners  and  Regis- 
tration of  Architects,  and  must  be  added  to  from  time  to  time. 


Schools  Registered  or  Accredited  1777 

Louisiana.  Registered:  School  of  Architecture  and  Architectural  Engi- 
neering, Tulane  University,  New  Orleans.     (Courses,  four  years.) 

Massachusetts.  Registered:  Departments  of  Architecture  and  Archi- 
tectural Engineering,  Massachusetts  Institute  of  Technology,  Cambridge. 
(Courses,  four  years.) 

School  of  Architecture,  Harvard  University,  Cambridge.  (Graduate  Course, 
three  years.) 

Michigan.  Registered:  College  of  Architecture,  University  of  Michigan, 
Ann  Arbor.     (Course,  four  years.) 

Minnesota.  Registered:  Department  of  Architecture,  University  of 
Minnesota,  MinneapoHs.     (Course,  four  years.) 

Missouri.  Registered:  School  of  Architecture,  Washington  University, 
St.  Louis.     (Course,  four  years.) 

Nebraska.  Registered:  Department  of  Architectural  Engineering,  Uni- 
versity of  Nebraska',  Lincoln.     (Course,  four  years.) 

New  York.  Registered:  College  of  Architecture,  Cornell  University, 
Ithaca.     (Course,  four  or  five  years.) 

Department  of  Architecture,  Syracuse  University,  Syracuse.  (Course,  four 
years.) 

School  of  Architecture,  Columbia  University,  New  York.  (Course,  four 
years.) 

Ohio.  Registered:  Department  of  Architecture,  Ohio  State  University, 
Columbus.     (Course,  four  years.) 

Oklahoma.  Registered:  Department  of  Architecture,  Oklahoma  Agri- 
cultural and  Mechanical  College,  Stillwater.     (Courses,  four  years.) 

Pennsylvania.  Registered:  Department  of  Architectural  Engineering, 
Pennsylvania  State  College,  State  College.     (Course,  four  years.) 

Department  of  Architecture,  University  of  Pennsylvania,  Philadelphia. 
(Courses,  four  years.) 

Department  of  Architecture,  Carnegie  Institute  of  Technology,  Pittsburgh. 
(Course,  four  years.) 

Texas.  Registered:  Departments  of  Architecture  and  Architectural 
Engineering,  Agricultural  and  Mechanical  College  of  Texas,  College  Station. 
(Courses,  four  years.) 

School  of  Architecture,  University  of  Texas,  Austin.     (Course,  four  years.) 

Canada 

Ontario.  Registered:  Department  of  Architecture,  University  of  Toronto, 
Toronto.     (Course,  four  years.) 

Quebec.  Department  of  Architecture,  McGill  University,  Montreal 
(Course,  five  years.) 

SYNOPSIS  OF  REGISTRATION  LAWS*    • 

This  study  t  is  made  for  those  who  would  see  at  a  glance  the  statutory 
requirements  for  the  practice  of  architecture  throughout  the  Umted  States. 

*As  States  are  added  to  the  list  of  those  which  have  laws  f«^the  Registration  of 
Architects  these  lists  must  be  revised  from  time  to  time.  Georgia,  Michigan,  Penn- 
syTvant  Vi  gS^  Washington  have  been  added  to  the  list  up  to  January   x92x^ 

t  Taken  from  Handbook  No.  35,  published  annually  by  The  University  of  the  State 
of  New  Yortand  containing  information  relating  to  the  Registration  of  Architects, 


1778  Synopsis  of  Registration  Laws  Part  3 

There  are  four  distinct  lines  of  statutory  requirements:  (i)  Preliminary  educa- 
tion; (2)  professional  training;  (3)  licensing  test;  (4)  registry.  These  four 
items  with  (5)  the  title  of  the  executive  officer  and  the  administrative  board 
are  given  uniformly  in  this  synopsis.*  If  there  are  no  statutory  requirements 
the  word  "none"  covers  the  item. 

California,  (i)  None;  (2)  none;  (3)  examination;  (4)  with  the  recorder 
of  the  county  of  residence  annually;  (5)  secretary,  State  Board  Architecture, 
San  Francisco. 

Colorado,  (i)  None;  (2)  none;  (3)  examination  or  certificate  from  a 
similarly  constituted  board  of  another  state;  (4)  with  the  secretary  of  state  and 
annually  with  the  board;  (5)  Secretary,  State  Board  of  Examiners  of  Archi- 
tects, Denver. 

Idaho,  (i)  Approved  high  school  course  or  its  equivalent  and  in  addition  a 
two-year  course  in  English  and  mathematics  such  as  is  required  in  an  approved 
B.  A.  course;  (2)  three  years'  practical  experience  in  the  office  of  a  reputable 
architect;  (3)  examination  or  in  lieu  of  all  examinations,  graduation  from  an 
approved  architectural  school  or  registartion  as  an  architect  in  another  state 
whose  standard  equals  that  of  this  board;  (4)  with  the  secretary  of  state;  (5) 
Secretary,  State  Board  of  Examiners  of  Architects. 

Illinois,  (i)  None;  (2)  none;  (3)  examination;  (4)  with  the  clerk  of  the 
county  of  practice,  annually;  (5)  Secretary,  Department  of  Registration  and 
Examination,  Springfield. 

Louisiana,  (i)  Good  primary  education;  (2)  none;  (3)  examination  or 
diploma  from  an  approved  school  of  architecture;  (4)  with  the  district  court 
clerk  of  the  parish  of  residence  and  annually  with  the  board;  (5)  Secretary 
Board  of  Architectural  Examiners,  New  Orleans. 

Montana,  (i)  None;  (2)  none;  (3)  examination  or  a  license  from  another 
state  l)oard;  (4)  with  the  clerk  and  recorder  of  the  county  of  residence  and 
annually  with  the  state  treasurer;  (5)  Secretary,  Board  of  Architectural  Exami- 
ners. 

New  Jersey,  (i)  None;  (2)  none;  (3)  examination  or  a  license  from  a 
similarly  constituted  board  of  another  state  or  membership  in  the  American 
Institute  of  Architects;  (4)  with  the  board,  annually  and  with  the  secretary 
of  state;   (5)  Secreta'-y,  State  Board  of  Architects,  Trenton. 

New  York,  (i)  Approved  high  school  course  or  the  equivalent  and  in 
addition  such  course  in  mathematics,  liistory  and  one  modern  language  as  are 
included  in  an  approved  two-year  B.  A.  course;  (2)  at  least  five  years'  practical 
experience  in  the  office  of  a  reputable  architect;  (3)  examination  or  graduation 
from  an  approved  architectural  school  with  three  years'  experience  or  regis- 
tration in  another  state  or  country  having  standards  equal  to  that  of  this  board; 
(4)  with  the  Board  of  Regents;  (5)  Secretary,  State  Board  of  Examiners  and 
Registration  of  Architects,  New  York. 

North  Carolina,  (i)  Prescribed  bj'-  the  board;  (2)  prescribed  by  the 
board;  (3)  examination  or  a  certificate  from  a  similarly  constituted  board  in 
another  state  or  membership  in  the  American  Institute  of  Architects;  (4) 
with  the  clerk  of  the  superior  court  of  the  county  of  residence;  (5)  Secretary  of 
the  Board  of  Architectural  Examination  and  Registration. 

North  Dakota,  (i)  Approved  high  school  course  or  its  equivalent;  (2) 
three  years'  practical  experience  in  the  office  of  a  reputable  architect;    (3) 

*  The  names  of  the  executive  officers,  Secretaries  of  the  Boards,  etc.,  are  omittec} 
here,  as  the  personnel  is  constantly  changing. 


Institutions  Teaching  Architecture  1779 

examination  or  a  license  from  another  state  board  whose  standard  equals  that 
of  this  board  or  membership  in  the  American  Institute  of  Architects;  (4)  with 
the  secretary  of  state  and  annually  with  the  board;  Secretary,  State  Board  of 
Architecture,  Bismarck- 
South  Carolina,  (i)  None;  (2)  at  least  two  years'  experience  in  archi- 
tectural work;  (3)  examination  or  graduation  from  an  approved  school  of 
architecture;  (4)  with  the  board,  annually;  (5)  Secretary,  State  Board  of 
Architectural  Examiners,  Columbia. 

Utah,  (i)  None;  (2)  none;  (3)  examination;  (4)  with  the  board,  annually; 
(5)  Secretary,  State  Board  of  Architecture. 

Wisconsin.  (0  None;  (2)  at  least  five  years'  practical  experience  in  the 
ofhce  of  a  reputable  architect;  (3)  examination  or  a  satisfactory  certificate 
from  a  recognized  architectural  school  with  three  years'  experience  or  registra- 
tion with  the  1)oard  of  another  state  or  country  whose  standards  are  not  lowe. 
than  those  of  this  board;  (4)  with  the  Industrial  Commission;  (5)  Secretary 
of  the  Board  of  Examiners  of  Architects,  Madison. 

FmiCATIONAL     INSTITUTIONS     IN     THE     UNITED 
??ATES  AND  CANADA  OFFERING   COURSES  IN 
ARCHITECTURE.    TRAVELLING  FELLOW- 
SHIPS AND  SCHOLARSHIPS 

1.  Association  of  Collegiate  Schools  of  Architecture 
A         •  ♦•««  nf  rnlleeiate  Schools  of  Architecture.    Organized  in  1912 

and  ftl^Sme  ieT.^  M^^^^^^^^  "^  Technology.     (Office-9- 

pl^trEmilLorch;  Vice-Presid»t.^V^Ham  Emerson^ 

broadly    sun^marized    as  follows:     (       ^^^^^^^^^^^^  „f  both  general  and 

Foundation;    (2)  A  course  of  at  least  "° ^f;"^    anoroved  method  of  presen- 

professional  studies  of  cenamm^^^^^^^^^^^^ 

tat  on,  leading  to  a  degree  not  le.s  cna  adequacy  of  equipment 

of  staff   and  administration,  ^andrngj^co^^^^^^^ 

as  will  reasonably  assure  quahty  .«' /^f  "™^^^'f 'f^;;  years.     The  Association 

of  all  American  schools  are  welcomed. 

2.  Educational  Institutions.  Fellowships,  and  Scholarships 

Academy  of  Architecture  and  Indusu;  IS  ie„ce.^  ^^^ 

is  a  private  school  ^""ded  by  Mr^  Maj^A^n        5.  .^^  ^^^^  ^^^^  .„         ^^^ 


1780  Institutions  Teaching  Architecture  Part  3 

understanding  of  the  plans  and  details  of  complicated  buildings.  There  is 
also  a  special  course  for  those  desiring  to  fit  themselves  for  positions  as  draughts- 
men in  architects'  offices.  Tuition  for  the  regular  course  is  $50  for  a  three- 
months'  term,  or  $300  for  the  full  course  of  eight  terms,  or  $100  for  the  year. 
Several  special  courses  with  varying  tuition. 

Alabama  Polytechnic  Institute,  Auburn,  Ala.  Department  of 
Architecture,  (i)  Full  four-year  course  leading  to  the  degree  of  Bachelor 
of  Science  in  Architecture.  (2)  Full  four-year  course  leading  to  the  degree 
of  Bachelor  of  Science  in  Architectural  Engineering.  (3)  Two-year  special 
course  for  draftsmen  and  college  graduates.  Tuition  free  to  residents  of 
Alabama;  $20  per  year  for  others.  About  two  dozen  loan-scholarships  of 
$100  or  more  per  annum.  Limited  number  of  fellowships  of  $250  for  post- 
graduates.    Illustrated  Announcement  giving  details,  sent  on  request. 

American  Academy  in  Rome,  Fellowship  in  Architecture.  Roman 
Prize.  The  fellowship  is  awarded  annually  and  is  of  the  value  of  $1  000  a  year 
for  three  years.  The  award  is  made  on  competitions  which  are  open  only  to 
unmarried  male  citizens  of  the  United  States,  who  comply  with  the  regulations 
of  the  Academy.  Candidates  are  required  to  be  (i)  graduates  of  one  of  the 
architectural  schools  included  in  the  accepted  list  of  the  Academy;  or  (2)  grad- 
uates of  a  college  or  university  of  high  standing  who  hold  certificates  of  at  least 
two  years*  study  in  one  of  such  architectural  schools;  or  (3)  Americans  who 
are  pupils  of  the  first  class  of  the  School  of  Fine  Arts  at  Paris,  and  who  have 
obtained  at  least  three  values  in  that  class.  There  is  no  age-limit.  Information 
as  to  the  terms  and  conditions  of  the  competitions  may  be  obtained  from  the 
Secretary  of  the  Academy,  10 1  Park  Avenue,  New  York  City. 

American  School  of  Correspondence,  Chicago,  111.  Correspondence- 
courses  in  Architecture,  Architectural  Engineering,  Contracting  and  Building, 
Reinforced  Concrete,  Architectural  Design,  and  Structural  Draughting.  Bulle- 
tin sent  on  application. 

Armour  Institute  of  Technology,  Chicago,  III.  Full  four-year  course 
leading  to  the  degree  of  Bachelor  of  Science  in  Architecture.  Applicants  for 
admission  must  have  completed  the  regular  four-year  high-school  course. 
A  Home  Traveling- Scholarship,  four  prizes,  and  a  medal  are  awarded  annu- 
ally.    Tuition,  $180  per  year. 

Beaux  ATts  Institute  of  Design,  126  East  75th  Street,  New  York,  N.  Y. 
Department  of  Architecture.  (Address  all  communications  to  this  depart- 
ment.) The  course,  established  in  1893,  consists  (1920)  of  a  seriesof  thirty-five 
competitions,  issued  annually,  for  the  study  of  architectural  design  and  the  styles 
of  architecture,  open  to  the  draughtsmen  and  students  in  architectural  schools 
in  the  United  States  and  Canada,  and  modeled  on  the  system  of  instruction 
adopted  by  the  Ecole  des  Beaux  Arts  in  Paris.  The  course  is  free,  except  for 
the  annual  fee  of  $2  for  registration  of  each  student.  There  are  no  restrictions 
as  to  the  age,  nationality,  or  sex  of  the  students.  No  preliminary  examinations 
are  given,  but  new  students  are  expected  to  have  a  knowledge  of  the  five  orders 
of  architecture.  Bronze  and  silver  medals  are  awarded  for  excellence  in 
design  and  money-prizes  are  offered  in  special  prizes  for  decoration,  group- 
planning  of  buildings,  etc.  Certificates  are  presented  to  all  students  of 
Class  A  completing  the  course  as  defined  in  the  circular  of  information,  which 
is  furnished  on  request.  During  the  season  1917-1918  the  work  was  carried 
on  by  one  hundred  and  eleven  correspondents  of  the  Institute  in  eighty-eight 
different  cities,  with  a  total  of  seven  hundred  and  seventy- four  students. 

Department  of  Interior  Decoration  (Address  all  communications  to  this 


\  Institutions  Teaching  Agriculture  1781 

department).  The  course  consists  of  programmes  for  competitions  issued 
every  sLx  weeks  to  those  who  apply  for  them.  These  may  be  executed  by 
students  situated  in  any  locaUty  and  sent  in  to  the  Institute  where  they  will  ' 
be  criticized  and  judged  on  fixed  dates  by  a  jury  of  experts.  Bkonze  and 
SILVER  MEDALS  are  awarded  for  excellence.  An  atelier  for  male  students  under 
the  instruction  of  several  decorators  exists  in  the  building  of  the  Institute. 
There  are  no  fees  of  any  kind.  No  formalities  or  examinations  are  necessary 
for  admission  to  the  atelier.     A  circular  is  furnished  on  request. 

Department  of  Sculpture.  (Address  all  communications  to  this  depart- 
ment). Ateliers  for  male  students  for  each  one  of  the  three  courses  (Archi- 
tectural Ornament,  Life  Drawing,  and  Modeling  and  Composition)  exist  in 
the  building  of  the  Institute.  No  examinations,  formalities,  or  fees  of  any 
kind.  Open  all  day  all  the  year  round.  Instructors  visit  their  classes  twice 
a  week.  Judgments  by  expert  juries  every  four  weeks  on  the  work  of  the 
preceding  month.  Bronze  and  silver  medals  awarded.  A  circular  is  fur- 
nished on  request. 

Department  of  Mural  Painting  (Address  all  communications  to  this 
department).  The  course  consists  of  pioblems,  programmes  of  which  are 
issued  every  month  to  those  who  apply  for  them.  Judgments  by  a  jury  of 
artists  every  month  on  the  designs  handed  in.  Bronze  and  silver  medals 
awarded.  No  examinations,  formalities,  or  fees  of  any  kind.  There  is  no 
atelier  for  this  department  at  the  Institute  and  students  work  up  their  problems 
under  their  own  instructors  wherever  they  may  be  situated.  A  circular  is 
furnished  on  request. 

Beaux  Arts  Archhects,  Society  of.  126  East  75th  Street,  New 
York,  N.  Y.  The  course  in  Architectural  Design  estabUshed  in  1893  and 
formerly  conducted  by  the  Committee  on  Education  of  this  Society,  is  now 
carried  on  by  the  Beaux  Arts  Institute  of  Design.  (See  Beaux  Arts  Institute 
of  Design.) 

Paris  Prize.  This  scholarship-prize  is  usually  conducted  annually  by 
the  Society  of  Beaux  Arts  Architects.  Under  its  conditions  the  winner  re- 
ceives $1  200  per  annum  for  two  years  and  a  half,  to  study  architecture  in 
Paris  at  the  Ecole  des  Beaux  Arts,  into  the  upper  class  of  which  he  is  received 
without  further  examinations.  The  competition  beginning  January  loth, 
1920,  for  this  scholarship  consisted  of  two  preliminaries  and  one  final  com- 
petition and  was  open  to  all  male  citizens  of  the  United  States  under  thirty.-two 
years  of  age  on  July  ist,  1920.     A  circular  is  furnished  on  request. 

Carnegie  Institute  of  Technology,  Pittsburgh,  Pa.  Division  of  the 
Arts;  School  of  Architecture,  (i)  A  complete  course  in  architecture  for  day- 
students  for  which  the  degree  of  Bachelor  of  Architecture  in  Design  is  awarded 
to  those  speciaHzing  in  design  and  allied  subjects  (Option  i).  and  the  degree  ot 
Bachelor  of  Architecture  in  Construction  to  those  in  construction  and  allied 
subjects  (Option  2).  From  four  to  five  years  are  required  for  the  ^omPleUon  of 
prescribed  work.  (2)  For  graduate  day-students  a  course  of  ^d^^ced  studies 
in  design  and  allied  subjects,  scheduled  to  cover  one  y^l^^"}^.^'^^^^^^ 
degree  of  Master  of  Arts.  (3)  A  partial  day-course  schedukd  ^  cov^^^^^^^ 
years,  for  experienced  draughtsmen  and  designers.  f^^^^^^^Vh  a  Scate 
proficiency  is  awarded.  (4)  A  course  for  night -students  for  which  a  Certificate 
Tpr'toy  is  awarded'^  This  course  includes  the  same  w-k  as  is  requned 
of  day-students  in  design,  freehand  drawing  and  modehng.  Tuition.  For  day 
school,  $7s:   for  night-school,  $20  per  year. 

Columbia  University.  New  York.  N.  Y.  f^'Twof  ^4?™' 
(i).  FuU  four-year  course  leading  to  the  degree  of  Baciielor  of  Architecture. 


1782  Institutions  Teaching  Architecture  Part  3 

Receives  only  students  with  at  least  two  years  of  college  training.  In  con- 
nection with  Columbia  College,  there  is  a  six-year  course  giving  the  degree 
of  A.B.,  at  the  end  of  four  years  and  B.Arch.  at  the  end  of  six  years.  (2) 
Advanced  courses  leading  to  the  degree  of  Master  of  Science  in  Architecture. 
Tuition  $6  per  "tuition-point,"  totahng  about  $250  per  year.  There  are  three 
Traveling-Fellowships,  awarded  as  follows:  One  is  available  each  year, 
with  a  stipend  of  about  $1  500;  the  McKim  Fellowship  every  third  year, 
beginning  19 16-17;  the  Schermerhorn  Fellowship,  every  third  year,  begin- 
ning 19 18-19;  and  the  Perkins  Fellowship,  every  third  year,  beginning 
1920-21.  Each  of  these  requires  the  winner  to  devote  one  year  to  foreign 
travel  and  study. 

Extension-Teaching,  evening  and  afternoon  courses.  A  course  leading 
to  a  Certificate  of  Proficiency  in  Architecture  is  offered.  This  covers  roughly 
six  years,  depending  on  how  much  is  taken  each  year.  Equivalent  of  day-course 
in  instruction.  Tuition,  $6  per  "tuition-point,"  each  course  having  a  stated 
point-value.  Graduation  accepted  in  lieu  of  examinations  for  state  Hcense. 
There  are  Special  Students,  also,  under  Extension-Teaching  who  select  their 
own  course  of  study  in  subjects  for  which  they  are  quahfied.  All  information 
may  be  obtained  from  the  Curator, 

Cornell  University,  Ithaca,  N.  Y.,  College  of  Architecture,  (i)  A 
four-year  general  course  in  architecture,  leading  to  the  [degree  of  Bachelor 
of  Architecture,  and  a  similar  course  with  engineering  elcctives,  leading  to  the 
degree  of  Bachelor  of  Science  in  Architecture.  (2)  Five-year  courses  in  archi- 
tecture, the  same  as  the  above,  but  with  additional  work  in  the  arts  and  sciences, 
leading  to  the  same  degrees.  (3)  Six-year  courses  in  arts  and  sciences  and 
architecture,  or  in  engineering  and  architecture,  leading  to  the  degrees  of  A.B. 
and  B.Arch.,  or  C.E.  and  B.S.Arch.  (4)  A  two-year  special  course  in  archi- 
tecture, leading  to  a  certificate.  (5)  Graduate  courses  in  architecture,  leading 
to  the  degree  of  Master  of  Architecture.     Tuition,  $200  a  year. 

Georgia  School  of  Technology,  Atlanta,  Ga.  Department  of  Archi- 
tecture, (i)  Full  four-year  course  leading  to  the  degree  of  Bachelor  of 
Science  in  Architecture.  (2)  Two-year  special  course  leading  to  a  certificate  of 
proficiency.  Tuition,  $25  per  year  for  residents  of  Georgia;  $100  for  non-residents. 
The  Georgia  Chapter  of  the  American  Institute  of  Architects  has  provided  a 
loan-fund  in  this  department  for  one  or  two  students  needing  pecuniary  assist- 
ance. 

George    Washington    University,    Washington,    D.    C.      Department 

OF  Arts  and  Sciences.  Course  in  Architecture.  Four-year  course  in  archi- 
tecture, leading  to  the  degree  of  Bachelor  of  Science  in  Architecture.  Courses 
of  instruction  open  to  qualified  special  students,  without  reference  to  any 
degree.  Full  tuition  $180;  part-time  students  pay  $6  for  each  semester-hour 
credit. 

Harvard    University,    Faculty    of    Architecture,    Cambridge,    Mass. 

School  of  Architecture.  Professional  training  in  architecture,  (i)  Open 
to  graduates  of  colleges,  scientific  schools  and  professional  schools  of  good  stand- 
ing, leading  to  the  degree  of  Master  in  Architecture,  or  Master  in  Architecture 
in  Architectural  Engineering.  Length  of  period  of  study  for  men  with  no 
professional  preparation,  commonly  three  years,  depending  on  ability  and  pre- 
vious training.  (2)  Open  to  competent  special  students,  who  must  be  over 
twenty-one  years  of  age,  and  must  hare  had  at  bast  three  years  of  oflFice- 
experience;  admitted  to  special  course  leading  to  certificate.  Tuition  $200 
per  year. 


Institutions  Teaching  Architecture  1783 

School  of  Landscape- Architecture,  (i)  Professional  training  in  landscape- 
architecture,  open  to  graduates  of  colleges  and  technical  schools  of  good  standing, 
leading  to  the  degree  of  Master  in  Landscape-Architecture.  (2)  Competent 
special  students  admitted  to  any  courses  for  which  their  previous  training 
fits  them.     Tuition,  $200  per  year. 

Two  Traveling-Fellowships,  the  Julia  Amory  Appleton  and  the  Robin- 
son, are  offered  for  competition  in  alternate  years,  each  having  an  annual 
value  of  $1 100,  tenable  for  two  years,  for  travel  and  study  in  Europe  under 
the  direction  of  the  School  of  Architecture.  The  Charles  Eliot  Fellow- 
ship IN  Lansdcape-Architecture  (stipend  $1 100)  is  offered  for  travel  and 
study  in  landscape-architecture,  under  the  direction  of  the  School  of  Landscape- 
Architecture.  These  fellowships  are  open  for  competition  to  graduates  in 
architecture  and  in  landscape-architecture,  respectively. 

Resident  Scholarships.  Two  Austin  Scholarships  in  Architecture  and 
one  in  Landscape-Architecture,  annual  value,  $350.  The  Cummings 
Scholarship  in  Landscape-Architecture,  annual  value,  $350.  One  Eveleth 
Scholarship  in  Architecture,  annual  value,  I250.  Three  Scholarships 
FOR  Special  Students  in  Architecture,  open  to  competition  to  properly 
quahfied  draughtsmen,  annual  value,  $200.  Six  University  Scholarships  open 
to  regular  students  in  Architecture  or  Landscape-Architecture,  annual  value, 
$200.  Other  scholarships  available  to  candidates  of  special  claims  as  to 
residence,  college,  or  descent. 

International  Correspondence  Schools,  Scranton,  Pa.  A  corporation 
formed  to  furnish  instruction  by  correspondence  and  to  hold  examinations  to 
establish  proficiency.  The  architectural  course  is  designed  particularly  to  meet 
the  wants  of  those  already  engaged  in  the  building  trades  or  drafting-room. 
It  includes  sixty-one  subjects  covering  the  elements  of  building-construction, 
masonry,  carpentry,  plumbing,  etc.,  and  the  principles  of  design,  drawing, 
rendering,  and  specification-writing.  The  tuition  includes  text-books  and 
instruction,  that  is,  criticisms  on  written  lessons,  sent  to  the  schools,  and  also 
answers  to  questions  on  subjects  connected  with  the  course,  that  may  be  asked 
by  the  students.  Information  regarding  fees  can  be  obtained  on  inquiry. 
Shorter  courses  are  available  for  building-contractors,  building-foremen,  and 
also  special  courses  in  structural  engineering. 

Kansas  State  Agricultural  College,  Manhattan,  Kan.  Department  of 
Architecture.  Full  four-year  course  in  architecture,  leading  to  a  degree  in 
Bachelor  of  Science.  Tuition  free  to  residents  of  the  state.  Incidental  fees 
amount  to  about  $12  a  semester. 

Massachusetts  Institute  of  Technology,  Boston,  Mass.  Two  four-year 
courses  are  offered  in  architecture,  leading  to  the  degree  of  Bachelor  of  Science: 
(i)  Course  in  general  architecture;  (2)  Course  in  architectural  engineering. 
Opportunities  are  offered  in  each  course  for. advanced  professional  work  leading 
to  the  degree  in  (i)  of  Master  in  Architecture  and  in  (2)  of  Master  of  Science. 
Special  students  must  be  college-graduates,  or  twenty-one  years  of  age,  with  not 
less  than  two  years  of  office-experience.  In  all  cases  they  must  demonstrate 
their  fitness  for  the  work  of  the  department  by  personal  conference  with  the 
head  of  the  department,  or  his  representative,  and  by  the  presentation  of 
letters  from  former  employers,  together  with  drawings  covenng  their  experience 
as  fully  as  possible.  All  special  students  must  take  in  their  first  year  of  residence 
at  the  Institute  courses  in  descriptive  geometry  and  mechanical  drawing,  unless 
these  subjects  have  been  passed  at  the  September  examinations  for  advanced 
standing,  or  excuse  from  one  or  both  has  been  obtained  on  the  basis  of  equivalent 


1784  Institutions  Teaching  Architecture  Part  3 

work  accomplished  elsewhere.  Tuition,  $250  per  year.  An  Annual  Traveling- 
Fellowship  amounting  to  $1  000  is  given  solely  on  the  basis  of  distinguished 
merit,  candidates  being  received  from  both  regular  and  special  students.  Eight 
prizes,  varying  from  $10  to  $200  each,  are  equally  divided  between  the  regular 
and  the  special  students.  Certain  funds  are  available  for  the  assistance  of  well- 
quahfied  regular  students  for  undergraduate  and  for  post-graduate  work. 

McGill  University,  Montreal,  Canada.  Department  of  Architecture. 
(i)  Full  five-year  course  leading  to  the  degree  of  Bachelor  of  Architecture. 
(2)  Competent  special  students  are  admitted  to  take  a  partial  course,  but  no 
university  certificate  is  granted  for  this  work.     Tuition,  $150  per  year. 

North  Dakota  Agricultural  College,  Fargo,  N.  D.  Department  of 
Engineering.  Draughtsmen's  and  builders'  course  of  three  years  (six  months 
each).  Full  four-year  course  in  architecture,  leading  to  Bachelor  of  Science  in 
Architecture.  Full  four-year  course  in  Architectural  Engineering,  leading 
to  Bachelor  of  Science  in  Architectural  Engineering.  Tuition  free.  Fees 
amounting  to  $35  per  year. 

Ohio  Mechanics-  Institute,  Cincinnati,  Ohio.  Department  of  Archi- 
tecture. Technical  high- school  course  preparatory  to  architecture,  cover- 
ing four  years.  Two-year  intensive  course  in  architecture.  Evening  classes 
in  architectural  drawing  and  alUed  building-trade  subjects.  Graduates  of 
grammar-schools  are  trained  in  draughting  and  elementary  architectural 
subjects  simultaneously  with  their  high-school  subjects.  Graduates  of  high- 
schools  are  trained  intensively  in  technical  architectural  work,  including  colle- 
giate mathematics  and  sciences,  and  receive  a  Certificate  of  Proficiency  in 
Architecture.     Tuition,  $75  per  year. 

Ohio  State  University,  Columbus,  Ohio.  Course  in  Architecture. 
Two  four-year  courses,  leading  to  the  degrees  of  Bachelor  of  Architecture  and 
Bachelor  of  Architectural  Engineering.     Tuition  free. 

Oklahoma  Agricultural  and  Mechanical  College,  Stillwater,  Okla. 
Departments  of  Architecture  and  Architectural  Engineering.  Four- 
year  course  in  Architecture  and  Architectural  Engineering,  leading  to  a  degree 
of  Bachelor  of  Science.  Two-year  special  course  for  draftsmen,  leading  to  a 
certificate  of  completion  in  this  work.  Tuition  free.  The  registration-fee  is 
$2  a  semester. 

Pennsylvania  State  College,  State  College,  Pa.  Course  in  Architec- 
tural Engineering.  Full  four-year  course,  leading  to  the  degree  of  Bachelor 
of  Science  in  Architectural  Engineering.  Tuition  is  free.  Incidental  fees 
amount  to  about  $30  per  semester,  these  fees  including  the  college  fees.  No 
course  in  architectural  design. 

Pratt  .Institute,  Brooklyn,  N.  Y.  Course  in  Architecture.  School  of 
Fine  and  Applied  Arts,  (i)  Two-year  course  in  architectural  design.  (2) 
Two-year  course  in  architectural  construction.  (3)  Full  three-year  course  in 
architectural  design  and  architectural  construction.  The  course  in  archi- 
tectural design  aims  to  give  students  a  general  training  thaj:  will  prepare  them 
to  pursue  the  profession  of  architecture  as  competent  assistants  in  architects' 
offices,  and  leads  to  positions  of  responsibility  and  independence.  The  course 
in  architectural  construction  aims  to  fit  the  student  for  general  draughting  in 
builders'  offices,  or  for  general  detailing  and  construction-work  in  an  architects' 
ofiice,  and  leads  to  the  position  of  superintendent  of  construction- work.  Tuition, 
$80  per  year. 

Princeton   University,    Princeton,   N.    J.     School   of   Architecture. 


Institutions  Teaching  Architecture  17,S5 

Three  courses  in  Architecture:  (i)  For  students  enrolled  as  candidates  for 
the  degree  of  Bachelor  of  Arts  on  graduation  and  for  the  degree  of  Master  of 
Fine  Arts  in  Architecture  after  two  years  of  graduate  work.  (2)  For  students 
who  have  not  begun  the  study  of  architecture  in  the  sophomore  year,  but 
who  wish  to  receive  the  degree  of  Bachelor  of  Arts  on  graduation  and  the  degree 
of  Master  of  Fine  Arts  in  Architecture  after  two  years  of  graduate  work. 
(3)  For  students  entering  the  School  as  candidates  for  the  degree  of  Master 
of  Fine  Arts  in  Architecture  without  previous  study  in  architecture.  For  the 
average  student,  three  years  and  a  half  are  required  for  this  course.  Tuition, 
$100  a  year  for  students  on  full  time,  and  $40  for  those  on  part  time.  Annual 
fees,  $15.  The  graduate  fellowship  and  scholarships  of  the  University 
are  open  to  members  of  the  School.  They  are  over  fifty  in  number,  and  range 
in  stipend  from  $150  to  $1  000  per  annum. 

Rice  Institute,  Houston,  Tex.  Architectural  Department.  Full 
four-year  course  leading  to  the  degree  of  Bachelor  of  Science  in  Architecture. 
Tuition  free. 

Rochester   Athenaeum   and   Mechanics   Institute,  Rochester,  N.  Y. 

Department  of  Applied  Arts.  Three-year  courses  in  Architectural  Drawing 
and  Design,  and  Architectural  Construction,  leading  to  Diplomas.  There 
are  also  courses  for  properly  prepared  students  who  do  not  wish  to  take  the 
diploma-courses.  Tuition  for  full  courses,  $90  per  year;  for  part-time  students, 
$4  per  term  of  twelve  weeks  for  one  session  per  week. 

Rose  Polytechnic  Institute,  Terre  Haute,  Ind.  Department  of  Archi- 
tectural Engineering.  P'ull  four-year  course,  designed  to  give  a  thorough 
training  in  architectural  engineering,  together  with  systematic  instruction  irv 
architectural  design.     Tuition  and  incidental  fees,  $110. 

Rotch  Traveling-Scholarship,  Inc.  (For  particulars  address  the  Secretary, 
20  Beacon  Street,  Boston,  Mass.)  Candidates  must  be  under  thirty  years  of 
age  at  the  date  of  the  beginning  of  the  preliminary  examinations.  At  that 
date  they  must  have  been  engaged  in  professional  work  during  two  years 
in  Massachusetts  in  the  employ  of  a  practicing  architect  resident  in  Massa- 
chusetts, and  will  be  required  to  pass  preliminary  examinations  upon  the  follow- 
ing subjects:  (i)  History  of  architecture;  (2)  Freehand  drawing  from  the 
cast;  (3)  Construction,  theory  and  practice;  (4)  An  elementary  knowledge 
of  the  French  language.  Holders  of  a  degree  in  Architecture  from  the  Massa- 
chusetts Institute  of  Technology,  Columbia  University,  University  of  Penn- 
sylvania, Cornell  University,  Harvard  University,  or  University  of  Illinois 
will  be  allowed  to  present  such  diploma  which  will  be  accepted  in  lieu  of  the 
examinations  in  the  preliminaries.  Candidates  who  pass  in  these  preliminary 
examinations'  are  admitted  to  a  competition  in  design,  the  successful  can- 
didate in  which  is  awarded  the  scholarship  and  receives  annually,  for  two 
years,  $1  400,  to  be  expended  in  foreign  travel  and  study.  The  Boston  Society 
of  Architects,  through  a  committee,  has  complete  charge  of  the  examinations, 
and  supervises  the.  work  of  the  scholar.  The  Society  of  Architects  awards 
the  sum  of  $75  as  a  second  prize. 

Syracuse  University,  Syracause,  N.  Y.,  College  of  Fine  Arts.  Depart- 
ment OF  Architecture.  This  school  offers:  Four-year  courses  in  (i)  Ardu- 
tecture,  (2)  Architectural  Design,  (3)  Architectural  Engineering,  all  leading 
to  the  degree  of  Bachelor  of  Architecture  (BAr.);  (4)  Special  two-year  course 
for  architectural  draughtsmen  of  two  or  more  years'  experience;  (5)  Graduate 
course   in   architecture;     (G)     Interior   architectural   design   and   decoraUon.. 


1786  Institutions  Teaching  Architecture  Part  3 

Tuition,   $150   per  year.     Bulletins  and   full  information   available  from   the 
Registrar. 

Texas.  Agricultural  and  Mechanical  College  of  Texas,  College  Station, 
Tex.  Department  of  Architecture.  Four-year  course  in  architecture, 
offering  an  option  through  the  junior  and  senior  years  in  architectural  eng'ineer- 
ing.     Qualified  special  students  admitted.     Tuition  free. 

Tulane  University  of  Louisiana,  New  Orleans,  La.  Department  of 
Architecture  in  the  College  of  Technology,  (i)  Full  four-year  course 
leading  to  a  degree  in  architecture.  (2)  Special  courses  for  students  not  can- 
didates for  a  degree.  Tuition,  $100  per  year.  Special  attention  given  to 
subtropical  conditions. 

University  of  California,  Berkeley,  Cal.  School  of  Architecture. 
(i)  Full  four-year  course  leading  to  the  degree  of  Bachelor  of  Arts.  (2)  One- 
year-graduate  course  leading  to  the  degree  of  Master  of  Arts.  (3)  Two-year 
graduate  course  leading  to  the  degree  of  Graduate  in  Architecture.  (4)  Special  or 
elective  courses  for  students  not  candidates  for  a  degree.  Tuition  free  to 
residents  of  the  state  of  California. 

University  of  Illinois,  Urbana,  111.  Courses  in  Architecture  and 
Architectural  Engineering,  (i)  Full  four-year  course  leading  to  tlie 
degree  of  Bachelor  of  Science  in  Architecture.  (2)  Full  four-year  course, 
leading  to  the  degree  of  Bachelor  of  Science  in  Architectural  Engineering. 
Tuition  is  free.  Incidental  fee,  $30  per  year.  Plym  Traveling-Fellowship, 
$1  coo  for  one  year  of  travel  abroad;  awarded  by  comi:)etition  to  graduates  of 
the  Departmtrnt  of  Architecture  of  the  University  of  Illinois. 

University  of  Kansas,  Lawrence,  Kan.  Department  of  Architecture 
AND  Architectural  Encinekring.  Full  four-year  course  in  Architecture, 
leading  to  the  degree  of  Bachelor  of  Science  in  Architecture.  Full  four-year 
course  in  Architectural  Engineering,  leading  to  the  degree  of  Bachelor  of  Science 
in  Architectural  Engineering.  Four-year  courses  in  each,  based  on  one  year 
in  the  College  of  Liberal  Arts,  leading  to  the  degree  of  Bachelor  of  Science. 
Tuition  free.  Fees  amounting  to  $15  per  year  for  residents  of  the  state,  and 
$25  per  year  for  non-residents. 

University  of  Michigan,  Ann  Arbor,  Mich.  College  of  Architecture 
(i)  A  general  four-year  course  leading  to  the  degree  of  Bachelor  of  Science  in 
i.\rchitecture.  (2)  A  four-year  course  in  which  architectural  design  is  em- 
phasized, leading  to  the  same  degree.  (3)  A  four-year  course  in  which  there  is 
a  large  proportion  of  engineering  subjects,  leading  to  the  degree  of  Bachelor 
of  Science  in  Architectural  Engineering.  (4)  Five-year  courses  leading  to  the 
degrees  of  Master  of  Science  in  Architecture  and  Master  of  Science  in  Archi- 
tectural Engineering.  (5)  A  two-year  course,  leading  to  a  Certificate,  for  special 
students  (experienced  draughtsmen  or  college-graduates).  (6)  Students  may 
earn  the  degree  of  Bachelor  of  Arts  and  the  degree  in  Architecture  in  from 
five  to  six  years.  There  are  two  scholarships.  Annual  fees,  $57  for  students 
from  Michigan  and  $87  for  others. 

University  of  Minnesota,  Minneapolis,  Minn.  Department  of  Archi- 
tecture. Full  four-year  course,  leading  to  the  degree  of  Bachelor  of  Science 
in  Architecture.  Fifth  year,  leading  to  the  degree  of  Master  of  Science  in 
Architecture.  Special  students  of  maturity  and  practical  experience  are 
admitted.  Instruction  is  provided  in  Architectural  Engineering.  Tuition  ii^-r.. 
Incidental  fee,  $60  per  year. 

University   of   Nebraska,   Lincoln,   Neb.     College   of  Engineer: 


Institutions  Teaching  Architecture  1787 

Full  four-year  course  in  architectural  engineering,  leading  to  Bachelor  of  Science 
in  Architectural  Engineering.     Tuition  free.    Total  fees  for  four  years,  $iio. 

University  of  Notre  Dame,  Notre  Dame,  Ind.  Department  of  Archi- 
tecture, (i)  Full  four-year  course  in  design  leading  to  the  degree  of  Bachelor 
of  Science  in  Architecture.  (2)  Full  four-year  course  in  architectural  engi- 
neering leading  to  the  degree  of  Bachelor  of  Science  in  Architectural  Engineering. 
(3)  Two-year  special  course  leading  to  a  Certificate  of  Proficiency.  Tuition, 
$120  per  year;   room  $60  and  upwards;   board,  $180  and  upwards. 

University  of  Oregon,  Eugene,  Ore.  School  of  Architecture  and 
Allied  Arts.  Two  architectural  options  in  design  and  structural  work, 
(i)    Four-year    course   leading    to    the    degree   of   Bachelor   in    Architecture. 

(2)  Five-year  course  leading  to  the  degree  of  Master  in  Architecture.  (3)  Ex- 
tension-courses in  Portland,  Ore.,  in  design,  etc.  (4)  Special  courses  for  ex- 
perienced draughtsmen.  Tuition  free  for  university-courses;  $5  a  term  for 
extension-courses. 

University  of  Pennsylvania,  Philadelphia,  Pa.  School  of  Fine  Arts, 
Department  of  Architecture,  (i)  Four-year  course  leading  to  the  degree 
of  Bachelor  of  Architecture.  (2)  Graduate  course  of  one  year,  with  choice 
between    major    subjects,  leading    to  the   degree  of  Master  of  Architecture. 

(3)  Two-year  special  course  leading  to  a  professional  certificate.  (4)  Six-year 
arrangement  of  courses  in  liberal  arts  and  architecture  leading  to  the  degrees 
of  A.  B.  and  also  B.  Arch.  (5)  Option  in  Architectural  Engineering  leading  to 
the  degree  of  Bachelor  of  Architecture.  Summer  school  providing  instruction 
in  many  architectural  subjects  of  the  regular  session.  The  degree  and  certificate 
are  accepted  by  the  American  Institute  of  Architects  in  satisfaction  of  its 
educational  requirements  for  membership  and  are  credited  by  State  Boards  for 
licensing  of  architects.  Tuition  $300  per  year.  Descriptive  circular,  includ- 
ing information  concerning  all  courses  in  the  School  of  Fine  Arts,  on  applica- 
tion to  the  Dean  of  the  School  of  Fine  Arts,  University  of  Pennsylvania,  Phila- 
delphia, Pa. 

The  Woodman  Scholarship  in  Architecture  of  the  University  of  Penn- 
sylvania, for  one  year  of  foreign  travel  and  study,  is  open  to  graduates  of  this 
school,  they  being  also  eligible  to  the  general  competition  for  the  Fellowship 
OF  THE  American  Academy  in  Rome.  The  Paris  Prize  of  the  Beaux-Arts 
Institute  of  Design  is  open  to  seniors  and  graduates  and  the  Stewardson 
Traveling-Schot.arship  is  available  to  students  who  are  residents  of  Penn- 
sylvania. The  medals  of  the  American  Institute  of  Architects  and  the 
SociETE  DES  Architectes  Diplomhs  are  conferred  in  this  school  as  well  as 
other  medals  and  prizes  open  to  its  students  alone. 

University  of  Southern  California,  Los  Angeles,  Cal.  Four-year  general 
course  in  architecture,  leading  to  the  degree  of  B.S.  in  Architecture. 

University  of  Texas,  Austin,  Tex.  School  of  Architectitre.  (i) 
Four-year  and  five-year  courses  leading,  respectively,  to  the  degrees  of  Bachelor 
of  Science  in  Architecture,  and  Master  of  Science  in  Architecture.  (2)  Four- 
year  course  leading  to  the  degree  of  Bachelor  of  Science  in  Architectural 
Engineering.     Tuition  free. 

University  of  Toronto,  Toronto,  Canada.  Department  of  Archi- 
tecture Full  four-year  course  leading  to  the  degree  of  Bachelor  of  Applied 
Science  (B  A  Sc  )  with  an  option  of  architectural  engineering,  replacing  archi- 
tectural design  in  the  fourth  year.  The  fees  are,  first  year,  $100;  second  year, 
$110;  third  and  fourth  years,  $120.  The  university  is  supported  by  the 
Province  of  Ontario. 


1788       Architectural  Societies  and  Organizations  of  the  World    Part  3 

University  of  Virginia.  McIntire  School  of  Fine  Arts.  Four-year 
course  in  architecture,  leading  to  the  degree  of  Bachelor  of  Science  in  Archi- 
tecture. Annual  average  of  tuition  and  laboratory  fees:  For  non- Virginians, 
$i8o;  for  Virginians,  $75. 

University  of  Washington,  Seattle,  Wash.  Course  in  Architecture. 
Four-year  course,  leading  to  the  degree  of  Bachelor  of  Architecture.  There  is 
a  fourth-year  option  in  architectural  engineering.  Tuition,  $20  per  year., 
Entrance  fee,  $10;   graduation  fee,  $5. 

Washington,  The  State  College  of,  Pullman,  Wash.  Department  op 
Architecture,  (i)  Full  four-year  course  leading  to  the  degree  of  Bachelor 
of  Science  in  Architecture.  (2)  Two-year  special  course  leading  to  a  Certificate 
of  Proficiency.  (3)  Special  students,  adequately  prepared,  are  admitted  to  all 
classes.    Tuition  free. 

Washington  University,  St.  Louis,  Mo.  School  of  Architecture 
(i)  Four-year  courses  in  architecture  and  in  architectural  engineering  leading 
to  the  degrees  of  Bachelor  of  Architecture,  and  Bachelor  of  Science  in  Archi- 
tectural Engineering,  respectively.  (2)  One-year  course  leading  to  the  degree 
of  Master  of  Architecture.  (3)  Special  two-year  course  with  Certificate. 
Tuition,  $150  per  year. 

Wentworth  Institute,  Boston,  Mass.  Courses  in  architectural  con- 
struction, carpentry  and  building,  and  twelve  other  technical  trades  or  indus- 
tries, (i)  Two-year  course  in  architectural  construction  trains  for  positions 
of  foremen,  superintendents,  detail-designers,  etc.  Tuition,  $54  per  year  and 
$15  laboratory  fee.  (2)  One-year  course  in  carpentry  and  building  planned 
for  those  wishing  to  enter  the  wood-working-trades  and  industries  as  advanced 
apprentices  or  high-grade  artisans.  Tuition  $30  per  year  and  $15  laboratory  fee. 

Yale  University,  New  Haven,  Conn.  Department  of  Architecture. 
Regular  course  covers  four  years.  Special  degree.  Bachelor  of  Fine  Arts,  to 
be  competed  for  at  end  of  course.  Portions  of  the  first-year's  work,  including 
lectures  on  history  of  chief  styles  of  architecture  and  principles  of  composition 
and  practice  in  elementary  design,  may  be  taken  as  electives  by  juniors  and 
seniors  in  the  academic  course.  Alice  Kimball  English  Scholarship,  sup- 
ported from  fund  of  $11  000,  for  a  year's  travel  abroad.  William  Wirt  Win- 
chester Scholarship,  supported  from  fund  of  $20000,  for  a  year's  travel 
abroad.     Tuition,  $180  per  year. 

ARCHITECTURAL   SOCIETIES   AND   ORGANIZA- 
TIONS OF  THE   WORLD 

I.  United  States 

(i)  THE  AMERICAN  INSTITUTE  OF  ARCHITECTS 

•The  Octagon,  Washington.  D.  C. 

List  of  Chapters  (192  i)  of  the  The  American  Institute  of  Architects 

The  year  indicates  the  date  of  the  chapter's  organization 

Alabama  Chapter.     19 16  Central  New  York  Chapter.     1887 

Baltimore  Chapter.     1870  Cincinnati  Chapter.     1870 

Boston  Chapter.     1870  Cleveland  Chapter.     1890 

Brooklyn  Chapter.     1894  Colorado  Chapter.     1892. 

Buffalo  Chapter.    1890  Columbus  (Ohio)  Chapter.     19 13 


Architectural  Societies  and  Organizations  of  the  World      1789 


Connecticut  Chapter.     1902 
Dayton  Chapter.     1899 
Georgia  Chapter.     1906 
Illinois 'Chapter.     1869 
Iowa  Chapter.     1903 
Kansas  City  Chapter.     1890 
Kentucky  Chapter.     1908 
Louisiana  Chapter. 
Michigan  Chapter. 
Minnesota  Chapter 
Nebraska  Chapter. 
New  Jersey  Chapter. 
New  York  Chapter 
North  Carolina  Chapter.     1913 
Oregon  Chapter.     191 1 


1910 


1919 

1900 
1S67 


Philadelphia  Chapter.     1869 
Pittsburgh  Chapter.     1891 
Rhode  Island  Chapter.     1875 
St.  Louis  Chapter.     1890 
San  Francisco  Chr.pter.     1881 
South  Carolina  Chapter.     19 13 
Southern  California  Chapter.     1894 
Southern  Pennsylvania  Chapter.     1909 
Tennessee  Chapter.     19 19 
Texas  Chapter.     1913 
Toledo  Chapter.     1914 
Virginia  Chapter.     1914 
Washington  (D.  C.)  Chapter.     1887 
Washington  State  Chapter,  1894 
Wisconsin  Chapter.     191 1 


[921:    Arkansas,  Florida,  Indiana, 


Note. — ^These  new  chapters  were  organized  in 
Kansas  State,  Montana,  and  Utah. 

List  of  State  Associations  of  The  American  Institute  of  Architects 
New  York  State  Society  of  Architects.     1919 
Ohio  State  Association.      19 15 
Pennsylvania  State  Association.     1909 

(2)  MISCELLANEOUS  SOCIETIES  * 
\merican  Society  of  Landscape  Architects 
\rchitects'  Association  of  Indianapolis 
Architectural  Club  of  Minneapohs 
Architectural  League  of  Pacific  Coast 
Architectural  League  of  New  York 
Architectural  Society  of  the  University  of  California    . 
Architectural  Society  of  the  University  of  Pennsylvania 
Association  of  Collegiate  Schools  of  Architecture 
Baltimore  Architectural  Club 
Birmingham  Society  of  Architects 
Boston  Architectural  Club 
Boston  Society  of  Architects 
Brooklyn  Institute  of  Arts  and  Sciences 
Chicago  Architects'  Business  Association 
Chicago  Architectural  Club 
Chicago  Association  of  Architects 
Cincinnati  Architectural  Club 
Cleveland  Architectural  Club 
Columbus  Society  of  Architects 
Detroit  Architectural  Club 
Duluth  Architectural  Club  .     .„     x- 

Engineers'  and  Architects'  Club  of  Louisville,  Ky. 
Florida  Association  of  Architects 
Gargoyle  Club  of  St.  Paul 
Georgia  Architectural  Association 
Indianapolis  Architectural  Club 
Kansas  State  Architects'  Association 


1790       Architectural  Societies  and  Organizations  of  the  World    Part  3 

Los  Angeles  Architectural  Club 

I^.Iassachusetts  Institute  of  Technology  Architectural  Association 

IMinneapolis  Architectural  Club 

Minneapolis  Society  of  Architects 

New  Orleans  Architectural  Club 

New  York  Society  of  Architects 

Norfolk  Society  of  Architects 

North  Carolina  Architectural  Association 

Oakland  Architects'  Association 

Oakland  Architectural  Club 

Oklahoma  State  Association  of  Architects 

Pittsburgh  Architectural  Club 

Portland,  Oregon,  Architectural  Club 

Portland,  Oregon,  Association  of  Architects 

St.  Joseph,  Missouri,  Society  of  Architects 

St.  Louis  Architectural  Club 

St.  Paul  Architectural  Club 

San  Antonio  Society  of  Architects 

San  Diego  Architectural  Association 

San  Francisco  Architectural  Club 

Society  of  Architects  of  Akron,  Ohio 

Society  of  Architects  of  Columbia  University 

Society  of  Beaux-Arts  Architects 

Society  of  Naval  Architects  and  Marine  Engineers 

South  Bend  Architectural  Club 

South  Carolina  Association  of  Architects 

Southern  States  Engineering  Society 

Spokane  Architectural  Club 

T  Square  Club  of  Philadelphia 

Tacoma  Society  of  Architects 

Texas  State  Association  of  Architects 

Utah  Association  of  Architects 

Washington,  D.  C,  Architectural  Club 

2.    Argentine  Republic 
Sociedad  Central  de  Arquitectos.     Buenos  Aires 

3.   Austria 

Austrian  Society  of  Civil  Engineers  and  Architects.     Vienna 

Architekten-Kiub  der  Weiner  Kunstlergenossenschaft.     Vienna 

Gesellschaft  Osterreichischer  Architekten.     Vienna 

Weiner  Bauhiitte.     Vienna 

Towarzystwo  Politechniczne  we  Lwowie.     Leopoi 

Towarzystwo  Technisczne  we  Krakowie.     Cracow 

4.   Belgium 

Association  des  Architectes,  de  Liege.     Liege  i 

Societe  Centrale  D  Architecture  de  Belgique.     Brussels 

Societe  Roy  ale  des  Architectes  D'Anvers.     Antwerp 

Kring  Voor  Bouwhunde  D'Anvers.     Antwerp 

Chambre  Syndicate  des  Architectes  de  Bruxelles.     Brussels 


Foreign  Architectural  Societies  1791 


Association  des  Architectcs  de  Bruxelles.     Brussels 
Societe  des  Architectes  de  la  Flandre  Orientale.     Ghent 
Societe  des  Architectes  de  la  Flandre  Orientale.     Bruges 

5.   Bulgaria 

Societe  des  Ingenieurs  et  des  Architectes  Bulgares.     Sofia 

6.   Canada 

Architectural  Association  of  Canada 
Royal  Architectural  Institute  of  Canada.     Montreal 
Alberta  Association  of  Architects.     Calgary  and  Ed^nonton,  Alta. 
Architects'  Association  of  Victoria.     Victoria,  B.  C. 
British  Columbia  Association  of  Architects. 
Calgary  Architectural  Club 

Manitoba  Association  of  Architects.    Winnipeg,  Man. 
Ontario  Association  of  Architects.     Toronto 
Province  of  Quebec  Association  of  Architects.     Montreal 
Regina  Architectural  Association.     Regina,  Sask. 
Saskatchewan  Association  of  Architects.     Regina,  Sask. 

7.   Cuba 

Society  of  Engineers  and  Architects  of  Havana.     Havana 

8.   France 

Permanent  Committee  of  International  Congresses  of  Architects.     Paris 

Societe  des  Architectes  Diplomes  par  le  Gouvernement.     Paris. 

Societe  Nationale  des  Architectes  de  France.     Paris. 

Societe  Centrale  des  Architectes  Frangais.     Paris 

Union  Syndicale  des  Architectes  Frangais.     Paris 

Societe  des  Diplomes  de  I'Ecole  Speciale  d'Architecture.     Paris 

Association  Provenciale  des  Architectes  Frangais.     Versailles 

Societe.  Regionale  des  Architectes  du  Centre  de  la  France.     Bourges 

Societe  Regionale  des  Architectes  de  Dauphine  et  de  la  Savoie.     Grenoble 

Societe  des  Architectes  de  I'Est  de  la  France.     Nancy 

Societe  Regionale  des  Architectes  du  Limousin,  de  TAngoulerae  et  du  Perigord. 

Gueret  (Creuse) 
Societe  Regionale  des  Architectes  du  Midi.     Toulouse 
Societe  Regionale  des  Architectes  du  Nord.     Lille 

Societe  Regionale  des  Architectes  du  Poitou  et  de  la  Saintonge.     Parthenay 
Societe  Regionale  des  Architectes  du  Puy-de-D6me,  du  Cantal,  de  la  Haute- 

Loire  et  de  I'Allier.     Clermont-Ferrand 
Societe  Regionale  des  Architectes  de  Saone-et-Loire,  de  I'Ain  et  du  Jura.     Cha- 

lons-sur-Sa6ne 
Association  Regionale  des  Architectes  du  Sud-Est    Nice 
Societe  des  Architectes  de  I'Aisne.     St.  Quentin 
Societe  des  Architectes  de  I'Allier.     Moulins 
Societe  des  Architectes  de  I'Anjou.     Angers 
Societe  des  Architectes  de  I'Aube.     Troyes 
Societe  des  Architectes  de  Blois.     Blois 

Societe  des  Architectes  de  Bordeaux  et  du  Sud-Ouest.     Bordeaux  ^ 

Societe  des  Architectes  des  Bouches-du-Rhone.    Marseilles 


1792      Architectural  Societies  and  Organizations  of  the  World     Part  3 

Socicti  des  Architectes  du  Doubs;     Besangon 

Societe  des  Architectes  de  la  Drome  et  de  I'Ardeche.     Valence 

Societe  des  Architectes  d'Eure-et-Loir.     Chartres 

Societe  Amicale  et  Syndicat  des  Architectes  du  Gard.     Nlmes 

Societe  des  Architectes  de  la  Haute-Marne.     Chalons-sur-Mame 

Societe  Academique  d'Architecture  de  Lyon.     Lyon 

Societe  des  Architectes  de  la  Marne.     Paul-Chandon 

Societe  des  Architectes  de  Nantes.     Nantes 

Societe  des  Architectes  de  I'Oise.     Compiegne 

Societe  des  Architectes  d'Orleans.     Orleans 

Societe  des  Architectes  de  Rennes.     Rennes 

Societe  des  Architectes  de  la  Seine  Inferieure  et  de  I'Eure.     Rouen 

Societe  des  Architectes  de  Seine-et-Marne.     Melun 

Societe  des  Architectes  de  Seine-et-Oise.     Versailles 

Societe  des  Architectes  de  la  Touraine.     Tours 

Societe  des  Architectes  de  I'Yonne.     Joigny 

Association  Amicale  des  Architectes.     Paris 

Reunion  Amicale  des  Anciens  Eleves  de  I'Atelier  Quest  el- Pascal.    Paris 

Union  Mutuelle  des  Architectes.     Paris 

Association  Provinciale  des  Architectes  Frangais.     Bordeaux 

Societe  des  Architectes  de  la  Cote-d'Or.     Dijon 

Societe  dss  Architectes  du  Nord-Ouest.     Guingamp  (C6tes-du-Nord) 

Societe  des  Architectes  de  la  Loire.     Saint-Etienne 

Societe  des  Architectes  du  Loiret.     Orleans 

Societe  des  Architectes,  Geometres  et  Experts  de  la  Lozcre.     Mende 

Syndicat  des  Architectes  du  Rhone.     Villeurbanne 

Societe  des  Architectes  du  Havre.     Le  Havre  (Seine-Inferieure) 

Union  Architecturale  de  Lyon.     Lyon 

Association  des  Architectes  Fran^ais.     Marseilles 

Syndicat  des  Architectes  de  Basse-Normandie.     Caen 

Societe  Historique  de  Campiege.     Campiege 

Societe  d'Assistance  Confraternelle  des  Architectes  Frangais.     Versailles 

9.   Germany 

Architekten-Verein  zu  Berlin.     Berlin.  W. 

Verbund.  Deutscher  Architekten-und-Ingenieur-Vereine.     Berlin.  S.W. 
Wiirttembergerischer  Verein  fur  Baukunde.     Stuttart 
Sachsischer  Ingenieur-und-Architekten-Verein.     Dresden 
Vereinigung  Berliner  Architekten.     Berlin.  W. 
Architekten-und-Ingenieur-Verein  zu  Hannover.     Hannover 
Architekten-und-Ingenieur-Verein  zu  Osnabriick.     Osnabriick 
Architekten-und-Ingenieur- Verein  zu  Hamburg.     Hamburg 
Architekten-und-Ingenieur-Verein  zu  Cassel.     Cassel 
Architekten-und-Ingenieur-Verein  zu  Liibeck.     Lubeck 
Schleswig-Holsteinischer,  Architekten-und-Ingenieur-Verein.     Keil 
Baierischer  Architekten-und-Ingenieur- Verein.     Munich 
Architekten-und-Ingenieur-Verein  zu  Breslau.     Breslau 
Badischer  Architekten-und-Ingenieur-Verein.     Karlsruhe 
Architektenrund-Ingenieur- Verein  zu  Oldenburg.     Oldenburg 
Ostpreussischer  Architekten-und-Ingenieur-Verein.     Konigsberg 
Frankfurter  Architekten-und-Ingenieur- Verein.     Frankfort-on-Main 
Westpreussicher  Architekten-und-Ingenieur- Verein  zu  Danzig.     Danzig 
Architekten-und-Ingenieur- Verein  fiir  Elsass-Lothringen.     Strassburg 


Foreign  Architectural  Societies  l'J^93 

Mittelrheinischer  Architekten-  und  Ingenieur-Verein.     Darmstadt 
Dresdener  Architekten-Verein.    Dresden 

Architekten-und-Ingenieur-Verein  fur  Niederrhein  und  Westfalen.     Cologne 
Verein  Leipziger  Architekten.    Leipzig 
Architekten-und-Ingenieur-Verein  fiir  das  Herzogtum  Braunschweig.    Bruna" 

wick 
Architekten-und-Ingenieur- Verein  zu  Madgeburg.    Magdeburg 
Architekten-und-Ingenieur-Verein  zu  Bremen.    Bremen 
Architekten-und-Ingenieur- Verein  zu  Aachen.     Aix-la-Chapelle 
Architekten-und-Ingenieur- Verein  zu  Metz.     Metz 
Mecklenbiirgischer  Architekten  -  und  -  Ingenieur  -  Verein   zu   Schwerin,  i.M. 

Schwerin 
Vereinigung  Berliner  Architekten.     Berhn.     W. 
Architekten-und-Ingenieur- Verein  zu  Diisseldorf.     Diisseldorf 
Bromberger  Architekten-und-Ingenieur-Verein.     Bromberg 
Architekten-und-Ingenieur-Verein  zu  Munster,  i.W.     Miinster 
Architekten-und-Ingenieur-Verein  zu  Potsdam.     Potsdam 
Architekten-und-Ingenieur-Verein  zu  Stettin.     Stettin 
Architekten-und-Ingenieur-Verein  zu  Posen.     Posen 
Architekten-und-Ingenieur- Verein  zu  Erfurt.     Erfurt 
Verein  der  Architekten  und  Bauing-Enieure  zu  Dortnaund.     Dortmund 
Vereiningung  Schlesischer  Architekten.     Breslau 
Towarzystwo  Przyjaciol  Nauk.     Posen 

10.    Great  Britain 

Royal  Institute  of  British  Architects.     London,  W. 

Northern  Architectural  Association.     Newcastle-upon-Tyne 

Leeds  and  Yorkshire  Architectural  Society.     Leeds 

Sheffield  Society  of  Architects  and  Surveyors.     Sheffield 

Manchester  Society  of  Architects.     Manchester 

Liverpool  Architectural  Society  (Inc.).     Liverpool 

Nottingham  Architectural  Association.     Nottingham 

Birmingham  Architectural  Association.     Birmingham 

Leicester  and  Leistershire  Society  of  Architects.     Leicester 

Bristol  Society  of  Architects.     Bristol 

Cardiff,  South  Wales  and  Monmouth  Architects'  Society.     Cardiff 

Devon  and  Exeter  Architectural  Society.     Exeter 

Glasgow  Institute  of  Architects.     Dundee 

Dundee  Institute  of  Architects.     Dundee 

Aberdeen  Society  of  Architects.     Aberdeen 

Edinburgh  Architectural  Association.     Edinburgh 

York  and  Yorkshire  Architectural  Society.     York 

Royal  Institute  of  Architects  of  Ireland  (Inc.).     Dublin 

Architectural  Association  of  Ireland.     Dublin 

Institute  of  Architects  of  New  South  Wales  (Inc.).    Sydney 

Royal  Victorian  Institute  of  Architects  (Inc.).     Melbourne 

West  Australian  Institute  of  Architects  (Inc.).     Perth 

Cape  Institute  of  Architects.     Cape  Town,  South  Africa 

Transvaal  Institute  of  Architects.     Johannesburg.     Transvaal,  South  Afnca 

Natal  Institute  of  Architects.     Durban.     Natal,  South  Afnca 

The  Architectural  Association.     London,  E.C. 


1794       Architectural  Suciviub  and  Organizations  of  the  World     Part  3 

11.   Greece 

Melienic  Polytechiiical  Society.     Athens 

n,   Holland 

Society  for  the  Propagation  of  Architecture.     Amsterdam 
Genootschap  Architectura  et  Amicitia.     Amsterdam 
Bouwhunst  en  Vriendschap.     Rotterdam 

13.   Hungary 

Society  of  Engineers  and  of  Architects.     Budapest 
Magyar  IVIernok-es  Epitesz-Egylet.     Budapest 
Society  of  Private  Architects.     Budapest 

11.   Italy 

Societa  degli  Ingegnerie  e  degli  Architetti.     Rome 

Associazione  Artistica  fra  i  Cultori  di  Architettura.     Rome 

College  dcs  Ingenieurs  et  des  Architectes  de  Gjncs.     Genes 

Collegio  degli  Ingegneri  ed  Architetti  in  Palermo.     Palermo 

Collegio  Toscano  degli  Ingegneri  ed  Architetti  in  Firenze.     Florence 

Societa  degU  Ingegneri  di  Bologna.     Bologna 

Collegio  degli  Ingegneri  ed  Architetti  di  Milano.     Milan 

Collegio  degli  Ingegneri  ed  Architetti  di  Torino.     Turin 

Collegio  degli  Ingegneri  ed  Arciiitetti  di  Messina 

Collegio  degli  Ingegneri  ed  Architetti  PugUe.     Bari 

Collegio  Veneto  degh  Ingegneri  Venezia.     Venise 

15.    Japan 

Society  of  Architects.    Tokyo 

16.  Norway 
Societe  des  Architectes  et  des  Ingenieurs.     Christiania 

17.  Portugal 

Real  Associo  dos  Architectos  Civis  e  Archeologos  Portuguezes.     Lisbon 
Sociedad  dos  Architectos  Portuguezes.     Lisbon 

18.  Russia 

Societe  Imperiale  des  Architectes  Russes.     Petrograd 
Societe  des  Architectes  de  Moscow.     Moscow 
Stowarzyszenie  Technikow  Kolo  Architektow.     Varsovie 

19.    Spain 

Sociedad  Centrale  de  Arquitectos  de  Madrid.     Madrid 

Associacion  des  Architectes  de  Cataluna.     Bajos 

Associacion  des  Architectes  de  Vizcaya.     Bilboa 

Associacion  des  Architectes  de  Navarra.     Pamplona 

Associacion  de  Arquitectos  de  Valencia.     Valencia 

Associacion  de  Arquitectos  de  Galicia.     Santiago  (Coruna) 

Associacion  de  Arquitectos  de  Guipuzcoa.     San  Sebastian 

Agrupacion  Regional  Central  dc  Arquitectos  de  Castilla  la  Nueva.     Madrid 


Foreign.  Architectural  Societies  1795 

Acrupacion  Regional  de  Arquitcctos  do  Castilla  la  Vieja.     Zamora 
Agrupacion  Regional  de  Arquitcctos  de  Norte.     Bilboa 
Agrupacion  Regional  de  Arquitcctos  de  Catalana-Balear.     Bajos 
Agrupacion  Regional  de  Arquitcctos  de  Andalucia.     Cadiz 
Agrupacion  Regional  de  Arquitcctos  de  Galicia.     Santiago  (Coruna) 
Agrupacion  Regional  de  Arquitcctos  de  Cantabrico-Lconcsa.     Santander 
Agrupacion  Regional  de  Arquitcctos  de  Aragon.     Teruel 
Agrupacion  Regional  de  Arquitcctos  de  Levante.     Valencia 
Agrupacion  Regional  de  Arquitcctos  de  Canarias.     Canaries 
Agrupacion  Regional  de  Arquitcctos  de  Occidente.    Caceres 

30.   Sweden      . 

Societe  des  Architectes  et  Ingenieurs.     Stockholm 
Svepska  Teknologforenique.     Stockholm 

31.   Switzerland 

Scheizerischer  Ingenieur  und  Architekten  Verein.    Bale 

33.   Venezuela 

Sociedad  de  Arquitectura  y  Construccion  du  Venezuela.     Caracas 


1796 


Glossary 


Parts 


CORINTHIAN  ABACUS 


GLOSSARY  * 

Technical  Terms,  Ancient  and  Modern,  Used  by  Architects,  Builders, 
and  Draughtsmen 

Aaron*s-Rod.  An  ornamental  figure  representing  a  rod  with  a  serpent  twined 
about  it.  It  is  sometimes  confounded  witli  the  caduceus  of  Mercury.  The 
distinction  between  tiie  caduceus  and  the  Aaron's-rod  is  that  the  former  has  two 
serpents  twined  in  opposite  directions,  while  the  latter  has  but  one. 

Abacus.  The  upper  member  of  the  capital  of  a  column.  It  is  sometimes 
square  and  sometimes  curved,  forming  on  the  plan 
segments  of  a  circle  called  the  arch  of  the  abacus,  and 
is  commonly  decorated  with  a  rose  or  other  ornament 
in  the  center,  having  the  angles,  called  horns  of  the 
abacus,  cut. off  in  the  direction  of  the  radius  or  curve. 
In  the  Tuscan  or  Doric,  it  is  a  square  tablet;  in 
the  Ionic,  the  edges  are  molded;  in  the  Corinthian, 
its  sides  are  concave  and  frequently  enriched  with 
carving.  In  Gothic  pillars  it  has  a  great  variety  of 
forms. 

Abbey.      A  term  for  the  church  and  other  build- 
ings used  by  conventual  bodies  presided  over  by  an 

abbot  or  abbess,  in  contradistinction  to  cathedral,  which  is  presided  over  by  a 
bishop;   and  priory,  the  head  of  which  was  a  prior  or  prioress. 

Abutment.     That  part  of  a  pier  from  which  the  arch  springs. 

Abuttals.     The  boundings  of  a  piece  of  land  on  other  land,  street,  river,  etc. 

Acanthus.     A  plant  found  in  the  south  of  Europe,  representations  of  whose 
leaves  are  employed  for  decorating  the  Corinthian  and 
Composite  capitals.     The  leaves  of  the  acanthus  are 
used  on  the  bell  of  the    capital,  and  distinguish  the 
two  rich  orders  from  the  three  others. 

Acroteria.  The  small  pedestals  placed  on  the 
extremities  and  apex  of  a  pediment.  They  are  usu- 
ally without  bases  or  plinths,  and  were  originally 
intended  to  receive  statues. 

Aile,  Aisle.  The  wings;  inward  side  porticos  of  a  church;  the  inward  lateral 
corridors  which  enclose  the  choir,  the  presbytery,  and  the  body  of  the  church 
along  its  sides.  Any  one  of  the  passages  in  a  church  or  hall  into  which  the  pews 
or  seats  open. 

Alcove.  The  original  and  strict  meaning  of  this  word,  which  is  derived  from 
the  Spanish  alcoba,  is  confined  to  that  part  of  a  bed-chamber  in  which  the  bed 
stands,  separated  from  the  other  parts  of  the  room  by  columns  or  pilasters.  It 
is  now  commonly  used  to  express  any  large  recess  in  a  room,  generally  separated 
by  an  arch. 

Alipterion.  In  ancient  Roman  architecture,  a  room  used  by  bathers  for 
anointing  themselves. 

*  This  Glossary  was  compiled  by  Mr.  Kidder  from  various  sources,  and  with  the 
exception  of  some  changes  in  typographical  details  to  make  it  conform  generally  to  the 
matter  in  the  rest  of  the  book,  it  is  left  as  published  in  the  preceding  editions. 


ACANTHUS 


Glossary  1797 

Almonry.  The  place  or  chamber  where  alms  were  distributed  to  the  poor  in 
churches,  or  other  ecclesiastical  buildings.  At  Bishopstone  Church,  Wiltshire, 
England,  it  is  a  sort  of  covered  porch  attached  to  the  south  transept,  but  not 
communicating  with  the  interior  of  the  church.  At  Worcester  Cathedral,  Eng- 
land, the  alms  are  said  to  have  been  di':tributed  on  stone  tables,  on  each  side, 
within  the  great  porch.  In  large  monastic  establishments,  as  at  Westminster', 
it  seems  to  have  been  a  separate  building  of  some  importance,  either  joining  the 
gate-house  or  near  it,  that  the  establishment  might  be  disturbed  as  little  as 
possible. 

Altar.  In  ancient  Rom.an  arc  hitecture,  a  place  on  which  offerings  or  sacri- 
fices were  made  to  the  gcds.  In  Protestant  churches,  t!ie  communion  table  is 
often  designated  as  the  Altar,  and  in  Roman  Catholic  churches  it  is  a  square 
table  placed  at  the  east  end  of  the  church  for  the  celebration  of  mass. 

Altar  of  Incense.  A  small  table  covered  with  plates  of  gold  on  which  was 
placed  the  smoking  censer  in  the  temple  at  Jerusalem. 

Altar-piece.  The  entire  decorations  of  an  altar;  a  painting  placed  behind  an 
altar. 

Altar-screen.  The  back  of  the  altar  from  which  the  canopy  was  suspended, 
and  separating  the  choir  from  the  lady  chapel  and  presbytery.  The  Altar-screen 
was  generally  of  stone,  and  composed  of  the  richest  tabernacle  work  of  niches, 
finials,  and  pedestals,  supporting  statues  of  the  tutelary  saints. 

Alto-rilievo.  High  relief.  A  sculpture,  the  figures  of  which  project  from  the 
surface  on  which  they  are  carved. 

Ambo.  A  raised  platform,  a  pulpit,  a  reading  desk,  a  marble. -pulpit  —  an 
oblong  enclosure  in  ancient  churches,  resembling  in  its  uses  and  positions  the 
modern  choir. 

Ambry.  A  cupboard  or  closet,  frequently  found  near  the  altar  in  ancient 
churches  to  hold  sacred  utensils. 

Ambulatory.     An  alley  —  a  gallery  —  a  cloister.  * 

Amphiprostylos.  A  Grecian  temple  which  has  a  columned  portico  on  both 
ends. 

Amphitheater.  A  double  theater,  of  an  elliptical  form  on  the  plan,  for  the 
exhibition  of  the  ancient  gladiatorial  fights  and  other  shows.  Its  arena  or  pit,  in 
which  those  exhibitions  took  place,  was  encompassed  with  seats  rising  above 
each  other,  and  the  exterior  had  the  accommodation  of  porticos  or  arcades  for 
the  pubHc. 

Amphora.     A  Grecian  vase  with  two  handles,  often  seen  on  medals. 

Ancones.  The  consoles  or  ornaments  cut  on  the  key-stones  of  arches  or  on 
the  sides  of  door-cases.  They  are  sometimes  made  use  of  to  support  busts  or 
other  figures. 

Angle-bar.  In  joinery,  an  upright  bar  at  the  angles  of  polygonal  windows; 
a  mullion. 

Angle-capital.  In  Greek  architecture,  those  Ionic  capitals  placed  on  the  flank 
columns  of  a  portico,  which  have  one  of  their  volutes  placed  horizontally  at  an 
angle  of  a  hundred  and  thirty-five  degrees  with  the  plane  of  the  frieze. 

Annulated  Columns.  Columns  clustered  together  by  rings  or  bands;  much 
used  in  English  architecture. 

Annular  Vault.  A  vault  rising  from  two  parallel  walls— the  vault  of  a 
corridor.     Ssune  as  Barrel  Vault. 


1798 


Glossary 


Part  3 


Annulet.     A  small  square  molding  used  to  separate  others.    The  fillet  which 
separates  the  flutings  of  columns  is  sometimes  known 
by  this  term. 

Anta,  Antae.     A  name  given  to  a  pilaster  when 
attached  to  a  wall.     Vitruvius  calls  pilasters  par- 
asiatcB  when   insulated.     They  are   not  usually  di- 
minished, and  in  all  Greek  examples  their  capitals  are  ANNULET 
different  from  those  of  the  columns  they  accompany. 

Antechamber.  An  apartment  preceded  by  a  vestibule  and  from  which  is 
approached  another  room. 

Antechapel.  A  small  chapel  forming  the  entrance  to  another.  There  are 
examples  at  Merton  College,  Oxford,  and  at  King's  College,  Cambridge,  England, 
besides  several  others.  The  antechapel  to  the  lady-chapel  in  cathedrals  is 
generally  called  the  Presbytery. 

Antechoir.  The  part  under  the  rood  loft,  between  the  doors  of  the  choir 
and  the  outer  entrance  of  the  screen,  forming  a  sort  of  lobby.  It  is  also  called 
the  Fore-choir. 

Antefixa.  In  classical  architecture  (gargoyles,  in  Gothic  architecture),  the 
ornaments  of  hons'  and  other  heads  below  the  eaves  of  a 
temple,  through  channels  in  which,  usually  by  the  mouth,  the 
water  is  carried  from  the  eaves.  By  some  this  term  is  ap- 
plied to  the  upright  ornaments  above  the  eaves  in  ancient 
architecture,  which  hid  the  ends  of  the  Harmi  or  joint  tiles. 

Apophyge.  The  lowest  part  of  the  shaft  of  an  Ionic  or  Corinthian  cplumn, 
or  the  highest  member  of  its  base  if  the  column  be  considered  as  a  whole  The 
Apophyge  is  the  inverted  cavetto  or  concave  sweep,  on  the  upper  edge  of  which 
the  diminishing  shaft  rests. 

Apron.  A  plain  or  molded  piece  of  finish  below  the  stool  of  a  window,  put 
on  to  cover  the  rough  edge  of  the  plastering. 

Apse.     The  semicircular  or  polygonal  termination  to  the  chancel  of  a  church. 
Apteral.     A  temple  without  columns  on  the  flanks  or  sides. 
Aqueduct.     An  artificial  canal  for  the  conveyance  of  water,  either  above  or 
under  ground.     The  Roman  aqueducts  are  mostly  of  the  former  construction. 

Arabesque.  A  building  after  the  manner  of  the  Arabs.  Ornaments  used  by 
the  same  people,  in  which  no  human  or  animal  figures  appear. 
Arabesque  is  sometimes  improperly  used  to  denote  a  species  of  or- 
naments composed  of  capricious  fantastics  and  imaginary  repre- 
sentations of  animals  and  foliage  so  much  employed  by  the  Romans 
in  the  decorations  of  walls  and  ceiHngs. 

Arabian  Architecture.  A  style  of  architecture  the  rudiments  ^ 
of  which  appear  to  have  been  taken  from  surrounding  nations,  the 
Egyptians,  Syrians,  Chaldeans,  and  Persians.  The  best  preserved 
specimens  partake  chiefly  of  the  Gra^co-Roman,  Byzantine,  and 
Egyptian.  It  is  supposed  that  they  constructed  many  of  their  finest 
buildings  from  the  ruins  of  ancient  cities. 

Araeostyle.  That  style  of  building  in  which  the  columns  are 
distant  from  one  another  from  four  to  five  diameters.  Strictly 
speaking,  the  term  should  be  limited  to  intercolumniation  of  four 
diameters,  which  is  only  suited  to  the  Tuscan  order. 

Ar»osystylos.     That  style  of  building  in  which  four  columns  arabesqte 
are  used  in  the  space  of  eight  diameters  and  a  half;    the  central 


Glossary  I799 

intercolumniation  being  three  diameters  and  a  half,  and  the  others  on  each 
side  being  only  half  a  diameter,  by  which  arrangement  coupled  columns  are 
mtroduced. 

Arbores.  Large  bronze  candelabra,  in  the  shape  of  a  tree,  placed  on  the  floor 
of  ancient  churches,  so  as  to  appear  growing  out  of  it. 

Arcade.  A  range  of  arches,  supported  cither 
on  columns  or  on  piers,  and  detached  or  attached 
to  the  wall. 

Arch.  In  building,  a  mechanical  arrange- 
ment of  building  materials  arranged  in  the  form 
of  a  curve,  which  preserves  a  given  form  when 
resisting  pressure,  and  enables  them,  supported 
by  piers  or  abutments,  to  carry  weights  and 
resist  pressure. 

Arch-buttress.     Sometimes  called  a  flying  arcade 

buttress;   an  arch  springing  from  a  buttress  or  pier. 

Architrave.  That  part  of  an  entablature  which  rests  upon  the  capital  of  a 
column,  and  is  beneath  the  frieze. 

Architrave  Cornice.  An  entablature  consisting  of  an  architrave  and  cor- 
nice, without  the  intervention  of  the  frieze,  sometimes  introduced  when  incon- 
venient to  give  the  entablature  the  usual  height. 

Architrave  of  a  Door.  The  finished  work  surrounding  the  aperture;  the 
upper  part  of  the  lintel  is  called  the  traverse;   and  the  sides,  the  jambs. 

Archives.     A  repository  or  closet  for  the  preservation  of  writings  or  records. 

Archivolt.  A  collection  of  members  forming  the  inner  contour  of  an  arch, 
or  a  band  or  frame  adorned  with  moldings  running  over  the  faces  or  the  arch- 
stones,  and  bearing  upon  the  imposts. 

Area.  The  superficial  contents  of  any  figure;  an  open  space  or  court  within 
a  building;  also,  an  uncovered  space  surrounding  the  foundation  walls  to  give 
light  to  the  basement. 

Arena.  The  plain  space  in  the  middle  of  the  amphitheater  or  other  place  of 
public  resort. 

Arris.     The  meeting  of  two  surfaces  producing  an  angle. 

Arsenal.     A  public  storehouse  for  arms  and  ammunition. 

Artificer,  or  Artisan.  A  person  who  works  with  his  hands,  and  manufac- 
tures any  commodity  in  iron,  brass,  wood,  etc. 

Ashlar,  or  Ashler.  A  facing  made  of  squared  stones,  or  a  facing  made  of 
thin  slabs,  used  to  cover  walls  of  brick  or  rubble.  Coursed  ashlar  is  where  the 
stones  run  in  level  courses  all  around  the  building;  random  ashlar,  where  the 
stones  are  of  different  heights,  but  level  beds.  Common  freestones  of  small 
size,  as  they  come  from  the  quarry,  are  also  called  ashlar. 

Asphaltum.  A  kind  of  bituminous  stone,  principally  found  in  the  province 
of  Neufchatel.  Mixed  with  stone,  it  forms  an  excellent  cement,  incorruptible 
by  air  and  impenetrable  by  water. 

Astragal.  A  small  semicircular  molding,  sometimes  plain  and  sometimes 
ornamented. 

Asymptote.  A  straight  line  which  continually  approaches  to  a  curve  with- 
out touching  it. 


1800 


Glossary 


Part  3 


Atlases,  or  Atlantes.     Figures  or  half-figures  of  men,  used  instead  of  col- 
umns  or   pilasters   to    support   an    entablature;  • 
called  also  Telamoncs.  ^ 

Atrium.  A  court  in  the  interior  division  of 
Roman  houses. 

Attached  Columns.  Those  which  project 
three-fourths  of  their  diameter  from  the  wall. 

Attic.  A  low  story  above  an  entablature,  or 
above  a  cornice  which  limits  the  height  of  the 
main  part  of  an  elevation.  Although  the  term  is 
evidently  derived  from  the  (ireek,  we  find  noth- 
ing exactly  answering  to  it  in  Greek  architec- 
ture; but  it  is  very  common  in  both  Roman  and 
Italian  practice.  What  are  otherwise  called 
tholobates  in  St.  Peter's  and  St.  Paul's  Cathe-  atlantes 

drals  are  frequently  termed  attics. 

Attic  Order.     A  term  used  to  denote  the  low  pilasters  employed  in  the 
decoration  of  an  attic  story. 

Attributes.     In  painting  and  sculpture,  symbols  given  to  figures  and  statues 
la  indicate  their  office  and  character. 

Auditory.     In  ancient  churches,  that  part  of  the  church  where  the  people 
usually  stood  to  be  instructed  in  the  Gospel,  now  called  the  nave. 

Aula.     A  court  or  hall  in  ancient  Roman  houses. 

Aviary.     A  large  apartment  for  breeding  birds. 

Axis.     The  spindle  or  center  of  any  rotative  motion.     In  a  sphere,  an  imag- 
inary line  through  the  center. 

Back-choir.     A  place  behind  the  altar  in  the  principal  choir,  in  which  there 
is,  or  was,  a  small  altar  standing  back  to  back  with  the  former. 

Backing  of  a  Rafter  or  Rib.     The  forming  of  an  upper  or  outer  surface, 
that  it  may  range  with  the  edges  of  the  ribs  or  rafters  on  either  side. 

Backing  of  a  Wall.     The  rough  inner  face  of  a  wall;  earth  deposited  behind 
a  retaining  wall,  etc. 

Back  of  a  Window.     That  piece  of  wainscoting  which  is  between  the  bottom 
of  the  sash  frame  and  the  floor. 

Balcony.     A  projection  from  the  face  of  a  wall,  supported  by  columns  or  con- 
soles, and  usually  surrounded  by  a  balustrade. 

Baldachin.     A  building  in  the  form  of  a  canopy,  supported  with  columns,  and 
serving  as  a  crown  or  covering  to  an  altar. 

Baluster.  A  small  pillar  or  column,  supporting  a  rail, 
of  various  forms,  used  in  balustrades. 

Baluster  Shaft.  The  shaft  dividing  a  window  in  Saxon 
architecture.  At  St.  Albans  are  some  of  these  shafts,  evi- 
dently out  of  the  old  Saxon  church,  which  have  been  fixed 
up  with  Norman  capitals. 

Balustrade.     A  series  of  balusters  connected  by  a  rail. 

Band.  A  sort  of  flat  frieze  or  fascia  running  horizon- 
tally round  a  tower  or  other  parts  of  a  building,  particu- 
larly the  base  tables  in  perpendicular  work,  commonly  used 
with  the  long  shafts  characteristic  of  the  thirteenth  cen- 
tury.    It  generally  has  a  bold,  projecting  molding  above 


PAI^ACHIN 


Glossaiy  jgQ^ 

and  below,  and  is  carved  sometimes  with  foliages,  but  in  general  with  cusped 
circles,  or  quatrefoils,  in  which  frequently  are  shields  of  arms. 

of  fh?.t  ?L^  fo^^^^-  A  series  of  annulets  and  hollows  going  round  the  middle 
of  the  shafts  of  columns,  and  sometimes  of  the  entire  pier.  They  are  often  beau- 
tif ully  carved  with  foliages,  etc.,  as  at  Amiens.  In  several  cathedrals  there  are 
rings  ot  bronze  apparently  covering  the  junction  of  the  frusta  of  the  columns 
At  Worcester  and  Westminster  they  appear  to  have  been  gilt;  they  are  there 
more  properly  called  Shaft-rings. 

Baptistery.  A  separate  building  to  contain  the  font,  for  the  rite  of  baptism 
Ihey  are  frequent  on  the  Continent;  that  at  Rome,  near  St.  John  Lateran  and 
those  at  Horeace,  Pisa,  Pavia,  etc.,  are  all  well-known  examples.  The  only  ex- 
amples in  England  are  at  Cranbrook  and  Canterbury;  the  latter,  however  is 
supposed  to  have  been  originally  part  of  the  treasury. 

Barbican.  An  outwork  for  the  defence  of  a  gate  or  drawbridge;  also,  a  sort 
of  pent-house  or  construction  of  timber  to  shelter  warders  or  sentries  from  arrows 
or  other  missiles. 

Barge  Board.     See  Verge  Board. 

Bartizan.     A  small  turret,  corbeled  out  at  the  angle  of  a  wall  or  tower,  to  pro- 
tect a  warder  and  enable  him  to  see  around  him. 
They  generally  are  furnished  with  oylcts  or  arrow- 
slits. 

Basement.     The  lower  part  of  a  building,  usu- 
ally in  part  below  the  grade  of  the  lot  or  street. 

Base    Moldings.     The   moldings   immediately 
above  thf^.  plinth  of  a  wall,  pillar,  or  pedestal. 

Base  of  a  Column.     That  part  which  is  between  bartizan 

the  shaft  and  the  pedestal,  or,  if  there  be  no  pedes- 
tal, between  the  shaft  and  the  plinth.     The  Grecian  Doric  had  no  base,  and  the 
Tuscan  has  only  a  single  torus,  or  a  plinth. 

Basilica.  A  term  given  by  the  Greeks  and  Romans  to  the  public  buildings 
devoted  to  judicial  purposes. 

Bas-relief.     See  Basso-rilievo. 

Basse-cour.  A  court  separated  from  the  principal  one,  and  destined  for 
stables,  etc. 

Basso-rilievo,  or  Bas-relief.  The  representations  of  figures  projected  from 
a  background  without  being  detached  from  it.  It  is  divided  into  three  parts: 
Alto-rilievo,  when  the  figure  projects  more  than  one-half;  Mezzo-rilievo,  that  in 
which  the  figure  projects  one-half;  and  Basso-rilievo,  when  the  projection  of  the 
figure  is  less  than  one-half,  as  in  coins. 

Bat.     A  part  of  a  brick. 

Batten.  Small  scantlings,  or  small  strips  of  boards,  used  for  various  purposes. 
Small  strips  put  over  the  joints  of  sheathing  to  keep  out  the  weather. 

Batten-door.  A  door  made  of  sheathing,  secured  by  strips  of  board,  put 
crossways,  and  nailed  with  cHnched  nails. 

Batter.  A  term  used  by  bricklayers,  carpenters,  etc.,  to  signify  a  wall,  piece 
of  timber,  or  other  material,  which  does  not  stand  upright,  but  inclines  from  you 
when  you  stand  before  it;  but  when,  on  the  contrary,  it  leans  toward  you,  it  is 
said  to  overhang. 


1802  Glossary  Part  3 

Battlement.  A  parapet  with  a  series  of  notches  in  it,  from  which  arrows  may 
be  shot,  or  other  instruments  of  defence 
hurled  on  besiegers.  The  raised  portions 
are  called  merlons;  and  the  notches,  em- 
brasures or  crenelles.  The  former  were 
intended  to  cover  the  soldier  while  dis- 
charging his  weapon  through  the  latter. 
Their  use  is  of  great  antiquity;  they  are 
found  in  the  sculptures  of  Nineveh,  in  the 
tombs  of  Egypt,  and  on  the  famous  Fran-  battlement 

gois  vase,  where  there  is  a  delineation  of 

the  siege  of  Troy.  In  ecclesiastical  architecture  the  early  battlements  have  small 
shallow  embrasures  at  some  distance  apart.  In  the  Decorated  period  they  are 
closer  together,  and  deeper,  and  the  moldings  on  the  top  of  the  merlon  and  bot- 
tom of  the  embrasure  are  richer.  During  this  period,  and  the  early  part  of  the 
Perpendicular,  the  sides  or  cheeks  of  the  embrasures  are  perfectly  square  and 
plain.  In  later  times  the  moldings  were  continued  round  the  sides,  as  well  as 
at  top  and  bottom,  mitring  at  the  angles,  as  over  the  doorway  of  Magdalen  Col- 
lege, Oxford,  England.  The  battlements  of  the  Decorated  and  later  periods  are 
often  richly  ornamented  by  paneling,  as  in  the  last  example.  In  castellated 
work  the  merlons  are  often  pierced  by  narrow  arrow-shts,  (See  Oylel.)  In 
South  Ital}^  some  battlements  are  found  strongly  resembling  those  of  old  Rome 
and  Pompeii;  in  the  Continental  ecclesiastical  architecture,  the  parapets  are  very 
rarely  embattled.  • 

Bay.  Any  division  or  compartment  of  an  arcade,  roof,  etc.  Thus  each  space, 
from  pillar  to  pillar,  in  a  cathedral,  is  called  a  bay,  or  severy. 

Bay  Window.  Any  window  projecting  outward  from  the  wall  of  a  building, 
either  square  or  polygonal  on  plan,  and  commencing  from  the  ground.  If  they 
are  carried  on  projecting  corbels,  they  are  called  Oriel  windows.  Their  use  seems 
to  have  been  confined  to  the  later  periods.  In  the  Tudor  and  Elizabethan  styles 
they  are  often  semicircular  in  plan,  in  which  case  some  think  it  more  correct  to 
call  them  Bow  Windows. 

Bazaar.     A  kind  of  Eastern  mart,  of  Arabic  origin. 

Bead.  A  circular  molding.  When  several  are  joined,  it  is  called  Reeding; 
when  flush  with  the  surface,  it  is  Called  Quirk-bead;  and  when  raised.  Cock-bead. 

Beam.  A  piece  of  timber,  iron,  stone,  or  other  material,  placed  horizontally^ 
or  nearly  so,  to  support  a  load  over  an  opening,  or  from  post  to  post. 

Bearing.     The  portion  of  a  beam,  truss,  etc.,  that  rests  on  the  supports. 

Bearing  Wall,  or  Partition.  A  wall  which  supports  the  floors  and  roofs  in 
a  building. 

Beauf et,  or  Buffet.  A  small  cupboard,  or  cabinet,  to  contain  china.  It  may 
either  be  built  into  a  wall,  or  be  a  separate  piece  of  furniture. 

Bed.     In  bricklaying  and  masonry,  the  horizontal  surfaces  on  which  the  stones 
or  bricks  of  walls  lie  in  courses. 
Bed  of  a  Slate.    The  lower  side. 

Bed  Moldings.  Those  moldings  in  all  the  orders  between  the  corona  and 
frieze. 

Belfry.  Properly  speaking,  a  detached  tower  or  campanile  containing  bells, 
as  at  Evesham,  England,  but  more  generally  applied  to  the  ringing- room  or  loft 
of  the  tower  of  a  church.     See  Tower. 


Glossary  1803 

Bell-cot,  Bell-gable,  or  Bell-turret.  The  place  where  one  or  more  bells  are 
hung  in  chapels,  or  small  churches  which  have  no  towers.  Bell-cots  are  some- 
times double,  as  at  Northborough  and  Coxwell,  England;  a  very  common  form 
in  France  and  Switzerland  admits  of  three  bells.  In  these  countries,  also,  they 
are  frequently  of  wood,  and  attached  to  the  ridge.  Those  which  stand  on  the 
gable,  dividing  the  nave  from  the  chancel,  are  generally  called  Sanctus  Bells.  A 
^ery  curious  and,  it  is  beheved,  unique  example  at  Cleves  Abbey,  England,  juts 
out  from  the  wall.  In  later  times  bell-turrets  were  much  ornamented;  these  are 
often  called  Fleches. 

Bell  of  a  Capital.  In  Gothic  work,  immediately  above  the  necking  is  a  deep, 
hollow  curve;  this  is  called  the  bell  of  a  capital.  It  is  often  enriched  with  foli- 
ages.    It  is  also  applied  to  the  body  of  the  Corinthian  and  Composite  capitals. 

Belt.  A  course  of  stones  or  brick  projecting  from  a  brick  or  stone  wall,  gen- 
erally placed  in  a  line  with  the  sills  of  the  windows;  it  is  either  molded,  fluted, 
plane,  or  enriched  with  patras  at  regular  intervals.  Sometimes  called  Stone 
String. 

Belvedere,  or  Look-out.  A  turret  or  lantern  raised  above  the  roof  of  an 
observatory  for  the  purpose  of  enjoying  a  fine  prospect. 

Bema.  The  semicircular  recess,  or  hexedra,  in  the  basiUca,  where  the  judges 
sat,  and  where  in  after-times  the  altar  was  placed.  It  generally  is  roofed  with  a 
half-dome  or  concha.  The  seats  of  the  priests  were  against  the  wall,  looking  into 
the  body  of  the  church,  that  of  the  bishop  being  in  the  center.  The  bema 
is  generally  ascended  by  steps,  and  railed  off  by  cancelli. 

Bench  Table.  The  stoiie  seat  which  runs  round  the  walls  of  large  churches, 
and  sometimes  round  the  piers;  it  very  generally  is  placed  in  the  porches. 

Bevel.  An  instrument  for  taking  angles.  One  side  of  a  soHd  body  is  said  to 
be  beveled  with  respect  to  another,  when  the  angle  contained  between  those  two 
sides  is  greater  or  less  than  a  right  angle. 

Bezantee.  A  name  given  to  an  ornamental  molding  much  used  in  the  Nor- 
man period,  resembling  bezants,  coins  struck  in  Byzantium. 

Billet.  A  species  of  ornamented  molding  much  used  in  Norman,  and  some- 
times in  Early  English  work,  like  short  pieces  of  stick  cut  off  and  arranged  alter- 
nately. 

Blocking,  or  Blocking-course.  In  masonry,  a  course  of  stones  placed  on 
the  top  of  a  cornice  crowning  the  walls. 

Bond.  In  bricklaying  and  masonry,  that  connection  between  bricks  or  stones 
formed  by  lapping  them  upon  one  another  in  carrying  up  the  work,  so  as  to  form 
an  inseparable  mass  of  building,  by  preventing  the  vertical  jomts  falhng  oyer 
each  other.  In  brickwork  there  are  several  kinds  of  bond.  In  common  bnck 
walls  in  every  sixth  or  seventh  course  the  bricks  are  laid  crossways  of  the  wall 
called  Headers.  In  face  work,  the  back  of  the  face  brick  is  clipped  so  as  to  get 
in  a  diagonal  course  of  headers  behind.  In  Old  Enghsh  bond,  every  a  erna  e 
course  is  a  header  course.  In  Flemish  bond,  a  header  and  stretcher  alternate 
in  each  course. 

Bond-stones.  Stones  running  through  the  thickness  of  the  wall  at  nght 
ani,^les  to  its  face,  in  order  to  bind  it  together. 

Bond-timbers.  Timbers  placed  in  a  horizontal  direction  in  the  walls  o  a 
I.  i  1  buildL  in  tiers,  and  to  which  the  battens,  laths,  etc.,  are  secured.  In  rub- 
l,U  work   walls  are  better  plugged  for  this  purpose. 

Border.     Useful  ornamental  pieces  around  the  edge  of  anythmg. 


1804 


Glossary 


Parts 


Boss.  An  ornament,  generally  carved,  forming  the  key-stone  at  the  intersec- 
tion of  the  ribs  of  a  groined  vault.  Early  Norman  vaults  have  no  bosses.  The 
carving  is  generally  foliage,  and  resembles  that  of  the  period  in  capitals,  etc.  ■ 
Sometimes  they  have  human  heads,  as  at  Notre  Dame  at  Paris,  and  sometimes 
grotesque  figures.    In  Later  Gothic  vaulting  there  are  bosses  at  every  intersection. 

Boutell.  The  mediaeval  term  for  a  round  molding,  or  torus.  When  it 
follows  a  curve,  as  round  a  bench  end,  it  is  called  a  Roving  Boutell. 

Bow.  Any  projecting  part  of  a  building  in  the  form  of  an  arc  of  a  circle.  A 
bow,  however,  is  sometimes  polygonal. 

Bow  Window.     A  window  placed  in  the  bow  of  a  building. 

Brace.  In  carpentry,  an  inclined  piece  of  tim]3cr,  used  in  trussed  partitions, 
or  in  framed  roofs,  in  order  to  form  a  triangle,  and  thereby  stiffen  the  framing. 
When  a  brace  is  used  by  way  of  support  to  a  rafter,  it  is  called  a  strut.  Braces 
in  partitions  and  span-roofs  are,  or  always  should  be,  disposed  in  pairs,  and 
introduced  in  opposite  directions. 

Brace  Mold.  [  \  J  Two  rcssaunts  or  ogees  united  together  like  a  brace  in 
printing,  sometimes  with  a  small  bead  between  them. 

Bracket.  A  projecting  ornament  carrying  a  cornice.  Those  which  support 
vaulting  shafts  or  cross  springers  of  a  roof  are  more  generally  called  Corbels. 

Break.     Any  projection  from  the  general  surface  of  a  building. 

Breaking  Joint.  The  arrangement  of  stones  or  bricks  so  as  not  to  allow 
two  joints  to  come  immediately  over  each  other.     See  Bond. 

Breast  of  a  Window.  The  masonry  forming  the  back 
of  the  recess  and  the  parapet  under  the  window-sill. 

Bressummer.  A  hntcl,  beam,  or  iron  tie,  intended  to 
carry  an  external  wall  and  itself  supported  by  piers  or 
posts;  used  principally  over  shop  windows.  This  term 
is  now  seldom  used,  the  word  beam,  or  girder,  taking  its 
place. 

Bridging.  A  method  of  stiffening  floor  joist  and  parti- 
tion studs,  by  cutting  pieces  in  between.  Cross  bridging 
of  floor  joist  is  illustrated  in  cut. 

Bulwark.  In  ancient  fortification,  nearly  the  same  as 
Bastion  in  modern. 

Burse,  or  Bourse.  A  public  edifice  for  the  assembly  of  merchant  traders' 
an  exchange. 

Bust.  In  sculpture,  that  portion  of  the  human  figure 
which  comprises  the  head,  neck,  and  shoulders. 

Buttery.     A  store-room  for  provisions. 

Butt-joint.  Where  the  ends  of  iwo  pieces  of  timber  or 
molding  butt  together. 

Buttress.  Masonry  projecting  from  a  wall,  and  intended 
to  strengthen  the  same  against  the  thrust  of  a  roof  or  vault. 
Buttresses  are  no  doubt  derived  from  the  classic  pilasters  wliich 
serve  to  strengthen  walls  where  there  is  a  pressure  of  a  girder 
or  roof-timber.  In  very  early  work  they  have  little  projection, 
and,  in  fact,  are  "strippilasters."  In  Norman  work  they  are 
wider,  with  very  Httle  projection,  and  generally  stop  under  a 
cornice  or  corbel  table.  Early  English  buttresses  project  con- 
siderably, sometimes  with  deep  sloping  weatherings  in  several 


CROSS-BRIDGING 


FLYING  BUTTRESS 


Glossary  1.S05 

stages,  and  sometimes  with  gabled  heads.  Sometimes  they  are  chamfered,  and 
sometimes  the  angles  have  jamb  shafts.  At  Wells  and  Salisbury,  England, 
they  are  richly  ornamented  with  canopies  and  statues.  In  the  Decorated  period 
they  became  richly  paneled  in  stages,  and  often  finish  with  niches  and  statues 
and  elegantly  carved  and  crocketcd  gablets,  as  at  York,  England.  In  the 
Perpendicular  period  the  weatherings  became  waved,  and  they  frequently 
terminate  with  niches  and  pinnacles. 

Buttress,  Flying.     A  detached  jjuttress  or  pier  of  masonry  at  some  distance 
from  a  wall,  and  connected  therewith  by  an  arch  or  por- 
tion of  an  arch,  so  as  to  discharge  the  thrust  of  a  roof  or 
vault  on  some  strong  point. 

Buttress  Shafts.  Slender  columns  at  the  angle  of 
buttresses,  chiefly  used  in  the  Early  English  period. 

Byzantine  Architecture.  A  style  developed  in  the 
Byzantine  Empire.  The  capitals  of  the  pillars  are  of 
endless  variety  and  full  of  invention;  some  are  founded 
on  the  Greek  Corinthian,  some  resemble  the  Norman 
and  the  Lombard  style,  and  arc  so  varied  that  no  two  sides 
of  the  same  capital  are  alike.  They  are  comprised  under 
the  style  Romanesque,  which  comprehends  the  round- 
arch  style.  Byzantine  architecture  reached  its  height  in 
the  Church  of  St.  Sophia  at  Constantinople. 

Cabinet.  A  highly  ornamented  kind  of  buffet  or  chest  of  drawers  set  apart 
for  the  preservation  of  things  of  value. 

Cabling.  The  flutes  of  columns  are  said  to  be  cabled  when  they  are  partly 
occupied  by  solid  convex  masses,  or  appear  to  be  refilled  with  cylinders  after 
they  had  been  formed. 

Caduceus.     Mercury's  rod,  a  wand  entwined  by  two  serpents  and  surmounted 
by  two  wings.     The  rod  represents  power;   the  serpents,  wisdom; 
and  the  wings,  diligence  and  activity. 

Caisson.  A  panel  sunk  below  the  surface  in  flat  or  vaulted  ceil- 
ings.    See  Cassoon 

Caisson.  In  bridge  building,  a  chest  or  vessel  in  which  the  piers 
of  a  bridge  are  built,  gradually  sinking  as  the  work  advances  till  its 
bottom  comes  in  contact  with  the  bed  of  the  river,  and  then  the 
sides  are  disengaged,  being  so  constructed  as  to  allow  of  their  being 
thus  detached  without  injury  to  its  floor  or  bottom. 

Caliber,  or  Caliper.  The  diameter  of  any  round  body;  the  width 
of  the  mouth  of  a  piece  of  ordnance. 

Camber.  In  carpentry,  the  convexity  of  a  beam  upon  the  surface, 
in  order  to  prevent  its  becoming  concaVfe  by  its  own  weight,  or  by 
the  burden  it  may  have  to  sustain. 

Campanile.  A  name  given  in  Italy  to  the  bell-tower  of  a  town-hall  or  church. 
In  that  country  this  is  almost  always  detached  from  the  latter. 

Candelabrum.  Stand  or  support  on  which  the  ancients  placed  their  lamps. 
Candelabra  were  made  in  a  variety  of  shapes  and  with  much  taste  and  elegance. 
The  term  is  also  used  to  denote  a  tall  ornamental  candlestick  with  several  arms, 
or  a  bracket  with  arms  for  candles. 

Canopy.  The  upper  part  or  cover  of  a  niche,  or  the,projection  or  ornament 
over  an  altar,  seat,  or  tomb.     The  word  is  supposed  to  be  derived  from  cone- 


1806  Glossary  Part  3 

paeum,  the  gauze  covering  over  a  bed  to  keep  off  the  gnats;  a  mosquito  curtain. 
Early  English  canopies  are  generally  simple,  with  trefoilcd  or  cinque-foiled  heads; 
but  in  the  later  styles  they  are  very  rich,  and  divided  into  compartments  with 
pendants,  knots,  pinnacles,  etc.  The  triangular  arrangement  over  an  Early  Eng- 
lish and  Decorated  doorway  is  often  called  a  canopy.  The  triangular  canopies 
in  the  North  of  Italy  are  peculiar.  Those  in  England  are  generally  part  of  the 
arrangement  of  the  arch  moldings  of  the  door,  and  form,  as  it  were,  the  hood- 
molds  to  them,  as  at  York.  The  former  are  above  and  independent  of  the  door 
moldings,  and  frequently  support  an  arch  with  a  tympanum,  above  which  is  a 
triangular  canopy,  as  in  the  Duomo  at  Plorence.  Sometimes  the  canopy  and 
arch  project  from  the  wall,  and  are  carried  on  small  jamb  shafts,  as  at  San  Pietro 
Martiro  at  Verona.  Canopies  are  often  used  over  windows,  as  at  York  Minster 
over  the  great  west  window,  and  lower  ties  in  the  towers.  These  are  triangular, 
while  the  upper  windows  in  the  towers  have  ogee  canopies. 

Ca'pital.  The  upper  part  of  a  column,  pilaster,  pier,  etc.  Capitals  have  been 
used  in  every  style  down  to  the  present  time.  That  mostly  used  by  the  Egyp- 
tians was  bell-shaped,  with  or  without  ornaments.  The  Persians  used  the  double- 
headed  bell,  forming  a  kind  of  bracket  capital.  The  Assyrians  apparently  made 
use  of  the  Ionic  and  Corinthian,  which  were  developed  by  the  Greeks,  Romans, 
and  Italians  into  their  present  well-known  forms.  The  Doric  was  apparently  an 
invention  or  adaptation  by  the  Greeks,  and  was  altered  by  the  Romans  and 
Italians.  But  in  all  these  examples,  both  ancient  and  modern,  the  capitals  of  an 
order  are  all  of  the  same  form  throughout  the  same  building,  so  that  if  one  be 
seen  the  form  of  all  the  others  is  known.  The  Romanesque  architects  altered 
aU  this,  and  in  the  carving  of  their  capitals  often  introduced  such  figures  and 
emblems  as  helped  to  tell  the  story  of  their  building.  Another  form  was  intro- 
duced by  them  in  the  curtain  capital,  rude  at  first,  but  afterward  highly  deco- 
rated. It  evidently  took  its  origin  from  the  cutting  off  of  the  lower  angles  of  a 
square  block,  and  then  rounding  them  off.  The  process  may  be  distinctly  seen, 
in  its  several  stages,  in  Mayence  Cathedral.  But  this  form  of  capital  was  more 
fully  developed  by  the  Normans,  with  whom  it  became  a  marked  feature.  In 
the  early  English  capitals  a  peculiar  flower  of  three  or  more  lobes  was  used 
spreading  from  the  necking  upward  in  most  graceful  forms.  In  Decorated  and 
Perpendicular  styles  this  was  abandoned  in  favor  of  more  realistic  forms  of 
crumpled  leaves,  enclosing  the  bell  like  a  Wreath.  In  each  style  bold  abacus 
moldings  were  always  used,  whether  with  or  without  foliage. 

Caravansary.  A  huge,  square  building,  or  inn,  in  the  East,  for  the  reception 
of  travelers  and  lodging  of  caravans. 

Carriage.     The  timber  or  iron  joist  which  supports  the  steps  of  a  wooden  stair- 
Carton,  or  Cartoon.     A  design  made  on  strong  paper,  to  be 
transferred  on  the  fresh  plaster  wall  to  be  afterward  painted  in 
fresco;   also,  a  colored  design  for  working  in  mosaic  tapestry. 

Cartouche.  An  ornament  which  like  an  escutcheon,  a  shield 
or  an  oval  or  oblong  panel  has  the  central  part  plain,  and  usually 
slightly  convex,  to  receive  an  inscription,  armorial  bearings,  or  an 
ornamental  or  significant  piece  of  painting  or  sculpture.  Frequently 
used  in  French  Renaissance  and  Modern  Architecture. 

Caryatides.  Human  female  figures  used  as  piers,  columns,  or 
supports.  Caryatic  is  applied  to  the  human  figure  generally,  when 
used  in  the  manner  of  caryatides. 

Cased.  Covered  with  other  materia^  generally  of  a  better 
quality. 


Glossary  1807 

Casement.  A  glass  frame  which  is  made  to  open  by  turning  on  hinges 
affixed  to  its  vertical  edges. 

Casspon,  or  Caisson.  A  deep  panel  or  coffer  in  a  soffit  or  ceiling.  This 
term  is  sometimes  written  in  the  French  form,  caisson;  sometimes  derived 
directly  from  the  Italian  cassone,  the  augmentative  of  cassa,  a  chest  or  coffer. 

Cast.  A  term  used  in  sculpture  for  the  impression  of  any  figure  taken  in 
plaster  of  Paris,  wax,  or  other  substances. 

Catacombs.  Subterranean  places  for  burying  the  dead.  Those  of  Egypt, 
and  near  Rome,  are  believed  to  be  the  most  important. 

Catafalco.     An  ornamental  scaffold  used  in  funeral  solemnities. 

Cathedral.     The  principal  church,  where  the  bishop  has  his  seat  as  diocesan. 

Cauliculus.  The  inner  scroll  of  the  Corinthian  capital.  It  is  not  uncommon, 
however,  to  apply  this  term  to  the  larger  scrolls  or  volutes  also. 

Causeway.     A  raised  or  paved  way. 

Cavetto.  A  concave  ornamental  molding,  opposed  in  effect  to  the  ovolo  — 
the  quadrant  of  a  circle. 

Ceiling.  That  covering  of  a  room  which  hides  the  joists  of  the  floor  above, 
or  the  rafters  of  the  roof  Most  European  churches  either  have  open  roofs,  or 
arc  groined  in  stone.  At  Peterborough  and  St.  Albans,  England,  there  are  very 
old  flat  ceilings  of  boards  curiously  painted.  In  later  times  the  boarded  ceilings, 
and,  in  fact,  some  of  those  of  plaster,  have  molded  ribs,  locked  with  bosses  at 
the  intersection,  and  are  sometimes  elaborately  carved.  In  many  English 
churches  there  are  ceilings  formed  of  oak  ribs,  filled  in  at  the  spandrels 
with  narrow,  thin  pieces  of  board,  in  exact  imitation  of  stone  groining.  In 
the  Elizabethan  and  subsequent  periods  the  ceilings  are  enriched  with 
most  elaborate  ornaments  in  stucco.  Matched  and  beaded  boards,  planed 
and  smoothed,  used  for  wainscoting.  In  the  New  England  States  it  is  called 
sheathing. 

Cenotaph.  An  honorary  tomb  or  monument,  distinguished  from  monuments 
in  being  empty,  the  individual  it  is  to  memorialize  having  received  interment 
elsewhere. 

Centaur.  A  poetical  imaginary  being  of  heathen  mythology,  half-man  and 
half-horse. 

Centring.     In  building,  the  frames  on  which  an  arch  is  turned. 

Chamfer,  Champf er,  or  Chaumf er.  When  the  edge  or  arris  of  any  work  is 
cut  off  at  an  angle  of  45°  in  a  small  degree,  it  is  said  to  be  chamfered;  if 
to  a  large  scale,  it  is  said  to  be  a  canted  corner.  The  chamfer  is  much  used  in 
mediaeval  work,  and  is  sometimes  plain,  sometimes  hollowed  out,  and  sometimes 
jmolded. 

Chamfer  Stop.  Chamfers  sometimes  simply  run  into  the  arris  by  a  plane 
face;  more  commonly  they  are  first  stopped  by  some  ornament,  as  by  a  bead; 
they  are  sometimes  terminated  by  trefoils,  or  cinque-foils,  double  or  single,  and- 
in  general  form  very  pleasing  features  in  mediaeval  architecture. 

Chancel.  A  place  separated  from  the  rest  of  a  church  by  a  screen  The  word 
is  now  generally  used  to  signify  the  portion  of  an  Episcopal  or  Catholic  church 
containing  the  altar  and  communion  table. 

Chantry.  A  small  chapel,  generally  built  out  from  a  church.  They  generally 
contain  a  founder's  tomb,  and  are  often  endowed  places  where  masses  might 


1808 


Glossary 


Parts 


CHAPTREL 


be  said  for  his  soul.  The  officiator,  or  mass  priest,  being  often  unconnected 
with  the  parochial  clergy.  The  chantry  has  generally  an  entrance  from  the 
outside. 

Chapel.  A  small,  detached  building  used  as  a  substitute  for  a  church  in  a 
large  parish;  an  ai:)artment  in  any  large  building,  a  palace,  a  nobleman's  house,  a 
hospital  or  prison,  used  for  pubhc  worship;  or  an  attached  building  running  out 
of  and  forming  part  of  a  large  church,  generally  dedicated  to  different  saints, 
each  having  its  own  altar,  piscina,  etc.,  and  screened  off  from  the  body  of  the 
building. 

Chapter  House.  The  chamber  in  which  the  chapter  or  heads  of  the  monastic 
bodies  assembled  to  transact  business.  They  are  of  various  forms;  some  are 
oblong  apartments,  some  octagonal,  and  some  circular. 

Chaptrel.  In  Gothic  architecture,  the  capital  of  a  pier  or  column  which 
receives  an  arch. 

Charnel  House.  A  place  for  depositing  the  bones  which  might  be 
thrown  up  in  digging  graves.  Sometimes  it  was  a  portion  of  lli. 
crypt;  sometimes  it  was  a  separate  building  in  the  church-yan 
sometimes  chantry  chapels  were  attached  to  these  buildings.  .  Al. 
Viollet-le-Duc  has  given  two  very  curious  examples  of  ossuaires  — 
one  from  Fleurance,  the  other  from  Faouet. 

Cherub — Gothic.     A  representation  of  an  infant's  head  joined  to 
two  wings,  used  in  the  churches  on  key-stones  of  arches  and  corbels. 

Chevron  —  Gothic.     An  ornament  turning  this  and  that  way,  like 
a  zigzag,  or  letter  Z. 

Chiaro-oscuro.  The  effects  of  light  and 
shade  in  a  picture. 

Choir.  That  part  of  a  church  or  monastery 
where  the  breviary  service,  or  "hora;,"  is 
chanted. 

Church.  A  building  for  the  performance  of 
public  worship.    The  first  churches  were  built  on  CHE\':ron 

the  plan  of  the  ancient  basilicas,  and  afterward 

on  the  plan  of  a  cross:  a  church  is  said  to  be  in  Greek  cross  when  the  length  of 
the  transverse  is  equal  to  that  of  the  nave;  in  Latin  cross,  when  the  nave  is 
longer  than  the  transverse  part;  in  rotundo,  when  it  is  a  perfect  circle;  simple, 
when  it  has  only  a  nave  and  choir;  with  aisles,  when  it  has  a  row  of  porticos  in 
form  of  vaulted  galleries,  with  chapels  in  its  circumference. 

Ciborium.  A  tabernacle  or  vaulted  canopy  supported  on  shafts  standing  over 
the  high  altar. 

Cincture.  A  ring,  list,  or  fillet  at  the  fop  and  bottom  ot  a 
column,  serving  to  divide  the  shaft  of  the  column  from  its 
capital  and  base. 

Cinque-foil.  A  sinking  or  perforation,  like  %.  flower,  of 
five  points  or  leaves,  as  a  quatre-foil  is  of  four.  The  points 
are  sometimes  in  a  circle,  and  sometimes  form  the  cusping 
of  a  head. 

Civic  Crown.     A  garland  of  oak-leaves  and  acorns,  given 
as  honorary  distinction  among  the  Romans  to  such  as  had  preserved  the  life 
of  a  fellow-citizen. 


CINQUE-FOIL 


Glossary 


1809 


Clere-story  Clear-story.  When  the  middle  of  the  nave  of  a  church  rises 
above  the  aisles  and  is  pierced  with 
windows,  the  upper  story  is  thus 
called.  Sometimes  these  windows 
are  very  small,  being  mere  quatre- 
foils,  or  spherical  triangles.  In  large 
buildings,  however,  they  are  impor- 
tant objects  both  for  beauty  and 
utility.  The  window  of  the  clere- 
stories of  Norman  work,  even  in  large 
churches,  are  of  less  importance  than 
in  the  later  styles.  In  Early  English 
they  became  larger  j  and  in  the  Deco- 
rated they  are  more  important  still, 
being  lengthened  as  the  triforium 
diminishes.  In  Perpendicular  work 
the  latter  often  disappears  altogether, 
and  in  many  later  churches  the  clere- 
stories are  close  ranges  of  windows. 
The  word  clere-story  is  also  used  to 
denote  a  similar  method  of  lighting 
other  buildings  besides  churches,  es- 
pecially factories,  depots,  sheds,  etc. 

Cloister.  An  enclosed  square,  like 
the  atrium  of  a  Roman  house,  with  a 
walk  or  ambulatory  around,  sheltered 
by  a  roof,  generally  groined,  and  by 
tracery  windows,  which  were  more 
or  less  glazed. 

Close.     The  precinct  of  a  cathedral 
Sometimes  the  walls  •  are 
but    now    generally    the 
is    only    known    by    tradi- 


or  abbey, 
traceable, 
boundary 
tion. 

Close  String,  or  Box  String. 


Bath  Abbey 

FLYING   BUTTRESS   AND   CLERE-STORY 


A,  buttress  with  pinnacle;  B,  flying 
method  of  r,„ishin«  the  outer  edge  of  Ij^XTroo^rj^T  D  t'fel^dTiding 


nave  from  aisle;  E,  vaulted  roof  of  nave. 


tairs,  by  bull-ding  up  a  sort  of  curb 
string  on  which  the  balusters  set, 
and  the  treads  and  risers  stop  against  it. 

Clustered.  In  architecture,  the  coalition  of  several  members 
which  penetrate  each  other. 

Clustered  Column.  Several  slender  pillars  attached  to  each 
other  SD  as  to  form  one.  The  term  is  used  in  Roman  architecture 
to  denote  two  or  four  columns  which  appear  to  intersect  each  other 
at  the  angle  of  a  building  to  answer  at  each  return. 

Coat.  A  thickness  or  coveiang  of  paint,  plaster,  or  other  work, 
done  at  one  rime.  The  first  coat  of  plastering  is  called  the  scratch 
coat,  the  second  coat  (when  there  are  three  coats)  is  called  the  brown 
coat,  and  the  last  coat  is  variously  known  as  the  slipped  coat, 
skimcoat,  or  white  coat.  It  varies  in  composition  in  different 
iocaiities. 

Coffer,     A  deep  panel  in  a  ceiling. 


1810 


Glossary 


Parlfl 
?  watl^B 
piked  !^1: 


LFTJ 

cyma-recta 
.fillet:zz 
cornice-^  corona_ 

OVCLO  ' 

fillet; 
lcavetto 

FRIEZE-^   FRIEZE 

TENiAr; 

ARCHI-  J  UPPER  FASCI 
RAVE 

LOWER  FASCI 


I 


Coffer  Dam.     A  frame   used  in  the  building  of  a  bridge  in  deep  watsj 
similar  to  a  caisson. 

Collar  Beam.     A  beam  above  the  lower  ends  of  the  rafters,  and  spiked!^ 
them. 

Colonnade.  A  row  of  columns.  The  colonnade  is  termed,  according  to 
the  number  of  columns  which  support  the  entablature:  Tetrastyle,  when  there 
are  four;  hexastyle,  when  six;  octostyle,  when  eight,  etc.  When  in  front  of  a 
building  they  are  termed  porticos;  when  surrounding  a  building,  peristyle;  and 
when  double  or  more,  polystyle. 

Colosseum,  or  Coliseum.  The  immense  amphitheater  built  at  Rome  by 
Flavins  Vespasian,  A  d.  72,  after  his  return  from  his  victories  over  the  Jews.  It 
would  contain  ninety  thousand  persons  sitting,  and  twenty  thousand  more 
standing.  The  name  is  now  employed 
to  denote  an  unusually  large  audience 
building,  generally  of  a  temporary 
nature. 

Colossus.  The  name  of  a  brazen 
statue  which  was  erected  at  the 
entrance  of  the  harbor  at  Rhodes, 
one  hundred  and  five  feet  in  height. 
Vessels  could  sail  between  its  legs. 

Column.  A  round  pillar.  The 
parts  are  the  base,  on  which  it  rests; 
its  body,  calbd  the  shaft;  and  the 
head,  called  the  capital.  The  capital 
finishes  with  a  horizontal  table,  called 
the  abacus,  and  the  base  commonly 
stands  on  another,  called  the  plinth. 
Columns  may  be  either  insulated  or 
attached.  They  are  said  to  be  at- 
tached or  engaged  when  they  form 
part  of  a  wall,  projecting  one-half  or 
more,  but  not  the  whole,  of  their 
substance. 

Common.  A  line,  angle,  surface, 
etc.,  which  belongs  equally  to  several 
objects.  Common  centring  is  a  cen- 
tring without  trusses,  having  a  tie 
beam  at  bottom.  Common  joists  are 
the  beams  in  naked  flooring  to  which 
the  joists  are  fixed.  Common  rafters 
in  a  roof  are  those  to  which  the  laths  are  attached. 
Composite  Arch.     Is  the  pointed  or  lancet  arch.  ^ 

Composite  Order.  The  most  elaborate  of  the  orders  of  classical  arch- 
itecture. 

Compound  Arch.  A  usual  form  of  medieval  arch,  which  may  be  resolved 
into  a  number  of  concentric  archways,  successively  placed  within  and  behind 
each  other. 

Conduit.  A  long  narrow  passage  between  two  walls  or  underground  for 
secret  communication  between  different  apartments;  also,  a  canal  or  pipe  for  the 
conveyance  of  water.  jM 


APOPHYCES 

FILLET-~-r-: 

TORUS 


r 


SECTION   OF  COLUMN    AND    ENTABLATURE 

(Divided  according  to  the  Tuscan  Order.) 


Glossary  1811 

Confessional.    The  seat  where  a  priest  or  confessor  sits  to  hear  confessions 

Conge.     Another  name  for  tho  ecliinus  or  quarter  round. 

Conservatory.  A  building  for  the  protection  and  rearing  of  tender  phmts 
often  attached  to  a  house  as  an  apartment.  Also,  a  public  place  of  instruction,' 
designed  to  preserve  and  perfect  the  knowledge  of  som3  branch  of  learning  or 
the  fine  arts;   as,  a  conservatory  of  music. 

Consistory.     The  judicial  hall  of  the  College  of  Cardinals  at  Rome. 

Consol,  or  Console.     A  bracket  or  truss,  generally  with  scrolls  or  volutes  at 
the  two  ends,  of  unequal  size  and  contrasted,  but 
connected  by  a  flowing  line  from  the  back  of  the 
upper  one  to  the  inner  convolving  face  of  the  lower. 

Coping.  The  capping  or  covering  of  a  wall.  This 
is  of  stone,  weathered  to  throw  off  the  wet.  In  Nor- 
man times,  as  far  as  can  be  judged  from  the  little  there 
is  left,  it  was  generally  plain  and  flat,  and  projected 
over  the  wall  with  a  floating  to  form  a  d.ip.  After- 
ward it  assumed  a  torus  or  bowtell  at  the  top,  and  be- 
came deeper,  and  in  the  Decorated  period  there  were 

generally  several  sets-off.  The  copings  in  the  Perpendicular  period  assumed 
something  of  the  wavy  section  of  the  buttress  caps,  and  mitred  round  the  sides 
of  the  embrasure,  as  well  as  the  top  and  bottom. 

Corbel.  The  name,  in  mediaeval  architecture,  for  a  piece  of  stone  jutting  out 
of  a  wall  to  carry  any  superincumbent  weight.  A  piece  of  timber  projecting  in 
the  same  way  was  called  a  tassel  or  a  bragger.  Thus,  the  carved  ornaments  from 
which  the  vaulting  shafts  spring  at  Lincoln  are  corbels.  Norman  corbels  are 
generally  plain.  In  the  Early  English  period  they  are  sometimes  elaborately 
carved.  They  sometimes  end  with  a  point,  apparently  growing  into  the  wall, 
or  forming  a  knot,  and  often  are  supported  by  angles  and  other  figures.  In  the 
later  periods  the  foliage  or  ornaments  resemble  tho33  in  the  capitals.  In  modern 
architecture,  a  short  piece  of  stone  or  wood  projecting  from  a  wall  to  form  a 
support,  generally  ornamented. 

Corbel  Out.  To  build  out  one  or  more  courses  of  brick  or  stone  from  the  face 
of  a  wall,  to  form  a  support  for  timbers. 

Corbel  Table.  A  projecting  cornice  or  parapet,  supported  by  a  range  of 
corbels  a  short  distance  apart,  which  carry  a  molding,  above  which  is  a  plain 
piece  of  projecting  wall  forming  a  parapet,  and  covered  by  a  coping.  Sometimes 
small  arches  are  thrown  across  from  corbel  to  corbel,  to  carry  the  projection. 

Cornice.  The  projection  at  the  t>p  of  a  wall  finished  by  a  blocking-course, 
common  in  classic  architecture.  In  Norman  times,  the  wall  finished  with  a  cor- 
bel table,  which  carried  a  portion  of  plain  projecting  work,  which  was  finished 
by  a  coping,  and  the  whole  formed  a  parapet.  In-  Early  English  times  the  para- 
pet was  much  the  same,  but  the  work  was  executed  in  a  much  better  way,  espe- 
cially the  small  arches  connecting  the  corbels.  In  the  Decorated  ixir:od  the  corbel 
table  was  nearly  abandoned,  and  a  large  hollow,  with  one  or  two  subordinate 
moldings,  substituted;  this  is  sometimes  filled  with  the  ball-flowers,  and  some- 
times with  running  foliages.  In  the  Perpendicular  style  the  parapet  frequently 
did  not  project  beyond  the  .waH-line  below;  the  molding  then  became  a  stnng 
(thou-h  often  improperly  calleda  cornice),  and  was  ornamented  by  a  quatre-foil, 
or  small  rosettes,  set  at  equal  intervals  immediately  under  the  battlements.  In 
many  French  examples  the  molded  string  is  very  bold,  and  ennched  with  fohage 
ornaments 


1812  Glossary  Part  3 

Corona.  The  brow  of  the  cornice  which  projects  over  the  bed  moldings  to 
throw  off  the  water. 

Corridor.  A  long  gallery  or  passage  in  a  mansion  connecting  various  apart- 
ments and  running  round  a  quadrangle.     Any  long  passage-way  in  a  building. 

Countersink.  To  make  a  cavity  for  the  reception  of  a  plate  of  iron,  or  the 
head  of  a  screw  or  bolt,  so  that  it  shall  not  project  beyond  the  face  of  the  work. 

Coupled  Columns.     Columns  arranged  in  pairs. 

Course.  A  continued  layer  of  bricks  or  stones  in  buildings;  the  term  is  also 
applicable  to  slates,  shingles,  etc. 

Court.  An  open  area  behind  a  house,  or  in  the  center  of  a  building  and  the 
wings.     Courts  admit  of  the  most  elegant  ornamentations,  such  as  arcades,  etc. 

Cove  —  Coving.  The  molding  called  the  cavetto,  or  the  scotia  inverted,  on 
a  large  scale,  and  not  as  a  mere  molding  in  the  composition  o^  a  cornice,  is  called 
a  cove  or  a  coving. 

Cove-bracketing.  The  wooden  skeleton  mold  or  framing  of  a  cove,  applied 
chielly  to  the  bracketing  of  a  cove  ceihng. 

Cove  Ceiling.     A  ceiling  springing  from  the  walls  with  a  curve. 

Coved  and  Flat  Ceiling.  A  ceiling  in  which  the  section  is  the  quadrant  of 
a  circle,  rising  from  the  walls  and  intersecting  in  a  flat  surface. 

Cradling.     Timber  work  for  sustaining  the  lath  and  plaster  of  vaulted  ceilings. 

Cresting.  An  ornamental  finish  in  the  wall  or  ridge  of  a  building,  which  is 
common  on  the  Continent  of  Europe.  An  example  occurs  at  Exeter  Cathedral, 
the  ridge  of  which  is  ornamented  with  a  range  of  small  fleurs-de-lis  in  lead. 

Crocket.     An  ornament  running  up  the  sides  of  gablets,  hood-molds,  pinna- 
cles, spires;   generally,  a  winding  stem  like  a  creeping  plant, 
with  flowers  or  leaves  projecting  at  intervals,  and  terminat- 
ing in  a  fiftial. 

Cross.  This  religious  symbol  is  almost  always  placed  on 
the  ends  of  gables,  the  summit  of  spires,  and  other  conspicu- 
ous places  of  old  churches.  In  early  times  it  was  generally 
very  plain,  often  a  simple  cross  in  a  circle.  Sometimes  they 
take  the  form  of  a  light  cross,  crosslet,  or  a  cross  in  a  square. 
In  the  Decorated  and  later  styles  they  became  richly  floriated, 
and  assumed  an  endless  variety  of  forms.  Of  memorial 
crosses  the  finest  examples  are  the  Eleanor  crosses,  erected  crocket 

by  Edward  I.     Of  these  a  few  yet  remain,  one  of  which  has 
recently  been  reerected  at  Charing  Cross.     Preaching  crosses  were  often  set  up 
by  the  wayside  as  stations  for  preaching;   the  most  noted  is  that  in  front  of  St. 
Paul's,  England.     The  finest  remaining  sepulchral  crosses  are  the  old  elaborately 
carved  examples  found  in  Ireland. 

Cross-aisle.     An  old  name  for  a  transept. 

Cross-springer.     The  transverse  ribs  of  a  vault. 

Cross-vaulting.     A  common  name  given  to  groins  and  cylindrical  vaults. 

Crown.  In  architecture  the  uppermost  member  of  the  cornice;  called  also 
Corona  and  Larmier. 

Crypt,     A  vaulted  apartment  of  greater  or  less  size,  usually  under  the  choir. 

Cupola.  A  small  room,  either  circular  or  polygonal,  standing  on  the  top  of  a 
dome.    By  some  it  is  callec]  a  Lantern, 


r 

H 

\              i 

1 1 

CYMA  RECTA 

1                                        b 

"^  • 

wmA 

CYMA 

REVERSA 

Glossary  1813 

Curb  Roof,  or  Mansard  Roof.  A  roof  formed  of  four  contiguous  planes, 
each  two  having  an  external  inclination.  ^ 

Curtail  Step.  The  hrst  step  in  a  stair,  which  is  generally  finished  in  the  form 
of  a  scroll. 

Cusp.  The  point  where  the  foliations  of  tracery  intersect.  The  earliest 
examplj  in  England  of  a  plain  cusp  is  probaljly  that  at  Pythagoras  School,  at 
Cambridge,  of  an  ornamental  cusp,  at  Ely  Cathedral,  where  a  small  roll,  with  a 
rosette  at  the  end,  is  formed  at  the  termination  of  a  cusp.  In  the  later  styles  the 
terminations  of  the  cusps  were  more  richly  decorated;  they  also  sometimes 
terminate  not  only  in  leaves  or  foHages,  but  in  rosettes,  heads,  and  other  fanciful 
ornaments. 

Cyclostyle.  A  structure  composed  of  a  circular  range  of  columns  without  a 
core  is  cyclostylar;  with  a  core,  the  range  would  be  a  peristyle.  This  is  the  spe- 
cies of  edifice  called  by  Vitruvius  monopteral. 

Cyma.     The  narhe  of  a  molding  of  very  frequent  use.     It  is  a  simple,  waved 
line,  concave  at  one  end  and  convex  at  the  other,  Hke  an 
Italic  /.     When  the  concave  part  is  uppermost  it  is  called 
a  cyma  recta,  but  if  the  convexity  appear  above,  and  the 
concavity  below,  it  is  then  a  cyma  reversa. 

Cymatium.     When  the  crowning  molding  of  an  en-  ] 
tablature  is  of  the  cyma  form,  it  is  termed  the  Cyma- 
tium. 

Cyrtostyle.     A  circular  projecting  portico.     Such  are 
those  of  the  transept  entrances  to  St.  Paul's  Cathedral,  London. 

Dado,  or  Die.  The  vertical  face  of  an  insulated  pedestal  between  the  base 
and  cornice,  or  surbase.  It  is  extended  also  to  the  similar  part  of  all  stereobates 
which  are  arranged  Hke  pedestals  in  Roman  and  Italian  architecture. 

Dais.  A  part  of  the  floor  at  the  end  of  a  mediaeval  hall,  raised  a  step  above 
the  rest  of  the  floor.  On  this  the  lord  of  the  mansion  dined  with  his  friends  at 
the  great  table,  apart  from  the  retainers  and  servants.  In  mediaeval  halls  there 
was  generally  a  denp  recessed  bay  window  at  one  or  at  each  end  of  the  dais, 
supposed  to  be  for  retirement,  or  greater  privacy  than  the  open  hall  could  afford. 
In  France  the  word  is  understood  as  a  canopy  or  hanging  over  a  seat;  probably 
the  name  was  given  from  the  fact  that  the  seats  of  great  men  were  then  sur- 
mounted by  such  an  ornament. 

Darby.  A  flat  tool  used  by  plasterers  in  working,  especially  on  ceilings.  It 
is  generally  about  seven  inches  wide  and  forty-two  inches  long,  with  two  handles 
on  the  back. 

Decastyle.     A  portico  of  ten  columns  in  front. 

Decorated  Style.  The  second  stage  of  the  Pointed  or  Gothic  style  of  archi- 
tecture considered  the  most  complete  and  perfect  development  of  Gothic  archi- 
tecture  the  best  examples  of  which  are  found  in  England. 

Demi-metope.     The  half  of  a  metope,  which  is  found  at  the  retiring  or  pro- 
jecting angles  of  a  Doric  frieze.  .      ,     u    ,       i ^    r     r^„-„ 
Dentil.     The  cogged  or  toothed  member,  common  m  the  hjd-mo^^^  a  Conn 
thian  entablature,  is  said  to  be  dentiled,  and  each  cog  or  tooth  is  called  a  denti . 
Depressed  Arches,  or  Drop  Arches.     Those  of  less  pitch  than  the  eqmlateral. 

application  to  a  technical  portion  of  the  design. 


1814  Glossary  Part  3 

Detail.  As  used  by  architects,  detail  means  the  smaller  parts  into  which  a 
composition  may  be  divided.  It  is  applied  generally  to  moldings  and  other 
enrichments,  and  again  to  their  minutiae. 

Diameter.  The  line  in  a  circle  passing  through  its  center,  or  tliickest  part, 
which  gives  the  measure  proportioning  the  intercolumniation  in  some  of  the 
otders. 

Diameters.  The  diameters  of  the  lower  and  upper  ends  of  the  shaft  of  a 
column  are  called  its  inferior  and  superior  diameters,  respectively;  the  former  is 
the  greatest,  the  latter  the  least  diameter  of  the  shaft. 

Diaper.  A  method  of  decorating  a  wall,  panel,  stained  glass,  or  any  plain  sur- 
face, by  covering  it  with  a  continuous  design  of  flowers,  rosettes,  etc.,  either  in 
squares  or  lozenges,  or  some  geometrical  form  resembHng  the  pattern  of  a  dia- 
pered table-cloth,  from  which,  in  fact,  the  name  is  supposed  by  some  to  have 
been  derived. 

Diastyle.  A  spacious  intercolumniation,  to  which  three  diameters  are 
assigned. 

Dipteros.  A  double- winged  temple.  The  Greeks  are  said  to  have  constructed 
temples  with  two  ranges  of  columns  all  around,  which  were  called  dipteroi.  A 
portico  projecting  two  columns  and  their  interspaces  is  of  dipteral  or  pseudo- 
dipteral  arrangement. 

Discharging  Arch.  An  arch  over  the  opening  of  a  door  or  window,  to  dis- 
charge or  relieve  the  superincumbent  weight  from  pressing  on  the  lintel. 

Distemper.  Term  applied  to  painting  with  colors  mixed  with  size  or  ..  ther 
glutinous  substance.  All  the  cartoons  of  the  ancients,  previous  to  the  year  1410, 
are  said  to  be  done  in  distemper. 

Distyle.  A  portico  of  two  columns.  This  is  not  generally  applied  to  the  mere 
porch  with  two  columns,  but  to  describe  a  portico  with  two  columns  in  anti$. 

Ditriglyph.     An  intercolumniation  in  the  Doric  order,  of  two  triglyphs. 

Dodecastyle.  A  portico  of  twelve  columns  in  front.  The  lower  one  of  the 
west  front  of  St.  Paul's  Cathedral,  London,  is  of  twelve  columns,  but  they  are 
coupled,  making  the  arrangement  pseudo-dodecastyle.  The  Chamber  of  Depu- 
ties in  Paris  has  a  true  dodecastyle. 

Dog-tooth.  A  favorite  enrichment  used  from  the  latter  part  of  the  Normaa 
period  to  the  early  part  of  the  Decorated.  It  is  in  the  form  of  a  four-leaved 
flower,  the  center  of  which  projects,  and  probably  was  named  from  its  resem- 
bLnce  to  the  dog-toothed  violet. 

Dome.  A  cupola  or  inverted  cup  on  a  building.  The  application  of  this  term 
to  its  generally*  received  purpose  is  irom  the  Italian  custom  of  calling  an  archi- 
cpiscopal  church,  by  way  of  eminence,  II  Duomo,  the  temple;  for  to  one  of  that 
rank,  the  Cathedral  of  Florence,  the  cupola  was  first  applied  in  modern  practice. 
The  Italians  themselves  never  call  a  cupola  a  dome;  it  is  on  this  side  of  the  Alps 
the  application  has  arisen,  from  the  circumstance,  it  would  appear,  that  the  Ital- 
ians use  the  term  with  reference  to  those  structures  whose  most  distinguishing 
feature  is  the  cupola,  tholus,  or  (as  we  now  call  it)  dome. 

Domestic  Architecture.    That  branch  which  relates  to  private  buildings. 

Donjon.     The  principal  tower  of  a  castle,  generally  containing  the  prison. 

Door  Frame.  The  surrounding  case  into  and  out  of  which  the  door  shuts  and 
opens.  It  consists  of  two  upright  pieces,  called  jambs,  and  a  head,  generally  fixed 
together  by  mortices  and  tenons,  and  wrought,  rebated,  and  beaded. 

Doric  Order.     The  oldest  of  the  three  orders  of  Grecian  architecture. 


Glossary  1815 

Dormer  Window,  ri  window  belonging  to  a  room  in  a  roof,  which  conse- 
quently projects  from  it  with  a  valley  gutter  on  each  side.  They  are  said  not  to 
be  earlier  than  the  fourteenth  century.  In  Germany  there  are  often  several  rows 
of  dormers,  one  above  the  other.  In  Italian  Gothic  they  are  very  rare:  in  fact, 
the  former  have  an  unusually  steep  roof,  while  in  the  latter  country,  where  the 
Italian  tile  is  used,  the  roofs  are  rather  flat. 

Dormitory.  A  room,  suite  of  rooms,  or  building  used  to  sleep  in.  The  name 
was  first  applied  to  the  place  where  the  monks  slept  at  night.  It  was  sometimes 
one  long  room  like  a  barrack,  and  sometimes  divided  into  a  succession  of  small 
chambers  or  cells.  The  dormitory  was  generally  on  the  first  floor,  and  connected 
with  the  church,  so  that  it  was  not  necessary  to  go  out-of-doors  to  attend  the 
nocturnal  services.  In  the  large  houses  of  the  Perpendicular  period,  and  also  in 
some  of  the  Elizabethan,  the  entire  upper  story  in  the  roof  formed  one  large 
apartment,  said  to  have  been  a  place  for  exercise  in  wet  weather,  and  also  for  a 
dormitory  for  the  retainers  of  the  household,  or  those  of  visitors. 

Double  Vault.  Formed  by  a  dupHcate  wall;  wine  cellars  are  sometimes  so 
formed. 

Dovetailing.  In  carpentry  and  joinery,  the  method  of  fastening  boards  or 
other  timbers  together,  by  letting  one  piece  into  another  in  the  form  of  the 
expanded  tail  of  a  dove. 

Dowel.  A  pin  let  into  two  pieces  of  wood  or  stone,  where  they  are  joined 
together.  A  piece  of  wocd  driven  into  a  wall  so  that  other  pieces  may  be  nailed 
to  it.     This  is  also  called  plugging. 

Draw-bridge.  A  bridge  made  to  draw  up  or  let  down,  much  used  in  fortified 
places.  In  navigable  rivers,  the  arch  over  the  deepest  channel  is  made  to  draw 
or  revolve,  in  order  to  let  the  masts  of  ships  pass  through. 

Drawing-room.  A  room  appropriated  for  the  reception  of  company;  a  room 
to  which  company  withdraws  from  the  dining-room. 

Dresser.     A  cupboard  or  set  of  shelves  to  receive  dishes  and  cooking  utensils. 

Dressing.  Is  the  operation  of  squaring  and  smoothing  stones  for  building; 
also  applied  to  smoothing  lumber. 

Dressing-room.     An  apartment  appropriated  for  dressing  the  person. 

Drip.  A  name  given  to  the  member  of  a  cornice  which  has  a  projection 
beyond  the  other  parts  for  throwing  off  water  by  small  portions,  drop  by  drop. 
It  is  also  called  Larmier. 

Drip-stone.  The  label  molding  which  serves  on  a  canopy  lor  an  opening, 
and  to  throw  off  the  rain.     It  is  also  called  Weather  Molding.       - 

Drop-scene.  A  curtain  suspended  by  pulleys,  which  descends  or  drops  m 
front  of  the  stage  in  a  theater. 

Drum.  The  upright  part  of  a  cupola  over  a  dome;  also,  the  solid  part  or  vase 
of  the  Corinthian  and  Composite  capitals.  ^ 

Drv-rot.  A  rapid  decay  of  timber,  by  which  its  substance  is  converted  mto 
a  dry  powderV  which  issues  from  minute  cavities  resembhng   the  bonngs  of 

""  Dungeon.     The  prison  in  a  castle  keep,  so  called  because  the  Norman  name 
for  thelatter  is  donfon,  and  the  dungeons,  or  prisons,  are  generally  m  its  lowest 

'Twarf  Wall.     The  walls  enclosing  courts  above  which  are  raihngs  of  iron; 
low  walls,  in  general,  receive  this  name. 


1816  Glossary  Part  3 

Eaves.  In  slating  and  shingling,  the  margin  or  lower  part  of  the  slating 
hanging  over  the  wall,  to  throw  the  water  ofif  from  the  masonry  or  brickwork. 

Echinus.  A  molding  of  eccentric  curve,  gener- 
ally cut  (when  it  is  carved)  into  the  forms  of  eggs 
and  anchors  alternating,  whence  the  molding  is 
called  by  the  name  of  the  more  conspicuous.  It  is 
the  same  as  Ovolo. 

Edifice.  Is  synonymous  with  the  terms  building,  fabric,  erection,  but  is 
more  strictly  apphcable  to  arcliitecture  distinguished  for  size,  dignity,  and 
grandeur. 

Efflorescence.  In  architecture,  the  formation  of  a  whitish  loose  powder,  or 
crust,  on  the  surface  of  stone  or  brick  walls. 

Egyptian  Architecture.  The  earliest  civilization  and  cultivation  of  the  arts 
was  in  Upper  Egypt.  The  most  remarkable  and  most  ancient  monuments  of  the 
Eg3'ptians,  with  the  exception  of  the  pyramids,  are  nearly  all  included  in  Upper 
Egypt.  The  buildings  of  Egypt  are  characterized'  by  solidity  and  massiveness 
of  construction,  originality  of  conception,  and  boldness  of  form.  The  walls,  the 
pillars,  and  the  most  sacred  places  of  their  religious  buildings  were  ornamented 
with  hieroglyphics  and  symbolical  figures,  while  the  ceilings  of  the  porticos 
exhibited  zodiacs  and  celestial  planispheres.  The  temples  of  Egypt  were  gener- 
ally without  roofs,  and,  consequently,  the  interior  colonnades  had  no  pediments, 
supporting  merely  an  entablature,  composed  of  only  architrave,  frieze,  and 
cornice,  formed  of  immense  blocks  united  without  cement  and  ornamented  with 
hieroglyphics. 

Element.  The  outline  of  the  design  of  a  Decorated  window,  on  which  the 
centers  for  the  tracery  are  formed.  These  centers  will  all  be  found  to  fall  on 
points  which,  in  some  way  or  other,  will  be  equimultiples  of  parts  of  the  openings. 
To  draw  tracery  well,  or  understand  even  the  principles  of  its  composition,  much 
attention  should  be  given  to  the  study  of  the  element. 

Elevation.  The  front  facade,  as  the  French  term  it,  of  a  structure;  a  geo- 
metrical drawing  of  the  external  upright  parts  of  a  building. 

Embattlement.     An  indented  parapet;  battlement. 

Emblazon.     To  adorn  with  figures  of  heraldry,  or  ensigns  armorial. 

Embossing.  Sculpture  in  rilievo,  the  figures  standing  partly  out  from  the 
plane. 

Embrasure.  The  opening  in  a  battlement  between  the  two  raised  solid  por- 
tions or  merlons,  sometimes  called  a  crenelle. 

Encaustic.  Pertaining  to  the  art  of  burning  in  colors,  apphed  to  painting  on 
glass,  porcelain,  or  tiles,  where  colors  are  fixed  by  heat;  hence,  encaustic  tiles, 
bricks,  etc. 

Engaged  Columns.  Are  those  attached  to,  or  built  into  walls  or  piers,  a 
portion  being  concealed. 

Enrichment.  The  addition  of  ornament,  carving,  etc.,  to  plain  work;  decora- 
tion; embellishment. 

Ensemble.  Means  the  whole  work  or  composition  considered  together,  and 
not  in  parts. 

Entablature.  The  assemblage  of  parts  supported  by  the  column.  It  coi>^ 
sists  of  three  parts:   the  architrave,  frieze,  and  cornice. 

Entail.     In  Gothic  architecture,  dehcate  carving. 


Glossary  1817 

Entasis.  The  swelling  of  a  column,  etc.  In  medic-eval  architecture,  some 
spires,  particularly  those  called  "broach  spires,"  have  a  slight  swelhng  in  the 
sides,  but  no  more  than  to  make  them  look  straight;  for,  from  a  particular 
"deceptio  visus,"  that  which  is  quite  straight,  when  viewed  at  a  height,  looks 
hollow. 

Entry.     A  hall  without  stairs  or  vestibule. 

Epistyle-  This  term  may  with  propriety  be  applied  to  the  whole  entablature, 
with  which  it  is  synonymous;  but  it  is  restricted  in  use  to  the  architrave,  or 
lowest  member  of  the  entablature. 

Escutcheon.  (Her.)  The  field  or  ground  on  which  a  coat-of-arms  is  repre- 
sented. (Arch.)  The  shields  used  on  tombs,  in  the  spandrels  of  doors,  or  in 
tring-courses;  also,  the  ornamented  plates  from  the  centre  of  which  door  rings, 
inockers,  etc.,  are  suspended,  or  which  protect  the  wood  of  the  key-hole  from 
:he  wear  of  the  key.  In  mediaeval  times  these  were  often  worked  in  a  very 
Deautiful  manner. 

Etching.  A  mode  of  engraving  on  glass  or  metal  (generally  copper)  by  means 
Df  lines,  eaten  in  or  corroded  by  means  of  some  strong  acid. 

Eustyle.  A  species  of  intercolumniation  to  which  a  proportion  of  two  diam- 
:ters  and  a  quarter  is  assigned.  This  term,  together  with  the  others  of  similar 
mport  —  pycnostyle,  systyle,  diastyle,  and  araeostyle  —  referring  to  the  distance 
3f  columns  from  one  another  in  composition,  is  from  Vitruvius,  who  assigns  to 
2ach  the  space  it  is  to  express.  It  will  be  seen,  however,  by  reference  to  them 
ndividually,  that  the  words  themselves,  though  perhaps  sufficiently  applic- 
ble  convey  no  idea  of  an  exactly  defined  space,  and,  by  reference  to  the 
:olumnar  structures  of  the  ancients,  that  no  attention  was  paid  by  them  to 
uch  limitations.  It  follows,  then,  that  the  proportions  assigned  to  each  are 
>urely  conventional,  and  may  or  may  not  be  attended  to  without  vitiating  the 
)ower  of  applying  the  terms.  Eustyle  means  the  best  or  most  beautiful  ar- 
angement;  but,  as  the  effect  of  a  columnar  composition  depends  on  many 
hings  besides  the  diameter  of  the  columns,  the  same  proportioned  inter- 
:olumniation  would  look  well  or  ill  according  to  those  other  circumstances, 
o  that  the  limitation  of  Eustyle  to  two  diameters  and  a  quarter  is  absurd. 

Extrados.  The  exterior  or  convex  curve  forming  the  upper  line  of  the  arch 
tones;   the  term  is  opposed  to  the  intrados,  or  concave  side. 

Eye  of  a  Dome.     The  aperture  at  its  summit. 

Eye  of  a  Volute.     The  circle  in  its  center. 

Facade,  or  Face.  The  whole  exterior  side  of  a  building  that  can  be  seen  at 
ne  view;   strictly  speaking,  the  principal  front. 

Face  Mold.  The  pattern  for  marking  the  plank  or  board  out  of  which 
irnamental  hand-railings  for  stairs  and  other  works  are  cut. 

Fan  Tracery.  The  very  complicated  m_ode  of  roofing  used  in  the  Perpen- 
lieular  style,  in  which  the  vault  is  covered  by  ribs  and  veins  of  tracery. 

Fascia.     A  flat,  broad  member  in  the  entablature  of  columns  or  other  parts  of 

puildings,  but  of  small  projection.     The  architraves  in  some  of  the  orders  are 

omposed  of  three  bands,  or  fascia;  the  Tuscan  and  the  Doric  ought  to  have  only 

ne.     Ornamental  projections  from  the  walls  of  brick  buildings  over  any  of  the 

/indows,  except  the  uppermost,  are  called  Fasciae. 

Fenestral.  A  frame,  or  "chassis,"  on  which  oiled  paper  or  thin  cloth  was 
trained  to  keep  out  wind  and  rain  when  the  windows  were  not  glazed. 


1818 


Glossary 


Parts 


fmTmmMMMmm^ 

immm^ 

l^&^^^w^^ 

g^^as^ 

Im^P 

(m;^ 

FESTOON 


FINIALS 


Festoon.     An  ornament  of  carved  work,  representing  a  wreath  or  garland  of 
flowers  or  leaves,  or  both,  interwoven  with  each 
other.     It  is  thickest  in  the  middle,  and  small 
at  each  extremity,  where  it  is  tied,  a  part  often 
hanging  down  below  the  knot. 

Fillet.  A  narrow  vertical  band  or  listel  of 
frequent  use  in  congeries  of  moldings,  to  sepa- 
rate and  combine  them,  and  also  to  give  breadth 
and  firmness  to  the  upper  edge  of  a  crowning 

cyma  or  cavetto,  as  in  an  external  cornice.  The  narrow  slips  or  breadth  between 
the  flutes  of  Corinthian  and  Ionic  columns  are  also  called  fillets.  In  mediaeval 
work  the  fiUet  is  a  small,  flat,  projecting  square,  chiefly  used  to  separate  hollows 
and  rounds,  and  often  found  in  the  outer  parts  of  shafts  and  boutels.  In  this 
situation  the  center  fillet  has  been  termed  a  keel,  and  the  two  side  ones,  wmgs; 
but,  apparently,  this  is  not  an  ancient  usage. 

Finial.  The  flower,  or  bunch  of  flowers,  with  which  a  spire,  pinnacle,  gablet, 
canopy,  etc.,  generally  terminates.  Where  there  are 
crockets,  the  finial  generally  bears  as  close  a  resem- 
blance as  possible  to  them  in  point  of  design.  They 
are  found  in  early  work  where  there  are  no  crockets. 
The  simplest  form  more  resembles  a  bud  about  to 
burst  than  an  open  flower.  They  soon  became  more 
elaborate,  as  at  Lincoln,  and  still  more,  as  at  West- 
minster and  the  Hotel  Cluny  at  Paris.  Many  per- 
pendicular finials  are  like,  four  crockets  bound  to- 
gether. Almost  every  known  example  of  a  finial  has 
a  sort  of  necking  separating  it  from  the  parts  below 

Fish-joint.  A  splice  where  the  pieces  are  joined  butt  end  to  end,  and  are  con- 
nected by  pieces  of  wood  or  iron  placed  on  each  side  and  firmly  bolted  to  the 
timbers,  or  pieces  joined. 

Flags.     Flat  stones,  from  i  to  3  inches  thick,  for  floors. 

Flamboyant.  A  name  applied  to  the  Third  Pointed  style  in  France,  which 
seems  to  have  been  developed  from  the  Second,  as  the  English  Perpendicular  was 
from  the  Decorated.  The  great  characteristic  is,  that  the  element  of  the  tracery 
flows  upward  in  long  wavy  divisions  like  flames  of  fire.  In  most  cases,  also,  every 
division  has  only  one  cusp  on  each  side,  however  long  the  division  may  be.  1  he 
moldings  seem  to  be  as  much  inferior  to  those  of  the  preceding  period  as  the 
Perpendicular  moldings  were  to  the  Early  English,  a  fact  which  seems  to  show 
that  the  decadence  of  Gothic  architecture  was  not  confined  to  one  country. 

Flange.  A  projecting  edge,  rib,  or  rim.  Flanges  are  often  cast  on  the  top  o! 
bottom  of  iron  columns,  to  fasten  them  to  those  above  or  below;  the  top  and 
bottom  of  I-beams  and  channels  are  called  the  flange. 

Flashings.  Pieces  of  lead,  tin,  or  copper,  let  into  the  joints  of  a  wall  so  as  to 
lap  over  gutters  or  other  pieces;  also,  pieces  worked  in  the  slates  or  shingles 
around  dormers,  chimneys,  and  any  rising  part,  to  prevent  leaking. 

Flatting.     Painting  finished  without  leaving  a  gloss  on  the  surface. 

Fleche.  A  general  term  in  French  architecture  for  a  spire,  but  more  par- 
ticularly usad  for  the  small,  slender  erection  rising  from  the  intersection  oi 
the  nave  and  transepts  in  cathedrals  and  large  churches,  and  carrying  the 
sanctus  bell. 

Fleur-de-lis.    The  royal  insignia  of  France,  much  used  in  decoration. 


Glossary  1819 

Flight.     A  run  of  steps  or  stairs  from  one  landing  to  c^notiier. 

Floating.  The  equal  spreading  of  plaster  or  stucco  on  the  surface  of  walls, 
by  means  of  a  board  called  a  float;   as  a  rule,  only  rough  plastering  is  floated.  ' 

Floriated.     Having  florid  ornaments,  as  in  Gothic  pillars. 

Flue.  The  space  or  passage  in  a  chimney  through  which  the  smoke  ascends. 
Each  passage  is  called  a  flue,  while  aU  together  make  the  chimney. 

Flush.     The  continued  surface,  in  the  same  plane,  of  two  contiguous  masses. 

Flute.  A  concave  channel.  Columns  whose  shafts  are  channeled  are  said 
to  be  fluted,  and  the  flutes  are  collectively  called  Flutings. 

Flying  Buttress.  An  arched  buttress  used  when  extra  strength  was  required 
for  the  upper  part  of  the  wall  of  the  nave,  etc.,  to  resist  the  outward  thrust  of  a 
vaulted  ceiling.  The  flying  buttress  generally  rests  on  the  wall  and  buttress  of 
the  aisle. 

Foils.     The  small  arcs  in  the  tracery  of  Gothic  windows,  panels,  etc. 
Foliage.     An  ornamental  distribution  of  leaves  on  various  parts  of  buildings. 
Foliation.     The  use  of  small  arcs  or  foils  in  forming  tracery. 

Font.  The  vessel  used  in  the  rite  of  baptism.  The  earliest  extant  is  supposed 
to  be  that  in  which  Constantine  is  said  to  have  been  baptized;  this  is  a  porphyry 
labrum  from  a  Roman  bath.  Those  in  the  baptisteries  in  Italy  are  all  large,  and 
were  intended  for  immersion;  as  time  went  on,  they  seem  to  have  become 
smaller.  Fonts  are  sometimes  mere  plain  hollow  cylinders,  generally  a  little 
smaller  below  than  above;  others  are  massive  squares,  supported  on  a  thick  stem, 
round  which  sometimes  there  are  smaller  shafts.  In  the  Early  English  this  form 
is  still  pursued,  and  the  shafts  are  detached;  sometimes,  however,  they  are  hex- 
agonal and  octagonal,  and  in  this  and  the  later  styles  assume  the  form  of  a  vessel 
on  a  stem.  Norman  fonts  frequently  have  curious  carvings  on  them,  approach- 
ing the  grotesque;  in  later  times  the  foliages,  etc.,  partook  absolutely  of  the 
character  of  those  used  in  other  architectural  details  of  their  respective  periods. 
The  font  in  European  churches  is  usually  placed  close  to  a  pillar  near  the  en- 
trance, generally  that  nearest  but  one  to  the  tower  in  the  south  arcade;  or,  in 
large  buildings,  in  the  middle  of  the  nave,  opposite  the  entrance  porch,  and 
sometimes  in  a  separate  building.  In  Protestant  churches  in  this  country,  the 
font  is  generaUy  placed  inside  the  communion  rail,  or  on  the  steps  of  the  chancel. 

Footings.  The  spreading  courses  at  the  base  or  foundation  of  a  wall.  ^  When 
a  layer  of  different  material  from  that  of  the  wall  (as  a  bed  of  concrete)  is  used, 
it  is  called  the  Footing. 

Foundation.  That  part  of  a  building  or  wall  which  is  below  the  surface  of 
the  ground. 

Foxtail  Wedging.     Is  a  peculiar  mode  of  mortising,  in  which  the  end  of  the 
tenon  is  notched  beyond  the  mortise,  and  is  split  and  a  wedge  inserted,  which, 
being  forcibly  driven  in,  enlarges  the  tenon  and  renders  the  jomt  firm  and  mi-   ■ 
movable. 

Frame.  The  name  given  to  the  wood-work  of  windows,  doors,  etc.;  and  m 
carpentry,  to  the  timber  works  supporting  floors,  roofs,  etc. 

Framing.  The  rough  timber  work  of  a  house,  including  the  flooring,  roofing, 
partitioning,  ceiling,  and  beams  thereof. 

Freestone.  Stone  which  can  be  used  for  moldings,  tracery  and  other  work 
required  to  be  executed  with  the  chisel.  The  ooht.c  and  sandstones  are  those 
/■er-^rally  included  by  this  term. 


1820  Glossary  Part  3 

Fresco.  The  method  of  painting  on  a  wall  while  the  plastering  is  wet.  The 
color  penetrates  through  the  material,  which,  therefore,  will  bear  rubbing  or  clean-» 
ing  to  almost  any  extent.  The  transparency,  the  chiaro-oscuro,  and  lucidity,  as 
well  as  force,  which  can  be  obtained  by  this  method,  cannot  be  conceived  unless 
the  frescos  of  Fra  Angelico  or  Raphael  are  studied.  The  word,  however,  is  often 
applied  improperly  to  painting  on  the  surface  in  distemper  or  body  color,  mixed 
with  size  or  white  of  egg,  which  gives  an  opaque  effect. 

Fret.  An  ornament  consisting  of  small  fillets  inter- 
secting each  other  at  right  angles. 

Frieze.  That  portion  of  an  entablature  between-the 
cornice  above  and  architrave  below.  It  derives  its 
name  from  being  the  recipient  of  the  sculptured  en-  fret 

richments  either  of  foliage  or  figures  which  may  be 

relevant  to  the  object  of  the  sculpture.     The  frieze  is  also  called  the  Zoophorus. 
I    Frigidarium.     An  apartment  in  the  Roman  bath,  supplied  with  cold  water. 

Furniture.  A  name  given  to  the  metal  trimmings  of  doors,  windows,  and 
other  similar  parts  of  a  house.  In  this  country  the  word  ''hardware"  is  more 
generally  used  to  denote  the  same  thing. 

Furrings.  Flat  pieces  of  timber  used  to  bring  an  irregular  framing  to  an  even 
surface. 

Gable.  When  a  roof  is  not  hipped  or  returned  on  itself  at  the  ends,  its  ends 
are  stopped  by  carrying  up  the  walls  under  them  in  the  triangular  form  of  the 
roof  itself.  This  is  called  the  gable,  or,  in  the  case  of  the  ornamental  and  orna- 
mented gable,  the  pediment.  Of  necessity,  gables  follow  the  angles  of  the  slope 
of  the  roof,  and  differ  in  the  various  styles.  In  Norman  work  they  are  generally 
about  half-pitch;  in  Early  English,  seldom  less  than  equilateral,  and  often  more. 
In  Decorated  work  they  become  lower,  and  still  more  so  in  the  Perpendicular 
style.  In  all  important  buildings  they  are  finished  with  copings  or  parapets.  In 
the  Later  Gothic  styles  gables  are  often  surmounted  with  battlements,  or  enriched 
with  crockets;  they  are  also  often  paneled  or  perforated,  sometimes  very  richly. 
The  gables  in  ecclesiastical  buildings  are  mostly  terminated  with  a  cross;  in 
others,  by  a  finial  or  pinnacle.  In  later  times  the  parapets  or  copings  were  broken 
into  a  sort  of  steps,  called  corbie  steps.  In  buildings  of  less  pretension  the  tiles 
or  other  roof  covering  passed  over  the  front  of  the  wall,  which  then,  of  course, 
had  no  coping.  In  this  case,  the  outer  pair  of  rafters  were  concealed  by  molded 
or  carved  verge  boards. 

Gable  Window.  A  term  sometimes  applied  to  the  large  window  under  a  gable, 
but  more  properly  to  the  windows  in  the  gable  itself. 

Gabled  Towers.  Those  which  are  finished  with  gables  instead  of  parapets. 
Many  of  the  German  Romanesque  towers  are  gabled. 

Gablets.  Triangular  terminations  to  buttresses,  much  in  use  in  the  Early 
English  and  Decorated  periods,  after  which  the  buttresses  generally  terminate  in 
pinnacles.  The  Early  English  gablets  are  generally  plain,  and  very  sharp  in 
pitch.  In  the  Decorated  period  they  are  often  enriched  with  paneling  and 
crockets.  They  are  sometimes  finished  with  small  crosses,  but  oftener  with 
finials. 

Gain.  A  beveled  shoulder  on  the  end  of  a  mortised  brace,  for  the  purpose  of 
giving  additional  resistance  to  the  shoulder. 

Gallery.  Any  long  passage  looking  down  into  another  part  of  a  building,  or 
into  the  court  outside.  In  like  manner,  any  stage  erected  to  carry  a  rood  or  an 
organ,  or  to  receive  spectators,  was  latterly  called  a  gallery,  though  originally  a 


Glossary  1821 

loft.     Ill  later  times  the  name  was  given  to  any  very  long  rooms,  particularly 
those  intended  for  purposes  of  state,  or  for  the  exhibition  of  pictures. 

Gambrel  Roof.     A  roof  with  two  pitches,  similar  to  a  mansard  or  curb  roof. 

Gargoyle,  or  Gurgoyle.  The  carved  termination 
to  a  spout  which  conveyed  away  the  water  from  the 
gutters,  supposed  to  be  called  so  from  the  gurgling 
noise  made  by  the  water  passing  through  it.  Gar- 
goyles are  mostly  grotesque  figures. 

Gate-house.  A  building  forming  the  entrance  to 
a  town,  the  door  of  an  abbey,  or  the  enceinte  of  a 
castle  or  other  important  edifice.  They  generally  had 
a  large  gateway  protected  by  a  gate,  and  also  a  port- 
cullis, over  which  were  battlemented  parapets  with 
holes  (machicolations)  for  throwing  down  darts,  melted 
lead,  or  hot  sand  on  the  besiegers.  Gate-houses 
always  had  a  lodge,  with  apartments  for  the  porter,  gargoyle 

and    guard-rooms    for  the  soldiers;    and,  generally, 

rooms  over  for  the  officers,  and  often  places  for  prisoners  beneath.     The  name  is 
now  commonly  applied  to  the  gate-keeper's  lodge  on  large  estates. 

Gauge.  To  mix  plaster  of  Paris  with  common  plaster  to  make  it  set  quick, 
called  gauged  mortar.  A  tool  used  by  carpenters,  to  strike  a  line  parallel  to  the 
edge  of  a  board. 

Girder.  A  large  timber  or  iron  beam,  either  single  or  built  up,  used  to  sup- 
port joists  or  walls  over  an  opening. 

Glyph.     A  vertical  channel  in  a  frieze. 

Gothic  Style.  The  name  of  Gothic  was  given  to  the  various  Mediaeval  styles 
at  a  period  in  the  sixteenth  century  when  a  great  classic  revival  was  going  on, 
and  everything  not  classic  was  considered  barbarian,  or  Gothic.  The  term  was 
thus  originally  intended  as  one  of  stigma,  and,  although  it  conveys  a  false  idea  of 
the  character  of  the  Mediaeval  styles,  it  has  long  been  used  to  distinguish  them 
from  the  Grecian  and  Roman.  The  true  principle  of  Gothic  architecture  is  the 
vertical  division,  relation  and  subordination  of  the  different  parts,  distinct  and 
yet  at  unity  with  each  other,  and  while  this  principle  was  adhered  to,  Gothic 
architecture  may  be  said  to  have  retained  its  vitality. 

Grange.  A  word  derived  from  the  French,  signifying  a  large  barn  or  granary. 
Granges  were  usually  long  buildings  with  high  wooden  roofs,  sometimes  divided 
by  posts  or  columns  into  a  sort  of  nave  and  aisles,  with  walls  strongly  buttressed. 
In  England  the  term  was  appHed  not  only  to  the  barns,  but  to  the  whole  of  the 
buildings  which  formed  the  detached  farms  belonging  to  the  monasteries;  m 
most  cases  there  was  a  chapel  either  included  among  these  or  standing  apart  as  a 
separate  edifice. 

GriUage.  A  framework  of  beams  laid  longitudinally  and  crossed  by  simUar 
beams  notched  upon  them,  used  to  sustain  walls  to  prevent  irregular  setting. 

GriUe.  The  iron-work  forming  the  enclosure  screen  to  a  chapel,  or  the  pro- 
tecting railing  to  a  tomb  or  shrine;  more  commonly  found  m  France  than  m 
England.  They  are  of  wrought  iron,  ornamented  by  the  swage  and  Punch  and 
put  together  either  by  rivets  or  clips.  In  modern  times  grilles  are  used  exten- 
^vely  for  protecring  L  lower  windows  in  city  houses,  also  the  glass  openmg  m 
outside  doors.  .  ,,       i        xu    . 

Groin.  By  some  described  as  the  line  of  intersection  of  two  vaults  where  they 
cross  eacL  other,  which  others  caU  the  groin  point;  by  others  the  curved  section 


1822 


Glos 


iossiiry 


Part  :i 


GROINED    VAULTING 


or  spandrel  of  such  vaulting  is  called  a  groin,  and  by  others  the  whole  system  of 
vaulting  is  so  named. 

Groin  Arch.  The  cross-rib  in  the  later  styles 
of  groining,  passing  at  right  angles  from  wall  to 
wall,  and  dividing  the  vault  into  bays  or  travees. 

Groin  Ceiling.  A  ceiling  to  a  building  com- 
posed of  oak  ribs,  the  sj)andrcls  of  wiiicli  are  filled  , 
in  with  narrow,  thin  slips  of  wood.  There  arc 
several  in  England;  one  at  the  Early  English  church 
at  VVarmington,  and  one  at  Winchester  Cathedral, 
exactly  resembling  those  of  stone. 

Groin  Centring.  In  groining  without  ribs,  the 
whole  surface  is  supported  by  centring  during 
the  erection  of  the  vaulting.  In  ribbed  work  the 
8tone  ribs  only  are  sui)ported  by  timber  ribs  during 
the  progress  of  the  work,  any  light  stuff  being  used  while  filling  in  the  spandrels. 

Groin  Point.     The  name  given  by  workmen  to  the  arris  or  line  of  intersection 
of  one  vault  with  another  where  there  are  no  ribs. 

Groin  Rib.     The  rib  which  conceals  the  groin  point  or  joints,  where  the  span- 
drels intersect. 

Groined  Vaulting.  The  system  of  covering  a  building  with  stone  vaults 
which  cross  and  intersect  each  other,  as  opposed  to  the  barrel  vaulting,  or  series 
of  arches  placed  side  by  side.  The  earliest  groins  are  plain,  without  any  rib  , 
except  occasionally  a  sort  of  wide  band  from  wall  to  wall,  to  strengthen  the  coi 
btruction.  In  later  Norman  times  ribs  were  added  on  the  line  of  intersection  ol 
the  spandrels,  crossing  each  other,  and  having  a  boss  as  a  key  common  to  both; 
these  ribs  the  French  authors  call  ncr/s  en  ogive.  Their  introduction,  however, 
caused  an  entire  change  in  the  system  of  vaulting;  instead  of  arches  of  uniform 
thickness  and  great  weight,  these  ribs  were  first  put  up  as  the  main  construction, 
and  spandrels  of  the  lightest  and  thinnest  ix>ssible  material  placed  uixjn  them,  the 
haunches  only  being  loaded  sufikiently  to  counterbalance  the  pressure  from  the 
crown.  Shortly  after,  half-ribs  against  the  walls  (formercts)  were  introduced  to 
carry  the  spandrels  without  cutting  into  the  walling,  and  to  add  to  the  apjx^'arance. 
'J'he  work  was  now  not  treated  as  continued  vaulting,  but  as  divided  into  bays, 
and  it  was  formed  by  keeping  up  the  ogive,  or  intersecting  ribs  and  their  bosses; 
a  sort  of  construction  having  some  affinity  to  the  dome  was  formed,  which  added 
much  to  the  strength  of  the  groining.  Of  course,  the  top  of  the  soffit  or  ridge  of 
the  vault  was  not  h(jriz(^ntal,  but  rose  from  the  level  of  the  top  of  the  formeret-rib 
to  the  boss  and  fell  again;  but  tliis  could  not  be  perceived  from  below.  As  this 
system  of  construction  got  more  into  use,  and  as  the  vaults  were  required  to  be  of 
greater  span  and  of  higher  pitch,  the  spandrels  became  larger,  and  re(|uired  more 
support.  To  give  this,  another  set  of  ribs  was  introduced,  passing  from  the 
springers  of  the  ogive  ribs,  and  going  to  about  half-way  between  these  and  the 
ogive,  and  meeting  on  the  ridge  of  the  vault;  these  intermediate  ribs  are  called 
by  the  French  tiercerons,  and  began  to  come  into  use  in  the  transition  from  Early 
English  to  Decorated.  About  the  same  period  a  system  of  vaulting  came  into 
use  called  hcxpartite,  from  the  fact  that  every  bay  is  divided  into  six  compart- 
ments instead  of  four.  It  was  invented  to  cover  the  naves  of  churches  of  unusual 
width.  The  filling  of  the  spandrels  in  this  style  is  very  peculiar,  and,  where  the 
diflerent  compartments  meet  at  the  ridge,  some  pieces  of  harder  stone  have 
been  used,  which  give  rather  a  pleasing  effect.  The  arches  against  the  wall, 
being  of  smaller  span  than  the  main  arches,  cause  the  centre  springers  to  be  per- 


Glossary  1823 

peiidicular  and  parallel  for  some  height,  and  the  spandrels  themselves  are  very 
hollow.  As  styles  progressed,  and  the  desire  for  greater  richness  increased, 
another  s(-Ties  of  ribs,  called  Hemes,  was  introduced;  these  passt;d  crossways  from 
the  ogives  to  tin;  liercerons,  and  thence  to  tiie  doublcaux,  dividing  the  spandrels 
nearly  horizontally.  'J'hese  various  systems  increased  in  the  reri)endicu!ar 
period,  so  that  the  walls  were  (juite  a  net-work  of  ribs,  and  led  at  last  to  the 
Tudor,  or,  as  it  is  called  by  many,  fan-tracery  vaulting.  In  this  system  the  ribs 
are  no  part  of  the  real  construction,  but  are  merely  carved  upon  the  voussoirs, 
which  form  the  actual  vaulting.  Fan  Tracery  is  so  called  because  the  ribs 
radiate  from  the  springers,  and  sj^read  out  like  the  sticks  of  a  fan.  These  later 
methods  arc;  not  strii  tly  groins,  for  the  ixMuIcntives  are  not  square  on  plan,  but 
circular,  and  Ihere  is,  theref(jre,  no  arris  intersection  or  groin  point. 

Groins,  Welsh,  or  Underpitch.  When  the  main  longitudinal  vault  of  any 
groining  is  higher  than  the  cross  or  transverse  vaults  which  run  from  the  windows, 
the  system  of  vaulting  is  called  unden)it(:li  groining,  or,  as  termed  by  the  work- 
men, Welsh  groining.  A  very  fine  example  is  at  St.  George's  Chapel,  Windsor, 
England. 

Groove.  In  joinery,  a  term  used  to  signify  a  sunk  channel  whose  section  is 
rectangular.  It  is  usually  employed  on  the  edge  of  a  molding,  stile,  or  mil, 
etc.,  into  which  a  tongue  corresponding  to  its  section,  and  in  the  substance  of 
the  wood  to  which  it  is  joined,  is  inserted. 

Grotesque.  A  singular  and  fantastic  style  of  ornament  found  in  ancient 
buildings. 

Grotto.     An  artificial  cavern. 

Ground  Floor.  The  floor  of  a  building  on  a  level,  or  nearly  so,  with  the 
ground. 

Ground  Joist.    Joist  that  is  blocked  up  from  the  ground. 

Grounds.  IMeces  of  wood  embedded  in  the  plastering  of  walls  to  which 
skirting  and  other  joiner's  work  is  attached.  They  arc  also  used  to  stop  the 
plastering  around  door  and  window  openings. 

Grouped  Columns.  Three,  four,  or  more  columns  put  together  on  the  same 
pedestal.     When  two  are  placed  together,  they  arc  said  to  be  coupled. 

Grout.  Mortar  made  so  thin  by  the  addition  of 
water  that  it  will  run  into  all  the  joints  and  cavities 
of  the  mason-work,  and  fill  it  up  solid. 

Guilloche,  or  Guillochos.  An  interlaced  orna- 
ment  like  net-work,  used  most  frequently  to  enrich    ^X:"xx««x. 

Gutta.  The  small  cylindrical  drops  used  to  en- 
rich the  mutulcs  and  regular  of  the  Doric  entabla- 
ture arc  so  called. 

Guttei.  The  channel  for  carrying  off  rain-water 
The  medireval  gutters  differed  little  from  others,  except 
that  they  are  often  hollows  sunk  in  .the  top  of  stone 
cornices,  in  which  case  they  are  generally  called  chan-  CUTT^. 

nels  in  English,  and  chcncaux  \n  Lrench.  ,     ^      ,       .. 

Gymnasium.  A  building  cj-ed  in  0.  f^st  ^^^^^^^ 
them  they  instructed  the  youth  m  all  the  arth  of  peace  ana  wa  . 
athletic  exercises. 


1S24 


Glossary 


Part  3 


Hall.  The  principal  apartment  in  the  large  dwellings  of  the  Middle  Ages, 
used  for  the  purposes  of  receptions,  feasts,  etc.  In  the  Norman  castle  the  hall 
was  generally  in  the  keep  above  the  ground  floor,  where  the  retainers  lived,  the 
basement  being  devoted  to  stores  and  dungeons  for  confining  prisoners.  Later 
halls  —  indeed,  some  Norman  halls  (not  in  castles)  —  are  generally  on  the  ground 
floor,  as  at  Westminster,  approached  by  a  porch  either  at  the  end,  as  in  this  last 
example,  or  at  the  side,  as  at  Guildhall,  London,  having  at  one  end  a  raised  dais 
or  estrade.  The  roofs  are  generally  open  and  more  or  less  ornamented.  In  the 
middle  of  these  was  an  opening  to  let  out  the  smoke,  though  in  later  times  the 
halls  have  large  chimney-places  with  funnels  or  chimney-shafts  for  this  purpose. 
At  this  period  there  were  usually  two  deeply  recessed  bay  windows  at  each  end 
of  the  dais,  and  doors  leading  into  the  withdrawing-rooms,  or  the  ladies'  apart- 
ments; they  are  also  generally  wainscoted  with  oak,  in  small  panels,  to  the  height 
of  five  or  six  feet,  the  panels  often  being  enriched.  Westminster  Hall  was 
originally  divided  into  three  parts,  like  a  nave  and  side  aisles,  as  are  some  on  the 
Continent  of  Europe.  A  room  or  passage-way  at  the  entrance  of  a  house,  or 
suite  of  chambers.     A  place  of  pubHc  assembly,  as  a  town-hall,  a  music-hall. 

Halving.     The  junction  of  two  pieces  of  timber,  by  letting  one  into  the  other. 

Hammer  Beam.  A  beam  in  a  Gothic  roof,  not  extending  to  the  opposite 
side;   a  beam  at  the  foot  of  a  rafter. 

Hanging  Buttress.  A  buttress  not  rising  from  the  ground,  but  supported  on 
a  corbel,  applied  chiefly  as  a  decoration  and  used  only  in  the  Decorated  and 
Perpendicular  style. 

Hanging  Stile.     Of  a  door,  is  that  to  which  the  hinges  are  fixed. 

Hangings.  Tapestry;  originally  invented  to  hide  the  coarseness  of  the  walls 
of  a  chamber.  Different  materials  were  employed  for  this  purpose,  some  of 
them  exceedingly  costly  and  beautifully  worked  in  figures,  gold  and  silk. 

Hatching.  Drawing  parallel  lines  close  together  for  the  purpose  of  indicat- 
ing a  section  of  anything.  The  lines  are  generally  drawn  at  an  angle  of  45°  with 
a  horizontal. 

Haunches.  The  sides  of  an  arch,  about  half-way  from  the  springing  to  the 
crown. 

Headers.  In  masonry,  are  stones  or  bricks  extending  over 
the  thickness  of  a  wall.  In  carpentry,  the  large  beam  into 
which  the  common  joists  are  framed  in  framing  openings  for 
Stairs,  chimneys,  etc. 

Heading  Courses.  Courses  of  a  wall  in  which  the  stone 
or  brick  are  all  headers. 

Head-way.  Clear  space  or  height  under  an  arch,  or  over 
a  stairway,  and  the  like. 

Heel.  Of  a  rafter,  the  end  or  foot  that  rests  upon  the 
wall  plate. 

Height.  Of  an  arch,  a  line  drawn  from  the  middle  of  the 
chord  to  the  intrados. 

Helix.  A  small  volute  or  twist  like  a  stalk,  representing 
the  twisted  tops  of  the  acanthus,  placecf  under  the  abacus  of 
the  Corinthian  capital. 

Hermes.  A  rough  quadrangular  stone  or  pillar,  having 
a  head,  usually  of  Hermes  or  Mercury,  sculptured  on  the 
top,  without  arms  or  body,  placed  by  the  Greeks  ia  front  of 
buildings. 


HERMES 


Glossary  1825 

.   Herring-bone  Work.     Bricks,  tile,  or  other  materials  arranged  diagonally 
in  building.  ^ 

Hexastyle.     A  portico  of  six  columns  in  front  is  of  this  description. 

High  Altar.  The  principal  altar  in  a  cathedral  or  church.  Where  there  is  a 
second,  it  is  generally  at  the  end  of  the  choir  or  chancel,  not  in  the  lady  chapel. 

Hip-knob.  The  finial  on  the  hip  of  a  roof,  or  between  the  barge  boards  of  a 
gable. 

Hip-roof.  A  roof  which  rises  by  equally  inclined  planes  from  all  four  sides 
of  the  building. 

Hippodrome.     A  place  appropriated  by  the  ancients  for  equestrian  exercises. 

Hips.  Those  pieces  of  timber  placed  in  an  inclined  position  at  the  corners  or 
angles  of  a  hip-roof. 

Hood-mold.  A  word  used  to  signify  the  drip-stone  for  label  over  a  window 
or  door  opening,  whether  inside  or  out. 

Hotel  de  Ville.  The  town-hall,  or  guild-hall,  in  France,  Germany,  and 
Northern  Italy.  The  building,  in  general,  serves  for  the  administration  of  justice, 
the  receipt  of  town  dues,  the  regulation  of  markets,  the  residence  of  magistrates, 
barracks  for  police,  prisons,  and  all  other  fiscal  purposes.  As  may  be  imagined, 
they  differ  very  much  in  different  towns,  but  they  have  almost  invariably 
attached  to  them,  or  closely  adjacent,  a  large  clock-tower  containing  one  or 
more  bells,  for  caUing  the  people  together  on  special  occasions. 

Hotel  Dieu.  The  name  for  a  hospital  in  mediaeval  times.  In  England  there 
are  but  few  remains  of  these  buildings,  one  of  which  is  at  Dover;  in  France  there 
are  many.  The  most  celebrated  is  the  one  at  Angers,  described  by  Parker. 
They  do  not  seem  to  differ  much  in  arrangement  of  plan  from  those  in  modern 
days,  the  accommodation  for  the  chaplain,  medicine,  nurses,  stores,  etc.,  being 
much  the  same  in  all  ages,  except  that  in  some  of  the  earlier,  instead  of  the  sick 
being  placed  in  long  wards  like  galleries,  as  is  now  done,  they  occupied  large 
buildings,  with  naves  and  side  aisles,  like  churches. 

Housing.  The  space  taken  out  of  one  solid  to  admit  the  insertion  of  another. 
The  base  on  a  stair  is  generally  housed  into  the  treads  and  risers;  a  niche  for  a 
statue. 

Hypaethros.  A  temple  open  to  the  air,  or  uncovered.  The  term  may  be  the 
more  easily  understood  by  supposing  the  roof  removed  from  over  the  nave  of  a 
church  in  which  columns  or  piers  go  up  from  the  floor  to  the  ceiling,  leaving  the 
aisles  still  covered. 

Hypogea.  Constructions  under  the  surface  of  the  earth,  or  in  the  sides  of  a 
hill  or  mountain. 

Ichnography.  A  horizontal  section  of  a  building  or  other  object,  showing  its 
true  dimensions  according  to  a  geometric  scale,  a  ground  plan. 

Impluvium.  The  central  part  of  an  ancient  Roman  court,  which  was  un- 
covered. 

Impost.  A  term  in  classic  architecture  for  the  horizontal  moldings  of  piers 
or  pilasters,  from  the  top  of  which  spring  the  archivolts  or  moldings  which  go 
round  the  arch. 

In  Antis.  When  there  are  two  columns  between  the  antai  of  the  lateral  waUs 
and  the  cella. 

Incise.     To  cut  in;  to  carve;  to  engrave. 

Indented.     Toothed  together. 


1826  Glossary  Part  3 

Inlaying.  Inserting  pieces  of  ivory,  metal,  or  choice  woods,  or  the  like,  into 
a  groundwork  of  some  other  material,  for  ornamentation. 

Insulated.  Detached  from  another  building.  A  church  is  insulated,  when  not 
contiguous  to  any  other  edifice.  A  column  is  said  to  be  insulated,  when  standing 
free  from  the  wall;   thus,  the  columns  of  peripteral  temples  were  insulated. 

Intaglio.  A  sculpture  or  carving  in  which  the  figures  are  sunk  below  the  gen- 
eral surface,  such  as  a  seal  the  impression  of  which  in  wax  is  in  bas-relief;  op- 
posed to  Cameo. 

Intercolumniation.  The  distance  from  column  to  column,  the  clear  space 
between  columns. 

Interlaced  Arches.  Arches  where  one  passes  over  two  openings,  and  they 
consequently  cut  or  intersect  each  other. 

Intrados.     Of  an  arch,  the  inner  or  concave  curve  of  the  arch  stones. 

Inverted  Arches.     Those  whose  key-stone  or  brick  is  the  lowest  in  the  arch. 

Ionic  Order.     One  of  the  orders  of  Classical  architecture. 

Iron  Work.  In  mediaeval  architecture,  as  an  ornament,  is  chiefly  confined  to 
the  hinges,  etc.,  of  doors  and  of  church  chests,  etc.  In  some  instances  not  only 
do  the  hinges  become  a  mass  of  scroll  work,  but  the  surface  of  the  doors  is  covered 
by  similar  ornaments.  In  almost  all  styles  the  smaller  and  less  important  doors 
had  merely  plain  strap  hinges,  terminating  in  a  few  bent  scrolls,  and  latterly  in 
fleurs-de-lis.  Escutcheon  and  ring  handles,  and  the  other  furniture,  partook 
more  or  less  of  the  character  of  the  time.  On  the  Continent  of  Europe  the 
knockers  are  very  elaborate.  At  all  periods  doors  have  been  ornamented  with 
nails  having  projecting  heads,  sometimes  square,  sometimes  polygonal,  and  some- 
times ornamented  with  roses,  etc.  The  iron  work  of  windows  is  generally  plain, 
and  the  ornament  confined  to  simple  fleur-de-lis  heads  to  the  stanchions.  The 
iron  work  of  screens  enclosing  tombs  and  chapels  is  noticed  under  Grille,  q.v. 

Jack.  An  instrument  for  raising  heavy  loads,  either  by  a  crank,  siren  and 
pinion,  or  by  hydraulic  power,  and  in  all  cases  worked  by  hand. 

Jack  Rafter.     A  short  rafter,  used  especially  in  hip-roofs. 

Jamb.  The  side-post  or  lining  of  a  doorway  or  other  aperture.  The  jambs 
of  a  window  outside  the  frame  are  called  Reveals. 

Jamb-shafts.  Small  shafts  to  doors  and  windows  with  caps  and  bases;  when 
in  the  inside  arris  of  the  jamb  of  a  window  they  are  sometimes  called  Esconsons. 

Joggle.  A  joint  between  two  bodies  so  constructed  by  means  of  jogs  or 
notches  as  to  prevent  their  sliding  past  each  other. 

Joinery.  That  branch  in  building  confined  to  the  nicer  and  more  ornamental 
parts  of  carpentry. 

Joist.  A  small  timber  to  which  the  boards  of  a  floor  or  the  laths  of  ceiling  are 
nailed.     It  rests  on  the  wall  or  on  girders. 

Keep.  The  inmost  and  strongest  part  of  a  mediaeval  castle,  answering  to  the 
citadel  of  modern  times.  The  arrangement  is  said  to  have  originated  with  Gun- 
dulf,  the  celebrated  Bishop  of  Rochester.  The  Norman  keep  is  generally  a  very 
massive  square  tower,  the  basement  or  stories  partly  below  ground  being  used 
for  stores  and  prisons.  The  main  story  is  generally  a  great  deal  above  ground 
level,  with  a  projecting  entrance,  approached  by  a  flight  of  steps  and  drawbridge. 
This  floor  is  generally  supposed  to  have  been  the  guard-room  or  place  for  the 
soldiery;  above  this  was  the  hall,  which  generally  extended  over  the  whole  area 
of  the  building,  and  is  sometimes  separated  by  columns;  above  this  are  other 
apartments  for  the  residents.    There  are  winding  staircases  in  the  angles  of  the 


Glossary  jg27 

buildings,  and  passages  and  small  chambers  in  the  thickness  of  tho  walls  The 
keep  was  intended  for  the  last  refuge,  in  case  the  outworks  were  scaled  and  the 
other  buildmgs  stormed  There  is  generally  a  well  in  a  mediaeval  keep,  ingen 
lousb^  concealed  m  the  thickness  of  a  wall,  or  in  a  pillar.  The  most  celebrated 
of  Norman  times  are  the  White  Tower  in  London,  the  castles  at  Rochester 
Arundel,  and  Newcastle,  Castle  Hedingham,  etc.  The  keep  was  often  circular! 
Key-stone.  The  stone  placed  in  the  center  of  the  top  of  an  arch  The  char 
acter  of  the  key-stone  varies  in  different  orders.  In  the  Tuscan  and  Doric  it  is 
only  a  srniple  stone  projecting  beyond  the  rest;  in  the  Ionic  it  is  adorned  with 
nioldings  m  the  manner  of  a  console;  in  the  Corinthian  and  Composite  it  is  a 
rich-sculptured  console. 

King-post.  The  middle  post  of  a  trussed  piece  of  framing  for  supporting  the 
tie-beam  at  the  middle  and  the  lower  ends  of  the  struts. 

Knee.  A  piece  of  timber  naturally  or  artificially  bent  to  receive  another  to 
Xelieve  a  weight  or  strain. 

Knob,  Knot.     The  bunch  of  flowers  carved  on  a  corbel,  or  on  a  Boss. 

Kremlin.     The  Russian  name  for  the  citadel  of  a  town  or  city. 

Label.     Gothic:  the  drip  or  hood-molding  of  an  arch,  when  it  is  returned  to 

the  square. 

Label  Terminations.  Carvings  on  which  the  labels  terminate  near  the 
springing  of  the  windows.  In  Norman  times  those  were  frequently  grotesque 
heads  of  fish,  birds,  etc.,  and  sometimes  stiff  fohage.  In  the  Early  English  and 
Decorated  periods  they  are  often  elegant  knots  of  flowers,  or  heads  of  kings, 
queens,  bishops,  and  other  persons  supposed  to  be  the  founders  of  churches.  In 
the  Perpendicular  period  they  are  often  finished  with  a  short  square,  mitred  return 
or  knee,  and  the  foliages  are  generally  leaves  of  square  or  octagonal  form. 

Lacunar.  A  paneled  or  coffered  ceiling  or  soffit.  The  panels  or  cassoons  of 
a  ceiling  are  by  Vitruvius  called  lacunaria. 

Lady-chapel.     A  small  chapel  dedicated  to  the 
Virgin  Mary,  generally  found  in  ancient  cathedrals. 

Lancet.     A  high  and  narrow  window  pointed  like 
a  lancet,  often  called  a  lancet  window. 

Landing.     A  platform  in  a  flight  of  stairs  between 
two  stories;   the  terminating  of  a  stair. 

Lantern.     A  turret  raised  above  a  roof  or  tower 
and  very  much  pierced,  the  better  to  transmit  light. 
In  modern  practice  this  term  is  generally  applied  to    lacunars  in  ceiling 
any  raised  part  in  a  roof  or  ceiling  containing  vertical 

windows,  but  covered  in  horizontally.  The  name  was  also  often  applied  to  the 
louver  or  femerell  on  a  roof  to  carry  off  the  smoke;  sometimes,  too,  to  the  open 
constructions  at  the  top  of  towers,  as  at  Ely  Cathedral,  probably  because  lights 
were  placed  in  them  at  night  to  serve  as  beacons. 

Lanterns  of  the  Dead.  Curious  smaU  slender  towers,  found  chiefly  in  the 
centre  and  west  of  France,  having  apertures  at  the  top,  where  a  light  was  ex- 
hibited at  night  to  mark  the  place  of  a  cemetery.^  Some  have  supposed  that  the 
round  towers  in  Ireland  may  have  served  for  this  purpose. 

Lath.     A  slip  of  wood  used  in  slating,  tiling,  and  plastering. 

Lattice.  Any  work  of  wood  or  metal  made  by  crossing  laths,  rods,  or  bars, 
and  forming  a  net-work.    A  reticulated  window,  made  of  laths  or  slips  of  iron, 


1828  Glossary  Part  3 

separated  by  glass  windows,  and  only  used  where  air  rather  than  light  is  to  be 
admitted,  as  in  cellars  and  dairies. 

Lavabo.  The  lavatory  for  washing  hands,  generally  erected  in  cloisters  of 
monasteries.  A  very  curious  one  at  Fontenay,  surrounding  a  pillar,  is  given  by 
VioUet-le-Duc.  In  general,  it  is  a  sort  of  trough,  and  in  some  places  has  an 
almry  for  towels,  etc. 

Lavatory.     A  place  for  washing  the  person. 

Lean-to.  A  small  building  whose  rafters  pitch  or  lean  against  another  build- 
ing, or  against  a  wall. 

Lectern.     The  reading-desk  in  the  choir  of  churches. 

Ledge,  or  Ledgement.  A  projection  from  a  plane,  as  slips  on  the  side  of 
window  and  door  frames  to  keep  them  steady  in  their  places. 

Ledgers.  The  horizontal  pieces  fastened  to  the  standard  poles  or  timbers  of 
scafifolding  raised  around  buildings  during  their  erection.  Those  which  rest  on 
the  ledgers  are  called  putlogs,  and  on  these  the  boards  are  laid. 

Lewis.     An  iron  clamp  dovetailed  into  a  large  stone  to  lift  it  by. 

Lich-gate.  A  covered  gate  at  the  entrance  of  a  cemetery,  under  the  shelter 
of  which  the  mourners  rested  with  the  corpse,  while  the  procession  of  the  clergy 
came  to  meet  them.     There  are  several  examples  ijTi  England. 

Light.  A  division  or  space  in  a  sash  for  a  single  pane  of  glass;  also  a  pane 
of  glass. 

Linen  ScroU.  An  ornament  formerly  used  for  filling  panels,  and  so  called 
from  its  resemblance  to  the  convolutions  of  a  folded  napkin. 

Lining.  Covering  for  the  interior,  as  casing  is  covering  for 
the  exterior  surface  of  a  building;  also,  such  as  linings  of  a 
door  for  windows,  shutters,  and  similar  work. 

Lintel.     The  horizontal  piece  which  covers  the  opening  of  a      _ 
door  or  window. 

Lip  Mold.     A  molding  of  the  Perpendicular  period  like  a  hanging  lip.     i 

List,  or  ListeL  A  little  square  molding,  to  crown  a  larger;  also  termed  a 
fillet. 

Lithograph.     A  print  from  a  drawing  on  stone. 

Lobby.  An  open  space  surrounding  a  range  of  chambers,  or  seats  in  a  theater: 
a  small  hall  or  waiting  room. 

Lodge.     A  small  house  in  a  park. 

Loft.  The  highest  room  in  a  house,  particularly  if  in  the  roof;  also,  a  gallery 
raised  up  in  a  church  to  contain  the  rood,  the  organ,  or  singers. 

Loggia.  An  outside  gallery  or  portico  above  the  ground,  and  contained 
within  the  building. 

Loop-hole.  An  opening  in  the  wall  of  a  building,  very  narrow  on  the  outside, 
and  splayed  within,  from  which  arrows  or  darts  might  be  discharged  on  an 
enemy.  They  are  often  in  the  form  of  a  cross,  and  generally  have  round  holes 
at  the  ends. 

Lombard  Architecture.  A  name  given  to  the  round-arched  architecture  of 
Italy,  introduced  by  the  conquering  Goths  and  Ostrogoths,  and  which  super- 
seded the  Romanesque.  It  reigned  between  the  eighth  and  twelfth  centuries, 
during  the  time  that  the  Saxon  and  Norman  styles  were  in  vogue  in  England,  and 
corresponded  with  them  in  its  development  into  the  Continental  Gothic. 


W^- 


Glossary 


1829 


LOZENGE   MOLDING 


LOUVER  WINDOW 


Lotus.     A  plant  of  great  celebrity  amongst  the  ancients,  the  leaves  and 
blossoms  of  which  generally  form  the  capitals  of  Egyptian  columns. 

Louver.     A  kind  of  vertical  window,  frequently  in  the  peaks  of  gables,  and  in 
the  top  of  towers,  and  provided  with  horizontal  slats  which 
permit  ventilation  and  exclude  rain. 

Lozenge  Molding.  A  kind  of  molding  used  in  Norman 
architecture,  of  many  dififcrent  forms,  all  of  which  are  char- 
acterized by  lozenge-shaped  ornaments. 

Lunette.  The  French  term 
for  the  circular  opening  in  the 
groining  of  the  lower  stories  of 
towers,  through  which  the  bells 
are  drawn  up. 

Machicolation..  A  parapet 
or  gallery  projecting  from  the  upper  part  of  the  wall  of  a  house  or  fortifica- 
tion, supported  by  brackets  or  corbels,  and  perforated  in  the  lower  part  so  that 
the  defenders  of  the  building  might  throw  down  darts,  stones,  and  sometimes 
hot  sand,  molten  lead,  etc.,  upon  their  assailants  below. 

Man-hole.     A  hole  through  which  a  man  may  creep  into  a  drain,  cesspool, 
steam-boiler,  etc. 

Manor-house.     The  residence  of  the  suzerain  or  lord  of  the  manor;  in  France 
the  central  tower  or  keep  of  a  castle  is  often  called  the  manoir. 

Mansard  Roof.     Curb  roof,  invented  by  Francois  Mansard,  a  distinguished 
French  architect,  who  died  in  1666. 

Mansion.     A  residence  of  considerable  size  and  pretension. 

Mantel.     The  work  over  a  fireplace  in  front  of  a.  chimney;  especially,  a  shelf, 
usually  ornamented,  above  the  fireplace. 

Marquetry.     Inlaid  work  of  fine  hard  pieces  of  wood 
of  different  colors,  also  of  shells,  ivory,  and  the  hke. 

Mausoleum.     A  magnificent  tomb  or  sumptuous  sepul- 
chral monument. 

Medallion.     Any  circular  tablet  on  which  are  embossed 
figures  or  busts. 

Mediaeval   Architecture.     The  architecture  of   Eng- 
land, France,  Germany,  etc.,  during  the  Middle  Ages,  including  the  Norman  and 
Early  Gothic  styles.     It  comprises  also  the  Romanesque,  Byzantme  and  bara- 
cenic,  Lombard,  and  other  styles. 

Members.     The  different  parts  of  a  building,  the  different  parts  of  an  entab- 
lature, the  different  moldings  of  a  cornice,  etc. 

Merlon.     That  part  of  a  parapet  which  lies  between 
two  embrasures. 

Metope.     The  square  recess  between  the  triglypns  in 
a  Doric  frieze.     It  is  sometimes  occupied  by  sculptures. 

Mezzanine.     A  low  story  between  two  lofty  ones. 
It  is  called  by  the  French  entresol,  or  inter-story. 

Mezzo-riiievo.     Or  mean  relief,  in  comparison  with 
^Ito-riUevo,  or  high  relief. 


MACHICOLATION 


•^^ 


METOPE 


1830 


Glossary 


Parts 


MINARET 


MODILLION 


Minaret.  Turkish:  a  circular  turret  rising  by  different  stages  or  divisions, 
each  of  which  has  a  balcony. 

Minster.  Probably  a  corruption  of  monasterium  —  the  large  church  at- 
tached to  any  ecclesiastical  fraternity.  If  the  latter  be  presided  over  by  a 
bishop,  it  is  generally  called  a  Cathedral;  if  by  an  abbot,  an  Abbey;  if  by  3 
prior,  a  Priory. 

Minute.  The  sixtieth  part  of  the  lower  diameter  of  a  column ;  it 
is  the  measure  used  by  architects  to  determine  the  proportions  of 
an  order. 

Miserere.  A  seat  in  a  stall  of  a  large  church  made  to  turn  up 
and  afford  support  to  a  person  in  a  position  between  sitting  and 
standing.  The  under  side  is  generally  carved  with  some  ornament, 
and  very  often  with  grotesque  figures  and  caricatures  of  diJereut 
persons. 

Miter.  A  molding  returned  upon  itself  at  right  angles  is  said  to 
miter.  In  joinery,  the  ends  of  any  two  pieces  of  wood  of  correspond- 
ing form,  cut  off  at  45°,  necessarily  abut  upon  one  another  so  as  to 
form  a  right  angle,  and  are  said  to  miter. 

Modillion.     So  called  because  of  its  arrangement  in  regulated  distances;  the 
enriched  block  or  horizontal  bracket  generally  found 
under  the  cornice  of  the  Corinthian  entablature.    Less 
ornamented,  it  is  sometimes  used  in  the  Ionic. 

Module.  This  is  a  term  which  has  been  generally 
used  by  architects  in  determining  the  relative  propor- 
tions of  the  various  parts  of  a  columnar  ordinance. 
The  semi-diameter  of  the  column  at  its  base  is  the 

module,  which  being  divided  into  thirty  parts  called  minutes,  any  part  of  the 
composition  is  said  to  be  of  so  many  modules  and  minutes,  or  minutes  alone,  in 
height,  breadth,  or  projection.  The  whole  diameter  is  now  generally  preferred 
as  a  module,  it  being  a  better  rule  of  proportion  than  its  half. 

Monastery.  A  set  of  buildings  adapted  for  the  reception  of  any  of  the  vari^ 
ous  orders  of  monks,  the  different  parts  of  which  are  described  in  the  separate 
article.  Abbey. 

Monotriglyph.  The  intercolumniations  of  the  Doric  order  are  determined  by 
the  number  of  triglyphs  which  intervene,  instead  of  the  number  of  diameters  of 
the  column,  as  in  other  cases;  and  this  term  designates  the  ordinary  intercolum- 
niation  of  one  trig ly ph. 

Monument.  A  name  given  to  a  tomb,  particularly  to  those  fine  structures 
recessed  in  the  walls  of  mediaeval  churches. 

Mosaic.  Pictorial  representations,  or  ornaments,  formed  of  small  pieces  of 
stone,  marble,  or  enamel  of  various  colors.  In  Roman  houses  the  floors  are  often 
entirely  of  mosaic,  the  pieces  being  cubical.  The  best  examples  of  mosaic  work 
arc  found  in  St.  Mark's,  at  Venice. 

Mosque.     A  Mahometan  temple,  or  place  of  worship. 

Molding.  When  any  work  is  wrought  into  long  regular  channels  or  projec- 
tions, forming  curves  or  rounds,  hollows,  etc.,  it  is  said  to  be  molded,  and  each 
separate  member  is  called  a  molding.  In  mediaeval  architecture  the  principal 
moldings  are  those  of  the  arches,  doors,  windows,  piers,  etc.  In  the  Early 
English  style,  the  moldings,  for  some  time,  formed  groups  set  back  in  squares, 
and  frequently  very  deeply  undercut.     The  scroll  molding  is  also  common. 


Glossary  IH'Sl 

Small  fillets  now  become  very  frequent  in  the  keel  molding,  from  its  resemblance 
in  section  to  the  bottom  of  a  ship;  sometimes,  also,  it  has  a  pecuHar  hollow  on 
each  side,  like  two  wings.  Later  in  the  Decorated 
style  the  moldings  are  more  varied  in  design,  though 
hollows  and  rounds  still  prevail.  The  undercutting  is 
not  so  deep,  fillets  abound,  ogees  are  more  frequent, 
and  the  wave  mold,  double  ogee,  or  double  ressaunt,  is 
often  seen.  In  many  places  the  strings  and  labels  are 
a  round,  the  lower  half  of  which  is  cut  off  by  a  plain 
chamfer.  The  moldings  in  the  later  styles  in  some 
degree  resemble  those  of  the  Decorated,  flattened  and 
extended;    they  run  more  into  one  another,  having  moldings 

fewer  fillets,  and  being,  as  it  were,  less  grouped.  ^'  astragal;  b,  ogee; 
One  of  the  principal  features  of  the  change  is  the  ^'  cymatium;  d,  cavet- 
substitution  of  one,  or  perhaps  two  (seldom  more),  ^o;  e,  scotia,  or  case- 
very  large  hollows  in  the  set  of  moldings.  These  hoi-  ment;  /,  apophyges; 
lows  are  neither  circular  nor  elliptical,  but  obovate,  S,  ovolo,  or  quarter 
like  an  egg  cut  across,  so  that  one  half  is  larger  round;  h,  •  torus;  i, 
than  the  other.  The  brace  mold  also  has  a  small  reeding;  j,  band, 
bead,  where  the  two  ogees  meet.     Another  sort  of 

molding,  which  has  been  called  a  lip  mold,  is  common  in  parapets,  bases,  and 
weatherings. 

Moldings,  Ornamented.  The  Saxon  and  early  Norman  moldings  do  not 
seem  to  have  been  much  enriched,  but  the  complete  and  later  styles  of  Norman 
are  remarkable  for  a  profusion  of  ornamentation,  the  most  usual  of  which  is 
what  is  called  the  zigzag.  This  seems  to  be  to  Norman  architecture  what  the 
meander  or  fret  was  to  the  Grecian;  but  it  was  probably  derived  from  the 
Saxons,  as  it  is  very  frequently  found  in  their  pottery.  Bezants,  quatrefoils, 
lozenges,  crescents,  billets,  heads  of  nails,  are  very  common  ornaments.  Besides 
these,  battlements,  cables;  large  ropes  round  which  smaller  ropes  are  turned,  or, 
as  our  sailors  say,  "wormed";  scallops,  pellets,  chains,  a  sort  of  conical  barrels, 
quaint  stiff  foliages,  beaks  of  birds,  heads  of  fishes,  ornaments  of  almost  every  con- 
ceivable kind,  are  sculptured  in  Norman  moldings;  and  they  are  used  in  such 
profusion  as  has  been  attempted  in  no  other  style.  The  decorations  on  Early 
English  moldings  are  chiefly  the  dog-tooth,  which  is  one  of  the  great  charac- 
teristics of  this  Style,  though  it  is  to  be  found  in  the  Transition  Norman.  It  is 
generally  placed  in  a  deep  hollow  between  two  projecting  moldings,  the  dark 
shadow  in  the  hollow  contrasting  in  a  very  beautiful  way  with  the  light  in  these 
moldings.  In  this  period  and  in  the  next  the  tympanum  over  doorways,  par- 
ticularly if  they  are  double  doors,  is  highly  ornamented.  Those  of  the  Decorated 
period  resemble  the  former,  except  that  the  foliage  is  more  natural  and  the  dog- 
tooth gives  way  to  the  ball-flower.  Some  of  the  hollows,  also,  arc  ornamented  . 
with  rosettes  set  at  intervals,  which  are  sometimes  connected  by  a  running  tendril, 
as  the  ball-flowers  are  frequently.  Some  very  pleasing  leaf -like  ornaments  in  the 
labels  of  windows  are  often  found  in  Continental  architecture.  In  the  Perpen- 
dicular period  the  moldings  are  ornamented  very  frequenUy  by  square  four- 
leaved  flowers  set  at  intervals,  but  the  two  characteristic  ornaments  of  the  time 
are  running  patterns  of  vine  leaves,  tendrils,  and  grapes  in  the  hollows  which 
by  old  writers  are  called  "vignettes  in  casements,"  and  upright  stitt  leaves 
generally  called  the  Tudor  leaf.  On  the  Continent  moldings  partook  much  of 
the  same  character. 

Mullion,  Munion..  The  perpendicular  pieces  of  stone,  sometimes  like  col- 
umns, sometimes  like  s.^^nder  piers,  which  divide  the  bays  or  lights  of  windows 


1832  Glossary  Part  3 

or  screen-work  from  each  other.  In  all  styles,  in  less  important  work,  the  mul- 
lions  are  often  simply  plain  chamfered,  and  more  commonly  have  a  very  flat  hol- 
low on  each  side.  In  larger  buildings  there  is  often  a  bead  or  boutell  on  the  edge, 
and  often  a  single  very  small  column  with  a  capital.  As  tracery  grew  richer,  the 
windows  were  divided  by  a  larger  order  of  mullion,  between  which  came  a  lesser 
or  subordinate  set  of  mullions,  which  ran  into  each  other.  The  term  is  also 
applied  to  a  wood  or  iron  division  between  two  windows. 

Multifoil.  A  leaf  ornament  consisting  of  more  than  five  divisions,  applied  to 
foils  in  windows. 

Mutule.  The  rectangular  impending  block  under  the  corona  of  the  Doric 
cornice,  from  which  guttle  or  drops  depend.  Mutule  is  equivalent  to  modillion 
but  the  latter  terra  is  applied  more  particularly  to  enriched  blocks  or  brackets, 
such  as  those  of  Ionic  and  Corinthian  entablatures. 

Narthex.  The  long  arcaded  porch  forming  the  entrance  into  the  Christian 
basihca.  Sometimes  there  was  an  inner  narthex,  or  lobby,  before  entering  the 
church.  When  this  was  the  case,  the  former  was  called  exo-narthex,  and  the 
latter  eso-narthex.  In  the  Byzantine  churches  this  inner  narthex  forms  part  of 
the  solid  structure  of  the  church,  being  marked  off  by  a  wall  or  row  of  columns, 
whereas  in  the  Latin  churches  it  was  usually  formed  only  by  a  wooden  or  other 
temporary  screen. 

Natural  Beds.  In  stratified  rocks,  the  surface  of  a  stone  as  it  lies  in  the 
quarry.     If  not  laid  in  walls  in  their  natural  bed  the  laminse  separate. 

Nave.  The  central  part  between  the  arches  of  a  church,  which  formerly  wa3 
separated  from  a  chancel  or  choir  by  a  screen.  It  is  so  called  trom  its  fancied 
resemblance  to  a  ship.  In  the  nave  were  generally  placed  the  pulpit  and  font. 
In  continental  Europe  it  often  also  contains  a  high  altar,  but  this  is  of  rare 
occurrence  in  England. 

Necking.  The  annulet  or  round,  or  series  of  horizontal  moldings,  which 
separate  the  capital  of  a  column  from  the  plain  part  or  shaft. 

Newel.  In  mediaeval  architecture,  the  circular  ends  of  a  winding  staircase 
which  stand  over  each  other,  and  form  a  sort  of  cylindrical  column. 

Newel  Post.  The  post,  plain  or  ornamented,  placed  at  the  first,  or  lowest 
step,  to  receive  or  start  the  hand-rail  upon. 

Niche.  *  A  recess  sunk  in  a  wall,  generally  for  the  reception  of  a  statue. 
Niches  sometimes  terminate  by  a  simple  label,  but  more  commonly  by  a  canopy, 
and  with  a  bracket  or  corbel  for  the  figure,  in  which  case  they  are  often  called 
tabernacles. 

Norman  Style.  Was  that  species  of  Romanesque  which  was  practised  by  the 
Normans,  and  which  was  introduced  and  fully  developed  in  England  after  they 
had  established  themselves  in  it.  The  chief  features  of  this  style  are  plainness 
and  massiveness.  The  arches,  windows,  and  doorways  were  semicircular,  the 
pillars  were  very  massive,  and  often  built  up  of  small  stones  laid  like  brickwork. 

Nosings.  The  rounded  and  projecting  edges  of  the  treads  of  a  stair,  or  the 
edge  of  a  landing. 

Obelisk.  Lofty  pillars  of  stone,  of  a  rectangular  form,  diminishing  toward  the 
top,  and  generally,  ornamented  with  iriscriptions  and  hieroglyphics  among  the 
ancient  Egyptians. 

Observatory.  A  building  erected  on  an  elevated  spot  of  ground  for  making 
astronomical  observations. 

Octostyle.    A  portico  of  eight  columns  in  front. 


Glossary  I833 

Offsets.  When  the  face  of  a  wall  is  not  one  continued  surface  but  sets  in  b v 
honzontal  jogs,  as  the  wall  grows  higher  and  thinner,  the  jogs  are  caMsets": 

^f  ^•*  I  ^^^T  f  PP^^^"^  ^^  ^  "'^^^^^'^^'  P^^tly  a  hollow  and  partly  a  round 
and  denved  no  doubt  from  its  resemblance  to  an  O  placed  over  a  G.  U  is  rare  y 
found  m  Norman  work,  and  is  not  very  common  in  Early  English.  It  is  o^fre^ 
wa?.  J^'r  ^^^'°'^ff^/«'-k^, where  it  becomes  sometimes  double,  and  is  called  a 
wave  moldmg;  and  later  still,  two  waves  are  connected  with  a  small  bead,  which 
IS  then  called  a  brace  molding.     In  ancient  MSS.  it  is  called  a  Ressaunt. 

Ofchestra.  In  ancient  theaters,  where  the  chorus  used  to  dance;  in  modern 
■  theaters,  where  the  musicians  sit. 

Order.  A  column  with  its  entablature  and  stylobate  is  so  called.  The  term  is 
the  result  of  the  dogmatic  laws  deduced  from  the  writings  of  Vitruvius  and  has 
been  exclusively  applied  to  those  arrangements  which  they  were  thought  to 
warrant. 

Oriel  Window.  Gothic:  a  projecting  angular  window,  commonly  of  a  tri- 
agonal  or  pentagonal  form,  and  divided  by  mullions  and  transoms  into  different 
bays  and  compartments. 

Orthography.  A  geometrical  elevation  of  a  building  or  other  object  in  which 
it  is  represented  as  it  actually  exists  or  may  exist,  and  not  perspectively,  or  as  it 
would  appear. 

Orthostyle.     A  columnar  arrangement  in  which  the  columns  are  placed  in  a 

straight  line. 

Ovolo.     Same  as  Echinus. 

Pagoda.     A  name  given  to  temples  in  India  and  China. 

Palace.     The  dwelHng  of  a  king,  prince,  or  bishop. 

Pale.     A  fence  picket,  sharpened  at  the  upper  end. 

Pane.  Probably  a  diminutive  of  panneau,  a  term  applied  to  the  different 
pieces  of  glass  in  a  window;   same  as  Light. 

Panel.  Properly  a  piece  of  wood  framed  within  four  other  pieces  of  wood,  as 
in  the  styles  and  rails  of  a  door,  filling  up  the  aperture,  but  often  applied  both  to 
the  whole  square  frame  and  the  sinking  itself;  also  to  the  ranges  of  sunken  com- 
partments in  wainscoting,  cornices,  corbel  tables,  groined  vaults,  ceilings,  etc. 

Pantograph,  or  Pentagraph.  An  instrument  for  copying  on  the  same,  or  an 
enlarged  or  reduced  scale. 

Pantry.  An  apartment  or  closet  in  which  bread  and  other  provisions  are 
kept. 

Papier-mache,  A  hard  substance  made  of  a  pulp  from  rags  or  paper  mixed 
with  size  or  glue,  and  molded  into  any  desired  shape.  Much  used  for  architec- 
tural ornaments. 

Parapet.  A  dwarf  wall  along  the  edge  of  a  roof,  or  round  a  terrace  walk,  etc., 
to  prevent  persons  from  falling  over,  and  as  a  protection  to  the  defenders  in  case 
of  a  siege.  Parapets  are  either  plain,  embattled,  perforated,  or  paneled.  ^  The 
last  two  are  found  in  all  styles  except  the  Norman.  Plain  parapets  are  simply 
portions  of  the  wall  generally  overhanging  a  little,  with  coping  at  the  top  and 
corbel  table  below.  Embattled  parapets  are  sometimes  paneled,  but  oftener 
pierced  for  the  discharge  of  arrows,  etc.  Perforated  parapets  are  pierced  in 
various  devices  —  as  circles,  trefoils,  quatrefoils,  and  other  designs—  so  that  the 
light  is  seen  through.  Paneled  parapets  are  -those  ornamented  by  a  series  of 
panels,  eitner  oblong  or  square,  and  more  or  less  enriched,  but  are  not  perforated. 
These  are  common  in  the  Decorated  and  Perpendicular  periods. 


1834  Glossary  Part  3 

Pargeting.  A  species  of  plastering  decorated  by  impressing  pattern^,  on  it 
when  wet.  These  seem  generally  to  have  been  made  by  sticking  a  number  of 
pins  in  a  board  in  certain  lines  or  curves,  and  then  pressing  on  the  wet  plaster  in 
various  directions,  so  as  to  form  geometrical  figure  j.  Sometimes  these  devices 
are  in  rehef,  and  in  the  time  of  Elizabeth  represent  figures,  birds,  foliages,  etc. 
Rough  plastering,  commonly  adopted  for  the  interior  surface  of  chimneys. 

Parlor.  A  room  in  a  house  which  the  family  usually  occupy  for  society  and 
conversation,  and  for  receiving  visitors.  The  apartment  in  a  monastery  or 
nunnery  where  the  inmates  are  permitted  to  meet  and  converse  with  each  other, 
or  with  visitors  and  friends  from  without. 

Parochial.     Belonging  or  relating  to  a  parish. 

Parquetry,  or  Marquetry.  A  kind  of  inlaid  floor  composed  of  small  pieces 
of  wood  either  square  or  triangular,  which  are  capable  of  forming,  by  their  dis- 
position, various  combinations  of  figures;  this  description  of  joinery  is  very 
suitable  for  the  floors  of  libraries,  halls,  and  public  apartments. 

Party  Walls.  Partitions  of  brick  or  stone  between  buildings  on  two  adjoining 
properties. 

Patera.  A  circular  ornament  resembling  a  dish,  often  worked  in  relief  on 
friezes,  etc. 

Pavement.  Tessellated,  a  pavement  of  mosaic  work, 
used  by  the  ancients,  made  of  square  pieces  of  stone,  etc., 
called  Tessera. 

Pavilion.  A  turret  or  small  insulated  building,  and 
comprised  beneath  a  single  roof;  also,  the  projecting 
part  in  front  of  a  building  which  marks  the  centre,  and 
which  sometimes  flanks  a  corner,  when  it  is  termed  an 
angular  pavilion.  patera 

Pedestal.  The  square  support  of  a  column,  statue, 
etc.;  and  the  base  or  lower  part  of  an  order  of  columns:  it  consists  of  a  plinth 
for  a  base,  the  die,  and  a  talon  crowned  for  a  cornice.  When  the  height  and 
width  are  equal,  it  is  termed  a  square  pedestal;  one  which  supports  two  columns, 
a  double  pedestal;  and  if  it  supports  a  row  of  columns  without  any  break,  it  is 
a  continued  pedestal. 

Pediment.  A  low  triangular  crowning,  ornamented,  in  front  of  a  building, 
and  over  doors  and  windows.  Pediments  are  sometimes  made  in  the  form  of  a 
segment;  the  space  enclosed  within  the  triangle  is  called  the  tympanum.  Also, 
the  gable  ends  of  classic  buildings,  where  the  horizontal  cornice  is  carried  across 
the  front,  forming  a  triangle  with  the  end  of  the  roof. 

Pendent.  A  name  given  to  an  elongated  boss,  either  molded  or  foliated, 
such  as  hang  down  from  the  intersection  of  groins,  especially  in  fan  tracery,  or 
at  the  end  of  hammer  beams.  Sometimes  long  corbels,  under  the  wall  pieces, 
have  been  so  called.  The  name  has  also  been  given  to  the  large  masses  depend- 
ing from  enriched  ceihngs,  in  the  later  works  of  the  Pointed  style. 

Pendent  Posts.  A  name  given  to  those  timbers  which  hang  down  the  side  of 
a  wall  from  the  plate  in  hammer  beam  trusses,  and  which  receive  the  hammer 
braces. 

Pendentive.  A  name  given  to  an  arch  which  cuts  off,  as  it  were,  the  corners 
of  a  square  building  internally,  so  that  the  superstructure  may  become  an  octagon 
or  a  dome.  In  mediaival  architecture  these  arches,  when  under  a  spire  in  the 
interior  of  a  tower,  are  called  Squinches. 


Glossary  jg^,^ 

Pendentive  Bracketing,  or  Cove  Bracketing.  Springing  from  the  rec- 
tangular wa  is  of  an  apartment  upward  to  the  ceiling,  and  forming  the  horizon- 
tal part  of  the  ceihng  mto  a  circle  or  ellipse. 

Pentastyle.     Having  five  columns  in  front. 

Pent-roof.     A  roof  with  a  slope  on  one  side  only. 

Perch.  A  measure  used  in  measuring  stone  work,  being  24%  cu  ft  and  16^^ 
cu  ft,  according  to  locality  and  custom. 

Periptery.     An  ediiice  or  temple  surrounded  by  a  peristyle. 

Peristyle.  A  range  of  columns  encircling  an  edifice,  such  as  that  which  sur- 
.•ounds  the  cylindrical  drum  under  the  cupola  of  St.  Paul's.  The  columns  of  a 
Greek  peripteral  temple  form  a  peristyle  also,  the  former  being  a  circular,  and 
the  latter  a  quadrilateral  peristyle. 

Perpendicular  Style.  The  third  and  last  of  the  Pointed  or  Gothic  styles; 
also  called  the  Florid  style. 

Perspective  Drawing.  The  art  of  making  such  a  representation  of  an  object 
upon  a  plane  surface  as  shall  present  precisely  the  same  appearance  that  the 
object  itself  would  to  the  eye  situated  at  a  particular  point. 

Pews.  A  word  of  uncertain  origin,  signifying  fixed  seats  in  churches,  com- 
posed of  wood  framing,  mostly  with  ornamented  ends.  They  seem  to  have  come 
into  general  use  early  in  the  reign  of  Henry  VI,  and  to  have  been  rented  and 
"well  paid  for"  before  the  Reformation.  Some  bench  ends  are  certainly  of  a 
decorated  character,  and  some  have  been  considered  to  be  of  the  Early  English 
period.  They  are  sometimes  of  plain  oak  board,  two  and  a  half  to  three  inches 
thick,  chamfered,  and  with  a  necking  and  finial,  generally  called  a  poppy  head; 
others  are  plainly  paneled  with  bold  cappings;  in  others  the  panels  are  orna- 
mented with  tracery  or  with  the  hnen  pattern,  and  sometimes  with  running 
foliages.  The  divisions  are  filled  in  with  thin  chamfered  boarding,  sometimes 
reaching  to  the  floor,  and  sometimes  only  from  the  capping  to  the  seat. 

Picket.  A  narrow  board,  often  pointed,  used  in  making  fences;  a  pale  or 
paling. 

Pier-glass.     A  mirror  hanging  between  windows. 

Piers.  The  solid  parts  of  a  wall  between  windows,  and  between  voids  gener- 
ally. The  term  is  also  applied  to  masses  of  brick-work  or  masonry  "which  are 
insulated  to  form  supports  to  gates  or  to  carry  arches,  posts,  girders,  etc. 

Pilasters.  Are  flat  square  columns,  attached  to  a  wall,  behind  a  column,  or 
along  the  side  of  a  building,  and  projecting  from  the  wall  about  a  fourth  or  a 
sixth  part  of  their  breadth.  The  Greeks  had  a  slightly  different  design  for  the 
capitals  of  pilasters,  and  made  them  the  same  width  at  top  as  at  bottom,  but  the 
Romans  gave  them  the  same  capitals  as  the  columns,  and  made  them  of  di- 
minished width  at  the  top,  similar  to  the  columns. 

Pile.  A  large  stake  or  trunk  of  a  tree,  driven  into  soft  ground,  as  at  the 
bottom  of  a  river,  or  in  made  land,  for  the  support  of  a  building.  (See  p.  188.) 
Pillar,  or  Pyller.  A  word  generally  used  to  express  the  round  or  polygonal 
piers,  or  those  surrounded  with  clustered  columns,  which  carry  the  main  arches 
of  a  building.  Saxon  and  Early  Norman  pillars  are  generally  stout  cylindrical 
shafts  built  up  of  small  stones.  Sometimes,  however,  they  are  quite  square, 
sometimes  with  other  squares  breaking  out  of  them  (this  is  more  common  m 
French  and  German  work),  sometimes  with  angular  shafts,  and  sometimes  they 
are  plain  octagons.  In  Romanesque  Norman  work  the  pillar  is  sometimes 
square  with  two  or  more  semicircular  or  half-columns  attached.    In  the  Early 


183G  Glossary  Part  3 

English  period  the  pillars  become  loftier  and  lighter,  and  in  most  important 
buildings  are  a  series  of  clustered  columns,  frequentlj''  of  marble,  placed  side  by 
side,  soinetimes  set  at  intervals  round  a  circular  centre,  and  sometimes  almost 
touching  each  other.  These  shafts  are  often  wholly  detached  from  the  central 
pillar,  though  grouped  round  it,  in  which  case  they  are  almost  always  of  Purbeck 
or  Bethersden  marbles.  In  Decorated  work  the  shafts  on  plan  are  very  often 
placed  round  a  square  set  anglewise,  or  a  lozenge,  the  long  way  down  the  nave; 
the  centre  or  core  itself  is  often  worked  into  hollows  or  otfier  moldings,  to  show 
between  the  shafts,  and  to  form  part  of  the  composition.  In  this  and  the  latter 
part  of  the  previous  style  there  is  generally  a  fillet  on  the  outer  part  of  the  shaft, 
forming  what  has  been  called  a  keel  molding.  They  are  also  often,  as  it  were, 
tied  together  by  bands  formed  of  rings  of  stone  and  sometimes  of  metal.  The 
small  pillars  at  the  jambs  of  doors  and  windows,  and  in  arcades,  and  also  those 
slender  columns  attached  to  pillars,  or  standing  detached,  are-  generally  called 
shafts. 

Pin.  A  cylindrical  piece  of  wood,  iron,  or  steel,  used  to  hold  two  or  more 
pieces  together,  by  passing  through  a  hole  in  each  of  them,  as  in  a  mortise  and 
tenon  joint,  or  a  pin  joint  of  a  truss. 

Pinnacle.  An  ornament  originally  forming  the  cap  or  crown  of  a  buttress  or 
small  turret,  but  afterwards  used  on  parapets  at  the  corners  of 
towers  and  in  many  other  situations.  It  was  a  weight  to  counter- 
act the  thrust  of  the  groining  of  roofs,  particularly  where  there 
were  flying  buttresses;  it  stopped  the  tendency  to  sHp  of  the  stone 
copings  of  the  gables,  and  counterpoised  the  thrust  of  spires;  it 
formed  the  piers  to  steady  the  elegant  perforated  parapets  of 
later  periods;  and  in  France,  especially,  served  to  counterbalance 
the  weight  of  overhanging  corbel  tables,  huge  gargoyles,  etc.  In 
the  Early  Engish  period  the  smaller  buttresses  frequently  finished 
with  gablets,  and  the  more  important  with  pinnacles  supported 
with  clustered  shafts.  At  this  period  the  pinnacles  were  often 
supported  on  these  shafts  alone,  and  were  open  below;  and  in 
.larger  work  in  this  and  the  subsequent  periods  they  frequently  form 
niches  and  contain  statues.  In  France,  pinnacles,  hke  spires, 
seem  to  have  been  in  use  earlier  than  in  England.  There  are  small 
pinnacles  at  the  angles  of  the  tower  in  the  Abbey  of  Saintes.  At 
Roullet  there  are  pinnacles  in  a  similar  position,  each  composed  of  piajj^^CLE 
four  small  shafts,  with  caps  and  bases  surmounted  with  small 
pyramidal  spires.  In  all  these  examples  the  towers  have  semicircular  headed 
windows. 

Pitch  of  a  Roof.  The  proportion  obtained  by  dividing  the  height  by  the 
span;  thus,  we  speak  of  its  being  one-half,  one- third,  one-fourth.  When  the 
length  of  the  rafters  is  equal  to  the  breadth  of  the  building  it  is  denominated 
Gothic. 

Pitching-piece.  A  horizontal  d^rtber,  with  one  of  its  ends  wedged  into  the 
wall  at  the  top  of  a  flight  of  stairs,  to  support  the  upper  end  of  the  rough  strings. 

Place.  An  open  piece  of  ground  surrounded  by  buildings,  generally  decorated 
with  a  statue,  column,  or  other  ornament. 

Plan.  A  horizontal  geometrical  section  of  the  walls  of  a  building;  or  indi- 
cations, on  a  horizontal  plane,  of  the  relative  positions  of  the  walls  and  partitions, 
with  the  various  openings,  such  as  windows  and  doors,  recesses  and  projections, 
chimneys  and  chimney-breasts,  columns,  pilasters,  etc.  This  term  is  often 
incorrectly  used  in  the  sense  of  Desiirn. 


Glossary  1837 

Planceer.  Is  sometimes  used  in  the  same  sense  as  soflSt,  but  is  more  correctly 
cipplicd  to  the  soffit  of  the  corona  in  a  cornice. 

Plastering.  A  mixture  of  lime,  hair,  and  sand,  to  cover  lath-work  between 
timbers  or  rough  walling,  used  from  the  earliest  times,  and  very  common  in 
Roman  work.  In  the  Middle  Ages,  too,  it  was  used  not  only  in  private,  but  in 
public  constructions.  On  the  inside  face  of  old  rubble  walls  it  was  not  only  used 
for  purposes  of  cleanHness,  rough  work  holding  dirt  and  dust,  but  as  a  ground 
for  distemper  painting  (tempera,  or,  as  it  is  often  improperly  called,  fresco),  a 
species  of  ornament  often  used  in  the  Middle  Ages.  At  St.  Albans  Abbey,  Eng- 
land, the  Norman  work,  is  plastered,  and  covered  with  lines  imitating  the  joints 
of  stone.  The  same  thing  is  found  in  English  Perpendicular  work.  On  the  out- 
side of  rubble  walls,  and  often  of  wood  framing,  it  was  used  as  roughcast;  when 
ornamented  in  patterns  outside,  it  is  called  pargeting. 

Plate.  The  piece  of  timber  in  a  building  which  supports  the  end  of  the 
rafters. 

Plinth.  The  square  block  at  the  base  of  a  column  or  pedestal.  In  a  wall,  the 
term  plinth  is  applied  to  the  projecting  base  or  water  table,  generally  at  the  level 
of  the  first  floor. 

Plumb.  Perpendicular;  that  is,  standing  according  to  a  plumb  line,  as,  the 
post  of  a  house  or  wall  is  plumb. 

Plumbing.  '  The  lead  and  iron  pipes  and  other  apparatus  employed  in  con- 
veying water,  and  for  toilet  purposes  in  a  building;  originally  the  art  of  casting 
and  working  in  lead. 

Ply.  Used  to  denote  the  number  of  thicknesses  of  roofing  paper,  as  three  ply. 
four  ply,  etc. 

Podium.  A  continued  pedestal;  a  projection  from  a  wall,  forming  a  kind  of 
gallery. 

Polytriglyph.  An  intercolumniation  in  the  Doric  order  of  more  than  two 
triglyphs. 

Poppy  Heads.  Probably  from  the  French  poupee:  the  finials  or  other  orna- 
ments which  terminate  the  tops  of  bench  ends,  either  to  pews  or 
stalls.  They  are  sometimes  small  human  heads,  sometimes  richly 
carved  images,  knots'  of  foliage,  or  finials,  and  sometimes  fleurs- 
de-lis  simply  cut  out  of  the  thickness  of  the  bench  end  and  cham- 
fered. 

Porch.  A  covered  erection  forming  a  shelter  to  the  entrance 
door  of  a  large  building.  The  earliest  known  are  the  long  arcaded 
porches  in  front  of  the  early  Christian  basilicas,  called  Narthex. 
In  later  times  they  assume  two  forms-one,  the  projectmg  erection 
covering  the  entrance  at  the  west  front  of  cathedrals,  and  divided 
into  three  or  more  doorways,  etc.;  and  the  other,  a  kind  of  covered 
chambers  open  at  the  ends,  and  having  small  windows  at  the  sides 
as  a  protection  from  rain. 

Portal.  A  name  given  to  the  deeply  recessed  and  richly  decorated  entrance 
doors  to  the  cathedrals  in  Continental  Europe. 

Portcullis.     A  strong-framed  grating  of  oak,  the  lower  points  shod  with  Kon, 
i-ortcuiiis.     t\  birung  6  J  j^^ij  ijj  grooves 

and  sometimes  entirely  made  of  nietal,  hung  »>  ^^  to  suae    p 
with  counterbalances,  and  intended  to  protect  the  gateways  of  castles,  etc. 

Portico  An  open  space  before  the  door  or  other  entrance  to  any  building, 
fronted  wiih  ^olumL.  'a  portico  is  distinguished  as  prostyle  or .»  anHs  accord- 


1838  Glossary  Part  3 

ing  as  it  projects  from  or  recedes  within  the  building,  and  is  further  designated 
by  the  number  of  columns  its  front  may  consist  of. 

Post.  Square  timbers  set  on  end.  The  term  is  especially  applied  to  those 
which  support  the  corners  of  a  building,  and  are  framed  into  brcssummers  or 
crossbeams  under  the  walls. 

Posticum.     A  portico  behind  a  temple. 

Presbytery.  A  word  applied  to  various  parts  of  large  churches  in  a  very 
ambiguous  way.  Some  consider  it  to  be  the  choir  itself;  others,'  what  is  now 
named  the  sacrarium.  Traditionally,  however,  it  seems  to  be  applied  to  the 
vacant  space  between  the  back  of  the  high  altar  and  the  entrance  to  the  lady- 
chapel,  as  at  Lincoln  and  Chichester;   in  other  words,  the  back-  or  retro-choir. 

Priming.  The  laying  on  of  the  first  shade  of  color,  in  oil  paint,  and  generally 
consisting  mostly  of  oil,  to  protect  and  fill  the  wood. 

Priory.  A  monastic  establishment,  generally  in  connection  with  an  abbey, 
and  presided  over  by  a  prior,  who  was  a  subordinate  to  the  abbot,  and  held  much 
the  same  relation  to  that  dignitary  as  a  dean  does  to  a  bishop. 

Profile.  The  outline;  the  contour  of  a  part,  or  the  parts  composing  an  order, 
as  of  a  base,  cornice,  etc.;  also,  the  perpendicular  section.  It  is  in  the  just 
proportion  of  their  profiles  that  the  chief  beauties  of  the  different  orders  of 
architecture  depend.  The  ancients  were  most  careful  of  the  profiles  of  their 
moldings. 

Proscenium.  The  front  part  of  the  stage  of  ancient  theaters,  on  which  the 
actors  performed. 

Prostyle.  A  portico  in  which  the  columns  project  from  the  building  to  which 
it  is  attached. 

Protractor.  A  mathematical  instrument  for  laying  down  and  measuring 
angles  on  paper,  used  in  drawing  or  plotting. 

Pseudo-dipteral.  False  double-winged.  When  the  inner  row  of  columns  of 
a  dipteral  arrangement  is  omitted  and  the  space  from  the  wall  of  the  building  to 
the  columns  is  preserved,  it  is  pseudo-dipteral. 

Puddle.  To  settle  loose  dirt  by  turning  on  water,  so  as  to  render  it  firm  and 
solid. 

Pugging.  A  coarse  kind  of  mortar  laid  on  the  boarding,  between  floor  joists, 
to  prevent  the  passage  of  sound;   also  called  deafening. 

Pulpit.  A  raised  platform  with  enclosed  front,  whence  sermons,  homilies,  etc., 
were  delivered.  Pulpits  were  probably  derived  in  their  modern  form  from  the 
ambones  in  the  early  Christian  church.  There  are  many  old  pulpits  of  stone, 
though  the  majority  are  of  wood.  Those  in  the  churches  are  generally  hexagonal 
or  octagonal;  and  some  stand  on  stone  bases,  and  others  on  slender  wooden 
stems,  like  columns.  The  designs  vary  according  to  the  periods  in  which  they 
were  erected,  having  paneling,  tracery,  cuspings,  crockets,  and  other  ornaments 
then  in  use.  Some  are  extremely  rich,  and  ornamented  with  color  and  gilding. 
A  few  also  have  fine  canopies  or  sounding  boards.  Their  usual  place  is  in  the 
nave,  mostly  on  the  north  side,  against  the  second  pier  from  the  chancel  arch. 
Pulpits  for  addressing  the  people  in  the  open  air  were  common  in  the  Mediaeval 
period,  and  stood  near  a  road  or  cross.  Thus,  there  was  one  at  Spitalfields,  and 
one  at  St.  Paul's,  London.  External  pulpits  still  remain  at  Magdalen  College, 
Oxford,  and  at  Shrewsbury,  England. 

Purlins.  Those  pieces  of  timbers  which  support  the  rafters  to  prevent  them 
from  sinking. 


Glossary  1839 

Putlog.  Horizontal  pieces  for  supporting  the  floor  of  a  scaffold,  one  end  being 
inserted  into  putlog  holes,  left  for  that  purpose  in  the  masonry. 

Putty  in  Plastering.  Lump  lime  slacked  with  water  to  the  consistency  of 
cream,  and  then  left  to  harden  by  evaporation  till  it  becomes  like  soft  putty.  It 
is  then  mixed  with  plaster  of  Paris,  or  sand,  for  the  finishing  eoat. 

Puzzolana.     A  grayish  earth  used  for  building  under  water. 

Pyramid.  A  solid,  having  one  of  its  sides,  called  a  base,  a  plane  figure,  and 
the  other  sides  triangles,  these  points  joining  in  one  point  at  the  top,  called  the 
vertex.  Pyramids  are  called  triangular,  square,  etc.,  according  to  the  form  of 
their  bases. 

Pyx.     In  Roman  Catholic  churches,  the  box  in  which  the  host,  or  consecrated 

wafer,  is  kept. 

Quadrangle.  A  square  or  quadrangular  court  surrounded  by  buildings,  as 
was  often  done  formerly  in  monasteries,  colleges,  etc. 

Quarry.     A  pane  of  glass  cut  in  a  diamond  or  lozenge  form. 

Quarry-face.  Ashlar  as  it  comes  from  the  quarry,  squared  off  for  the  joints 
only,  with  split  face.  In  distinction  from  Rock-face,  in  that  the  latter  may  be 
weather-worn,  while  Quarry-face  should  be  fresh  split.  The  terms  are  often 
used  indiscriminately. 

Quatref  oil.  Any  small  panel  or  perforation  in  the  form  ofa  four-leaved  flower. 
Sometimes  used  alone,  sometimes  in  circles  and  over  the  aisle  windows,  but  more 
frequently  in  square  panels.  They  are  generally  cusped,  and  the  cusps  are  often 
feathered. 

Queen  Truss.  A  truss  framed  with  two  vertical  tie-posts,  in  distinction  from 
the  king-post,  which  has  but  one.     The  upright  ties  are  called  Queen-posts. 

Quirk  Moldings.  The  convex  part  of  Grecian  moldings  when  they  recede  at 
the  top,  forming  a  reentrant  angle,  with  the  surface  which  covers  the  moldings. 

Quoins.  Large  squared  stones  at  the  angles  of  buildings,  buttresses,  etc., 
generally  used  to  stop  the  rubble  or  rough  stone  work,  and  that  the  angles  may 
be  true  and  stronger.  Saxon  quoin  stones  are  said  to  have  been  composed  of 
one  long  and  one  short  stone  alternately.  Early  quoins  are  generally  roughly 
axed;  in  later  times  they  had  a  draught  tooled  by  the  chisel  round  the  outside 
edges,  and  later  still  were  worked  fine  from  the  saw. 

Rafters.  The  joist  to  which  the  roof  boarding  is  nailed.  Principal  rafters 
are  the  upper  timbers  in  a  truss,  having  the  same  inclination  as  the  common 
rafters. 

Rail.  A  piece  of  timber  or  metal  extending  from  one  post  to  another,  as  in 
fences,  balustrades,  staircases,  etc.  In  framing  and  paneling,  the  horizontal 
pieces  are  called  rails,  and  the  perpendicular,  stiles. 

Raking.     Moldings  whose  arrises  are  inclined  to  the  horizon. 

Ramp.  \  concavity  on  the  upper  side  of  hand  railings  formed  over  risers, 
made  by  a  sudden  rise  of  the  steps  above.  Any  concave  bend  or  slope  in  the  cap 
or  upper  member  of  any  piece  of  ascending  or  descending  workmanship. 

Rampant.  A  term  applied  to  an  arch  whose  abutments  spring  from  an 
incUned  plane. 

Random  Work.  A  term  used  by  stone-masons  for  stones  fitted  together  at 
random  without  any  attempt  at  laying  them  in  courses.  Random  Coursed  Work 
is  a  like  term  applied  to  work  coursed  in  horizontal  beds,  but  the  stones  are  of  any 
height,  and  fitted  to  one  another. 


1840  Glossary  Part  3 

Range  Work.     Ashlar  laid  in  horizontal  courses;  same  as  coursed  ashlar. 

Rebate.     A  groove  on  the  edges  of  a  board. 

Recess.     A  depth  of  some  inches  in  the  thickness  of  a  wall,  as  a  niche,  etc. 

Refectory.  The  hall  of  a  monastery,  convent,  etc.,  where  the  religious  took 
their  chief  meals  together.  It  much  resembled  the  great  halls  of  mansions, 
castles,  etc.,  except  that  there  frequently  was  a  sort  of  ambo,  approached  by 
steps,  from  which  to  read  the  Legenda  Sanctorum,  etc.,  during  meals. 

Reglet.  A  flat,  narrow  molding,  used  to  separate  from  each  other  the  parts 
or  members  of  compartments  and  panels,  to  form  frets,  knots,  etc. 

Renaissance  (a  new  birth).  A  name  given  to  the  revival  of  Roman  architec- 
ture which  sprang  into  existence  in  Italy  as  early  as  the  beginning  of  the  fifteenth 
century,  and  reached  its  zenith  in  that  country  at  the  close  of  the  century. 
There  are  several  divisions  of  this  style  as  developed  in  different  localities;  viz., 

The  Florentine  Renaissance,  of  which  the  Pitti  Palace,  by  Brunelleschi,  is  one 
of  the  best  examples. 

The  Venetian  Renaissance,  characterized  by  its  elegance  and  richness. 

The  Roman  Renaissance,  which  originated  in  Rome,  under  the  architects 
knov/n  as  Bronte,  Vignola,  and  Michael  Angelo.  Of  this  style  the  Farnese  Palace, 
St.  Peter's,  and  the  modern  Capitol  at  Rome  are  the  best  examples. 

The  French  Renaissance,  introduced  into  France  in  the  latter  part  of  the  fif- 
teenth century,  by  Italian  architects,  where  it  flourished  until  the  middle  of  the 
•seventeenth  century.  The  Renaissance  style  was  introduced  into  Germany 
about  the  middle  of  the  sixteenth  century,  and  into  England  about  the  sanie 
time  by  John  of  Padua,  architect  to  Henry  VIII.  This  style  in  England  is  gen- 
erally known  mider  the  name  of  Elizabethan. 

Rendering.  In  drawing,  finishing  a  perspective  drawing  m  ink  or  color,  to 
bring  out  the  spirit  and  effect  of  the  design.  The  first  coat  of  plaster  on  brick 
or  stone  work. 

Reredos,  Dorsal,  or  Dossel.  The  screen  or  other  ornamental  work  at  the 
back  of  an  altar.  In  some  large  EngHsh  cathedrals,  as  Winchester,  Durham,  St. 
Albans,  etc.,  this  is  a  mass  of  splendid  tabernacle  work,  reaching  nearly  to  the 
groining.  In  smaller  churches  there  are  sometimes  ranges  of  arcades  or  panelings 
behind  the  altars;  but,  in  general,  the  walls  at  the  back  and  sides  of  them  were  of 
plain  masonry,  and  adorned  with  hangings  or  paraments.  In  the  large  churches 
of  Continental  Europe  the  high  altar  usually  stands  under  a  sort  of  canopy  or 
ciborium,  and  the  sacrarium  is  hung  round  at  the  back  and  sides  with  curtains  on 
movable  rods. 

Reticulated  Work.  That  in  which  the  courses  are  arranged  in  a  form  like 
the  meshes  of  a  net.     The  stones  or  bricks  are  square  and  placed  lozenge-wise. 

Return.  The  continuation  of  a  molding,  projection,  etc.,  in  an  opposite 
direction. 

Return  Head.    One  that  appears  both  on  the  face  and  edge  of  a  work. 

Reveal.  The  two  vertical  sides  of  an  aperture,  between  the  front  of  a  wall  and 
the  window  or  door  frame. 

Rib.  A  molding  or  projecting  piece  upon  the  interior  of  a  vault,  or  used  to 
form  tracery  and  the  like.  The  earliest  groining  had  no  ribs.  In  early  Norman 
times  plain  flat  arches  crossed  each  other,  forming  ogive  ribs.  These  by  degrees 
became  narrower,  had  greater  projection,  and  were  chamfered.  In  later  Nor- 
man work  the  ribs  were  often  formed  of  a  large  roll  placed  upon  the  flat  band, 
and  then  of  two  rolls  side  by  side  wi£h  a  smaller  roll  or  a  fillet  between  them. 


Glossary  lg41 

much  like  the  lower  member.  Sometimes  they  are  enriched  with  zigzags  and 
other  Norman  decorations,  and  about  this  time  bosses  became  of  very  general 
use.  As  styles  progressed,  the  moldings  were  more  undercut,  richer,  and  more 
elaborate,  and  had  the  dog-tooth  or  ball-flower  or  other  characteristic  ornament 
in  the  hollows.  In  all  instances  the  moldings  are  of  similar  contours  to  those 
of  arches,  etc.,  of  .the  respective  periods.  Later,  wooden  roofs  are  often  formed 
into  cants  or  polygonal  barrel  vaults,  and  in  these  the  ribs  are  generally  a  cluster 
of  rounds,  and  form  square  or  stellar  panels,  with  carved  bosses  or  shields  at  the 
intersections. 

Ridge.     The  top  of  a  roof  which  rises  to  an  acute  angle. 

Ridge-pole.  The  highest  horizontal  timber  in  a  roo^,  extending  from  top  to 
top  of  the  several  pairs  of  rafters  of  the  trusses,  for  supporting  the  heads  of  the 
jack  rafters. 

Rilievo,  or  Relief.     The  projection  of  an  architectural  ornament. 

Rise.  The  distance  through  which  anything  rises,  as  the  rise  of  a  stair,  or 
incHned  plane. 

Riser.     The  vertical  board  under  the  tread  in  stairs. 

Rococo  Style.  A  name  given  to  that  variety  of  the  Renaissance  which  was  in 
vogue  during  the  seventeenth  and  the  latter  part  of  the  sixteenth  century. 

Romanesque  Style.  The  term  Romanesque  embraces  all  those  styles  of  ar- 
chitecture which  prevailed  between  the  destruction  of  the  Roman  Empire  and  the 
beginning  of  Gothic  architecture.  In  it  are  included  the  Early  Roman  Christian 
architecture,  Byzantine,  Mahometan,  and  the  later  Romanesque  architecture 
proper,  which  was  developed  in  Italy,  France,  England,  and  Germany.  This 
later  Romanesque,  which  was  quite  different  from  the  preceding,  came  into  vogue 
during  the  tenth  century,  and  reached  its  height  during  the  twelfth  century,  and 
in  the  thirteenth  century  gave  way  to  the  Pointed  or  Gothic  style.  In  England, 
Romanesque  architeqture  is  known  under  the  name  of  the  Saxon,  Norman,  and 
Lombard  styles,  according  to  the  different  political  periods. 

Rood.  A  name  appHed  to  a  crucifix,  particularly  to  those  which  were  placed 
in  the  rood-loft  or  chancel  screens.  These  generally  had  not  only  the  image  of 
the  crucified  Saviour,  but  also  those  of  St.  John  and  the  Virgin  Mary  standing 
one  on  each  side.  Sometimes  other  scants  and  angels  are  by  them,  and  the  top 
of  the  screen  is  set  with  candlesticks  or  other  decoration. 

Rood-loft,  Rood-screen,  Rood-beam,  Jube  Gallery,  etc.  The  arrange- 
ment to  carry  the  crucifix  or  rood,  and  to  screen  off  the  chancel  from  the  rest  of 
the  church  during  the  breviary  services,  and  as  a  place  whence  to  read  certain 
parts  of  those  services.  Sometimes  the  crucifix  is  carried  simply  on  a  strong  trans- 
verse beam,  with  or  without  a  low  screen,  with  folding-doors  below  but  forming  no 
part  of  such  support.  In  European  churches  the  general  construction  of  wooden 
screens  is  close  paneling  beneath,  about  3  feet  to  3  feet  6  inches  high,  on  which 
stands  screen  work  composed  of  slender  turned  balusters  or  regular  wooden 
mullions,  supporting  tracery  more  or  less  rich,  with  cornices,  crestnig,  etc.,  and 
often  painted  in  brilliant  colors  and  gilded.  These  not  only  enclose  the  chancels, 
but  also  chapels,  chantries,  and  sometimes  even  tombs.  In  English  mansions, 
and  some  private  houses,  the  great  halls  were  screened  off  by  a  low  passage  at  the 
end  opposite  to  the  dais,  over  which  was  a  gallery  for  the  use  of  minstrels  or 
spectators.     These  screens  were  sometimes  close  and  sometimes  glazed. 

Rood-tower.  ^  A  name  given  by  some  writers  to  the  central  tower,  or  that 
over  the  intersection  of  the  nave  and  chancel  with  the  transepts. 


1842  Glossary  Part  3 

Roof.     The  covering  or  upper  part  of  any  building. 
Roofing.     The  material  put  on  a  roof  to  make  it  water-tight. 

Rose  Window.  A  name  given  to  a  circular  window  with  radiating  tracery; 
called  also  wheel  window. 

Rostrum.     An  elevated  platform  from  which  a  speaker  addresses  an  audience. 

Rotunda.  A  building  which  is  round  both  within  and  without.  A  circular 
room  under  a  dome  in  large  buildings  is  also  called  the  rotunda. 

Roughcast.  A  sort  of  external  plastering  in  which  small  sharp  stones  are 
mixed,  and  which,  when  wet,  is  forcibly  thrown  or  cast  from  a  trowel  against  the 
wall,  to  which  it  forms  a' coating  of  pleasing  appearance.  Roughcast  work  has 
been  used  in  Europe  for  several  centuries,  where  it  was  much  used  in  timber 
houses,  and  when  well  executed  the  work  is  sound  and  durable.  The  mortar  for 
roughcast  work  should  always  have  cement  mixed  with  it. 

Rubble  Work.  Masonry  of  rough,  undressed  stones.  When  only  the  rough- 
est irregularities  are  knocked  off,  it  is  called  scabbled  rubble,  and  when  the  stones 
in  each  course  are  rudely  dressed  to  nearly  a  uniform  height,  ranged  rubble. 

Rudenture.  The  figure  of  a  rope  or  staff,  which  is  frequently  used  to  fill  up 
the  flutings  of  columns,  the  convexity  of  which  contrasts  with  the  concavity  of 
the  flutings,  and  serves  to  strengthen  the  edges.  Sometimes,  instead  of  a  convex 
shape,  the  flutings  are  filled  with  a  flat  surface;  sometimes  they  are  ornamentally 
carved,  and  sometimes  on  pilasters,  etc.  Rudentures  are  used  in  relief  without 
flutings,  as  their  use  is  to  give  greater  solidity  to  the  lower  part  of  the  shaft,  and 
secure  the  edges.  They  are  generally  only  used  in  columns  which  rise  from  the 
ground  and  are  not  to  reach  above  one-third  of  the  height  of  the  shaft. 

Rustic  or  Rock  Work.  A  mode  of  building  in  imitation  of  nature.  This 
term  is  applied  to  those  courses  of  stone  work  the  face  of  which  is  jagged  or 
picked  so  as  to  present  a  rough  surface.  That  work  is  also  called  rustic  in  which 
the  horizontal  and  vertical  channels  are  cut  in  the  joinings  of  stones,  so  that  when 
placed  together  an  angular  channel  is  formed  at  each  joint.  Frosted  rustic  work 
has  the  margins  of  the  stones  reduced  to  a  plane  parallel  to  the  plane  of  the  wall, 
the  intermediate  parts  having  an  irregular  surface.  Vermiculated  rustic  work  has 
these  intermediate  parts  so  worked  as  to  have  the  appearance  of  having  been 
eaten  by  worms.  Rustic  chamfered  work,  in  which  the  face  of  the  stones  is 
smooth,  and  parallel  to  the  face  of  the  wall,  and  the  angles  beveled  to  an  angle  of 
one  hundred  and  thirty-five  degrees  with  the  face  so  that  two  stones  coming 
together  on  the  wall,  the  beveling  will  form  an  internal  right  argle. 

Sacristy.  A  small  chamber  attached  to  churches,  where  the  chalices,  vest- 
ments, books,  etc.,  were  kept  by  the  officer  called  the  sacristan.  In  the  early 
Christian  basilicas  there  were  two  semicircular  recesses  or  apsides,  one  on  each 
side  of  the  altar.  One  of  these  served  as  a  sacristy,  and  the  other  as  the  biblio- 
theca  or  library.  Some  have  supposed  the  sacristy  to  have  been  the  place  where 
the  vestments  were  kept,  and  the  vestry  that  where  the  priests  put  them  on;  but 
we  find  from  Durandus  that  the  sacrarium  was  used  for  both  these  purposes. 
Sometimes  the  place  where  the  altar  stands  enclosed  by  the  rails  has  been  called 
sacrarium. 

Saddle  Bars.     Narrow  horizontal  iron  bars  passing  from  mullion  to  mullion, 

and  often  through  the  whole  window,  from  side  to  side,  to  steady  the  stone  work, 

and  to  form  stays,  to  which  the  lead  work  is  secured.     When  the  bays  of  the 

.  windows  are  wide,  the  lead  lights  are  further  strengthened  by  upright  bars 

passing  through  eyes  forged  on  the  saddle  bars,  and  called  stanchioni.    When 


Glossary  lg43 

Scoddle  bars  pass  right  through  the  mullions  in  one  piece,  and  are  secured  to  the 
jambs,  thfry  have  sometimes  been  called  stay  bars. 

Sagging.  The  bending  of  a  body  in  the  middle  by  its  own  weight,  or  the  load 
upon  it. 

Salient.     A  projection. 

Salon.  A  spacious  and  elegant  apartment  for  the  reception  of  company,  or 
for  state  purposes,  or  for  the  rece|5tion  of  paintings,  and  usually  extending 
through  two  stories  of  the  house.  It  may  be  square,  oblong,  polygonal,  or 
circular. 

Sanctuary.  That  part  of  a  church  where  the  altar  is  placed;  also,  the  most 
sacred  or  retired  part  of  a  temple.     A  place  for  divine  worship;  a  church. 

Sanctus  Bell-cot,  or  Turret.  A  turret  or  enclosure  to  hold  the  small  bell 
sounded  at  various  parts  of  the  service,  particularly  where  the  words  "Sanctus," 
etc.,  are  read.  This  differs  but  little  from  the  common  bell-cot,  except  that  it  is 
generally  on  the  top  of  the  arch  dividing  the  nave  from  the  chancel.  Sometimes, 
however,  the  bell  seems  to  have  been  placed  in  a  cot  outside  the  wall.  In  Eng- 
land sanctus  bells  have  also  been  placed  over  the  gables  of  porches.  In  Conti- 
nental Europe  they  run  up  into  a  sort  of  small  slender  spire,  ca-Wed  fleche  in 
France,  and  guglio  in  Italy. 

Saracenia  Architecture.  That  Eastern  style  employed  by  the  Saracens,  and 
which  distributed  itself  over  the  world  with  the  religion  of  Mahomet.  It  is  a 
modification  and  combination  of  the  various  styles  of  the  countries  which  they 
conquered. 

Sarcophagus.  A  tomb  or  coffin  made  of  stone,  and  intended  to  contain  the 
body. 

Sash.     The  framework  which  holds  the  glass  in  a  window.  * 

Scabble.  To  dress  off  the  rougher  projections  of  stones  for  rubble  masonry 
with  a  stone  axe  or  scabbling  ham.mer. 

Scagliola.  An  imitation  of  colored  marbles  in  pla.s.ter  work,  made  by  a  com- 
bination of  gypsum,  glue,  isinglass,  and  coloring  matter,  and  finished  with  a  high 
polish,  invented  between  1600  and  1649. 

Scantling.  The  dimensions  of  a  piece  of  timber  in  breadth  and  thickness; 
also,  studding  for  a  partition,  when  under  five  inches  square. 

Scarfing.  The  joining  and  bolting  of  two  pieces  of  timber  together  trans- 
versely, so  that  the  two  appear  as  one. 

Sconce.     A  fixed  hanging  or  projecting  candlestick. 

Scotia.  A  concave  molding,  most  commonly  used  in  bases,  which  projects  a 
deep  shadow  on  itself,  and  is  thereby  a  most  effective  molding  under  the  eye, 
as  in  a  base.  It  is  like  a  reversed  ovolo,  or,  rather,  what  the  mold  of  an  ovolo 
would  present. 

Scratch  Coat.  The  first  coat  of  plaster,  which  is  scratched  to  afford  a  bond 
for  the  second  coat. 

Screeds.  Long  narrow  strips  of  plaster  put  on  horizontally  along  a  wall,  and 
carefully  faced  out  of  wind,  to  serve  as  guides  for  plastering  the  wide  mtervals 
between  them.  .  . 

Screen.     Any  construction  subdividing  one  part  of  a  h"Mmgf™m  another 
as  a  choir,  chantry,  chapel,  etc.     The  eariiest  screens  are  '^e  low  ^arbk  P^dia 
shutting  off  the  chorus  cantantium  in  the  Rr^K^l'     .  ,'nd  nresbvt«s     The 
cancelli  enclosing  the  bema,  altar,  and  seats  of  the  ^f  °P^  f  "^  p^'.y^^^^^^^^ 
chief  screens  in  a  church  are  those  which  enclose  the  choir  or  the  place  where 


1844  Glossary  Part  3 

the  breviary  services  are  recited.  In  Continenta'  Europe  this  is  done  not  only  by 
doors  and  screen  work,  but  also,  when  these  are  of  open  work,  by  cur^ins,  the 
laity  having  no  part  in  these  services.  In  England  screens  were  of  two  kinds: 
one,  of  open  wood-work,  generally  called  rood-screens  or  jubes,  and  which  the 
French  call  grilles,  clotures  du  chceiir;  the  other,  massive  enclosures  of  stone  work 
enriched  with  niches,  tabernacles,  canopies,  pinnacles,  statues,  crestings,  etc.,  as 
at  Canterbury,  York,  Gloucester,  and  many  other  places. 

Scribing.     Fitting  wood-work  to  an  irregular  surface. 

Section.  A  drawing  showing  the  internal  heights  of  the  various  parts  of  a 
building.  It  supposes  the  building  to  be  cut  through  entirely,  so  as  to  exhibit 
the  walls,  the  heights  of  the  internal  doors  and  other  apertures,  the  heights  of 
the  stories,  thicknesses  of  the  floors,  etc..  It  is  one  of  the  species  of  drawings 
necessary  to  the  exhibition  of  a  Design. 

Sedilia.  Seats  used  by  the  celebrants  during  the  pauses  in  the  mass.  They 
are  generally  three  in  number  —  for  the  priest,  deacon,  and  sub-deacon  —  and 
are  in  England  almost  always  a  species  of  niches  cut  into  the  south  walls  of 
churches,  separated  by  shafts  or  by  a  species  of  mullions,  and  crowned  with 
canopies,  pinnacles,  and  other  enrichments  more  or  less  elaborate.  The  piscina 
and  ambry  sometimes  are  attached  to  them.  In  Continental  Europe  the  scdiha 
are  often  movable  seats;   a  single  stone  seat  has  rarely  been  found. 

Set-off.  The  horizontal  line  shown  where  a  wall  is  reduced  in  thickness,  and, 
consequently,  the  part  of  the  thicker  portion  appears  projecting  before  the 
thinner.  In  plinths  this  is  generally  simply  chamfered.  In  other  parts  of  work 
the  set-off  is  generally  concealed  by  a  projecting  string.  Where,  as  in  parapets, 
the  upper  part  projects  before  the  lower,  the  break  is  generally  hid  by  a  corbei 
table.  The  portions  of  buttress  caps  which  recede  one  behind  another  are  also 
called  set-offs. 

Shaft.  In  Classical  architecture  that  part  of  a  column  between  the  necking 
and  the  apophyge  at  the  top  of  the  base.  In  later  times  the  term  is  applied  to 
slender  columns  either  standing  alone  or  in  connection  with  pillars,  buttresses, 
jambs,  vaulting,  etc. 

Shed  Roof,  or  Lean-to.  A  roof  with  only  one  set  of  rafters,  falling  from 
a  higher  to  a  lower  wall,  like  an  aisle  roof. 

.  Shore.  A  piece  of  timber  placed  in  an  oblique  direction  to  support  a  building 
or  wall  temporarily  while  it  is  being  repaired  or  altered. 

Shrine.  A  sort  of  ark  or  chest  to  hold  relics.  It  is  sometimes  merely  a  small 
box,  generally  with  a  raised  top  Hke  a  roof;  sometimes  an  actual  model  of 
churches;  'sometimes  a  large  construction,  like  that  of  Edward  the  Confessor  at 
Westminster,  of  St.  Genevieve  at  Paris,  etc.  Many  are  covered  with  jewels  ii 
the  richest  way;   that  of  San  Carlo  Borromeo,  at  Milan,  is  of  beaten  silver. 

Sills.  Are  the  timbers  on  the  ground  which  support  the  posts  and  superstruc- 
ture of  a  timber  building.  The  term  is  most  frequently  applied  to  those  pieces 
of  timber  or  stone  at  the  bottom  of  doors  or  windows. 

Skewback.     The  inclined  stone  from  which  an  arch  springs. 

Skirtings.  The  narrow  boards  which  form  a  plinth  around  the  margin  of  a 
floor,  now  generally  called  the  base. 

Sleeper.     A  piece  of  timber  laid  on  the  ground  to  receive  floor  joists. 

Soffit.  The  lower  horizontal  face  of  anything  as,  for  example,  of  an  entab- 
lature resting  on  and  lying  open  between  the  columns,  or  the  under  face  of  an  arch 
where  its  thickness  is  seen. 


Glossary  1845 

Sound  Board.     The  covering  of  a  pulpit  to  deflect  the  sound  into  a  church, 

Spall.     Bad  or  broken  brick;   stone  chips. 

Span.     The  distance  between  the  supports  of  a  beam,  girder,  arch,  truss,  etc 

Spandrel,  or  Spandril.  The  space  between  any  arch  or  curved  brace  and  the 
level  label,  beams,  etc.,  over  the  same.  The  spandrels  over  doorways  in  Perpen- 
dicular works  are  generally  richly  decorated. 

Specification.  Architect's.  The  designation  of  the  kind,  quality,  and 
quantity  of  work  and  material  to  go  in  a  building,  in  conjunction  with  the  working 
drawings. 

Spire.  A  sharply  pointed  pyramid  or  large  pinnacle,  generally  octagonal  in 
England,  and  forming  a  finish  to  the  tops  of  towers.  Timber  spires  are  very 
common  in  England.  Some  are  covered  with  lead  in  flat  sheets,  others  with  the 
same  metal  in  narrow  strips  laid  diagonally.  Very  many  are  covered  with 
shingles.  In  Continental  Europe  there  are  some  elegant  examples  of  spires  of 
open  timber  work  -covered  with  lead. 

Splayed.  The  jamb  of  a  door,  or  anything  else  of  which  one  side  makes  an 
oljlique  angle  with  the  other. 

Springer.  The  stone  from  which  an  arch  springs;  in  some  cases  this  is  a 
capital,  or  impost;  in  other  cases  the  moldings  continue  down  the  pier.  The 
lowest  stone  of  the  gable  is  sometimes  called  a  springer. 

Squinches.  Small  arches  or  corbeled  set-offs  running  diagonally  and,  as  it 
were,  cutting  off  the  corners  of  the  interior  of  towers,  to  bring  them  from  the 
square  to  the  octagon,  etc.,  to  carry  the  spire. 

Squint.  An  oblique  opening  in  the  wall  of  a  church;  especially,  in  mediaeval 
architecture,  an  opening  so  placed  as  to  afford  a  view  of  the  high  altar  from  the 
transept  or  aisles. 

Staging.  A  structure  of  posts  and  boards  for  supporting  workmen  and 
material  in  building. 

Stall.  A  fixed  seat  in  the  choir  for  the  use  of  the  clergy.  In  early  Christian 
times  the  thronus  cathedra,  or  seat  of  the  bishop,  was  in  the  center  of  the  apsis 
or  bema  behind  the  altar,  and  against  the  wall;  those  of  the  presbyters  also  were 
against  the  wall,  branching  off  from  side  to  side  around  the  semicircle.  In  later 
times  the  stalls  occupied  both  sides  of  the  choir,  return  seats  being  placed  at  the 
ends  for  the  prior,  dean,  precentor,  chancellor,  or  other  officers.  In  general,  in 
cathedrals,  each  stall  is  surmounted  by  tabernacle  work,  and  rich  canopies, 
generally  of  oak. 

Stanchion.  A  word  derived  from  the  French  etancon,  a  wooden  post,  applied 
to  the  upright  iron  bars  which  pass  through  the  eyes  of  the  saddle  bars  or  hori- 
zon^tai  irons  to  steady  the  lead  lights.  The  French  call  the  latter  /m..r...,  the 
stanchions  montants,  and  the  whole  arrangement  armature.  Stanchions  fre- 
quently finish  with  ornamental  heads  forged  out  of  the  iron. 

Steeple.    A  general  name  for  the  whole  arrangement  of  tower,  belfry,  spire,  etc. 

Stereobate.  A  basement,  distinguished  from  the  nearly  equivalent  term  sty- 
lobate  by  the  absence  of  columns. 

Stile.     The  upright  piece  in  framing  or  paneling. 

Stilted.  Anything  raised  above  its  usual  level  An  arch  is  stilted  when  its 
centre  is  raised  above  theline  from  which  the  arch  appears  to  spring. 

Stoop.  A  seat  before  the  door;  often  a  porch  with  a  balustrade  and  seats  on 
the  sides. 


1846  Glossary  Part  3 

Stoup.  A  basin  for  holy  water  at  the  entrance  of  Roman  Catholic  churches, 
into  wliich  all  who  enter  dip  their  lingers  and  cross  themselves. 

Straight  Arch.  A  form  of  arch  in  which  the  intrados  is  straight,  but  with  its 
joints  radiating  as  in  a  common  arch. 

Strap.  An  iron  plate  for  connecting  two  or  more  timbers,  to  which  it  is 
screwed  by  bolts.     It  generally  passes  around  one  of  the  timbers. 

Stretcher.     A  brick  or  block  of  masonry  laid  lengthwise  of  a  wall. 

String  Board.  A  board  placed  next  to  the  well-hole  in  wooden  stairs,  termi- 
nating the  ends  of  the  steps.  The  string  piece  is  the  piece  of  board  put  under 
the  treads  and  risers  for  a  support,  and  forming  the  support  of  the  stair. 

String-course.  A  narrow,  vertically  faced  and  slightly  projecting  course  in 
an  elevation.  If  window-sills  are  made  continuous,  they  form  a  string-course; 
but  if  this  course  is  made  thicker  or  deeper  than  ordinary  window-sjlls,  or  covers 
a  set-off  in  the  wall,  it  becomes  a  blocking-course.  Also,  horizontal  moldings 
running  under  windows,  separating  the  walls  from  the  plain  part  of  the  parapets, 
dividing  towers  into  stories  or  stages,  etc.  Their  section  is  much  the  same  as 
the  labels  of  the  respective  periods;  in  fact,  these  last,  after  pa::sing  round  the 
windows,  frequently  run  on  horizontally  and  form  strings.  Like  labels,  they  are 
often  decorated  with  foliages,  ball-flowers,  etc. 

Studs,  or  Studding.  The  small  timbers  used  in  partitions  and  outside  wooden 
walls,  to  which  the  laths  and  boards  are  nailed. 

Style.  The  term  style  in  architecture  has  obtained  a  conventional  meaning 
beyond  its  simpler  one,  which  applies  only  to  columns  and  columnar  arrange- 
ments. It  is  now  used  to  signify  the  differences  in  the  moldings,  general  out- 
lines, ornaments,  and  other  details  which  exist  between  the  works  of  various 
nations,  and  also  those  differences  which  are  found  to  exist  between  the  works  of 
any  nation  at  different  times. 

Stylobate.  A  basement  to  columns.  Stylobate  is  synonymous  with  pedeslul, 
but  is  applied  to  a  continued  and  unbroken  substructure  or  basement  to  columns, 
while  the  latter  term  is  confined  to  insukited  supports.  The  Greek  temples  gen- 
erally had  three  or  more  steps  all  around  the  temple,  the  base  of  the  column 
resting  on  the  top  step;   this  was  the  stylobate. 

Subsellium.  A  name  sometimes  given  to  the  seat  in  the  stalls  of  churches; 
same  as  miserere. 

Summer.  A  girder  or  main-beam  of  a  floor;  if  supported  on  two-story  posts 
and  open  below,  it  is  called  a  Brace-summer. 

Surbase.  A  cornice  or  series  of  moldings  on  the  top  of  the  base  of  a  pedestal, 
podium,  etc.;  a  molding  above  the  base. 

Surface.    To  make  plane  and  smooth. 

Systyle.     An  intercolumniation  to  which  two  diameters  are  assigned. 

Tabernacle.  A  species  of  niche  or  recess  in  which  an  image  may  be  placed. 
They  are  generally  highly  ornamented  and  often  surmounted  with  crocketed 
gables.  The  word  tabernacle  is  alsc  often  used  to  denote  the  receptacle  for  relics, 
which  was  often  made  in  the  form  of  a  small  house  or  church. 

Tabernacle  Work.  The  rich  ornamental  tracery  forming  the  canopy,  etc., 
to  a  tabernacle,  is  called  tabernacle  work;  it  is  common  in  the  stalls  and  screens 
•f  cathedrals,  and  in  them  is  generally  open  or  pierced  through. 

Tail  Trimmer.  A  trimmer  next  to  the  wall,  into  which  the  ends  of  joists  are 
fastened  to  avoid  flues. 


Glossary  2^^^ 

Tamp.     To  pound  the  earth  down  around  a  wall  after  it  has  been  thrown  in. 

Tapestry.  A  kind  of  woven  hangings  of  wool  or  silk,  ornamented  with  figures 
and  used  formerly  to  cover  and  adorn  the  walls  of  rooms.  They  were  often  of 
the  most  costly  materials  and  beautifully  embroidered. 

Temple.  An  edifice  destined,  in  the  earliest  times,  for  the  public  exercise  of 
religious  worship. 

Templet,  or  Template.  A  mold  used  by  masons  for  cutting  or  setting  work. 
A  short  piece  of  timber  sometimes  laid  under  a  girder. 

Terminal.     Figures  of  which  the  upper  parts  only,  or  perhaps  the  head  and 
shoulders  alone,  are  carved,  the  rest  running  into 
a  parallelopiped,  and  sometimes  into  a  diminishing 
pedestal,  with  feet  indicated  below,  or  even  with- 
out them,  are  called  terminal  figures. 

Terra-cotta.  Baked  clay  of  a  fine  quahty. 
Much  used  for  b'as-reliefs  for  adorning  the  friezes 
of  temples.  In  modern  times  employed  for  archi- 
tectural ornaments,  statues,  vases,  etc. 

Tessellated  Pavements.  Those  formed  of 
*esserae,  or,  as  some  write  it,  tessellae,  or  small 
'^ubes  from  half  an  inch  to  an  inch  square,  like 
*ice,  of  pottery,  stone,  marble,  enamel,  etc. 

Tetrastyle.     A  portico  of  four  columns  in  front. 

Tholobate.  That  on  which  a  dome  or  cupola 
rests.  This  is  a  term  not  in  general  use,  but  it  is  not 
the  less  of  useful  application.  What  is  generally 
termed  the  attic  above  the  peristyle  and  under  the  cupola  of  St.  Paul's,  London, 
would  be  correctly  designated  the  tholobate.  A  tholobate  of  a  different  descrip- 
tion, and  one  to  which  no  other  name  can  well  be  applied,  is  the  circular  sub- 
structm"e  to  the  cupola  of  the  University  College,  London. 

Throat.  A  channel  or  groove  made  on  the  under-side  of  a  string-course, 
coping,  etc.,  to  prevent  water  from  running  inward  toward  the  walls. 

Tie.  A  timber,  rod,  chain,  etc.,  binding  two  bodies  together,  which  have  a 
tendency  to  separate  or  diverge  from  each  other.  The  tie-beam  connects  the 
bottom  of  a  pair  of  principal  rafters,  and  prevents  them  from  bursting  out  the 
wall. 

Tiles.  Flat  pieces  of  clay  burned  in  kilns,  to  cover  roofs  in  place  of  slates  or 
lead.  Also,  flat  pieces  of  burned  clay,  either  plain  or  ornamented,  glazed  or 
unglazed,  used  for  floors,  wainscoting,  and  about  fireplaces,  etc.  Small  square 
pieces  of  marble  are  also  called  tile. 

Tongue.     The  part  of  a  board  left  projecting,  to  be  inserted  into  a  groove. 

Tooth  Ornament.  One  of  the  peculiar  marks  of  the  Early  English  period  of 
Gothic  architecture,  generally  inserted  in  the  hollow  moldings  of  doorways, 
windows,  etc. 

Torso.  A  mutilated  statue  of  which  nothing  remains  but  the  trunk.  Columns 
with  twisted  shafts  have  also  this  term.     Of  this  kind  there  are  several  varieties. 

Torus.     A    protuberance    or    swelling,    a    molding    ^ r-r^ 


ANCIENT  TERMINI 


ig,    a    momuig    ^ 
whose  form  is  convex,  and  generally  nearly  approaches  T 
a  semicircle.     It  is  most  frequently  used  in  bases,  and 
i.s  generally  the  lowest  molding  in  a  base. 


-L-4.- 


i; 


1S48  Glossary  Part  3 

Tower.  An  elevated  building  originally  designed  for  purposes  of  defence. 
Those  buildings  are  of  the  remotest  antiquity,  and  are,  indeed,  mentioned  in  the 
earliest  Scriptures.  In  mediaeval  times  tl\ey  were  generally  attached  to  churches, 
to  cemeteries,  to  castles,  or  used  as  bell-towers  in  public  places  of  large  cities. 
In  churches,  the  towers  of  the  Saxon  period  were  generally  square.  Norman 
towers  were  also  generally  square.  Many  were  entirely  without  buttresses; 
others  had  broad,  flat,  shallow  projections  which  served  for  this  purpose.  The 
lower  windows  were  very  narrow,  with  extremely  wide  splays  inside,  probably  in- 
tended to  be  defended  by  archers.  The  upper  windows,  like  those  of  the  preced- 
ing style,  were  generally  separated  into  two  lights,  but  by  a  shaft  or  short  column, 
and  not  by  a  baluster.  Early  English  towers  were  generally  taller,  and  of  more 
elegant  proportions.  They  almost  always  had  large  projecting  buttresses,  and 
frequently  stone  staircases.  The  lower  windows,  as  in  the  former  style,  were 
frequently  mere  arrow-slits;  the  upper  were  in  couplets  or  triplets,  and  sometimes 
the  tower  top  had  an  arcade  all  around.  The  spires  were  generally  broach  spires; 
but  sometimes  the  tower  tops  finished  with  corbel  courses  and  plain  parapets,  and 
(rarely)  with  pinnacles.  There  are  a  few  Early  English  towers  which  break  into 
the  octagon  from  the  square  toward  the  top,  and  still  fewer  which  finish  with  two 
gables.  Both  these  methods  of  termination,  however,  are  common  in  Continental 
Europe.  At  Vendome,  Chartres,  and  Senlis  the  towers  have  octagonal  upper 
stages  surrounded  with  pinnacles,  from  which  elegant  spires  arise.  In  the  North 
of  Italy,  and  in  Rome,  they  are  generally  tall  square  shafts  in  four  to  six  stages, 
without  buttresses,  with  couplets  or  triplets  of  semicircular  windows  in  each 
stage,  generally  crenellated  at  top,  and  covered  with  a  low  pyramidal  roof.  The 
well-known  leaning  tower  at  Pisa  is  cylindrical,  in  five  stories  of  arcaded  colon- 
nades. In  Ireland  there  are  in  some  of  the  churchyards  very  curious  round 
towers. 

Tracery.  The  ornamental  filling  in  of  the  heads  of  windows,  panels,  circular 
windows,  etc.,  which  has  given  such  characteristic  beauty  to  the  architecture  of 
the  fourteenth  century.  Like  almost  everything  connected  with  mediaeval  archi- 
tecture, this  elegant  and  sometimes  fairy-like  decoration  seems  to  have  sprung 
from  the  smallest  beginnings.  The  circular-headed  window  of  the  Norman? 
gradually  gave  way  to  the  narrow-pointed  lancets  of  the  Early  English  period, 
and^  as  less  light  was  afforded  by  the  latter  system  than  by  the  former,  it  was 
necessary  to  have  a  greater  number  of  windows;  and  it  was  found  convenient  to 
group  them  together  in  couplets,  triplets,  etc.  When  these  couplets  were  as- 
sembled under  one  label,  a  sort  of  vacant  space  or  spandrel  was  formed  over  the 
lancets  and  under  the  label.  To  relieve  this,  the  first  attempts  were  simply  to 
perforate  this  flat  spandrel,  first  by  a  simple  lozenge-shaped  or  circular  opening, 
and  afterward  by  a  quatrefoil.  By  piercing  the  whole  of  the  vacant  spaces  in 
the  window  head,  carrying  moldings  around  the  tracery,  and  adding  cusps  to  it, 
the  formation  of  tracery  was  complete,  and  its  earliest  result  was  the  beautiful  _ 
geometrical  work  such  as  is  found  at  Westminster  Abbey. 

Transept.  That  portion  of  a  church  which  passes  transversely  between  the 
nave  and  choir  at  right  angles,  and  so  forms  a  cross  on  the  plan. 

Transom.  The  horizontal  construction  which  divides  a  window  into 
heights  or  stages.  Transoms  are  sometimes  simple  pieces  of  mullions  placed 
transversely  as  cross-bars,  and  in  later  times  are  richly  decorated  with 
cuspings,  etc. 

Traverse.  To  plane  in  a  direction  across  the  grain  of  the  wood,  as  to  traverse 
a  floor  by  planing  across  the  boards. 

Tread.    The  horizontal  part  of  a  step  of  a  stair. 


Glossary  1S49 

Trefoil.  A  cusping  the  outline  of  which  is  derived  from  a  three-leaved  flowci 
or  leaf,  as  the  quatrefoil  and  cinque-foil  are  from  those  with  four  and  five. 

Trellis.     Lattice-work  of  metal  or  wood  for  vines  to  run  on. 

Trestle.  A  movable  frame  or  support  for  anything;  when  made  of  a  cross 
piece  with  four  legs  it  is  called  by  carpenters  a  horse. 

Triforium.  The  arcaded  story  between  the  lower  range  of  piers  and  arches 
and  the  clere-story.  The  name  has  been  supposed  to  be  derived  from  trcs  and 
fores  —  three  doors,  or  openings  —  that  being  a  frequent  number  of  arches  in 
each  bay. 

Triglyph.  The  vertically  channeled  tablets  of  the  Doric  frieze  are  called 
triglyphs,  because  of  the  three  angular  channels  in  them  —  two  perfect  and  one 
divided  —  the  two  chamfered  angles  or  hemiglyphs  being  reckoned  as  one.  The 
square  sunk  spaces  between  the  triglyphs  on  a  frieze  are  called  metopes. 

Trim.     Of  a  door,  sometimes  used  to  denote  the  locks,  knobs,  and  hinges. 

Trimmer.     The  beam  or  floor  joist  into  which  a  header  is  framed. 

Trimmer  Arch.  An  arch  built  in  front  of  a  fireplace,  in  the  thickness  of  the 
floor,  between  two  trimmers.  The  bottom  of  the  arch  starting  from  the  chimney 
and  tlie  top  pressing  against  the  header. 

Tuck-pointing.  Marking  the  joints  of  brickwork  with  a  narrow  parallel 
ridge  of  fine  putty.  • 

Tudor  Style.  The  architecture  which  prevailed  in  England  during  the  reign 
of  the  Tudors;  its  period  is  generally  restricted  to  the  end  of  the  reign  of  Heniy 
VIII. 

Turret.  A  small  tower,  especially  at  the  angles  of  larger  buildings,  sometimes 
overhanging  and  built  on  corbels,  and  sometimes  rising  from  the  ground. 

Tuscan  Order.     The  plainest  of  the  five  orders  of  Classic  architecture. 

Tympanum.  The  triangular  recessed  space  enclosed  by  the  cornice  which 
bounds  a  pediment.  The  Greeks  often  placed  sculptures  representing  subjects 
connected  with  the  purposes  of  the  edilice  in  the  tympana  of  temples,  as  at  the 
Parthenon  and  ^gina. 

Under-croft.     A  vaulted  chamber  under  ground. 

Upset.  To  thicken,  and  shorten  as  by  hammering  a  heated  bar  of  iron  on  the 
end. 

Vagina.  The  upper  part  of  the  shaft  of  a  terminus,  from  which  the  bust  or 
figure  seems  to  rise. 

Valley.     The  internal  angle  formed  by  two  inclined  sides  of  a  roof. 

Valley  Rafters.  Those  which  are  disposed  in  the  internal  angle  of  a  roof  to 
form  the  valleys. 

Vane.  The  weathercock  on  a  steeple.  In  eariy  times  it  seems  to  have  been 
of  various  forms,  as  dragons,  etc.;  but  in  the  Tudor  period  the  favonte  design 
was  a  beast  or  bird  sitting  on  a  slender  pedestal,  and  carrying  an  upn^ht  rod,  on 
which  a  thin  plate  of  metal  is  hung  Hke  a  flag,  ornamented  in  various  ways. 

Vault.     An  arched  ceiling  or  roof.     A  vault  is.  indeed,  a  laterally  co^^^^^^^^^^ 
series  of  arches.     The  arch  of  a  bridge  is,  strictly  speaking,  a  vault.     I^™^ 
vaults  are  said  to  be  groined.     See  Gro^n^d  VaulHng  for  fuller  description  of 

""^Verge.     The  edge  of  the  riling,  slate  or  shingles,  projecting  over  the  gable  of  a 
roof,  that  on  the  horizontal  portion  being  called  eaves. 


1850 


Glossary 


Pari  i 


VERMICULATED 


Verge  Board.  Often  corrupted  into  Barge  Board;  the  board  under  the  verge 
of  gables,  sometimes  molded,  and  often  very,  richly  carved,  perforated,  and 
cuspcd,  and  frequently  having  pendants,  and  sometimes  finials,  at  the  apex. 

Vermiculated.  Stones,  etc.,  worked  so  as  to  have  the  appearance  of  having 
been  worked  by  worms.  

Vestibule.     An  anti-hall,  lobby,  or  porch. 

Vestry.  A  room  adjoining  a  church,  where  the  vest- 
ments of  the  minister  are  kept  and  parish  meetings  held. 
In  American  Protestant  churches,  the  Sunday-school 
room  is  often  called  the  vestry. 

Viaduct.  A  structure  of  considerable  magnitude,  and 
usually  of  masonry,  for  carrying  a  railway  across  a 
valley. 

Vignette.  A  running  ornament,  representing,  as  its  name  imports,  a  little 
vine,  with  branches,  leaves,  and  grapes.  It  is  common  in  the  Tudor  period, 
and  runs  or  roves  in  a  large  hollow  or  casement.     It  is  also  called  Trayle. 

Villa.     A  country  house  for  the  retreat  of  the  rich. 

Volute.  .The  convolved  or  spiral  ornament  which  forms  the  characteristic  of 
the  Ionic  capital.  Volute,  scroll,  helix,  and  cauliculus  are  used  indifferently  for 
the  angular  horns  of  the  Corinthian  capital. 

Voussoir.  One  of  the  wedge-Uke  stones  which  form  an  arch;  the  middle  one 
is  called  the  key-stone.  .  ' 

Wainscot.     The  wooden  lining  of  walls,  generally  in  panels. 

Wall  Plates.  Pieces  of  timber  which  are  placed  on  top  of  brick  or  stone  walls 
so  as  to  form  the  support  to  the  roof  of  a  building. 

Warped.     Twisted  out  of  shape  by  seasoning. 

Water  Table.  A  slight  projection  of  the  lower  masonry  or  brickwork  on  the 
outside  of  a  wall  a  few  feet  above  the  ground  as  a  protection  against  rain. 

Weather  Boarding.  Boards  lapped  over  each  other  to  prevent  rain,  etc., 
from  passing  through. 

Weathering.  A  slight  fall  on  the  top  of  cornices,  window-sills,  etc.,  to  throw 
off  the  rain. 

Wicket.  A  small  door  opening  in  a  larger.  They  are  common  in  medixval 
doors,  and  were  intended  to  admit  single  persons,  and  guard  against  sudden 
surprises. 

Wind.  A  turn,  a  bend.  A  wall  is  out  of  wind  when  it  is  a  perfectly  flat 
surface. 

Wing.     A  side  building  less  than  the  main  building. 

Withes.     The  partition  between  two  chimney  flues  in  the  same  stack. 


A 


Architectural  Terms  as  Defined  in  Various  Building  Laws     1851 


ARCHITECTURAL  TERMS  AS  DEFINED  IN  VARIOUS 
BUILDING  LAWS 

Compiled  by  The  American  Architect  and  Building 
News,  Page  150,  Vol.  XXXIII 

(Republished  by  permission  of  Ticknor  &  Co.) 


Terms  Defined 


[The  following  terms  chance  to  be  defined  in  sundry  building  codes,  which  are 
nentioned  in  each  case.  The  fact  that  other  codes  are  not  mentioned  is  not  neces- 
arily  a  proof  that  the  term  is  not  also  elsewhere  in  use  as  defined.] 

Adjoining  Owner.  The  owner  of  the  premises  adjoining  those  on  which 
vork  is  doing  or  to  be  done.     [District  of  Columbia.] 

Alteration.  Any  change  or  addition  except  necessary  repairs  in,  to,  or  upon 
ny  building  affecting  an  external,  party,  or  partition  wall,  chimney,  floor,  or 
tairway,  and  "to  alter"  means  to  make  such  change  or  addition.  [Boston  and 
)enver] 

Appendages.  Dormer-windows,  cornices,  moldings,  bay-windows,  towers, 
pires,  ventilators,  etc.     [Chicago  and  Minneapolis.] 

Areas.  Sub-surface  excavations  adjacent  to  the  building-line  for  lighting  or 
entilation  of  cellars  or  basements.     [District  of  Columbia.] 

Attic  Story.  A  story  situated  either  in  whole  or  in  part  in  the  roof.  [Denver 
nd  District  of  Columbia-] 

Base.  "The  base  of  a  brick  wall"  means  the  course  immediately  above  the 
Dundation  wall.     [Cincinnati  and  Cleveland.] 

Basement  Story.  One  whose  floor  is  12"  or  more  below  the  sidewalk,  and 
.'hose  height  does  not  exceed  12'  in  the  clear;  all  such  stories  that  exceed  12' 
igh  shall  be  considered  as  first  stories.     [Chicago  and  Louisville.] 

A  story  whose  floor  is  12"  or  more  below  the  grade  of  sidewalk.     [Milwaukee.] 

A  story  whose  floor  is  3'  or  more  below  the  sidewalk,  and  whose  height  does 
ot  exceed  11'  in  the  clear;  all  such  stories  that  exceed  11'  high  shall  he  con-. 
idered  as  first  stories.     [Minneapolis.] 

A  story  suitable  for  habitation,  partially  below  the  level  of  the  adjoining  street 
r  ground.*     [District  of  Columbia  and  Denver.] 

(See  Cellar.) 

Bay-window.     A  first-floor  projection  for  a  window  other  than  a  tower-pro- 

ction  or  show-window.     [District  of  Columbia.] 

Any  projection  for  a  window  other  than  a  show-window.     [Denver.] 

Bearing  Walls.  Those  on  which  beams,  trusses,  or  girders  rest.  [New  York 
nd  San  Francisco.] 

Brick  Building.     A  building  the  walls  of  which  are  built  of  brick,  stone,  iron, 

other  substantial  and  incombustible  materials.  [Boston,  Denver,  and  Kansas 
'ity.] 

*  And  below  the  first  floor  of  joists.    [District  of  Columbia.] 


1852  Architectural  Terms  in  Building  Laws  Jrad 

Building.  Any  construction  within  the  scope  and  purview  of  these  regula- 
tions.    [District  of  Columbia.] 

Building  Line.  The  line  of  demarcation  between  public  and  private  space 
[District  of  Columbia.] 

Building  Owner.  The  owner  of  premises  on  which  work  is  doing  or  to  be 
done.     [District  of  Columbia.] 

Business  buildings  shall  embrace  all  buildings  used  principally  for  business 
purposes,  thus  including,  among  others,  hotels,  theaters,  and  office-buildings. 
[Chicago,  Louisville,  Milwaukee,  and  Minneapolis.] 

Cellar.  Basement  or  lower  story  of  any  building,  of  which  one-half  or  more 
of  the  height  from  the  floor  to  the  ceiling  is  below  the  level  of  the  street*  ad- 
joining.!    [Boston,  Denver,  and  Kansas  City.] 

Portion  of  building  below  first  floor  of  joists,  if  partially  or  entirely  belpw  the 
level  of  the  adjoining  parking,  street,  or  ground,  and  not  suitable  for  habitation. 
[District  of  Columbia.] 

Cement-mortar.  A  proper  proportion  of  cement  and  sand  without  the  ad- 
mixture of  lime.     [Kansas  City.] 

Division  Wall.  One  that  separates  part  of  any  building  from  another  part 
of  the  same  building.     [Cincinnati  and  Cleveland.] 

Floor-bearing  walls  extending  through  buildings  from  front  to  rear,  and  sepa- 
rating stores  and  tenements  in  buildings  or  blocks  owned  by  the  same  party. 
[Minneapolis.] 

(See  Partition-wall.) 

Dwelling-house  Class.  All  buildings  except  public  buildings  and  buildings 
of  the  warehouse  class.     [Cincinnati  and  Cleveland.] 

Shall  not  apply  to  buildings  accommodating  more  than  three  families.  [San 
Francisco.] 

External  Wall.  Every  outer  wall  or  vertical  enclosure  of  a  building  other 
than  a  party-wall.  [Boston,  Cincinnati,  Cleveland,  Denver,  District  of  Columbia, 
Kansas  City,  and  Providence.] 

First  Story.  The  story  the  floor  of  which  is  at  or  first  above  the  level  of  th€ 
sidewalk  or  adjoining  ground,  the  other  stories  to  be  numbered  in  regular  ^M 
cession,  counting  upward.     [Denver  and  District  of  Columbia.]  'IHI 

Footing  Course.  A  projecting  course  or  courses  under  base  of  foundation 
wall.     [Cincinnati  and  Cleveland.] 

Foundation.  That  portion  of  wall  below  level  of  street  curb,t  and,  where  the 
wall  is  not  on  a  street,  that  portion  of  wall  below  the  level  of  the  highest  ground 
next  to  the  wall.     [Boston,  Kansas  City,  New  York,  and  Providence.] 

Portion  of  exterior  wall  below  surface  of  adjoining  earth  or  pavement,  and 
portion  of  partition  or  party  wall  below  level  of  basement  or  cellar  floor.  [Dis- 
trict of  Columbia  and  Denver.] 

Foundation,  Basement,  or  Cellar  Walls.  That  part  of  walls  of  building  that 
is  below  the  floor  or  joists,  which  are  on  Or  next  above  the  grade  line.     [Detroit.] 

Portion  of  the  wall  below  the  level  of  street  curb,  in  front  of  the  central  line  of 
building.     [San  Francisco.] 

*  Ground.     [Providence.] 
t  And  not  suitable  for  habitation.     [Denver.] 

X  "  And    serve  as  supports   for   piers,  columns,  girders,  beams,  or  other   wi 
iNew  York.] 


1 


Architectural  Terms  as  Defined  in  Various  Building  Laws     1853 

Incombustible  Scantling  Partition.  One  plastered  on  both  sides  upon  iron 
lath  or  wire  cloth,  and  filled  in  with  brickwork  8"  high  from  floor,  provided  the 
building  is  not  over  80'  high.     [Chicago.] 

Incombustible  Roofing.  Covered  with  not  less  than  three  (3)  thicknesses 
roofing-felt,  and  good  coat  of  tar  and  gravel,  or  with  tin,  corrugated-iron,  or  other 
fire-resisting  material  with  standing-seam  or  lap-joint.     [Denver.] 

Lengths.  Walls  are  deemed  to  be  divided  into  distinct  lengths  by  return 
walls,  and  the  length  of  every  wall  is  measured  from  the  center  of  one  return  wall 
to  the  center  of  another,  provided  that  such  return  walls  are  external  or  party 
cross-walls  of  the  thickness  herein  required,  and  bonded  into  the  walls  so  deemed 
to  |je  divided.     [Cincinnati  and  Cleveland.] 

Inflammable  Material.  Dry  goods,  clothing,  millinery,  and  the  like  in 
stores,  flyings  or  goods  in  factories,  or  other  substance  readily  ignited  by  drop- 
pings or  flyings  from  electric  lights.     [Minneapolis.] 

Lodging-house.     A  building  in  which  persons  are  temporarily  accommodated 

with  sleeping*  apartments,  and  includes  hotels.     [Boston  and  Kansas  City.] 

Any  building  or  portion  thereof  in  which  persons  are  lodged  for  hire  for  less 
than  a  week  at  one  time.     [District  of  Columbia  and  Providence.] 

Any  building  or  portion  thereof  in  which  persons  are  lodged  for  hire  tempo- 
rarily, and  includes  hotels.     [Denver.] 

Mansard  Roof.  One  formed  with  an  upper  and  under  set  of  rafters,  the 
upper  set  more  inclined  to  the  horizon  than  the  lower  set.  [Denver  and  District 
oj  Columbia.] 

Oriel  Window.  A  projection  for  a  window  above  the  first  floor.  [Distria 
of  Columbia.] 

Partition.  An  interior  division  constructed  of  iron,  glass,  wood,  lath  and 
plaster,  or  other  destructible  natures.     [District  of  Columbia.] 

Partition-wall.  Any  interior  wall  of  masonry  in  a  building.  [Boston, 
Kansas  City,  and  Providence.] 

An  interior  wall  of  non-combustible  material.     [District  of  Columbia.] 

Any  interior  division  constructed  of  iron,  glass,  wood,  lath  and  plaster,  or 
any  combination  of  those  materials.     [Denver.] 

(See  Division  Wall.) 

Party-wall.  Every  wall  used,  or  built,  in  order  to  be  used,  as  a  separation  of 
two  or  more  buildings. f     [Boston,  Cincinnati,  Cleveland,  Denver,  Kansas  City, 

^^td  PTOV'tdEftCE  1 

A  wall  built  upon  dividing  line  between  adjoining  premises  for  their  common 
use.     [District  of  Columbia.] 

Parking.  The  space  between  the  sidewalk  and  the  building  line.  [District 
of  Columbia.] 

Parking  Line.  The  line  separating  parking  and  sidewalk.  [District  of 
Columbia.] 

PubUc  Building.  Every  building  used  as  church,  chapel,  or  other  place  of 
public  worship;  also  every  building  used  as  a  college  school  P"bl>chal^  hospital 
theater,  public  concert-room,  public  baU-room,  P"bl.c  lecture-room  or  for  any 
public  assemblage.  [Boston.  Chicago,  Cincnmh.  CMand.  Denver  Kansas 
City,  and  Minneapolis.] 


na^f 


1854  Architectural  Terms  in  Building  Laws  Pa^ 

Such  buildings  as  shall  be  owned  and  occupied  for  public  purposes  for  | 
State,  the  United  States,  the  corporation  of  the  City  of  Brooklyn,  or  other  pd 
schools  within  said  city.     [Brooklyn.] 

Public  Hall.  Every  theater,  opera-house,  hall,  church,  school,  or  other  b^ 
ing  intended  to  be  used  for  public  assemblage.     [Milwaukee  and  Louisville.] 

Return  Wall.     No  wall  subdividing  any  building  shall  be  deemed  a  return 
wall,  as  before  mentioned,  unless  it  is  two-thirds  the  height  of  the  externa^ 
party-walls.     [Cincinnati  and  Cleveland.] 

Shed.     A  skeleton  structure  for  storage  or  shelter.     [District  of  Columbia 

Open  structure,  enclosed  only  on  one  side  and  end,  and  erected  on  the  ground. 
[San  Francisco.] 

Open  or  closed  board  structure.     [Denver.] 

Show-window.  A  store-window  in  which  goods  are  displayed  for  sale  or 
advertisement.     [District  of  Columbia  and  Denver.] 

Square  thereof.  The  square  or  level  of  the  walls  before  commencing  the 
pitch  for  roof.     [District  of  Columbia.] 

Standard  Depth  for  Foundations.  For  brick  and  stone  buildings,  14' 
below  curb  line.     [San  Francisco.] 

Standard  Depth  of  Cellars.  16',  measured  down  from  sidewalk  grade  at 
property  line.     [Memphis.] 

Standard  Iron  Door.  Made  of  No.  12  plate- iron,  frame  or  continuous 
2"  X  2"  X  %"  angle-iron,  firmly  riveted.  Two  panel  doors,  to  have  proper  cross- 
bars, one  panel  on  either  side,  fastened  together  with  hooks  or  proper  bolts  top 
and  bottom,  and  with  not  less  than  two  lever-bars.  All  doors  hung  on  iron 
frames  of  %"  x  4"  iron,  securely  bolted  together  through  wall,  swung  on  three 
hinges,  fitting  close  to  frame  all  around;  sill  between  doors,  iron,  brick,  or  stone, 
to  rise  not  less  than  two  (2)  inches  above  floor  on  each  side  of  opening.  Lintel 
over  door,  brick,  iron,  or  stone.  Floors  of  basement,  when  doors  are  to  swing, 
stone  or  cement,  in  no  case  wood.     [Denver.] 

Standard  Skylight.  Constructed  of  wrought-iron  frames,  with  hammered 
or  desk-light  glass  not  less  than  ^-'2"  thick;  not  larger  than  10'  by  12',  except  by 
special  permission  of  the  Inspector.     [Denver.] 

Storehouse.     (See  Warehouse  Class.) 

Street.     All  streets,  avenues,  and  pubhc  alleys.     [Minneapolis.] 

Tenement-house.  A  building  which,  or  any  portion  of  which,  is  to  be  occu- 
pied, or  is  occupied,  as  a  dwelling  by  more  than  three*  families  living  independ- 
ently of  one  another,  and  doing  their  cooking  upon  the  premises.  [Boston, 
Denver,  and  Kansas  City.] 

Or  by  more  than  two  familiesf  above  the  second  floor,  so  living  and  cooking. 
[Bosfon  and  Kansas  City.] 

Building  which  shall  contain  more  than  two  rooms  in  front  on  each  floor,  or 
which  shall  be  built  with  a  passage  or  arched  way  between  distinct  parts  of  the 
same  building,  or  which  building  shall  be  intended  for  the  separate  accommoda- 
tion of  different  families  or  occupants.     [Charleston.] 

Theater.  Public  hall  containing  movable  scenery  or  fixed  scenery  which  is 
not  made  of  metal,  plaster,  or  other  incombustible  material.  [Chicago,  Louis- 
ville, and  Milwaukee.] 

*  Two  instead  of  three.     [District  of  Columbia  and  Minneapolis.] 
t  Upon  one  floor,  but  having  a  common  right  in  the  halls,  stairways,  yards,  etc.     [Provi' 
denc€.] 


Architectural  Terms  as  Defined  in  Various  Building  Laws     1855 

Thickness  of  a  Wall.     The  minimum  thickness  of  such  wall.*     [Boston, 

ticinnali,  Cleveland,  Kansas  City,  Milwaukee,  and  Providence.] 

Tinned  Covered  Fire-door.     Wood  doors  or  shutters,  double  thickness  of 

jod,  cross  or  diagonal  construction,  covered  on  both  sides  and  all  edges  with 

eet-tin,  joints  securely  clinched  and  nailed.     [Denver.] 

Tower  Projection.     A  projection  designed  for  an  ornamental  door-entrance, 

r  ornamental  windows,  or  for  buttresses.     [District  of  Columbia.] 

Vault.     \\\  underground  construction  beneath  parking  or  sidewalk.     [District 

Colmnbia.] 

Veneered  Building.     Frame  structure,  the  walls  covered  above  the  sill  by  a 

wall  of  brick,  instead  of  clapboards.  [Common  understanding  in  Chicago, 
ilwaukee,  and  Minneapolis,  but  not  defined  by  law.] 

Warehouse  Class.  Buildings  used  for  the  storage  of  merchandise,  manufac- 
ries  in  which  machinery  is  operated,  breweries,  and  distilleries.  [Cincinnati 
id  St.  Louis.] 

Width  of  buildings  shall  be  computed  by  the  way  the  beams  are  placed;  the 
igthwise  of  the  beams  shall  be  considered  and  taken  to  be  the  widthwise  of  the 
lilding.     [New  York  and  San  Francisco.] 
Wholesale  store,  or  storehouse,  shall  embrace  all  buildings  used  (or  intended 

be  used)  exclusively  for  purpose  of  mercantile  business  or  storage  of  goods. 
'hicago,  Louisville,  and  Milwaukee.] 

Wooden  Building.  A  wooden  or  framef  building.  [Boston,  Kansas  City, 
id  Minneapolis.] 

Any  building  of  which  an  external  or  party  wall  is  constructed  in  whole  or  in- 
irt  of  wood.     [Denver  and  District  of  Columbia.] 

Having  more  wood  on  the  outside  than  that  required  for  the  door  and  window 
ames,  doors,  shutters,  sash  porticos,  and  wooden  steps,  and  all  frame  buildings 
:  sheds,  although  the  sides  and  ends  are  proposed  to  be  covered  with  corrugated 
on  or  other  metal,  shall  be  deemed  a  wooden  building  under  this  law.  [CharUs- 
n  and  Nashville.] 

*  As  applied  to  solid  walls.     [Minneapolis  and  Providenci.] 
t  Or  veneered.    [MinneapoHs.l 


INDEX 


By 

CLINTON   L.   BOGERT 

Associate  Member  of  American  Society  of  Civil  Engineers 

Numbers  refer  to  Pages.     Consult  also  the  Glossary,  pages  1796-1850. 


Abacus  (Glossary),  179& 
Abbreviations  of  terms,  122,  123 
Abutments,  arch,  305 

pier,  306 
Acetylene  gas,  1431  , 
Acoustics,  architectural,  1486-1500 
Advertising,  ethics,  1729 
Aetna  radiator,  1266 
Agate,  130,  1501 
Aggregate,  concrete,  241,  287,908,909, 

945 
Agreement,  form,  1765 
Agreements,  1751 
Air-compressor,  water-supply,  1390 
Air,  condUioning,  1352 
density,  1247,  i339 
flow,  resistance,  i333 
hot-water  systems,  removal,  130? 
properties,  12  54-1 2  56 
quantity,  symbol,  1247 
specific  heat,  1250,  1255 
ventilation,  requirements,  1260,  1354. 

1356 
vitiated,  effects,  1352 
Air-ducts,  1333-1341 
Air-lift,  1396 

Air-lock,  pneumatic  caisson,  211 
Air-pressure,  pneumatic  caisson,  211 
Alabaster,  131,  1501 
Alca  lime,  is  S3  ■,        -  vA 

Alcohol,    specific    gravity    and    weigMf, 

1501 
Almonry  (Glossary),  i797 
Alterations,  defined,  1851  . 

Aluminum,  specific  gravity  and  weight, 

Americir  Blower    Co.,    heater,    1329- 

Americ'an'  Institute      of      Architects^ 

canons  of  ethics,  173© 
chapters,  1788 
competitions,  1733 
documents,  1767 
professional  practice,  1727 
schedule  of  charges,  1728.  I73i 
standard  documents,  I74» 


American  Steel  &  Wire  Go's  gauge, 

401,  402 
Amperes,  defined,  1457 
Anchor,  box,  753,  790,  792,  793 
reinforced-concrete,  919 
steel  beams,  619 
trusses,  1150,  11S2,  1168 
wooden  beams,  616,  762,  783-800 
Anchor-bolts,  adhesion,  240 
placing,  1 194 
steel  beams,  619 
steel  stacks,  137 7 
Ancient  measures  and  weights,  34 
Aneroid,  barometer,  1249 
Angle  in  geometry,  36 
bisected,  69 
critical,  domes,  12 13 
friction,  retaining  walls,  2S3 
measure,  two-foot  rules,  68 
repose,  materials,  253,  2S4,  256 
Angle  of  structural  steel,  361-367 
beams,  safe  loads,  566,  s86-59o 
connections,  beams,  616 
double,  properties,  370-372 
moment  of  inertia,  339,  362-367 
oblique  loading,  593 
price,  X204,  1211 
properties  of,  steel,  362-367 
shelf,  787-790 
struts,  488,  Soi-503 
tension-members,  loads,  385,  399 
deduction,  399,  400,  702 
Angle-anchor,  619 
Angle-and-plate  columns,  475,  47 o 
Angle-bar  (Glossary),  i797 
Angle-bracket,  422 
Angular  measure,  30,  68 
Anhydrite,  131 
Annealing,  rivets,  382,  414 
Anthracite  coal,  combustibles,  1271 

for  hot-air  heating,  131 7 
Apartment-houses,  floor-joists,  737 
live  loads,  i49,  "98 
I  beams  in  floor,  size,  864 
steel,  weight,  1207 
Apatite,  131 
1857 


1858 


Index 


Apostles  and  Saints,  symbols,  1727 
Apothecaries'  weight,  29 
Apple-tree,  wood,  hardness,  1558 
Apron,  retaining-walls,  263 
Aragonite,  131 
Arbitration,  contract,  1763 
Arbitration  bar,  cast-iron  test,  380 
Arc,  arcs,  circular,  38,  69,  70 

lengths,  54 
Arc-lamps,  1462 

Arch,  arches,  masonry,  305-321  (Glos- 
sary), 1799 

angle  of  friction,  311 

brick,  306 

center  of  pressure,  311,  313 

centers,  308 

concrete,  reinforced,  321 

cut-stone,  310 

depth  of  keystone,  308-310 

elliptical,  306 

failure  of,  311-313 

floor,  827-844 

forms  of,  306 

groined,  1235-1240 

inverted,  in  footings,  227,  228 

keystone,  305,  308-310 

line  of  fracture,  316 

line  of  pressure,  311-321 

line  of  resistance,  311-321 

load,  actual,  masonry,  318 

loaded,  317 

middle  third,  principle  of,  311-315, 
1225,  1227,  1240 

New  York  City  requirements,  307 

plate-girder  arches,  1131 

pointed,  failure  of,  312 

rings,  308,  317 

rise,  307 

segmental,  305,  306,  307,  321 

semicircular,  306 

semielliptical,  321 

solid  ribs,  1132 

stability,  determination,  311-321 

strength,  306 

surcharged,  317 

three-centered,  306 

thrust,  305,  307,  311-321 

tie-rods,  for  I  beams,  619,  865 
roof -trusses,  11 20 
segmental  arches,  307 

trussed,  1121 

unloaded,  311 

voussoirs,  :>o5,  311 
Arched  trusses,  1035-1043 

stresses,  11 18- 11 20 

wooden,  1020-1024 
Architects,  canons  of  ethics,  1730 

certificates,  1771 

charges,  schedule,  1728,  1731 

competitions,  1 733-1747 

drawings,  1718,  L728,  1731,  1754 


Architects,  estimates,  1728 

examinations,  1772 

inspection  of  work,  1755 

organizations,  1788-1795 

professional  practice,  1727 

registration  laws,  1768-1779 

status  and  decisions,  1754 

superintendence,  1728 
Architectural  acoustics,  1486-1500 
Architectural    engineering,  terms,  124- 

128 
Architectural  fellowships,  1779-1788 

medals,  1779-1788 
Architectural  societies,  1788-1795 
Architectural  terms    (Glossary),   1796- 
1850 

building  laws,  1851-1855 
Architecture,  schools  of,  1779 
Areas,  circles,  tables,  42-54 

elementary,  332 

geometrical    figures,    38-54,    59-61 
334-338,  348-351 

net    sectional,    of    tension-members 
386 
Arithmetic,  practical,  3-24 
Armories,  steel,  weight,  1208 
Artificial  cements,  236-240 
Asbestic  plaster,  818,  819        *' 
Asbestos,  building-lumber,  819 

corrugated  sheathing,  819 

metal,  819 

products,  819 

roofing-shingles,  819 

sheathing,  1501,  1567 

specific  gravity  and  weight,  1501 
Ash  (wood)  deflection  in  beams,  664 

hardness,  1558 

specific  gravity,  1501 

ultimate  unit  stresses,  651 

weight,  651.  isoi,  1558 
Ashes,  angle  of  repose,  256 

specific  gravity,  1501 

weight,  651,  1501,  1558 
Ashlar  (Glossary),  1799 

masonry,  233,  269,  441,  1538,  I5S9 
Asphalt,  1608 

floors,  1608,  1609 

mastic,  1608 

pavements,  1608 

rock,  1608 

roofing,  1608 

specific  gravity  and  weight,  1501 
Asphalt-gravel  roofing,  871,  1598 
Asphaltum,  1608,  1799 

specific  gravity  and  weight,  1501 
Assembly-halls,  joists,  739,  744- 

live-loads,  719,  720,  1198 
Asylums,  non-fire-proof,  height,  813 

ventilating  and  heating,  1355 
Asymptote  (Glossary),  1799 


Index 


1859 


Atlanta  building  code,  loads  on  founda- 
tion-beds, 143 

office-building  loads,  151 
Auditoriums,    heating    and    ventilating 
requirements,  1354 

lighting,  1 45 1 

live  loads,  719,  720,  1198 
Augite,  131 

Automobile  factory,  design  and  cost,  803 
Automobiles,  dimensions,  1642 
Avoirdupois  weight,  28 
Axial  force,  definition,  375 
Axis,  conjugate,  38 

neutral,  295,  332-338,  555,  621 

transverse,  38 

Back,  arch,  305 

Baltimore,  fire,  reinforced  concrete  in, 
957 

building  code,  steel  columns,  481 
Band  of  column  (Glossary),  1801 
Barometer,  1249 

pressure,  measurement,  1249,  1252 
Barns,  cost,  16 13 
Barrel,  dimensions,  1644 
Barrel  vault,  1231-1235 
Barrett  specifications,  roofing,  1595 
Bars  (steel),  385-398      • 

areas,  1514-1521 

base  price,  1205 

circumferences,  1514-1521 

lacing,  385 

reinforcing,  915-921 

safe  loads,  388-392 

standard,  classification  and  cost,  1211 

weights,  1514-1521 
Bartizan  (Glossary),  1801 
Basalt,  131 

specific  gravity  and  weight,  1501 
Base,  columns  (Glossary),  1801 

cast-iron  column,  457,  459 

material,  1195 

mill-construction,  782-788 

pipe  columns,  470,  471,  47^ 

pressures,  265,  441,  1200 

steel  columns,  473-477 
Base-plates,  440-445,  1524 
Basement,  defined,  1851 

walls,  228,  229 
Basin-slabs,  marble,  1641 
Bath,  foot,  1 64 1 

plunge,  1422 

seat,  1641 
Bath-tubs,  dimensions,  1640 

symbols  for,  1426 
Batter,  iSoi 

cellar  walls,  229 

retaining-walls,  259 
Battlement  (Glossary),  1802 
Bay  window  (Glossary),  1802 
Beam,  beams  (see  also  Girders) 


Beam,  bearing  on  wall,  634,  687 
bearing-plate  areas,  440-444 
bending  moment,  324-331,  555,  939 
continuous  beams,  673 
iniluence-lines,  1134 
reinforced-concrete,  935 
Bethlehem,  357,  358,  592-602 
buckling,  183,  565,  567,  569^ 
girders,  686,  705 
separators,  612 
wooden,  627 
cantilever  (see  Cantilever,  beams) 
Carnegie,  352-356,  574-591,  605,  606 
cast-iron  (see  Lintels) 
channel  (see  Channels) 
clamps  for  connecting,  616 
coefficient  of  strength,  556,  628 
compound,  652-654,  763 
compression  in,  555 
concrete  fire-protection,  860 
concrete,  not  reinforced,  628,  637 
connections,  steel  beams  (see  Fram- 
ing, steel  beams) 
wooden  beams,  749-757,  789,  790 
continuous,  555,  671-680,  979,  980 
cross-section  irregular,  557 
cylindrical,  667 
deck,  565 
deflection,  663-670 

allowed,  566,  628,  664,  736 
continuous  girders,  674-676 
steel,  566,  612,  668-670,  676 
wooden,  636,  653,  654,  664,  667 
double,  564,  603,  604,  607-611 
elasticity,  555,  663 
external  forces,  325 
factors  of  safety,  556 
fixed,  strengths,  331,  634 
flexure,  324-331,  332-334,  555 

reinforced-concrete  beams,  924-941 

steel  beams,  564-573 

wooden  beams,  627-637,  652-656 

floor,  steel,  specifications,  1201,  1202    . 

girder  (see  I  beams;    also  Girders) 

grillage,  foundations,   165-169,   181- 

185,  678-680 
H  beams,  356,  474,  585,  1204 
I  beams  (see  I  beams) 
inclined,  564,  665 
influence-lines,  1134 
internal  forces,  325 
keyed,  653-655 
lateral  deflection,  566,  670 
loads,    general    principles,    555,    565. 
593,  629,  665 
tables  (see  Beams,  steel,  etc.) 
materials  used  for,  564 
neutral  axis,  definition,  555 
neutral  surface,  definition,  555 
overhanging  (see  Cantilever,  beams) 
reactions,  322-324 


1860 


Index 


Beam,    rectangular,  relative    strength, 
633,634 
stiffness,  665,  666 
reinforced-concrete,  924-941,  971-97S 
resisting  moment,  333,  555.  635,  683, 

929 
shear,  183,  411,  413,  565,  567-570 
simple,  323-330,  555 
span,  555 
span-limit,  566 
steel,  anchors  for,  619 
base  price,  1204 

bending  moments,  table  of   maxi- 
mum, 574-576 
Bethlehem,  357,  358,  592-602 
buckling,  183,  565,  567,  569,  612, 

627 
Carnegie,  352-356,  574,   59i,  605, 

606 
channels  (see  Channels) 
connections    (see     Framing,    steel 

beams) 
crippling  (same  as  buckling) 
deflection,  vertical  (see  above) 
dimensions,  352,  565 
economy  and  strength,  565 
end-reactions,  569,  574-576 
fiber-stress,  556,  557,  569 
fireproofing,.    780-782,    827-842, 

844.  849,  854-860 
flange-thickness,  592 
forms  of,  565 
framing      and      connecting      (see 

Framing) 
H  beams,  474,  585,  1204 
H  beams,  properties,  356 
heavy,  565 

I  beams  (see  I  beams) 
lateral  deflection,  566,  670 
light,  565 

loads,  safe,  565,  577-591,  594-602 
separators,  612-614,  1202 
shearing-stresses,     181-185,     567, 

568,  569^  574,  575 
standard,  352 

strength    affected    by    dimensions, 

556,  565 
strut,  571,  572 
T  beams,  337,  368,  369,  591,  1211, 

1212 
tie,  572 

tie-rods,  619,  865 
unit  stresses,  1200 
web-buckling,  181-185,  $65,  567, 

569,  612 
web-thickness,  592 

stiffness,  565,  635,  663-670 
stone,  637 

coefficients  of  strength,  556,  628 
stresses,  555-557,  567,  569,  603,  604, 
628,  635 


Beam,  strut,  steel  571,  572 

wooden,  633 
supplementary,  352,  561 
T  beam,  337,   368,  369,   591,   1211, 

1212 
tension  in,  555 
tie-beams,  steel,  572 

wooden,  430-432,  434,  435,  633 
wall-support,  612 

wooden,  627-668,  717-757,  780,  789- 
795  , 

anchors,  6x6,  762,  783-800 

bolted,  429,  653,  655 

buckling,  627 

built-up,  652,  656 

cantilever,  629 

cedar,  628,  640,  664 

chestnut,  deflection,  664 
distributed  loads,  641 

coefficients,  628 

compound,  652-654,  763 

connections,  749-757,  789,  792  (see 
also  Framing,  floors,  wooden) 

conversion  factors,  637,  668 

cross-sections,  627,  637 

cut  from  log,  strongest,  634 

cylindrical,  634,  667 

cypress,  distributed  loads,  641 

deflection.  636,  653,  654,  664,  667 

Douglas  fir, 'distributed  loads,  628, 
642,  664 

dressed,  667 

Eastern  fir,  loads,  639 

end-bearing,  634 

flitch-plate,  655 

framing,  749-757 

framing  to  steel  beams,  789,  790 

hangers  (see  Hangers) 

hemlock,  loads,  628,  638,  664 

keyed,  653-655 

loads,  safe,  638-646,  667 

mill-construction,  758-769 

nominal     dimensions,     636,     667, 
736,  1559 

Norway  pine,  loads,  641,  664 

redwood,  loads,  640 

shear,  horizontal,  412,  635 

sizes,    nominal    and    actual,    636, 
667,  736,  1559 

spans,  maximum,  737-746 

spruce,  loads,  628,  639,  664 

stiffness,  664 

strongest  cut  from  log,  634 

strut,  633 

tension,  635 

tie,  430-432,  434,  435,  633 

trussed,  656-662 

unit  stresses,  557,  627,  635,  647-651 

white  oak,  loads,  643,  664 

white  pine,  loads,  639,  664 

yellow  pine,  628 


•  Index 


1861 


Beam,  wooden,  yellow  pine,  deflection, 
664 
loads,  642,  643,  666 
wrought  iron,  628 
deflection,  664 
Beam-box,  753,  762,  790,  792,  793 
Beam  girders  (see  I  beams) 
Beam-hangers  (see  Hangers) 
Bearing-brackets,     cast-iron     columns, 

445-447 
Bearing-plates,  440-445,  1524 

pressures,  441,  1200 
Bearing  values  (see  materials  in  ques- 
tion) 
Bed,  masonry  (Glossary),  1802    , 
Bedsteads,  dimensions,  1638,  1640 
Beechwood,  hardness,  1558 
Bell-cot  or  gable  (Glossary),  1803 
Bells,  1725 
Belt,  for  shafting,  1721 

mill-construction,  764,  765 
Bending    moments,    beams,    324-331, 
555,  939 

bolts  in  wooden  construction,   429, 
431 

channels,  table,  576 

columns,  485 

continuous  girders,  673 

diagrams  for  beams  and  girders,  328, 
330,  564,  678,  690,  695,  698 

footings,  174,  175,  178 

I    beams,    table   of    maximum,    574, 
575 

influence  lines,  1134 

moving  loads,  1134-113S 

pins,  423-429 

reinforced  concrete,  934,  935 

slabs,    concrete,    932,    936,  984-991, 
994 

T  beams,  concrete,  992 
Berger's  studding,  881 

metal  lumber,  852,  858,  881 
Bessemer  steel,  380 
Bethlehem  beams,  357,  358,  592,  594- 

604 
Bethlehem  columns,  475,  479,  482-488, 

loads,  483,  506-515 
Bevels,  90 

Billard-tables,  dimensions,  1638 
Birchwood,  hardness,  1558 
Bitumen,  1608,  1609 
Bituminous  coal,  combustibles,  1271 
Blackboards,  dimensions,  1644,  1645 
Black-line  prints,  1719 
Block-tin,  pipe,  1419 
Blocks,  hollow  building,  filling,  287 

concrete  (see  Concrete,  blocks) 
Blower  system,  heating,  1324 
Blue-prints,  17 18 
Bluestone,  beams,  coefl&cient  for,  628 

flagging,  282,  1539 


Board-measure,  table,  1 560-1 562 
Boiler,  12  73-1 283 

connections,  1279 

covering,  1361 

horsepower,  1274 

incrustation,  1429 

location,  1357 
in  mills,  765 
in  warehouses,  780 

rating,  1301 

residence,  specification,  1362 

shops,  steel,  weight,  1208 

symbols,  1351 

water,  for  ranges,  1642 
Boiler-plants,  mill-construction,  765 
Bolsters,  mill-construction,  454,  795 
Bolt,  bolts,  anchoring,  240 

bearing  strength,  429,  439,  1138 

bending,  1138 

bending  moment,  429,  431 

beveled  washers,  1202 

built-up  beams,  652,  654 

expansion,  1534 

fiber-stress,  1138 

foot  of  rafter,  437 

girders,  432,  433 

heads,  1525-1528 

safe  bearing  in  timber,  430 

screw-ends,  upset,  387 

shearing  value,  412,  429-439,  1138 

shock  loads,  1202 

steel,  table,  431 

stresses,  618,  1138,  1200 

strap-joints  in  trusses,  436 

swedge,  619 

tension,  431,  1138 

truss-joints  (see  Roof-trusses) 

weight,  1527 

wrought  iron,  table,  431,  1138 
Bolt-heads,  15  25-1 5  28, 

standard  dimensions,  1525-1526 

weight,  1526-1528 
Bonanza  reinforced-cement  tiles,  868 
Bond,  brickwork,  268,  306 

masonry  (Glossary),  1803 

timber  (Glossary),  1803 
Bond-stones  in  piers,  269 
Bonds,  form,  1763 

guaranty,  1757 
Book-stacks,  library,  1696 
Book-tile,  roofing,  868 
Borings,  for  foundations,  144 
Boss  (Glossary),  1804 
Boston  building  code,  column-formula, 
460,  481,  493-496 

loads  on  foundation-beds,  142 

loads  on  masonry,  267 

office-buildings,  assumed  loads,  151 

rivets,  bearing  and  shear,  419 

steel  column  formula,  481,  493-49^ 

thickness  of  walls,  230,  231,  232 


1862 


Index   * 


Boston,  Chamber  of  Commerce  Build- 
ing, 192 
Bostwick  lath,  884 
Boulders,  134,  136,  141 

safe  loads  on,  foundations,  141 
Bowling-alleys,  dimensions,  1643 
Bowstring  truss,  1035 

stresses,  1094,  1096 
Box  anchors,  beam-supports,  753,  762, 

790,  792,  793 
Box  columns,  467,  479,  484 

moment  of  inertia,  342 

plate-and-angle,  479 
Box  girders,  681-716 

bending  moment,  683,  695,  697,  698, 
699 

buckling,  686,  705 

construction,  details  of,  682 

cover-plates,  696 

end-reactions,    maximum,    703,    706- 
716 

examples,  694-703 
^  flange-area,  683,  692,  696,  699, 
*  framing  and  connections,  615 

moment  of  inertia,  section,  341,  342 

rivet-holes,  loss  of  area,  702 

shear,  684-687,  690,  691,  696,  698 

specification,  1201,  1202,  1203 

steel-beam,  607-611 

stififeners,  681,  686,  691,  696,  1201, 
1203 

web-plate,  buckling  value,  686,  705 
shearing  value,  684,  703 

weight,  687,  701 
Box-hangers  (see  Beam-boxes) 
Bracing,  steel  structures,  1202 

wind  buildings,  1171-1193 
Brackets,  cast-iron  columns,  445-447 

terra-cotta,  278 
Brads,  1529 
Brass,  castings,  shrinkage,  1521 

specific  gravity,  1502,  1510,  1511 

weight,  1502,  1510,  isn 
Br  east- walls,  262-263 
Breeching,  dimensions,  1366 
Breuchaud  method,  underpinning,  221 
Brick,  bricks,  angle  of  friction,  253 

arches,  laying,  306-307 

burning,  1540 

clay,  27s,  1540 

coefficient  of  friction,  253 

color,  1540,  1543,  1544,  1547 

cost,  1544 

crushing-height,  269 

crushing  strength,  270,  271 

dry-pressed,  1540 

enameled,  1543 

fiber-stresses,  557 

fire,  1540 

fire-resistance,  814 

flexure,  17$ 


Brick,  footings,  226,  227 
glazed,  1543 
lime-mortar,  1541 
machine-made,  1540 
manufacture,  1542 
molded,  1540 
paving,  1540 
piers,  267-276,  278 
piling,  space  required,  1547 
repressed,  1540 
retaining-walls,  259,  260 
sand-lime,  1541 

properties  of,  1543 
size,  1540,  1543 
soft-mud,  1540 
specffic  gravity,  1502 
strength,  ultimate,  270 
stiff-mud,  1540 
tests,  270,  275,  281,  1542 
vaults,  1238 
weight,  1502,  1541 
Brickwork,   1 540-1 548    (see,  also,  Ma- 
sonry, Walls,  etc.) 
arches,  306 

bond,  effect  on  strength,  268 
cement  mortar  required,  239 
compared  with  concrete,  968 
cost,  1544-1547 

mill-buildings,  808-810 
crushing  strength,  270-276 
data,  1 540-1548 
efflorescence,  1547 
estimating  quantities  and  cost,  1544- 

1546 
fire-resistance,  814 
floor-arches,  827-828 
footings,  226,  227 
lintels  supporting,  623 
loads,  safe,  265-268,  287,  441 
moisture,  1547 
mortar,  239,  276,  818 
mortar-colors  for,  1547 
piers,  267-276,  278 

bond-stones,  269 

crushing  strength,  271-276 

safe  loads,  267-268 

tests,  272-278 
pressures,  265,  441,  1200 
quantity  estimates,  1 544-1 547 
specific  gravity,  1502 
strength,  safe,  265-268,  287,  441 
tensional  strength,  178 
walls,  safe  loads,  265,  441 
warehouse,  778 
weight,  1502 
Bridging    (Glossary,    1804)    floor-joists, 

748,  749 
British   thermal  unit,   33,    1250,    1251, 

1255,  1684 
Bronze,  door-frames,  895 

specific  gravity  and  weight,  1502 


Index 


1863 


Bronze,  window-frames,  895 

Brown  &  Sharpe  wire-gauge,  401,  402, 

1469,  1473,  1509,  1510 
Brown-line  prints,  1720 
Brownstone,  crushing  strength,  279,  281 
Buckling,  plate  girders,  686,  705 

steel  beams,  565,  567-569,  612,  627 
web,  box  girders,  705 

plate  girders,  705 
wooden  beams,  627 
Buffalo  building  code,  loads  on  founda- 
tion, 142 
masonry  loads,  267,  287 
office-buildings,  assumed  loads,  151 
Building,  alterations,  1851 
steel,  drafting,  1207 
cost,  1611-1634 

of  slow-burning,  758,  802,  1619 
per  cubic  foot,  1611-1634 
per  square  foot,  1627-1634 
reinforced-concrete,  1618 
cubage,  1612 
depreciation,  1634 
drainage,  1407-1414,  1419-1421 
factory,  968 

fire-proof,  cost,  802,  812,  1619-1625 
fireproofing,  811-905 
government,  cost,  1628-1634 
heating,  1 247-1363 

temperatures,  1256 
iron  and  steel,  1627 
legal  definition,  1852 
loads,  1 196 

mill-construction,  1618 
non-fire-proof,  812,  813 
office,  specifications,  1194-1212 
papers,  1564 
protection  from  outside  hazard,  901- 

903 
reinforced-concrete,  968-997 
shrinkage  in,  1427-1428 
signing  by  architects,  1729 
steel,  cost,  1206 
weight,  1207 
structural-steel  specifications,    1194- 

1212 

veneered,  269,  1855 
ventilating,  1348-1354,  i356 
wind  bracing,  1171-1193.  1202 
wooden,  defined,  1855 
Building  laws,  bearing  on  masonry,  441 
bearing- walls,  269 
brickwork,  267 
column-protection,  822-826 
concrete  columns,  length  of,  94i 
concrete  fire-protection,  955-960 

floor-slabs,  937 
electric  work,  1480-1481 
elevator-installation,  1663 
fire-proof       construction,       811-905, 
1618-1620 


Building  laws,  fire-proof  paint,  821 

fire-proof  wood,  820 

floor  fire  tests,  827 

flooring,  fire-proof,  892-893 

floor-loads,  719,  730,  1198 

footings,  assumed  loads  on,  151 

formulas,  steel  columns,  481 

foundation-beds,  loads  on,  142 

hooped  columns,  942 

loads,  on  brickwork,  269 
on  floors,  719,  730 
on  foundation-beds,  142 
on  masonry,  267,  287 

non-fire-proof  buildings,  areas,  812 
heights,  812,  813 

reinforced-concrete  columns,  940,  941 

sand  in  concrete,  908 

terms  defined,  1851-1855 

unit  stresses  for  woods,  647 

walls,  thickness,  230,  231,  232 

wind-bracing,  1171-1172 
Building  materials,  1634-163  7 

depreciation,  1634 

estimating,  1635 

quantity  systern,  1635-1637 

wear  and  tear,  1634 
Building  papers,  1564-1568 
Bureaus,  dimensions,  1638,  1640 
Butternut  wood,  hardness,  1558 

unit  stresses,  651 
Buttresses,  1804 

center  of  gravity,  300,  303 

stability,  297-304 

Cables,  carrying  capacity,  1473 

measure,  25 
Caissons,  210-214 
Calcareous  minerals,  130,  131 
Calcite,  131 

specific  gravity  and  weight,  1502 
Calendar,  old  and  new,  30 
California,  registration  law,  1778 
Cambered     truss      (see     Roof-truss, 

cambered) 
Calorimetry,  1250 
Candle-power,  1439,  i440»  1462 
Canopy  (Glossary),  1805 
Cantilever,  beams,  555,  io43 

moments,  325,  326,  558,  559 
wooden,  629 

buildings  as  cantilevers,  11 73 

compound  footings,  178 

flat  slabs,  concrete,  950 

foundations,  165-169,  978 

truss,  1043-1045,  1105-1107 
Canvas  roofs,  801 
Cap,  cast-iron  columns,  459 
mill-construction,  762 

steel-pipe  columns,  470,  471 

stone  (see  Coping) 

wooden  columns,  454 


1864 


Index 


Cap-plates,  795 
Capital  (Glossary),  1806 
Car-bams,  steel,  weight,  1209 
Carbon,  in  steel,  381 
Carnegie  shapes  (see  Beams,  etc.) 
Carpenter's  rule,  heat-loss,  1261 
Carpenter's  work,  data  on  lumber  and 
work,  1 5 58-1 564 

cost  of  labor,  1564 
Carriages,  dimensions,  1642 
Cars,  railroad,  capacities,  1643 

dimensions,  1642 
Case-work,  dimensions.  1640 
Cast  iron,  379 

appearance,  379 

castings,  379,  380 
shrinkage,  1521 

columns  (see  Columns) 

crushing-loads,  449 

defects,  379 

fiber-stresses,  557 

fire-resistance,  819-820 

lintels,  620-628 

manufacture,  379 

modulus  of  elasticity,  664 

plates,  weight,  1524 

shearing-stresses,  1505 

specific  gravity,  1505 

specifications,  379 

strength,  376,  379,  412 

tension,  376 

weight,  1505,  1521,  1524 
estimating,  1505,  1521 

weight  of  castings,  1521 
Castings,  shrinkage,  15  21 

specifications,  for  cast  iron,  379,  1196 

steel,  stresses,  1138,  1200 

structural,  painting,  1203 

weights,  1521 
Cathedrals,  seating  capacity,  1654 
Cedar,  beams,  deflection,  664 
fiber-stress,  flexure,  557 
safe  loads,  640 

columns,  safe  loads,  450,  452 

crushing  strength,  449,  454 

hardness,  1558 

specific  gravity,  1502 

unit  stresses,  557,  647,  650 

weight,  650,  1502 
Ceiling  (Glossary),  1807 

corrugated  metal,  1604 

loads,  1 197 

matched,  1563 

suspended,  871-872 
Ceiling-joists,  wooden,  framing  to  roof- 
trusses,  1004 
maximum  spans,  736,  737,  742 
Cellar,  defined,  1852 

walls,  129,  228,  229 
Cellar-drainer,  142 1 
Celsius  thermometer,  1250 


Cement,  235-240,  907,  908 

artificial,  236 

chemical  composition,  237,  908 

constancy  of  volume,  907 

corrosion  of  steel,  960 

cost,  238,  248,  910 

fineness,  237,  907 

grappier,  236 

La  Farge,  236,  238 

manufacture,  236 

mixing,  238 

mortars,  freezing,  239 
proportions,  235,  247 
specific  gravity  and  weight,  1506 
water  required,  238 

natural,  235,  284  (see  Hydraulic  lime) 

neat,  237,  907 

painting  of,  1573 

Portland  (see  Portland  cement) 

Puzzolan,»236,  237 

quantities  in  concrete,  247,  248,  249 

reinforced-concrete,  907 

setting,  237,  907 

slag,  236,  237,  238 

specific  gravity,  237,  907,  1502 

specifications,  236,  907 

stainless,  238 

strength,  235,  237,  240,  283,  284,  907 

tests,  237,  240,  907 

water  required,  238 

waterproofing,  1711,  1717 

weight,  235,  723,  1502 
Cement  blocks,  269 
Cement-gun,  column-protection,  826 
Cement-plants,  steel,  weight,  1209 
Center,  striking  for  arch,  308 
Center  of  gravity,  127,  291-296 

circle,  sector  and  segment  of,  293 

compound  figures,  294,  295 

found  by  moments,  294 

irregular  figures,  292,  295 

lines,  292 

particles,  heavy,  293,  294 

quadrant  of  circle,  293 

quadrilaterals,  292 

regular  figures,  292 

surface,  292 

table  of,  293 

triangles,  292,  293 

voussoir  of  arch,  313,  318 

wall  and  buttress,  300-301 
Center  of  pressure,  arches,  311,  313 

pier-joints,  300 
Centigrade  thermometer,  1250 
Ceramic  tile,  1605,  1607 
Certificates,  architects,  1771 
Chain,  408-410 
Chain-blocks,  1723 
Chain-cables,  409 
Chain-hoists,  1723 
Chain-hooks,  1724 


Index 


1865 


Chairs,  dimensions,  1638,  1639,  1653 
Chalk,  132 

specific  gravity  and  weight,  1502 
Chamber  of  Commerce  Building,  Bos- 
ton, piiing-plan,  192 
Chamfer  (Glossary),  1807 
Channel,  beams,  safe  loads,  582-584 
bending  moments,  table,  576 
buckling,  576 

columns,  467,  476-480,  486-489 
safe  loads,  499,  500,  533-554 
deflection,  coefficients,  582-584 
depth,  576 

dimensions  of  standard,  353,  360 
double  sections,  359,  373,  374,  499- 

500 
end-bearing,  576 
moment  of  inertia,  337,  338 
oblique  loading,  573 
properties  of,  359,  360,  373,  499,  500 
radius  of  gyration,  337,  338 
sections,  359 
set  flatwise,  572 
shearing,  576 
small  grooved,  360 
steel,  prices,  1204,  1212 
web-resistance,  table,  576 
weight,  360,  576 
Chapel  (Glossary),  1808 
Charcoal,  combustion,  1272 
Charges,  schedule,  1728,  1731 
Charles'  law,  gases,  1254 
Check-nuts,  shock-loads,  1202 
Chert,  130 

Chestnut,  beams,  coefficients  for,  628 
deflection,  664 
distributed  loads,  641 
fiber-stress,  safe,  flexure,  557 
columns,  safe  loads,  450,  452 
crushing   strength,   across   the   grain, 

454 
crushing-loads,  with  the  grain,'  449 
hardness,  1558 
specific  gravity,  1502 
tension,  376 

unit  stresses,  647,  648,  651 
weight,  651,  1502,  1558 
Cherry,  hardness,  1558 

weight,  1502 
Cheval-glasses,    dimensions    of,    1638, 

1640 
Chicago  building  code,  bearing  pressure, 
masonry,  441 
column-formula,  450,  460,  481,  482 
safe  loads,  493-495 
steel-pipe  column,  469,  474,  497, 
498 
compression,  steel  members,  495 
concrete  flat  slabs,  997 
masonry-loads,  267,  287,441 
method  of  excavating,  209 


Chicago  building  code,  office-buildings 

assumed  loads,  151 

piers,  strength,  268 

skeleton  construction,  234 

thickness  of  walls,  230,  231,  232 
Chiffoniers,  dimensions,  1638,  1640 
Chimneys,  1281,  1364-1380 

for  boilers,  1281,  1282,  1283,  1367 

for  fire  places,  1282 

for  kitchen  ranges,  1282 

formula,  1366,  1368 

for  tall  buildings,  1283,  1368 

gas-velocity,  1364 

height,  draft-relation,  1281,  1364 

radial-brick,  1368-1373,  1377 

reinforced-concrete,  1373-1375 

steel,  1376 

wind  load,  1199,  1368 

tall,  list  of,  1379 
Chlorite,  131 
Chords,  of  arcs,  38 

of  truss,  definitions,  998 

table,  81-89 
Churches  (Glossary),  1808 

air-changes,  1260,  1353 

cost,  1613 

floor-loads,  719,  720,  1198 

seating-space,  1653,  1654 
Cinciimati  building  code,    office-build- 
ings, assumed  loads,  151 

loads  on  foundation-beds,  143 
Cinder,  cinders,  angle  of  repose,  256 

Concrete,  242,  250,  909,  930 

corrosive  action,  818,  960 

reinforced  work,  242 

weight,  250 

weight  of  loose,  256 
Circles  and  parts,  37,38,41 

areas,  tables,  42-54 

arcs,  mensuration,  54-59 

chords,  tables,  81-89 

circumferences,  42-54 

geometrical  problems,  66-74 

moment  of  inertia,  337 

radius  of  gyration,  337 

section-modulus,  337 
Circuit-breakers,  1461 
Circular  measure,  30 
Circular  mil,  1469,  1473 
Circular  ring,  61 
Circumference,  37 

circles,  42-54* 
Cisterns,  capacity  of,  1404-1405 
Clapboards,  1563 
Classical  moldings,  1697 
Classical  orders,  1 698-1 704 
Clay,  angle  of  repose,  256 

bricks,  275 

foundation-beds,  135,  138,  139 

moisture  in,  138 

safe  loads,  141,  143 


1866 


Index 


Clay,  specific  gravity,  1503 

weight,  loose,  256,  1503 
Clerestory  or  Clearstory,  ( Glossary )  ,1 809 
Clerk  of  the  works,  1728,  1733 
Cleveland     building     code,     loads     on 
foundation-beds,  143 

office-buildings,  assumed  loads,  151 
Clevises,  standard,  387,  398 
Climax,  cellar-drainer,  142 1 

floor  system,  855 
Clinched  lath,  886 
Clinton  stiffened  lath,  887 
Clips,  for  steel  beams,  616 
Clocks,  tower,  1695 
Closet,  water,  141 1,  1428,  1641 
Closet-ranges,  dimensions,  1641 
Coach-screws,  1535 
Coal,  calorific  value,  1271 

classification,  1271 

composition,  1271 

specific  gravity  and  weight,  1503 
Coal-bunkers,  steel  weight,  1209 

loads,  1 198 
Coal-fields,  1271 
Coal-gas,  1273,  1 43 1 
Codes,  building  terms,  1851-1855 
Coefiicient  of  elasticity  (see  Modulus) 
Coefficients,  beams,  556,  628 

deflection,  steel  beams,  668 

expansion,  steel,  382 

flow  of  water,  1383 

friction,  253 

sound  absorption,  1488-1493 
Coins,  weights,  29 
Coke,  combustion,  1272 

specific  gravity  and  weight,  1503 
Cold-air  ducts,  furnaces,  1319 
Cold-bending  tests,  iron  and  steel,  378, 

384,  385,  914 
Cold-storage,  temperature,  1693 
Collar-beam,  1810 
Colleges,  architectural,  1779 
Color,  light-sources,  1438 

mortar,  1547 
Colorado,  registration  law,  1778 
Column,  columns, 

bases  (see  Bases,  columns)     • 

base-plates,  440-445,  1524 

bearing-brackets,  445-447 

bearing-plates,  440-445,  1524 

bending  moments,  485. 

Bethlehem,  475,  479,  482-488 
loads,  tables,  483,  506-515 

box,  342,  467,  479,  484 

caps  (see  Column-caps) 

cast-iron,  455,  466 

advantages  and  disadvantages,  455 
bearing-brackets,  445-447 
breaking-loads,  462 
connections,    445,    447,    457,    458, 


Column,  cast-iron,  cylindrical,  456, 457, 
459,  461,  1523' 
design,  456-459 
failure  by  fire,  780 
fireproofing  for,  781,  822-826 
H-shape,  456,  458 
inspection,  456 
reinforced-concrete,    connections, 

945 
safe  loads,  461-466 
square,  hollow,  456,  458,  461,  1522 
strength,  459-466,  480-482 
weight,  1522,  1523 
channel  (see  Channel,  columns) 
classification,  448 
concrete,  not  reinforced,  284 
cross-sections,    moments    of    inertia, 
342,  343 
radii  of  gyration,  344,  345 
definitions,  448,  467,  477,  1810 
eccentric  loading,  pipe  columns,  472 
eccentric  loading,  steel  columns,  485- 

488 
eccentric  loading,    wooden    columns, 

453,  454 
fireproofing  for,  468,  780-782,  822- 

826,  959,  960 
footings  (see  Column-footings) 
general  principles,  448 
H  columns,  456,  458,  459 

economy,  458,  474,  483 

safe  loads,  cast-iron,  466 

safe  loads,  steel,  506-515 
I-beam  columns,  474,  488,  504,  505 
Lally,  467^  474,  477 

loads,  488,  516 
lattice,  477-479 
lengths,  schedule  for,  492 
loads,  live,  proportion,  148-152,  489, 
490,  1196,  1198 

tables,  488-490,  493-554 
mill-construction,  782-788,  969,  976- 
978,  980,  981 

cost,  810 
pipe,  469-474,  488 

loads,  488,  497,  498 
plate-and-angle  (see  Columns,  steel) 
reinforced-concrete,    941-946,    969, 
980 

calculations  for,  976,  977 

fire-proofed,  958-959 

metal-core,  944-945 
safe   loads,    tables,    482,    490,    493- 

554 
slenderness-ratio,  448 
steel,  467-554 

bases  for,  473-477 

beam  columns,  safe  loads,  504-50S 

box,  342,  343,  467,  479 

channel  (see  Channel,  columns) 

rhniVp  of  tvne.  a67— a68 


Index 


1867 


Column,   steel,   connections,   468,   470, 
471,  473-478,  945-946 
connections  in  wind-bracing,  11 74, 

1175,  1179,  1189,  1190 
cost,  467,  468,  1207 
design,  482-485 
eccentric  loading,  485-488 
examples,  482-488 
failure,  469,  819 
fireproofing  for,  468,  780,  782,  819, 

822-826 
formulas,  480-482,  485,  493-496 
diagram,  496 
Gordon's  formula,  481,  484,  485, 

486,  487,  493-485,  496 
Rankine's  formula,  481,  484,  493, 

469 
straight-line,  481,  482,  493,  496, 
1139 
H-column,    table    of    loads,    483, 

504-515 
lattice,  477-479 
loads,  1196,  1198,  1201 
loads,  proportion,   148-152,  489- 

490,  1196,  1198 
loads,  tables,  488-490,  493-554 
plate-and-angle,  467,488,517-532 
(see    Plate-and-angle    column) 
reinforced  concrete,  946 
section,  467,  468 
splices,  1201 
strength,    general   principles,   480- 

482 
stresses,  618,  1138,  1200 
struts,  angle,  safe  loads,  488,  501- 

503 
types,  467,  477 
steel-pipe,  469-474 

loads,  488,  497,  498 
struts  in  trusses,  480,  499-503 
wind-bracing,  1174,  1183,  1189,  1190 
wooden,  bases  for,  782-788 
bolsters,  454,  795 
eccentric  loading,  453,  454 
factor  of  safety,  448 
formulas,  450,  11 39 
metal  caps,  454,  762,  782-788,  795- 

800 
mill-construction,  782-788 
safe  loads,  448,  449,  45© 

tables,  451,  452 
strength,   general   principles,   448- 
450 
wrought-iron,  fireproofing,  780,819 
Column-bases  (see  Bases) 
Column-caps,  metal  for  wood,  454,  762, 
782-788,  795-800 
for  steel-pipe  columns,  470, 471,  472 
Column-footings,      bearing-plates     for, 

440-445 
•  desiern.  178-188 


Column-footings,  loads  for  design,  151, 
152,  160 

moments,  176-178 

plan,  1 195 

proportioning,  152-164 

reinforced  concrete,  186,  974,  978-982 
Colunin-sheets,  490 
Combined  stresses,  128,  480,  572,  11 14 
Commercial   weights    and    measures, 

28 
Commodes,  dimensions,  1638,  1640 
Competitions,  architectural,  1 733-1 747 

ethics,  1729 
Composite  Order,  1702 
Composite  piles,  timber  and  concrete, 

198 
Composition,  forces,  288 
Compound  sections,  moment  of  inertia, 

radius  of  gyration,  344 
Compression,  127 

members,   steel,   specification,    1201- 

1203 
sig-,  1065,  1068 
Concrete    (see,    also,    Reinforced  con- 
crete), 240 
adhesion  to  steel,  912,  919,  920,  938, 

940 
aggregates,  241,  287,  908,  909,  945 

effect  of  heat,  817 

strength,  287 
beam-protection,  860 
beams,  not  reinforced,  628,  637 

coefficients  for,  628 

fiber-stresses,  557 
bearing  surface,  285 
blocks,  816,  956 

fire  test,  956,  957 

machinery  for,  816 

walls,  233 
bonding  old  and  new,  965 
capping  of  piles,  191 
cinder,  242,  250,  909,  930 

corrosion  of  steel,  818,  960,  961 

fire-resistance,  818 

weight,  250 
column-protection,     780-782,    822- 

826 
columns,  284 
compression-tests,  283 
compressive  strength,  283,  287,  441 

tests,  284-286 

working    stresses,    265-267,    287, 

441,  911 
consistency,  243,  286 
corrosion  of  steel,  818,  960,  961 
cost,  249-250,  910 
dehydration  of,  245 
design  of  massive,  246 
electrical  action,  17 13 
finish  of  surfaces,  246,  965 


1S6^ 


Index 


Concrete,  fireproofing,  column-protec- 
tion, 780,  782,  822-826 

concrete  blocks,  816,  956 

roofs,  866,  871 

tests,  245,  955-960 

warehouse-construction,  780-782 
flour-mixtures,  17 12 
forms,  245,  962-965 
freezing-temperature,  244 
gravel,  241,  286,  908 
heat,  conductivity,  245 

effect  of,  245,  817,  957-958 
I-beam  protection,  780,  847 

ceilings,  849 

roofs,  871 
I  beams,  854 
laitance,  244 
limestone,  weight,  250 
mass,  strength,  267 

design,  246 
materials,  proportions,  243,  247,  907, 

909-910,945 
mechanical  analysis,  910 
mixers,  963 
mixing,  242,  243,  963 
mixtures,    909-910,    945,    963-964, 

1712 
modulus  of  elasticity,  934,  935 

blocks,  heated,  956 

design,  assumption,  924 

ratio  to  steel,  912 
modulus  of  rupture,  284 
molds  for,  962-966 
natural  cement,  235,  267,  284 
painting,  1573 
partitions,  876,  881 
penetrative  washes,  171 2 
permeability,  causes,  1710 
pile-capping,  191 
piles  (see  Piles) 
pipe-column  filling,  469 
placing,  244 
plant-cost,  250 
Portland-cement,  240-251 
pouring,  964 
preparing,  242 
properties,  240 
proportions,  240,  243,  247-249,  907, 

910,945,  1712 
protective  coatings,  171 2 
ramming,  964 

reinforced  (see  Reinforced  concrete) 
retempering,  244 
rubble,  244 
saline  waters,  1713 
sand  in,  241,  247,  908 

grading,  241 
shearing  strength,  284 
shrinkage,  245 
slag,  fire-resistance,  817 
specific  gravity,  1503 


Concrete,   stone   (see  Concrete,  aggre- 
gate) 
strength  (see  Concrete,  compression) 

tensile,  284 
surface-finish,  246,  965,  1555 
temperature-changes,  245 
tensile  strength,  284 
test  for  hardening,  245 
tests,  283-287,  817 
tile,  strength  of,  817 
tiles,  816 
tools,  963-964 

cost,  250 
transporting,  964 
trap-rock,  250,  817 
tremie,  use  of,  244 
under-water,  244 
uses,  240,  906 
walls,  228-229,  946-947,  965,  966 

cost,  250 
water  used  in,  242,  909 
waterproofing,  246,  1 709-1 717 
weight,  250,  1503 
Conductors,  electricity,  1458 
lightning,  1704-1707 
water,  roofs,  1658 
Conduits,  electric-wiring,  1479 
Cone,  38 

center  of  gravity,  295 
frustum,  38,  61,  63 
surface,  61 
volume,  63 
Conic  sections,  38 
Coniferous  woods,  ultimate  unit  stresses, 

649 
Connections      (see      under      Columns, 

Beams,  etc.) 
Consoles  (Glossary),  181 1 

terra-cotta,  278 
Construction,  insurance  during,  1756 
Continuous   beams   and   girders,    555, 

671-680,  979,  980 
Contract  drawings,  1753 
Contracts,  arbitration,  1763 

architect  and  ov/ner,  1740,  1746 
contractor  and  owner,  1751 
forms,  1750,  1752 
owner  and  competitor,  1740,  1746 
subcontractor  and  contractor,  1765 
uniform,  1749 
Contractor  vs.  Architect,  relation,  1729 
Contractor's  insurance,  1756 
Conversion  tables,  metric,  33-35 
Coping  (Glossary),  181 1 

stone,  1539 
Copper,  roofs,  1604    - 
sheets,  1049,  1510-1511 
specific    gravity    and    weight,    1503, 

1510 
wire,  401,  1469,  1474,  1513 
current  capacity,  1470 


Index 


1869 


Corbel  (Glossary),  iSii 
Cords,  sash  i,see  Sash-cords) 
Core-borings,    foundation-bed    testing, 

145 
Cores,  steel,  in  concrete  columns,  441 

reduction  for,  in  castings,  1521 
Corinthian  Order,  1702,  1703 
Comer-basins,  dimensions,  1641 
Comer-slabs,  dimensions,  1641 
Cornices  (Glossary),  181 1 

mills,  764,  769 
Corr-bars,  916,  923 
Corr-mesh,  853 
Corrosion,  cinder  concrete  on  sleel,  818, 

960,  961 
Corrugated  bars,  916 
Corrugated  iron  and  steel  roofing,  1046, 

1049,  i599-'i6o4 
Cormgated  sheets,  1599-1604 

anti-condens-  tion  lining,  1603 
ceilings,  1604 

covering  capacity,  1603 

floors  and  roofs,  851 

galvanizing,  1600,  1604 

gauges,  402,  1 5 10,  1600 

laying,  1601 

sides,  building,  1603 

weight,  1600,  1603 
Cosecants,  tables  of  natural,  117 
Cosines,  tables  of  natural,  95 
Cost,  costs,  brickwork,  1 544-1 547 
mill-buildings,  808-810 

buildings,  cubic  foot,  1611-1634 

building-papers,  1568 

carpenters'  work,  1564 

cement,  238,  248,  910 

columns,  mill-construction,  810 

concrete,  249-250,  9io.  i6i3,  1618 

cubic  foot,  buildings,  1611-1634 

cut  stonework,  1539 

drafting,  structural  steel,  1206 

driving  wooden  piles,  195 

ilvvellings,  161 3 

elevators,  1659,  1670 

enameled  bricks,  IS44 

erecting  structural  steel,  1206 

estimating,  buildings,  1611-1635 

excavating,  153^^ 

exposition-buildings,  1627 

Federal  buildings,  1613,  1626-1633 

felts,  1565,  1568 

tire-proof  partitions,  889 

flagstones,  i539 

floors  in  mills,  810 

glass,  1574-1577 
polished  plate,  1576 
sheet,  1575 
skylight,  1580 
window,  1577 

incandescent  lighting,  1482 

labor,  1564 


Cost,  lathing  and  plastering,  1557 
library-stacks,  1697 
mill-construction,  reinforccd-concreto, 
777,  1613,  1618 
slow-burning,  758,  77: 
mineral  wool,  i6io 
office-buildings,  1613 
partitions,  sound-deadening,  889 
piles,  driving,  195 
pitch-slag,  roofs,  1598 
plumbing-fixtures,  810 
public  building,  1613,  1628-1634 
refrigeration,  1695 
reinforced  concrete,  250,  910,  1613, 

1618 
roofs,  mill-buildings,  777,  810 
roofing,  asphalt-gravel,  i599 
gravel,  1598 
slag,  1598 
slate,  1046,  1585 
tile,  1046,  1587.  1607 
tin,  1046.  1589,  1593,  1594 
saw-tooth  roofs,  777 
school-buildings,  1613,  1614,  1616 
slates,  1046,  1585 
slow-burning  construction,  758,  802- 

810,  1619 
square  foot,  buildings,  1627-1634 
steel,  structural,  1204-1212 
stonework,  1538 
tiles,  1046,  1587,  1607 
tin,  gutter-strips,  1594 
rolls,  1594 

roofing,  1046,  1589,  1593,  1594 
trusses,  steel,  1206 
warehouses,  777,  802-810 
Cotangents,  tables  of  natural,  115 
Cotton,  weight,  72a 
Cotton-mill,  design  and  cost,  803 
Cotton  rope,  406 
Counterbraces,  wooden  trusses,   1000- 

1006,  1034,  1 104 
Counterforts,  retaining  walls,  263 
Counter-ties,  3S6 
Counterthrust,  305 
Cover-plates,  box  girders,  696 
plate  girders,  687 
riveting,  421,422 
Crane,  chain,  410 

clearance-diagram,  119S 
load,  1197,  1201 
truss,  1069 
Creosote,  1570 

oil,  1503 
Crockery,  weight,  723 
Cross  (Glossary),  181  a 
Cross-sections,  332-374 
Crown,  of  arch,  305 

Crushing  strength  (see  under  each  ma- 
terial) 
Cubage,  161 2 


1870 


Index 


Cube,  cubes,  38 
Cube  root,  4 

tables,  8-24 
Cubic  measure,  27 

metric,  31 
Cummings  system,  reinforcing,  923 
Cupola  process,  iron,  1379 
Curbing-stones,  1539 
Cycloid,  definition,  80 

problems  on,  80 
Cylinders,  38,  63 

contents  of,  various  diameters  .1403 
Cypress,  beams,  distributed  loads,  641 
deflection,  664 
flexure-stress,  557,  650 

columns,  safe  loads,  450,  452 

crushing-loads,  across  the  grain,  454 
with  the  grain,  449 

specific  gravity,  1503 

ultirtiate  stresses,  650 

weight,  650,  1503 

working  stresses,  647 

Dahlstrom  metal  doors,  896 
Dams,  concrete,  cost  of,  250 
Dead  load,  definition,  126 
Deadening  partitions,  890 
Deadening-quilts,  1565 
Decagon,  37 

Decimals  of  inch,  table,  26 
Deck-beams,  steel,  loads,  565 
Deflection,  beams,  663-670 

allowed,  566,  628,  664,  736 
steel,  566,  612,  668-670,  677 
wooden,  636,  653,  654-657 

continuous  girder,  674-676 

diagram,  670 
Deformation,  definition,  125 
Degree,  degrees,  of  heat,  1250 
Density,  1247 

Denver  building  code,   masonry-loads, 
267,  287 

thickness  of  walls,  231-232 
Department-stores,  steel,  weight,  1208 
Depreciation  of  buildings,  1634 
Derrick,  rope  for,  408 
Desks,  sizes,  1640,  1645 
Details,  structural,  specifications,  1202 
Diagonals,  37 
Diameters,  37,  1814 
Diamond  bar,  reinforcement,  917 
Diamond  bits,  foundation-bed,  testing,  145 
Diamond-mesh  lath,  884 
Dimensions,  useful,  1637-1658 
Dodecagon,  37 
Dogwood,  hardness,  1558 
Dolomite,  131,  132 
Domes,  1213-1231 

(Glossary),  1814 

angle,  critical,  1213 

reintorced  concrete,  121 7,  1225-1231 


Domes,  ribbed,  1222 

secondary  stresses,  1220 

smooth-shell,  12 13 

steel,  1222 
weight,  1224 
Door,  doors,  fire-resisting,  801 

iron,  standard,  definition,  1854 

metal    and    metal-covered,    894-897, 
901-902 

school-buildings,  1648 
Door-frames,  cement,  898 

metal,  897 

terra-cotta,  898-899 
Door-sills,  stone,  1539 
Doric  Order,  1 699-1 700 
Double-plenum-chamber  system,  heat- 
ing, 1327 
Douglas  fir,   beams,  distributed  loads, 
642 
deflection  in,  664 
flexure,  557,  628,  647,  650 

columns,  safe  loads,  451 

crushing-loads,  with  the  grain,  449 

crushing  strength,   across   the   grain, 
454 

specific  gravity,  1503 

unit  stresses,  376,  412,  647,  650 

weight,  650,  1503 
Dovetailing  (Glossary),  181 5 
Dowel  (Glossary),  1815 
Documents,      American     Institute     of 
Architects,  list,  1767 

standard,      American      Institute      of 
Architects,  1748 
Draft,  definition,  1364 

natural,  air-velocity,  1302 
Drafting,  structural,  cost,  1206 
Drain,  drains,  1407-1414 

area,  1408 

cellar,  142 1 

house,  1407-1414,  1419-1421 
Drain-pipes  (see  Pipes) 
Drainage  of  buildings,  1407-1414, 1419- 

1421 
Drainer,  cellar,  142 1 
Drawings,  architect's,  1728,  1754 

competitive,  1737,  I744.  I745>  174^ 

contract,  1753 

property  of  architect,  1733 

shop,  1754 

working,  steelwork,  1195 
Drift-pins,  414,  682 
Drill-rooms,  floor-loads,  719 
Drop-hammer,  pile-driving,  190 
Drum-trap,  141 3 
Dry  measure,  27 
Dry-rot,  759 

Du  Long's  formula,  heat  of  coal,  1272 
Duchemin's  formula,  wind,  1199 
Ducts,  air,  design,  1333-1341 

cold-air,  furnaces,  1319 


Index 


IS71 


Ducts,  fresh-air,  sizes,  1322 

hot-air,  area,  1301 

metal  gauge,  1336 

system,  design,  1346 
Dwellings  (see  also  Residences) 

cellar  walls,  229 

cost  of  constructing,  1613,  1614 

floor-joists,  737,  742 

floor-loads,  149,  719,  1198 

heating,  1256,  1353,  1361-1363 

wall-thickness,  230,  232 
Dyestaffs,  weight  of,  723 

Earthy  material,  132 

weight,  1537 
Eastern  fir,  safe  load,  639 

safe  stress,  647 
Ecceitric  loads  (see  Loads,  eccentric) 
EchiDes,  acoustics,  1487 
Edncitioa,  registration  laws,  1769 
Eljcitioaal  institutions,  1779 
Ejflaressence,  brickwork,  1547 
Egyptiii  long  measures,  34 
Egyptian  style,  architecture,  1704 
Elastic  limit,  definition,  126,  381,  913 
Elasticity,    coefficient   or    modulus   of, 
126,  626,  662 

reinforced  concrete,  912,  934 

steel,  381,  912,  934 

timbsr.  647,  731-734 
Elbows,  heating,  pressure-loss,  1338 
Electric  work  for  buildings,  1457-1485 

cabinet-wiring,  i477,  1481 

center  of  distributioA,  1471 

circuit-breakers,  1461 

cods-requirements,  1480-1482 

conductors,  1458 

conduit  system,  1479 

cost,  of  lighting-equipment,  1482 
of  wiring,  1482 

design  of  lighting  systems,  1446-1448 

drop  of  potential,  1470 

feed-wires,  1478 

fuse,  enclosed,  1461 

fuse-block,  1481 

insulators,  1458 

interior  wiring,  1482 

knife-switch,  i477,  1479 

lamp-arrangement,  1465,  1466 

lamps,  number  of,  1446,  i449»  ^475 

national  electrical  code,  1480 

power-computations,  I4S9 

speciflcations,  1482 

switches,  1478,  I479 

systems  of  lighting,  1464-1469 

wire-calculations,  1469-1472 

wire,  dimensions,  weights,  i474,  i475, 

1477 
carrying  capacity,  1470,  I473,  I475 
wiring-diagram,  1476 

symbols,  1476-1478,  1484 


Electricity,  1457-1464 
Electrolysis,     reinforced-concrete    foot- 
ings, 186 
Elevator,  1659-1677 

car-platform,  1661,  1666,  1675,  1676 
comparison    of    types,    1660,    1664, 

1670 
cost,  1659,  1670 

counterweights,  protection  of,  1662 
development  of  systems,  1667-1669 
economic  considerations,  167 1 
efficiency,  1659 
electric,  1659,  1666,  1669,  1676,  1677 

versus  hydraulic,  1660,  1664,  1670 

passenger  systems,  1667-1670 
express,  1661,  1673,  1675 
geared,  1659,  1669 
gearless,  1659,  1665 
hatchway,  size,  1660,  1667,  1675,  1676 
hoistway,  1660,  1662 
hydraulic  plunger,  1670 

versus  electric,  1660,  1664,  1670 
installation-data,  1663,  1674,  1675 
laws  governing,  1663 
loads,  1662,  1674 
local,  1661,  1673,  1675 
machinery-room,  1660 
motors,  current-consumption,  1677 

feeders,  1677 

sizes,  1676,  1677 
number  required,  i66i,  1673 
operating-costs,  1670 
power-diagrams,  167 1 
push-button  control,  1666 
safety-appliance,  1664,  1669,  1672 
service,  formulas  for,  1673 
signal-systems,  1672 
sizes,  1661,  1667,  1675 
specifications,  1663 
speeds,  1662,  1674 
standard  designs,  1663 
time-schedule,  167 1 
towers  for,  in  mills,  764,  765,  768 
traction,  1665,  1669,  1670 
traffic-capacity,  1672 
types,  1660,  1668 
use  of,  1667 
Elevator-tower,  mill-construction,   764, 

765 

storehouse,  768 
Ellipse,  38 

center  of  gravity,  293 

problems  on,  74,  79 
Ellipsoids,  60,  65 
Elm,  ha  dne-.3,  1558 

specific  gravity,  1503 

ultimate  unit  stresses,  651 

weight,  651,  1503 

working  stress,  flexure,  557 
Elongation,  eye-bars,  386 

steel,  38T,  384,  913 


1872 


Index 


Enamel,  painting,  1570 
Enameled  tile,  1605-1607 
Energy,  work,  1248 

and  power,  relation,  1250 
Engineering,  architectural,  terms  used, 

124,  128 
Engineering    News    formula    for    pile 

foundations,  193 
Engines,  fire,  dimensions,  1642 

foundations  for,  1716 

hot-air,  1393 
Eimeagon,  37 
Entasis  (Glossary),  1817 
Entropy,  of  steam,  1254 
Equilibrium,  124 

of  parallel  forces,  290 

polygon,    forces,    289,    299,    313-315, 
319 
Estimates,  architects',  1728 

guaranteed,  1731 
Estimating  (see  Costs) 

quantity  system  of,  1635-1637 
Ethics,  professional,  1729,  1731 
Eustyle  (Glossary),  181 7 
Evaporation,  1251-1254 

equivalent,  boiler,  1274 
Evolution,  mathematics,  3-5 
Examination,     architects.     New     York 

state,  1.772 
Excavation,  200-222 

below  water,  203 

bracing,  201 

Chicago  method,  209 

data  on,  1536 

dredged  wells,  210 

earth-pressure,  201,  205 

freezing  process,  214 

needling,  218-222 

open-caisson  method,  210 

pneumatic -caisson  method,  21 1-2 14 

poling-board  method,  209 

protecting  adjoining  structures,  214- 
222 

quicksand,  137,  211 

rock,  1537 

sheet  piling,  200-209 

shoring,  214-222 

underpinning,  214,  218-222 

volume  of,  computing,  65 

well-curb  method,  210 

well-digger's  method,  211 
Expanded  metal,  846-847,  883-884,  919 
Expansion-bolts,  1534 
Expansion- tank,  1360 

hot-water  heating,  1307,  1308 
Exposition-buildings,  cost  of,  1627 
Expenses,  architects,  1731 
Expert,  in  competitions,  i735 

services,  payment,  1728 
Extrados,  arch,  305 
Eye-bars,  386,  395 


Face,  arch,  305 
Face-wall,  definition,  255 
Factor  of  safety,  126,  375,  556 
Factories,  air-changes,  1260,  1353 
brick,  808-810 

heating,  direct  radiation,  1296 
hot-blast,  1324,  1336,  1342-1347 
temperature,  1256 
non-fireproof,  height,  813 
reinforced-concrete,  968-997 
steel,  1210,  1627 

wooden  construction,  758-810,  1634 
Fahrenheit  thermometer,  1250 
Fan,  maximum  speed,  1357 

ventilation,  1341-1347,  1357 
Fj.n  system,  heating,  13  24-1341 
Fan  trusses,  1025-1029,1145 

stresses,  1058-1060,  1078,  1145 
Federal  buildings,  cost,  1613,  1626  1633 
Feed-wires,  electric,  1478 
Fees,  architects',  1731 
Feet  converted  into  meters,  34,  35 
Feldspar,  131 

specific  gravity  and  weight,  1504 
Fellowships,  architectural,  177 9- 1788 
Felts,  asbestos,  1567 
building,  1564-1568 
cost,  1565,  1568 
Ferroinclave,  floors,  850-851 
roofs,  851 

stair-construction,  900-901 
Fiber-stresses    (see,    also,    under  each 

material),  126,  556,  557 
Field-rivets  (see  Rivets) 
Fillers,  web-stififeners,  686 
Filters,  water,  142 1 
Finial  (Glossary),  181 8 
Fink  truss,  1025-1030,  1161-1164 
cambered,  stresses,  1079-1081 
stresses,  1058-1061 
steel  members,  1148,  1 161-1 164 
Fir,  Douglas  (see  Douglas  fir) 
Eastern,  beams,  safe  loads,  639 
unit  stresses,  647 
Fire-clay,  flue-linings,  1281 
Fire-doors,      metal-covered,      894-897, 
901-902 
stairways,  779 
tin-covered,  901,  1855 
Fire-engines,  dimensions,  1642 
Fire-escapes,     warehouses,     764,     765, 

778,  779 
Fire-extinguishers,  903-905 
Fire-protection,  alarm  system,  electric, 
903-905 
doors  (see  Fire-doors) 
fire-extinguishers,  903-905 
fire-retardants,  759 
hose,  768 
hose-reels,  905 
outside  hazard,  901-903 


Index 


1873 


Fire-protection,  partitions,  8oi 
pumps  for  fire-streams,  759,  1401 
roof  nozzles,  801 
scuppers,  767 

shutters,  759,  778,  801,  901,  902 
signaling  systems,  905 
sprinklers,  801,  903   90S 
mill-buildings,  759,  7^8 
timber-spacing,  777 
tanks,  779 
stairways,  764,  765,  778,  779 
'      standpipes,  768,  801,  905 
steam-pumps,  1401 
steelwork,   468,    760,    780-782,   819, 

822-826 
tanks,  779,  1402 
water-supplies,  802 
wire-glass,  759,  778,  821 
Fire-pumps,  steam,  759,  1401 
Fire -resistance  of  materials  (see  Fire- 
proofing) 
Fire-stops,  mill-construction,  759 
Fire-streams,  1397 
pumps  for,  1401 
Fire-tests  (see  Tests)  * 

Fire-towers,  764,  765,  778,  779 
Fire- walls,  storehouses,  765 
Fireplaces,  flues,  1282 
Fireproofing,  asbestic  plaster,  818 
asbestos,  819 
beams  and  girders,  780-782,  827-842, 

844,  849,  854-860 
brickwork,  814 
buildings,  811-905 

cost  of,  802,  812,  1619-1625 
percentages  of  cost,  1619 
ceilings,  871-872 
columns,  cast-iron,  781,  822-826 
steel,  468,  780-782,  822-826 
wrought-iron,  780,  819 
concrete,  column-protection,  824-826 
concrete  blocks,  816-818,  956 
floors,  860-866 
roofs,  866 
tests,  245,  955-960 
warehouse-construction,  780-702 

flooring,  892-893 

floors,  826-866 

interior  finish  and  fittings,  893-901 

materials,  811-905 

fire-resistance,   245,  814-822,  955 
960 
mortars,  818 

municipal  definitions,  811,  i»53 

paint,  821-822,  894 

partitions,  873-892 

plaster,  818,  878  882,  889-891 

plaster  of  Paris,  818 

prism  glass,  821 

reinforced-concrete,   781,  811,  955 

960 


Fireproofing,  roofs,  801,866-872,  1597 
stairs,  899-900.  947,  983 
steel,  468,  760,  780,  822-  826 
stone,  814 
terra-cotta,      234,      814-815,     828, 

874 
trusses,  860 

wall-coverings,  881-892 
wire-glass,  821 

wood,  fire-proof,  820,  894-895 
Fires,  cast-iron  in,  819 

steel  and  wrought-iron  in,  819 
concrete  affected,  245,  955-96o 
Fish-plate,  roof -trusses,  11 55 
Flagpoles,  dimensions,  1644 
Flagstones,  282,  1539 
Flashings  (Glossary),  1818 
Flats,  steel,- safe  loads,  389 
Flexure,  126,  324-331,  332-334,  555 
reinforced-concrete  beams,  924-941 
steel  beams,  564-573 
wooden  beams,  627-637,  647-656 
Flint,  130 

specific  gravity  and  weight,  1504 
tile,  1605 
Flitch-plates,  beams  and  girders,    655. 

656 
Floor,  floors,  asphalt,  1608 
Akme  system,  949 
beam-and-slab,  968 
Berger's  metal  lumber  and  concrete, 

852,858 
brick  arches,  827 
cantilever  flat  slab,  95© 
Climax  system,  85s 
Corr-plate  system,  950 
Excelsior,  tile,  838 
expanded-metal  and  concrete,  847 
Ferroinclave,  850-851 
fire-proof,  brick  and  tile,  826-842 

concrete,  842-866 
fire  tests,  827 

flat  reinforced,  845-846,  949-952 
Floredome  system,  953 
Floretyle  system,  952-953 
framing,  steel  (see  Frammg) 
girderless,  968,  993-997     _ 
girders,    steel,    specifications,     1201, 

1202 
Guastavino,  841-842,  843,  i243 
heat-transmission,  1259 
heating  pipes  through,  1360 
Herculean,  838-839 
I-beam  system,  concrete,  854-855 
Johnson  construction,  837-841 
joists  (see  Floor-joists) 
keys,  tile,  835 
loads  (see  Loads) 
lock-woven  fabric,  849-850 
M  system,  948-949 
metal  lumber,  858 


1874 


index 


Floor,  mill, 730,  760,  766,  769,  782-794 
(see  Mill-construction) 
New  York,  tile.  S40 
reinforced-concrete,     842-856,     924- 
940,  948  955,  968,  971 

cost,  250 

design,  985-99? 

four-way  reinforcement,  949 

girderless,  968,  993-997 

mushroom  system,  950,  993-997 

S.  M.  I.  system,  950 

top  coat,  239 

triangular-mesh  fabric,  850 
reinforced  tile,  838-842 
sectional  systems,  853-854 
segmental,  concrete,  844-845 

tile,  831,  832 
separately-molded,  953     - 
side-construction,  830-833 
Siegwart  system,  855 
skewbacks,  tile,  834,  835 
square-panel  system,  968 
steel  framing,  computations,  861-866 
System  M,  948 

terra-cotta,  828-840,  1604-1607 
tie-rods,  307,  832 
tile,  828-840,  953,  1 604- 1 607 
tile-and-concrete,  951-952 

end-construction,  829,  833,  837 
Vaughan  system,  856 
Waite's  concrete  I-beam  system,  854 
warehouses,  764,  777 
Watson  system,  856 
weight  (see  Loads) 

of  wooden  construction,  718 
welded-metal  fabric,  848 
wire  fabrics,  848-850 
wooden,  cost,  810 

estimating,  1563 

framing,  721-731,  746-757 

mill-construction,  730,  760,  766 

old,  strength,  749 

plank,  730-735 

strength  and  stiffness,  717-757 

warehouses,  764,  777,  893 
workshop,  769 
Floor-joists,    wooden,    assembly-halls, 
maximum  span,  739,  744 
bridging,  748,  749,  1804 
churches,  738,  743 
continuous,  717 
corridors,  739,  744 
dwellings,  span,  737,  742 
framing-details,  749-757,  782-795 
hangers,  750-757,  782-794 
nominal  and  actual  sizes,  637 
office-buildings,  738,  743 
plans,  717,  727,  747 
school-buildings,  717,  737,  742 
size,  637 
spans,  maximum,  736-746 


Floor-joists,   wooden,   stiffness,  tablei 
635,  638-646 
stirrups,  750,  751,  754-757,  787-79 
stores,  span,  739,  744 
strength,  tables,  635,  638-646 
tenements,  737,  742 
theaters,  maximum  span,  738,  743 
weight,  wooden,  718 
Floor-slabs   (see  Reinforced  concrete 

slabs) 
Floor-tiling  (see  Flooring) 
Flooring,  banks,  893 
cem^ent,  831,  893 
composition,  893 
concrete  finish,  965 
fire-proof,  893 
hotels,  893 
matched,  1563 
mortar  over  concrete,  965 
Mosaic,  1607 
slate,  1606 
terrazzo,  1607 
tiling,  1604-1607 
toilet-rooms,  893 
•    warehouses,  764,  777,  892,  893 
wooden,  cost,  810 
estimating,  1563 
mill-construction,  760,  766 
old,  strength,  749 
plank,  730-735  _ 
strength  and  stiffness,  717-757 
Floredome,  953 
Flore tyle,  952-953 
Floriluxe,  1579 
Flues,  1281-1283,  1365 
gas-velocity,  1364 
vent,  1356,  1357 
Fluid  measure,  28 
Flushometer,  Kenney,  1420 
Font  (Glossary),  1819 
Foot-baths,  dimensions,  1641 
Foot-car  die,  1439,  1440 
Footings,  129,  223   (see  also,  Founda- 
tions) 
areas,  minimum,  152 
bending-stresses,  172-178 
brick,  226,  227 
cantilever,  165-169,  978 
columns,  design,  178-188 

loads  for  design,  151,  152,  i6o 
proportioning,  155-164 
moments,  176-178. 
reinforced-concrete,  974,  978-982 
compound,  178 
concentric  loads,  160 
concrete,  225,  226 
cost,  250 
design,  179 

reinforced,  186,  946,  978 
conditions  affecting,  188 
continuous  beams,  979 


Index 


1875 


Footings,  courses,  129,  169-172,  223 

cracks  in,  224 

crushing,  failure  by,  171 

defined,  1852 

depth  of,  minimum,  188 

design  of,  178,  978 

eccentric  loads,  162 

factor  of  safety,  178 

failure  of,  170-172 

flexural  strength,  178-179 

grillage,  steel,  166-169,  181-185 

homogeneous  slabs,  178 

inverted  arches,  227-228 

light  buildings,  223 

loads,  148-163,  170,  223,  265-267,  978 

offsets,  163-165,  179,  223-227 

piers    (see   Footings,   columns,   and 
Piers,  footings) 

projection  and  depth,  ratio,  180-181 

reinforced-concrete,  186,  946,  978 
electrolysis    186 

retainiug-vvalls,  261,  262 

settlement,  152-160 

shear,  failure  by,  170-171 

size  and  form,  169 

slabs,  homogeneous,  178 

spreading,  failure  by,  171 

steel  beams  in,  181-185 

stone,  223-224 

stresses,  169-178 

timber,  186-188 

unit    and    separate-layer    compared, 
i8o 
Foot-pound,  290 
Foot-pound-second  system,  1247,  1250 

to  B.t.u.,  1251 
Force,  forces,  124 

axial,  375 

center  of  gravity,  127,  291-296 

composition,  288,  1065 

compression,  127,  1065,  1068-1072 

equilibrium,  124,  289,  299,  313-315, 

319 
external,  125,  325,  1066 
graphic  statics,  1065 
internal,  125,  325,  1066 
lever,  principle  of,  165,  290-294 
line  of  action,  289 
magnitude,  288 
moments  of,  127,  289,  322 
parallel,  290-291 
parallelogram  of^  289 
point  of  application,  289 
polygon  of,  289,  1070 
reactions,  beams,  322-324 

trusses,  1066 
resolution,  288,  1065 
resultant,  288 
sense  of,  289 

signs  for,  1065,  1068,  1072 
shear,  128 


Force,  stress  (see  Stress) 

tension,  127,  1065,  1068,  1072 
torsion,  128 
triangle  of,  289 
Forge-shop,  steel,  weight,  1209 
Forked  loop,  tension-member,  387 
Forms  for  concrete,  245,  962-965 
Fossiliferous  limestones,  132 
Foundation    (  ee,    also.    Footings    and 
Foundation-beds),  129-222 
adjoining  excavations,  130,  147 
adjoining  structures,  protecting,  214 
brick,  226-227 
caisson,  210-214 
cantilevers  in,  165-169,  978 
Cathedral  of  St.  John  the  Divine,  251 
columns,  161-163,  176-178,  184,  974, 

978-982 
concrete,  225,  226,  249-251 
early  examples,  251 
pile,  188,  196-200 
reinforced,  186,  196,  978 
conditions  affecting,  188 
definition,  129,  1852 
depth,  188 

engine,  water-proof  cement,  17 16 
excavating    for,    200-214    (see,    also, 

Excavation) 
footings  (see  Footings) 
general  requirements,  129,  130 
girdering-method,  166-169 
grillage,  steel,  166-169,  181-185,  678 
light  buildings,  223-229 
Manhattan  Life  Insurance  Building, 

251 
mining  districts,  147 
needling,  218-222 
piers,  129,  188    200 
pile,  reinforced-concrete,  196-200 

sheet,  201-209 

wooden, 188-196 
reinforced-concrete,  186,  946-947,978 
screw-jacks,  215,  216,  221 
settlement,  equal,  152-160 
sewers,  147 
shafts,  147 
shoring,  214-222 

spread,  166-169,  181-188,  978,  980 
subways,  148 
temporary  buildings,  187 
timber,  spread,  186-188 
trenches,  147 
tunnels,  148 

underuinning,  214,  218-222 
walls,  129,  200,  228,  229,  979 
Washington  Monument,  251 
waterproofing,  1709-1717 
wedges,  215 

wells,  147  ,         »        J 

Foundation-beds    (see,    also.    Founda- 
tions), 129  -148,  223, 


1876 


Index 


Foundation-beds,    boulders,    134,    136, 
141 
clay,  13s,  138,  139,  141,  143 
dirt,  135 
drill  tests,  145 
earthy  material,   132-133,   135,   138- 

140 
filled  ground,  140 
geological  considerations,  130 
glacial  deposits,  133 
hard-pan,  135,  141,  143 
gravel,  134,  136,  141.  i43 
loads  on,  140-143,  148-160,  223 

tests,  142-146 
loam,  13s,  143 

materials  composing,  130-140 
mould,  13s 
mud,  135,  139 
peat,  135,  139 
pipe-borings,  144,  145 
quicksand,  136,  137,  141,  143 
river-deposits,  133 
rock,  130-132,  134,  135,  141 
sand,  134,  136-138,  141,  143 
shale,  13  s 
silt,  135,  139 
soil,  132,.  135,  143 
testing,  141-146 
topographical  conditions,  146 
trenches  for  footings,  226 
varying  pressure  on,  163-164 
Foundry-castings,  379 
Foundry,  heating-temperature,  1256 
lighting,  1451 
steel,  weight,  1209 
Frames,  door,  898,  899 

window  (see  Window-frames) 
Framing,  floors,  wooden,  721-731,  746- 
757 
mill-construction,    760-764,    766, 
769,  782-794 
saw-tooth  roof,  772-777 
steel  beams,  612-618 

cast-iron  columns,   445,   447,   457, 

458,  946 
fire-proof  floors,  861-86G 
Lally  columns,  474,  477 
steel  columns,  468,  470,  471,  473- 

478,  945,  946 
wooden  floors,  616,  752,  753,  755, 
786-792 
truss-jomts,  1149-1170 
arched,  1024,  1039 
heel,  434-439,  1003,  11S0-1170 
iron  ties,  1019 
lattice  truss,  1008,  1009 
pin-connected,  423-429 
wind-bracing,  1174-1176,  1183-1193 
Freight  rates,  structural  steel,  1205 
Freight-cars,  capacity,  1643 
French  truss,  1026 


Friction,  theorem,  252-254 

water  in  pipes,  1388 
Frostproofing,  pipes,  1400 
Frustum,  of  cone,  38,  61,  63-64 

of  pyramid,  38,  61,  64 
Fuels,  1 271-1273 

air  required,  1272 

boiler-rating  affected,  1277 

calorific  value,  1271,  1272,  1273 

combustion,  1272,  1273 

consumption,  heating-boilers,  1278 

heating,  example,  131 7 
Fulcrum,  grillage,  166 
Furnace,  combination,  1358 

pipes,  1311,  1318,  1322,  1358-1360 

ratings,  1314 

registers,     1317-1320,     1355,     1358 
1360 
air-velocity,  1367 
pressure  loss,  1338 
symbol,  1350 

stack,  1312,  1317,  1322,  1358 

work,  specifications,  1357-1359 
Furnace-heating,  1310-1324 

fuels,  1317 

specifications,  1357-1359 

where  used,  1355 
Furnace-iron,  379 

Furnace-leaders,  1311,  1317,  1324,  i35{ 
Furniture,  dimensions,  1637-1640 

metallic,  898-899 

weight,  149 
Furring,  metal,  881,  892 

mill-construction,  759 

outside  walls,  891 
Fuses,  electric  work,  1461 
Fusion,  latent  heat,  1251 

Gable  (Glossary),  1820 

Gallon,  capacity,  1247 

Galvanized  iron  and  steel,  1600,  1604 

Garage,  floor-load,  1198 

Gargoyle  (Glossary),  182 1 

Gas,  acetylene,  143 1 

coal,  143 1 
as  fuel,  1273 

gasoline,  1432 

illuminating,  143 1-1436 

illumination  by,  1448,  1450,  1451 

lamps,  1451 

natural,  143 1 

perfect,  1256 

piping  for,  1432-1436,  1445 

velocities,  flue  and  chimney,  1364 

water,  1431 

weight,  1273 
Gas-pipe,  separators,  steel  beam,  614 
Gas-piping,  1432-1436 

symbols,  1445 
Gaskets,  pipe,  1389 
Gasoline,  1432 


Index 


1877 


Gauges,  American  Steel  and  Wire,  401, 
402,  1512 

Brown    &    Sharpe,    401,   402,    1469, 
1473,  1509,  1510 

circular-mil,  wire,  1469,  1473 

corrugated  sheets,  15 10,  1600 

for  air-duct  metal,  1336 

piano  wire,  401 

pressure,  1248 

railroad-tracks,  1642 

Roebling's  wire,  403,  1509 

sheet-thickness,  1509 

standard,  compared,  400,  402 

U.   S.   standard,   metal  sheets,   402, 
1600 

Washburn  &  Moen,  wire,  402,  1509 
jears,  size  and  speed,  1720 
jener  itor,  electric,  1463 

heat,  1309,  1316 
jealo^lcal  data,  foundations,  130-140 
jeo  nstrical  problems,  66-90 
je  3  me  try  and  Mensuration,  36-65 
jirder,  girders  (see,  also,  Beams) 

bearing,  634,  687 

Bethlehem  girder  beams,  358,  594- 
597 

box  (see  Box  girders) 

built-up,  wooden,  652-656 

continuous,  555,  671-680,  979-980 

deflection,  663-670 

continuous  girders,  674-676 

double-beam,  564,  603,  604 
tables,  607-611 

fireproofing   for,    780-782,    827-842, 
849,  854-860 

framing  (see  under  Framing) 

grillage-foundations,  678 

I  beam,  603-611 

latticed,  1008-1010,  1089-1091,  1181 
wind-bracing,  1176,  1181,  1182 

loads,  tables   of  safe,   S74-S9I,   594, 
6o2,  605-611 

plate  (s33  Plate  girders) 

reinforced-concrete,  972-974 

riveted  (see  Box  and  Plate  girders) 

steel  (s3  3  Beams,  steel) 

wall-support,  612,  792 

wind-bracing,  iiTi 

wooden  (;c3  Beams,  wooden) 
jirdering,  cantilever  foundations,  166, 

169,  978 
jliciil  deposits,  133 
jUss,  cast,  1606 

cost,  1574-1577 

crystal-sheet,  157S 

defects,  1575 

diffusion   of   light,    I453-I456,    i577- 
1580 

figured  rolled,  i577 

grades,  1574 

leaded,  1573 


Glass,  mills  and  warehouses,  759,  763 
764,  769,  772 
saw-tooth  roof,  775 

mirrors,  1580 

Novus  sanitary,  1606 

plate,  1576 

prism,  821,  1454-1456,  1578-1580 

prism-plate,  1577 

polished-plate,  1576 

saw-tooth  roof,  775 

sheet,  1574 

sizes,  1574-1577 

skylights,  1580 

specific  gravity,  1504 

tile,  1606 

types  of,  for  lighting,  1454 

weight,  723,  1504.  165 1 

window,  1577 

wire,  fire-protection,  759,  821 
Glossary,  1796-1850 
Gneiss,  132,  282 

specific  gravity  and  weight,  1504 
Gold,    specific     gravity    and    weight, 

1504 
Gordon's   formula,    cast-iron  and  steel 
columns,  460,  461,  481,  484,  485, 
487,  493-495,  496 
Government  buildings,  cost,  1628-1634 
Grain,  weight,  723 
Granite,  131 

angle  of  friction,  253 

beams,  coefficients  for,  628 
fiber-stress,  557 

compressive  strength,  266,  280,  281, 
282 
allowed,  267,  287 

curbing  for  sidewalks,  1539 

fire-resistance,  814 

modulus,  of  elasticity, '282 
of  rupture,  282 

shearing  strength,  282 

specific  gravity,  282,  1504 

tension,  282 

weight.  282,  1504 
Graphical  analysis,  arches,  311-321 

bending    moments   in    beams,   328- 
336,  564,  678,  690,  695,  698 

bending  moments,  in  pins,  426-429 

column  formulas,  496 

deflection  of  beams,  670 

domes,  1224 

forces,  252,  288-291 

friction,  252 

moment  of  inertia,  345 

piers  and  buttresses,  297-304 

retaining-walls,  257-259 

roof -trusses,  1065-1137 

vaults,  1 234-1243 
Graphite,  specific  gravity  and  weight, 

1504 
Grappier  cement,  236 


1878 


Index 


Grate-area,  boilers,  1276,  1283 
Grate,  furnace,  13  21 

surface,  heating-furnace,  1315 
Gravel,  angle  of  repose,  256 

beds  of,  133,  134 

concrete  aggregate,  286,  908 
graded,  241 

cost,  249,  250 

definition  of,  134,  136 

roofing,  871,  1027,  i595-i599 

safe  loads  for  foundations,  141,  143 

specific  gravity,  1504 

weight,  256,  1504,  1537 
Gravity,  center  of  (see  Center  of  grav- 
ity) 
Gravity,  specific,  substances,  1500-1508 
Gray-iron  castings,  379 

specific  gravity  and  weight,  1505 
Grease-traps,  141 4 
Grecian  long  measures,  34 
Greek  letters,  symbols,  123 
Grillages,  beams,  spacing,  182 

cantilever  foundations,  166 

column-footings,  184 

foundations,  166-169,  181-185 
continuous  girders,  678 

fulcrum,  foundations,  167 
Groin  (Glossary),  1821 
Groined  vaults,  1235-1240,  1822 
Groins,  1235 
Grouting,  269 

brick  footings,  227 
Guastavino  tile-arch  system,  841,  8.12, 

1243 
Gum  wood,  unit  stresses,  651 

weight,  651 
Gunnite,  column-protection,  826 
Gunter's  chain,  measure,  25 
Gusset-plates,  truss-joints,  11 60,  ti6i 

wind-bracing,  1176, 1179-1186,1189, 
1190,  1193 
Gutters,  1590 

mill-building,  769 

proportioning,  1658 

saw-tooth  roof,  775 
Gutter-strips,  tin,  cost,  1594 
Guys,  wire,  406 
Gypsinite,  partitions,  877-878 
Gypsum,  131 

floors,  856 

plaster,  818,  1555 

slabs,  heat-transmission,  1259 

specific  gravity  and  weight,  1505 
Gypsum-block,  partitions,  876 
Hjyration,  radius  of  (see  Radius  of  gyra- 
tion) 

H  beams,  base  price,  1204 
loads,  table,  585 
properties,  356 
struts  and  columns,  474 


H  columns,  456,  458,  459 

Bethlehem,  475,  479,  482-484,  487 
table  of  loads,  483,  506   515 

cast-iron,  456,  458,  459 
safe  loads,  466 
Hair  in  plaster,  1555 
Halls,  air-changes,  1260,  1353 
Hammer-beam  truss,  1013-1018,  1087- 

1089 
Hammers,  pile-drivers,  190,  193,  204 

sheeting-plank,  202,  203 
Hangers,  beam  and  joist,  750-757,  782- 
795 

box,  753,  790,  792,  793 

Duplex,  752-754,  784,  788-791,  793, 
794 

Goetz,  752,  792,  793 

I-beam,  752,  753,  755,  788-790 

Ideal,  754,  786 

Lane,  756 

mill-construction,  782,  785,  789 

National,  755,  756 

stirrup,  750,  756-757 

strength,  756 

Van  Dorn,  755,  786,  791,  792 

wall,  750-757,  783-788,  792-794 
Hard-pan,  135,  141,  143 
Hardwoods,  unit  stresses,  649 
Hatchway,  elevators,  1660,  1667,  1675, 

1676 
Haunch,  arch,  305,  312 

arches,  filling  of,  832    . 
Havermeyer  bar,  917 
Hawser-rope,  404 
Hazlewood,  hardness,  1558 
Headers  (Glossary),  1824  _ 

brick  footings,  226 

floor-framing,  728,  747,  749 
Heat,  1249- 1 25 1 

absolute,  1250 

British  thermal  unit,  33,  1250,  1084 

concrete  fireproofing,  effect  on,  245, 
827,  937.  955-959 

furnace-rating,  13 14 

horse-power  equivalent,  1251 

insulation,  1360,  1363,  1430,  1610 

intensity,  1249-1251 

latent,  1251-1252 

loss,  1256-1264 

furnace  heating,  13 12 
walls,  1256 

measurement,  1247-1250 

mechanical  equivalent,  1251 

of  evaporation,  1251 

of  liquefaction,  1684 

of  the  liquid,  1251 

of  vaporization,  1684 

sensible,  1251 

specific,  1250,  1684 

steam,  1 249-1 254 

thermometers,  1250 


Index 


1879 


Heat,  total,  vapor,  i2,';4 

transfer  of,  1256-1264,  1684 
transmission  by  walls,  1 256-1264, 1684 
Heater-room,  location,  1357 
Heaters,  hot-blast,  1329 
Heating,  1247-1363 

air-changes     per   hour,    1260,    1261, 

1353,  1354 
blower  system,  1324 
cold-air  supply,  1319,  1333 
direct-indirect  radiation,  1264 
direct  radiation,  1264,  1283,  1296 
fan  system,  1324-1341 
furnace  heating,     1310-1324,     1355 

(see  Furnace  heating) 
gravity  system.s,  1283,  1298 
hot-air,  1310-1324 
hot-and-cold  system,  1327 
hot-blast  system,  1324-1341,  1346 

example,  1342-1347 
hot-water,  1302-1310 

radiators,  1264,  1270 

specification,  1359 

Treasury  Department,  1303,  1308 

U.  S.  Gov't  Buildings,  1303-1306, 
1308 

where  used,  1355 
mains  and  branches,  1284,  1289,  1291, 

1350 
radiating-surface,    walls    and     win- 
dows, 1256,  1258,  1259 
radiators  (see  Radiators) 
re-^isters  (see  Registers) 
residences,  air-changes,  1353 

hot-air,  1310-1324,  1357 

hot-water,  1302-1310,  1359 

temperatures,  1256 

rules,  1354 

steam,  1361-1363 
requirements,    buildings,    1 256-1 264, 

1354 
saw-tooth  roofs,  776 
specifications  (see  under  each  system) 
steam,  1264,  1283-1302 

Bishop  -  Babcock  -  Becker    system, 
1287 

direct,  12  83-1291 

gravity  system,  1283,  1298 

hot-blast,  1324 

low-pressure  system,  1 291-1298 

one-pipe  gravity  system,  1283-1285 

Paul  system,  1286 

pipes  (see  Pipes) 

special  gravity  system,  1286 

specification,  1361-1363 

two-pipe  gravity  system,  1286 

where  used.  1355 
structures,  large,  1324 
symbol?  used,  1350 
tanks,  1400 
vacuum  system,  1 287-1 291 


Heating,  water,  by  steam-coils,  1430 

workshops,  769,  776 
Hemlock,  beams,  coefficients  for,  628 
deflection,  664 
ilexural  strength,  557,  648 

columns,  safe  loads,  452 

compression,  449,  454,  647,  648,  650 

crushing  strength,  across  grain,  454, 
648 

crushing  strength,  with  grain,  449,  648 

modulus  of  elasticity,  647 

safe  loads,  638 

shearing-stresses,  412,  647,  648,  650 

specific  gravity,  1505 

tensile  strength,  376,  647,  648,  650 

weight,  650,  1505,  1558 
Hemp  rope,  406-408 
Hennebique  system,  920,  940 
Heptagon,  37 

Herculean  floor-arch,  838-839 
Herringbone  metal  lath,  884,  885 
Hexagon,  37 
Hickory,  hardness,  1558 

specific  gravity,  1505 

unit  stress,  651 

weight,  651,  1505 
Hides,  weight,  723 
Hip-rafters,  lengths  and  bevels,  90 
Hoists,  1723 

rope  for,  404,  407 
Hollow  tile  (see  Terra-cotta) 
Homes,    heating    and    ventilating    re- 
quirements, 1354 
Honeywell  heat-generators,  1309,  1310 
Hook-splice,  roof -trusses,  1155 
Hooks,  for  chains,  1723-1725 
Hoops,  water-tanks,  1398 
Hornblende,  131 

specific  gravity  and  weight,  1505 
Horse-power,  1248,  1250,  1460,  1720- 
1722 

boilers,  1274 

chimney,  1368 

electrical,  1460 

heat-equivalent,  1251 

machinery,  1720 

pumps,  1397 

raising  water,  1397 

transmitted,  by  belting,  17 21 
by  shafting,  1722 

windmills,  1394 
Horse-stalls,  dimensions,  1643 
Hose,  768 

Hose-carriages,  dimensions,  1642 
Hose-reels,  905 

Hospitals,  heating-temperature,  1256 
and       ventilating       requirements, 
I354-I3S7 

non-fire-proof,  height,  813 

ventilation,   1349,  i352,  I3S3.   I3S4- 
1357 


1880 


Index 


Hot-air  engines,  1393 
Hot-air  heating,  1310-1324 

fuels,  13 1 7 
Hot-and-cold  system,  heating,  1327 
Hot-blast  heating,  1324-1341 

example,  1342-1347 

radiation,  1324 
Hot-water  heating,  direct,  1302-1310 

radiators,  1264 

specification,  1359 

U.  S.  Gov't    Buildings,    1303,    1306, 
1308 

where  used,  1355 
Hotels,  fire-hose  in,  905 

floor-loads,  live,  719,  1198 

flooring,  fire-proof,  892-893 

furniture,  weicht  of,  149 

non-fire-proof,  height,  813 

steel,  weight,  1208 

ventilation,  1353 
House-tanks,  size,  141 5 
Howe  truss,  999-1  ooS 

design  of,  1142-1143 

joint-details,  1151-1156 

stresses  by  computation,  1063,  1065 
by  graphics,  1075-1077,  1102-1105 

types,  1000- 1008 

weight,  1057 
Humidifying-apparatus,  hot-blast  heat- 
ing, 1324 
Humidity,  temperature-relation,  1352 
Hydrants,  mills,  759 
Hydrated  lime,  155 1 
Hydraulic  jacks,  shoring,  215,  216.  221 
Hydraulic  lime,  235  (see  Cements) 
Hydraulic  limestone,  132 
Hydraulic  ram,  1390 
Hydraulics,  1381-1406 
Hyperbola,  38 

problems  on,  79-80 
Hyperboloid  of  revolution,  volume,  65 
Hy-rib,     concrete-reinforcement,  •  853, 
886 

I  beams,  anchors  for,  619 

bending    moments,    maximum,    574- 

575 
Bethlehem,  592 

loads,  safe,  592,  593,  598-602 

properties,  357 
buckling  of  web,  181-185,  565,  567- 
569,  612 

table,  574,  575  _ 
Carnegie,  dimensions,  352-353 

properties,  354,  355 

safe  loads,  577-581 
concrete,  854 
connections,  anchors,  619 

floor-framing,  612-619 

limiting  values,  618 

separators,  612-614,  1202 


I  beams,  connections,  standard,  616,  617 
with  Bethlehem  H  columns,  473 
with  built-up  columns,  475,  476 
with  cast-iron  co|lumns,   446,   447, 

^457,  458 
with  plate  and  box  girders,  615 
continuous,  677-680 
cost,  base  price,  1204 
crippling  of  web  (same  as  buckling) 
deflection,  lateral,  566,  670 

vertical,  566,  577-581,  668,  669 
dimensions,  352,  353,  565 
double-beam     girders,     loads,     564^ 

603,  604,  607-611 
economy,  relative,  565 
end-bearing,  minimum,  574-575 
end-reactions,  569,  574,  575 
fireproofing  '  (see  Beams,   steel,   fire- 
proofing) 
framing,  between  columns,  614 

to  wooden  beams  and  joists,  616, 
752,  753,  755,  786-792 
girders,  603-611 

double,  safe  loads,  607-611 
single,  safe  loads,  605-606 
grillage    foundations,    167-169,    181- 

185,  678-680 
light  versus  heavy,  565 
loads,  Bethlehem,  table,  594-602 
Carnegie,  table,  577-581 
examples  solved,  570-573 
moment  of  inertia,  336 
needling,  218-221 
oblique  loading,  573 
properties,  352-355,  357,  358 
radius  of  gyration,  336 
separators  for,  612-614,  1202 
shearing,  181-185,  567,  568,  569 

table,  574-575 
single-beam  girders,  loads,  605,  606 
span-lengths,  limiting,  618 
standard,  dimensions,  352-353 
properties,  Bethlehem,  357-358 
properties,  Carnegie,  352-355 
supplementary,  352 
tie-rods  for,  619,  865 
web-resistance,  181-185,  567-569 
table,  574-575 
Ice,  melting- temperature,  1251 

specific  gravity  and  v/eight,  1505 
Ice-making,  1693- 169  5 
Idaho,  registration  law,  1778 
Igneous  rocks,  131 
Illinois,  registration  law,  1778 
Illuminants,  hygiene  of,  1452 

selection,  1452 
Illuminating  gas,    lighting,    143 1- 1436, 

1451 
Illumination   (see  Lighting  and  Illumi- 
nation) 
Incandescent  lamps,  1462,  1471.  1482 


Index 


1881 


Incandescent  lighting  (see  Lighting) 

Inch,  equivalents,  25,  26 

Inch- pound,  290 

Inclined  plane,  friction,  252 

Incrustation,  boilers,  1429 

Inertia,    moment    of    (see    Moment   of 

inertia) 
Influence  lines,  1134-1137 
Institutions,  educational,  architectural, 

1779 
Insulating  quilts,  1565 
Insulation,  1683,  1690 

heat,  1430,  1566 

mineral  wool,  1610 

pipe,  1430 
Insulators,  electric,  1458 
Insurance  during  construction,  1756 
Interphones,  1707 
Intrados,  arch,  305 
Inverse  squares,  law,  light,  1440 
Involution,  arithmetic,  3 
Ionic  Order,  1 699-1 702 
Ionic  Volute,  1702 
Iron,  cast  (see  Cast  iron) 

galvanized,  1604 

properties,  375 

wire,  400 
Iron,  wrought  (see  Wrought  iron) 
Isosceles  triangle,  293 

Jack,  jacks,  hydraulic,  216,  221 

Jack-rafters,  lengths  and  bevels,  90 

Jack-screws,  shoring,  215,  216,  221 

Jacket,  furnace,  13 10,  13 11 

Jewish  long  measures,  34 

Johnson     floor-construction,     837-840, 

S41 
Joint,  rupture,  dome,  12 13 
Joints  (see  under  each  subject) 
Joist  (Glossary),  1826 
Joists,  floor  (see  Floor- joists) 

ceihng  (see  Ceiling-joists) 
Joist-hangers  (see  Hangers) 
Joule,  1250 
Jury,  competitions,  i737,  i743  . 

Kahn  bar,  921 

system,  940 
Kalamein  iron,  894  89s 
Keene's  cement  plasters,  1556 
Kelsey  warm-air  generator,  13 16 
Kenney  fiushometer,  1420 
Kent's  chimney-formula,  1366 
Key  expanded-metal  lath,  884 
Keyed  beams,  653-655 
Keys,  compound  beams,  654 
Keystone  arches,  305,  3o8,  310  (Glos- 
sary), 1827 

Rankine's  formila,  308 

Trautwine's  formula,  309 
Keystone  hair  insulator,  1566 


Kilowatts,  defined,  1460 
King-post  truss  (see  Roof -truss) 
King-rod  truss  (see  Roof-truss) 
Kitchen  ranges,  flues,  1282 
Kitchen-sinks,  dimensions,  1641 
Knee-braces,  trusses,  1025-1027    1116- 
1118,  1164,  1168 
v/ind-bracing,  1179,  1181,  1185-1190 
Knife-switch,  1477,  1479 
Kno-bum  lath,  884 
Kno-fur  lath,  885 

Labor,  cost,  1564 
Laboratories,  lighting  for,  1451 
Lacing-bars,  385 

Ladder-wagons,  dimensions,  1642 
La  Farge  cement,  236,  238 
Lag-screws,  1535 

roof -trusses,  1157 
Laitance,  244 
Lally  columns,  467,  474,  477 

loads,  488,  516 
Lamps,  arc,  1462,  1463 

arrangement,  1465,  1466 

bowl-size,  1443 

brilliancy,  1439 

gas,  1451 

height,  1444 

incandescent,  1462,  1471,  1482 

kinetic  burner,  1451 

location,  1442,  1443,  1446 

number,  1446,  T449>  I47S 

sizes,  1443,  1444 

tungsten,  I444,  I447 

Welsbach,  i444,  i45i 
Land,  measure,  27 
Lard-oil,  weight,  723 
Lath,  metal  (see  Metal  lath) 

wire  (see  Metal  lath) 

wooden, 1554 
Lathing,  1554 

cost,  1557 
Lattice-bars,  columns,  477-479 

specifications,  1202 
Lattice  columns,  477-479 
Lattice  girders,  1008-1010,  1089-1091 

wind-bracing,  1176,  1181,  1182 
Lattice  trusses,  1008-1010,  1089-1091 
Laundry-tubs,  dimensions,  1641 
Lava,  131 

crushing  strength,  280 
Lavatories,  dimensions.  1641 
Laws,  building  (see  Bmlding  laws) 
registration,  architects,  1768-17 79 
ventilation,  1354 
Lead,  anchor-bolts,  240 
castings,  shrinkage,  1521 
pipe.  1408,  1413,  1416-1418 
sheet,  1418,  1511 
specific  gravity,  1505 
weight,  1505,  1511 


1882 


Index 


Leaders,    furnace,    131T,    1317,    1324, 

1358 
Leather,  weight,  723 
Length,  unit  of,  1247 
Lever,  principle  of,  165,  290,  293,  294 
Libraries,  book-stacks,  1696 

ventilation,  1353 
License  law,  architects,  1768-1779 
Light,  brilliancy,  1439 

candle-power,  1439,  1440,  1462 

diffusion,  1453-1456,  1577-1580 

heat,  emission,  1261 

versus  illumination,  1437 

intensity,  1439 

nature  of,  1438 

refraction,  1453 -1456,  1577-1580 

sources,  1438 
colors,  1438 
Lighting  and  illumination,  143 7-1456 

accounti.ig-oilices,  1446 

auditoriums,  1451 

bibliography,  1456 

ceiling-lights,  1446 

ceiling-outlets,.  1449 

class-rooms,  145 1 

coloring  of  ceilings,  1442 

design  of  system,  1444,  1446 

diffusion  by  glass,    1453-1456,    iS77" 
1580 

direct,  1441,  1442.  1446-1448 

drafting-rooms,  145 1 

electric-lighting  systems,  1464-1469 
cost,  1482 
design,  1446-1448 

electric  power  required,  1441 

factories,  969 

feed-wires,  1478 

fixtures,  care  of,  1443 

in  direct  systems,  1446-1448 

in  semiindirect  systems,  1448-1450 

foundries,  145 1 

gas,  1448,  1450,  1451 

amount  of  gas  required,  1441 
calculations,  1448 
pipe,  sizes,  1432-1436 
piping,  symbols,  1445 

general  principles,  1437 

heights  of  lamps,  1444 

Holophane  reflector,  1447 

hygiene  of,  1452 

indirect,  1441,  1442,  1448-1450 

intensity,  1439,  1440 

laboratories,  1451 

law  of  inverse  squares,  1440 

lecture-halls,  145 1 

machine-shops,  1451 

mill-buildings,  969 

outlets,  1442,  1443,  1446 

piping  for  gas,  1432-1436,  1445 

reflectors,  1447,  1448 

roof -lights,  775 


Lighting   and   illumination,   saw-tooth 
roofs,  772,  775 

school-rooms,  1451 

semiindirect,  1442,  1448-1450 

single-phase  system,  1464  , 

switches,  1478,  1479,  1481 

systems,  1464-1469 

three-phase  system,  1464-1469 

three-wire  system,  1464-1469 

two- wire  system,  1464 

windows,  775,  1453-1456 

wiring,  cost,  1482 

workshops,  769,  145 1 
Lightning-conductors,  1704-1707 
Lignite,  combustible,  1271,  1272 
Lignum-vitae,     ultimate    unit     stresses, 
651 

weight,  651 
Lime,  1548-1553 

Alca,  1553 

chemical  properties,  1550 

classification,  1549 

data,  1553 

hydrated,  155 1 

hydraulic,  235 

inspection,  1550,  i5S2 

nature,  1548 

properties,  1548,  1550,  1552 

sampling,  1549 

specific  gravity,  1506 

specifications,  1 549-1 551 

tests,  1549 

weight,  723,  1506 
Limestone,  132 

beams,  coefhcients  for,  628 

calcite,  131 

calcium,  1549 

compressive  strength,  266,  280,   281, 
282,  287 

constituents,  1548 

dolomitic,  131,  1549 

fiber-stresses,  557 

fire-resistance,  814 

modulus  of  elasticity,  282 
of  rupture,  282 

shearing  strength,  282 

specific  gravity  and  weight,  282,  1505, 
1506 

tensile  strength,  282 
Line  of  fracture,  arches,  316 
Linear  measures,  25 

metric,  31 

Gunter's  chain,  25 

ropes  and  cables,  25 
Lines,  center  of  gravity  of,  292 

geometrical  problems,  66 
Lines  of  pressure,  arches,  31 1-3  21 

buttresses,  297-304 
Links,  strength  of,  chains,  410 
Linseed-oil,  1568,  1569  jS 

specific  gravity  and  weight,  1505    l|H 


Index 


1883 


Lintels,  305 

cast-iron,  620-627 

cross-section,  ideal,  620 
deflection,  628,  664 
formulas,  620-621 
safe  lead,  tables,  624-627 
reinforced-concrete,  975 
stone,  1539 
Liquid  measure,  27 

metric,  32 
Liquefaction,  heat  of,  1684 
Live  loads  (see  member  loaded) 

definition,  126,  149 
Load,    loads    (see,    also,    each    member 
loaded;    also  Weight) 
cast-iron  columns,  461 

footings,  162-1-65 
eccentric,  columns,  489,  946 
footings,  162-165 
steel  column,  485-489 
steel-pipe  column,  472 
wooden  column,  453 
oblique,  steel  beams,  573,  593 
on   columns,    method   of   computing, 

148-152,  489,  490 
on    floors,    fire-proof,    833,  837-844, 
850-852,856,863-865 
mill-buildings,  802-808 
reinforced  concrete,  936,  948,  967, 

971,  984-987 
steel,  1 197 

various  buildings,  149 
wooden,  717-749 
on  foundation-beds,  141-143,  148-160 
on  masonry,  265-267,  287,  441,  442, 

1200 
on  roofs,    740-741,    745,    746,    1048- 

1057, 1196 
on    reinforced-concrete    slabs,    984- 

987 
safe-load,  definition,  125 
snow-loads,  1049,  1052-1057 
tests,  fire-proof  floors,  827,  866,  956- 
958,  967 
foundation-beds,  141-146 
wind-loads,     148-160,     1049,     1052- 
1057,  1171-1173,  1198 
Lock-woven  fabric,  849 
Locomotives,  dimensions,  1642 
Locust,    safe    fiber-stress,    flexure,    557, 
648 
specific  gravity,  1506 
unit  stresses,  651 
weight,  651,  1506 
Lodging-ho-ase,  defined,  1853 
Loit  buildings,  chimneys,  1368 
Lofts,  cost,  1 61 3 

live  loads  on  floors,  149,  "97 
Logwood,  extract  of,  723 
Loop-eyes,  386 
Loop-rods,  386,  396 


Louisiana,  registration  law,  1778 
Louisville   code,   loads   on  foundation- 
beds,  143 

masonry  loads,  287 
Lumber  (see,  also.  Timber  and  differ- 
ent woods) 

asbestos,  819 

data,  1558-1564 

framing,  1559 

hardness,  relative,  1558 

measurement,  1559-1563 

metal,  858 

specific  gravity,  1501-1508 

weight,  1501-1508,  1558 
Luten  truss,  923 

McGill  University,  tests  on  brick  piers, 

275 
Machine-shop,  design  and  cost,  802-803 
saw-tooth  roofs,  774 
steel,  weight,  1209 
Machinery,  vibration  of,  763 
Machines,  dynamo-electric,  1463 

refrigerating,  1685- 1690 
Mackolite,  partition-blocks,  877 
Mahogany,  uiiit  stresses,  651 
specific  gravity,  1506 
weight,  651,  1506 
Mail-chutes,  167  7- 1679 
Mains,  steam,  1284,  1289,  1291,  1350 
Manhattan    Life    Insurance    Building, 

foundations,  251 
Manila  rope,  406-408 
Mansard  roof,  tiles  for,  870 
Mantle-tile,  1605 
Maple,  deflection  in  beams,  664 
hardness,  1558 
unit' stresses,  651 
weight,  651,  1558 
Marble,  beams,  coefficients  for,  628 
compression,  266,  282 
crushing  strength,  280,  282 
fiber-stresses,  flexure,  557 
fire-resistance,  814 
loads,  safe,  masonry,  266 
shearing  strength,  282 
specific  gravity,  282,  1506 
strength,  267 
tension,  282 
tile,  1605 
weight,  282,  1506 
Marbleithic  tile,  1606,  1607 
Masonry,  1538,  i539  (see,  also,  Brick- 
work, Stonework,  Walls,  etc  ) 
arches  (see  Arches) 
bearing  pressure,  allowable,  441-444 
bed  (Glossary),  1802 
bond  (Glossary),  1803 
bond-stones,  effect  of,  269 
building  codes,  267,  287 
cement  mortar  required,  239,  247 


1884 


Index 


Masonry,  classification,  1538 

coefficients  of  friction,  253 

compressive  strength,  265,  441 

cost,  1538,  1539 

crushing  strength  of  stone,  279-282 

footings,  178,  223-225 

tensional  strength,  178-179 

grouting^  269 

measurement,  1538 

mortar  for,  229-239,  247 

piers,  270 

pressures    allowed,    265,    267,    287, 
441,  1200 

safe    working   loads,    265-267,    287, 
441 

strength,  265-282,  441,  1200 

stresses  in,  265 

thickness  of  walls,  229-234 

walls,  228-234 

weii^ht,  1506 
Mass-concrete,  strength,  267 
Mathematical  signs  and  characters,  3 
Mathematics,  practical,  3-5 

McGill   University,  tests  on    brick 
piers,  275 
Measure,  measures,  25-35 

ancient,  34 

circular  and  angular,  30 

conversion  tables,  33-35 

cubic,  27 
metric,  31 

dry,  27 
metric,  32 

Egyptian  long,  34 

fluid,  28 

Grecian  long,  34 

Jewish  long,  34 

land,  27 

linear,  metric,  31 

liquid,  27 
metric,  32 

metric  system,  30-33 

miscellaneous,  26,  28,  34 

nautical,  26 

Roman  long  and  weight,  34 

Scripture  and  ancient,  34 

surface,  27,  31 

time,  30 

value,  29 

volume,  27,  31 

weight,  28-29 
metric,  32 
Mechanical  refrigeration,  1684-1695 
Mechanics,  applied,  definition,  124 
Mechanics  of  materials,  terms  used,  124 
Medals,  architectural,  17 79-1 788 
Melan  arch,  844 
Mensuration,  38-65 

definition,  38 

solids,  61-65 

surfaces,  38-61 


Merchandise,  weights,  721-723 
Merchant- bar  iron,  377 
Metal,  asbestos-protected,  819 

data,  1509 

doors,  894-897,  901,  902 

finish,  896 

sheet,  standard  gauges,  402 
Metal  frames,  fire-proof  buildings,  89-: 
Metal  furring,  881,  892 
Metal  lath,  882-892,  919 

column-protection,  822 

expanded,  884 

fireproofing,  781 

partitions,  878,  882,  888,  890 

sheet,  402,  886,  1510,  1599 

woven-wire,  887 
Metal  lumber,  858 
Metal-rib  plaster-board,  888 
Metal  sashes,  fire-proof   buildings,   89 
Metallic  furniture  and  fittings,  898-89 
Metamorphic  rocks,  131,  132 
Metric  system,  30-32 

conversion  tables,  32-35 
Mica,  131 

specific  gravity  and  weight,  1506 
Mica-schist,  132 
Middle  third,  theorem  of,  254 

arches,  311-315 

buttresses,  301,  304 

domes,  1225,  1227 

footings,  164 

retaining- walls,  259 

vaults,  1233,  1234,  1240 
Mill-buildings     (see,    also,    Mill-con 
struction),  brick,  808-810 

cost,  808-810,  1206 

depreciation,  1634 

reinforced  concrete,  968-997 

steel,  cost,  1206 

weight,  1208,  1209,  1210 

wooden,  758-810 
Mill-construction,         reinforced-con 
Crete,  948,  968-997 

columns,  969,  976,  978,  980 
loads,  distribution,  976 

cost,  777.  1613,  1618 

floors,  968,  971,  993 
beams,  secondary,  971 
formulas  for  design,  985-997 
girderless,  968,  993-997 

footings,  978,  982 

girders,  974,  975 

lighting,  969 

lintels,  975 

stairs,  899-901,  982,  983 
Mill-construction,  slow-burning,  758- 
810 

belts,  shafts,  765 

boiler-plant,  765,  780 

columns,  cost,  810 

fireproofing,  780,  781,  822-826 


Index 


1885 


Mill-construction,    slow-burning     col- 
umns, framing,  769,  782-800 
conductors,  775 
cornices,  764,  769 
cost,  758,  777,  802-810,  1613,  1618 
doors,  801 
dry-rot,  759 

elevator-towers,  764,  768 
fire-protection,    768,   777,   779,   801, 

903-905 
fire-retardants,  759 
fire-shutters,  759,  778,  801,  901,  902 
fire-stops,  759 

fireproofing  metal  members,  780-782 
floors,  760-764,  766 

cost,  810 

estimating,  1563 

framing  (see  Framing,  floors) 

old,  strength,  749 

plank,  730-735 

strength  and  stiffness,  717-757 

surfacing,  769 

warehouses,  777 
frames  and  shutters,  764 
framing,  steel,  786,  788 
general  description,  758-760 
girder-supports,  792 
glass,  759,  763,  764,  769,  772,  775 
gutters,  769,  775 
hangers,  782,  785,  789 
heating,  769,  776 
height,  of  buildings,  777-778,  813 

of  stories,  765,  810 
joist-supports,  792-794 
painting,  759,  763 
partitions,  759,  801 
plumbing-fixtures,  810 
post  and  girder-connections,  795-800 
post-caps  and  bases,  782-788,   791, 

795-800 
pumps,  759 

roofing-materials,  760,  800-801 
roofs,  760 

cost,  810 

example,  769 

materials  (see  Roofing,  materials) 

timber  framing,  765 

walls,  768 
saw-tooth,  772-777 
scuppers,  767 
shafting,  765 
skylights,  765 

sprinklers,  768,  777,  779,  801,  904 
stairways,  759,  810 

tower,  764,  768,  778,  779 
steam-pipes,  764 
stirrups,     wrought-iron,    750,    754" 

757,  787-794 
storehouses,  765-788 
structural    details,    782-792,    ii94- 


Mill-construction,    slow-buming    tim- 
bers,   759,    762,  763 

towers,  764,  768,  778,  779 

trusses,  772 

ventilation,  769,  775,  776 
of  timbers,  763 

walls,  760,  765,  768,  778,  809 

warehouses,  777-782 

weave-shed,  773 

windows,  763,  769,  772,  775,  778 
fire-guards,  759 
frames,  764 
Milwaukee  building  code,  formula  for 

steel  columns,  481 
Mineral  wool,  1566,  1609,  16 10 
Minneapolis  building  code,  formula  for 
steel  columns,  481 

loads  on  foundation-beds,  143 

office-buildings,  assumed  loads,  151 

thickness  of  walls,  231-232 
Mineral  oil,  fuel,  1272 
Minerals,  forming  rock,  130 
Mirrors,  1580 
Modulus  of  elasticity,  126.  626,  662 

concrete,  912,  924,  934,  935,  956 

definition,  126 

notation,  symbols,  122 

steel,  381,  912,  934 

stone,  282-283 

various  materials,  647,  664 
Modulus  of  rupture,  126 

concrete,  mortar,  and  stone;  282-283 

woods,  650-651 
Modulus,  section  (see  Section-modulus) 
Molding  (Glossary),  1830 
Moldings,  classical,  1697,  1698 

plaster,  1556 
Molds,  concrete,  962-966 
Moment  of  force,  definitions,  127,  289, 

322 
Moments,   bending    (see  Bending   mo- 
ments) 

of  inertia  (see  Moments  of  inertia) 

of  resistance,  333,  55^ 

principle  of,  289-291,  294,  301,  322- 

324 
Moments  of  inertia,  areas,  332-352 

compound  sections,  339-345 

definitions,  33  2-333 

determined  graphically,  345 

notation,  122 

rectangles,  tables,  346-347 

structural  shapes,  354-359,  362-369 

transferring,  338-345 
Moments    of    resistance,     flexure-for- 
mula, 333,  556 
Money,  United  States,  29 
Montana  registration  law,  1778 
Mortar,  adhesive  strength,  240 

aggregates,  241 

alca  lime,  15 53 


1886 


Index 


Mortar,  brickwork,  227,  271 

cement,  235-240 

cement-gun,  826 

colors,  1547 

durability,  818 

fire-resistance,  818 

floor-tiles,  829 

for  plastering,  239,  1554-1558 

freezing,  effect  of,  239 

grouting,  227^  269 

hair  in,  1555 

hot  water  in,  239 

hydrated  lime,  1551 

lime,  compressive  strength,  282 

mixing,  cement,  239 

natural-cement,  235 

compressive  strength,  283 

Portland-cement,  238 

compressive  strength,  283 

quantity  required,  239,  247 

relative     compressive      and     tensile 
strength,  283 

salt  in,  239 

specific  gravity,  1506 

stone  walls,  229,  230 

water  required,  238 

weight,  1506 
Mortar-colors,  1547 
Mortuary,  refrigerator,  1683 
Mosaics  (see,  also,  Tile) 

Ceramic,  1605,  1607 

Florentine,  1605 

Roman,  1605,  1607 

terrazzo,  1607 
Motion,  definition,  124 

rate,  1247 
Motor,  1463 

for  elevator,  1676,  1677 

for  fan-drive,  1347 

heat-emission,  1261 
Mud,  139 

Mullion  and  munion  (Glossary),  183 1 
Mushroom  system,  reinforced  concrete, 
950,  993-997 

Nails,  1 5  29-1 534 

National  Board   of  Fire   Underwriters 
code,  masonry-load,  287 

concrete,  958 
National  Electric  code,  1480,  1481 
Natural  cement,  235 

concrete,  235,  267,  284 

mortar,  235 

compressive  strength,  283 

production,  235 

strength,  235,  284 

weight,  235 

where  used,  235 
Natural  gas,  1431 
Nautical  measures,  26 
Needling,  218-222 


Neutral   axis,    beam-sections,    332-338 

555,  621 
New  Jersey  registration  law,  1778 
New  Orleans  building  code,  load  on 
foundation-bed,  142 
thickness  of  walls,  231 
New  York  City  building  code,  arches, 
307 
bearing  pressure  on  masonry,  44 1,  444 
column-formula,  cast-iron,  460 
compression,  steel  members,  495 
formula  for  steel  columns,  481,  493, 

495 
loads  on  foundation-beds,  143 
masonry-loads,  267 
office-buildings,  assumed  loads,  151 
pipe-column  formula,  469,  474,  497, 

498       _ 
rivets,  bearing  and  shear,  419 
skeleton  construction,  234,  1171 
terra-cotta,  276 

thickness  of  walls,  230,  231-232 
wind  bracing,  1171 
New  York  State,  registration  law,  1768- 

1776,  1778 
Nickel  tuijing,  141 5 
Nicking  test,  wrought  iron,  378 
Nonagon,  37 

North  Carolina,  registration  law,  1778 
North  Dakota,  registration  law.  1778 
Novus  sanitary  glass,  1606 
Norway  pine,  beams,  loads,  641 
deflection,  664 
fiber-stress,  safe,  557 
columns,  safe  loads,  450,  452 
crushing-load,  449 
crushing  strength,  across  grain,  454 
specific  gravity,  1507 
unit  stresses,  376,  647,  650 
weight,  650,  1507 
Notation  mathematical,  122,  123 
Nozzles,  roof,  801 
Nuts,  1525 

standard  dimensions,  1526 
weight,  1527 

Oak,  beams,  coefficients  for,  628 
deflection,  664 
distributed  loads,  safe,  643 
fiber-stresses,  557 
columns,  safe  loads,  450,  451 
crushing-load,  with  the  grain,  449  ' 
crushing   strength,  across  the   grain, 

454 
hardness,  1558 
shearing-stresses,  412 
specific  gravity,  1506 
unit  stresses,  376,  412,  647,  648,  651 
weight,  651,  1506,  1558 
Obsidian,  131 
Octagon  37 


J  ndex 


1887 


OfRce-buildings,  chimney,  1368 

cost,  1613 

fire-hose  in,  905 

floor-joists,  738,  743 

floor-loads,  149,  151,  719,  720,  1198 

furniture,  weight,  149 

I  beams,  sizes,  864 

steel,  weight,  1207,  1208 
Offices,  air-change,  1353 
Offsets,  footings,  163-165,  179,  223-227 
Ohm,  defined,  1458 
Oil,  mineral,  as  fuel,  1272 
Open-hearth,  steel,  380 
Opera-houses,  dimensions,  1657 

chairs,  1653 

seating  capacity,  1654-1656 
Orders,  classical,  1698-1704 
Oregon  Pine  (see  Douglas  fir) 
Organizations,  architectural,  1788-1795 
Ottawa  sand,  235,  241,  908 
Overdraft,  in  furnace,  1310 
Owner,  competitions,  1739,  1740,  1746 
Owner's  right,  in  contract,  1760 

Paint,  Painting,  1568- 1573 

cement  and  concrete,  1573 

driers,  1569 

enamel,  1570 

fire-proof,  821-822,  894 

inside,  1570 

mill-construction,  759 

old  work,  1 571 

outside,  1569 

paints,  1568-1570 

pigments,  1568 

plastered  walls,  1571 

priming,  1569 

repainting,  1571 

steelwork,  1203,  1206,  1572 

timbers,  763 

tin  roofs,  1570,  1589,  1590 

varnish,  1568,  1570,  1573 

vehicle,  1568 
Pantry-sinks,  dimensions,  1641 
Paper,  building,  1564-1568 

weight,  722 
Paper-mills,  cost,  805 

steel,  weight,  1210 
Parabola,  38 

center  of  gravity,  293 

problems,  79 
Paraboloid  of  revolution,  volume,  65 
Parallelogram,  37,  39 

of  forces,  289 
Parallels,  36 
Parapets  on  mills,  768 

architecture,  1833 
Parchment,  water-proof  sheathing,  1568 
Parking,  defined,  1853 
Partitions,  brick,  873 

concrete,  876,  880 


Partitions,  defined,  1853 

double,  880,  890 

fire-proof,  873-892 

fire  test,  873,  889 

gypsum-block,  876 

heating  pipes  through,  1358,  1360 

hollow-tile,  873-874,  890 

mackolite,  877 

metal-lath.  878,  882-888,  890 

mill-construction,  759,  801 

rib-stud,  881 

soundproofing,  889-891 

scantling,      incombustible,      defined, 
i8S3 

solid  plaster,  878,  880,  890 

terra-cotta,  873,  875,  890 

types,  873 

wooden,  ^25-727,  748 
Partition-wall,  defined,  1853 
Party  walls,  873 

defined,  1853 

floor-loads  on,  234 
Patent  rights,  payment,  1759 
Patterns,  castings,  1521 
Paul,  air-line  system,  heating,  1286 
Pavement-prisms,  1579 
Pavements,  asphalt,  1608 
Payments,  on  contract,  1758 
Pearl-alum,  weight,  723 
Peat,  139,  1272 
Pedestal-piles,  198 
Peerless  radiators,  1265,  1266 
Pentagon,  37 
Perimeter,  37 

of  triangles,  center  of  gravity,  292 
Persons,  heat-emission,  1261 
Pews  (Glossary),  1835 
Philadelphia     building    code,     bearing 
pressure  on  masonry,  444 

formula  for  steel  columns,  481,  493 

loads  on  foundation-beds,  143 

masonry-loads,  267 

pipe-column  formula,  469,  474 
Phosphorus  in  steel,  381,  383 
Pianos,  dimensions,  1638 
Piers,  arch,  305 

brick,  267-269,  271-276,  278 
bond-stones,  269 
safe  loads,  265,  267,  268 
strength,  268,  271-276,  278 
tests,  275 

caisson,  212,  214 

center  of  gravity,  300.  30i,  302 

footings  for,  161,.  162,  176-178,    184. 

185 
foundation,  129,  188,  200 
line  of  pressure,  300 
on  concrete  and  wooden  piles,  i99 

grillage,  184,  185 
pneumatic-caisson  method,  212,  214 
reinforced-concrete,  980 


1888 


Index 


Piers,  stability,  297-304 
stone,  270 

terra-cotta,  276-278 
thrust,  297,  298 
Pigments,  paints,  1568-1570 
Pilasters  (Glossary),  1835 
Pile-drivers,  190,  194-196,  202-204 
Piles,  durability,  188,  196 
iron-pipe,  199 

reinforced  concrete,  196-200,  945 
versus  wooden,  strength,  196 
wooden, 188-196 

capping,  190-192,  198 

timber-grillage,  191,  192 
cost  of  driving,  195 
crushing  strength,  196 
driving,  189,  190,  194-196,  202-204 
durability,  188,  196      ' 
Engineering  News  formula,  193 
municipal  requirements,  189 
plan  of,  for  building,  192 
safe  loads,  189,  193,  195 
specifications,  193 
strength  versus  concrete  piles,  196 
under  piers,  199 
woods  used,  189 
Piling,  sheet,  200-209 
Pillars  (Glossary),  1835 
Pin,  pins,  in  trusses,  423-429 

steel,  stresses,  618,  1138,  1200 
Pine,  specific  gravity  and  weight,  1507 
Norway  (see  Norway  pine) 
white  (see  White  pme) 
yellow  (see  Yellow  pine) 
Pinnacle  (Glossary),  1836 
Pipe,  pipes  (see,  also,  Ducts)  . 
block-tin,  1418,  1419 
brass,  1429 
capacity,  1383,  1403 
cast-iron,  1389,  1407,  1427,  1428 
conduits,  1479 

coverings,  1360,  1363,  1430,  1610 
drain,  1407-1412,  1419,  1420 
expansion,  1427-1429 
flow    of    water    through,    1382-1400, 

1420 
friction  in,  1388 
frostproofing,  1400 
furnace,     1311,    1318,     1322,     1358, 

1360 
gas,  1432-1436 

hot-water    heating,    covering,    1360, 
1430 
size,  1305,  1306 
specifications,  1359 
hot-water  supply,  1415,  1428,  1429 
lead,  1408,  1413,  1415,  1416-1418 
location,  fireproof,  826 
sewer,  1407-1409,  1419,  1420-1422 
sheet-metal,  1337 
smoke,  1362 


Pipe,  soil,  1407-1410,  1427 

steam-heating,  764,  1362 
covering,  1363 
pressure-loss,  1292 
size,  1294 
specifications,  1362 

steel,  1408 

supply,  1390-1398,  1415 

symbols,  1350,  1424-1426 

tests,  1388,  1412 

tin-lined,  1418 

vent,  1407,  1410 

warm-air,  size,  1318 

waste,  1407-1411,  1416,  1417,  1427 

wrought-iron,  1408,  1429,  1432-1436 
Pipe-columns,  469-474,  488 

loads,  488,  497-498 
Pipe-coverings,  steam-pipes,  1360,  1363, 

1430, 1610 
Pitch  of  roofs,  867,  869,  1046,  1053 
Pitch,  gravel  roofs,  1595-1599 

slag  roofs,  1595-1599 

specific  gravity  and  weight,  1507 
Plane,  36 

inclined,  252 
Plaster,  alca-lime,  1553 

asbestic,  818 

fire-resistance,  818 

gypsum,  818,  1555 

hard- wall,  1556 

hydrated-lime,  1551  . 

Keene's  cement,  1556 

machine-made,  1555 

measuring,  1556 

mortar  for,  239,  1554-1558 

staff,  1558 

wall,  1555 

weight,  723 
Plaster-blocks,  876 
Plaster  of  Paris,  column-protection,  822 

fire-resistance  818 
Plastering,  1554-1558 

coats,  1554 

cornices  and  moldings,  1556 

cost,  1557 
Plate,  base,  forms  of,  441 

bearing,  440 
.  pressures,  441,  1200 

cast-iron,  weight,  1524 

cover,  riveted  joints,  421 

steel,  384,  385 

base  price.  1204,  1205 
punching,  effect,  382,  414,  688 

wall  (see  Wall-plates) 
Plate-and-angle  columns,  46^,  479 

connections,  477 

moment  of  inertia,  343 

radius  of  gyration,  344 

tables,  488,  517-532 
Plate  girders,  681-716 

construction,  details,  682-683 


Index 


1SS9 


Plate  girders,  elements,  706-716 

end-reactions,    maximum,  70s,    706- 
716 

examples,  688-694 

framing  and  connections,  614-  616,  682 

moment  of  inertia,  section,  340-342 

safe  loads,  706-716 

shear,  684-687,  690,  691,  696,  698, 
703 

specifications,  1201,  1202,  1203 

splice-plates,  693 

stifTeners,  681,  686,  691,  696,  1201, 
1203 

stresses,  design,  683,  1201 

web,  681,  703-  70s 
buckling,  686,  705 
shearing  value,  703-704 
stresses,  684,  686,  691 

weight,  687 
Platforms,  stone,  1539 
Plenum  chamber,  1350 
Plenum  system,  ventilating,  1356 
Plumbing,  1407-1430 

definition  of  terms,  1407 

fixtures  (sec  Plumbing-Fixtures) 

pipes  (see  Pipes) 

symbols,  1423-1426 

testing,  141 2 
Plumbing-fixtures,     1410-1415,     1420- 
i4-'6 

cost,  mill-buiMings,  810 

dimensions,  1640-1642 
Plunge-bath,  1422 
Plutonic  rocks  131,  132 
Pneumatic,  caisson,  21 1-2 14 

water-supply,  1396 
Point,  36 

Poling-board  method,  foundations,  209 
Polygons,  definition,  36 

equilibrium,  289,  299,  313-31S,  3i9 

factors  for  determining  elements,  40 

force,  289,  1070 
Polyhedrons,  regular,  63 
Poplar  (see,  also.  White  wood) 

columns,  safe  loads,  450,  452 

crushing-loads,  with  the  grain,  449 

hardness,  1558 

specific  gravity,  1507 

unit  stresses,  651 

weight,  651,  1507,  1558 
Portal  bracing,  117 6,  1182 
Portland,  Ore.,  building  code,  loads  on 

foundation-beds,  143 
Portland  cement,  236-240 

adhesive  strength.  240 

composition,  236 

concrete,  reinforced,  907,  908 

concrete  blocks,  233 

cost,  238 

defined,  237 

fineness,  237,  907 


Portland  cernent,  manufacture,  236 

mixing,  238 

mortar,  238 

compressive  strength,  283 

proportions,  235,  247 

specific  gravity  and  weight,  1506 

quantities  in  concrete,  247,  248,  249 

setting-time,  237,  907 

specific  gravity,  237,  907,  1502 

specifications,  236,  907 

strength,  237,  240,  283,  284,  907 

testing,  237,  240,  907 

weight,  235,  723,  1502 
Post-caps,  782  788,  791,  795-800 
Post-office  buildings,  cost,  1630 
Posts  (,ce  Columns) 
Pound-feet,  290 
Pound-inches,  290 
Power,  1248,  1250 
Power-hammer,  underpinning,  221 
Power-houses,  steel,  weight,  1210 
Pratt  truss,  1026, 1029,  1031, 1032 

economy,  1055 

with  inclined  ties,  1077 
Pressure,  barometric,  1249 

earth,  201,  205 

gauges,  1248 
Prism,  38,  62 
Prism-glass,  1454-1456,  1578-1580 

fire-resistance,  821 
Prismoid,  quadrangular,  62 
Prisons,  ventilation,  1353 
Prizes,  architecture,  17 79 -1788 
Professional  practice,  A. I. A.,  1727 
Programme,  competitions,  1737,  1741 
Public  building  (see,  also,  Federal  build- 
ings) 

cost,  1613,  1628-1634 

defined,  1853 

registers,  heating,  135S 
Pulleys,  arrangement,  1722 

sash,  1649 

size  and  speed,  1720 
Pulpit  (Glossary),  1838 
Pumice,  131 
Pumps,  air-lift,  1395 

deep- well,  1391 

fire,  1401 

mills,  759 

plunger,  1391 

pneumatic  system,  1396 

private  water-supply,  139° 

single-acting,  1393 

slip,  1247  . 

steam,  1401 

vacuum,  size,  1290 
Punchmg,   effect  on  steel   plates,   382, 

414,  688 
Purlins  (Glossary,  1838),  998,  1838 

channels,  1169 

connections,  1153,  "69,  11 70 


1X90 


Index 


Pml-ns,  design,  1144,  1169,  1170 

I-beam,  1169 

oblique,  stress,  573,  593 

spacing,  1003-1004,  1006 

steel,  specifications,  1201,  1204 

supports,  1004,  1046,  1047 

weight,  1050,  1055 

wooden,  1003,  ii44>  ii53,  1169 

workshops,  771 

Z-bar,  1 1 59 
Puzzolan  cement,  236,  237 
Pyramid,  38 

center  of  gravity,  293 
frustum,  38 

surface-area,  61 

volume,  64 
surface-area,  61 
vertex,  38  • 

volume,  64 
Pyrometer,  1249,  1250 

Quadrangular  prismoid,  62 
Quadrangular  truss,  1032,  1033,  1091, 

1094 
Quadrant  of  circle,  center  of  gravity, 

293 
Quadrilaterals,  36 

center  of  gravity,  292-293 
Quantity  system  of  estimating,   1635- 

1637 
Quartz,  130 

specific  gravity  and  weight.,  1507 
Quartzite,  132 
Queen  truss,  999-1004 

example,  of  analysis,  1055,  1139 

graphic  analysis,  107 1 

wind-stresses,  1112-1116 
Quicklime,  1549 
Quicksand,  136 

excavations  in,  137,  211 

foundation-beds  in,  137,  141 

pockets,  137 

safe  load  on,  141 
Quilts,  building,  1564-1568 
Quoins  (Glossary),  1839 

Radial  Brick  Chimney,  1369-1373,  i377 
Radiation,  1264-1271 

versus  hot-blast  heating,  1324 
Radiators,  1 264-1 271 

air-removal,  1285 

cast-iron,  1265-1267 

concealed,  1270 

connections,  1264,  1283 

direct,  1264.  1283 

direct-indirect,  1264,  1268 

hot-water,  1264,  1270 

indirect  heating,    1264,    1299,    1300, 
1356 
location,  1355 
specifications,  1360,  1362 


Radiators,  indirect  heating,  symbol,  1350 

materials,  1264 

measurement,  1265 

pipe  coil,  1267,  1269 

pressed-metal,  1264,  1265,  1267,  1268 

rating,  1265 

types,  1265    1270 

wall,  1268 
Radius  of  gyration,.  333 

areas,   334-338    (see,   also.  Moments 
of  inertia) 

compound  sections,  344 

definition,  333 

hollow-round  sections,  table,  348-349 

hollow-square    sections,    table,    345, 
350-351 

notation,  122 

steel-pipe  columns,  472,  497-498 

structural  shapes,  354^359,  362-374 
double  angles,  371,  372,  503 
double  channels,  373,  374,  499,  500 
plates  and  angles,  344,  517-532 
plates  and  channels,  533-554 
Rafters,  1003,  1046,  1836 

bevel  and  length,  90 

details,  1150-1154 

hammer-beam  truss,  1014-1016 

on  steel  purlins,  11 69 

span,  maximum,  740-,  741,  745,  746 

stresses,  1140,  1141 

weight,  1050 
Rags,  weight,  722 
Rams,  hydraulic,  1390 
Random  work  (Glossary),  1839 
Range-boilers,  dimensions,  1642 
Rankine's  formula,   cast-iron  columns, 
460-461 

depth  of  keyst   ne,  308-309 

steel  columns,  481,  484,  493-496 
Raymond  concrete  pile,  197 
Reactions,  beams,  322,  671 
Reaming,  steel,  382,  414,  423,  682 
Reaumur  thermometer,  1250 
Reciprocals,  7,  8,  24 
Rectangles,  37,  39 

axis  of  moments,  335 

moment  of  inertia,  335,  346 

radius  of  gyration,  335 

section-modulus,  335 
Redwood,  beams,  loads,  640 
deflection,  664 
fiber-stress,  safe,  557 

columns,  safe  loads,  450,  452 

crushing-loads,  with  the  grain,  449 

crushing   strength,   across   the   grain, 
454 

shear,  647 

tension,  sife  stress,  376,  647 

unit  stresses,  647,  650 

weight,  650 
Reflection,  multiple  (acoustics),  1487 


Index 


1891 


Refraction  of  light,   I453-I4S6,    1577- 

1580 
Refrigeration,  mechanical,  1684-1695 
Refrigerators,  1679-1683,  1691-1693 
Register-boxes,  1358 
Registers,  air- velocity,  1357 
furnace,  1317-1320 
pressure-loss,  1338 
in  public  buildings,  1355 
size,  1358 

specifications,  1360 
symbol,  1350 
Registration  of  architects,  1768-17 76 
Reinforced  concrete  (see,  also,  Concrete 
and  Reinforcement),  906-997 
adhesion  (see  bond,  below) 
aggregate,  241,  287,  908,  909,  945 
beams,  924-941 

bending  moments,  935-936 

compression-rods,  921-922,  941 

diagonal  tension,  921,  938 
bond,  940 

allowed  stresses,  911,  912 

tests,  919 

use  in  design,  938 
cantilever  flat-slab  system,  950 
cast-iron  column-connections,945-946 
cement  used,  907 
chimneys,  i373-i375 
cinders,  242,  250,  909,  930 

corrosion  of  steel,  818,  960-961 
columns,  941-946,  969,  980 

calculations,  976 

fire-proofed,  958,  959 

metal-cored,  944-945 
compressive  strength,  910-91 1 
conductivity,  955 
connections,  944-947 
construction  in  general,  906-967 
corrosion-protection,  960-962 
cost,  250,  910,  1613,  1618 
Cummings  system,  923,  945 
design  of,  924-947 
diagonal  tension,  921,  938 
electrolysis,  186 
erection,  906,  962-963 
factors  of  safety,  911 
factory-construction,  968-997 
fire  tests,  956,  957,  960 
Fire  Underwriters'  requirements,  958 
fireproofing,  781,  811.  955,  957-958 
flat-slab  construction,  949 
floors,     842-856,     924-940,     948-955 
(see  slabs-,  below) 

load  tests,  967 

surface-finish,  239,  246,  965 
footings,  186,  946-947,  978 
forms,  245,  962,  964-965.  966 

permanent  centering,  852,  853 
foundations,  186,  196,  946-947,  978 
four-way  system,  949,  95o,  993-997 


Reinforced  concrete,  gravel,  908 

heat,  effect  of,  245,  827,  937,  955- 

959 
Hennebique  system,  919-920,  940 
historical  notes,  906 
hollow-tile  and  concrete,  951-952 
I  beams,  reinforced,  854 
inspection,  965-966 
joining  new  work  to  old,  965 
Kahn  system,  921,  940 
metal-core  columns,  944-945 
materials  used,  907-923 
mill-construction,  948,  968-997 
mixing,  963,  964 

mixtures,  909-910,  945,  963,  964 
modulus  of  elasticity,  912,  924,  934, 

935,  956 
molds,  962,  963,  964-965,  966 

permanent  centering,  852,  853 
Mushroom  system,  950,  993-997 
piers,  978 
piles,  196-200,  945 
pouring  and  ramming,  964,  966 
proportions  of  materials,  240,  247  - 

249,  910,  1712 
protected  from  fire,  958 
reinforcements  (see  Reinforcement) 
retaining-walls,  261-263 
roofs,  866-872,  968,  976 
sand,  908 

sectional  systems,  853-854 
separately  moulded  system,  953-955 
shear,  912,  921,  937-940 
shrinkage-stresses,  937 
skeleton  construction,  948 
slabs  (3ee,  also,  floors,  above) 

bending  moments,  932,  936,  984. 
987 

cost,  250 

design,  example,  971 

diagrams  for  strength,  984-987 

flat-slab    construction,    845,    846, 
949-952 

girderless  floors,  968,  993-997 

loads,  safe,  984-987 

rectangular,  formulas,  932 

separately  molded,  953 

strength,  932,  97i,  984-987 
in  T-beam  design,  934,  975 
stairs,  900,  947,  982,  983 
stirrups,  921-923,  939,  940,  973 
stone,  908-909,  935 
superintendence,  965-966 
System  M,  948-949 
T  beams,   932,  933,  937,  94©,  97i. 

975,  988-991 
temperature-stresses,  937 
tension-members,  913-91S 
tensional  stress,  924 
tests,  adhesion,  920 

corrosion,  961 


1892 


Index 


Reinforced    concrete,   tests,  fire-resist- 
ance, 955-960 
hooped  columns,  942 
loads,  967 

thickness  of  concrete,  958 

tile-and-concrete  floors,  952 

tile-protection,  959 

two-way  tile  system,  949-953 

types  of  construction,  948-955,  968 

unit  system  of  reinforcement.  922-923 

Yaughan  system,  856 

Waite's  concrete  I  beam,  854 

wall-piers,  978 

walls,  946,  948;  968,  975-978 

water  for,  909 

wet-concrete  mixtures,  963-964 

working  stresses,  911-913,  935 

wrought  iron,  907 
Reinforcement,     913-924      (see,     also, 
Reinforced  concrete) 

adhesion    (see  Reinforced    concrete, 
bond) 

Akme  system,  949-95° 

bars,  915-921 
area,  1514-1521 

compression,  921,  922,  941 

Corr-mesh,  853 

corrosion,  960,  961 

corrugated  bars,  916 

Cummings  system,  923,  945 

deformed  bars,  915,  919 

Diamond  bar,  917 

dovetailed  corrugated  sheets,  850 

expanded  metal,  846,  883,  884,  919 

Ferrornclave,  850-851 

grades  used,  913 

Havermeyer  bar,  917 

Hennebique  system,  919,  920,  940 

hollow -tile  and  reinforced,  951 

yiy-rib,  853 

Kahn  bar,  921,  940 

Kalman  bar,  918 

lock-woven  fabric,  849 

loop  truss,  923 

Luten  truss,  923 

metal  fabric,  welded,  848 

metal  lath,  882-888,  922 

Monotype,  918 

multiplex,  Berger's,  852 

Ovcid  bar,  918 

peicentage,  925,  937 

permanent  centering,  852,  853 

Ransome  bar,  915 

Rib-bar,  917-918 

rib-metal,  847-848 

rib-truss,  853 

rivet-grip  bar,  919 

rods,  number,  937-938 

rust,  186 

Self-Centering,  Duplex,  853 

Self-Sentering,  853,  885-886 


Reinforcement,  spacing,  922,  938 

specifications,  904 

System  M,  948 

triangle  niesh,  850 

types,  843,  855,  880-890,  913-923 

unit  system,  922-923 

welded-metal  fabric,  848 

wire-fabric,  850 

wire-mesh,  919 

working  stresses,  912,  913 

wrought-iron,  907 
Repose,   slopes   and  angles,    253,    254, 

256 
Residences  (see,  also,  Dwellings) 

air-change,  1353 

heat-temperature,  1256 

non-fireproof,  height,  813 

steam-heating    specifications,     1361- 
1363 
Resisting  moment,  333,  556 
Resolution,  forces,  288,  289,  1065 
Rest,  definition,  124 
Resultant,  force,  288,  289 
Retaining- walls,  252-264 

angles  of  friction,  253 

angles  of  repose,  256,  259-260 

batter,  259-260 

breast  walls,  262-263 

cleavage-plane,  257-258 

coeflacients  of  friction,  253 

construction,  details,  259 

footings,  261-262 

friction,  theorem  of,  252 
angles  of,  253 

grouted,  269 

internal  stresses,  257 

pressures  on,  257 

principles  of,  252-255 

proportions,  261 

reinforced-concrete,  261-26^ 

slopes  of  repose,  256 

thickness,  260 

theories,  255 

vault-walls,  263-264 
Reverberation,  acoustics,  1487 
Rhomboid,  37 
Rhombus,  37 
Rib-bar,  918 

Rib-metal,  properties,  847-848 
Rib-stud,  plaster  partitions,  881-882 
Rib-truss,  853 

Richmond     building     code,     loads     on 
foundation-beds,  143 

office-buildings,  assumed  loads,  151 
Risers,  stairs,  rules,  1648 

table,  1646-1647 
River-deposits,  133 
Rivet,  rivets  (see,  also,  Riveting),  413 

American      Bridge      Co.,      standard, 
table,  420 

annealing,  382,  414 


Index 


1893 


Rivet,  arrangement,  414,  415 
base-price,  1205 
bearing  value,  415,  416 

area  used,  416 

Boston  law,  418 

by  proportion,  692 

column-connections,  469 

Cambria,  418 

Carnegie,  418 

determination  of,  415 

field-rivets,  618 

formula  for,  416 

live  loads,  415 

New  York  law,  418 

riveted  girders,  table,  418 

shop-rivets,  618 

steel-beam  connections,  table,  419 

steel  trusses,  table,  419 

tables,  418,  4x9 

wrought  iron,  415 

wrought  iron,  table,  418 
bending-stress,  422,  423 
bridge-work,  423 
butt-joints,    comparative    efficiency, 

421 
chain,  definition,  421 
clearance,  414 
columns,  number  of  rows,  diagrams, 

467 
conventional  sign,  417 
cost,  base-price  for  rivets,  1205 

punching  holes,  1204 
cover-plates,  diagrams,  421,  422 
diameters,  plate  and  box  girders,  682 

standard  connections,  617 
distance  from  edge  of  plate,  682 
drift-pins,  414,  682 
driving-tools,  1203 
failure  of  joints,  415 
field,  423 

lengths,  table,  420 

shearing  value,  618 

symbols,  617 

weight,  percentage  added,  617 
grips,  table,  420 
heads,  413,  414,  682  , 

diagram,  416 

eccentric,  414 
holes,  413 

aline  ment,  414 

allowance  for  errors,  615 

deductions,    plate    girders,    tables, 
702,  703,  704     - 

deductions,      plates     and    .angles, 
tables,  399,  400,  702 

deductions,  from  various  authorities, 
60 J,  604 

diameter,  414,  415?  682 

punching,  382,  414,  4i5»  1203 
in  flange-angles,  687,  691 

spacing,  specifications,  1202 


Rivet,  in  plate  girders,  diagram,  615 
in  stiffeners,  687 
initial  slip,  422 
inspection,  414 
lap-joints,  diagram,  421 
lengths,  413 

field-rivets,  table,  420 
loose,  414 

machine-driven,  414,  683 
material  of,  413 
number  of,  column-connections,  469 

equation  for  determining,  687 

examples,  699,  700,  701 
joints,  421,  422 
plate  girders,  691,  696,  701 

for  double  shear,  416 

standard  connections,  616,  617 
pitch  (see  spacing) 
proportions,  diagrams,  416 
punching,  diameter  of  die,  414,  682 
reaming,  382,  414,  423,  682 
shanks,  diagram,  416 
shearing  value,  411,  413,  416,  692 

area  used,  416 

by  proportion,  692 

column-connections,  469 

determination  of,  415 

double  shear,  411,  416 

field-rivets,  618 

live  loads,  415 

shop-rivets,  618 

single  shear,  411,  416 

steel-beam  connections,  table,  419 

steel  trusses,  table,  419 

tables,  418,  419 

wrought  iron,  415 
shop,  414,  417,  423 

bearing  value,  618 

shearing  value,  618 
signs,  conventional  diagram,  417 
sizes,  determination  of,  415,  1201 

diagrams,  416 

for  plate-thicknesses,  41 S 

shop-practice,  415 

table,  420 
spacing,  414 

cover-plates  of  plate  girders,  683 

flange-angle,    examples,    696,    697, 

699-701 
.plate  girder,  example,  691,  692,  693 

specifications,  1202 

standard  connections,  617 

steel  columns,  469 
staggering,  414 

standard  connections,  616,  617,  618 
symbols,  417 
taper-rivets,  423 
weights,  standard  connections,  617 

steel  rivets,  1528 
working  stresses,  41S,  4i6,  423,  618, 
1138,  1200 


1894 


Index 


Rivet,  working  stresses,  column-connec- 
tions, 469 
compared,  692 
for  bridges,  423 

standard  connections,  table,  618 
Riveting  (see,  also,  Rivets),  413-^23 

definitions,  413,  421 

field,  compared  with  shop,  423 

machines,  414 

shop,  414,  415,  423 

single,  definition,  421 
Rock,  angle  of  repose,  256 

argillaceous,  131,  132 

boulders,  134,  136 

classification,  131-132,  134 

composition,  130 

disintegration,  133,  134 

excavation,  cost,  1537 

foundation-bed,  130-132,  134, 135,141 
loads, 143 

igneous,  131 

inclined  strata,  146 

ledge,  134,  13s 

loose,  134,  135 

metamorphic,  131,  132 

plutonic,  131,  132 

rotten,  134,  135,  256 

safe  loads,  141,  143 

sedimentary,  131 

siliceous,  131 

testing,  145 

under  caisson-piers,  214 

weight,  loose,  256 
Rococo  radiator,  1265 

wall,  1266 
Rods  and  bars,  steel,  385-398 

forked-loop,  387 

looped,  386,  396 

safe  loads,  388-392 

screw-ends,  387,  393-398 

weights,  1 514-152 1 
Roebling's  Sons,  wire-gauge,  400 

standard  wire  lath,  887 
Roman  long  measures,  34 

weight,  34 
Roof,  roofs  (see,  also,  Roofing  and  Roof- 
trusses) 

cost,  777,  810 

conductors,  1658 

dampness,  800 

fire-proof,  866-872 

fire-protected,  801,  1597 

flooding,  801 

gutters,  1658 

heat-transmission,  1259 

leaks,  800 

loads,  740,  741,  745,  746,  104S  1057, 

1196 

mansard,  870-871 

mill-constrdction,  760  (see  Mill-con- 
struction) 


Roof,  mill-construction,  cost,  810 
example,  769 

materials  (see  Roofing,  materials) 
timbers  and  framing,  765 
walls,  768 
nozzles,  801 

pitch  or  slope,  867,  869,  1046,  1053 
rafters  (see  Rafters) 
reinforced-concrete,  866-872,  968,  976 
saw-tooth,  772-777 
trusses  (see  Roof -trusses) 
Roof-loads  (see  Loads) 
Roof-trusses,  998-1170  (see,  also,  Roof 
and  Roofing) 
anchoring,  1150-1152,  1168 
arched  trusses,  1035-1043 
stresses  in,  1118-1123 
wooden,  1020-1024 
arches,  trussed,  1121-1133 
bending  moments,  moving  load,  1134, 

1 13s 
bolt-connections,  429-439,  1138 
Bow's  notation,  1066 
bowstring,  1035,  1094,  io9S 
cambered,     1011-1019,     1026,     1028, 
1033-1035     (see,    also.    Scissors 
truss) 
stresses  in,  1056,  1060,  1061,  1079- 
1086,  1093-1095 
cantilever,  1043-1045,  1 105 -i  108 
car-barn,  1028,  1056,  1209 
cost,  1208 

counterbracing,  1000-1006, 1034, 1104 
crane,  1069 

diagrams,  lettering,  1066 
fan  (see  Fan  truss) 
Fink  (see  Fink  truss) 
fireproofing  for,  860,  861 
fixed  arch,  1043,  1131 
fixed    and    free    ends,    wind-stresees, 

1109,  mo 
flat  roofs,  example,  1057,  1143 

stresses,  graphics,  1075,  1077,  1089- 

1092,  1102-1104 
types,  1030-1034 
forces  acting,  1066,  1070 
French,  1026 
hammer-beam    (see     Hammer-beam 

truss) 
hinged,  1038-1043,  1121-1130 
hook-splice,  11 55 
horizontal  chords,  1004 
horizontal       deflection,        1085- 1088 

I119,  1 1 29 
horizontal   thrust,    1085- 1088,    11 10. 

1129-1130 
Howe  (see  Howe  truss) 
influence-lines,  1134--1137 
joints,  steel,  423-429,  1160-1170 
wooden,  412,  413,    429-439,  1149 
1160 


Index 


1895 


Roof -trusses,  king-post,  998,  1000 
king-rod,  998,  1153,  1154 

stresses,  1048,  1069,  io99 
knee-braces,    1025-1027,    1116-1118, 

1164,  1168 
lateral  bracing,  1033 
lattice,  1008-1010,  1089-1091 
loads  (see  Loads) 
members,  proportioning,  1139 
notation.  Bow's,  1066 
pin-connections,  423-429 

use,  1030,  1032,  1034 
Pratt,  1026,  1031,  1032,  1077 
purlins  (see  Purlins) 
quadrangular,  1032,  1033,  1091-1094 
queen,  999-1004,  1139,  1140 

load-distribution,  1055 

stresses,  1071,  H12-1116 
reactions,  1066 

unsymmetrical  loads,  1096,  1098 

wind-loads,  mo 
roller-bearing,     wind-stresses,     iiii, 

1118 
sag-tie,  1025 
saw-tooth  roofs,  772-777 
scissors  (see  Scissors  trusses) 
shed,  1025 

spacing,  1047,  1048,  1051 
splicing  in  wooden,  11 55 
steel,  1025-1045,     1144-1149,     ii6o- 
1170 

cost,  1206 

saw-tooth  roofs,  772-777 

secondary  stresses,  1137 

shop-drawings,  1162,  1207 

specifications,  1201 

weight,  1050,  1051,  1209 
steel  columns  in  trusses,  1139 
stresses,  1046-1137,  1138 

influence-lines,  1134-1137 

coefficients,  1058-1065 

graphics,  1065-1137 

unit,  timber,  1138 

wind-load,  1118,  1123-1128 
suspended,  1032,  1089 
types,  998-1045 

unsymmetrical,      1096-1098,      iioo- 
1107 

loads,  1096,  1098 
wall-plates,    1 1 50-1 152,    1156,    1158, 

1165,  1168 

Warren  (see  Warren  truss) 
weight,  1050-1051 
white-pine,  1138 
wooden,  439 

bolted  connections,  429-439 

cantilever,  1044 

design,  1138-1144 

joints,  II 49-1 160 

types,  998-1024 

unit  stresses.  1138 


Roof- trusses,    wooden,  washers,    1157- 
II 60 
weight,  1050-1057 
Roofing,    1 581 -1604    (see,    also,   Roofs 
and  Roof -trusses) 

asbestos,  corrugated  sheathing,  819 
sKingles,  819 

asphalt-gravel,  871,  1598 

asphaltic  materials,  1608 
.     Barrett,  1595 

Bonanza  tile,  868,  869 

book-tile,  868 

canvas,  801 

cement  tiles,  868,  869 

copper,  1049,  1604 

corrugated   iron,    1046,    1049,    1599- 
1604 

dampness,  800 

felt,  weight,  1049 

flat  roofs,  866,  1046 

galvanized,  1604 

gravel,  871,  1027,  I59S-IS99 
fire-resistance,  1597 

incombustible,  defined,  1853 

leaks,  800 

materials,  800, 1046, 1567,  1581-1604, 
1608 
fire-resistant,  819,  817,  1597 
weight,  1049 

mill-construction,  760,  800 

pitched  roofs,  867-869,  1046 

prepared,  1599 

ready,  1027,  1046,  1049,  1599 

reinforced-cement  tiles,  867,  868 

sheathing,  1049,  1055,  1567 
paper,  1567 

shingles,  1046,  1581 

slag,  801,  1595-1599 

slate,  871,  1046,  1049,  1582-1586 

steel  sheets,  1 599-1604 
asbestos-covered,  819 

tar-and-gravel,  871,  1027 

tile,  866,  867,  871,  1586 

tin,  801,  1046,  1049,  1588,  1595  (see 
also,  Tin,  roofing) 

warehouses,  800 
Roofs,  heat-transmission,  1259 
Room,  fresh  air  for  furnace,  1322 
Rope,  for  bells,  1726 

cotton,  hemp  and  Manila,  406-408 

weight,  723 

wire,  404-406 
Ropes  and  cables,  measures,  25 
Rosin,  weight,  723    • 
Rotary  converter,  1463 
Rotten  rock,  134,  135,  256 
Royalties,  payments,  17 59 
Round  rods,  safe  loads,  388 
Rubble  (Glossary),  1842 
Rubblework,  266,  441,  1538,  1842 

cement,  235 


1896 


Index 


Rupture,  Modulus  of   (see  Modulus  of 

rupture) 
Rust,  reinforced  concrete  footings,  i86 

Safe  load,  definition,  125 
Safety,  factor  of,  definition,  126,  375, 
556 
appliances,    elevators,    1664,    1669, 
1672 
St.  John  the  Divine,  Cathedral,  founda- 
tions, 251 
St.  Louis  building  code,  loads  on  foun- 
dation-beds, 143 
loads  on  masonry,  267 
office-buildings,  assumed  loads,  151 
thickness  of  walls,  230-232 
St.  Paul  building  code,  loads  on  foun- 
dation-beds, 143 
office-buildings,  assumed  loads,  151 
Saints,  symbols,  1727 
San  Francisco  building  code,  loads  on 
foundation-beds,  143 
thickness  of  walls,  231 
San  Francisco  fire,  tests  of  materials, 

957 
Sand,  134,  1553 
angle  of  repose,  256 
beds  of,  134 
chemical  analysis,  138 
classification  and  composition,  136 
cost,  249 

foundation-beds  on,  141 
in  reinforced  concrete,  908 
Ottawa,  235,  241,  908 
proportions,  in  concrete,  241-243,  247- 
251,  908 
in  lime  mortar,  1553 
quicksand,  136,  137,  141,  211 
safe  loads  on,  141,  143 
screening,  1553 
sieve  tests,  138,  241 
source  of,  130,  1553 
specific  gravity,  1507 
voids,  247-249 

weight,  248;  256,  1507,  I537>  I554 
Sand-bars,  formation  of,  133 
Sand  finish,  plastering,  1555 
Sandstone,  131 

beams,  coefficients  for,  628 
fiber-stresses,  557 
tensional  strength,  282 
bituminous,  paving,  1609 
crushing  strength,  266,  270,  279-282 
fire-resistance,  814 
loads,  safe,  266,  267,  279,  282 
modulus,  of  elasticity,  282 

of  rupture,  282 
shearing  strength,  282 
specific  gravity,  282,  1507.  1508 
weight,  282,  1507,  1508 
Sash,  hollo \v-metal,  897 


Sash,  weights  for,  1649,  1651 

Sash-balances,  1652 

Sash-chains,  1650 

Sash-cords,  1649 

Sash- pulleys,  1649 

Sash-ribbons,  1650 

Sash-weights,  1649,  1651 

Saw-tooth  roofs,  772-777 

Schedule  of  charges,  architects,  1728, 

1731 
Schists,  132 

Schlierenmethode,    photographing    air- 
disturbances,  1495-1499 
Scholarships,  architectural,  1779-1788 
School-buildings,  1644- 1648 

cost,  1613,  1614,  1616 

doors,  1648 

flagpoles,  1644 

floor-joists,  717 
spans,  737,  742 

floor-loads,  live,  719    720,  1198 

heating-temperature,  1256 

hot-blast  heating,  1324 

non-fire-proof,  height,  813 

size  of  rooms,  717 

stairs,  1648 

ventilation,  1353 

wa»ter-closets,  1641 
Schoolrooms,  blackboards,  1644,  1645 

desks,  1645 

dimensions  of,  717,  1644 

floor-loads,  719,  720,  1198 

heating,  1256,  1324 

lighting,  145 1 

seats,  1645 

ventilation,  1349,  1353 
Schools,  architectural,  1769,  1775,  1776, 
■      _         1779-1788 

Scissors  trusses,  1004,  1010-1013,  1055, 
1056 

stresses,  1081-1087 

wall-joint,  1156 
Screen  (Glossary),  1843 
Screw-ends,  386-398 
Screw-jacks,  215,  216,  221 
Screws,  1535,  1536 

lag,  1157,  1535 

threads,  standard,  1525 
Scripture  measures  and  weights,  34 
Scuppers,  767 

Seat-baths,  dimensions,  1641 
Seating  capacity,  165 3- 1656 
Seating-space,  churches,  1653,  1654 

schools,  1645 

theaters,  1653-1656 
Seats,     dimensions     of,      1638,     i6;i5, 

1653 
Seattle  building  code,  masonry  loads 

287 
Secants,  table  of  natural,  ii6 
SeQtiQn-f actor  (see  Section-modulus) 


Index 


1897 


Section-modulus,  333 

elementary  sections,  334-338 
structural  shapes,  354-359,  362-369 
Sectar  of  circle,  38 

ceater  of  gravity,  293 
Sedimentary  rocks,  131 
Segneat  of  circle,  38 

center  of  gravity,  293 
Segnental  arch,  305,  307,  321 
Seleriite,  131 

Senicircle,  center  of  gravity,  293 
Separators   for   steel   beams,   612-614, 

1202 
Services,  architects,  1731 
Sevige,  ejectment  of,  1422 
Se,v3r-pipes,    1407-1409,    1419,    1420, 

1422 
Sewers,  as  afifecting  foundations,  147 

house,  1409 
Sexigon,  37 

Shift,   elevator,  1659,  1660,  1666,  1675, 
1676 

fire-proof,  889,  890 

for  mills,  764,  768 
Shafting,  loads,  1197 

machinery,  1720-1722 
Shale,  132,  143 

bricks,  275 

specific  gravity  and  weight,  1508 
Shear,  128,  411 

beams  (see  Beams) 

baits  (see  Bolts) 

buildings,  wind-pressure,  1176-1183 

cast  iron,  412 

double,  411 

failures,   illustrations,   170,   171,  411, 
412 

girders  (see  Beams) 

horizontal,  wooden  beams,  412,  635 

pins,  423,  424 

plate  girders,  684-687,  690,  691,  696, 
698,  703 

reinforced-concrete,  912,  921,  937-940 

rivets  (see  Rivets) 

single,  /,.ii 

steel,  382,  412,  567,  569,  1132 
specifications,  1203 

vertical,  beams,  411,  565,  567 
diagrams,  685,  686,  690,  698 
wind-bracing,  11 76-1 183 

web-plates,  in  plate  girders,  703 

wind-bracing,  1176-1183 

woods,  412,  647-651,  1138 
Shearing,   effect  on  steel,  382,  414,  688 
Sheathing,  asbestos  corrugated,  819 

mill-construction,  759 

papers,  1564-1568 

roof,  weight,  1049 

wooden,  1049,  1563 
Sheathing- quilt,  1564-1568 
Sheet  lath,  886 


Sheet,  metal,  402,886,  1510,  1511,  1599 

tile,  1587 
Sheet- piling,  200-209 
Sheet  iron  and  steel,  asbestos-covered, 
819 

base-price,  1205 

ceiling,  1604 

corrugated,  1599-1604 

galvanized,  1604 

gauges,  402,  1 5 10,  1600 

roofing, 1599-1604 

siding,  1603 
Shelf-angle,  beam-framing,  787-790 
Shelf-hangers,  752,  788,  790 
Shingles,  1581 

asbestos,  819 

dimensions,  1582 

nails  required,  1581,  1582 

sizes,  1 581 

staining,  1570 

tin,  1046,  1049 

weight,  1046,  1049,  1581 

wooden,  1046,  1049,  1570,  1581 
Shop  drawings,  1754 
Shops,  hot-blast  heating,  1324 
Shoring,  excavations,  214-222 
Shot-drills,  foundation-bed  testing,  145 
Shutters,  fire,  759,  778,  801,  901-902 
Sideboards,  dimensions,  1638,  1640 
Sidewalks,  flagstones,  1539 

granite  curbing,  1539 

vault-walls,  263-264 
Siding,  beveled  and  drop,  wooden,  1563 

corrugated  metal,  1603 
Silica  minerals,  130 
Silicates,  130 
Sills,  stone,  1539 
Silt,  139 
Silver,    specific     gravity    and     weight, 

1508 
Simplex  concrete  pile  method,  197 
Sines,  table  of  natural,  95 
Sinks,  141 2,  1641 
Sirocco,  fans,  1341,  1344 
Skeleton  construction,  234,  948,  11 71 
Skewback,  arch,  305,307 

floor-arches,  834-835 

vaults,  1232 
Skylights,  glass  for,  1580 

mills  and  warehouses,  765 

saw-tooth,  769,  772-777 

standard,  defined,  1854 

weight,  1049 
Sky-signs,  wind  load,  1199 
Slabs,    reinforced-concrete   (see    Rein- 
forced concrete) 
Slag,  in  cement,  236,  237 
roofing,  801,  1595-1599 
Slag' cements,  characteristics,  236,  237, 

238 
Slag  concrete,  fire-resistance,  817 


1898 


Index 


Slate,  132,  1582 

beams,  coefficients  for,  628 
safe  fiber-stress,  557 

cost,  1046,  1585 

crushing  strength,  282 

flooring,  1606 

grading  of,  1583 

laying,  1583 

Old  English  method,  1584 

measurement,  1584 

modulus  of  elasticity,  282 

modulus  of  rupture,  282 

nails  required,  1585 

punching,  1583 

roofs,  871,  1046,  1049,  1582-1586 

sizes,  1583 

specific  gravity,  282,  1508 

strength,  282,  557 

thickness,  1583 

tile,  1606 

weight,  282,  1049,  1508,  1585 
Sleeve-nuts,  386,  387,  397 
Slenderness-ratio,  columns,  448 
Slip,  in  pump  action,  1247 
Slop-sinks,  dimensions  of,  1641 
Slope,  of  roofs,  867,  869,  1046,  1053 

of  repose,  256 
Slow-burning    construction    (see    Mill- 
construction,  slow-burning) 
Smoke-pipe,  1362 
Snow-loads,  1049,  1052-1057 
Soapstone,  131 

Societies,  architectural,  1 788-1 795 
Sofas,  dimensions,  1640 
Soffit,  arch,  305 
Softwoods,  ultimate  unit  stresses,  649- 

651 
Soil,  132 

angle  of  repose,  256 

foundation-beds,  135-148,  980 

weight  of  loose,  256 
Soil-pipes,  1407,  1410,  1427 
Solids,  m.ensuration  of,  61 
Sound  (see  Acoustics) 
Soundproofing,  partitions,  891 
South.  Carolina,  registration  law,  1779 
Span,  arch,  305 

beams,  definition,  555 

wooden  joists,  736-746 
Spandrels,  arch,  305 
Specifications,  cast  iron,  379 

column-connections,    cast-iron,    457, 
458 

electric  wiring,  1482 

elevator-installation,  1 663-1664 

fire-shutters,  tinned,  901-902 

furnace-heating,  1357-1359 

gravel  roofing,  1 595-1 599 

hot-water  heating,  1359 

hydrated  lime,  1551 

lime,  1549 


Specifications,  paint,  fire-proof,  821 

plate  girders,  682 

plumbing-fixtures,  1640 
Portland  cement,  236,  907 

reinforcing-steel,  914 

roofing-tiles,  1586 

slag  roofing,  1 595-1 599 

standard,  A. I. A.,  1752-1764 

steam-heating,  1361^ 

steel,  in  reinforced  concrete,  914 
structural,  383,  1194-1204 

tile  roofing,  15S6 

wiring,  electric  work,  1482 

wooden-pile  foundations,  193 

wrought  iron,  377 
Specific  gravity,  1500-1508 
Specific  heat,  1250,  1684 
Specific  volume,  gases,  1256 
Spheres,  38,  60,  64 
Spheroids,  60,  65 
Spider,  domes,  1222 
Spikes,  cut  steel,  1532 

steel-wire,  1533 
Spinning-mills,  cost,  805 
Spring-hne,  arch,  305 
Spring-needles,  221 
Springers,  arch,  305 
Sprinklers,  automatic,  801,  903-905 

framing  to  accommodate,  777 

mills,  759,  768 

tanks,  779 
Spruce,  beams,  coefficients  for,  628 
deflection,  664 
distributed  loads,  safe,  639 
fiber-stress,  557,  647,  648 

columns,  safe  loads,  451 

crushing-loads,  with  the  grain,  449 

crushing   strength,   across   the   grain, 
454 

modulus  of  elasticity,  647,  664 

shearing  strength,  412,  647,  648 

specific  gravity,  1508 

stiffness,  664 

tension,  376,  647,  648 

unit  stresses,  376,  412,  647,  648,  650 

weight,  650,  1508,  1558 
Square,  squares,  37,  39 

hollow,  moment  of  inertia,  335 

pleasures,  27 

moment  of  inertia,  334 

radius  of  gyration,  334 

section-modulus,  334 

tables  of,  8-24 
Square  roots,  3 

tables,  8-24 
Stability  of  structures,  definition,  125 
Stack,  looilcr,  1283 

furnace,  1312,  1317,  1322,  1358 

steel,  1376 

anchor-bolts,  1377 

tall  buildings,  1283,  1368 


Index 


1.S99 


Staff,  1558 

Stainless  cements,  238 

Stairs,  dimensions,  1646,  1647,  1648 

Ferroinclave  foundation,  900 

fire-proof,  899-900,  947,  983 

hand-rail,  1648 

hollow-tile  steps,  899,  904 

mill-construction,  759,  810 
tower,  764,  768,  778,  779 

reinforced-concrete,  900,  947,  983 

risers,     1648 

table,  1646,  1647 

school-houses,  1648 

towers  for,  764,  768,  778,  779 

treads,  899,  1648 
table,  1646,  1647 
Stairways,  loads,  1198 

protection,  fire,  764,  765,  778,  779 
Standpipes,  768,  801,  905 
States,  registration  of  architects,  1768, 

1777 
Stitistics,  definition,  124 
Stitis,  architects,  1728,  1754 
Sieim,  1251-1254 

consumption,  engines,  1247 

heating,  1264,  1 283-1302  (see  Heat- 
ing, steam) 

saturated,  properties,  1253 
Steitn-coils,  hcaiing  water  by,  1344 
Steam-heating  (see  Heating) 
St3el,  adhesion  to  concrete,  912,  919, 
920,  938,  940 

bars,  385-398 

areas,  etc.,  1514-1521 
safe  loads,  388-392 
weight,  1514-1521 

bas3-price,  1204,  1210-1212 

beams  (see  Beams) 

Bessemer  process,  380 

branding,  385 

carbon-content,  381 

chemical  properties,  383 

chimneys,  1376 

coefficient  of  expansion  382 

cold-bend  test,  378,  384,  385,914 

columns  (see  Columns) 

compressive  strength,  449 

corrosion  in  concrete,  960-962 

corrugated,  base-price,  1205 
weight,  1600,  T603 

cost,  1 204-1212 

defined,  380 

elastic  behjivior,  381 

elastic  limit,  381,  913 

eloi^ation,  381,  384,  9^3 

eye-bars,  386,  595 

finished  material,  384 

fire-resistance,  819 

form  of  test-specimen,  384 

manufacture,  380,  383 

merchant,  cost,  12 10 


Steel,  modulus  of  elasticity,  381,  912, 
934 
open-hearth  process,  380 
plates,  384,  385,  1204 
phosphorus-content,  381,  383 
properties,  chemical  and  physical,.383 
punching,   effect  on  plates,  382,  414, 

688 
reinforcing  (see  Reinforcement) 
roof-trusses  (see  Roof-trusses) 
rope,  404-406 
rupture-stress,  381 
shearing,  382,  412,  567,  569,  1138 
sheet,  1 599-1604 

asbestos-covered,  819 

base-price.  1205 

corrugated,  1205, 1599-1604 

gauges,  402,  1510 
specifications,  383 
specimens  for  tests,  383,  384,  407 
strength,  407,  914 

carbon  and  phosphorus,  effect,  381 

specification,  383 

ultimate,  482 

wire,  401,  406 

working,  376,  412,  557,  1138,  1199 
stress-strain  diagram,  382 
stresses  (see  strength) 
structural  (see  Structural  steel) 
tests,  383-385,  1195 
thickness,  corrosive  agents,  1202 
weight,  382,  1510-1521 

estimating,  rule  for,  152 1 

sheets,  1510,  1511 

variation  in,  385 
wire,  400-406,  1512 

weight,  1512 
yield-point,  381,  383,  912,  913 
Steel-pipe  columns,  469-474,  488 

safe  loads,  488,  497,  498 
Steelwork,  1194-1206 

bolted  connections,  1204,  1206 

buildings,  weight,  1 207-1 209 

cost-data,  1204- 1 212 

cut  to  length,  1206 

design,  1201 

drafting,  cost,  1206 

erection,  1203,  1206 

fire-protection,  468,  760,  780,  822- 

826 
foundations,  1203 
freight-rates,  1205 
inspection,  1203,  1205 
mill-buildings,  786,  788,  i2to 
painting,  1203,  1206,  1572,  I573 
specifications,  383,  1 194-1204 
stresses,  618,  1138,  ii99 
weight,  estimates,  1207-1210 
workmanship.  1202 
Steps,  hollow-tile,  899 
stone,  1539 


1900 


Index 


Stevedore-rope,  407 

Stiffeners,  girder-webs,  681,   686,   691, 

921-923,  939,  940,  973 
Stiffness,  definition,  125 
Stirrups,      reinforced-concrete      beams, 
921-923,  939,  940,  973 

wooden    beams,    750,    754-757,    787- 
794 
Stone  (see,  also,  Stonework    and  each 
kind  of  stone) 

angle  of  friction,  253 

beams,  628 

fiber-stress,  557 

building-data,  282 

caps,  1539 

coefiicient  of  friction,  253 

concrete,  908 

coping,  1539 

cost,  1538,  1613 

crushed,  cost,  249 

crushing  height,  269 

crushing  strength,  279-282 

fire-resistance,  814 

footings,  223,  224 

lintels,  1539 

masonry,  265-270,  1538 

modulus  of  elasticity,  282,  283 

piers,  270 

quantities  in  concrete,  247-249 

sills,  1539 

steps,  1539 

strength,  265-770,  279-282 

weights,  282 
Stonework  (see,  also,  Masonry,  Stone, 
Walls,  etc.) 

ashlar,  441,  1538 

bluestone,  cut,  1539 

coefficients  of  friction,  253 

cost,  data  for  estimating,  1538 

crushing  strength,  265 

cut-work,  1538 

data,  1538-1539 

hammer-dressed,  1538 

loads,  safe,  266 

measurement,  1538 

rubble,  441,  1538 

sidewalks,  1539 
Storehouse-construction,  765-788 
Straight-line  formula,  cast-iron  columns, 
460-461 

depth  of  keystone,  308-309 

steel  columns,  481-482,  493-496 
Strain,  definition,  125 
Strength,  beams,  law  of  variation,  565 

breaking,  556 

coefficient  of,  556,  628 

compressive,  448 

definition,  125 

elastic,  126 

elongation-relation,  steel,  381 

flexural,  definition,  125,  556,  635 


Strength,  of  materials,  definition,  125 

shearing,  411,  635,  657,  667 

tensile,  375 

ultimate,   definitions,    125,   375,   381 
•  411,  448 

working,  definition,  125,  375 
Strength  of  materials  (see  name  of  ma 
terial  in  question) 

definition,  125 
Stress,    stresses,    125,    254    (see,  also 
materials  in  question) 

bearing,  415 

bending,  265,  628,  647 

combined,  128,  480,  572,  1114 

compressive,  127,  647 

constants,  wooden  beams,  628 

diagrams  and  formulas,  1065-1137 

distribution  of,  254 

elastic  limit,  126,  381 

fiber,  126.  32s,  555,  556 

flexural,  126,  325,  333,  555 

intensity,  definitions,  125,  254,  375 

modulus  of  rupture,  126 

notation,  122 

resultant,  254,  1183 

reversal  of,  1104 

rupture,  381 

secondary,  1137 

shearing,  128,  411,  415,  647 
horizontal,  635,  687 

shrinkage,  in  concrete,  937 

stress-strain  diagram,  382 

temperature,  in  concrete,  937 
trusses,  11 28 

tensional,  127,  375,  415,  647 

torsion,  128 

transverse,  265,  480,  555,  628 

ultimate,  375 

uniform,  254 

unit,  definitions,   125;  126,  375,  1172 

varying,  254 

wind,  trusses,  1109-1118,  1123-1128 

wind-bracing,  1176-1183 

working,  definitions,  125,  375 

yield-point,  381 
Stress-strain  diagram,  382 
String-course  (Glossary),  1846 
Structural  shapes,  332-374  (see  Angles, 

Channels,  I  beams,  etc.) 
Structural  steel  (see  Steelwork) 
Structures,  definition,  124 

domical,  1213-1231 

large,  heating,  1324 

theory  of,  124 

vaulted,  1231-1243 
Struts,  angle,  tables,  488,  501-503 

as  beams,  571,  572 

bracing,  formulas,  495 

cast-iron,  trussed  girders,  661 

channel,  loads,  table,  499-500 

compression-formulas,  496 


Index 


1901 


Struts,  double-steel-angle,  loads,  503 

eccentric  loads,  453,  489 

I-beam,  strength  of,  489 

in  trusses,  steel,  480 

loads,  1 201 

tables,  488,  493-495 

single-steel-angle,  loads,  501 

trusses,  998 

wood,  633 

strength  of,  448-452 
trussed  girders,  661 
Subcontractor's  agreement,  1765 
Subcontracts,  1761 
Sugar,  specific  gravity,  1508 

weight  of,  723,  1508 
Sulphur,  anchoring-bolts,  240 
Superintendent,  architects,  1728 
Surcharges,  306 
Surface,  center  of  gravity,  292 

finish,  concrete,  246,  965,  1555 

measures,  27 
metric,  31 
Sway-rods,  wind-bracing,  11 76,  1181 
Swedge-bolts,  steel  columns,  619 
Switches,  electric  lighting,  1478,  1479, 

1481 
Sycamore,  specific  gravity,  1508 

weight,  1508,  1558 
Syenite,  131 

compression,  282 

tension,  282 
Symbols,  Apostles  and  Saints,  1727 

electric  wiring,  1476-1478,  1484 

gas-piping,  1445 

mathematical  122.  123 

pipes  and  fittings,  1350 

plumbing,  1424-1426 
System  of  units,  engineers',  1247 

T  beams,  reinforced  concrete,  diagrams 
for  strength,  988-991 

example,  971,  97 5 

formulas,  933-934 

reinforcement,  937,  94° 
Tsectioris,  steel,  base-price,  1212 

fire-proof  ceilings,  872 

girder  flange,  682 

size  and  properties,  337,  3^8,  369,  5^5 

strength,  as  beams,  591,682 
Tables,    furniture,    dimensions,    1638. 

1639 
Tacks,  wire,  i533,  iS34 
Tail-beams,  floors,  749 
Talc,  131 

specific  gravity  and  weight,  1508 
Tall  buildings,  stack,  1283,  1368  . 
Tangents,  38 

tables  of  natural,  104 
Tanks,  capacity,  1 404-1406 

construction,  1398-1402 

expansion-tanks,  1307,  1360 


Tanks,  frost-proofing  pipes,  1400 
gravity-tanks,  water,  779 
heating,  1400 
house-tanks,  1415 
incrustation,  1429 
materials,  1398 
standard  sizes,  1401 
steel,  1402 

wind-load,  1199 
wooden,  1398 
Telephones,  automatic,  1707 
Telltale  (Plumbing),  1400 
Temperature,  absolute,  1250 
concrete,  244,  245 
humidity-relation,  1352 
inside,  table,  1256 

maintenance,  heating  buildings,  1256 
outside,  in  U.  S.  table,  1257 
roof -trusses  affected  by,  11 28 
United  St'.tes,  1257 
Tempering-coil,  heating,  1328 
Tenement-house,  defined,  1854 
floor  loads,  719,  1198 
specifications,  1200 
•  Tension,  127,  375 

building  materials,  376 
members,  steel,  385-387 
-    safe  loads,  388-392,  399 
sign,  1065,  1068,  1072 
Terms,  architectural  (Glossary),  1796- 
1850 
building  codes,  1851-1855 
building  laws,  1851-1855 
engineering,  124-129 
technical,  1796-1855 
Terra-cotta,  beam-protection,  782 
book-tile,  867,  868 
column-protection,  782,  822-826 
composition,  276,  814 
dense,  814,  816,  875 
facing  of  walls,  269 
fire-resistance,    234,   815,   816,   828, 

874 
floors,  828-840,  1604-1607 
heat-transmission,  1258-1259 
hollow  walls,  233-234 
ornamental,  fire-resistance,  814 
inside  finish,  898-899 
staircases,  899 
partitions,  873-875,  889 
piers,  276-278 
porous,  815,  875 
properties,  276 
roof -construction,    866,    867,    871, 

1586 
semiporous,  815 
sound-resistance,  889,  890 
strength,  266,  276-278,  287,  815 
tests,  276-278,  816,  873 
truss-protection,  860 
weight,  278 


1902 


Index 


Terrazzo  flooring,  1607 

Tests  (see,  also,  materials  in  question) 

brick  piers,  272-278 

bricks,  270,  281,  1542 

cast  iron,  380,  446,  819-820 

cement,  236-237,  240,  907 

chains,  408-410 

column-coverings,  822-823 

columns,  cast-iron,  460,  823 
steel,  822 
steel-pipe,  472 
wooden,  449 

concrete,  283-287,  817,  911 

eye-bars,  386 

fire-proof  floors,  827,  841,  844,  866 

fire-proof  partitions,  828,  873,  889 

fire-proof  wood,  820 

floors,  720-721,  866,  967 

foundation-beds,  141 -146 

joist-hangers,  756,  794 

mortar,  283 

nails,  holding-power,  1531 

pipe,  water,  1388 

plumbing,  1412 

reinforced-concrete,   adhesion*,   919-' 
920 
corrosion,  961 
elastic  properties,  935 
fire-resistance,  955-960 
hooped  columns,  942 
loads  on  floors,  967 

sash-cords  and  sash-chains,  1650 

sound-absorption,  1486-1500 

steel,  382-385 

stone,  279-281 

terra-cotta,  276,  278,  816,  873-874 

wooden  beams,  built-up,  652-654 
columns,  449 

wrought  iron,  377-379 
Theater-curtains,  asbestos,  819 
Theaters,  chairs,  1653 

defined, 1854 

dimensions  of,  1657 

floor-loads,  719,  720,  1198 

heating  and  ventilating  layout,  1348, 
1353 

seating  capacity,  1654-1656 

seating-space,  1653 
Thermometers,  thermometry,  1249 
Threads  of  screws,  standard,  1525 
Thrusts,  305 

Tie-beams,  wooden,  430,  432,  434,  43s, 
633 

built-up,  432 

steel,  stresses  in,  572 
Tie-plates,  steel,  1202 
Tie-rods,  for  1  beams,  619,  865 

roof -trusses,  11 20 

segmental  arches,  307,  832 
Tile,  1 604-1 607 

aseptic,  1605 


Tile,  cast-glass,  1606 

cement,  reinforced,  867—869 

ceramic,  1605,  1607 

concrete,  8i6 

copper,  1587 

cost,  1046,  1587,  1607 

enameled,  1605,  1607 

encaustic,  1604,  1607 

faience,  1607 

fireproofing,  234,  815,  828,  874 

flint,  1605 

flooring,  892-893,  1604-1607 

Florentine  mosaic,  1605 

glass,  1606 

glazed,  1605,  1607 

hollow  (see  Terra-cotta) 
and  concrete,  951-952 

interlocking  rubber,  1606 

lozenge,  1605 

Ludowici,  1049 

mantel,  1605 

marble,  1605 

mosaic,  1607 

piers,  278 

reinforced,  838-842 

reinforced-cement,  867-869 

Roman,  1049,  1605,  1607 
floor-construction,  953 

roofing,  866,  1586 
cost,  1587 
laying,  1586 
specifications,  1586 

rubber,  1606 

semivitreous,  1604 

sheet-metal,  1587 

slate,  1606 

Spanish,  1049 

specific  gravity,  1508 

steel,  1587 

terrazzo,  1607 

tin,  1587 

vaults,  1243 

vitreous,  1604,  1605,  1607 

wall,  1604,  1606,  1607 

weight,  1049,  1508 
Tile-arch,  Guastavino,  841,  842,  1243 
Timber  (see,  also.  Lumber  and  different 
woods ) 

board-measure,  1560-1562 

bond  (Glossary),  1803 

data,  1558-1563 

footings,    temporary    buildings,    186, 
187 

framing,  sizes,  1559 

hardness,  relative,  1558 

measurement,  1559-1563 

modulus     of     elasticity,     647,    731- 
734 

painting,  763 

piles,  188-196,  198 

shrinkage,  table,  1428 


Index 


1903 


Timber,  sizes  in  slow-burning  construc- 
tion, 759,  762 

stresses  (see  woods  in  question) 

ventilation,  763 

weight,  1501-1508,  1558 

working  unit  stresses,  647,  648,  650, 
1138 
Time,  measures,  30 

unit  of,  1247 
Tin,  block,  pipe,  1419 

brands,  1588 

casting,  1521 

fire-doors,  894-897,  901-904,  1853 

gutters,    1590 

lined  pipe,  141 5 

roofing,  801,  1588-1595 

cost,  1046,  1589,  1593,  1594 
covering  capacity,  1591-1594 
durability,  1589 
gutters,  1590 
laying,  1 590-1 593 
painting,  1570,  1589,  i59o 
rolls,  1594 
valley,  1590 

sheets,  1588 

specific  gravity,  1508 

terne-plates,  1588 

weight,   723,   1049,   1508,  1521,  1588, 
1591 
Tinned  fire-doors,   894-897,  901-904, 

1853 
Toncan  metal,  1604 
Torsion,  definition,  128 
Tower  (Glossary,  1848),  belt,  764,  765 

elevator,  764,  765,  768 

fire-escape,  779 

stairway,  764,  765 

warehouses,  768,  779 

water,  wind-bracing,  1184 
Tower-clocks,  1695 
Tracings,  1718-1720 

black-line  copies,  17 19 

blue-prints,  17 18 

brown-line  copies,  1720 
Train-sheds,  steel,  weight,  12 10 

trusses  for,  1039 
Transferred  heat,  1684 
Transformers,  current,  1463 
Transmission  of  heat,  12 56-1 2 59,  1684 
Trapezium,  37 
Trapezoid,  37,  4° 

moment  of  inertia,  336,  337 

radius  of  gyration,  336 

section-modulus,  336 
Trap-rock,  131 

compressive  strength,  282,  287 

concrete  aggregate,  817 

specific  gravity  and  weight,  282,  1508 
Traps,  plumbing,  1410.  1412-1414 

drum,  1413.  1414 

grease,  1414 


Traps,  sewer,  1409 

ventilation,  141 2 
Trautwine's  formula,  depth  of  keystone, 

309 
Travertine,  131 
Treads,  marble,  900 

rules  for,  1648 

slate,  900 

table,  1646,  1647 
Treasury  Department,  hot-water  heat- 
ing, 1303,  1308 
Tremies,  244 
Trenches,  as  afi'ecting  foundations,  147 

preparing  for  footings,  226 
Triangles,  36,  39,  7i 

center  of  gravity,  292 

moment  of  inertia,  336 

oblique-angled,  92 

of  forces,  289 

radius  of  gyration,  336 

section-modulus,  336 

trigonometrical  functions,  91-94 
Trigonometry,  90-117 
Trim,  cement,  898 

electroplated,  898 

hollow-tile,  898,  899 

metal-covered,  894-899 
Trimmers,  floor,  728,  748 

safe  loads,  747 
Troy  weight,  29 
Truss-metal  lath,  885 
Trusses  (see  Roof-trusses) 
Tubing,  Benedict  nickel,  141 5 

seamless-drawn,  141 5 
Tungsten,  specific  gravity  and  weight, 

1508 
Tungsten-lamps,  1444,  i447 
Tumbuckles,  386,  387,  397 
Tuscan  Order,  1699 

Underpinning,  214,  218-222 

Unit  stress,   definitions,  125,  126,  332. 

375,  1172 
Unit  system,  reinforcement,  922 
Units,  system  of,  1247 

electrical    and    mechanical,    equiva- 
lents,  1248 
foot-pound-second  system,  1247 
University   of  Illinois,    tests   on   brick 
piers,  275 

tests  on  terra-cotta  piers,  277 
Urinal-stalls,  dimensions  of,  1641 
United  States  Goverment  buildings,  hot- 
water  heating,  1303,  1306,  1308 
United  States  measure  of  value,  29 
United     States     Naval      Observatory, 

foundations,   251 
Utah,  registration  law,  i779 

V  cuum-cleaners,  types,  1708 
,num-gauges,  1248 


1904 


Index 


Vacuum,  pumps,  size,  1290 

systems,  steam-heating,  1287-1291 
Valleys  and  gutters,  1590 
Valves,  equalizing,  caissons,  212 

heating,  symbol,  1350 
Vapor,  1249-1254  (see  Steam) 
Vaporization,  heat  of,  1684 
Varnish,  1568,  1570,  1573 
Vault,  1 231-1243 

barrel,  1231-1235 

(Glossary),  1849 

framed,  1243 

groined,  1235-1240,  1822 

legal  definition,  1855 

ribbed,  1240 

tile,  1243 
Vault-walls,  263-264 
Vaulting  (Glossary),  1822 
Velocity,  unit,  1247 
Veneer,  buildings,  269 

defined,  1855 
Vent-flues,  air-velocity,  1357 

coils,  1356 
Vent-pipes,  plumbing,  1407,  1410 

sizes,  1410 
Vent-shafts,  fire-proof,  889 
Vento  heater,  1330-1332,  1338 
Ventilating  fans,  1341-1347,  1357 
Ventilation,  1348-13  54 

air  required,  amounts,  1260, 1354, 1356 

buildings,  1348-1354,  1356 

capacity  of  fans,  1341 

fans,  1341-1347,  1357 

furnace-heating,  1313 

gravity  indirect  heating,  1299 

hot-blast  system,  1325,  1327 

laws,  1354 

mill-buildings,  769,  775-776 

saw-tooth  roofs,  776 

systems,  1349 

timbers,  763 

warehouses,  776 

workshops,  769,  1353 
Verona  radiators,  1266 
Vibration  of  machinery,  763 
Volt,  defined,  1457 
Voltage,  candle-power,  1462 
Volume,  measures,  27,  31,  1247 
Volumes,  geometrical,  38,  60-65 
Voussoirs,  arch,  305,  311,  313 

center  of  gravity,  313,  318 

Walks,  cement,  239 

Wall   (see,   also,  Brickwork,   Masonry, 
Stonework,  etc.) 
ashlar,  thickness,  233 
basement,  228,  229 
bearing-plates  on,  442 
breast,  262-263 
brick,  229 
backing,  269 


Wall,  brick,  over  openings,  318 
safe  loads,  265,  441 
buckling,  229 

buildings,  mercantile,  230-232 
cantilevering,  169 
cellar,  129,  228,  229 
cement-block-faced,  269 
center  of  gravity,  300,  301 
concrete,  229,  946-947,  965,  966 

cost,  250 
concrete  blocks,  233 
crushing  height,  269,  270 
curtain,  234 
dwellings,  230,  232 
external,  thickness,  229,  231 
face,  269 

faced,  with  ashlar,  233,  269 
with  cement  blocks,  269 
with  terra-cotta,  269 
fire,  765 

fire-resistance,  229,  234 
footings  (see  Footings) 
foundation,      129,      200,.    228,     229, 

979 
heat-transmission,  1256 
hollow-tile,  233 
loads  over  openings,  318 
mills   and   factories,    760,    765,    768, 

778,  809 
needling,  218-222 
openings  in,  318,  778 
parapet,  768 
party,  234 
reinforced-concrete,  946,     948,     968, 

975,  978 
retaining  (see  Retaining- wall) 
roof,  768 

safe  loads,  265-267 
self-sustaining,  234 
shoring,  214-222 
skeleton  construction,  234 
stability,  229,  301 
stone,  229,  233 

safe  loads,  266,  267 
stone-faced,  233,  269 

ashlar,  233,  269 
strength,  265-267,  269,  270 
superstructure,  229-234 
supports,  girders,  792 
terra-cotta  facing,  269 
thickness,    229-234,    260-261,    269, 

760 
tile,  hollow,  233 
tiling,  1604,  1605,  r6o7 
underpinning,  214,  218-222 
vault,  263-264 

warehouses,  230-232,  768,  778 
Wall-boards,  asbestos,  819 

metal-rib,  888 
Wall-boxes,  782,  785,  786;  792,  793 
Wall-hangers  (see  Hangers) 


Index 


1905 


Wall-openings,  31 8,  778 
Wall-pipe  (furnaces),  dimensions,  1320 
Wall-plasters  (see  Plaster) 
Wall-plates,    beams   and   girders,    783, 
785,  787,  788,  793 

roof-trusses,    1150-1152,    1156,    1158 
1165,  1168 
Walnut,  hardness,  1558 

specific  gravity,  1508 

unit  stresses,  651 

weight,  651,  1508,  1558 
War   Department,    hot-water   heating, 

1303 
Wardrobes,  dimensions,  1638,  1640 
Warehouses,  basement  walls,  229 

beams,  762,  763,  779,  800 

boilers,  780 

cast-iron  columns,  780,  781 

cement  floors,  892 

construction,  general,  758-810 

cost,  777,  802-810 

defined,  1855 

fire-escape,  768,  778 

fireproofing,  780-782 

fire-protection  (see  sprinklers, below) 

floor-areas,  765,  777,  778 

floor-loads,  721,  1198 

floors,  764,  777,  892,  893 

size  and  weight  of  I  beams,  865" 

girders,  762,  763,  779-800 

gravity-tanks,  779 

heating,  776 

height,  777 

live  loads,  721 

mill-construction  for,  777-782 

openings  in  walls,  778 

roofs,  768,  772,  800 

roofing-materials,  800,  801 

scuppers,  767 

sprinklers,  768,  777,  779>  801,  903- 
905 

stairs,  759,  764,  768,  778,  779,  810 

standpipes,  768,  801,  905 

steel,  weight,  1208 

story-heights,  765 

structural  details,  780,  788,  810 

towers,  768,  779 

ventilation,  776 

walls,  230-232,  768,  778 

wooden    columns    versus    iron    and 
steel,  780 

water-supplies,  802 
Warren  truss,  types,  1030,  103 1 

stresses,  1089-1091 
Wash-basins,  dimensions,  1641 
Washers,  437,  1157-1160 

beveled,  437,  1202 
Washington   building   code,   steel   col- 
umns, 481 
Washington    Monument,    foundations, 
251 


Wash-pipes,  foundation-bed  testing,  144 
Wash-stands,  dimensions  of,  1638 
Wash-tubs,  141 2 
Waste-pipes,    1407-1411,    1416,    1417, 

1427 
Waste-stacks,  expansion,  1427 
Water,  density,  1247 

evaporation,  1251-1254 

filters,  142 1 

flow  in  pipes,  1382-1388 

freezing-point,  1250 

hard,  softening,  1429 

head,  1381-1383,  1389 

heating,  house-supply,  1430 

incrustation  of  tanks,  1429 

pressure,  1381,  1382,  1389 

properties,  1381 

required  for  mortar,  238 

softening,  1429 

specific  grav  ty,  1381,  1500,  1508 

supply,  802,  1390-1398,  141S 

tanks  (see  Tanks) 

temperatures,  boiling,  1251 

weight,  1381,  1500,  1508 
Water-backs,  capacity,  1430 
Water-closets,  141 1,  1428,  1641 
Water-curtains,  901,  903 
Water-filters,  142 1 
Water-gas,  1431 
Water-heaters,  1421,  1425 
Water-meters,  1425 
Water-pipes  (see  Pipes) 
Water-seal,  1413 
Water-supply,  1390-1398,  1415 

fire-protection,  802 
Water-tables,  stone,  1539 
Water-tanks  (see  Tanks) 
Water-towers,  wind-bracing,  11 84 
Waterproofing,  17  09-1717 

cement,  1711,  1717 

concrete,  246,  1711,  1717 
foundations,  1709 

external,  17 13 

foundations,  1 709-1 71 7 

water-proof  cement,  1714 
paper,  1567 
Watt,  33,  1248,  1459 
Web    (see,  also.    Box   Girders,   Plate 
girders,  and  Beams,  steel) 

box  girders,  buckling  value,  686,  705 
shearing  value,  684,  703 
stiffeners,  681,  686,  691,  696,  1201, 
1203 

domes,  1241 

plate  girders,  681,  703-716 
buckling  value,  686,  705 
shearing  value,  703 
stresses,  684,  686,  691 

steel   beams,  web-buckling,  181-185, 
565,  567-569,  612,  627 
w«b-thickness,  592 


1906 


Index 


Wedges,  shoring,  215 
Weight    (see   each   substance,   and  also 
Loads) 
adult  persons,  1644 
measures  of,  28-29 

metric  system,  32 
merchandise,  721-723 
sash,  1649-1651 

substances,  per  cubic  foot,  1501-1508 
unit  of,  1247 
Weights  and  measures,  25-35 
Weld,  iron,  377 

steel,  377 
Welded-metal  fabric,  948-949 
Wellington's  formula  for  pile  founda- 
tions, 193 
Wells,  dredged,  foundations,  210 
driven,  water-supply,  1391 
foundations  affected,  147 
Welsbach  lamps,  1444-145 1 
Wemlinger  sheet-piling,  209 
Wheat,  weight,  723 
White-coating,  plastering,  1555 
White  pine,  beams,  coefficients  for,  62S 
deflection,  664 
fiber-stress,  flexure,  safe,  557,  647, 

648, 1138 
safe  loads,  639 
columns,  safe  loads,  450,  452 
crushing-loads,  with  the  grain,   449, 

650 
crushing  strength,  across  the  grain, 

454,  650 
hardness,  1558 
modulus,  of  elasticity,  647,  664 

of  rupture,  650 
safe  loads  on  columns,  450,  452 
shearing-stresses,  412,  647,  648,  1138 
specific  gravity,  1507 
stiffness,  664 

tension,  376,  647,  648,  650,  1138 
unit  stresses,  376,  412,  647,  650,  1138 
weight,  650,  1507,  1558 
White  wood     (poplar),    columns,    safe 
loads,  450,  452 
crushing-loads,  with  the  grain,  449 
hardness,  1558 

specific  gravity  and  weight,  651,1507 
unit  stresses,  651 
Wind,  force  of,  17 17 
pressure,  1171-1173 
resistance,  1175 
stresses,  bracing,  11 76-1 183 
trusses,  1109-1118,  1123-1128 
Wind-bracing,  1171-1193 

building  law,  1171-1172,  1176,  1202 
column-connections,  1174-1175, 

1179,  IT89,  1190 
columns,  types,  1183 
conditions  determining,  1172 
details,  1189,  1190 


Wind-bracing,  examples,  1187-1193 

general  theory,  1173-1174 

gusset-plate  type,  1176,  1179,    1189, 
1190 

knee-brace  type,  1176,  1179,  1180 

lattice-girder  type,  11 76,  1181 

moment-increments,  1176,  1178 

portal  type,  1176,  1182 

resistance-factors,  indeterminate,  1 178 

stresses,  computation  of,  1176-1183 

sway-rods,  11 76,  1181 

types,  1174-1176,  1187-1193 

water-towers,  1184 
Wind-loads,  1053,  1198 
Wind-shields,  scuppers,  767 
Wind-stresses  (see  Stresses) 
Windmills,  capacity,  1394 
Window-frames,  bronze, <395 

fire-resisting,  902 

Kalamein  iron,  895 

metal,  897 

metal-covered,  895 

mill-construction,  764 
Window-sashes,  fire-resisting,  902 

metal,  897 

metal-covered,  895 

weights,  1649- 1651 
Window-sills,  stone,  1534 
Windows,  bay  (Glossary),  1802 

fire-protection,  901 

glazing,  1573-1580 

heat-transmission,  1258 

loads  over,  318 

metal-frame-and-wire-glass,  901-902 

mill-construction,  759,  763,  769 
saw-tooth,  772,  775,  778 

sheet-metal,  902 

water-curtains,  901,  903 

wire-glass  in  warehouses,  778 
Winslow  formula,  wooden  columns,  450 
Wire,  402,  403 

annealed,  1513 

aviator,  401 

Bessemer,  1513 

bright,  1513 

copper,  401,  1469,  I470»  i474,  iSi3 

electric  wiring,  1466-1485  (see,  also, 
Wiring) 
calculations,  1469-1479 
lighting,  1469 
resistance,  1474 

fabric,  reinforcement,  850 

feed,  1478 

finish,  400 

fire-detecting,  903 

galvanized,  406,  1513 

gauges,  401,  1469,  1509,  1512 

gun-screw,  1513 

in  glass,  759,  821 

iron,  401 

lath,  887 


Index 


1907 


Wire,  length  per  pound,  403 
machinery,  15 13 
manufacture,  400,  1513 
market,  15 13 
nails,  1529 

piano,  401 

plough,  401 

rope,  404-406 
_  weight,  403,  1474,  1512 

size  and   weights,   403,   1474,   1475, 
1477,  1512 

steel,  400,  401,  403,  404,  406,  1 5 13 

strength,  400-401,  403,  1512 

telegraph,  401 

telephone,  401 

tinned.  15 13 

uses,  401 
Wire-glass,  759,  778,  821 
Wire-mesh,  919 
Wiring,  electric-lighting,  1466-1485 

cabinet,  1477 

conduits,  1479 

cost,  1482 

national  electrical  code,  1480 

specifications,  1482 

symbols,  1476-1478,  1484 

tables,  1475 
Wisconsin,  registration  law,  1779 
Wood  (see,  also,  Lumber,  Timber,  and 
wood  in  question) 

beams  (see  Beams) 

columns  (see  Columns,  wooden) 

.compression,    across    the    grain,  454, 
647,  650,  651,  1138 
with  the  grain,  449,  647,  650,  651, 
1138 

fire-proof,  820,  894 

flexure,  557,  647,  650,  651,  J138 

friction-coefficient,  253 

fuel,  1272 

hardness,  relati^^i,  1558 

metal-covered,  894-895 

modulus  of  elasticity,  647,  664 

painting,  1569-1572 

shear,  412,  647-651,  1138 

sheathing,  1049,  1563,  1564 

specific  gravity,  1501-1508 

tension,  376,  647,  650,  651,  1138 

weight,  650,  651,  1501-1508,  1558 

working  stresses,  647,  648,  650,  1138 
Wool,  weight,  721 
Work,  contractor's  changes,  1757 

energy,  1248 
Working  stresses  (see  Stress  and  ma- 
terials in  question) 
Works,  Clerk  of  the,  1728,  1733 
Workshops,  slow-burning,  769-771 

ventilation,  769,  1353 
Wrought  iron,  377 

appearance,  377 

beams,  coefficients  for,  628 


Wrought  iron,  beams,  deflection,  664 

stiffness,  664 
bending  moments,  431 
bolts,  431,  1138 

bearing  strength,  1138 
chains,  408,  410 
compression,  bolts,  1138 
crushing-loads,  449 
elongation,  378,  410 
finish,  378 
fire-resistance,  819 
flexure,  431,  557,  1138 
grades,  378 
manufacture^of,  378 
modulus  of  elasticity,  664 
physical  properties,  377,  378 
pipe,  1408, 1429, 1432-1436 
reinforcement,  907 
rivets,  418 
rope,  404-406 

shearing-stresses,  412,  431,  1138 
specific  gravity,  1505,  1510 
specifications,  377-378 
stirrups,  750,  757 

tension,  376,  377-378,  410,  431,  1138 
tests,  377-379 
use,  377 
weight,  1505,  1510,  1521 

estimating,  1521 

sheets,  1510 
welding,  377 
yield-point,  378  . 

Yellow  pine,  beams,  coefficients  for,  628 

deflection,  664 

fiber-stress,  flexure,  557,  647,  648 
safe  loads,  642,  643,  666 
columns,  safe  loads,  450,  451,  452 
crushing-loads,  with  the  grain,  449, 

650 
crushing  strength,  across  the  grain, 

464,  650 
hardness,  1558 

modulus  of  elasticity,  647,  664 
modulus  of  rupture,  650 
safe  loads  on  columns,  450,  451 
shearing-stresses,  412,  647,  648,  650 
specific  gravity,  1507 
stiffness,  664 

tension,  376,  647,  648,  650 
unit  stresses,  376,  412,  647,  648,  650 
weight,  650,  1507,  1508 
Yield-point,  steel,  381,  383,  912,  913 

wrought  iron,  378 
Young's  modulus,  126 

Z  bars,  base  price,  1204 

purlins,  11 69 
Zinc,  castings,  shrinkage,  1521 

specific  gravity  and  weight,  1508 
Zone  of  sphere,  volume,  64 


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